Popular Scientific Lectures / Populär-wissenschaftliche Vorlesungen
{"WorkMasterId":5690,"WpPageId":270003,"ParentWpPageId":193823,"Slug":"popular-scientific-lectures","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/ernst-mach/popular-scientific-lectures/","RelativeUrl":"theos/humanities/philosophy/philosophers/ernst-mach/popular-scientific-lectures/","HasFullText":true,"RawHtmlLength":932413,"CleanHtmlLength":876303,"Kicker":"Philosophy Work","Title":"Popular Scientific Lectures / Populär-wissenschaftliche Vorlesungen","Deck":"Mach presents physics, psychology, and scientific method for a broad audience while emphasizing empirical clarity and conceptual economy.","BackLink":{"Text":"Back to Ernst Mach","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/ernst-mach/"},"AuthorCard":{"Label":"Author","Title":"Ernst Mach","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/ernst-mach/","MediaHref":"","ImageSrc":"https://chrisdeasy.com/wp-content/uploads/ernst-mach-01-science-history-institute-portrait.jpg","ImageAlt":"Portrait of Ernst Mach","FilterTerra":"Western Europe","ClickText":"Ernst Mach","ClickHref":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/ernst-mach/","Copies":["1838 CE – 1916 CE","Chrlice / Chirlitz, near Brno","Austrian physicist and philosopher from Moravia whose anti-metaphysical empiricism, analysis of sensations, historical criticism of mechanics, and economy of thought shaped modern philosophy of science."]},"ContextCards":[{"Label":"Period","Key":"Period:4","Title":"Modern History","DateText":"1800 CE – 1944 CE","Url":"https://chrisdeasy.com/theos/humanities/philosophy/eras-of-thought/philosophers-of-modern-history/"},{"Label":"Era","Key":"Era:11","Title":"Long 19th Century","DateText":"1870 CE – 1913 CE","Url":"https://chrisdeasy.com/theos/humanities/philosophy/eras-of-thought/philosophers-of-modern-history/philosophers-of-the-long-19th-century/"},{"Label":"Composition","Title":"1895 CE","Url":"","DateText":""}],"DateNote":"Proxy ordering year 1895. Lecture collection; Project Gutenberg is evidence only and HasFullText remains false.","GeoCards":[{"Label":"Region","Key":"Region:1"},{"Label":"Terra Avita","Key":"TerraAvita:1"},{"Label":"Terra Avita Region","Key":"TerraAvitaRegion:3"},{"Label":"Modern Country","Key":"Country:CZE:1"}],"OriginalTitle":"Populär-wissenschaftliche Vorlesungen","Language":"German","DisciplineCards":[{"Label":"Primary Discipline","Key":"Discipline:philosophy-of-science"},{"Label":"Secondary Discipline","Key":"Discipline:epistemology"}],"Tradition":"Empiricism / philosophy of science","FullText":{"Title":"Full Text","Copy":"Public-domain full text from Project Gutenberg eBook #39508 .","Url":"","Label":"","Kicker":"","Cards":[]},"CoreThesis":["Mach presents physics, psychology, and scientific method for a broad audience while emphasizing empirical clarity and conceptual economy."],"Classification":{"AlternateTitles":"Popular Scientific Lectures","KeyConcepts":"Sensation; elements; economy of thought; mechanics; inertia; mass; Mach principle; psychophysics; motion; heat; optics; anti-metaphysics; empiricism; science history; concepts; language; knowledge and error","Methodology":"Historical-critical analysis, experimental physics, psychophysical observation, conceptual economy, anti-metaphysical critique, and reconstruction of scientific concepts from experience.","Structure":"The page records a direct Mach work with visible scientific, lecture-collection, translation, posthumous, or edition status and no imported full-text badge."},"Arguments":["Mach presents physics, psychology, and scientific method for a broad audience while emphasizing empirical clarity and conceptual economy."],"Influence":{"InfluencedBy":"Kant, Gustav Fechner, Hermann von Helmholtz, Darwinian biology, Hume, Berkeley, and nineteenth-century physics and psychophysics.","InfluenceOn":""},"Significance":["Included as one of the fourteen Ernst Mach work pages approved for the full-process update.","The work remains relevant to empiricism, scientific modeling, concept formation, theory choice, relativity reception, psychophysics, and the relation between physics and experience."],"EvidenceNote":["Direct work page approved in the Ernst Mach update. Collected works, modern translations, textbooks, school manuals, individual lecture fragments, Mach-Zehnder material not authored by Mach, Einstein/Lenin/Carnap works, catalog rows, and scholarship remain evidence/Other Voices unless separately approved."],"MainSections":[{"Kind":"RawSection","Title":"Full Versions","BodyHtml":"\u003cdiv class=\"dz-philo__full-version-grid\"\u003e\n \u003carticle class=\"dz-philo__full-version-card\"\u003e\n \u003cp class=\"dz-philo__full-version-provider\"\u003eProject Gutenberg\u003c/p\u003e\n \u003ch3 class=\"dz-philo__full-version-title\"\u003eProject Gutenberg eBook #39508\u003c/h3\u003e\n \u003cp class=\"dz-philo__full-version-meta\"\u003eHtmlText · Imported\u003c/p\u003e\n \u003ca class=\"dz-philo__full-version-link\" href=\"https://www.gutenberg.org/ebooks/39508\"\u003eOpen full version\u003c/a\u003e\n \u003c/article\u003e\n \u003c/div\u003e"},{"Kind":"TextSection","Title":"Core Thesis","Paragraphs":["Mach presents physics, psychology, and scientific method for a broad audience while emphasizing empirical clarity and conceptual economy."]},{"Kind":"FieldSection","Title":"Classification","Fields":[{"Label":"Alternate Titles","Value":"Popular Scientific Lectures"},{"Label":"Key Concepts","Value":"Sensation; elements; economy of thought; mechanics; inertia; mass; Mach principle; psychophysics; motion; heat; optics; anti-metaphysics; empiricism; science history; concepts; language; knowledge and error"},{"Label":"Methodology","Value":"Historical-critical analysis, experimental physics, psychophysical observation, conceptual economy, anti-metaphysical critique, and reconstruction of scientific concepts from experience."},{"Label":"Structure","Value":"The page records a direct Mach work with visible scientific, lecture-collection, translation, posthumous, or edition status and no imported full-text badge."}]},{"Kind":"TextSection","Title":"Arguments","Paragraphs":["Mach presents physics, psychology, and scientific method for a broad audience while emphasizing empirical clarity and conceptual economy."]},{"Kind":"FieldSection","Title":"Influence","Fields":[{"Label":"Influenced By","Value":"Kant, Gustav Fechner, Hermann von Helmholtz, Darwinian biology, Hume, Berkeley, and nineteenth-century physics and psychophysics."},{"Label":"Influence On","Value":"Albert Einstein, Vienna Circle, Moritz Schlick, Rudolf Carnap, Philipp Frank, logical empiricism, operationalist debates, and later philosophy of science."}]},{"Kind":"TextSection","Title":"Significance","Paragraphs":["Included as one of the fourteen Ernst Mach work pages approved for the full-process update.","The work remains relevant to empiricism, scientific modeling, concept formation, theory choice, relativity reception, psychophysics, and the relation between physics and experience."]},{"Kind":"TextSection","Title":"Evidence Note","Paragraphs":["Direct work page approved in the Ernst Mach update. Collected works, modern translations, textbooks, school manuals, individual lecture fragments, Mach-Zehnder material not authored by Mach, Einstein/Lenin/Carnap works, catalog rows, and scholarship remain evidence/Other Voices unless separately approved."]},{"Kind":"RawSection","Title":"Full Text","BodyHtml":"\u003cp class=\"dz-philo__section-copy dz-philo__full-text-source\"\u003ePublic-domain full text from \u003ca href=\"https://www.gutenberg.org/ebooks/39508\"\u003eProject Gutenberg eBook #39508\u003c/a\u003e.\u003c/p\u003e\n \u003carticle class=\"dz-philo__full-text-body\"\u003e\r\n\u003ch1\u003ePOPULAR SCIENTIFIC LECTURES.\u003c/h1\u003e\r\n\r\n\r\n\u003chr/\u003e\r\n\r\n\u003ch2\u003e\u003ca name=\"BY_THE_SAME_AUTHOR\" id=\"BY_THE_SAME_AUTHOR\"\u003eBY THE SAME AUTHOR.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\u003cspan class=\"smcap\"\u003eThe Science of Mechanics.\u003c/span\u003e Translated from the\r\nSecond German Edition by T. J. McCormack.\r\n250 Cuts and Illustrations. 534 Pages. Half\r\nMorocco, Gilt Top. Price, $2.50.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003eContributions to the Analysis of the Sensations.\u003c/span\u003e\r\nTranslated by C. M. Williams. With Notes and\r\nNew Additions by the Author. 200 Pages. 36\r\nCuts. Price, $1.00.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003ePopular Scientific Lectures.\u003c/span\u003e Translated by T.\r\nJ. McCormack. Third Revised and Enlarged\r\nEdition. 411 Pages. 59 Cuts. Cloth, $1.50;\r\nPaper, 50 cents.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp class=\"center\"\u003eTHE OPEN COURT PUBLISHING CO.,\u003cbr /\u003e\r\n\u003cspan class=\"small\"\u003e324 DEARBORN ST., CHICAGO.\u003c/span\u003e\r\n\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_iii\" id=\"Page_iii\"\u003e[Pg iii]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003chr/\u003e\r\n\r\n\r\n\u003cp class=\"center big bold\"\u003ePOPULAR\u003cbr /\u003e\r\nSCIENTIFIC LECTURES\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003cspan class=\"small\"\u003eBY\u003c/span\u003e\u003cbr/\u003e\r\nERNST MACH\u003c/p\u003e\r\n\r\n\u003cp class=\"center small\"\u003eFORMERLY PROFESSOR OF PHYSICS IN THE UNIVERSITY OF PRAGUE, NOW\r\nPROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE\r\nSCIENCE IN THE UNIVERSITY OF VIENNA\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003cspan class=\"small\"\u003eTRANSLATED\u003cbr/\u003e\r\nBY\u003cbr/\u003e\u003c/span\u003e\r\nTHOMAS J. McCORMACK\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003eTHIRD EDITION, REVISED AND ENLARGED\u003c/p\u003e\r\n\u003chr/\u003e\r\n\u003cp class=\"center small\"\u003eWITH FIFTY-NINE CUTS AND DIAGRAMS\u003c/p\u003e\r\n\u003chr/\u003e\r\n\u003cp class=\"center big\"\u003eCHICAGO\u003cbr/\u003e\r\nTHE OPEN COURT PUBLISHING COMPANY\u003c/p\u003e\r\n\r\n\u003cp class=\"center small\"\u003eFOR SALE BY\u003cbr/\u003e\r\n\u003cspan class=\"smcap\"\u003eKegan Paul, Trench, Truebner \u0026amp; Co.\u003c/span\u003e, LONDON\u003cbr/\u003e\r\n1898\r\n\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_iv\" id=\"Page_iv\"\u003e[Pg iv]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\u003chr/\u003e\r\n\r\n\u003cp class=\"center\"\u003eCOPYRIGHT\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003cspan class=\"smcap\"\u003eBy The Open Court Publishing Co.\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cdiv class=\"center\"\u003e\r\n\u003ctable border=\"0\" cellpadding=\"0\" cellspacing=\"0\" summary=\"copyright dates\"\u003e\r\n\u003ctr\u003e\u003ctd align=\"left\"\u003ePages 1-258\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\"\u003e\u0026nbsp;in 1894.\u003c/td\u003e\u003c/tr\u003e\r\n\u003ctr\u003e\u003ctd align=\"left\"\u003ePages 338-374\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\"\u003e\u0026nbsp;in 1894.\u003c/td\u003e\u003c/tr\u003e\r\n\u003ctr\u003e\u003ctd align=\"left\"\u003ePages 259-281\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\"\u003e\u0026nbsp;in 1896.\u003c/td\u003e\u003c/tr\u003e\r\n\u003ctr\u003e\u003ctd align=\"left\"\u003ePages 282-308\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\"\u003e\u0026nbsp;in 1897.\u003c/td\u003e\u003c/tr\u003e\r\n\u003ctr\u003e\u003ctd align=\"left\"\u003ePages 309-337\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\"\u003e\u0026nbsp;in 1898.\u003c/td\u003e\u003c/tr\u003e\r\n\u003c/table\u003e\u003c/div\u003e\r\n\r\n\u003chr class=\"chap\" /\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_v\" id=\"Page_v\"\u003e[Pg v]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"AUTHORS_PREFACE_TO_THE_FIRST\" id=\"AUTHORS_PREFACE_TO_THE_FIRST\"\u003eAUTHOR\u0027S PREFACE TO THE FIRST\r\nEDITION.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003ePopular lectures, owing to the knowledge they presuppose,\r\nand the time they occupy, can afford only a \u003ci\u003emodicum\u003c/i\u003e\r\nof instruction. They must select for this purpose easy subjects,\r\nand restrict themselves to the exposition of the simplest and the\r\nmost essential points. Nevertheless, by an appropriate choice of\r\nthe matter, the \u003ci\u003echarm\u003c/i\u003e and the \u003ci\u003epoetry\u003c/i\u003e of research can be conveyed\r\nby them. It is only necessary to set forth the attractive and the\r\nalluring features of a problem, and to show what broad domains\r\nof fact can be illuminated by the light radiating from the solution\r\nof a single and ofttimes unobtrusive point.\u003c/p\u003e\r\n\r\n\u003cp\u003eFurthermore, such lectures can exercise a favorable influence\r\nby showing the substantial sameness of scientific and every-day\r\nthought. The public, in this way, loses its shyness towards scientific\r\nquestions, and acquires an interest in scientific work which is\r\na great help to the inquirer. The latter, in his turn, is brought to\r\nunderstand that his work is a small part only of the universal process\r\nof life, and that the results of his labors must redound to the\r\nbenefit not only of himself and a few of his associates, but to that\r\nof the collective whole.\u003c/p\u003e\r\n\r\n\u003cp\u003eI sincerely hope that these lectures, in the present excellent\r\ntranslation, will be productive of good in the direction indicated.\u003c/p\u003e\r\n\r\n\u003cp class=\"right\"\u003e\r\n\u003cspan class=\"smcap\"\u003eE. Mach.\u003c/span\u003e\u003cbr /\u003e\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003ePrague\u003c/span\u003e, December, 1894.\u003c/p\u003e\u003chr class=\"chap\" /\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_vii\" id=\"Page_vii\"\u003e[Pg vii]\u003c/a\u003e\u003cbr /\u003e\u003ca name=\"Page_vi\" id=\"Page_vi\"\u003e[Pg vi]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"TRANSLATORS_NOTE_TO_THE\" id=\"TRANSLATORS_NOTE_TO_THE\"\u003eTRANSLATOR\u0027S NOTE TO THE\r\nTHIRD EDITION.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eThe present third edition of this work has been enlarged by\r\nthe addition of a new lecture, \"On Some Phenomena Attending\r\nthe Flight of Projectiles.\" The additions to the second\r\nconsisted of the following four lectures and articles: Professor\r\nMach\u0027s Vienna Inaugural Lecture, \"The Part Played by Accident\r\nin Invention and Discovery,\" the lecture on \"Sensations of Orientation,\"\r\nrecently delivered and summing up the results of an important\r\npsychological investigation, and two historical articles (see\r\nAppendix) on Acoustics and Sight.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe lectures extend over a long period, from 1864 to 1898,\r\nand differ greatly in style, contents, and purpose. They were first\r\npublished in collected form in English; afterwards two German\r\neditions were called for.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs the dates of the first five lectures are not given in the footnotes\r\nthey are here appended. The first lecture, \"On the Forms\r\nof Liquids,\" was delivered in 1868 and published with that \"On\r\nSymmetry\" in 1872 (Prague). The second and third lectures, on\r\nacoustics, were first published in 1865 (Graz); the fourth and fifth,\r\non optics, in 1867 (Graz). They belong to the earliest period of\r\nProfessor Mach\u0027s scientific activity, and with the lectures on electrostatics\r\nand education will more than realise the hope expressed in\r\nthe author\u0027s Preface.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe eighth, ninth, tenth, eleventh, and twelfth lectures are of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_viii\" id=\"Page_viii\"\u003e[Pg viii]\u003c/a\u003e\u003c/span\u003e\r\na more philosophical character and deal principally with the methods\r\nand nature of scientific inquiry. In the ideas summarised in\r\nthem will be found one of the most important contributions to the\r\ntheory of knowledge made in the last quarter of a century. Significant\r\nhints in psychological method, and exemplary specimen-researches\r\nin psychology and physics, are also presented; while in\r\nphysics many ideas find their first discussion that afterwards, under\r\nother names and other authorship, became rallying-cries in this\r\ndepartment of inquiry.\u003c/p\u003e\r\n\r\n\u003cp\u003eAll the proofs of this translation have been read by Professor\r\nMach himself.\u003c/p\u003e\r\n\r\n\u003cp class=\"right\"\u003e\r\n\u003cspan class=\"smcap\"\u003eT. J. McCormack.\u003c/span\u003e\u003cbr /\u003e\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003eLa Salle, Ill.\u003c/span\u003e, May, 1898.\u003c/p\u003e\r\n\u003chr class=\"chap\" /\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_ix\" id=\"Page_ix\"\u003e[Pg ix]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"TABLE_OF_CONTENTS\" id=\"TABLE_OF_CONTENTS\"\u003eTABLE OF CONTENTS.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cul class=\"toc\"\u003e\r\n\u003cli\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label smcap\"\u003epage\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#THE_FORMS_OF_LIQUIDS\"\u003eThe Forms of Liquids\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e1\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#THE_FIBRES_OF_CORTI\"\u003eThe Fibres of Corti\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e17\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_THE_CAUSES_OF_HARMONY\"\u003eOn the Causes of Harmony\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e32\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#THE_VELOCITY_OF_LIGHT\"\u003eThe Velocity of Light\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e48\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#WHY_HAS_MAN_TWO_EYES\"\u003eWhy Has Man Two Eyes?\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e66\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_SYMMETRY\"\u003eOn Symmetry\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e89\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_THE_FUNDAMENTAL_CONCEPTS\"\u003eOn the Fundamental Concepts of Electrostatics\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e107\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_THE_PRINCIPLE_OF_THE_CONSERVATION\"\u003eOn the Principle of the Conservation of Energy\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e137\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#THE_ECONOMICAL_NATURE_OF\"\u003eOn the Economical Nature of Physical Inquiry\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e186\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_TRANSFORMATION_AND_ADAPTATION\"\u003eOn Transformation and Adaptation in Scientific Thought\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e214\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_THE_PRINCIPLE_OF_COMPARISON\"\u003eOn the Principle of Comparison in Physics\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e236\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#THE_PART_PLAYED_BY_ACCIDENT_IN\"\u003eOn the Part Played by Accident in Invention and Discovery\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e259\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_SENSATIONS_OF_ORIENTATION93\"\u003eOn Sensations of Orientation\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e282\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_SOME_PHENOMENA_ATTENDING\"\u003eOn Some Phenomena Attending the Flight of Projectiles\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e309\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#ON_INSTRUCTION_IN_THE_CLASSICS\"\u003eOn Instruction in the Classics and the Mathematico-Physical Sciences\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e338\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#APPENDIX\"\u003eAppendixes.\u003c/a\u003e\r\n\u003cul class=\"tocsub\"\u003e\u003cli\u003e\u003ca href=\"#A_CONTRIBUTION_TO_THE_HISTORY_OF_ACOUSTICS\"\u003eA Contribution to the History of Acoustics\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e375\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#REMARKS_ON_THE_THEORY_OF_SPATIAL_VISION\"\u003eRemarks on the Theory of Spatial Vision\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e386\u003c/span\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003ca href=\"#INDEX\"\u003eIndex\u003c/a\u003e\u0026nbsp; \u0026nbsp;\u003cspan class=\"label\"\u003e393\u003c/span\u003e\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_x\" id=\"Page_x\"\u003e[Pg x]\u003c/a\u003e\u003cbr /\u003e\u003ca name=\"Page_1\" id=\"Page_1\"\u003e[Pg 1]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\u003chr class=\"chap\" /\u003e\r\n\r\n\u003ch2\u003e\u003ca name=\"THE_FORMS_OF_LIQUIDS\" id=\"THE_FORMS_OF_LIQUIDS\"\u003eTHE FORMS OF LIQUIDS.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eWhat thinkest thou, dear Euthyphron, that the\r\nholy is, and the just, and the good? Is the holy\r\nholy because the gods love it, or are the gods holy because\r\nthey love the holy? By such easy questions did\r\nthe wise Socrates make the market-place of Athens unsafe\r\nand relieve presumptuous young statesmen of the\r\nburden of imaginary knowledge, by showing them how\r\nconfused, unclear, and self-contradictory their ideas\r\nwere.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou know the fate of the importunate questioner.\r\nSo called good society avoided him on the promenade.\r\nOnly the ignorant accompanied him. And finally he\r\ndrank the cup of hemlock\u0026mdash;a lot which we ofttimes\r\nwish would fall to modern critics of his stamp.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat we have learned from Socrates, however,\u0026mdash;our\r\ninheritance from him,\u0026mdash;is scientific criticism.\r\nEvery one who busies himself with science recognises\r\nhow unsettled and indefinite the notions are which he\r\nhas brought with him from common life, and how, on\r\na minute examination of things, old differences are\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_2\" id=\"Page_2\"\u003e[Pg 2]\u003c/a\u003e\u003c/span\u003e\r\neffaced and new ones introduced. The history of science\r\nis full of examples of this constant change, development,\r\nand clarification of ideas.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut we will not linger by this general consideration\r\nof the fluctuating character of ideas, which becomes a\r\nsource of real uncomfortableness, when we reflect that\r\nit applies to almost every notion of life. Rather shall\r\nwe observe by the study of a physical example how\r\nmuch a thing changes when it is closely examined, and\r\nhow it assumes, when thus considered, increasing definiteness\r\nof form.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe majority of you think, perhaps, you know\r\nquite well the distinction between a liquid and a solid.\r\nAnd precisely persons who have never busied themselves\r\nwith physics will consider this question one of\r\nthe easiest that can be put. But the physicist knows\r\nthat it is one of the most difficult. I shall mention\r\nhere only the experiments of Tresca, which show that\r\nsolids subjected to high pressures behave exactly as\r\nliquids do; for example, may be made to flow out in\r\nthe form of jets from orifices in the bottoms of vessels.\r\nThe supposed difference of kind between liquids and\r\nsolids is thus shown to be a mere difference of degree.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe common inference that because the earth is\r\noblate in form, it was originally fluid, is an error, in\r\nthe light of these facts. True, a rotating sphere, a few\r\ninches in diameter will assume an oblate form only\r\nif it is very soft, for example, is composed of freshly\r\nkneaded clay or some viscous stuff. But the earth,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_3\" id=\"Page_3\"\u003e[Pg 3]\u003c/a\u003e\u003c/span\u003e\r\neven if it consisted of the rigidest stone, could not\r\nhelp being crushed by its tremendous weight, and must\r\nperforce behave as a fluid. Even our mountains could\r\nnot extend beyond a certain height without crumbling.\r\nThe earth \u003ci\u003emay\u003c/i\u003e once have been fluid, but this by no\r\nmeans follows from its oblateness.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe particles of a liquid are displaced on the application\r\nof the slightest pressure; a liquid conforms\r\nexactly to the shapes of the vessels in which it is contained;\r\nit possesses no form of its own, as you have\r\nall learned in the schools. Accommodating itself in\r\nthe most trifling respects to the conditions of the vessel\r\nin which it is placed, and showing, even on its surface,\r\nwhere one would suppose it had the freest play, nothing\r\nbut a polished, smiling, expressionless countenance,\r\nit is the courtier \u003ci\u003epar excellence\u003c/i\u003e of the natural bodies.\u003c/p\u003e\r\n\r\n\u003cp\u003eLiquids have no form of their own! No, not for the\r\nsuperficial observer. But persons who have observed\r\nthat a raindrop is round and never angular, will not be\r\ndisposed to accept this dogma so unconditionally.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is fair to suppose that every man, even the weakest,\r\nwould possess a character, if it were not too difficult\r\nin this world to keep it. So, too, we must suppose\r\nthat liquids would possess forms of their own, if\r\nthe pressure of the circumstances permitted it,\u0026mdash;if\r\nthey were not crushed by their own weights.\u003c/p\u003e\r\n\r\n\u003cp\u003eAn astronomer once calculated that human beings\r\ncould not exist on the sun, apart from its great heat,\r\nbecause they would be crushed to pieces there by their\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_4\" id=\"Page_4\"\u003e[Pg 4]\u003c/a\u003e\u003c/span\u003e\r\nown weight. The greater mass of this body would\r\nalso make the weight of the human body there much\r\ngreater. But on the moon, because here we should\r\nbe much lighter, we could jump as high as the church-steeples\r\nwithout any difficulty, with the same muscular\r\npower which we now possess. Statues and \"plaster\"\r\ncasts of syrup are undoubtedly things of fancy, even\r\non the moon, but maple-syrup would flow so slowly\r\nthere that we could easily build a maple-syrup man on\r\nthe moon, for the fun of the thing, just as our children\r\nhere build snow-men.\u003c/p\u003e\r\n\r\n\u003cp\u003eAccordingly, if liquids have no form of their own\r\nwith us on earth, they have, perhaps, a form of their\r\nown on the moon, or on some smaller and lighter heavenly\r\nbody. The problem, then, simply is to get rid of\r\nthe effects of gravity; and, this done, we shall be able\r\nto find out what the peculiar forms of liquids are.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe problem was solved by Plateau of Ghent, whose\r\nmethod was to immerse the liquid in another of the\r\nsame specific gravity.\u003ca name=\"FNanchor_1_1\" id=\"FNanchor_1_1\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_1_1\" class=\"fnanchor\"\u003e[1]\u003c/a\u003e He employed for his experiments\r\noil and a mixture of alcohol and water. By\r\nArchimedes\u0027s well-known principle, the oil in this mixture\r\nloses its entire weight. It no longer sinks beneath\r\nits weight; its formative forces, be they ever so\r\nweak, are now in full play.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs a fact, we now see, to our surprise, that the oil,\r\ninstead of spreading out into a layer, or lying in a\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_5\" id=\"Page_5\"\u003e[Pg 5]\u003c/a\u003e\u003c/span\u003e\r\nformless mass, assumes the shape of a beautiful and\r\nperfect sphere, freely suspended in the mixture, as\r\nthe moon is in space. We can construct in this way a\r\nsphere of oil several inches in diameter.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf, now, we affix a thin plate to a\r\nwire and insert the plate in the oil\r\nsphere, we can, by twisting the wire\r\nbetween our fingers, set the whole ball\r\nin rotation. Doing this, the ball assumes\r\nan oblate shape, and we can, if\r\nwe are skilful enough, separate by such\r\nrotation a ring from the ball, like that\r\nwhich surrounds Saturn. This ring is\r\nfinally rent asunder, and, breaking up\r\ninto a number of smaller balls, exhibits\r\nto us a kind of model of the origin of\r\nthe planetary system according to the\r\nhypothesis of Kant and Laplace.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 150px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-015.jpg\" width=\"150\" height=\"491\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 1.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eStill more curious are the phenomena\r\nexhibited when the formative\r\nforces of the liquid are partly disturbed\r\nby putting in contact with the liquid\u0027s\r\nsurface some rigid body. If we immerse,\r\nfor example, the wire framework of a cube in our\r\nmass of oil, the oil will everywhere stick to the wire\r\nframework. If the quantity of oil is exactly sufficient\r\nwe shall obtain an oil cube with perfectly smooth walls.\r\nIf there is too much or too little oil, the walls of the\r\ncube will bulge out or cave in. In this manner we\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_6\" id=\"Page_6\"\u003e[Pg 6]\u003c/a\u003e\u003c/span\u003e\r\ncan produce all kinds of geometrical figures of oil, for\r\nexample, a three-sided pyramid, a cylinder (by bringing\r\nthe oil between two wire rings), and so on. Interesting\r\nis the change of form that occurs when we\r\ngradually suck out the oil by means of a glass tube\r\nfrom the cube or pyramid. The wire holds the oil\r\nfast. The figure grows smaller and smaller, until it is\r\nat last quite thin. Ultimately it consists simply of a\r\nnumber of thin, smooth plates of oil, which extend\r\nfrom the edges of the cube to the centre, where they\r\nmeet in a small drop. The same is true of the pyramid.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-016.jpg\" width=\"300\" height=\"204\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 2.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThe idea now suggests itself that liquid figures as\r\nthin as this, and possessing, therefore, so slight a\r\nweight, cannot be crushed or deformed by their weight;\r\njust as a small, soft ball of clay is not affected in this\r\nrespect by its weight. This being the case, we no\r\nlonger need our mixture of alcohol and water for the\r\nproduction of figures, but can construct them in the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_7\" id=\"Page_7\"\u003e[Pg 7]\u003c/a\u003e\u003c/span\u003e\r\nopen air. And Plateau, in fact, found that these thin\r\nfigures, or at least very similar ones, could be produced\r\nin the air, by dipping the wire nets described\r\nin a solution of soap and water and quickly drawing\r\nthem out again. The experiment is not difficult. The\r\nfigure is formed of itself. The preceding drawing\r\nrepresents to the eye the forms obtained with cubical\r\nand pyramidal nets. In the cube, thin, smooth films\r\nof soap-suds proceed from the edges to a small, quadratic\r\nfilm in the centre. In the pyramid, a film proceeds\r\nfrom each edge to the centre.\u003c/p\u003e\r\n\r\n\u003cp\u003eThese figures are so beautiful that they hardly admit\r\nof appropriate description. Their great regularity\r\nand geometrical exactness evokes surprise from all who\r\nsee them for the first time. Unfortunately, they are of\r\nonly short duration. They burst, on the drying of the\r\nsolution in the air, but only after exhibiting to us the\r\nmost brilliant play of colors, such as is often seen in\r\nsoap-bubbles. Partly their beauty of form and partly\r\nour desire to examine them more minutely induces us\r\nto conceive of methods of endowing them with permanent\r\nform. This is very simply done.\u003ca name=\"FNanchor_2_2\" id=\"FNanchor_2_2\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_2_2\" class=\"fnanchor\"\u003e[2]\u003c/a\u003e Instead of\r\ndipping the wire nets in solutions of soap, we dip them\r\nin pure melted colophonium (resin). When drawn\r\nout the figure at once forms and solidifies by contact\r\nwith the air.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is to be remarked that also solid fluid-figures can\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_8\" id=\"Page_8\"\u003e[Pg 8]\u003c/a\u003e\u003c/span\u003e\r\nbe constructed in the open air, if their weight be light\r\nenough, or the wire nets of very small dimensions. If\r\nwe make, for example, of very fine wire a cubical net\r\nwhose sides measure about one-eighth of an inch in\r\nlength, we need simply to dip this net in water to obtain\r\na small solid cube of water. With a piece of blotting\r\npaper the superfluous water may be easily removed\r\nand the sides of the cube made smooth.\u003c/p\u003e\r\n\r\n\u003cp\u003eYet another simple method may be devised for observing\r\nthese figures. A drop of water on a greased\r\nglass plate will not run if it is small enough, but will\r\nbe flattened by its weight, which presses it against\r\nits support. The smaller the drop the less the flattening.\r\nThe smaller the drop the nearer it approaches\r\nthe form of a sphere. On the other hand, a drop suspended\r\nfrom a stick is elongated by its weight. The\r\nundermost parts of a drop of water on a support are\r\npressed against the support, and the upper parts are\r\npressed against the lower parts because the latter cannot\r\nyield. But when a drop falls freely downward\r\nall its parts move equally fast; no part is impeded by\r\nanother; no part presses against another. A freely\r\nfalling drop, accordingly, is not affected by its weight;\r\nit acts as if it were weightless; it assumes a spherical\r\nform.\u003c/p\u003e\r\n\r\n\u003cp\u003eA moment\u0027s glance at the soap-film figures produced\r\nby our various wire models, reveals to us a great\r\nmultiplicity of form. But great as this multiplicity is,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_9\" id=\"Page_9\"\u003e[Pg 9]\u003c/a\u003e\u003c/span\u003e\r\nthe common features of the figures also are easily discernible.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"All forms of Nature are allied, though none is the same as the other;\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eThus, their common chorus points to a hidden law.\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003c/div\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eThis hidden law Plateau discovered. It may be\r\nexpressed, somewhat prosily, as follows:\u003c/p\u003e\r\n\r\n\u003cp\u003e1) If several plane liquid films meet in a figure\r\nthey are always three in number, and, taken in pairs,\r\nform, each with another, nearly equal angles.\u003c/p\u003e\r\n\r\n\u003cp\u003e2) If several liquid edges meet in a figure they are\r\nalways four in number, and, taken in pairs, form, each\r\nwith another, nearly equal angles.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis is a strange law, and its reason is not evident.\r\nBut we might apply this criticism to almost all laws.\r\nIt is not always that the motives of a law-maker are\r\ndiscernible in the form of the law he constructs. But\r\nour law admits of analysis into very simple elements\r\nor reasons. If we closely examine the paragraphs\r\nwhich state it, we shall find that their meaning is simply\r\nthis, that the surface of the liquid assumes the shape\r\nof smallest area that is possible under the circumstances.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf, therefore, some extraordinarily intelligent tailor,\r\npossessing a knowledge of all the artifices of the higher\r\nmathematics, should set himself the task of so covering\r\nthe wire frame of a cube with cloth that every piece\r\nof cloth should be connected with the wire and joined\r\nwith the remaining cloth, and should seek to accomplish\r\nthis feat with the greatest saving of material, he\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_10\" id=\"Page_10\"\u003e[Pg 10]\u003c/a\u003e\u003c/span\u003e\r\nwould construct no other figure than that which is here\r\nformed on the wire frame in our solution of soap and\r\nwater. Nature acts in the construction of liquid figures\r\non the principle of a covetous tailor, and gives no\r\nthought in her work to the fashions. But, strange to\r\nsay, in this work, the most beautiful fashions are\r\nof themselves produced.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe two paragraphs which state our law apply primarily\r\nonly to soap-film figures, and are not applicable,\r\nof course, to solid oil-figures. But the principle that\r\nthe superficial area of the liquid shall be the least\r\npossible under the circumstances, is applicable to all\r\nfluid figures. He who understands not only the letter\r\nbut also the reason of the law will not be at a loss\r\nwhen confronted with cases to which the letter does\r\nnot accurately apply. And this is the case with the\r\nprinciple of least superficial area. It is a sure guide\r\nfor us even in cases in which the above-stated paragraphs\r\nare not applicable.\u003c/p\u003e\r\n\r\n\u003cp\u003eOur first task will now be, to show by a palpable\r\nillustration the mode of formation of liquid figures by\r\nthe principle of least superficial area. The oil on the\r\nwire pyramid in our mixture of alcohol and water, being\r\nunable to leave the wire edges, clings to them, and\r\nthe given mass of oil strives so to shape itself that its\r\nsurface shall have the least possible area. Suppose\r\nwe attempt to imitate this phenomenon. We take a\r\nwire pyramid, draw over it a stout film of rubber, and\r\nin place of the wire handle insert a small tube leading\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_11\" id=\"Page_11\"\u003e[Pg 11]\u003c/a\u003e\u003c/span\u003e\r\ninto the interior of the space enclosed by the rubber\r\n(Fig. 3). Through this tube we can blow in or suck\r\nout air. The quantity of air in the enclosure represents\r\nthe quantity of oil. The stretched rubber film,\r\nwhich, clinging to the wire edges,\r\ndoes its utmost to contract, represents\r\nthe surface of the oil endeavoring\r\nto decrease its area. By\r\nblowing in, and drawing out the air,\r\nnow, we actually obtain all the oil\r\npyramidal figures, from those bulged\r\nout to those hollowed in. Finally, when\r\nall the air is pumped or sucked out, the\r\nsoap-film figure is exhibited. The rubber\r\nfilms strike together, assume the form of planes,\r\nand meet at four sharp edges in the centre of the\r\npyramid.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 150px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-021.jpg\" width=\"150\" height=\"256\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 3.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-021-1.jpg\" width=\"300\" height=\"173\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 4.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThe tendency of soap-films to assume smaller forms\r\nmay be directly demonstrated by a method of Van der\r\nMensbrugghe. If we dip a square wire frame to which\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_12\" id=\"Page_12\"\u003e[Pg 12]\u003c/a\u003e\u003c/span\u003e\r\na handle is attached into a solution of soap and water,\r\nwe shall obtain on the frame a beautiful, plane film of\r\nsoap-suds. (Fig. 4.) On this we lay a thread having its\r\ntwo ends tied together. If, now, we puncture the part\r\nenclosed by the thread, we shall obtain a soap-film\r\nhaving a circular hole in it, whose circumference is\r\nthe thread. The remainder of the film decreasing in\r\narea as much as it can, the hole assumes the largest\r\narea that it can. But the figure of largest area, with\r\na given periphery, is the circle.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 400px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-022.jpg\" width=\"400\" height=\"182\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 5.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eSimilarly, by the principle of least superficial area,\r\na freely suspended mass of oil assumes the shape of a\r\nsphere. The sphere is the form of least surface for a\r\ngiven content. This is evident. The more we put\r\ninto a travelling-bag, the nearer its shape approaches\r\nthe spherical form.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe connexion of the two above-mentioned paragraphs\r\nwith the principle of least superficial area may\r\nbe shown by a yet simpler example. Picture to yourselves\r\nfour fixed pulleys, \u003ci\u003ea\u003c/i\u003e, \u003ci\u003eb\u003c/i\u003e, \u003ci\u003ec\u003c/i\u003e, \u003ci\u003ed\u003c/i\u003e, and two movable\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_13\" id=\"Page_13\"\u003e[Pg 13]\u003c/a\u003e\u003c/span\u003e\r\nrings \u003ci\u003ef\u003c/i\u003e, \u003ci\u003eg\u003c/i\u003e (Fig. 5); about the pulleys and through the\r\nrings imagine a smooth cord passed, fastened at one\r\nextremity to a nail \u003ci\u003ee\u003c/i\u003e, and loaded at the other with a\r\nweight \u003ci\u003eh\u003c/i\u003e. Now this weight always tends to sink, or,\r\nwhat is the same thing, always tends to make the portion\r\nof the string \u003ci\u003ee h\u003c/i\u003e as long as possible, and consequently\r\nthe remainder of the string, wound round the\r\npulleys, as short as possible. The strings must remain\r\nconnected with the pulleys, and on account of the rings\r\nalso with each other. The conditions of the case, accordingly,\r\nare similar to those of the liquid figures discussed.\r\nThe result also is a similar one. When, as\r\nin the right hand figure of the cut, four pairs of strings\r\nmeet, a different configuration must be established.\r\nThe consequence of the endeavor of the string to\r\nshorten itself is that the rings separate from each other,\r\nand that now at all points only three pairs of strings\r\nmeet, every two at equal angles of one hundred and\r\ntwenty degrees. As a fact, by this arrangement the\r\ngreatest possible shortening of the string is attained;\r\nas can be easily proved by geometry.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis will help us to some extent to understand the\r\ncreation of beautiful and complicated figures by the\r\nsimple tendency of liquids to assume surfaces of least\r\nsuperficial area. But the question arises, \u003ci\u003eWhy\u003c/i\u003e do\r\nliquids seek surfaces of least superficial area?\u003c/p\u003e\r\n\r\n\u003cp\u003eThe particles of a liquid cling together. Drops\r\nbrought into contact coalesce. We can say, liquid\r\nparticles attract each other. If so, they seek to come\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_14\" id=\"Page_14\"\u003e[Pg 14]\u003c/a\u003e\u003c/span\u003e\r\nas close as they can to each other. The particles at\r\nthe surface will endeavor to penetrate as far as they\r\ncan into the interior. This process will not stop, cannot\r\nstop, until the surface has become as small as under\r\nthe circumstances it possibly can become, until as\r\nfew particles as possible remain at the surface, until\r\nas many particles as possible have penetrated into the\r\ninterior, until the forces of attraction have no more\r\nwork to perform.\u003ca name=\"FNanchor_3_3\" id=\"FNanchor_3_3\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_3_3\" class=\"fnanchor\"\u003e[3]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe root of the principle of least surface is to be\r\nsought, accordingly, in another and much simpler\r\nprinciple, which may be illustrated by some such analogy\r\nas this. We can \u003ci\u003econceive\u003c/i\u003e of the natural forces of\r\nattraction and repulsion as purposes or intentions of\r\nnature. As a matter of fact, that interior pressure\r\nwhich we feel before an act and which we call an intention\r\nor purpose, is not, in a final analysis, so essentially\r\ndifferent from the pressure of a stone on its support,\r\nor the pressure of a magnet on another, that it is\r\nnecessarily unallowable to use for both the same term\u0026mdash;at\r\nleast for well-defined purposes.\u003ca name=\"FNanchor_4_4\" id=\"FNanchor_4_4\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_4_4\" class=\"fnanchor\"\u003e[4]\u003c/a\u003e It is the purpose\r\nof nature, accordingly, to bring the iron nearer\r\nthe magnet, the stone nearer the centre of the earth,\r\nand so forth. If such a purpose can be realised, it is\r\ncarried out. But where she cannot realise her purposes,\r\nnature does nothing. In this respect she acts\r\nexactly as a good man of business does.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_15\" id=\"Page_15\"\u003e[Pg 15]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eIt is a constant purpose of nature to bring weights\r\nlower. We can raise a weight by causing another,\r\nlarger weight to sink; that is, by satisfying another,\r\nmore powerful, purpose of nature. If we fancy we\r\nare making nature serve our purposes in this, it will\r\nbe found, upon closer examination, that the contrary\r\nis true, and that nature has employed us to attain her\r\npurposes.\u003c/p\u003e\r\n\r\n\u003cp\u003eEquilibrium, rest, exists only, but then always, when\r\nnature is brought to a halt in her purposes, when the\r\nforces of nature are as fully satisfied as, under the\r\ncircumstances, they can be. Thus, for example, heavy\r\nbodies are in equilibrium, when their so-called centre\r\nof gravity lies as low as it possibly can, or when as\r\nmuch weight as the circumstances admit of has sunk\r\nas low as it can.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe idea forcibly suggests itself that perhaps this\r\nprinciple also holds good in other realms. Equilibrium\r\nexists also in the state when the purposes of the parties\r\nare as fully satisfied as for the time being they can\r\nbe, or, as we may say, jestingly, in the language of\r\nphysics, when the social potential is a maximum.\u003ca name=\"FNanchor_5_5\" id=\"FNanchor_5_5\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_5_5\" class=\"fnanchor\"\u003e[5]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eYou see, our miserly mercantile principle is replete\r\nwith consequences.\u003ca name=\"FNanchor_6_6\" id=\"FNanchor_6_6\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_6_6\" class=\"fnanchor\"\u003e[6]\u003c/a\u003e The result of sober research, it\r\nhas become as fruitful for physics as the dry questions\r\nof Socrates for science generally. If the principle\r\nseems to lack in ideality, the more ideal are the fruits\r\nwhich it bears.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_16\" id=\"Page_16\"\u003e[Pg 16]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eBut why, tell me, should science be ashamed of\r\nsuch a principle? Is science\u003ca name=\"FNanchor_7_7\" id=\"FNanchor_7_7\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_7_7\" class=\"fnanchor\"\u003e[7]\u003c/a\u003e itself anything more\r\nthan\u0026mdash;a business? Is not its task to acquire with the\r\nleast possible work, in the least possible time, with the\r\nleast possible thought, the greatest possible part of\r\neternal truth?\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_17\" id=\"Page_17\"\u003e[Pg 17]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"THE_FIBRES_OF_CORTI\" id=\"THE_FIBRES_OF_CORTI\"\u003eTHE FIBRES OF CORTI.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eWhoever has roamed through a beautiful country\r\nknows that the tourist\u0027s delights increase\r\nwith his progress. How pretty that wooded dell must\r\nlook from yonder hill! Whither does that clear brook\r\nflow, that hides itself in yonder sedge? If I only\r\nknew how the landscape looked behind that mountain!\r\nThus even the child thinks in his first rambles. It is\r\nalso true of the natural philosopher.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe first questions are forced upon the attention of\r\nthe inquirer by practical considerations; the subsequent\r\nones are not. An irresistible attraction draws\r\nhim to these; a nobler interest which far transcends the\r\nmere needs of life. Let us look at a special case.\u003c/p\u003e\r\n\r\n\u003cp\u003eFor a long time the structure of the organ of hearing\r\nhas actively engaged the attention of anatomists.\r\nA considerable number of brilliant discoveries has been\r\nbrought to light by their labors, and a splendid array\r\nof facts and truths established. But with these facts\r\na host of new enigmas has been presented.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhilst in the theory of the organisation and functions\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_18\" id=\"Page_18\"\u003e[Pg 18]\u003c/a\u003e\u003c/span\u003e\r\nof the eye comparative clearness has been attained;\r\nwhilst, hand in hand with this, ophthalmology\r\nhas reached a degree of perfection which the preceding\r\ncentury could hardly have dreamed of, and by the\r\nhelp of the ophthalmoscope the observing physician\r\npenetrates into the profoundest recesses of the eye,\r\nthe theory of the ear is still much shrouded in mysterious\r\ndarkness, full of attraction for the investigator.\u003c/p\u003e\r\n\r\n\u003cp\u003eLook at this model of the ear. Even at that familiar\r\npart by whose extent we measure the quantity of\r\npeople\u0027s intelligence, even at the external ear, the\r\nproblems begin. You see here a succession of helixes\r\nor spiral windings, at times very pretty, whose significance\r\nwe cannot accurately state, yet for which there\r\nmust certainly be some reason.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-028.jpg\" width=\"300\" height=\"205\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 6.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThe shell or concha of the ear, \u003ci\u003ea\u003c/i\u003e in the annexed\r\ndiagram, conducts the sound into the curved auditory\r\npassage \u003ci\u003eb\u003c/i\u003e, which is terminated by a thin membrane,\r\nthe so-called tympanic membrane, \u003ci\u003ee\u003c/i\u003e. This membrane\r\nis set in motion by the sound, and in its turn sets in\r\nmotion a series of little bones of very peculiar formation,\r\n\u003ci\u003ec\u003c/i\u003e. At the end of all is the labyrinth\r\n\u003ci\u003ed\u003c/i\u003e. The labyrinth consists of a group of\r\ncavities filled with a liquid, in which the\r\ninnumerable fibres of the nerve of hearing\r\nare imbedded. By the vibration of the chain of\r\nbones \u003ci\u003ec\u003c/i\u003e, the liquid of the labyrinth is shaken, and the\r\nauditory nerve excited. Here the process of hearing\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_19\" id=\"Page_19\"\u003e[Pg 19]\u003c/a\u003e\u003c/span\u003e\r\nbegins. So much is certain. But the details of the\r\nprocess are one and all unanswered questions.\u003c/p\u003e\r\n\r\n\u003cp\u003eTo these old puzzles, the Marchese Corti, as late\r\nas 1851, added a new enigma. And, strange to say,\r\nit is this last enigma, which, perhaps, has first received\r\nits correct solution. This will be the subject of our\r\nremarks to-day.\u003c/p\u003e\r\n\r\n\u003cp\u003eCorti found in the cochlea, or snail-shell of the\r\nlabyrinth, a large number of microscopic fibres placed\r\nside by side in geometrically graduated order. According\r\nto Kölliker their number is three thousand. They\r\nwere also the subject of investigation at the hands of\r\nMax Schultze and Deiters.\u003c/p\u003e\r\n\r\n\u003cp\u003eA description of the details of this organ would\r\nonly weary you, besides not rendering the matter much\r\nclearer. I prefer, therefore, to state briefly what in\r\nthe opinion of prominent investigators like Helmholtz\r\nand Fechner is the peculiar function of Corti\u0027s fibres.\r\nThe cochlea, it seems, contains a large number of\r\nelastic fibres of graduated lengths (Fig. 7), to which\r\nthe branches of the auditory nerve are\r\nattached. These fibres, called the fibres,\r\npillars, or rods of Corti, being of unequal\r\nlength, must also be of unequal elasticity,\r\nand, consequently, pitched to different\r\nnotes. The cochlea, therefore, is a species of pianoforte.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-029.jpg\" width=\"300\" height=\"290\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 7.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eWhat, now, may be the office of this structure,\r\nwhich is found in no other organ of sense? May it\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_20\" id=\"Page_20\"\u003e[Pg 20]\u003c/a\u003e\u003c/span\u003e\r\nnot be connected with some special property of the\r\near? It is quite probable; for the ear possesses a very\r\nsimilar power. You know that it is possible to follow\r\nthe individual voices of a symphony. Indeed, the\r\nfeat is possible even in a fugue of Bach, where it is certainly\r\nno inconsiderable achievement. The ear can\r\npick out the single constituent tonal parts, not only of a\r\nharmony, but of the wildest clash of music imaginable.\r\nThe musical ear analyses every agglomeration of tones.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe eye does not possess this ability. Who, for\r\nexample, could tell from the mere sight of white, without\r\na previous experimental knowledge of the fact,\r\nthat white is composed of a mixture of other colors?\r\nCould it be, now, that these two facts, the property of\r\nthe ear just mentioned, and the structure discovered\r\nby Corti, are really connected? It is very probable.\r\nThe enigma is solved if we assume that every note of\r\ndefinite pitch has its special string in this pianoforte\r\nof Corti, and, therefore, its special branch of the auditory\r\nnerve attached to that string. But before I can\r\nmake this point perfectly plain to you, I must ask\r\nyou to follow me a few steps into the dry domain of\r\nphysics.\u003c/p\u003e\r\n\r\n\u003cp\u003eLook at this pendulum. Forced from its position\r\nof equilibrium by an impulse, it begins to swing with a\r\ndefinite time of oscillation, dependent upon its length.\r\nLonger pendulums swing more slowly, shorter ones\r\nmore quickly. We will suppose our pendulum to execute\r\none to-and-fro movement in a second.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_21\" id=\"Page_21\"\u003e[Pg 21]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThis pendulum, now, can be thrown into violent\r\nvibration in two ways; either by a \u003ci\u003esingle\u003c/i\u003e heavy impulse,\r\nor by a \u003ci\u003enumber\u003c/i\u003e of properly communicated slight\r\nimpulses. For example, we impart to the pendulum,\r\nwhile at rest in its position of equilibrium, a very slight\r\nimpulse. It will execute a very small vibration. As\r\nit passes a third time its position of equilibrium, a\r\nsecond having elapsed, we impart to it again a slight\r\nshock, in the same direction with the first. Again after\r\nthe lapse of a second, on its fifth passage through the\r\nposition of equilibrium, we strike it again in the same\r\nmanner; and so continue. You see, by this process\r\nthe shocks imparted augment continually the motion\r\nof the pendulum. After each slight impulse, the pendulum\r\nreaches out a little further in its swing, and\r\nfinally acquires a considerable motion.\u003ca name=\"FNanchor_8_8\" id=\"FNanchor_8_8\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_8_8\" class=\"fnanchor\"\u003e[8]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eBut this is not the case under all circumstances.\r\nIt is possible only when the impulses imparted synchronise\r\nwith the swings of the pendulum. If we\r\nshould communicate the second impulse at the end of\r\nhalf a second and in the same direction with the first\r\nimpulse, its effects would counteract the motion of the\r\npendulum. It is easily seen that our little impulses\r\nhelp the motion of the pendulum more and more, according\r\nas their time accords with the time of the\r\npendulum. If we strike the pendulum in any other\r\ntime than in that of its vibration, in some instances, it\r\nis true, we shall augment its vibration, but in others\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_22\" id=\"Page_22\"\u003e[Pg 22]\u003c/a\u003e\u003c/span\u003e\r\nagain, we shall obstruct it. Our impulses will be less\r\neffective the more the motion of our own hand departs\r\nfrom the motion of the pendulum.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat is true of the pendulum holds true of every\r\nvibrating body. A tuning-fork when it sounds, also\r\nvibrates. It vibrates more rapidly when its sound is\r\nhigher; more slowly when it is deeper. The standard\r\n\u003ci\u003eA\u003c/i\u003e of our musical scale is produced by about four hundred\r\nand fifty vibrations in a second.\u003c/p\u003e\r\n\r\n\u003cp\u003eI place by the side of each other on this table two\r\ntuning-forks, exactly alike, resting on resonant cases.\r\nI strike the first one a sharp blow, so that it emits a\r\nloud note, and immediately grasp it again with my\r\nhand to quench its note. Nevertheless, you still hear\r\nthe note distinctly sounded, and by feeling it you may\r\nconvince yourselves that the other fork which was not\r\nstruck now vibrates.\u003c/p\u003e\r\n\r\n\u003cp\u003eI now attach a small bit of wax to one of the forks.\r\nIt is thrown thus out of tune; its note is made a little\r\ndeeper. I now repeat the same experiment with the\r\ntwo forks, now of unequal pitch, by striking one of\r\nthem and again grasping it with my hand; but in the\r\npresent case the note ceases the very instant I touch\r\nthe fork.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat has happened here in these two experiments?\r\nSimply this. The vibrating fork imparts to the air and\r\nto the table four hundred and fifty shocks a second,\r\nwhich are carried over to the other fork. If the other\r\nfork is pitched to the same note, that is to say, if it\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_23\" id=\"Page_23\"\u003e[Pg 23]\u003c/a\u003e\u003c/span\u003e\r\nvibrates when struck in the same time with the first,\r\nthen the shocks first emitted, no matter how slight they\r\nmay be, are sufficient to throw the second fork into rapid\r\nsympathetic vibration. But when the time of vibration\r\nof the two forks is slightly different, this does not\r\ntake place. We may strike as many forks as we will, the\r\nfork tuned to \u003ci\u003eA\u003c/i\u003e is perfectly indifferent to their notes;\r\nis deaf, in fact, to all except its own; and if you strike\r\nthree, or four, or five, or any number whatsoever, of\r\nforks all at the same time, so as to make the shocks\r\nwhich come from them ever so great, the \u003ci\u003eA\u003c/i\u003e fork will\r\nnot join in with their vibrations unless another fork \u003ci\u003eA\u003c/i\u003e\r\nis found in the collection struck. It picks out, in other\r\nwords, from all the notes sounded, that which accords\r\nwith it.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe same is true of all bodies which can yield\r\nnotes. Tumblers resound when a piano is played, on\r\nthe striking of certain notes, and so do window panes.\r\nNor is the phenomenon without analogy in other provinces.\r\nTake a dog that answers to the name \"Nero.\"\r\nHe lies under your table. You speak of Domitian,\r\nVespasian, and Marcus Aurelius Antoninus, you call\r\nupon all the names of the Roman Emperors that occur\r\nto you, but the dog does not stir, although a slight\r\ntremor of his ear tells you of a faint response of his\r\nconsciousness. But the moment you call \"Nero\" he\r\njumps joyfully towards you. The tuning-fork is like\r\nyour dog. It answers to the name \u003ci\u003eA\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou smile, ladies. You shake your heads. The\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_24\" id=\"Page_24\"\u003e[Pg 24]\u003c/a\u003e\u003c/span\u003e\r\nsimile does not catch your fancy. But I have another,\r\nwhich is very near to you: and for punishment you shall\r\nhear it. You, too, are like tuning-forks. Many are the\r\nhearts that throb with ardor for you, of which you take\r\nno notice, but are cold. Yet what does it profit you!\r\nSoon the heart will come that beats in just the proper\r\nrhythm, and then your knell, too, has struck. Then\r\nyour heart, too, will beat in unison, whether you will\r\nor no.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe law of sympathetic vibration, here propounded\r\nfor sounding bodies, suffers some modification for\r\nbodies incompetent to yield notes. Bodies of this\r\nkind vibrate to almost every note. A high silk hat,\r\nwe know, will not sound; but if you will hold your\r\nhat in your hand when attending your next concert you\r\nwill not only hear the pieces played, but also feel them\r\nwith your fingers. It is exactly so with men. People\r\nwho are themselves able to give tone to their surroundings,\r\nbother little about the prattle of others. But the\r\nperson without character tarries everywhere: in the\r\ntemperance hall, and at the bar of the public-house\u0026mdash;everywhere\r\nwhere a committee is formed. The high\r\nsilk hat is among bells what the weakling is among\r\nmen of conviction.\u003c/p\u003e\r\n\r\n\u003cp\u003eA sonorous body, therefore, always sounds when\r\nits special note, either alone or in company with others,\r\nis struck. We may now go a step further. What will\r\nbe the behaviour of a group of sonorous bodies which\r\nin the pitch of their notes form a scale? Let us picture\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_25\" id=\"Page_25\"\u003e[Pg 25]\u003c/a\u003e\u003c/span\u003e\r\nto ourselves, for example (Fig. 8), a series of rods\r\nor strings pitched to the notes \u003ci\u003ec d e f g\u003c/i\u003e…. On a\r\nmusical instrument the accord \u003ci\u003ec e g\u003c/i\u003e is struck. Every\r\none of the rods of Fig. 8 will see if its special note is\r\ncontained in the accord, and if it finds\r\nit, it will respond. The rod \u003ci\u003ec\u003c/i\u003e will give\r\nat once the note \u003ci\u003ec\u003c/i\u003e, the rod \u003ci\u003ee\u003c/i\u003e the note \u003ci\u003ee\u003c/i\u003e,\r\nthe rod \u003ci\u003eg\u003c/i\u003e the note \u003ci\u003eg\u003c/i\u003e. All the other\r\nrods will remain at rest, will not sound.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-035.jpg\" width=\"300\" height=\"337\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 8.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eWe need not look about us long\r\nfor such an instrument. Every piano\r\nis an instrument of this kind, with which the experiment\r\nmentioned may be executed with splendid success.\r\nTwo pianos stand here by the side of each other,\r\nboth tuned alike. We will employ the first for exciting\r\nthe notes, while we will allow the second to respond;\r\nafter having first pressed upon the loud pedal,\r\nso as to render all the strings capable of motion.\u003c/p\u003e\r\n\r\n\u003cp\u003eEvery harmony struck with vigor on the first piano\r\nis distinctly repeated on the second. To prove that\r\nit is the same strings that are sounded in both pianos,\r\nwe repeat the experiment in a slightly changed form.\r\nWe let go the loud pedal of the second piano and\r\npressing on the keys \u003ci\u003ec e g\u003c/i\u003e of that instrument vigorously\r\nstrike the harmony \u003ci\u003ec e g\u003c/i\u003e on the first piano. The harmony\r\n\u003ci\u003ec e g\u003c/i\u003e is now also sounded on the second piano.\r\nBut if we press only on one key \u003ci\u003eg\u003c/i\u003e of one piano, while\r\nwe strike \u003ci\u003ec e g\u003c/i\u003e on the other, only \u003ci\u003eg\u003c/i\u003e will be sounded on\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_26\" id=\"Page_26\"\u003e[Pg 26]\u003c/a\u003e\u003c/span\u003e\r\nthe second. It is thus always the like strings of the\r\ntwo pianos that excite each other.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe piano can reproduce any sound that is composed\r\nof its musical notes. It will reproduce, for example,\r\nvery distinctly, a vowel sound that is sung into\r\nit. And in truth physics has proved that the vowels\r\nmay be regarded as composed of simple musical\r\nnotes.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou see that by the exciting of definite tones in the\r\nair quite definite motions are set up with mechanical\r\nnecessity in the piano. The idea might be made use\r\nof for the performance of some pretty pieces of wizardry.\r\nImagine a box in which is a stretched string\r\nof definite pitch. This is thrown into motion as often\r\nas its note is sung or whistled. Now it would not be\r\na very difficult task for a skilful mechanic to so construct\r\nthe box that the vibrating cord would close a\r\ngalvanic circuit and open the lock. And it would not\r\nbe a much more difficult task to construct a box which\r\nwould open at the whistling of a certain melody. Sesame!\r\nand the bolts fall. Truly, we should have here\r\na veritable puzzle-lock. Still another fragment rescued\r\nfrom that old kingdom of fables, of which our day\r\nhas realised so much, that world of fairy-stories to\r\nwhich the latest contributions are Casselli\u0027s telegraph,\r\nby which one can write at a distance in one\u0027s own hand,\r\nand Prof. Elisha Gray\u0027s telautograph. What would\r\nthe good old Herodotus have said to these things who\r\neven in Egypt shook his head at much that he saw?\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_27\" id=\"Page_27\"\u003e[Pg 27]\u003c/a\u003e\u003c/span\u003e\r\n\u0026#7952;\u0026#956;\u0026#959;\u0026#7985; \u0026#956;\u0026#7953;\u0026#957;e \u0026#959;\u0026#973; \u0026#960;\u0026#953;\u0026#963;\u0026#964;\u0026#945;, just as simple-heartedly as then,\r\nwhen he heard of the circumnavigation of Africa.\u003c/p\u003e\r\n\r\n\u003cp\u003eA new puzzle-lock! But why invent one? Are\r\nnot we human beings ourselves puzzle-locks? Think\r\nof the stupendous groups of thoughts, feelings, and\r\nemotions that can be aroused in us by a word! Are\r\nthere not moments in all our lives when a mere name\r\ndrives the blood to our hearts? Who that has attended\r\na large mass-meeting has not experienced what\r\ntremendous quantities of energy and motion can be\r\nevolved by the innocent words, \"Liberty, Equality,\r\nFraternity.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eBut let us return to the subject proper of our discourse.\r\nLet us look again at our piano, or what will\r\ndo just as well, at some other contrivance of the same\r\ncharacter. What does this instrument do? Plainly,\r\nit decomposes, it analyses every agglomeration of\r\nsounds set up in the air into its individual component\r\nparts, each tone being taken up by a different string;\r\nit performs a real spectral analysis of sound. A person\r\ncompletely deaf, with the help of a piano, simply by\r\ntouching the strings or examining their vibrations with\r\na microscope, might investigate the sonorous motion of\r\nthe air, and pick out the separate tones excited in it.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe ear has the same capacity as this piano. The\r\near performs for the mind what the piano performs for\r\na person who is deaf. The mind without the ear is\r\ndeaf. But a deaf person, with the piano, does hear\r\nafter a fashion, though much less vividly, and more\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_28\" id=\"Page_28\"\u003e[Pg 28]\u003c/a\u003e\u003c/span\u003e\r\nclumsily, than with the ear. The ear, thus, also decomposes\r\nsound into its component tonal parts. I shall\r\nnow not be deceived, I think, if I assume that you\r\nalready have a presentiment of what the function of\r\nCorti\u0027s fibres is. We can make the matter very plain to\r\nourselves. We will use the one piano for exciting the\r\nsounds, and we shall imagine the second one in the\r\near of the observer in the place of Corti\u0027s fibres, which\r\nis a model of such an instrument. To every string of\r\nthe piano in the ear we will suppose a special fibre of\r\nthe auditory nerve attached, so that this fibre and this\r\nalone, is irritated when the string is thrown into vibration.\r\nIf we strike now an accord on the external\r\npiano, for every tone of that accord a definite string of\r\nthe internal piano will sound and as many different\r\nnervous fibres will be irritated as there are notes in\r\nthe accord. The simultaneous sense-impressions due\r\nto different notes can thus be preserved unmingled and\r\nbe separated by the attention. It is the same as with\r\nthe five fingers of the hand. With each finger I can\r\ntouch something different. Now the ear has three thousand\r\nsuch fingers, and each one is designed for the\r\ntouching of a different tone.\u003ca name=\"FNanchor_9_9\" id=\"FNanchor_9_9\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_9_9\" class=\"fnanchor\"\u003e[9]\u003c/a\u003e Our ear is a puzzle-lock\r\nof the kind mentioned. It opens at the magic melody\r\nof a sound. But it is a stupendously ingenious lock.\r\nNot only one tone, but every tone makes it open; but\r\neach one differently. To each tone it replies with a\r\ndifferent sensation.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_29\" id=\"Page_29\"\u003e[Pg 29]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eMore than once it has happened in the history of\r\nscience that a phenomenon predicted by theory, has\r\nnot been brought within the range of actual observation\r\nuntil long afterwards. Leverrier predicted the\r\nexistence and the place of the planet Neptune, but it\r\nwas not until sometime later that Galle actually found\r\nthe planet at the predicted spot. Hamilton unfolded\r\ntheoretically the phenomenon of the so-called conical\r\nrefraction of light, but it was reserved for Lloyd some\r\ntime subsequently to observe the fact. The fortunes\r\nof Helmholtz\u0027s theory of Corti\u0027s fibres have been somewhat\r\nsimilar. This theory, too, received its substantial\r\nconfirmation from the subsequent observations of\r\nV. Hensen. On the free surface of the bodies of Crustacea,\r\nconnected with the auditory nerves, rows of little\r\nhairy filaments of varying lengths and thicknesses\r\nare found, which to some extent are the analogues of\r\nCorti\u0027s fibres. Hensen saw these hairs vibrate when\r\nsounds were excited, and when different notes were\r\nstruck different hairs were set in vibration.\u003c/p\u003e\r\n\r\n\u003cp\u003eI have compared the work of the physical inquirer\r\nto the journey of the tourist. When the tourist ascends\r\na new hill he obtains of the whole district a\r\ndifferent view. When the inquirer has found the solution\r\nof one enigma, the solution of a host of others\r\nfalls into his hands.\u003c/p\u003e\r\n\r\n\u003cp\u003eSurely you have often felt the strange impression experienced\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_30\" id=\"Page_30\"\u003e[Pg 30]\u003c/a\u003e\u003c/span\u003e\r\nwhen in singing through the scale the octave\r\nis reached, and nearly the same sensation is produced\r\nas by the fundamental tone. The phenomenon finds its\r\nexplanation in the view here laid down of the ear. And\r\nnot only this phenomenon but all the laws of the theory\r\nof harmony may be grasped and verified from this\r\npoint of view with a clearness before undreamt of.\r\nUnfortunately, I must content myself to-day with the\r\nsimple indication of these beautiful prospects. Their\r\nconsideration would lead us too far aside into the fields\r\nof other sciences.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe searcher of nature, too, must restrain himself\r\nin his path. He also is drawn along from one beauty\r\nto another as the tourist from dale to dale, and as circumstances\r\ngenerally draw men from one condition of\r\nlife into others. It is not he so much that makes the\r\nquests, as that the quests are made of him. Yet let\r\nhim profit by his time, and let not his glance rove aimlessly\r\nhither and thither. For soon the evening sun\r\nwill shine, and ere he has caught a full glimpse of the\r\nwonders close by, a mighty hand will seize him and\r\nlead him away into a different world of puzzles.\u003c/p\u003e\r\n\r\n\u003cp\u003eRespected hearers, science once stood in an entirely\r\ndifferent relation to poetry. The old Hindu\r\nmathematicians wrote their theorems in verses, and\r\nlotus-flowers, roses, and lilies, beautiful sceneries,\r\nlakes, and mountains figured in their problems.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Thou goest forth on this lake in a boat. A lily\r\njuts forth, one palm above the water. A breeze bends\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_31\" id=\"Page_31\"\u003e[Pg 31]\u003c/a\u003e\u003c/span\u003e\r\nit downwards, and it vanishes two palms from its previous\r\nspot beneath the surface. Quick, mathematician,\r\ntell me how deep is the lake!\"\u003c/p\u003e\r\n\r\n\u003cp\u003eThus spoke an ancient Hindu scholar. This poetry,\r\nand rightly, has disappeared from science, but from\r\nits dry leaves another poetry is wafted aloft which cannot\r\nbe described to him who has never felt it. Whoever\r\nwill fully enjoy this poetry must put his hand to\r\nthe plough, must himself investigate. Therefore,\r\nenough of this! I shall reckon myself fortunate if you\r\ndo not repent of this brief excursion into the flowered\r\ndale of physiology, and if you take with yourselves the\r\nbelief that we can say of science what we say of poetry,\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"Who the song would understand,\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eNeeds must seek the song\u0027s own land;\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eWho the minstrel understand\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eNeeds must seek the minstrel\u0027s land.\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_32\" id=\"Page_32\"\u003e[Pg 32]\u003c/a\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_THE_CAUSES_OF_HARMONY\" id=\"ON_THE_CAUSES_OF_HARMONY\"\u003eON THE CAUSES OF HARMONY.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eWe are to speak to-day of a theme which is perhaps\r\nof somewhat more general interest\u0026mdash;\u003ci\u003ethe causes of\r\nthe harmony of musical sounds\u003c/i\u003e. The first and simplest\r\nexperiences relative to harmony are very ancient. Not\r\nso the explanation of its laws. These were first supplied\r\nby the investigators of a recent epoch. Allow me\r\nan historical retrospect.\u003c/p\u003e\r\n\r\n\u003cp\u003ePythagoras (586 B. C.) knew that the note yielded\r\nby a string of steady tension was converted into its\r\noctave when the length of the string was reduced one-half,\r\nand into its fifth when reduced two-thirds; and\r\nthat then the first fundamental tone was consonant\r\nwith the two others. He knew generally that the same\r\nstring under fixed tension gives consonant tones when\r\nsuccessively divided into lengths that are in the proportions\r\nof the simplest natural numbers; that is, in\r\nthe proportions of 1:2, 2:3, 3:4, 4:5.\u003c/p\u003e\r\n\r\n\u003cp\u003ePythagoras failed to reveal the causes of these laws.\r\nWhat have consonant tones to do with the simple natural\r\nnumbers? That is the question we should ask\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_33\" id=\"Page_33\"\u003e[Pg 33]\u003c/a\u003e\u003c/span\u003e\r\nto-day. But this circumstance must have appeared\r\nless strange than inexplicable to Pythagoras. This\r\nphilosopher sought for the causes of harmony in the\r\noccult, miraculous powers of numbers. His procedure\r\nwas largely the cause of the upgrowth of a numerical\r\nmysticism, of which the traces may still be detected in\r\nour oneirocritical books and among some scientists, to\r\nwhom marvels are more attractive than lucidity.\u003c/p\u003e\r\n\r\n\u003cp\u003eEuclid (300 B. C.) gives a definition of consonance\r\nand dissonance that could hardly be improved upon,\r\nin point of verbal accuracy. The consonance (\u0026#963;\u0026#965;\u0026#956;\u0026#966;\u0026#969;\u0026#957;\u0026#8055;\u0026#945;)\r\nof two tones, he says, is the mixture, the\r\nblending (\u0026#954;\u0026#961;\u0026#8118;\u0026#963;\u0026#953;\u0026#962;) of those two tones; dissonance\r\n(\u0026#948;\u0026#953;\u0026#945;\u0026#966;\u0026#969;\u0026#957;\u0026#8055;\u0026#945;), on the other hand, is the incapacity of\r\nthe tones to blend (\u0026#7936;\u0026#956;\u0026#953;\u0026#958;\u0026#8055;\u0026#945;), whereby they are made\r\nharsh for the ear. The person who knows the correct\r\nexplanation of the phenomenon hears it, so to speak,\r\nreverberated in these words of Euclid. Still, Euclid\r\ndid not know the true cause of harmony. He had unwittingly\r\ncome very near to the truth, but without\r\nreally grasping it.\u003c/p\u003e\r\n\r\n\u003cp\u003eLeibnitz (1646-1716 A. D.) resumed the question\r\nwhich his predecessors had left unsolved. He, of\r\ncourse, knew that musical notes were produced by vibrations,\r\nthat twice as many vibrations corresponded\r\nto the octave as to the fundamental tone, etc. A passionate\r\nlover of mathematics, he sought for the cause\r\nof harmony in the secret computation and comparison\r\nof the simple numbers of vibrations and in the secret\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_34\" id=\"Page_34\"\u003e[Pg 34]\u003c/a\u003e\u003c/span\u003e\r\nsatisfaction of the soul at this occupation. But how,\r\nwe ask, if one does not know that musical notes are\r\nvibrations? The computation and the satisfaction at\r\nthe computation must indeed be pretty secret if it is\r\nunknown. What queer ideas philosophers have! Could\r\nanything more wearisome be imagined than computation\r\nas a principle of æsthetics? Yes, you are not\r\nutterly wrong in your conjecture, yet you may be sure\r\nthat Leibnitz\u0027s theory is not wholly nonsense, although\r\nit is difficult to make out precisely what he meant by\r\nhis secret computation.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe great Euler (1707-1783) sought the cause of\r\nharmony, almost as Leibnitz did, in the pleasure which\r\nthe soul derives from the contemplation of order in the\r\nnumbers of the vibrations.\u003ca name=\"FNanchor_10_10\" id=\"FNanchor_10_10\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_10_10\" class=\"fnanchor\"\u003e[10]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eRameau and D\u0027Alembert (1717-1783) approached\r\nnearer to the truth. They knew that in every sound\r\navailable in music besides the fundamental note also\r\nthe twelfth and the next higher third could be heard;\r\nand further that the resemblance between a fundamental\r\ntone and its octave was always strongly marked.\r\nAccordingly, the combination of the octave, fifth, third,\r\netc., with the fundamental tone appeared to them \"natural.\"\r\nThey possessed, we must admit, the correct\r\npoint of view; but with the simple naturalness of a\r\nphenomenon no inquirer can rest content; for it is precisely\r\nthis naturalness for which he seeks his explanations.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_35\" id=\"Page_35\"\u003e[Pg 35]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eRameau\u0027s remark dragged along through the whole\r\nmodern period, but without leading to the full discovery\r\nof the truth. Marx places it at the head of his\r\ntheory of composition, but makes no further application\r\nof it. Also Goethe and Zelter in their correspondence\r\nwere, so to speak, on the brink of the truth.\r\nZelter knew of Rameau\u0027s view. Finally, you will be\r\nappalled at the difficulty of the problem, when I tell\r\nyou that till very recent times even professors of physics\r\nwere dumb when asked what were the causes of\r\nharmony.\u003c/p\u003e\r\n\r\n\u003cp\u003eNot till quite recently did Helmholtz find the solution\r\nof the question. But to make this solution clear\r\nto you I must first speak of some experimental principles\r\nof physics and psychology.\u003c/p\u003e\r\n\r\n\u003cp\u003e1) In every process of perception, in every observation,\r\nthe attention plays a highly important part.\r\nWe need not look about us long for proofs of this.\r\nYou receive, for example, a letter written in a very\r\npoor hand. Do your best, you cannot make it out.\r\nYou put together now these, now those lines, yet you\r\ncannot construct from them a single intelligible character.\r\nNot until you direct your attention to groups\r\nof lines which really belong together, is the reading of\r\nthe letter possible. Manuscripts, the letters of which\r\nare formed of minute figures and scrolls, can only be\r\nread at a considerable distance, where the attention is\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_36\" id=\"Page_36\"\u003e[Pg 36]\u003c/a\u003e\u003c/span\u003e\r\nno longer diverted from the significant outlines to the\r\ndetails. A beautiful example of this class is furnished\r\nby the famous iconographs of Giuseppe Arcimboldo in\r\nthe basement of the Belvedere gallery at Vienna. These\r\nare symbolic representations of water, fire, etc.: human\r\nheads composed of aquatic animals and of combustibles.\r\nAt a short distance one sees only the details,\r\nat a greater distance only the whole figure. Yet\r\na point can be easily found at which, by a simple voluntary\r\nmovement of the attention, there is no difficulty\r\nin seeing now the whole figure and now the smaller\r\nforms of which it is composed. A picture is often seen\r\nrepresenting the tomb of Napoleon. The tomb is surrounded\r\nby dark trees between which the bright heavens\r\nare visible as background. One can look a long time\r\nat this picture without noticing anything except the\r\ntrees, but suddenly, on the attention being accidentally\r\ndirected to the bright background, one sees\r\nthe figure of Napoleon between the trees. This case\r\nshows us very distinctly the important part which attention\r\nplays. The same sensuous object can, solely\r\nby the interposition of attention, give rise to wholly\r\ndifferent perceptions.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf I strike a harmony, or chord, on this piano, by\r\na mere effort of attention you can fix every tone of\r\nthat harmony. You then hear most distinctly the\r\nfixed tone, and all the rest appear as a mere addition,\r\naltering only the quality, or acoustic color, of the primary\r\ntone. The effect of the same harmony is essentially\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_37\" id=\"Page_37\"\u003e[Pg 37]\u003c/a\u003e\u003c/span\u003e\r\nmodified if we direct our attention to different\r\ntones.\u003c/p\u003e\r\n\r\n\u003cp\u003eStrike in succession two harmonies, for example,\r\nthe two represented in the annexed diagram, and first\r\nfix by the attention the upper note \u003ci\u003ee\u003c/i\u003e, afterwards the\r\nbase \u003ci\u003ee\u003c/i\u003e-\u003ci\u003ea\u003c/i\u003e; in the two cases you will hear the same\r\nsequence of harmonies differently.\r\nIn the first case, you have the impression\r\nas if the fixed tone remained\r\nunchanged and simply altered\r\nits \u003ci\u003etimbre\u003c/i\u003e; in the second case,\r\nthe whole acoustic agglomeration\r\nseems to fall sensibly in depth.\r\nThere is an art of composition to guide the attention\r\nof the hearer. But there is also an art of hearing,\r\nwhich is not the gift of every person.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 200px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-047.jpg\" width=\"200\" height=\"178\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 9.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThe piano-player knows the remarkable effects obtained\r\nwhen one of the keys of a chord that is struck\r\nis let loose. Bar 1 played on the piano sounds almost\r\nlike bar 2. The note which lies next to the key let\r\nloose resounds after its release as if it were freshly\r\nstruck. The attention no longer occupied with the\r\nupper note is by that very fact insensibly led to the\r\nupper note.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 500px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-047-1.jpg\" width=\"500\" height=\"175\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 10.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_38\" id=\"Page_38\"\u003e[Pg 38]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eAny tolerably cultivated musical ear can perform\r\nthe resolution of a harmony into its component parts.\r\nBy much practice we can go even further. Then,\r\nevery musical sound heretofore regarded as simple\r\ncan be resolved into a subordinate succession\r\nof musical tones. For example,\r\nif I strike on the piano the note 1, (annexed\r\ndiagram,) we shall hear, if we\r\nmake the requisite effort of attention,\r\nbesides the loud fundamental note the\r\nfeebler, higher overtones, or harmonics,\r\n2 … 7, that is, the octave, the twelfth, the double\r\noctave, and the third, the fifth, and the seventh of\r\nthe double octave.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 200px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-048.jpg\" width=\"200\" height=\"237\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 11.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThe same is true of every musically available\r\nsound. Each yields, with varying degrees of intensity,\r\nbesides its fundamental note, also the octave, the\r\ntwelfth, the double octave, etc. The phenomenon is\r\nobservable with special facility on the open and closed\r\nflue-pipes of organs. According, now, as certain overtones\r\nare more or less distinctly emphasised in a\r\nsound, the \u003ci\u003etimbre\u003c/i\u003e of the sound changes\u0026mdash;that peculiar\r\nquality of the sound by which we distinguish the music\r\nof the piano from that of the violin, the clarinet, etc.\u003c/p\u003e\r\n\r\n\u003cp\u003eOn the piano these overtones can be very easily\r\nrendered audible. If I strike, for example, sharply\r\nnote 1 of the foregoing series, whilst I simply press\r\ndown upon, one after another, the keys 2, 3, … 7,\r\nthe notes 2, 3, … 7 will continue to sound after the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_39\" id=\"Page_39\"\u003e[Pg 39]\u003c/a\u003e\u003c/span\u003e\r\nstriking of 1, because the strings corresponding to\r\nthese notes, now freed from their dampers, are thrown\r\ninto sympathetic vibration.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs you know, this sympathetic vibration of the like-pitched\r\nstrings with the overtones is really not to be\r\nconceived as sympathy, but rather as lifeless mechanical\r\nnecessity. We must not think of this sympathetic\r\nvibration as an ingenious journalist pictured it, who\r\ntells a gruesome story of Beethoven\u0027s F minor sonata,\r\nOp. 2, that I cannot withhold from you. \"At the\r\nlast London Industrial Exhibition nineteen virtuosos\r\nplayed the F minor sonata on the same piano. When\r\nthe twentieth stepped up to the instrument to play by\r\nway of variation the same production, to the terror of\r\nall present the piano began to render the sonata of its\r\nown accord. The Archbishop of Canterbury, who\r\nhappened to be present, was set to work and forthwith\r\nexpelled the F minor devil.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eAlthough, now, the overtones or harmonics which\r\nwe have discussed are heard only upon a special effort\r\nof the attention, nevertheless they play a highly important\r\npart in the formation of musical \u003ci\u003etimbre\u003c/i\u003e, as also\r\nin the production of the consonance and dissonance of\r\nsounds. This may strike you as singular. How can\r\na thing which is heard only under exceptional circumstances\r\nbe of importance generally for audition?\u003c/p\u003e\r\n\r\n\u003cp\u003eBut consider some familiar incidents of your every-day\r\nlife. Think of how many things you see which\r\nyou do not notice, which never strike your attention\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_40\" id=\"Page_40\"\u003e[Pg 40]\u003c/a\u003e\u003c/span\u003e\r\nuntil they are missing. A friend calls upon you; you\r\ncannot understand why he looks so changed. Not\r\nuntil you make a close examination do you discover\r\nthat his hair has been cut. It is not difficult to tell\r\nthe publisher of a work from its letter-press, and yet\r\nno one can state precisely the points by which this\r\nstyle of type is so strikingly different from that style.\r\nI have often recognised a book which I was in search\r\nof from a simple piece of unprinted white paper that\r\npeeped out from underneath the heap of books covering\r\nit, and yet I had never carefully examined the\r\npaper, nor could I have stated its difference from other\r\npapers.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat we must remember, therefore, is that every\r\nsound that is musically available yields, besides its\r\nfundamental note, its octave, its twelfth, its double\r\noctave, etc., as overtones or harmonics, and that these\r\nare important for the agreeable combination of several\r\nmusical sounds.\u003c/p\u003e\r\n\r\n\u003cp\u003e2) One other fact still remains to be dealt with.\r\nLook at this tuning-fork. It yields, when struck, a perfectly\r\nsmooth tone. But if you strike in company with\r\nit a second fork which is of slightly different pitch, and\r\nwhich alone also gives a perfectly smooth tone, you\r\nwill hear, if you set both forks on the table, or hold\r\nboth before your ear, a uniform tone no longer, but a\r\nnumber of shocks of tones. The rapidity of the shocks\r\nincreases with the difference of the pitch of the forks.\r\nThese shocks, which become very disagreeable for the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_41\" id=\"Page_41\"\u003e[Pg 41]\u003c/a\u003e\u003c/span\u003e\r\near when they amount to thirty-three in a second, are\r\ncalled \"beats.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eAlways, when one of two like musical sounds is\r\nthrown out of unison with the other, beats arise. Their\r\nnumber increases with the divergence from unison, and\r\nsimultaneously they grow more unpleasant. Their\r\nroughness reaches its maximum at about thirty-three\r\nbeats in a second. On a still further departure from\r\nunison, and a consequent increase of the number of\r\nbeats, the unpleasant effect is diminished, so that tones\r\nwhich are widely apart in pitch no longer produce\r\noffensive beats.\u003c/p\u003e\r\n\r\n\u003cp\u003eTo give yourselves a clear idea of the production\r\nof beats, take two metronomes and set them almost\r\nalike. You can, for that matter, set the two exactly\r\nalike. You need not fear that they will strike alike.\r\nThe metronomes usually for sale in the shops are poor\r\nenough to yield, when set alike, appreciably unequal\r\nstrokes. Set, now, these two metronomes, which strike\r\nat unequal intervals, in motion; you will readily see\r\nthat their strokes alternately coincide and conflict with\r\neach other. The alternation is quicker the greater the\r\ndifference of time of the two metronomes.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf metronomes are not to be had, the experiment\r\nmay be performed with two watches.\u003c/p\u003e\r\n\r\n\u003cp\u003eBeats arise in the same way. The rhythmical\r\nshocks of two sounding bodies, of unequal pitch, sometimes\r\ncoincide, sometimes interfere, whereby they alternately\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_42\" id=\"Page_42\"\u003e[Pg 42]\u003c/a\u003e\u003c/span\u003e\r\naugment and enfeeble each other\u0027s effects.\r\nHence the shock-like, unpleasant swelling of the tone.\u003c/p\u003e\r\n\r\n\u003cp\u003eNow that we have made ourselves acquainted with\r\novertones and beats, we may proceed to the answer of\r\nour main question, Why do certain relations of pitch\r\nproduce pleasant sounds, consonances, others unpleasant\r\nsounds, dissonances? It will be readily seen that\r\nall the unpleasant effects of simultaneous sound-combinations\r\nare the result of beats produced by those\r\ncombinations. Beats are the only sin, the sole evil of\r\nmusic. Consonance is the coalescence of sounds without\r\nappreciable beats.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 182px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-052.jpg\" width=\"182\" height=\"800\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 12.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eTo make this perfectly clear to you I have constructed\r\nthe model which you see in Fig. 12. It represents\r\na claviatur. At its top a movable strip of wood\r\n\u003ci\u003eaa\u003c/i\u003e with the marks 1, 2 … 6 is placed. By setting\r\nthis strip in any position, for example, in that where the\r\nmark 1 is over the note \u003ci\u003ec\u003c/i\u003e of the claviatur, the marks\r\n2, 3 … 6, as you see, stand over the overtones of \u003ci\u003ec\u003c/i\u003e.\r\nThe same happens when the strip is placed in any\r\nother position. A second, exactly similar strip, \u003ci\u003ebb\u003c/i\u003e,\r\npossesses the same properties. Thus, together, the\r\ntwo strips, in any two positions, point out by their\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_43\" id=\"Page_43\"\u003e[Pg 43]\u003c/a\u003e\u003c/span\u003e\r\nmarks all the tones brought into play upon the simultaneous\r\nsounding of the notes indicated by the marks 1.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe two strips, placed over the same fundamental\r\nnote, show that also all the overtones of those notes\r\ncoincide. The first note is simply intensified by the\r\nother. The single overtones of a sound lie too far apart\r\nto permit appreciable beats. The second sound supplies\r\nnothing new, consequently, also, no new beats.\r\nUnison is the most perfect consonance.\u003c/p\u003e\r\n\r\n\u003cp\u003eMoving one of the two strips along the other is\r\nequivalent to a departure from unison. All the overtones\r\nof the one sound now fall alongside those of the\r\nother; beats are at once produced; the combination\r\nof the tones becomes unpleasant: we obtain a dissonance.\r\nIf we move the strip further and further along,\r\nwe shall find that as a general rule the overtones always\r\nfall alongside each other, that is, always produce\r\nbeats and dissonances. Only in a few quite definite\r\npositions do the overtones partially coincide. Such\r\npositions, therefore, signify higher degrees of euphony\u0026mdash;they\r\npoint out \u003ci\u003ethe consonant intervals\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eThese consonant intervals can be readily found experimentally\r\nby cutting Fig. 12 out of paper and moving\r\n\u003ci\u003ebb\u003c/i\u003e lengthwise along \u003ci\u003eaa\u003c/i\u003e. The most perfect consonances\r\nare the octave and the twelfth, since in these two cases\r\nthe overtones of the one sound coincide absolutely\r\nwith those of the other. In the octave, for example,\r\n1\u003ci\u003eb\u003c/i\u003e falls on 2\u003ci\u003ea\u003c/i\u003e, 2\u003ci\u003eb\u003c/i\u003e on 4\u003ci\u003ea\u003c/i\u003e, 3\u003ci\u003eb\u003c/i\u003e on 6\u003ci\u003ea\u003c/i\u003e. Consonances,\r\ntherefore, are simultaneous sound-combinations not\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_44\" id=\"Page_44\"\u003e[Pg 44]\u003c/a\u003e\u003c/span\u003e\r\naccompanied by disagreeable beats. This, by the way,\r\nis, expressed in English, what Euclid said in Greek.\u003c/p\u003e\r\n\r\n\u003cp\u003eOnly such sounds are consonant as possess in common\r\nsome portion of their partial tones. Plainly we\r\nmust recognise between such sounds, also when struck\r\none after another, a certain affinity. For the second\r\nsound, by virtue of the common overtones, will produce\r\npartly the same sensation as the first. The octave is\r\nthe most striking exemplification of this. When we\r\nreach the octave in the ascent of the scale we actually\r\nfancy we hear the fundamental tone repeated. The\r\nfoundations of harmony, therefore, are the foundations\r\nof melody.\u003c/p\u003e\r\n\r\n\u003cp\u003eConsonance is the coalescence of sounds without\r\nappreciable beats! This principle is competent to introduce\r\nwonderful order and logic into the doctrines\r\nof the fundamental bass. The compendiums of the\r\ntheory of harmony which (Heaven be witness!) have\r\nstood hitherto little behind the cook-books in subtlety\r\nof logic, are rendered extraordinarily clear and simple.\r\nAnd what is more, all that the great masters, such as\r\nPalestrina, Mozart, Beethoven, unconsciously got\r\nright, and of which heretofore no text-book could render\r\njust account, receives from the preceding principle\r\nits perfect verification.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut the beauty of the theory is, that it bears upon\r\nits face the stamp of truth. It is no phantom of the\r\nbrain. Every musician can hear for himself the beats\r\nwhich the overtones of his musical sounds produce.\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_45\" id=\"Page_45\"\u003e[Pg 45]\u003c/a\u003e\u003c/span\u003e\r\nEvery musician can satisfy himself that for any given\r\ncase the number and the harshness of the beats can\r\nbe calculated beforehand, and that they occur in exactly\r\nthe measure that theory determines.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis is the answer which Helmholtz gave to the\r\nquestion of Pythagoras, so far as it can be explained\r\nwith the means now at my command. A long period\r\nof time lies between the raising and the solving of this\r\nquestion. More than once were eminent inquirers\r\nnearer to the answer than they dreamed of.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe inquirer seeks the truth. I do not know if the\r\ntruth seeks the inquirer. But were that so, then the\r\nhistory of science would vividly remind us of that\r\nclassical rendezvous, so often immortalised by painters\r\nand poets. A high garden wall. At the right a\r\nyouth, at the left a maiden. The youth sighs, the\r\nmaiden sighs! Both wait. Neither dreams how near\r\nthe other is.\u003c/p\u003e\r\n\r\n\u003cp\u003eI like this simile. Truth suffers herself to be\r\ncourted, but she has evidently no desire to be won.\r\nShe flirts at times disgracefully. Above all, she is determined\r\nto be merited, and has naught but contempt\r\nfor the man who will win her too quickly. And if,\r\nforsooth, one breaks his head in his efforts of conquest,\r\nwhat matter is it, another will come, and truth is always\r\nyoung. At times, indeed, it really seems as if\r\nshe were well disposed towards her admirer, but that\r\nadmitted\u0026mdash;never! Only when Truth is in exceptionally\r\ngood spirits does she bestow upon her wooer a glance\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_46\" id=\"Page_46\"\u003e[Pg 46]\u003c/a\u003e\u003c/span\u003e\r\nof encouragement. For, thinks Truth, if I do not do\r\nsomething, in the end the fellow will not seek me at all.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis one fragment of truth, then, we have, and it\r\nshall never escape us. But when I reflect what it has\r\ncost in labor and in the lives of thinking men, how it\r\npainfully groped its way through centuries, a half-matured\r\nthought, before it became complete; when I\r\nreflect that it is the toil of more than two thousand\r\nyears that speaks out of this unobtrusive model of\r\nmine, then, without dissimulation, I almost repent me\r\nof the jest I have made.\u003c/p\u003e\r\n\r\n\u003cp\u003eAnd think of how much we still lack! When, several\r\nthousand years hence, boots, top-hats, hoops, pianos,\r\nand bass-viols are dug out of the earth, out of the\r\nnewest alluvium as fossils of the nineteenth century;\r\nwhen the scientists of that time shall pursue their\r\nstudies both upon these wonderful structures and upon\r\nour modern Broadways, as we to-day make studies of\r\nthe implements of the stone age and of the prehistoric\r\nlake-dwellings\u0026mdash;then, too, perhaps, people will be unable\r\nto comprehend how we could come so near to\r\nmany great truths without grasping them. And thus\r\nit is for all time the unsolved dissonance, for all time\r\nthe troublesome seventh, that everywhere resounds in\r\nour ears; we feel, perhaps, that it will find its solution,\r\nbut we shall never live to see the day of the pure\r\ntriple accord, nor shall our remotest descendants.\u003c/p\u003e\r\n\r\n\u003cp\u003eLadies, if it is the sweet purpose of your life to\r\nsow confusion, it is the purpose of mine to be clear;\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_47\" id=\"Page_47\"\u003e[Pg 47]\u003c/a\u003e\u003c/span\u003e\r\nand so I must confess to you a slight transgression\r\nthat I have been guilty of. On one point I have told\r\nyou an untruth. But you will pardon me this falsehood,\r\nif in full repentance I make it good. The model\r\nrepresented in Fig. 12 does not tell the whole truth, for\r\nit is based upon the so-called \"even temperament\"\r\nsystem of tuning. The overtones, however, of musical\r\nsounds are not tempered, but purely tuned. By means\r\nof this slight inexactness the model is made considerably\r\nsimpler. In this form it is fully adequate for\r\nordinary purposes, and no one who makes use of it in\r\nhis studies need be in fear of appreciable error.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf you should demand of me, however, the full\r\ntruth, I could give you that only by the help of a mathematical\r\nformula. I should have to take the chalk into\r\nmy hands and\u0026mdash;think of it!\u0026mdash;reckon in your presence.\r\nThis you might take amiss. Nor shall it happen.\r\nI have resolved to do no more reckoning for to-day.\r\nI shall reckon now only upon your forbearance, and\r\nthis you will surely not gainsay me when you reflect\r\nthat I have made only a limited use of my privilege to\r\nweary you. I could have taken up much more of\r\nyour time, and may, therefore, justly close with Lessing\u0027s\r\nepigram:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"If thou hast found in all these pages naught that\u0027s worth the thanks,\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eAt least have gratitude for what I\u0027ve spared thee.\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_48\" id=\"Page_48\"\u003e[Pg 48]\u003c/a\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"THE_VELOCITY_OF_LIGHT\" id=\"THE_VELOCITY_OF_LIGHT\"\u003eTHE VELOCITY OF LIGHT.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eWhen a criminal judge has a right crafty knave\r\nbefore him, one well versed in the arts of prevarication,\r\nhis main object is to wring a confession from\r\nthe culprit by a few skilful questions. In almost a similar\r\nposition the natural philosopher seems to be placed\r\nwith respect to nature. True, his functions here are\r\nmore those of the spy than the judge; but his object\r\nremains pretty much the same. Her hidden motives\r\nand laws of action is what nature must be made to\r\nconfess. Whether a confession will be extracted depends\r\nupon the shrewdness of the inquirer. Not without\r\nreason, therefore, did Lord Bacon call the experimental\r\nmethod a questioning of nature. The\r\nart consists in so putting our questions that they\r\nmay not remain unanswered without a breach of etiquette.\u003c/p\u003e\r\n\r\n\u003cp\u003eLook, too, at the countless tools, engines, and instruments\r\nof torture with which man conducts his\r\ninquisitions of nature, and which mock the poet\u0027s\r\nwords:\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_49\" id=\"Page_49\"\u003e[Pg 49]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"Mysterious even in open day,\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eNature retains her veil, despite our clamors;\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eThat which she doth not willingly display\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eCannot be wrenched from her with levers, screws, and hammers.\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003c/div\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eLook at these instruments and you will see that the\r\ncomparison with torture also is admissible.\u003ca name=\"FNanchor_11_11\" id=\"FNanchor_11_11\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_11_11\" class=\"fnanchor\"\u003e[11]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThis view of nature, as of something designedly\r\nconcealed from man, that can be unveiled only by\r\nforce or dishonesty, chimed in better with the conceptions\r\nof the ancients than with modern notions. A\r\nGrecian philosopher once said, in offering his opinion\r\nof the natural science of his time, that it could only be\r\ndispleasing to the gods to see men endeavoring to spy\r\nout what the gods were not minded to reveal to them.\u003ca name=\"FNanchor_12_12\" id=\"FNanchor_12_12\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_12_12\" class=\"fnanchor\"\u003e[12]\u003c/a\u003e\r\nOf course all the contemporaries of the speaker were\r\nnot of his opinion.\u003c/p\u003e\r\n\r\n\u003cp\u003eTraces of this view may still be found to-day, but\r\nupon the whole we are now not so narrow-minded.\r\nWe believe no longer that nature designedly hides\r\nherself. We know now from the history of science\r\nthat our questions are sometimes meaningless, and\r\nthat, therefore, no answer can be forthcoming. Soon\r\nwe shall see how man, with all his thoughts and quests,\r\nis only a fragment of nature\u0027s life.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_50\" id=\"Page_50\"\u003e[Pg 50]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003ePicture, then, as your fancy dictates, the tools of\r\nthe physicist as instruments of torture or as engines of\r\nendearment, at all events a chapter from the history of\r\nthose implements will be of interest to you, and it will\r\nnot be unpleasant to learn what were the peculiar difficulties\r\nthat led to the invention of such strange apparatus.\u003c/p\u003e\r\n\r\n\u003cp\u003eGalileo (born at Pisa in 1564, died at Arcetri in\r\n1642) was the first who asked what was the velocity\r\nof light, that is, what time it would take for a light\r\nstruck at one place to become visible at another, a\r\ncertain distance away.\u003ca name=\"FNanchor_13_13\" id=\"FNanchor_13_13\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_13_13\" class=\"fnanchor\"\u003e[13]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe method which Galileo devised was as simple\r\nas it was natural. Two practised observers, with\r\nmuffled lanterns, were to take up positions in a dark\r\nnight at a considerable distance\r\nfrom each other, one at\r\n\u003ci\u003eA\u003c/i\u003e and one at \u003ci\u003eB\u003c/i\u003e. At a moment\r\npreviously fixed upon, \u003ci\u003eA\u003c/i\u003e was\r\ninstructed to unmask his lantern; while as soon as \u003ci\u003eB\u003c/i\u003e\r\nsaw the light of \u003ci\u003eA\u003c/i\u003e\u0027s lantern he was to unmask his.\r\nNow it is clear that the time which \u003ci\u003eA\u003c/i\u003e counted from\r\nthe uncovering of his lantern until he caught sight of\r\nthe light of \u003ci\u003eB\u003c/i\u003e\u0027s would be the time which it would take\r\nlight to travel from \u003ci\u003eA\u003c/i\u003e to \u003ci\u003eB\u003c/i\u003e and from \u003ci\u003eB\u003c/i\u003e back to \u003ci\u003eA\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-060.jpg\" width=\"300\" height=\"93\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 13.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThe experiment was not executed, nor could it, in\r\nthe nature of the case, have been a success. As we\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_51\" id=\"Page_51\"\u003e[Pg 51]\u003c/a\u003e\u003c/span\u003e\r\nnow know, light travels too rapidly to be thus noted.\r\nThe time elapsing between the arrival of the light at\r\n\u003ci\u003eB\u003c/i\u003e and its perception by the observer, with that between\r\nthe decision to uncover and the uncovering of\r\nthe lantern, is, as we now know, incomparably greater\r\nthan the time which it takes light to travel the greatest\r\nearthly distances. The great velocity of light will be\r\nmade apparent, if we reflect that a flash of lightning\r\nin the night illuminates instantaneously a very extensive\r\nregion, whilst the single reflected claps of thunder\r\narrive at the observer\u0027s ear very gradually and in appreciable\r\nsuccession.\u003c/p\u003e\r\n\r\n\u003cp\u003eDuring his life, then, the efforts of Galileo to determine\r\nthe velocity of light remained uncrowned with\r\nsuccess. But the subsequent history of the measurement\r\nof the velocity of light is intimately associated\r\nwith his name, for with the telescope which he constructed\r\nhe discovered the four satellites of Jupiter,\r\nand these furnished the next occasion for the determination\r\nof the velocity of light.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe terrestrial spaces were too small for Galileo\u0027s\r\nexperiment. The measurement was first executed\r\nwhen the spaces of the planetary system were employed.\r\nOlaf Römer, (born at Aarhuus in 1644, died\r\nat Copenhagen in 1710) accomplished the feat (1675-1676),\r\nwhile watching with Cassini at the observatory\r\nof Paris the revolutions of Jupiter\u0027s moons.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 600px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-062.jpg\" width=\"600\" height=\"373\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 14.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eLet \u003ci\u003eAB\u003c/i\u003e (Fig. 14) be Jupiter\u0027s orbit. Let \u003ci\u003eS\u003c/i\u003e stand\r\nfor the sun, \u003ci\u003eE\u003c/i\u003e for the earth, \u003ci\u003eJ\u003c/i\u003e for Jupiter, and \u003ci\u003eT\u003c/i\u003e for\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_52\" id=\"Page_52\"\u003e[Pg 52]\u003c/a\u003e\u003c/span\u003e\r\nJupiter\u0027s first satellite. When the earth is at \u003ci\u003eE\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e we\r\nsee the satellite enter regularly into Jupiter\u0027s shadow,\r\nand by watching the time between two successive\r\neclipses, can calculate its time of revolution. The\r\ntime which Römer noted was forty-two hours, twenty-eight\r\nminutes, and thirty-five seconds. Now, as the\r\nearth passes along in its orbit towards E\u003csub\u003e2\u003c/sub\u003e, the revolutions\r\nof the satellite grow apparently longer and longer:\r\nthe eclipses take place later and later. The greatest\r\nretardation of the eclipse, which occurs when the earth\r\nis at \u003ci\u003eE\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, amounts to sixteen minutes and twenty-six\r\nseconds. As the earth passes back again to \u003ci\u003eE\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, the\r\nrevolutions grow apparently shorter, and they occur\r\nin exactly the time that they first did when the earth\r\narrives at \u003ci\u003eE\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e. It is to be remarked that Jupiter changes\r\nonly very slightly its position during one revolution of\r\nthe earth. Römer guessed at once that these periodical\r\nchanges of the time of revolution of Jupiter\u0027s satellite\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_53\" id=\"Page_53\"\u003e[Pg 53]\u003c/a\u003e\u003c/span\u003e\r\nwere not actual, but apparent changes, which were\r\nin some way connected with the velocity of light.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us make this matter clear to ourselves by a simile.\r\nWe receive regularly by the post, news of the\r\npolitical status at our capital. However far away we\r\nmay be from the capital, we hear the news of every\r\nevent, later it is true, but of all equally late. The\r\nevents reach us in the same succession of time as that\r\nin which they took place. But if we are travelling\r\naway from the capital, every successive post will have\r\na greater distance to pass over, and the events will\r\nreach us more slowly than they took place. The reverse\r\nwill be the case if we are approaching the capital.\u003c/p\u003e\r\n\r\n\u003cp\u003eAt rest, we hear a piece of music played in the\r\nsame \u003ci\u003etempo\u003c/i\u003e at all distances. But the \u003ci\u003etempo\u003c/i\u003e will be\r\nseemingly accelerated if we are carried\r\nrapidly towards the band, or retarded if\r\nwe are carried rapidly away from it.\u003ca name=\"FNanchor_14_14\" id=\"FNanchor_14_14\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_14_14\" class=\"fnanchor\"\u003e[14]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 150px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-063.jpg\" width=\"150\" height=\"143\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 15.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003ePicture to yourself a cross, say the\r\nsails of a wind-mill (Fig. 15), in uniform\r\nrotation about its centre. Clearly, the rotation of the\r\ncross will appear to you more slowly executed if you\r\nare carried very rapidly away from it. For the post\r\nwhich in this case conveys to you the light and brings\r\nto you the news of the successive positions of the cross\r\nwill have to travel in each successive instant over a\r\nlonger path.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_54\" id=\"Page_54\"\u003e[Pg 54]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eNow this must also be the case with the rotation\r\n(the revolution) of the satellite of Jupiter. The greatest\r\nretardation of the eclipse (16-1/2 minutes), due to\r\nthe passage of the earth from \u003ci\u003eE\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e to \u003ci\u003eE\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, or to its removal\r\nfrom Jupiter by a distance equal to the diameter\r\nof the orbit of the earth, plainly corresponds to the\r\ntime which it takes light to traverse a distance equal to\r\nthe diameter of the earth\u0027s orbit. The velocity of light,\r\nthat is, the distance described by light in a second, as\r\ndetermined by this calculation, is 311,000 kilometres,\u003ca name=\"FNanchor_15_15\" id=\"FNanchor_15_15\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_15_15\" class=\"fnanchor\"\u003e[15]\u003c/a\u003e\r\nor 193,000 miles. A subsequent correction of the diameter\r\nof the earth\u0027s orbit, gives, by the same method,\r\nthe velocity of light as approximately 186,000 miles a\r\nsecond.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe method is exactly that of Galileo; only better\r\nconditions are selected. Instead of a short terrestrial\r\ndistance we have the diameter of the earth\u0027s orbit,\r\nthree hundred and seven million kilometres; in place\r\nof the uncovered and covered lanterns we have the\r\nsatellite of Jupiter, which alternately appears and disappears.\r\nGalileo, therefore, although he could not\r\ncarry out himself the proposed measurement, found\r\nthe lantern by which it was ultimately executed.\u003c/p\u003e\r\n\r\n\u003cp\u003ePhysicists did not long remain satisfied with this\r\nbeautiful discovery. They sought after easier methods\r\nof measuring the velocity of light, such as might\r\nbe performed on the earth. This was possible after the\r\ndifficulties of the problem were clearly exposed. A\r\nmeasurement of the kind referred to was executed in\r\n1849 by Fizeau (born at Paris in 1819).\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_55\" id=\"Page_55\"\u003e[Pg 55]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eI shall endeavor to make the principle of Fizeau\u0027s\r\napparatus clear to you. Let \u003ci\u003es\u003c/i\u003e (Fig. 16) be a disk free\r\nto rotate about its centre, and perforated at its rim\r\nwith a series of holes. Let \u003ci\u003el\u003c/i\u003e be a luminous point\r\ncasting its light on an unsilvered glass, \u003ci\u003ea\u003c/i\u003e, inclined at\r\nan angle of forty-five degrees to the axis of the disk.\r\nThe ray of light, reflected at this point, passes through\r\none of the holes of the disk and falls at right angles\r\nupon a mirror \u003ci\u003eb\u003c/i\u003e, erected at a point about five miles\r\ndistant. From the mirror \u003ci\u003eb\u003c/i\u003e the light is again reflected,\r\npasses once more through the hole in \u003ci\u003es\u003c/i\u003e, and, penetrating\r\nthe glass plate, finally strikes the eye, \u003ci\u003eo\u003c/i\u003e, of the observer.\r\nThe eye, \u003ci\u003eo\u003c/i\u003e, thus, sees the image of the luminous\r\npoint \u003ci\u003el\u003c/i\u003e through the glass plate and the hole of\r\nthe disk in the mirror \u003ci\u003eb\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 600px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-065.jpg\" width=\"600\" height=\"226\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 16.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eIf, now, the disk be set in rotation, the unpierced\r\nspaces between the apertures will alternately take the\r\nplace of the apertures, and the eye o will now see the\r\nimage of the luminous point in \u003ci\u003eb\u003c/i\u003e only at interrupted\r\nintervals. On increasing the rapidity of the rotation,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_56\" id=\"Page_56\"\u003e[Pg 56]\u003c/a\u003e\u003c/span\u003e\r\nhowever, the interruptions for the eye become again\r\nunnoticeable, and the eye sees the mirror \u003ci\u003eb\u003c/i\u003e uniformly\r\nilluminated.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut all this holds true only for relatively small velocities\r\nof the disk, when the light sent through an\r\naperture in \u003ci\u003es\u003c/i\u003e to \u003ci\u003eb\u003c/i\u003e on its return strikes the aperture at\r\nalmost the same place and passes through it a second\r\ntime. Conceive, now, the speed of the disk to be so increased\r\nthat the light on its return finds before it an\r\nunpierced space instead of an aperture, it will then no\r\nlonger be able to reach the eye. We then see the\r\nmirror \u003ci\u003eb\u003c/i\u003e only when no light is emitted from it, but\r\nonly when light is sent to it; it is covered when light\r\ncomes from it. In this case, accordingly, the mirror\r\nwill always appear dark.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf the velocity of rotation at this point were still\r\nfurther increased, the light sent through one aperture\r\ncould not, of course, on its return pass through the\r\nsame aperture but might strike the next and reach\r\nthe eye by that. Hence, by constantly increasing the\r\nvelocity of the rotation, the mirror \u003ci\u003eb\u003c/i\u003e may be made to\r\nappear alternately bright and dark. Plainly, now, if\r\nwe know the number of apertures of the disk, the number\r\nof rotations per second, and the distance \u003ci\u003esb\u003c/i\u003e, we\r\ncan calculate the velocity of light. The result agrees\r\nwith that obtained by Römer.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe experiment is not quite as simple as my exposition\r\nmight lead you to believe. Care must be\r\ntaken that the light shall travel back and forth over\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_57\" id=\"Page_57\"\u003e[Pg 57]\u003c/a\u003e\u003c/span\u003e\r\nthe miles of distance \u003ci\u003esb\u003c/i\u003e and \u003ci\u003ebs\u003c/i\u003e undispersed. This\r\ndifficulty is obviated by means of telescopes.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we examine Fizeau\u0027s apparatus closely, we shall\r\nrecognise in it an old acquaintance: the arrangement\r\nof Galileo\u0027s experiment. The luminous point \u003ci\u003el\u003c/i\u003e is the\r\nlantern \u003ci\u003eA\u003c/i\u003e, while the rotation of the perforated disk performs\r\nmechanically the uncovering and covering of the\r\nlantern. Instead of the unskilful observer \u003ci\u003eB\u003c/i\u003e we have\r\nthe mirror \u003ci\u003eb\u003c/i\u003e, which is unfailingly illuminated the instant\r\nthe light arrives from \u003ci\u003es\u003c/i\u003e. The disk \u003ci\u003es\u003c/i\u003e, by alternately\r\ntransmitting and intercepting the reflected light, assists\r\nthe observer \u003ci\u003eo\u003c/i\u003e. Galileo\u0027s experiment is here executed,\r\nso to speak, countless times in a second, yet the total\r\nresult admits of actual observation. If I might be\r\npardoned the use of a phrase of Darwin\u0027s in this field,\r\nI should say that Fizeau\u0027s apparatus was the descendant\r\nof Galileo\u0027s lantern.\u003c/p\u003e\r\n\r\n\u003cp\u003eA still more refined and delicate method for the\r\nmeasurement of the velocity of light was employed by\r\nFoucault, but a description of it here would lead us\r\ntoo far from our subject.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe measurement of the velocity of sound is easily\r\nexecuted by the method of Galileo. It was unnecessary,\r\ntherefore, for physicists to rack their brains further\r\nabout the matter; but the idea which with light\r\ngrew out of necessity was applied also in this field.\r\nKoenig of Paris constructs an apparatus for the measurement\r\nof the velocity of sound which is closely allied\r\nto the method of Fizeau.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_58\" id=\"Page_58\"\u003e[Pg 58]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe apparatus is very simple. It consists of two\r\nelectrical clock-works which strike simultaneously,\r\nwith perfect precision, tenths of seconds. If we place\r\nthe two clock-works directly side by side, we hear\r\ntheir strokes simultaneously, wherever we stand. But\r\nif we take our stand by the side of one of the works\r\nand place the other at some distance from us, in general\r\na coincidence of the strokes will now not be heard.\r\nThe companion strokes of the remote clock-work arrive,\r\nas sound, later. The first stroke of the remote\r\nwork is heard, for example, immediately after the first\r\nof the adjacent work, and so on. But by increasing\r\nthe distance we may produce again a coincidence of the\r\nstrokes. For example, the first stroke of the remote\r\nwork coincides with the second of the near work, the\r\nsecond of the remote work with the third of the near\r\nwork, and so on. If, now, the works strike tenths of\r\nseconds and the distance between them is increased\r\nuntil the first coincidence is noted, plainly that distance\r\nis travelled over by the sound in a tenth of a\r\nsecond.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe meet frequently the phenomenon here presented,\r\nthat a thought which centuries of slow and\r\npainful endeavor are necessary to produce, when once\r\ndeveloped, fairly thrives. It spreads and runs everywhere,\r\neven entering minds in which it could never\r\nhave arisen. It simply cannot be eradicated.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe determination of the velocity of light is not the\r\nonly case in which the direct perception of the senses\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_59\" id=\"Page_59\"\u003e[Pg 59]\u003c/a\u003e\u003c/span\u003e\r\nis too slow and clumsy for use. The usual method\r\nof studying events too fleet for direct observation consists\r\nin putting into reciprocal action with them other\r\nevents already known, the velocities of all of which\r\nare capable of comparison. The result is\r\nusually unmistakable, and susceptible of\r\ndirect inference respecting the character of\r\nthe event which is unknown. The velocity\r\nof electricity cannot be determined by direct\r\nobservation. But it was ascertained\r\nby Wheatstone, simply by the expedient of\r\nwatching an electric spark in a mirror rotating with\r\ntremendous known velocity.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 150px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-069.jpg\" width=\"150\" height=\"238\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 17.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 200px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-069-1.jpg\" width=\"200\" height=\"189\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 18.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eIf we wave a staff irregularly hither and thither,\r\nsimple observation cannot determine how quickly it\r\nmoves at each point of its course. But let us look at\r\nthe staff through holes in the rim of a\r\nrapidly rotating disk (Fig. 17). We\r\nshall then see the moving staff only\r\nin certain positions, namely, when a\r\nhole passes in front of the eye. The\r\nsingle pictures of the staff remain for a\r\ntime impressed upon the eye; we think we see several\r\nstaffs, having some such disposition as that represented\r\nin Fig. 18. If, now, the holes of the disk are equally\r\nfar apart, and the disk is rotated with uniform velocity,\r\nwe see clearly that the staff has moved slowly\r\nfrom \u003ci\u003ea\u003c/i\u003e to \u003ci\u003eb\u003c/i\u003e, more quickly from \u003ci\u003eb\u003c/i\u003e to \u003ci\u003ec\u003c/i\u003e, still more quickly\r\nfrom \u003ci\u003ec\u003c/i\u003e to \u003ci\u003ed\u003c/i\u003e, and with its greatest velocity from \u003ci\u003ed\u003c/i\u003e to \u003ci\u003ee\u003c/i\u003e.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_60\" id=\"Page_60\"\u003e[Pg 60]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eA jet of water flowing from an orifice in the bottom\r\nof a vessel has the appearance of perfect quiet and\r\nuniformity, but if we illuminate it for a second, in a\r\ndark room, by means of an electric flash we shall see\r\nthat the jet is composed of separate drops. By their\r\nquick descent the images of the drops are\r\nobliterated and the jet appears uniform.\r\nLet us look at the jet through the rotating\r\ndisk. The disk is supposed to be rotated so\r\nrapidly that while the second aperture\r\npasses into the place of the first, drop 1\r\nfalls into the place of 2, 2 into the place of 3, and so on.\r\nWe see drops then always in the same places. The\r\njet appears to be at rest. If we turn the disk a trifle\r\nmore slowly, then while the second aperture passes\r\ninto the place of the first, drop 1 will have fallen somewhat\r\nlower than 2, 2 somewhat lower than 3, etc.\r\nThrough every successive aperture we shall see drops\r\nin successively lower positions. The jet will appear to\r\nbe flowing slowly downwards.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 150px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-070.jpg\" width=\"150\" height=\"184\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 19.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eNow let us turn the disk more rapidly. Then while\r\nthe second aperture is passing into the place of the\r\nfirst, drop 1 will not quite have reached the place of 2,\r\nbut will be found slightly above 2, 2 slightly above 3,\r\netc. Through the successive apertures we shall see\r\nthe drops at successively higher places. It will now\r\nlook as if the jet were flowing upwards, as if the drops\r\nwere rising from the lower vessel into the higher.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou see, physics grows gradually more and more\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_61\" id=\"Page_61\"\u003e[Pg 61]\u003c/a\u003e\u003c/span\u003e\r\nterrible. The physicist will soon have it in his power\r\nto play the part of the famous lobster chained to the\r\nbottom of the Lake of Mohrin, whose direful mission,\r\nif ever liberated, the poet Kopisch humorously describes\r\nas that of a reversal of all the events of the\r\nworld; the rafters of houses become trees again, cows\r\ncalves, honey flowers, chickens eggs, and the poet\u0027s\r\nown poem flows back into his inkstand.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_62\" id=\"Page_62\"\u003e[Pg 62]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_63\" id=\"Page_63\"\u003e[Pg 63]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_64\" id=\"Page_64\"\u003e[Pg 64]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eYou will now allow me the privilege of a few general\r\nremarks. You have seen that the same principle\r\noften lies at the basis of large classes of apparatus\r\ndesigned for different purposes. Frequently it is some\r\nvery unobtrusive idea which is productive of so much\r\nfruit and of such extensive transformations in physical\r\ntechnics. It is not otherwise here than in practical\r\nlife.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe wheel of a waggon appears to us a very simple\r\nand insignificant creation. But its inventor was certainly\r\na man of genius. The round trunk of a tree\r\nperhaps first accidentally led to the observation of the\r\nease with which a load can be moved on a roller.\r\nNow, the step from a simple supporting roller to a\r\nfixed roller, or wheel, appears a very easy one. At\r\nleast it appears very easy to us who are accustomed\r\nfrom childhood up to the action of the wheel. But if\r\nwe put ourselves vividly into the position of a man\r\nwho never saw a wheel, but had to invent one, we shall\r\nbegin to have some idea of its difficulties. Indeed, it\r\nis even doubtful whether a single man could have accomplished\r\nthis feat, whether perhaps centuries were\r\nnot necessary to form the first wheel from the primitive\r\nroller.\u003ca name=\"FNanchor_16_16\" id=\"FNanchor_16_16\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_16_16\" class=\"fnanchor\"\u003e[16]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eHistory does not name the progressive minds who\r\nconstructed the first wheel; their time lies far back of\r\nthe historic period. No scientific academy crowned\r\ntheir efforts, no society of engineers elected them\r\nhonorary members. They still live only in the stupendous\r\nresults which they called forth. Take from\r\nus the wheel, and little will remain of the arts and industries\r\nof modern life. All disappears. From the\r\nspinning-wheel to the spinning-mill, from the turning-lathe\r\nto the rolling-mill, from the wheelbarrow to the\r\nrailway train, all vanishes.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn science the wheel is equally important. Whirling\r\nmachines, as the simplest means of obtaining quick\r\nmotions with inconsiderable changes of place, play a\r\npart in all branches of physics. You know Wheatstone\u0027s\r\nrotating mirror, Fizeau\u0027s wheel, Plateau\u0027s perforated\r\nrotating disks, etc. Almost the same principle\r\nlies at the basis of all these apparatus. They differ\r\nfrom one another no more than the pen-knife differs,\r\nin the purposes it serves, from the knife of the anatomist\r\nor the knife of the vine-dresser. Almost the same\r\nmight be said of the screw.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will now perhaps be clear to you that new\r\nthoughts do not spring up suddenly. Thoughts need\r\ntheir time to ripen, grow, and develop in, like every\r\nnatural product; for man, with his thoughts, is also a\r\npart of nature.\u003c/p\u003e\r\n\r\n\u003cp\u003eSlowly, gradually, and laboriously one thought is\r\ntransformed into a different thought, as in all likelihood\r\none animal species is gradually transformed into new\r\nspecies. Many ideas arise simultaneously. They fight\r\nthe battle for existence not otherwise than do the\r\nIchthyosaurus, the Brahman, and the horse.\u003c/p\u003e\r\n\r\n\u003cp\u003eA few remain to spread rapidly over all fields of\r\nknowledge, to be redeveloped, to be again split up, to\r\nbegin again the struggle from the start. As many\r\nanimal species long since conquered, the relicts of\r\nages past, still live in remote regions where their enemies\r\ncannot reach them, so also we find conquered\r\nideas still living on in the minds of many men. Whoever\r\nwill look carefully into his own soul will acknowledge\r\nthat thoughts battle as obstinately for existence\r\nas animals. Who will gainsay that many vanquished\r\nmodes of thought still haunt obscure crannies of his\r\nbrain, too faint-hearted to step out into the clear light\r\nof reason? What inquirer does not know that the\r\nhardest battle, in the transformation of his ideas, is\r\nfought with himself.\u003c/p\u003e\r\n\r\n\u003cp\u003eSimilar phenomena meet the natural inquirer in all\r\npaths and in the most trifling matters. The true inquirer\r\nseeks the truth everywhere, in his country-walks\r\nand on the streets of the great city. If he is\r\nnot too learned, he will observe that certain things,\r\nlike ladies\u0027 hats, are constantly subject to change. I\r\nhave not pursued special studies on this subject, but\r\nas long as I can remember, one form has always\r\ngradually changed into another. First, they wore hats\r\nwith long projecting rims, within which, scarcely accessible\r\nwith a telescope, lay concealed the face of the\r\nbeautiful wearer. The rim grew smaller and smaller;\r\nthe bonnet shrank to the irony of a hat. Now a tremendous\r\nsuperstructure is beginning to grow up in its\r\nplace, and the gods only know what its limits will be.\r\nIt is not otherwise with ladies\u0027 hats than with butterflies,\r\nwhose multiplicity of form often simply comes\r\nfrom a slight excrescence on the wing of one species\r\ndeveloping in a cognate species to a tremendous fold.\r\nNature, too, has its fashions, but they last thousands\r\nof years. I could elucidate this idea by many additional\r\nexamples; for instance, by the history of the\r\nevolution of the coat, if I were not fearful that my\r\ngossip might prove irksome to you.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_65\" id=\"Page_65\"\u003e[Pg 65]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_66\" id=\"Page_66\"\u003e[Pg 66]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eWe have now wandered through an odd corner of\r\nthe history of science. What have we learned? The\r\nsolution of a small, I might almost say insignificant,\r\nproblem\u0026mdash;the measurement of the velocity of light.\r\nAnd more than two centuries have worked at its solution!\r\nThree of the most eminent natural philosophers,\r\nGalileo, an Italian, Römer, a Dane, and Fizeau, a\r\nFrenchman, have fairly shared its labors. And so it\r\nis with countless other questions. When we contemplate\r\nthus the many blossoms of thought that must\r\nwither and fall before one shall bloom, then shall we\r\nfirst truly appreciate Christ\u0027s weighty but little consolatory\r\nwords: \"Many be called but few are chosen.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eSuch is the testimony of every page of history.\r\nBut is history right? Are really only those chosen\r\nwhom she names? Have those lived and battled in\r\nvain, who have won no prize?\u003c/p\u003e\r\n\r\n\u003cp\u003eI doubt it. And so will every one who has felt the\r\npangs of sleepless nights spent in thought, at first fruitless,\r\nbut in the end successful. No thought in such\r\nstruggles was thought in vain; each one, even the most\r\ninsignificant, nay, even the erroneous thought, that\r\nwhich apparently was the least productive, served to\r\nprepare the way for those that afterwards bore fruit.\r\nAnd as in the thought of the individual naught is in\r\nvain, so, also, it is in that of humanity.\u003c/p\u003e\r\n\r\n\u003cp\u003eGalileo wished to measure the velocity of light.\r\nHe had to close his eyes before his wish was realised.\r\nBut he at least found the lantern by which his successor\r\ncould accomplish the task.\u003c/p\u003e\r\n\r\n\u003cp\u003eAnd so I may maintain that we all, so far as inclination\r\ngoes, are working at the civilisation of the future.\r\nIf only we all strive for the right, then are we \u003ci\u003eall\u003c/i\u003e\r\ncalled and \u003ci\u003eall\u003c/i\u003e chosen!\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"WHY_HAS_MAN_TWO_EYES\" id=\"WHY_HAS_MAN_TWO_EYES\"\u003eWHY HAS MAN TWO EYES?\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eWhy has man two eyes? That the pretty symmetry\r\nof his face may not be disturbed, the\r\nartist answers. That his second eye may furnish a\r\nsubstitute for his first if that be lost, says the far-sighted\r\neconomist. That we may weep with two eyes\r\nat the sins of the world, replies the religious enthusiast.\u003c/p\u003e\r\n\r\n\u003cp\u003eOdd opinions! Yet if you should approach a modern\r\nscientist with this question you might consider\r\nyourself fortunate if you escaped with less than a rebuff.\r\n\"Pardon me, madam, or my dear sir,\" he would\r\nsay, with stern expression, \"man fulfils no purpose in\r\nthe possession of his eyes; nature is not a person, and\r\nconsequently not so vulgar as to pursue purposes of\r\nany kind.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eStill an unsatisfactory answer! I once knew a professor\r\nwho would shut with horror the mouths of his\r\npupils if they put to him such an unscientific question.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut ask a more tolerant person, ask me. I, I candidly\r\nconfess, do not know exactly why man has two\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_67\" id=\"Page_67\"\u003e[Pg 67]\u003c/a\u003e\u003c/span\u003e\r\neyes, but the reason partly is, I think, that I may see\r\nyou here before me to-night and talk with you upon\r\nthis delightful subject.\u003c/p\u003e\r\n\r\n\u003cp\u003eAgain you smile incredulously. Now this is one of\r\nthose questions that a hundred wise men together\r\ncould not answer. You have heard, so far, only five of\r\nthese wise men. You will certainly want to be spared\r\nthe opinions of the other ninety-five. To the first you\r\nwill reply that we should look just as pretty if we were\r\nborn with only one eye, like the Cyclops; to the second\r\nwe should be much better off, according to his\r\nprinciple, if we had four or eight eyes, and that in this\r\nrespect we are vastly inferior to spiders; to the third,\r\nthat you are not just in the mood to weep; to the\r\nfourth, that the unqualified interdiction of the question\r\nexcites rather than satisfies your curiosity; while of\r\nme you will dispose by saying that my pleasure is not\r\nas intense as I think, and certainly not great enough\r\nto justify the existence of a double eye in man since\r\nthe fall of Adam.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut since you are not satisfied with my brief and\r\nobvious answer, you have only yourselves to blame\r\nfor the consequences. You must now listen to a longer\r\nand more learned explanation, such as it is in my\r\npower to give.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs the church of science, however, debars the question\r\n\"Why?\" let us put the matter in a purely orthodox\r\nway: Man has two eyes, what \u003ci\u003emore\u003c/i\u003e can he see with\r\ntwo than with one?\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_68\" id=\"Page_68\"\u003e[Pg 68]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eI will invite you to take a walk with me? We see\r\nbefore us a wood. What is it that makes this real\r\nwood contrast so favorably with a painted wood, no\r\nmatter how perfect the painting may be? What makes\r\nthe one so much more lovely than the other? Is it the\r\nvividness of the coloring, the distribution of the lights\r\nand the shadows? I think\r\nnot. On the contrary, it\r\nseems to me that in this\r\nrespect painting can accomplish\r\nvery much.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe cunning hand of\r\nthe painter can conjure up\r\nwith a few strokes of his\r\nbrush forms of wonderful\r\nplasticity. By the help of\r\nother means even more\r\ncan be attained. Photographs\r\nof reliefs are so\r\nplastic that we often imagine\r\nwe can actually lay\r\nhold of the elevations and\r\ndepressions.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-078.jpg\" width=\"300\" height=\"496\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 20.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eBut one thing the painter never can give with the\r\nvividness that nature does\u0026mdash;the difference of near and\r\nfar. In the real woods you see plainly that you can\r\nlay hold of some trees, but that others are inaccessibly\r\nfar. The picture of the painter is rigid. The picture\r\nof the real woods changes on the slightest movement.\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_69\" id=\"Page_69\"\u003e[Pg 69]\u003c/a\u003e\u003c/span\u003e\r\nNow this branch is hidden behind that; now that behind\r\nthis. The trees are alternately visible and invisible.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us look at this matter a little more closely.\r\nFor convenience sake we shall remain upon the highway,\r\nI, II. (Fig. 20.) To the right and the left lies the\r\nforest. Standing at I, we see, let us say, three trees\r\n(1, 2, 3) in a line, so that the two remote ones are\r\ncovered by the nearest. Moving further along, this\r\nchanges. At II we shall not have to look round so far\r\nto see the remotest tree 3 as to see the nearer tree 2,\r\nnor so far to see this as to see 1. \u003ci\u003eHence, as we move\r\nonward, objects that are near to us seem to lag behind as\r\ncompared with objects that are remote from us, the lagging\r\nincreasing with the proximity of the objects.\u003c/i\u003e Very remote\r\nobjects, towards which we must always look in the\r\nsame direction as we proceed, appear to travel along\r\nwith us.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we should see, therefore, jutting above the brow\r\nof yonder hill the tops of two trees whose distance\r\nfrom us we were in doubt about, we should have in\r\nour hands a very easy means of deciding the question.\r\nWe should take a few steps forward, say to the right,\r\nand the tree-top which receded most to the left would\r\nbe the one nearer to us. In truth, from the amount\r\nof the recession a geometer could actually determine\r\nthe distance of the trees from us without ever going\r\nnear them. It is simply the scientific development of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_70\" id=\"Page_70\"\u003e[Pg 70]\u003c/a\u003e\u003c/span\u003e\r\nthis perception that enables us to measure the distances\r\nof the stars.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003ci\u003eHence, from change of view in forward motion the\r\ndistances of objects in our field of vision can be measured.\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eRigorously, however, even forward motion is not\r\nnecessary. For every observer is composed really of\r\n\u003ci\u003etwo\u003c/i\u003e observers. Man has \u003ci\u003etwo\u003c/i\u003e eyes. The right eye is\r\na short step ahead of the left eye in the right-hand direction.\r\nHence, the two eyes receive \u003ci\u003edifferent\u003c/i\u003e pictures\r\nof the same woods. The right eye will see the\r\nnear trees displaced to the left, and the left eye will\r\nsee them displaced to the right, the displacement being\r\ngreater, the greater the proximity. This difference is\r\nsufficient for forming ideas of distance.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may now readily convince ourselves of the following\r\nfacts:\u003c/p\u003e\r\n\r\n\u003cp\u003e1. With one eye, the other being shut, you have a\r\nvery uncertain judgment of distances. You will find\r\nit, for example, no easy task, with one eye shut, to\r\nthrust a stick through a ring hung up before you; you\r\nwill miss the ring in almost every instance.\u003c/p\u003e\r\n\r\n\u003cp\u003e2. You see the same object differently with the\r\nright eye from what you do with the left.\u003c/p\u003e\r\n\r\n\u003cp\u003ePlace a lamp-shade on the table in front of you\r\nwith its broad opening turned downwards, and look\r\nat it from above. (Fig. 21.) You will see with your\r\nright eye the image 2, with your left eye the image 1.\r\nAgain, place the shade with its wide opening turned\r\nupwards; you will receive with your right eye the image\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_71\" id=\"Page_71\"\u003e[Pg 71]\u003c/a\u003e\u003c/span\u003e\r\n4, with your left eye the image 3. Euclid mentions\r\nphenomena of this character.\u003c/p\u003e\r\n\r\n\u003cp\u003e3. Finally, you know that it is easy to judge of\r\ndistances with both eyes. Accordingly your judgment\r\nmust spring in some way from a co-operation of the\r\ntwo eyes. In the preceding example the openings in\r\nthe different images received by the two eyes seem\r\ndisplaced with respect to one another, and this displacement\r\nis sufficient for the inference that the one\r\nopening is nearer than the other.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 450px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-081.jpg\" width=\"450\" height=\"446\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 21.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eI have no doubt that you, ladies, have frequently\r\nreceived delicate compliments upon your eyes, but I\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_72\" id=\"Page_72\"\u003e[Pg 72]\u003c/a\u003e\u003c/span\u003e\r\nfeel sure that no one has ever told you, and I know not\r\nwhether it will flatter you, that you have in your eyes,\r\nbe they blue or black, little geometricians. You say\r\nyou know nothing of them? Well, for that matter,\r\nneither do I. But the facts are as I tell you.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou understand little of geometry? I shall accept\r\nthat confession. Yet with the help of your two eyes\r\nyou judge of distances? Surely that is a geometrical\r\nproblem. And what is more, you know the solution\r\nof this problem: for you estimate distances correctly.\r\nIf, then, \u003ci\u003eyou\u003c/i\u003e do not solve the problem, the little geometricians\r\nin your eyes must do it clandestinely and whisper\r\nthe solution to you. I doubt not they are fleet little\r\nfellows.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat amazes me most here is, that you know nothing\r\nabout these little geometricians. But perhaps they\r\nalso know nothing about you. Perhaps they are models\r\nof punctuality, routine clerks who bother about\r\nnothing but their fixed work. In that case we may\r\nbe able to deceive the gentlemen.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we present to our right eye an image which looks\r\nexactly like the lamp-shade for the right eye, and to\r\nour left eye an image which looks exactly like a lamp-shade\r\nfor the left eye, we shall imagine that we see\r\nthe whole lamp-shade bodily before us.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou know the experiment. If you are practised in\r\nsquinting, you can perform it directly with the figure,\r\nlooking with your right eye at the right image, and\r\nwith your left eye at the left image. In this way the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_73\" id=\"Page_73\"\u003e[Pg 73]\u003c/a\u003e\u003c/span\u003e\r\nexperiment was first performed by Elliott. Improved\r\nand perfected, its form is Wheatstone\u0027s stereoscope,\r\nmade so popular and useful by Brewster.\u003c/p\u003e\r\n\r\n\u003cp\u003eBy taking two photographs of the same object from\r\ntwo different points, corresponding to the two eyes, a\r\nvery clear three-dimensional picture of distant places\r\nor buildings can be produced by the stereoscope.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut the stereoscope accomplishes still more than\r\nthis. It can visualise things for us which we never see\r\nwith equal clearness in real objects. You know that\r\nif you move much while your photograph is being\r\ntaken, your picture will come out like that of a Hindu\r\ndeity, with several heads or several arms, which, at\r\nthe spaces where they overlap, show forth with equal\r\ndistinctness, so that we seem to see the one picture\r\n\u003ci\u003ethrough\u003c/i\u003e the other. If a person moves quickly away\r\nfrom the camera before the impression is completed,\r\nthe objects behind him will also be imprinted upon\r\nthe photograph; the person will look transparent.\r\nPhotographic ghosts are made in this way.\u003c/p\u003e\r\n\r\n\u003cp\u003eSome very useful applications may be made of this\r\ndiscovery. For example, if we photograph a machine\r\nstereoscopically, successively removing during the\r\noperation the single parts (where of course the impression\r\nsuffers interruptions), we obtain a transparent\r\nview, endowed with all the marks of spatial solidity,\r\nin which is distinctly visualised the interaction of parts\r\nnormally concealed. I have employed this method for\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_74\" id=\"Page_74\"\u003e[Pg 74]\u003c/a\u003e\u003c/span\u003e\r\nobtaining transparent stereoscopic views of anatomical\r\nstructures.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou see, photography is making stupendous advances,\r\nand there is great danger that in time some\r\nmalicious artist will photograph his innocent patrons\r\nwith solid views of their most secret thoughts and\r\nemotions. How tranquil politics will then be! What\r\nrich harvests our detective force will reap!\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_75\" id=\"Page_75\"\u003e[Pg 75]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_76\" id=\"Page_76\"\u003e[Pg 76]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_77\" id=\"Page_77\"\u003e[Pg 77]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_78\" id=\"Page_78\"\u003e[Pg 78]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_79\" id=\"Page_79\"\u003e[Pg 79]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_80\" id=\"Page_80\"\u003e[Pg 80]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_81\" id=\"Page_81\"\u003e[Pg 81]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_82\" id=\"Page_82\"\u003e[Pg 82]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_83\" id=\"Page_83\"\u003e[Pg 83]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_84\" id=\"Page_84\"\u003e[Pg 84]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_85\" id=\"Page_85\"\u003e[Pg 85]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_86\" id=\"Page_86\"\u003e[Pg 86]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eBy the joint action of the two eyes, therefore, we\r\narrive at our judgments of distances, as also of the\r\nforms of bodies.\u003c/p\u003e\r\n\r\n\u003cp\u003ePermit me to mention here a few additional facts\r\nconnected with this subject, which will assist us in the\r\ncomprehension of certain phenomena in the history of\r\ncivilisation.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou have often heard, and know from personal experience,\r\nthat remote objects appear perspectively\r\ndwarfed. In fact, it is easy to satisfy yourself that\r\nyou can cover the image of a man a few feet away\r\nfrom you simply by holding up your finger a short distance\r\nin front of your eye. Still, as a general rule,\r\nyou do not notice this shrinkage of objects. On the\r\ncontrary, you imagine you see a man at the end of a\r\nlarge hall, as large as you see him near by you. For\r\nyour eye, in its measurement of the distances, makes\r\nremote objects correspondingly larger. The eye, so to\r\nspeak, is aware of this perspective contraction and is\r\nnot deceived by it, although its possessor is unconscious\r\nof the fact. All persons who have attempted to draw\r\nfrom nature have vividly felt the difficulty which this\r\nsuperior dexterity of the eye causes the perspective\r\nconception. Not until one\u0027s judgment of distances is\r\nmade uncertain, by their size, or from lack of points\r\nof reference, or from being too quickly changed, is the\r\nperspective rendered very prominent.\u003c/p\u003e\r\n\r\n\u003cp\u003eOn sweeping round a curve on a rapidly moving\r\nrailway train, where a wide prospect is suddenly\r\nopened up, the men upon distant hills appear like\r\ndolls.\u003ca name=\"FNanchor_17_17\" id=\"FNanchor_17_17\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_17_17\" class=\"fnanchor\"\u003e[17]\u003c/a\u003e You have at the moment, here, no known\r\nreferences for the measurement of distances. The\r\nstones at the entrance of a tunnel grow visibly larger\r\nas we ride towards it; they shrink visibly in size as we\r\nride from it.\u003c/p\u003e\r\n\r\n\u003cp\u003eUsually both eyes work together. As certain views\r\nare frequently repeated, and lead always to substantially\r\nthe same judgments of distances, the eyes in\r\ntime must acquire a special skill in geometrical constructions.\r\nIn the end, undoubtedly, this skill is so\r\nincreased that a single eye alone is often tempted to\r\nexercise that office.\u003c/p\u003e\r\n\r\n\u003cp\u003ePermit me to elucidate this point by an example.\r\nIs any sight more familiar to you than that of a vista\r\ndown a long street? Who has not looked with hopeful\r\neyes time and again into a street and measured its\r\ndepth. I will take you now into an art-gallery where\r\nI will suppose you to see a picture representing a vista\r\ninto a street. The artist has not spared his rulers to\r\nget his perspective perfect. The geometrician in your\r\nleft eye thinks, \"Ah ha! I have computed that case a\r\nhundred times or more. I know it by heart. It is a\r\nvista into a street,\" he continues; \"where the houses\r\nare lower is the remote end.\" The geometrician in\r\nthe right eye, too much at his ease to question his\r\npossibly peevish comrade in the matter, answers the\r\nsame. But the sense of duty of these punctual little\r\nfellows is at once rearoused. They set to work at their\r\ncalculations and immediately find that all the points\r\nof the picture are equally distant from them, that is,\r\nlie all upon a plane surface.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat opinion will you now accept, the first or the\r\nsecond? If you accept the first you will see distinctly\r\nthe vista. If you accept the second you will see nothing\r\nbut a painted sheet of distorted images.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt seems to you a trifling matter to look at a picture\r\nand understand its perspective. Yet centuries\r\nelapsed before humanity came fully to appreciate this\r\ntrifle, and even the majority of you first learned it from\r\neducation.\u003c/p\u003e\r\n\r\n\u003cp\u003eI can remember very distinctly that at three years\r\nof age all perspective drawings appeared to me as\r\ngross caricatures of objects. I could not understand\r\nwhy artists made tables so broad at one end and so\r\nnarrow at the other. Real tables seemed to me just\r\nas broad at one end as at the other, because my eye\r\nmade and interpreted its calculations without my intervention.\r\nBut that the picture of the table on the\r\nplane surface was not to be conceived as a plane painted\r\nsurface but stood for a table and so was to be imaged\r\nwith all the attributes of extension was a joke that I\r\ndid not understand. But I have the consolation that\r\nwhole nations have not understood it.\u003c/p\u003e\r\n\r\n\u003cp\u003eIngenuous people there are who take the mock\r\nmurders of the stage for real murders, the dissembled\r\nactions of the players for real actions, and who can\r\nscarcely restrain themselves, when the characters of the\r\nplay are sorely pressed, from running in deep indignation\r\nto their assistance. Others, again, can never forget\r\nthat the beautiful landscapes of the stage are\r\npainted, that Richard III. is only the actor, Mr. Booth,\r\nwhom they have met time and again at the clubs.\u003c/p\u003e\r\n\r\n\u003cp\u003eBoth points of view are equally mistaken. To look\r\nat a drama or a picture properly one must understand\r\nthat both are \u003ci\u003eshows\u003c/i\u003e, simply \u003ci\u003edenoting\u003c/i\u003e something real.\r\nA certain preponderance of the intellectual life over\r\nthe sensuous life is requisite for such an achievement,\r\nwhere the intellectual elements are safe from destruction\r\nby the direct sensuous impressions. A certain\r\nliberty in choosing one\u0027s point of view is necessary, a\r\nsort of humor, I might say, which is strongly wanting\r\nin children and in childlike peoples.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us look at a few historical facts. I shall not\r\ntake you as far back as the stone age, although we\r\npossess sketches from this epoch which show very original\r\nideas of perspective. But let us begin our sight-seeing\r\nin the tombs and ruined temples of ancient\r\nEgypt, where the numberless reliefs and gorgeous colorings\r\nhave defied the ravages of thousands of years.\u003c/p\u003e\r\n\r\n\u003cp\u003eA rich and motley life is here opened to us. We\r\nfind the Egyptians represented in all conditions of life.\r\nWhat at once strikes our attention in these pictures\r\nis the delicacy of their technical execution. The contours\r\nare extremely exact and distinct. But on the\r\nother hand only a few bright colors are found, unblended\r\nand without trace of transition. Shadows are\r\ntotally wanting. The paint is laid on the surfaces in\r\nequal thicknesses.\u003c/p\u003e\r\n\r\n\u003cp\u003eShocking for the modern eye is the perspective.\r\nAll the figures are equally large, with the exception of\r\nthe king, whose form is unduly exaggerated. Near and\r\nfar appear equally large. Perspective contraction is\r\nnowhere employed. A pond with water-fowl is represented\r\nflat, as if its surface were vertical.\u003c/p\u003e\r\n\r\n\u003cp\u003eHuman figures are portrayed as they are never\r\nseen, the legs from the side, the face in profile. The\r\nbreast lies in its full breadth across the plane of representation.\r\nThe heads of cattle appear in profile,\r\nwhile the horns lie in the plane of the drawing. The\r\nprinciple which the Egyptians followed might be best\r\nexpressed by saying that their figures are pressed in\r\nthe plane of the drawing as plants are pressed in a\r\nherbarium.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe matter is simply explained. If the Egyptians\r\nwere accustomed to looking at things ingenuously\r\nwith both eyes at once, the construction of perspective\r\npictures in space could not be familiar to them.\r\nThey saw all arms, all legs on real men in their natural\r\nlengths. The figures pressed into the planes resembled\r\nmore closely, of course, in their eyes the\r\noriginals than perspective pictures could.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis will be better understood if we reflect that\r\npainting was developed from relief. The minor dissimilarities\r\nbetween the pressed figures and the originals\r\nmust gradually have compelled men to the adoption\r\nof perspective drawing. But physiologically the\r\npainting of the Egyptians is just as much justified as\r\nthe drawings of our children are.\u003c/p\u003e\r\n\r\n\u003cp\u003eA slight advance beyond the Egyptians is shown\r\nby the Assyrians. The reliefs rescued from the ruined\r\nmounds of Nimrod at Mossul are, upon the whole,\r\nsimilar to the Egyptian reliefs. They were made known\r\nto us principally by Layard.\u003c/p\u003e\r\n\r\n\u003cp\u003ePainting enters on a new phase among the Chinese.\r\nThis people have a marked feeling for perspective\r\nand correct shading, yet without being very logical\r\nin the application of their principles. Here, too,\r\nit seems, they took the first step but did not go far.\r\nIn harmony with this immobility is their constitution,\r\nin which the muzzle and the bamboo-rod play significant\r\nfunctions. In accord with it, too, is their\r\nlanguage, which like the language of children has not\r\nyet developed into a grammar, or, rather, according\r\nto the modern conception, has not yet degenerated\r\ninto a grammar. It is the same also with their music\r\nwhich is satisfied with the five-toned scale.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe mural paintings at Herculaneum and Pompeii\r\nare distinguished by grace of representation, as also\r\nby a pronounced sense for perspective and correct illumination,\r\nyet they are not at all scrupulous in construction.\r\nHere still we find abbreviations avoided.\r\nBut to offset this defect, the members of the body are\r\nbrought into unnatural positions, in which they appear\r\nin their full lengths. Abridgements are more frequently\r\nobserved in clothed than in unclothed figures.\u003c/p\u003e\r\n\r\n\u003cp\u003eA satisfactory explanation of these phenomena first\r\noccurred to me on the making of a few simple experiments\r\nwhich show how differently one may see the\r\nsame object, after some mastery of one\u0027s senses has\r\nbeen attained, simply by the arbitrary\r\nmovement of the attention.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 150px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-090.jpg\" width=\"150\" height=\"191\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 22.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eLook at the annexed drawing (Fig. 22).\r\nIt represents a folded sheet of paper with\r\neither its depressed or its elevated side\r\nturned towards you, as you wish. You can\r\nconceive the drawing in either sense, and\r\nin either case it will appear to you differently.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf, now, you have a real folded sheet of paper on\r\nthe table before you, with its sharp edges turned towards\r\nyou, you can, on looking at it with one eye, see\r\nthe sheet alternately elevated, as it really is, or depressed.\r\nHere, however, a remarkable phenomenon\r\nis presented. When you see the sheet properly, neither\r\nillumination nor form presents anything conspicuous.\r\nWhen you see it bent back you see it perspectively\r\ndistorted. Light and shadow appear much brighter\r\nor darker, or as if overlaid thickly with bright colors.\r\nLight and shadow now appear devoid of all cause.\r\nThey no longer harmonise with the body\u0027s form, and\r\nare thus rendered much more prominent.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn common life we employ the perspective and\r\nillumination of objects to determine their forms and\r\nposition. Hence we do not notice the lights, the\r\nshadows, and the distortions. They first powerfully\r\nenter consciousness when we employ a different construction\r\nfrom the usual spatial one. In looking at\r\nthe planar image of a camera obscura we are amazed\r\nat the plenitude of the light and the profundity of the\r\nshadows, both of which we do not notice in real objects.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn my earliest youth the shadows and lights on pictures\r\nappeared to me as spots void of meaning. When\r\nI began to draw I regarded shading as a mere custom\r\nof artists. I once drew the portrait of our pastor, a\r\nfriend of the family, and shaded, from no necessity,\r\nbut simply from having seen something similar in\r\nother pictures, the whole half of his face black. I was\r\nsubjected for this to a severe criticism on the part of\r\nmy mother, and my deeply offended artist\u0027s pride is\r\nprobably the reason that these facts remained so\r\nstrongly impressed upon my memory.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou see, then, that many strange things, not only\r\nin the life of individuals, but also in that of humanity,\r\nand in the history of general civilisation, may be explained\r\nfrom the simple fact that man has two eyes.\u003c/p\u003e\r\n\r\n\u003cp\u003eChange man\u0027s eye and you change his conception\r\nof the world. We have observed the truth of this fact\r\namong our nearest kin, the Egyptians, the Chinese,\r\nand the lake-dwellers; how must it be among some of\r\nour remoter relatives,\u0026mdash;with monkeys and other animals?\r\nNature must appear totally different to animals\r\nequipped with substantially different eyes from those\r\nof men, as, for example, to insects. But for the present\r\nscience must forego the pleasure of portraying this\r\nappearance, as we know very little as yet of the mode\r\nof operation of these organs.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is an enigma even how nature appears to animals\r\nclosely related to man; as to birds, who see\r\nscarcely anything with two eyes at once, but since\r\ntheir eyes are placed on opposite sides of their heads,\r\nhave a separate field of vision for each.\u003ca name=\"FNanchor_18_18\" id=\"FNanchor_18_18\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_18_18\" class=\"fnanchor\"\u003e[18]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe soul of man is pent up in the prison-house of\r\nhis head; it looks at nature through its two windows,\r\nthe eyes. It would also fain know how nature looks\r\nthrough other windows. A desire apparently never to\r\nbe fulfilled. But our love for nature is inventive, and\r\nhere, too, much has been accomplished.\u003c/p\u003e\r\n\r\n\u003cp\u003ePlacing before me an angular mirror, consisting of\r\ntwo plane mirrors slightly inclined to each other, I see\r\nmy face twice reflected. In the right-hand mirror I\r\nobtain a view of the right side, and in the left-hand\r\nmirror a view of the left\r\nside, of my face. Also\r\nI shall see the face of a\r\nperson standing in front\r\nof me, more to the right with my right eye, more to\r\nthe left with my left. But in order to obtain such\r\nwidely different views of a face as those shown in the\r\nangular mirror, my two eyes would have to be set much\r\nfurther apart from each other than they actually are.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 220px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-093.jpg\" width=\"220\" height=\"54\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 23.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eSquinting with my right eye at the image in the\r\nright-hand mirror, with my left eye at the image in\r\nthe left-hand mirror, my vision will be the vision of a\r\ngiant having an enormous head with his two eyes set\r\nfar apart. This, also, is the impression which my own\r\nface makes upon me. I see it now, single and solid.\r\nFixing my gaze, the relief from second to second is\r\nmagnified, the eyebrows start forth prominently from\r\nabove the eyes, the nose seems to grow a foot in\r\nlength, my mustache shoots forth like a fountain from\r\nmy lip, the teeth seem to retreat immeasurably. But\r\nby far the most horrible aspect of the phenomenon is\r\nthe nose.\u003c/p\u003e\r\n\r\n\u003cp\u003eInteresting in this connexion is the telestereoscope\r\nof Helmholtz. In the telestereoscope we view a landscape\r\nby looking with our right eye (Fig. 24) through\r\nthe mirror \u003ci\u003ea\u003c/i\u003e into the mirror \u003ci\u003eA\u003c/i\u003e, and with our left eye\r\nthrough the mirror \u003ci\u003eb\u003c/i\u003e into the mirror \u003ci\u003eB\u003c/i\u003e. The mirrors\r\n\u003ci\u003eA\u003c/i\u003e and \u003ci\u003eB\u003c/i\u003e stand far apart.\r\nAgain we see with the\r\nwidely separated eyes\r\nof a giant. Everything\r\nappears dwarfed and\r\nnear us. The distant\r\nmountains look like\r\nmoss-covered stones at our feet. Between, you see the\r\nreduced model of a city, a veritable Liliput. You\r\nare tempted almost to stroke with your hand the soft\r\nforest and city, did you not fear that you might prick\r\nyour fingers on the sharp, needle-shaped steeples, or\r\nthat they might crackle and break off.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 350px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-094.jpg\" width=\"350\" height=\"201\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 24.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eLiliput is no fable. We need only Swift\u0027s eyes,\r\nthe telestereoscope, to see it.\u003c/p\u003e\r\n\r\n\u003cp\u003ePicture to yourself the reverse case. Let us suppose\r\nourselves so small that we could take long walks\r\nin a forest of moss, and that our eyes were correspondingly\r\nnear each other. The moss-fibres would appear\r\nlike trees. On them we should see strange, unshapely\r\nmonsters creeping about. Branches of the oak-tree,\r\nat whose base our moss-forest lay, would seem to us\r\ndark, immovable, myriad-branched clouds, painted\r\nhigh on the vault of heaven; just as the inhabitants\r\nof Saturn, forsooth, might see their enormous ring.\r\nOn the tree-trunks of our mossy woodland we should\r\nfind colossal globes several feet in diameter, brilliantly\r\ntransparent, swayed by the winds with slow, peculiar\r\nmotions. We should approach inquisitively and should\r\nfind that these globes, in which here and there animals\r\nwere gaily sporting, were liquid globes, in fact\r\nthat they were water. A short, incautious step, the\r\nslightest contact, and woe betide us, our arm is irresistibly\r\ndrawn by an invisible power into the interior of\r\nthe sphere and held there unrelentingly fast! A drop\r\nof dew has engulfed in its capillary maw a manikin,\r\nin revenge for the thousands of drops that its big human\r\ncounterparts have quaffed at breakfast. Thou\r\nshouldst have known, thou pygmy natural scientist,\r\nthat with thy present puny bulk thou shouldst not joke\r\nwith capillarity!\u003c/p\u003e\r\n\r\n\u003cp\u003eMy terror at the accident brings me back to my\r\nsenses. I see I have turned idyllic. You must pardon\r\nme. A patch of greensward, a moss or heather forest\r\nwith its tiny inhabitants have incomparably more\r\ncharms for me than many a bit of literature with its\r\napotheosis of human character. If I had the gift of\r\nwriting novels I should certainly not make John and\r\nMary my characters. Nor should I transfer my loving\r\npair to the Nile, nor to the age of the old Egyptian\r\nPharaohs, although perhaps I should choose that time\r\nin preference to the present. For I must candidly\r\nconfess that I hate the rubbish of history, interesting\r\nthough it may be as a mere phenomenon, because we\r\ncannot simply observe it but must also \u003ci\u003efeel\u003c/i\u003e it, because\r\nit comes to us mostly with supercilious arrogance,\r\nmostly unvanquished. The hero of my novel would be\r\na cockchafer, venturing forth in his fifth year for the\r\nfirst time with his newly grown wings into the light,\r\nfree air. Truly it could do no harm if man would thus\r\nthrow off his inherited and acquired narrowness of\r\nmind by making himself acquainted with the world-view\r\nof allied creatures. He could not help gaining\r\nincomparably more in this way than the inhabitant of\r\na small town would in circumnavigating the globe and\r\ngetting acquainted with the views of strange peoples.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_87\" id=\"Page_87\"\u003e[Pg 87]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_88\" id=\"Page_88\"\u003e[Pg 88]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_89\" id=\"Page_89\"\u003e[Pg 89]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eI have now conducted you, by many paths and by-ways,\r\nrapidly over hedge and ditch, to show you what\r\nwide vistas we may reach in every field by the rigorous\r\npursuit of a single scientific fact. A close examination\r\nof the two eyes of man has conducted us not\r\nonly into the dim recesses of humanity\u0027s childhood,\r\nbut has also carried us far beyond the bourne of human\r\nlife.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt has surely often struck you as strange that the\r\nsciences are divided into two great groups; that the\r\nso-called humanistic sciences, belonging to the so-called\r\n\"higher education,\" are placed in almost a hostile\r\nattitude to the natural sciences.\u003c/p\u003e\r\n\r\n\u003cp\u003eI must confess I do not overmuch believe in this\r\npartition of the sciences. I believe that this view will\r\nappear as childlike and ingenuous to a matured age\r\nas the want of perspective in the old paintings of Egypt\r\ndoes to us. Can it really be that \"higher culture\" is to\r\nbe gotten only from a few old pots and palimpsests,\r\nwhich are at best mere scraps of nature, or that more\r\nis to be learned from them alone than from all the rest\r\nof nature? I believe that both these sciences are simply\r\nparts of the same science, which have begun at\r\ndifferent ends. If these two ends still act towards\r\neach other as the Montagues and Capulets, if their retainers\r\nstill indulge in lively tilts, I believe that after\r\nall they are not in earnest. On the one side there is\r\nsurely a Romeo, and on the other a Juliet, who, some\r\nday, it is hoped, will unite the two houses with a less\r\ntragic sequel than that of the play.\u003c/p\u003e\r\n\r\n\u003cp\u003ePhilology began with the unqualified reverence and\r\napotheosis of the Greeks. Now it has begun to draw\r\nother languages, other peoples and their histories, into\r\nits sphere; it has, through the mediation of comparative\r\nlinguistics, already struck up, though as yet somewhat\r\ncautiously, a friendship with physiology.\u003c/p\u003e\r\n\r\n\u003cp\u003ePhysical science began in the witch\u0027s kitchen. It\r\nnow embraces the organic and inorganic worlds, and\r\nwith the physiology of articulation and the theory of\r\nthe senses, has even pushed its researches, at times\r\nimpertinently, into the province of mental phenomena.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn short, we come to the understanding of much\r\nwithin us solely by directing our glance without, and\r\n\u003ci\u003evice versa\u003c/i\u003e. Every object belongs to both sciences.\r\nYou, ladies, are very interesting and difficult problems\r\nfor the psychologist, but you are also extremely pretty\r\nphenomena of nature. Church and State are objects\r\nof the historian\u0027s research, but not less phenomena of\r\nnature, and in part, indeed, very curious phenomena.\r\nIf the historical sciences have inaugurated wide extensions\r\nof view by presenting to us the thoughts of\r\nnew and strange peoples, the physical sciences in a\r\ncertain sense do this in a still greater degree. In\r\nmaking man disappear in the All, in annihilating him,\r\nso to speak, they force him to take an unprejudiced\r\nposition without himself, and to form his judgments by\r\na different standard from that of the petty human.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut if you should ask me now why man has two\r\neyes, I should answer:\u003c/p\u003e\r\n\r\n\u003cp\u003eThat he may look at nature justly and accurately;\r\nthat he may come to understand that he himself, with\r\nall his views, correct and incorrect, with all his \u003ci\u003ehaute\r\npolitique\u003c/i\u003e, is simply an evanescent shred of nature;\r\nthat, to speak with Mephistopheles, he is a part of the\r\npart, and that it is absolutely unjustified,\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"For man, the microcosmic fool, to see\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eHimself a whole so frequently.\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003c/div\u003e\u003c/div\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_SYMMETRY\" id=\"ON_SYMMETRY\"\u003eON SYMMETRY.\u003c/a\u003e\u003c/h2\u003e\u003cp\u003e\u003ca name=\"FNanchor_19_19\" id=\"FNanchor_19_19\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_19_19\" class=\"fnanchor\"\u003e[19]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\r\n\u003cp\u003eAn ancient philosopher once remarked that people\r\nwho cudgelled their brains about the nature of\r\nthe moon reminded him of men who discussed the\r\nlaws and institutions of a distant city of which they\r\nhad heard no more than the name. The true philosopher,\r\nhe said, should turn his glance within, should\r\nstudy himself and his notions of right and wrong; only\r\nthence could he derive real profit.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis ancient formula for happiness might be restated\r\nin the familiar words of the Psalm:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"Dwell in the land, and verily thou shalt be fed.\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003c/div\u003e\u003c/div\u003e\r\n\r\n\u003cp\u003eTo-day, if he could rise from the dead and walk\r\nabout among us, this philosopher would marvel much\r\nat the different turn which matters have taken.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_90\" id=\"Page_90\"\u003e[Pg 90]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eThe motions of the moon and the other heavenly\r\nbodies are accurately known. Our knowledge of the\r\nmotions of our own body is by far not so complete.\r\nThe mountains and natural divisions of the moon have\r\nbeen accurately outlined on maps, but physiologists\r\nare just beginning to find their way in the geography\r\nof the brain. The chemical constitution of many fixed\r\nstars has already been investigated. The chemical\r\nprocesses of the animal body are questions of much\r\ngreater difficulty and complexity. We have our \u003ci\u003eMécanique\r\ncéleste\u003c/i\u003e. But a \u003ci\u003eMécanique sociale\u003c/i\u003e or a \u003ci\u003eMécanique\r\nmorale\u003c/i\u003e of equal trustworthiness remains to be written.\u003c/p\u003e\r\n\r\n\u003cp\u003eOur philosopher would indeed admit that we have\r\nmade great progress. But we have not followed his\r\nadvice. The patient has recovered, but he took for his\r\nrecovery exactly the opposite of what the doctor prescribed.\u003c/p\u003e\r\n\r\n\u003cp\u003eHumanity is now returned, much wiser, from its\r\njourney in celestial space, against which it was so\r\nsolemnly warned. Men, after having become acquainted\r\nwith the great and simple facts of the world without,\r\nare now beginning to examine critically the world\r\nwithin. It sounds absurd, but it is true, that only after\r\nwe have thought about the moon are we able to take\r\nup ourselves. It was necessary that we should acquire\r\nsimple and clear ideas in a less complicated domain,\r\nbefore we entered the more intricate one of psychology,\r\nand with these ideas astronomy principally furnished\r\nus.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_91\" id=\"Page_91\"\u003e[Pg 91]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eTo attempt any description of that stupendous\r\nmovement, which, originally springing out of the physical\r\nsciences, went beyond the domain of physics and is\r\nnow occupied with the problems of psychology, would\r\nbe presumptuous in this place. I shall only attempt\r\nhere, to illustrate to you by a few simple examples the\r\nmethods by which the province of psychology can be\r\nreached from the facts of the physical world\u0026mdash;especially\r\nthe adjacent province of sense-perception. And I wish\r\nit to be remembered that my brief attempt is not to be\r\ntaken as a measure of the present state of such scientific\r\nquestions.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_92\" id=\"Page_92\"\u003e[Pg 92]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_93\" id=\"Page_93\"\u003e[Pg 93]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_94\" id=\"Page_94\"\u003e[Pg 94]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_95\" id=\"Page_95\"\u003e[Pg 95]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_96\" id=\"Page_96\"\u003e[Pg 96]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_97\" id=\"Page_97\"\u003e[Pg 97]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_98\" id=\"Page_98\"\u003e[Pg 98]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_99\" id=\"Page_99\"\u003e[Pg 99]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_100\" id=\"Page_100\"\u003e[Pg 100]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_101\" id=\"Page_101\"\u003e[Pg 101]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_102\" id=\"Page_102\"\u003e[Pg 102]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_103\" id=\"Page_103\"\u003e[Pg 103]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_104\" id=\"Page_104\"\u003e[Pg 104]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eIt is a well-known fact that some objects please us,\r\nwhile others do not. Generally speaking, anything\r\nthat is constructed according to fixed and logically\r\nfollowed rules, is a product of tolerable beauty. We see\r\nthus nature herself, who always acts according to fixed\r\nrules, constantly producing such pretty things. Every\r\nday the physicist is confronted in his workshop with\r\nthe most beautiful vibration-figures, tone-figures, phenomena\r\nof polarisation, and forms of diffraction.\u003c/p\u003e\r\n\r\n\u003cp\u003eA rule always presupposes a repetition. Repetitions,\r\ntherefore, will probably be found to play some\r\nimportant part in the production of agreeable effects.\r\nOf course, the nature of agreeable effects is not exhausted\r\nby this. Furthermore, the repetition of a\r\nphysical event becomes the source of agreeable effects\r\nonly when it is connected with a repetition of sensations.\u003c/p\u003e\r\n\r\n\u003cp\u003eAn excellent example that repetition of sensations\r\nis a source of agreeable effects is furnished by the\r\ncopy-book of every schoolboy, which is usually a treasure-house\r\nof such things, and only in need of an Abbé\r\nDomenech to become celebrated. Any figure, no matter\r\nhow crude or poor, if several times repeated, with\r\nthe repetitions placed in line, will produce a tolerable\r\nfrieze.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-102.jpg\" width=\"300\" height=\"185\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 25.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eAlso the pleasant effect of symmetry is due to the\r\nrepetition of sensations. Let us abandon ourselves a\r\nmoment to this thought, yet not imagine when we have\r\ndeveloped it, that we have fully exhausted the nature\r\nof the agreeable, much less of the beautiful.\u003c/p\u003e\r\n\r\n\u003cp\u003eFirst, let us get a clear conception of what symmetry\r\nis. And in preference to a definition let us take\r\na living picture. You know that the reflexion of an\r\nobject in a mirror has a great likeness to the object itself.\r\nAll its proportions and outlines are the same.\r\nYet there is a difference between the object and its reflexion\r\nin the mirror, which you will readily observe.\u003c/p\u003e\r\n\r\n\u003cp\u003eHold your right hand before a mirror, and you will\r\nsee in the mirror a left hand. Your right glove will\r\nproduce its mate in the glass. For you could never\r\nuse the reflexion of your right glove, if it were present\r\nto you as a real thing, for covering your right hand,\r\nbut only for covering your left. Similarly, your right\r\near will give as its reflexion a left ear; and you will at\r\nonce perceive that the left half of your body could very\r\neasily be substituted for the reflexion of your right half.\r\nNow just as in the place of a missing right ear a left ear\r\ncannot be put, unless the lobule of the ear be turned upwards,\r\nor the opening into the concha backwards, so,\r\ndespite all similarity of form, the reflexion of an object\r\ncan never take the place of the object itself.\u003ca name=\"FNanchor_20_20\" id=\"FNanchor_20_20\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_20_20\" class=\"fnanchor\"\u003e[20]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe reason of this difference between the object\r\nand its reflexion is simple. The reflexion appears as\r\nfar behind the mirror as the object is in front of it. The\r\nparts of the object, accordingly, which are nearest the\r\nmirror will also be nearest the mirror in the reflexion.\r\nConsequently, the succession of the parts in the reflexion\r\nwill be reversed, as may best be seen in the reflexion\r\nof the face of a watch or of a manuscript.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will also be readily seen, that if a point of the object\r\nbe joined with its reflexion in the image, the line\r\nof junction will cut the mirror at right angles and be\r\nbisected by it. This holds true of all corresponding\r\npoints of object and image.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf, now, we can divide an object by a plane into\r\ntwo halves so that each half, as seen in the reflecting\r\nplane of division, is a reproduction of the other half,\r\nsuch an object is termed symmetrical, and the plane\r\nof division is called the plane of symmetry.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf the plane of symmetry is vertical, we can say\r\nthat the body is vertically symmetrical. An example\r\nof vertical symmetry is a Gothic cathedral.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf the plane of symmetry is horizontal, we can say\r\nthat the object is horizontally symmetrical. A landscape\r\non the shores of a lake with its reflexion in the\r\nwater, is a system of horizontal symmetry.\u003c/p\u003e\r\n\r\n\u003cp\u003eExactly here is a noticeable difference. The vertical\r\nsymmetry of a Gothic cathedral strikes us at once,\r\nwhereas we can travel up and down the whole length\r\nof the Rhine or the Hudson without becoming aware\r\nof the symmetry between objects and their reflexions\r\nin the water. Vertical symmetry pleases us, whilst\r\nhorizontal symmetry is indifferent, and is noticed only\r\nby the experienced eye.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhence arises this difference? I say from the fact\r\nthat vertical symmetry produces a repetition of the\r\nsame sensation, while horizontal symmetry does not.\r\nI shall now show that this is so.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us look at the following letters:\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003ed b\r\nq p\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is a fact known to all mothers and teachers, that\r\nchildren in their first attempts to read and write, constantly\r\nconfound d and b, and q and p, but never d\r\nand q, or b and p. Now d and b and q and p are the\r\ntwo halves of a \u003ci\u003evertically\u003c/i\u003e symmetrical figure, while d\r\nand q, and b and p are two halves of a \u003ci\u003ehorizontally\u003c/i\u003e symmetrical\r\nfigure. The first two are confounded; but\r\nconfusion is only possible of things that excite in us\r\nthe same or similar sensations.\u003c/p\u003e\r\n\r\n\u003cp\u003eFigures of two flower-girls are frequently seen on\r\nthe decorations of gardens and of drawing-rooms, one\r\nof whom carries a flower-basket in her right hand and\r\nthe other a flower-basket in her left. All know how\r\napt we are, unless we are very careful, to confound these\r\nfigures with one another.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhile turning a thing round from right to left is\r\nscarcely noticed, the eye is not at all indifferent to the\r\nturning of a thing upside down. A human face which\r\nhas been turned upside down is scarcely recognisable\r\nas a face, and makes an impression which is altogether\r\nstrange. The reason of this is not to be sought in the\r\nunwontedness of the sight, for it is just as difficult to\r\nrecognise an arabesque that has been inverted, where\r\nthere can be no question of a habit. This curious fact\r\nis the foundation of the familiar jokes played with the\r\nportraits of unpopular personages, which are so drawn\r\nthat in the upright position of the page an exact picture\r\nof the person is presented, but on being inverted\r\nsome popular animal is shown.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is a fact, then, that the two halves of a vertically\r\nsymmetrical figure are easily confounded and that they\r\ntherefore probably produce very nearly the same sensations.\r\nThe question, accordingly, arises, \u003ci\u003ewhy\u003c/i\u003e do the\r\ntwo halves of a vertically symmetrical figure produce\r\nthe same or similar sensations? The answer is: Because\r\nour apparatus of vision, which consists of our\r\neyes and of the accompanying muscular apparatus is\r\nitself vertically symmetrical.\u003ca name=\"FNanchor_21_21\" id=\"FNanchor_21_21\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_21_21\" class=\"fnanchor\"\u003e[21]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eWhatever external resemblances one eye may have\r\nwith another they are still not alike. The right eye of\r\na man cannot take the place of a left eye any more\r\nthan a left ear or left hand can take the place of a\r\nright one. By artificial means, we can change the part\r\nwhich each of our eyes plays. (Wheatstone\u0027s pseudoscope.)\r\nBut we then find ourselves in an entirely new\r\nand strange world. What is convex appears concave;\r\nwhat is concave, convex. What is distant appears\r\nnear, and what is near appears far.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe left eye is the reflexion of the right. And the\r\nlight-feeling retina of the left eye is a reflexion of the\r\nlight-feeling retina of the right, in all its functions.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe lense of the eye, like a magic lantern, casts\r\nimages of objects on the retina. And you may picture\r\nto yourself the light-feeling retina of the eye, with its\r\ncountless nerves, as a hand with innumerable fingers,\r\nadapted to feeling light. The ends of the visual nerves,\r\nlike our fingers, are endowed with varying degrees of\r\nsensitiveness. The two retinæ act like a right and a\r\nleft hand; the sensation of touch and the sensation of\r\nlight in the two instances are similar.\u003c/p\u003e\r\n\r\n\u003cp\u003eExamine the right-hand portion of this letter T:\r\nnamely, T. Instead of the two retinæ on which this\r\nimage falls, imagine feeling the object, my two hands.\r\nThe \u0026#9484;, grasped with the right hand, gives a different\r\nsensation from that which it gives when grasped with\r\nthe left. But if we turn our character about from right\r\nto left, thus: \u0026#9488;, it will give the same sensation in the\r\nleft hand that it gave before in the right. The sensation\r\nis repeated.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we take a whole T, the right half will produce in\r\nthe right hand the same sensation that the left half\r\nproduces in the left, and \u003ci\u003evice versa\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe symmetrical figure gives the same sensation\r\ntwice.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we turn the T over thus: \u0026#9500;, or invert the half\r\nT thus: L, so long as we do not change the position\r\nof our hands we can make no use of the foregoing reasoning.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe retinæ, in fact, are exactly like our two hands.\r\nThey, too, have their thumbs and index fingers, though\r\nthey are thousands in number; and we may say the\r\nthumbs are on the side of the eye near the nose,\r\nand the remaining fingers on the side away from the\r\nnose.\u003c/p\u003e\r\n\r\n\u003cp\u003eWith this I hope to have made perfectly clear that\r\nthe pleasing effect of symmetry is chiefly due to the\r\nrepetition of sensations, and that the effect in question\r\ntakes place in symmetrical figures, only where\r\nthere is a repetition of sensation. The pleasing effect\r\nof regular figures, the preference which straight lines,\r\nespecially vertical and horizontal straight lines, enjoy,\r\nis founded on a similar reason. A straight line,\r\nboth in a horizontal and in a vertical position, can cast\r\non the two retinæ the same image, which falls moreover\r\non symmetrically corresponding spots. This also,\r\nit would appear, is the reason of our psychological\r\npreference of straight to curved lines, and not their\r\nproperty of being the shortest distance between two\r\npoints. The straight line is felt, to put the matter\r\nbriefly, as symmetrical to itself, which is the case also\r\nwith the plane. Curved lines are felt as deviations\r\nfrom straight lines, that is, as deviations from symmetry.\u003ca name=\"FNanchor_22_22\" id=\"FNanchor_22_22\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_22_22\" class=\"fnanchor\"\u003e[22]\u003c/a\u003e\r\nThe presence of a sense for symmetry in people\r\npossessing only one eye from birth, is indeed a riddle.\r\nOf course, the sense of symmetry, although primarily\r\nacquired by means of the eyes, cannot be wholly limited\r\nto the visual organs. It must also be deeply\r\nrooted in other parts of the organism by ages of practice\r\nand can thus not be eliminated forthwith by the\r\nloss of one eye. Also, when an eye is lost, the symmetrical\r\nmuscular apparatus is left, as is also the\r\nsymmetrical apparatus of innervation.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt appears, however, unquestionable that the phenomena\r\nmentioned have, in the main, their origin in\r\nthe peculiar structure of our eyes. It will therefore\r\nbe seen at once that our notions of what is beautiful\r\nand ugly would undergo a change if our eyes were different.\r\nAlso, if this view is correct, the theory of the\r\nso-called eternally beautiful is somewhat mistaken. It\r\ncan scarcely be doubted that our culture, or form of\r\ncivilisation, which stamps upon the human body its\r\nunmistakable traces, should not also modify our conceptions\r\nof the beautiful. Was not formerly the development\r\nof all musical beauty restricted to the narrow\r\nlimits of a five-toned scale?\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fact that a repetition of sensations is productive\r\nof pleasant effects is not restricted to the realm of\r\nthe visible. To-day, both the musician and the physicist\r\nknow that the harmonic or the melodic addition\r\nof one tone to another affects us agreeably only when\r\nthe added tone reproduces a part of the sensation\r\nwhich the first one excited. When I add an octave\r\nto a fundamental tone, I hear in the octave a part of\r\nwhat was heard in the fundamental tone. (Helmholtz.)\r\nBut it is not my purpose to develop this idea\r\nfully here.\u003ca name=\"FNanchor_23_23\" id=\"FNanchor_23_23\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_23_23\" class=\"fnanchor\"\u003e[23]\u003c/a\u003e We shall only ask to-day, whether there\r\nis anything similar to the symmetry of figures in the\r\nprovince of sounds.\u003c/p\u003e\r\n\r\n\u003cp\u003eLook at the reflexion of your piano in the mirror.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou will at once remark that you have never seen\r\nsuch a piano in the actual world, for it has its high\r\nkeys to the left and its low ones to the right. Such\r\npianos are not manufactured.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf you could sit down at such a piano and play in\r\nyour usual manner, plainly every step which you\r\nimagined you were performing in the upward scale\r\nwould be executed as a corresponding step in the\r\ndownward scale. The effect would be not a little surprising.\u003c/p\u003e\r\n\r\n\u003cp\u003eFor the practised musician who is always accustomed\r\nto hearing certain sounds produced when certain\r\nkeys are struck, it is quite an anomalous spectacle\r\nto watch a player in the glass and to observe that he\r\nalways does the opposite of what we hear.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut still more remarkable would be the effect of\r\nattempting to strike a harmony on such a piano. For\r\na melody it is not indifferent whether we execute a\r\nstep in an upward or a downward scale. But for a\r\nharmony, so great a difference is not produced by reversal.\r\nI always retain the same consonance whether\r\nI add to a fundamental note an upper or a lower third.\r\nOnly the order of the intervals of the harmony is reversed.\r\nIn point of fact, when we execute a movement\r\nin a major key on our reflected piano, we hear a\r\nsound in a minor key, and \u003ci\u003evice versa\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt now remains to execute the experiments indicated.\r\nInstead of playing upon the piano in the mirror,\r\nwhich is impossible, or of having a piano of this\r\nkind built, which would be somewhat expensive, we\r\nmay perform our experiments in a simpler manner, as\r\nfollows:\u003c/p\u003e\r\n\r\n\u003cp\u003e1) We play on our own piano in our usual manner,\r\nlook into the mirror, and then repeat on our real piano\r\nwhat we see in the mirror. In this way we transform\r\nall steps upwards into corresponding steps downwards.\r\nWe play a movement, and then another movement,\r\nwhich, with respect to the key-board, is symmetrical\r\nto the first.\u003c/p\u003e\r\n\r\n\u003cp\u003e2) We place a mirror beneath the music in which\r\nthe notes are reflected as in a body of water, and play\r\naccording to the notes in the mirror. In this way also,\r\nall steps upwards are changed into corresponding,\r\nequal steps downwards.\u003c/p\u003e\r\n\r\n\u003cp\u003e3) We turn the music upside down and read the\r\nnotes from right to left and from below upwards. In\r\ndoing this, we must regard all sharps as flats and all\r\nflats as sharps, because they correspond to half lines\r\nand spaces. Besides, in this use of the music we can\r\nonly employ the bass clef, as only in this clef are the\r\nnotes not changed by symmetrical reversal.\u003c/p\u003e\r\n\r\n\u003cp\u003eYou can judge of the effect of these experiments\r\nfrom the examples which appear in the annexed musical\r\ncut. (Page 102.) The movement which appears in\r\nthe upper lines is symmetrically reversed in the lower.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe effect of the experiments may be briefly formulated.\r\nThe melody is rendered unrecognisable. The\r\nharmony suffers a transposition from a major into a\r\nminor key and \u003ci\u003evice versa\u003c/i\u003e. The study of these pretty\r\neffects, which have long been familiar to physicists\r\nand musicians, was revived some years ago by Von\r\nOettingen.\u003ca name=\"FNanchor_24_24\" id=\"FNanchor_24_24\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_24_24\" class=\"fnanchor\"\u003e[24]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 525px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-112.jpg\" width=\"525\" height=\"800\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 26.\u003c/span\u003e\u003cbr /\u003e\r\n\u003ca href=\"music/112a.mid\"\u003eListen to 1.\u003c/a\u003e\u003cbr /\u003e\r\n\u003ca href=\"music/112b.mid\"\u003eListen to 2.\u003c/a\u003e\u003cbr /\u003e\r\n\u003ca href=\"music/112c.mid\"\u003eListen to 3.\u003c/a\u003e\u003cbr /\u003e\r\n\u003ca href=\"music/112d.mid\"\u003eListen to 4.\u003c/a\u003e\u003cbr /\u003e\r\n\u003ca href=\"music/112e.mid\"\u003eListen to 5.\u003c/a\u003e\u003cbr /\u003e\r\n\u003ca href=\"music/112f.mid\"\u003eListen to 6.\u003c/a\u003e\u003cbr /\u003e\r\n\u003ca href=\"music/112g.mid\"\u003eListen to 7.\u003c/a\u003e\u003cbr /\u003e\r\n\u003ca href=\"music/112h.mid\"\u003eListen to 8.\u003c/a\u003e\u003cbr /\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003e(See pages 101 and 103.)]\u003c/p\u003e\r\n\r\n\u003cp\u003eNow, although in all the preceding examples I have\r\ntransposed steps upward into equal and similar steps\r\ndownward, that is, as we may justly say, have played\r\nfor every movement the movement which is symmetrical\r\nto it, yet the ear notices either little or nothing of\r\nsymmetry. The transposition from a major to a minor\r\nkey is the sole indication of symmetry remaining. The\r\nsymmetry is there for the mind, but is wanting for\r\nsensation. No symmetry exists for the ear, because a\r\nreversal of musical sounds conditions no repetition of\r\nsensations. If we had an ear for height and an ear\r\nfor depth, just as we have an eye for the right and an\r\neye for the left, we should also find that symmetrical\r\nsound-structures existed for our auditory organs. The\r\ncontrast of major and minor for the ear corresponds to\r\ninversion for the eye, which is also only symmetry for\r\nthe mind, but not for sensation.\u003c/p\u003e\r\n\r\n\u003cp\u003eBy way of supplement to what I have said, I will\r\nadd a brief remark for my mathematical readers.\u003c/p\u003e\r\n\r\n\u003cp\u003eOur musical notation is essentially a graphical representation\r\nof a piece of music in the form of curves,\r\nwhere the time is the abscissæ, and the logarithms of\r\nthe number of vibrations the ordinates. The deviations\r\nof musical notation from this principle are only\r\nsuch as facilitate interpretation, or are due to historical\r\naccidents.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf, now, it be further observed that the sensation\r\nof pitch also is proportional to the logarithm of the\r\nnumber of vibrations, and that the intervals between\r\nthe notes correspond to the differences of the logarithms\r\nof the numbers of vibrations, the justification\r\nwill be found in these facts of calling the harmonies\r\nand melodies which appear in the mirror, symmetrical\r\nto the original ones.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_105\" id=\"Page_105\"\u003e[Pg 105]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_106\" id=\"Page_106\"\u003e[Pg 106]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_107\" id=\"Page_107\"\u003e[Pg 107]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eI simply wish to bring home to your minds by these\r\nfragmentary remarks that the progress of the physical\r\nsciences has been of great help to those branches of\r\npsychology that have not scorned to consider the results\r\nof physical research. On the other hand, psychology\r\nis beginning to return, as it were, in a spirit\r\nof thankfulness, the powerful stimulus which it received\r\nfrom physics.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe theories of physics which reduce all phenomena\r\nto the motion and equilibrium of smallest particles,\r\nthe so-called molecular theories, have been\r\ngravely threatened by the progress of the theory of the\r\nsenses and of space, and we may say that their days\r\nare numbered.\u003c/p\u003e\r\n\r\n\u003cp\u003eI have shown elsewhere\u003ca name=\"FNanchor_25_25\" id=\"FNanchor_25_25\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_25_25\" class=\"fnanchor\"\u003e[25]\u003c/a\u003e that the musical scale is\r\nsimply a species of space\u0026mdash;a space, however, of only\r\none dimension, and that, a one-sided one. If, now, a\r\nperson who could only hear, should attempt to develop\r\na conception of the world in this, his linear space, he\r\nwould become involved in many difficulties, as his space\r\nwould be incompetent to comprehend the many sides\r\nof the relations of reality. But is it any more justifiable\r\nfor us, to attempt to force the whole world into the\r\nspace of our eye, in aspects in which it is not accessible\r\nto the eye? Yet this is the dilemma of all molecular\r\ntheories.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe possess, however, a sense, which, with respect\r\nto the scope of the relations which it can comprehend,\r\nis richer than any other. It is our reason. This stands\r\nabove the senses. It alone is competent to found a\r\npermanent and sufficient view of the world. The\r\nmechanical conception of the world has performed\r\nwonders since Galileo\u0027s time. But it must now yield\r\nto a broader view of things. A further development of\r\nthis idea is beyond the limits of my present purpose.\u003c/p\u003e\r\n\r\n\u003cp\u003eOne more point and I have done. The advice of\r\nour philosopher to restrict ourselves to what is near\r\nat hand and useful in our researches, which finds a\r\nkind of exemplification in the present cry of inquirers\r\nfor limitation and division of labor, must not be too\r\nslavishly followed. In the seclusion of our closets, we\r\noften rack our brains in vain to fulfil a work, the\r\nmeans of accomplishing which lies before our very\r\ndoors. If the inquirer must be perforce a shoemaker,\r\ntapping constantly at his last, it may perhaps be permitted\r\nhim to be a shoemaker of the type of Hans\r\nSachs, who did not deem it beneath him to take a\r\nlook now and then at his neighbor\u0027s work and to\r\ncomment on the latter\u0027s doings.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet this be my apology, therefore, if I have forsaken\r\nfor a moment to-day the last of my specialty.\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_THE_FUNDAMENTAL_CONCEPTS\" id=\"ON_THE_FUNDAMENTAL_CONCEPTS\"\u003eON THE FUNDAMENTAL CONCEPTS\r\nOF ELECTROSTATICS.\u003c/a\u003e\u003ca name=\"FNanchor_26_26\" id=\"FNanchor_26_26\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_26_26\" class=\"fnanchor\"\u003e[26]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eThe task has been assigned me to develop before\r\nyou in a popular manner the fundamental quantitative\r\nconcepts of electrostatics\u0026mdash;\"quantity of electricity,\"\r\n\"potential,\" \"capacity,\" and so forth. It\r\nwould not be difficult, even within the brief limits of\r\nan hour, to delight the eye with hosts of beautiful experiments\r\nand to fill the imagination with numerous\r\nand varied conceptions. But we should, in such a\r\ncase, be still far from a lucid and easy grasp of the\r\nphenomena. The means would still fail us for reproducing\r\nthe facts accurately in thought\u0026mdash;a procedure\r\nwhich for the theoretical and practical man is of equal\r\nimportance. These means are the \u003ci\u003emetrical concepts\u003c/i\u003e of\r\nelectricity.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs long as the pursuit of the facts of a given province\r\nof phenomena is in the hands of a few isolated\r\ninvestigators, as long as every experiment can be easily\r\nrepeated, the fixing of the collected facts by provisional\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_108\" id=\"Page_108\"\u003e[Pg 108]\u003c/a\u003e\u003c/span\u003e\r\ndescription is ordinarily sufficient. But the case is\r\ndifferent when the whole world must make use of the\r\nresults reached by many, as happens when the science\r\nacquires broader foundations and scope, and\r\nparticularly so when it begins to supply intellectual\r\nnourishment to an important branch of the practical\r\narts, and to draw from that province in return stupendous\r\nempirical results. Then the facts must be so\r\ndescribed that individuals in all places and at all times\r\ncan, from a few easily obtained elements, put the facts\r\naccurately together in thought, and reproduce them\r\nfrom the description. This is done with the help of\r\nthe metrical concepts and the international measures.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe work which was begun in this direction in the\r\nperiod of the purely scientific development of the science,\r\nespecially by Coulomb (1784), Gauss (1833), and\r\nWeber (1846), was powerfully stimulated by the requirements\r\nof the great technical undertakings manifested\r\nsince the laying of the first transatlantic cable,\r\nand brought to a brilliant conclusion by the labors of\r\nthe British Association, 1861, and of the Paris Congress,\r\n1881, chiefly through the exertions of Sir William\r\nThomson.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is plain, that in the time allotted to me I cannot\r\nconduct you over all the long and tortuous paths which\r\nthe science has actually pursued, that it will not be\r\npossible at every step to remind you of all the little\r\nprecautions for the avoidance of error which the early\r\nsteps have taught us. On the contrary, I must make\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_109\" id=\"Page_109\"\u003e[Pg 109]\u003c/a\u003e\u003c/span\u003e\r\nshift with the simplest and rudest tools. I shall conduct\r\nyou by the shortest paths from the facts to the\r\nideas, in doing which, of course, it will not be possible\r\nto anticipate all the stray and chance ideas which may\r\nand must arise from prospects into the by-paths which\r\nwe leave untrodden.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_110\" id=\"Page_110\"\u003e[Pg 110]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_111\" id=\"Page_111\"\u003e[Pg 111]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_112\" id=\"Page_112\"\u003e[Pg 112]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_113\" id=\"Page_113\"\u003e[Pg 113]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_114\" id=\"Page_114\"\u003e[Pg 114]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_115\" id=\"Page_115\"\u003e[Pg 115]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_116\" id=\"Page_116\"\u003e[Pg 116]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_117\" id=\"Page_117\"\u003e[Pg 117]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_118\" id=\"Page_118\"\u003e[Pg 118]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_119\" id=\"Page_119\"\u003e[Pg 119]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_120\" id=\"Page_120\"\u003e[Pg 120]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_121\" id=\"Page_121\"\u003e[Pg 121]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_122\" id=\"Page_122\"\u003e[Pg 122]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_123\" id=\"Page_123\"\u003e[Pg 123]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_124\" id=\"Page_124\"\u003e[Pg 124]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_125\" id=\"Page_125\"\u003e[Pg 125]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_126\" id=\"Page_126\"\u003e[Pg 126]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_127\" id=\"Page_127\"\u003e[Pg 127]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eHere are two small, light bodies (Fig. 27) of equal\r\nsize, freely suspended, which we \"electrify\" either\r\nby friction with a third body or by contact with a body\r\nalready electrified. At once a repulsive force is set\r\nup which drives the two bodies away from each other\r\nin opposition to the action of gravity. This force could\r\naccomplish anew the same mechanical work which\r\nwas expended to produce it.\u003ca name=\"FNanchor_27_27\" id=\"FNanchor_27_27\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_27_27\" class=\"fnanchor\"\u003e[27]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 150px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-119-1.jpg\" width=\"150\" height=\"253\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 27.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 250px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-119-2.jpg\" width=\"250\" height=\"170\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 28.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eCoulomb, now, by means of delicate experiments\r\nwith the torsion-balance, satisfied himself that if the\r\nbodies in question, say at a distance of two centimetres,\r\nrepelled each other with the same force with\r\nwhich a milligramme-weight strives to fall to the\r\nground, at half that distance, or at one centimetre,\r\nthey would repel each other with the force of four\r\nmilligrammes, and at double that distance, or at four\r\ncentimetres, they would repel each other with the force\r\nof only one-fourth of a milligramme. He found that\r\nthe electrical force acts inversely as the square of the\r\ndistance.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us imagine, now, that we possessed some\r\nmeans of measuring electrical repulsion by weights,\r\na means which would be supplied, for example, by our\r\nelectrical pendulums; then we could make the following\r\nobservation.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe body \u003ci\u003eA\u003c/i\u003e (Fig. 28) is repelled by the body \u003ci\u003eK\u003c/i\u003e at\r\na distance of two centimetres with a force of one milligramme.\r\nIf we touch \u003ci\u003eA\u003c/i\u003e, now, with an equal body \u003ci\u003eB\u003c/i\u003e,\r\nthe half of this force of repulsion will pass to the body\r\n\u003ci\u003eB\u003c/i\u003e; both \u003ci\u003eA\u003c/i\u003e and \u003ci\u003eB\u003c/i\u003e, now, at a distance of two centimetres\r\nfrom \u003ci\u003eK\u003c/i\u003e, are repelled only with the force of one-half\r\na milligramme. But both together are repelled\r\nstill with the force of one milligramme. Hence, \u003ci\u003ethe\r\ndivisibility of electrical force\u003c/i\u003e among bodies in contact \u003ci\u003eis\r\na fact\u003c/i\u003e. It is a useful, but by no means a necessary\r\nsupplement to this fact, to imagine an electrical fluid\r\npresent in the body \u003ci\u003eA\u003c/i\u003e, with the quantity of which the\r\nelectrical force varies, and half of which flows over to\r\n\u003ci\u003eB\u003c/i\u003e. For, in the place of the new physical picture,\r\nthus, an old, familiar one is substituted, which moves\r\nspontaneously in its wonted courses.\u003c/p\u003e\r\n\r\n\u003cp\u003eAdhering to this idea, we define the \u003ci\u003eunit\u003c/i\u003e of electrical\r\nquantity, according to the now almost universally\r\nadopted centimetre-gramme-second (C. G. S.) system,\r\nas that quantity which at a distance of one centimetre\r\nrepels an equal quantity with unit of force, that\r\nis, with a force which in one second would impart to\r\na mass of one gramme a velocity-increment of a centimetre.\r\nAs a gramme mass acquires through the action\r\nof gravity a velocity-increment of about 981 centimetres\r\nin a second, accordingly, a gramme is attracted\r\nto the earth with 981, or, in round numbers, 1000 units\r\nof force of the centimetre-gramme-second system,\r\nwhile a milligramme-weight would strive to fall to the\r\nearth with approximately the unit force of this system.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe may easily obtain by this means a clear idea of\r\nwhat the unit quantity of electricity is. Two small\r\nbodies, \u003ci\u003eK\u003c/i\u003e, weighing each a gramme, are hung up by\r\nvertical threads, five metres in length and almost\r\nweightless, so as to touch each other. If the two bodies\r\nbe equally electrified and move apart upon electrification\r\nto a distance of one centimetre, their charge is approximately\r\nequivalent to the electrostatic unit of electric\r\nquantity, for the repulsion then holds in equilibrium\r\na gravitational force-component of approximately\r\none milligramme, which strives to bring the bodies together.\u003c/p\u003e\r\n\r\n\u003cp\u003eVertically beneath a small sphere suspended from\r\nthe equilibrated beam of a balance a second sphere is\r\nplaced at a distance of a centimetre. If both be equally\r\nelectrified the sphere suspended from the balance will\r\nbe rendered apparently lighter by the repulsion. If by\r\nadding a weight of one milligramme equilibrium is\r\nrestored, each of the spheres contains in round numbers\r\nthe electrostatic unit of electrical quantity.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn view of the fact that the same electrical bodies\r\nexert at different distances different forces upon one\r\nanother, exception might be taken to the measure of\r\nquantity here developed. What kind of a quantity is\r\nthat which now weighs more, and now weighs less, so\r\nto speak? But this apparent deviation from the\r\nmethod of determination commonly used in practical\r\nlife, that by weight, is, closely considered, an agreement.\r\nOn a high mountain a heavy mass also is less\r\npowerfully attracted to the earth than at the level of\r\nthe sea, and if it is permitted us in our determinations\r\nto neglect the consideration of level, it is only because\r\nthe comparison of a body with fixed conventional\r\nweights is invariably effected at the same level. In\r\nfact, if we were to make one of the two weights equilibrated\r\non our balance approach sensibly to the centre\r\nof the earth, by suspending it from a very long thread,\r\nas Prof. von Jolly of Munich suggested, we should\r\nmake the gravity of that weight, its heaviness, proportionately\r\ngreater.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us picture to ourselves, now, two different\r\nelectrical fluids, a positive and a negative fluid, of such\r\nnature that the particles of the one attract the particles\r\nof the other according to the law of the inverse squares,\r\nbut the particles of the same fluid repel each other by\r\nthe same law; in non-electrical bodies let us imagine\r\nthe two fluids uniformly distributed in equal quantities,\r\nin electric bodies one of the two in excess; in\r\nconductors, further, let us imagine the fluids mobile,\r\nin non-conductors immobile; having formed such pictures,\r\nwe possess the conception which Coulomb developed\r\nand to which he gave mathematical precision.\r\nWe have only to give this conception free play in our\r\nminds and we shall see as in a clear picture the fluid\r\nparticles, say of a positively charged conductor, receding\r\nfrom one another as far as they can, all making\r\nfor the surface of the conductor and there seeking out\r\nthe prominent parts and points until the greatest possible\r\namount of work has been performed. On increasing\r\nthe size of the surface, we see a dispersion,\r\non decreasing its size we see a condensation of the particles.\r\nIn a second, non-electrified conductor brought\r\ninto the vicinity of the first, we see the two fluids immediately\r\nseparate, the positive collecting itself on the\r\nremote and the negative on the adjacent side of its\r\nsurface. In the fact that this conception reproduces,\r\nlucidly and spontaneously, all the data which arduous\r\nresearch only slowly and gradually discovered, is contained\r\nits advantage and scientific value. With this,\r\ntoo, its value is exhausted. We must not seek in nature\r\nfor the two hypothetical fluids which we have\r\nadded as simple mental adjuncts, if we would not go\r\nastray. Coulomb\u0027s view may be replaced by a totally\r\ndifferent one, for example, by that of Faraday, and the\r\nmost proper course is always, after the general survey\r\nis obtained, to go back to the actual facts, to the electrical\r\nforces.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-124-1.jpg\" width=\"300\" height=\"310\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 29.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-124-2.jpg\" width=\"300\" height=\"276\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 30.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eWe will now make ourselves familiar with the concept\r\nof electrical quantity, and with the method of\r\nmeasuring or estimating it. Imagine a common Leyden\r\njar (Fig. 29), the inner and outer coatings of which\r\nare connected together by means of two common metallic\r\nknobs placed about a centimetre apart. If the\r\ninside coating be charged with the quantity of electricity\r\n+\u003ci\u003eq\u003c/i\u003e, on the outer coating a distribution of the\r\nelectricities will take place. A positive quantity almost\r\nequal\u003ca name=\"FNanchor_28_28\" id=\"FNanchor_28_28\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_28_28\" class=\"fnanchor\"\u003e[28]\u003c/a\u003e to the quantity +\u003ci\u003eq\u003c/i\u003e flows off to the earth, while\r\na corresponding quantity-\u003ci\u003eq\u003c/i\u003e is still left on the outer\r\ncoating. The knobs of the jar receive their portion of\r\nthese quantities and when the quantity \u003ci\u003eq\u003c/i\u003e is sufficiently\r\ngreat a rupture of the insulating air between the knobs,\r\naccompanied by the self-discharge of the jar, takes\r\nplace. For any given distance and size of the knobs,\r\na charge of a definite electric quantity \u003ci\u003eq\u003c/i\u003e is always necessary\r\nfor the spontaneous discharge of the jar.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us insulate, now, the outer coating of a Lane\u0027s\r\nunit jar \u003ci\u003eL\u003c/i\u003e, the jar just described, and put in connexion\r\nwith it the inner coating of a jar \u003ci\u003eF\u003c/i\u003e exteriorly connected\r\nwith the earth (Fig. 30). Every time that \u003ci\u003eL\u003c/i\u003e is\r\ncharged with +\u003ci\u003eq\u003c/i\u003e, a like quantity +\u003ci\u003eq\u003c/i\u003e is collected on\r\nthe inner coating of \u003ci\u003eF\u003c/i\u003e, and the spontaneous discharge\r\nof the jar \u003ci\u003eL\u003c/i\u003e, which is now\r\nagain empty, takes place. The\r\nnumber of the discharges of\r\nthe jar \u003ci\u003eL\u003c/i\u003e furnishes us, thus,\r\nwith a measure of the quantity\r\ncollected in the jar \u003ci\u003eF\u003c/i\u003e, and\r\nif after 1, 2, 3, … spontaneous\r\ndischarges of \u003ci\u003eL\u003c/i\u003e the jar \u003ci\u003eF\u003c/i\u003e is\r\ndischarged, it is evident that the charge of \u003ci\u003eF\u003c/i\u003e has been\r\nproportionately augmented.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-125.jpg\" width=\"300\" height=\"255\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 31.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eLet us supply now, to effect the spontaneous discharge,\r\nthe jar \u003ci\u003eF\u003c/i\u003e with knobs of the same size and\r\nat the same distance apart as those of the jar \u003ci\u003eL\u003c/i\u003e (Fig.\r\n31). If we find, then, that five discharges of the unit\r\njar take place before one spontaneous discharge of the\r\njar \u003ci\u003eF\u003c/i\u003e occurs, plainly the jar \u003ci\u003eF\u003c/i\u003e, for equal distances between\r\nthe knobs of the two jars, equal striking distances,\r\nis able to hold five times the quantity of electricity\r\nthat \u003ci\u003eL\u003c/i\u003e can, that is, has five times the \u003ci\u003ecapacity\u003c/i\u003e\r\nof \u003ci\u003eL\u003c/i\u003e.\u003ca name=\"FNanchor_29_29\" id=\"FNanchor_29_29\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_29_29\" class=\"fnanchor\"\u003e[29]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 400px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-126.jpg\" width=\"400\" height=\"345\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 32.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eWe will now replace the unit jar \u003ci\u003eL\u003c/i\u003e, with which we\r\nmeasure electricity, so to speak, \u003ci\u003einto\u003c/i\u003e the jar \u003ci\u003eF\u003c/i\u003e, by a\r\nFranklin\u0027s pane, consisting of two parallel flat metal\r\nplates (Fig. 32), separated only by air. If here, for\r\nexample, thirty spontaneous discharges of the pane are\r\nsufficient to fill the jar, ten discharges will be found\r\nsufficient if the air-space between the two plates be\r\nfilled with a cake of sulphur. Hence, the capacity\r\nof a Franklin\u0027s pane of sulphur is about three times\r\ngreater than that of one of the same shape and size\r\nmade of air, or, as it is the custom to say, the specific\r\ninductive capacity of sulphur (that of air being taken\r\nas the unit) is about 3.\u003ca name=\"FNanchor_30_30\" id=\"FNanchor_30_30\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_30_30\" class=\"fnanchor\"\u003e[30]\u003c/a\u003e We are here arrived at a\r\nvery simple fact, which clearly shows us the significance\r\nof the number called \u003ci\u003edielectric constant\u003c/i\u003e, or \u003ci\u003especific\r\ninductive capacity\u003c/i\u003e, the knowledge of which is so important\r\nfor the theory of submarine cables.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us consider a jar \u003ci\u003eA\u003c/i\u003e, which is charged with a\r\ncertain quantity of electricity. We can discharge the\r\njar directly. But we can also discharge the jar \u003ci\u003eA\u003c/i\u003e\r\n(Fig. 33) partly into a jar \u003ci\u003eB\u003c/i\u003e, by connecting the two\r\nouter coatings with each other. In this operation a\r\nportion of the quantity of electricity passes, accompanied\r\nby sparks, into the jar \u003ci\u003eB\u003c/i\u003e, and we now find both\r\njars charged.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-127-1.jpg\" width=\"300\" height=\"283\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 33.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-127-s.jpg\" width=\"300\" height=\"214\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 34.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eIt may be shown as follows that the conception of\r\na constant quantity of electricity can be regarded as\r\nthe expression of a pure fact. Picture to yourself any\r\nsort of electrical conductor (Fig. 34); cut it up into a\r\nlarge number of small pieces, and place these pieces by\r\nmeans of an insulated rod at a distance of one centimetre\r\nfrom an electrical body which acts with unit of\r\nforce on an equal and like-constituted body at the\r\nsame distance. Take the sum of the forces which\r\nthis last body exerts on the single pieces of the conductor.\r\nThe sum of these forces will be the quantity\r\nof electricity on the whole conductor. It remains the\r\nsame, whether we change the form and the size of the\r\nconductor, or whether we bring it near or move it\r\naway from a second electrical conductor, so long as we\r\nkeep it insulated, that is, do not discharge it.\u003c/p\u003e\r\n\r\n\u003cp\u003eA basis of reality for the notion of electric quantity\r\nseems also to present itself from another quarter.\r\nIf a current, that is, in the usual view, a definite\r\nquantity of electricity per second, is sent through a\r\ncolumn of acidulated water; in the direction of the\r\npositive stream, hydrogen, but in the opposite direction,\r\noxygen is liberated at the extremities of the column.\r\nFor a given quantity of electricity a given quantity\r\nof oxygen appears. You may picture the column\r\nof water as a column of hydrogen and a column of\r\noxygen, fitted into each other, and may say the electric\r\ncurrent is a chemical current and \u003ci\u003evice versa\u003c/i\u003e. Although\r\nthis notion is more difficult to adhere to in the field of\r\nstatical electricity and with non-decomposable conductors,\r\nits further development is by no means hopeless.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe concept quantity of electricity, thus, is not so\r\naerial as might appear, but is able to conduct us with\r\ncertainty through a multitude of varied phenomena,\r\nand is suggested to us by the facts in almost palpable\r\nform. We can collect electrical force in a body, measure\r\nit out with one body\r\ninto another, carry it\r\nover from one body into\r\nanother, just as we can\r\ncollect a liquid in a vessel,\r\nmeasure it out with\r\none vessel into another,\r\nor pour it from one into\r\nanother.\u003c/p\u003e\r\n\r\n\u003cp\u003eFor the analysis of\r\nmechanical phenomena,\r\na metrical notion, derived\r\nfrom experience,\r\nand bearing the designation \u003ci\u003ework\u003c/i\u003e, has proved itself\r\nuseful. A machine can be set in motion only when\r\nthe forces acting on it can perform work.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 350px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-129.jpg\" width=\"350\" height=\"431\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 35.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eLet us consider, for example, a wheel and axle\r\n(Fig. 35) having the radii 1 and 2 metres, loaded respectively\r\nwith the weights 2 and 1 kilogrammes. On\r\nturning the wheel and axle, the 1 kilogramme-weight,\r\nlet us say, sinks two metres, while the 2 kilogramme-weight\r\nrises one metre. On both sides the product\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003eKGR. M. KGR. M.\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e 1 × 2 = 2 × 1.\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eis equal. So long as this is so, the wheel and axle will\r\nnot move of itself. But if we take such loads, or so\r\nchange the radii of the wheels, that this product (kgr.\r\n× metre) on displacement is in excess on one side,\r\nthat side will sink. As we see, this product is characteristic\r\nfor mechanical events, and for this reason has\r\nbeen invested with a special name, \u003ci\u003ework\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn all mechanical processes, and as all physical\r\nprocesses present a mechanical side, in all physical\r\nprocesses, work plays a determinative part. Electrical\r\nforces, also, produce only changes in which work is performed.\r\nTo the extent that forces come into play in\r\nelectrical phenomena, electrical phenomena, be they\r\nwhat they may, extend into the domain of mechanics\r\nand are subject to the laws which hold in this domain.\r\nThe universally adopted measure of work,\r\nnow, is the product of the force into the distance\r\nthrough which it acts, and in the C. G. S. system, the\r\nunit of work is the action through one centimetre of\r\na force which would impart in one second to a\r\ngramme-mass a velocity-increment of one centimetre,\r\nthat is, in round numbers, the action through a centimetre\r\nof a pressure equal to the weight of a milligramme.\r\nFrom a positively charged body, electricity,\r\nyielding to the force of repulsion and performing work,\r\nflows off to the earth, providing conducting connexions\r\nexist. To a negatively charged body, on the other\r\nhand, the earth under the same circumstances gives\r\noff positive electricity. The electrical work possible\r\nin the interaction of a body with the earth, characterises\r\nthe electrical condition of that body. We will call\r\nthe work which must be expended on the unit quantity\r\nof positive electricity to raise it from the earth to the\r\nbody \u003ci\u003eK\u003c/i\u003e the \u003ci\u003epotential\u003c/i\u003e of the body \u003ci\u003eK\u003c/i\u003e.\u003ca name=\"FNanchor_31_31\" id=\"FNanchor_31_31\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_31_31\" class=\"fnanchor\"\u003e[31]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eWe ascribe to the body \u003ci\u003eK\u003c/i\u003e in the C. G. S. system\r\nthe potential +1, if we must expend the unit of work\r\nto raise the positive electrostatic unit of electric quantity\r\nfrom the earth to that body; the potential -1, if\r\nwe gain in this procedure the unit of work; the potential\r\n0, if no work at all is performed in the operation.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe different parts of one and the same electrical\r\nconductor in electrical equilibrium have the same potential,\r\nfor otherwise the electricity would perform\r\nwork and move about upon the conductor, and equilibrium\r\nwould not have existed. Different conductors of\r\nequal potential, put in connexion with one another, do\r\nnot exchange electricity any more than bodies of equal\r\ntemperature in contact exchange heat, or in connected\r\nvessels, in which the same pressures exist, liquids\r\nflow from one vessel to the other. Exchange of electricity\r\ntakes place only between conductors of different\r\npotentials, but in conductors of given form and position\r\na definite difference of potential is necessary for\r\na spark, which pierces the insulating air, to pass\r\nbetween them.\u003c/p\u003e\r\n\r\n\u003cp\u003eOn being connected, every two conductors assume\r\nat once the same potential. With this the means\r\nis given of determining the potential of a conductor\r\nthrough the agency of a second conductor expressly\r\nadapted to the purpose called an electrometer, just as\r\nwe determine the temperature of a body with a thermometer.\r\nThe values of the potentials of bodies obtained\r\nin this way simplify vastly our analysis of their\r\nelectrical behavior, as will be evident from what has\r\nbeen said.\u003c/p\u003e\r\n\r\n\u003cp\u003eThink of a positively charged conductor. Double\r\nall the electrical forces exerted by this conductor on a\r\npoint charged with unit quantity, that is, double the\r\nquantity at each point, or what is the same thing,\r\ndouble the total charge. Plainly, equilibrium still subsists.\r\nBut carry, now, the positive electrostatic unit\r\ntowards the conductor. Everywhere we shall have to\r\novercome double the force of repulsion we did before,\r\neverywhere we shall have to expend double the work.\r\nBy doubling the charge of the conductor a double potential\r\nhas been produced. Charge and potential go\r\nhand in hand, are proportional. Consequently, calling\r\nthe total quantity of electricity of a conductor \u003ci\u003eQ\u003c/i\u003e\r\nand its potential \u003ci\u003eV\u003c/i\u003e, we can write: \u003ci\u003eQ\u003c/i\u003e = \u003ci\u003eCV\u003c/i\u003e, where \u003ci\u003eC\u003c/i\u003e\r\nstands for a constant, the import of which will be understood\r\nsimply from noting that \u003ci\u003eC\u003c/i\u003e = \u003ci\u003eQ\u003c/i\u003e/\u003ci\u003eV\u003c/i\u003e.\u003ca name=\"FNanchor_32_32\" id=\"FNanchor_32_32\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_32_32\" class=\"fnanchor\"\u003e[32]\u003c/a\u003e But the\r\ndivision of a number representing the units of quantity\r\nof a conductor by the number representing its\r\nunits of potential tells us the quantity which falls to\r\nthe share of the unit of potential. Now the number\r\n\u003ci\u003eC\u003c/i\u003e here we call the capacity of a conductor, and have\r\nsubstituted, thus, in the place of the old relative determination\r\nof capacity, an absolute determination.\u003ca name=\"FNanchor_33_33\" id=\"FNanchor_33_33\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_33_33\" class=\"fnanchor\"\u003e[33]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eIn simple cases the connexion between charge, potential,\r\nand capacity is easily ascertained. Our conductor,\r\nlet us say, is a sphere of radius \u003ci\u003er\u003c/i\u003e, suspended\r\nfree in a large body of air. There being no other conductors\r\nin the vicinity, the charge \u003ci\u003eq\u003c/i\u003e will then distribute\r\nitself uniformly upon the surface of the sphere, and\r\nsimple geometrical considerations yield for its potential\r\nthe expression \u003ci\u003eV\u003c/i\u003e = \u003ci\u003eq\u003c/i\u003e/\u003ci\u003er\u003c/i\u003e. Hence, \u003ci\u003eq\u003c/i\u003e/\u003ci\u003eV\u003c/i\u003e = \u003ci\u003er\u003c/i\u003e; that is,\r\nthe capacity of a sphere is measured by its radius, and\r\nin the C. G. S. system in centimetres.\u003ca name=\"FNanchor_34_34\" id=\"FNanchor_34_34\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_34_34\" class=\"fnanchor\"\u003e[34]\u003c/a\u003e It is clear\r\nalso, since a potential is a quantity divided by a length,\r\nthat a quantity divided by a potential must be a length.\u003c/p\u003e\r\n\r\n\u003cp\u003eImagine (Fig. 36) a jar composed of two concentric\r\nconductive spherical shells of the radii \u003ci\u003er\u003c/i\u003e and \u003ci\u003er\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e,\r\nhaving only air between them. Connecting the outside\r\nsphere with the earth, and charging the inside\r\nsphere by means of a thin, insulated wire passing\r\nthrough the first, with the quantity \u003ci\u003eQ\u003c/i\u003e, we shall have\r\n\u003ci\u003eV\u003c/i\u003e = (\u003ci\u003er\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e-\u003ci\u003er\u003c/i\u003e)/(\u003ci\u003er\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e\u003ci\u003er\u003c/i\u003e)\u003ci\u003eQ\u003c/i\u003e, and for the capacity in this case\r\n(\u003ci\u003er\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e\u003ci\u003er\u003c/i\u003e)/(\u003ci\u003er\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e-\u003ci\u003er\u003c/i\u003e), or, to take\r\na specific example, if \u003ci\u003er\u003c/i\u003e = 16\r\nand \u003ci\u003er\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e = 19, a capacity of\r\nabout 100 centimetres.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 350px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-134.jpg\" width=\"350\" height=\"352\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 36.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eWe shall now use these\r\nsimple cases for illustrating\r\nthe principle by which\r\ncapacity and potential are\r\ndetermined. First, it is\r\nclear that we can use the\r\njar composed of concentric spheres with its known capacity\r\nas our unit jar and by means of this ascertain,\r\nin the manner above laid down, the capacity of any\r\ngiven jar \u003ci\u003eF\u003c/i\u003e. We find, for example, that 37 discharges\r\nof this unit jar of the capacity 100, just charges the\r\njar investigated at the same striking distance, that is,\r\nat the same potential. Hence, the capacity of the jar\r\ninvestigated is 3700 centimetres. The large battery\r\nof the Prague physical laboratory, which consists of\r\nsixteen such jars, all of nearly equal size, has a capacity,\r\ntherefore, of something like 50,000 centimetres,\r\nor the capacity of a sphere, a kilometre in diameter,\r\nfreely suspended in atmospheric space. This remark\r\ndistinctly shows us the great superiority which Leyden\r\njars possess for the storage of electricity as compared\r\nwith common conductors. In fact, as Faraday pointed\r\nout, jars differ from simple conductors mainly by their\r\ngreat capacity.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 450px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-135.jpg\" width=\"450\" height=\"356\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 37.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eFor determining potential, imagine the inner coating\r\nof a jar \u003ci\u003eF\u003c/i\u003e, the outer coating of which communicates\r\nwith the ground, connected by a long, thin wire\r\nwith a conductive sphere \u003ci\u003eK\u003c/i\u003e placed free in a large atmospheric\r\nspace, compared with whose dimensions\r\nthe radius of the sphere vanishes. (Fig. 37.) The\r\njar and the sphere assume at once the same potential.\r\nBut on the surface of the sphere, if that be sufficiently\r\nfar removed from all other conductors, a uniform layer\r\nof electricity will be found. If the sphere, having the\r\nradius \u003ci\u003er\u003c/i\u003e, contains the charge \u003ci\u003eq\u003c/i\u003e, its potential is \u003ci\u003eV\u003c/i\u003e = \u003ci\u003eq\u003c/i\u003e/\u003ci\u003er\u003c/i\u003e.\r\nIf the upper half of the sphere be severed from the\r\nlower half and equilibrated on a balance with one of\r\nwhose beams it is connected by silk threads, the upper\r\nhalf will be repelled from the lower half with the force\r\n\u003ci\u003eP\u003c/i\u003e = \u003ci\u003eq\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e/8\u003ci\u003er\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e = 1/8\u003ci\u003eV\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e. This repulsion \u003ci\u003eP\u003c/i\u003e may be counter-balanced\r\nby additional weights placed on the beam-end,\r\nand so ascertained. The potential is then \u003ci\u003eV\u003c/i\u003e =\r\n\u0026#8730;(8\u003ci\u003eP\u003c/i\u003e).\u003ca name=\"FNanchor_35_35\" id=\"FNanchor_35_35\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_35_35\" class=\"fnanchor\"\u003e[35]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThat the potential is proportional to the square\r\nroot of the force is not difficult to see. A doubling or\r\ntrebling of the potential means that the charge of all\r\nthe parts is doubled or trebled; hence their combined\r\npower of repulsion quadrupled or nonupled.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us consider a special case. I wish to produce\r\nthe potential 40 on the sphere. What additional weight\r\nmust I give to the half sphere in grammes that the\r\nforce of repulsion shall maintain the balance in exact\r\nequilibrium? As a gramme weight is approximately\r\nequivalent to 1000 units of force, we have only the\r\nfollowing simple example to work out: 40×40 = 8×\r\n1000.\u003ci\u003ex\u003c/i\u003e, where \u003ci\u003ex\u003c/i\u003e stands for the number of grammes.\r\nIn round numbers we get \u003ci\u003ex\u003c/i\u003e = 0.2 gramme. I charge\r\nthe jar. The balance is deflected; I have reached,\r\nor rather passed, the potential 40, and you see when I\r\ndischarge the jar the associated spark.\u003ca name=\"FNanchor_36_36\" id=\"FNanchor_36_36\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_36_36\" class=\"fnanchor\"\u003e[36]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe striking distance between the knobs of a machine\r\nincreases with the difference of the potential,\r\nalthough not proportionately to that difference. The\r\nstriking distance increases faster than the potential\r\ndifference. For a distance between the knobs of one\r\ncentimetre on this machine the difference of potential\r\nis 110. It can easily be increased tenfold. Of the\r\ntremendous differences of potential which occur in\r\nnature some idea may be obtained from the fact that\r\nthe striking distances of lightning in thunder-storms\r\nis counted by miles. The differences of potential in\r\ngalvanic batteries are considerably smaller than those\r\nof our machine, for it takes fully one hundred elements\r\nto give a spark of microscopic striking distance.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_128\" id=\"Page_128\"\u003e[Pg 128]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_129\" id=\"Page_129\"\u003e[Pg 129]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_130\" id=\"Page_130\"\u003e[Pg 130]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_131\" id=\"Page_131\"\u003e[Pg 131]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_132\" id=\"Page_132\"\u003e[Pg 132]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_133\" id=\"Page_133\"\u003e[Pg 133]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_134\" id=\"Page_134\"\u003e[Pg 134]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eWe shall now employ the ideas reached to shed\r\nsome light upon another important relation between\r\nelectrical and mechanical phenomena. We shall investigate\r\nwhat is the potential \u003ci\u003eenergy\u003c/i\u003e, or the \u003ci\u003estore of\r\nwork\u003c/i\u003e, contained in a charged conductor, for example,\r\nin a jar.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we bring a quantity of electricity up to a conductor,\r\nor, to speak less pictorially, if we generate by\r\nwork electrical force in a conductor, this force is able\r\nto produce anew the work by which it was generated.\r\nHow great, now, is the energy or capacity for work of\r\na conductor of known charge \u003ci\u003eQ\u003c/i\u003e and known potential\r\n\u003ci\u003eV\u003c/i\u003e?\u003c/p\u003e\r\n\r\n\u003cp\u003eImagine the given charge \u003ci\u003eQ\u003c/i\u003e divided into very small\r\nparts \u003ci\u003eq\u003c/i\u003e, \u003ci\u003eq\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003eq\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e …, and these little parts successively\r\ncarried up to the conductor. The first very small\r\nquantity \u003ci\u003eq\u003c/i\u003e is brought up without any appreciable work\r\nand produces by its presence a small potential \u003ci\u003eV\u003c/i\u003e\u003csub\u003e\u0027\u003c/sub\u003e. To\r\nbring up the second quantity, accordingly, we must do\r\nthe work \u003ci\u003eq\u003c/i\u003e\u003csub\u003e\u0027\u003c/sub\u003e\u003ci\u003eV\u003c/i\u003e\u003csub\u003e\u0027\u003c/sub\u003e, and similarly for the quantities which\r\nfollow the work \u003ci\u003eq\u003c/i\u003e\u003csub\u003e\u0027\u0027\u003c/sub\u003e\u003ci\u003eV\u003c/i\u003e\u003csub\u003e\u0027\u0027\u003c/sub\u003e, \u003ci\u003eq\u003c/i\u003e\u003csub\u003e\u0027\u0027\u0027\u003c/sub\u003e\u003ci\u003eV\u003c/i\u003e\u003csub\u003e\u0027\u0027\u0027\u003c/sub\u003e, and so forth. Now,\r\nas the potential rises proportionately to the quantities\r\nadded until the value \u003ci\u003eV\u003c/i\u003e is reached, we have, agreeably\r\nto the graphical representation of Fig. 38, for the\r\ntotal work performed,\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003ci\u003eW\u003c/i\u003e = 1/2\u003ci\u003eQV\u003c/i\u003e,\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003ewhich corresponds to the total energy of the charged\r\nconductor. Using the equation \u003ci\u003eQ\u003c/i\u003e = \u003ci\u003eCV\u003c/i\u003e, where \u003ci\u003eC\u003c/i\u003e\r\nstands for capacity, we also have,\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003ci\u003eW\u003c/i\u003e = 1/2\u003ci\u003eCV\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e, or \u003ci\u003eW\u003c/i\u003e = \u003ci\u003eQ\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e/2\u003ci\u003eC\u003c/i\u003e.\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will be helpful, perhaps, to elucidate this idea\r\nby an analogy from the province of mechanics. If we\r\npump a quantity of liquid, \u003ci\u003eQ\u003c/i\u003e, gradually into a cylindrical\r\nvessel (Fig. 39), the level of the liquid in the\r\nvessel will gradually rise. The more we have pumped\r\nin, the greater the pressure we must overcome, or the\r\nhigher the level to which we must lift the liquid. The\r\nstored-up work is rendered again available when the\r\nheavy liquid \u003ci\u003eQ\u003c/i\u003e, which reaches up to the level \u003ci\u003eh\u003c/i\u003e, flows\r\nout. This work \u003ci\u003eW\u003c/i\u003e corresponds to the fall of the whole\r\nliquid weight \u003ci\u003eQ\u003c/i\u003e, through the distance \u003ci\u003eh\u003c/i\u003e/2 or through\r\nthe altitude of its centre of gravity. We have\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003ci\u003eW\u003c/i\u003e = 1/2\u003ci\u003eQh\u003c/i\u003e.\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eFurther, since \u003ci\u003eQ\u003c/i\u003e = \u003ci\u003eKh\u003c/i\u003e, or since the weight of the\r\nliquid and the height \u003ci\u003eh\u003c/i\u003e are proportional, we get also\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003ci\u003eW\u003c/i\u003e = 1/2\u003ci\u003eKh\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e and \u003ci\u003eW\u003c/i\u003e = \u003ci\u003eQ\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e/2\u003ci\u003eK\u003c/i\u003e.\r\n\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-139-1.jpg\" width=\"300\" height=\"208\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 38.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-139-2.jpg\" width=\"300\" height=\"283\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 39.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eAs a special case let us consider our jar. Its capacity\r\nis \u003ci\u003eC\u003c/i\u003e = 3700, its potential \u003ci\u003eV\u003c/i\u003e = 110; accordingly,\r\nits quantity \u003ci\u003eQ\u003c/i\u003e = \u003ci\u003eCV\u003c/i\u003e = 407,000 electrostatic units and\r\nits energy \u003ci\u003eW\u003c/i\u003e = 1/2\u003ci\u003eQV\u003c/i\u003e = 22,385,000 C. G. S. units of\r\nwork.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe unit of work of the C. G. S. system is not readily\r\nappreciable by the senses, nor does it well admit of\r\nrepresentation, as we are accustomed to work with\r\nweights. Let us adopt, therefore, as our unit of work\r\nthe gramme-centimetre, or the gravitational pressure\r\nof a gramme-weight through the distance of a centimetre,\r\nwhich in round numbers is 1000 times greater\r\nthan the unit assumed above; in this case, our numerical\r\nresult will be approximately 1000 times smaller.\r\nAgain, if we pass, as more familiar in practice, to the\r\nkilogramme-metre as our unit of work, our unit, the\r\ndistance being increased a hundred fold, and the weight\r\na thousand fold, will be 100,000 times larger. The\r\nnumerical result expressing the work done is in this\r\ncase 100,000 times less, being in round numbers 0.22\r\nkilogramme-metre. We can obtain a clear idea of the\r\nwork done here by letting a kilogramme-weight fall 22\r\ncentimetres.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis amount of work, accordingly, is performed on\r\nthe charging of the jar, and on its discharge appears\r\nagain, according to the circumstances, partly as sound,\r\npartly as a mechanical disruption of insulators, partly\r\nas light and heat, and so forth.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe large battery of the Prague physical laboratory,\r\nwith its sixteen jars charged to equal potentials,\r\nfurnishes, although the effect of the discharge is imposing,\r\na total amount of work of only three kilogramme-metres.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the development of the ideas above laid down\r\nwe are not restricted to the method there pursued; in\r\nfact, that method was selected only as one especially\r\nfitted to familiarise us with the phenomena. On the\r\ncontrary, the connexion of the physical processes is so\r\nmultifarious that we can come at the same event from\r\nvery different directions. Particularly are electrical\r\nphenomena connected with all other physical events;\r\nand so intimate is this connexion that we might justly\r\ncall the study of electricity the theory of the general\r\nconnexion of physical processes.\u003c/p\u003e\r\n\r\n\u003cp\u003eWith respect to the principle of the conservation\r\nof energy which unites electrical with mechanical phenomena,\r\nI should like to point out briefly two ways of\r\nfollowing up the study of this connexion.\u003c/p\u003e\r\n\r\n\u003cp\u003eA few years ago Professor Rosetti, taking an influence-machine,\r\nwhich he set in motion by means of\r\nweights alternately in the electrical and non-electrical\r\ncondition with the same velocities, determined the\r\nmechanical work expended in the two cases and was\r\nthus enabled, after deducting the work of friction, to\r\nascertain the mechanical work consumed in the development\r\nof the electricity.\u003c/p\u003e\r\n\r\n\u003cp\u003eI myself have made this experiment in a modified,\r\nand, as I think, more advantageous form. Instead\r\nof determining the work of friction by special trial, I\r\narranged my apparatus so that it was eliminated of itself\r\nin the measurement and could consequently be\r\nneglected. The so-called fixed disk of the machine, the\r\naxis of which is placed vertically, is suspended somewhat\r\nlike a chandelier by three vertical threads of\r\nequal lengths \u003ci\u003el\u003c/i\u003e at a distance \u003ci\u003er\u003c/i\u003e from the axis. Only\r\nwhen the machine is excited does this fixed disk, which\r\nrepresents a Prony\u0027s brake, receive, through its reciprocal\r\naction with the rotating disk, a deflexion \u003ci\u003e\u0026#945;\u003c/i\u003e and a\r\nmoment of torsion which is expressed by \u003ci\u003eD\u003c/i\u003e = \u003ci\u003e(Pr\u003csup\u003e2\u003c/sup\u003e/l)\u0026#945;\u003c/i\u003e,\r\nwhere \u003ci\u003eP\u003c/i\u003e is the weight of the disk.\u003ca name=\"FNanchor_37_37\" id=\"FNanchor_37_37\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_37_37\" class=\"fnanchor\"\u003e[37]\u003c/a\u003e The angle \u003ci\u003e\u0026#945;\u003c/i\u003e is\r\ndetermined by a mirror set in the disk. The work expended\r\nin \u003ci\u003en\u003c/i\u003e rotations is given by \u003ci\u003e2n\u0026#960;D\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we close the machine, as Rosetti did, we obtain\r\na continuous current which has all the properties of a\r\nvery weak galvanic current; for example, it produces a\r\ndeflexion in a multiplier which we interpose, and so\r\nforth. We can directly ascertain, now, the mechanical\r\nwork expended in the maintenance of this current.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we charge a jar by means of a machine, the energy\r\nof the jar employed in the production of sparks,\r\nin the disruption of the insulators, etc., corresponds\r\nto a part only of the mechanical work expended, a\r\nsecond part of it being consumed in the arc which\r\nforms the circuit.\u003ca name=\"FNanchor_38_38\" id=\"FNanchor_38_38\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_38_38\" class=\"fnanchor\"\u003e[38]\u003c/a\u003e This machine, with the interposed\r\njar, affords in miniature a picture of the transference\r\nof force, or more properly of work. And in fact nearly\r\nthe same laws hold here for the economical coefficient\r\nas obtain for large dynamo-machines.\u003c/p\u003e\r\n\r\n\u003cp\u003eAnother means of investigating electrical energy is\r\nby its transformation into heat. A long time ago\r\n(1838), before the mechanical theory of heat had attained\r\nits present popularity, Riess performed experiments\r\nin this field with the help of his electrical\r\nair-thermometer or thermo-electrometer.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 200px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-143.jpg\" width=\"200\" height=\"320\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 40.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eIf the discharge be conducted\r\nthrough a fine wire\r\npassing through the globe of\r\nthe air-thermometer, a development\r\nof heat is observed\r\nproportional to the expression\r\nabove-discussed \u003ci\u003eW\u003c/i\u003e = 1/2\u003ci\u003eQV\u003c/i\u003e.\r\nAlthough the total energy has\r\nnot yet been transformed\r\ninto measurable heat by this\r\nmeans, in as much as a portion\r\nis left behind in the spark in the air outside the thermometer,\r\nstill everything tends to show that the total\r\nheat developed in all parts of the conductor and along\r\nall the paths of discharge is the equivalent of the work\r\n1/2\u003ci\u003eQV\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is not important here whether the electrical energy\r\nis transformed all at once or partly, by degrees.\r\nFor example, if of two equal jars one is charged with\r\nthe quantity \u003ci\u003eQ\u003c/i\u003e at the potential \u003ci\u003eV\u003c/i\u003e the energy present\r\nis 1/2\u003ci\u003eQV\u003c/i\u003e. If the first jar be discharged into the second,\r\n\u003ci\u003eV\u003c/i\u003e, since the capacity is now doubled, falls to \u003ci\u003eV\u003c/i\u003e/2.\r\nAccordingly, the energy 1/4\u003ci\u003eQV\u003c/i\u003e remains, while 1/4\u003ci\u003eQV\u003c/i\u003e is\r\ntransformed in the spark of discharge into heat. The\r\nremainder, however, is equally distributed between\r\nthe two jars so that each on discharge is still able to\r\ntransform 1/8\u003ci\u003eQV\u003c/i\u003e into heat.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_135\" id=\"Page_135\"\u003e[Pg 135]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_136\" id=\"Page_136\"\u003e[Pg 136]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_137\" id=\"Page_137\"\u003e[Pg 137]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eWe have here discussed electricity in the limited\r\nphenomenal form in which it was known to the inquirers\r\nbefore Volta, and which has been called, perhaps\r\nnot very felicitously, \"statical electricity.\" It is\r\nevident, however, that the nature of electricity is everywhere\r\none and the same; that a substantial difference\r\nbetween statical and galvanic electricity does not exist.\r\nOnly the quantitative circumstances in the two provinces\r\nare so widely different that totally new aspects\r\nof phenomena may appear in the second, for example,\r\nmagnetic effects, which in the first remained unnoticed,\r\nwhilst, \u003ci\u003evice versa\u003c/i\u003e, in the second field statical attractions\r\nand repulsions are scarcely appreciable. As a fact,\r\nwe can easily show the magnetic effect of the current\r\nof discharge of an influence-machine on the galvanoscope\r\nalthough we could hardly have made the original\r\ndiscovery of the magnetic effects with this current.\r\nThe statical distant action of the wire poles of\r\na galvanic element also would hardly have been noticed\r\nhad not the phenomenon been known from a\r\ndifferent quarter in a striking form.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we wished to characterise the two fields in their\r\nchief and most general features, we should say that in\r\nthe first, high potentials and small quantities come\r\ninto play, in the second small potentials and large\r\nquantities. A jar which is discharging and a galvanic\r\nelement deport themselves somewhat like an air-gun\r\nand the bellows of an organ. The first gives forth\r\nsuddenly under a very high pressure a small quantity\r\nof air; the latter liberates gradually under a very slight\r\npressure a large quantity of air.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn point of principle, too, nothing prevents our retaining\r\nthe electrostatical units in the domain of galvanic\r\nelectricity and in measuring, for example, the\r\nstrength of a current by the number of electrostatic\r\nunits which flow per second through its cross-section.\r\nBut this would be in a double aspect impractical. In\r\nthe first place, we should totally neglect the magnetic\r\nfacilities for measurement so conveniently offered by\r\nthe current, and substitute for this easy means a method\r\nwhich can be applied only with difficulty and is not\r\ncapable of great exactness. In the second place our\r\nunits would be much too small, and we should find\r\nourselves in the predicament of the astronomer who\r\nattempted to measure celestial distances in metres instead\r\nof in radii of the earth and the earth\u0027s orbit; for\r\nthe current which by the magnetic C. G. S. standard\r\nrepresents the unit, would require a flow of some\r\n30,000,000,000 electrostatic units per second through\r\nits cross-section. Accordingly, different units must\r\nbe adopted here. The development of this point, however,\r\nlies beyond my present task.\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_THE_PRINCIPLE_OF_THE_CONSERVATION\" id=\"ON_THE_PRINCIPLE_OF_THE_CONSERVATION\"\u003eON THE PRINCIPLE OF THE CONSERVATION\r\nOF ENERGY.\u003c/a\u003e\u003ca name=\"FNanchor_39_39\" id=\"FNanchor_39_39\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_39_39\" class=\"fnanchor\"\u003e[39]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eIn a popular lecture, distinguished for its charming\r\nsimplicity and clearness, which Joule delivered in\r\nthe year 1847,\u003ca name=\"FNanchor_40_40\" id=\"FNanchor_40_40\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_40_40\" class=\"fnanchor\"\u003e[40]\u003c/a\u003e that famous physicist declares that the\r\nliving force which a heavy body has acquired by its\r\ndescent through a certain height and which it carries\r\nwith it in the form of the velocity with which it is impressed,\r\nis the \u003ci\u003eequivalent\u003c/i\u003e of the attraction of gravity\r\nthrough the space fallen through, and that it would be\r\n\"absurd\" to assume that this living force could be destroyed\r\nwithout some restitution of that equivalent.\r\nHe then adds: \"You will therefore be surprised to\r\nhear that until very \u003ci\u003erecently\u003c/i\u003e the universal opinion has\r\nbeen that living force could be absolutely and irrevocably\r\ndestroyed at any one\u0027s option.\" Let us add\r\nthat to-day, after forty-seven years, the \u003ci\u003elaw of the conservation\r\nof energy\u003c/i\u003e, wherever civilisation exists, is accepted\r\nas a fully established truth and receives the\r\nwidest applications in all domains of natural science.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_138\" id=\"Page_138\"\u003e[Pg 138]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003eThe fate of all momentous discoveries is similar.\r\nOn their first appearance they are regarded by the\r\nmajority of men as errors. J. R. Mayer\u0027s work on the\r\nprinciple of energy (1842) was rejected by the first\r\nphysical journal of Germany; Helmholtz\u0027s treatise\r\n(1847) met with no better success; and even Joule, to\r\njudge from an intimation of Playfair, seems to have\r\nencountered difficulties with his first publication (1843).\r\nGradually, however, people are led to see that the new\r\nview was long prepared for and ready for enunciation,\r\nonly that a few favored minds had perceived it much\r\nearlier than the rest, and in this way the opposition of\r\nthe majority is overcome. With proofs of the fruitfulness\r\nof the new view, with its success, confidence\r\nin it increases. The majority of the men who employ\r\nit cannot enter into a deep-going analysis of it; for\r\nthem, its success is its proof. It can thus happen that\r\na view which has led to the greatest discoveries, like\r\nBlack\u0027s theory of caloric, in a subsequent period in a\r\nprovince where it does not apply may actually become\r\nan obstacle to progress by its blinding our eyes to facts\r\nwhich do not fit in with our favorite conceptions. If\r\na theory is to be protected from this dubious rôle, the\r\ngrounds and motives of its evolution and existence\r\nmust be examined from time to time with the utmost\r\ncare.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe most multifarious physical changes, thermal,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_139\" id=\"Page_139\"\u003e[Pg 139]\u003c/a\u003e\u003c/span\u003e\r\nelectrical, chemical, and so forth, can be brought\r\nabout by mechanical work. When such alterations\r\nare reversed they yield anew the mechanical work in\r\nexactly the quantity which was required for the production\r\nof the part reversed. This is the \u003ci\u003eprinciple of\r\nthe conservation of energy\u003c/i\u003e; \"energy\" being the term\r\nwhich has gradually come into use for that \"indestructible\r\nsomething\" of which the measure is mechanical\r\n\u003ci\u003ework\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eHow did we acquire this idea? What are the\r\nsources from which we have drawn it? This question\r\nis not only of interest in itself, but also for the important\r\nreason above touched upon. The opinions which\r\nare held concerning the foundations of the law of energy\r\nstill diverge very widely from one another. Many\r\ntrace the principle to the impossibility of a perpetual\r\nmotion, which they regard either as sufficiently proved\r\nby experience, or as self-evident. In the province of\r\npure mechanics the impossibility of a perpetual motion,\r\nor the continuous production of \u003ci\u003ework\u003c/i\u003e without\r\nsome \u003ci\u003epermanent\u003c/i\u003e alteration, is easily demonstrated. Accordingly,\r\nif we start from the theory that all physical\r\nprocesses are purely \u003ci\u003emechanical\u003c/i\u003e processes, motions of\r\nmolecules and atoms, we embrace also, by this \u003ci\u003emechanical\u003c/i\u003e\r\nconception of physics, the impossibility of a\r\nperpetual motion in the \u003ci\u003ewhole\u003c/i\u003e physical domain. At\r\npresent this view probably counts the most adherents.\r\nOther inquirers, however, are for accepting only a\r\npurely \u003ci\u003eexperimental\u003c/i\u003e establishment of the law of energy.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_140\" id=\"Page_140\"\u003e[Pg 140]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will appear, from the discussion to follow, that\r\n\u003ci\u003eall\u003c/i\u003e the factors mentioned have co-operated in the development\r\nof the view in question; but that in addition\r\nto them a logical and purely formal factor, hitherto\r\nlittle considered, has also played a very important part.\u003c/p\u003e\r\n\r\n\r\n\u003ch3\u003eI. THE PRINCIPLE OF THE EXCLUDED PERPETUAL\r\nMOTION.\u003c/h3\u003e\r\n\r\n\u003cp\u003eThe law of energy in its modern form is not identical\r\nwith the principle of the excluded perpetual motion,\r\nbut it is very closely\r\nrelated to it. The latter\r\nprinciple, however, is by\r\nno means new, for in the\r\nprovince of mechanics it\r\nhas controlled for centuries\r\nthe thoughts and investigations\r\nof the greatest thinkers. Let us convince\r\nourselves of this by the study of a few historical\r\nexamples.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-150.jpg\" width=\"300\" height=\"272\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 41.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eS. Stevinus, in his famous work \u003ci\u003eHypomnemata mathematica\u003c/i\u003e,\r\nTom. IV, \u003ci\u003eDe statica\u003c/i\u003e, (Leyden, 1605, p. 34),\r\ntreats of the equilibrium of bodies on inclined planes.\u003c/p\u003e\r\n\r\n\u003cp\u003eOver a triangular prism \u003ci\u003eABC\u003c/i\u003e, one side of which,\r\n\u003ci\u003eAC\u003c/i\u003e, is horizontal, an endless cord or chain is slung,\r\nto which at equal distances apart fourteen balls of\r\nequal weight are attached, as represented in cross-section\r\nin Figure 41. Since we can imagine the lower\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_141\" id=\"Page_141\"\u003e[Pg 141]\u003c/a\u003e\u003c/span\u003e\r\nsymmetrical part of the cord \u003ci\u003eABC\u003c/i\u003e taken away, Stevinus\r\nconcludes that the four balls on \u003ci\u003eAB\u003c/i\u003e hold in equilibrium\r\nthe two balls on \u003ci\u003eBC\u003c/i\u003e. For if the equilibrium were\r\nfor a moment disturbed, it could never subsist: the\r\ncord would keep moving round forever in the same direction,\u0026mdash;we\r\nshould have a perpetual motion. He says:\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"But if this took place, our row or ring of balls would come\r\nonce more into their original position, and from the same cause the\r\neight globes to the left would again be heavier than the six to the\r\nright, and therefore those eight would sink a second time and these\r\nsix rise, and all the globes would keep up, of themselves, \u003ci\u003ea continuous\r\nand unending motion, which is false\u003c/i\u003e.\"\u003ca name=\"FNanchor_41_41\" id=\"FNanchor_41_41\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_41_41\" class=\"fnanchor\"\u003e[41]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eStevinus, now, easily derives from this principle\r\nthe laws of equilibrium on the inclined plane and numerous\r\nother fruitful consequences.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the chapter \"Hydrostatics\" of\r\nthe same work, page 114, Stevinus sets\r\nup the following principle: \"Aquam\r\ndatam, datum sibi intra aquam locum\r\nservare,\"\u0026mdash;a given mass of water preserves\r\nwithin water its given place.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 150px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-151.jpg\" width=\"150\" height=\"172\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 42.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThis principle is demonstrated as follows (see Fig.\r\n42):\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"For, assuming it to be possible by natural means, let us suppose\r\nthat A does not preserve the place assigned to it, but sinks\r\ndown to D. This being posited, the water which succeeds A will,\r\nfor the same reason, also flow down to \u003ci\u003eD\u003c/i\u003e; \u003ci\u003eA\u003c/i\u003e will be forced out of\r\nits place in \u003ci\u003eD\u003c/i\u003e; and thus this body of water, for the conditions in it\r\nare everywhere the same, \u003ci\u003ewill set up a perpetual motion, which is\r\nabsurd\u003c/i\u003e.\"\u003ca name=\"FNanchor_42_42\" id=\"FNanchor_42_42\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_42_42\" class=\"fnanchor\"\u003e[42]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_142\" id=\"Page_142\"\u003e[Pg 142]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eFrom this all the principles of hydrostatics are deduced.\r\nOn this occasion Stevinus also first develops\r\nthe thought so fruitful for modern analytical mechanics\r\nthat the equilibrium of a system is not destroyed by\r\nthe addition of rigid connexions. As we know, the\r\nprinciple of the conservation of the centre of gravity\r\nis now sometimes deduced from D\u0027Alembert\u0027s principle\r\nwith the help of that remark. If we were to reproduce\r\nStevinus\u0027s demonstration to-day, we should have\r\nto change it slightly. We find no difficulty in imagining\r\nthe cord on the prism possessed of unending uniform\r\nmotion if all hindrances are thought away, but\r\nwe should protest against the assumption of an accelerated\r\nmotion or even against that of a uniform motion,\r\nif the resistances were not removed. Moreover,\r\nfor greater precision of proof, the string of balls might\r\nbe replaced by a heavy homogeneous cord of infinite\r\nflexibility. But all this does not affect in the least the\r\nhistorical value of Stevinus\u0027s thoughts. It is a fact,\r\nStevinus deduces apparently much simpler truths from\r\nthe principle of an impossible perpetual motion.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_143\" id=\"Page_143\"\u003e[Pg 143]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eIn the process of thought which conducted Galileo\r\nto his discoveries at the end of the sixteenth century,\r\nthe following principle plays an important part, that\r\na body in virtue of the velocity acquired in its descent\r\ncan rise exactly as high as it fell. This principle,\r\nwhich appears frequently and with much clearness in\r\nGalileo\u0027s thought, is simply another form of the principle\r\nof excluded perpetual motion, as we shall see it\r\nis also in Huygens.\u003c/p\u003e\r\n\r\n\u003cp\u003eGalileo, as we know, arrived at the law of uniformly\r\naccelerated motion by \u003ci\u003ea priori\u003c/i\u003e considerations, as that\r\nlaw which was the \"simplest and most natural,\" after\r\nhaving first assumed a different law which he was compelled\r\nto reject. To verify his law he executed experiments\r\nwith falling bodies on inclined planes, measuring\r\nthe times of descent by the weights of the water\r\nwhich flowed out of a small orifice in a large vessel.\r\nIn this experiment he assumes as a fundamental principle,\r\nthat the velocity acquired in descent down an\r\ninclined plane always corresponds to the vertical height\r\ndescended through, a conclusion which for him is the\r\nimmediate outcome of the fact that a body which has\r\nfallen down one inclined plane can, with the velocity it\r\nhas acquired, rise on another plane of any inclination\r\nonly to the same vertical height. This principle of\r\nthe height of ascent also led him, as it seems, to the\r\nlaw of inertia. Let us hear his own masterful words\r\nin the \u003ci\u003eDialogo terzo\u003c/i\u003e (\u003ci\u003eOpere\u003c/i\u003e, Padova, 1744, Tom. III).\r\nOn page 96 we read:\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_144\" id=\"Page_144\"\u003e[Pg 144]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"I take it for granted that the velocities acquired by a body\r\nin descent down planes of different inclinations are equal if the\r\nheights of those planes are equal.\"\u003ca name=\"FNanchor_43_43\" id=\"FNanchor_43_43\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_43_43\" class=\"fnanchor\"\u003e[43]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eThen he makes Salviati say in the dialogue:\u003ca name=\"FNanchor_44_44\" id=\"FNanchor_44_44\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_44_44\" class=\"fnanchor\"\u003e[44]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"What you say seems very probable, but I wish to go further\r\nand by an experiment so to increase the probability of it that it shall\r\namount almost to absolute demonstration. Suppose this sheet of\r\npaper to be a vertical wall, and from a nail driven in it a ball of lead\r\nweighing two or three ounces to hang by a very fine thread \u003ci\u003eAB\u003c/i\u003e four\r\nor five feet long. (Fig. 43.) On the wall mark a horizontal line \u003ci\u003eDC\u003c/i\u003e\r\nperpendicular to the vertical \u003ci\u003eAB\u003c/i\u003e, which latter ought to hang about\r\ntwo inches from the wall. If now the thread \u003ci\u003eAB\u003c/i\u003e with the ball\r\nattached take the position \u003ci\u003eAC\u003c/i\u003e and the ball be let go, you will see\r\nthe ball first descend through the arc \u003ci\u003eCB\u003c/i\u003e and passing beyond\r\n\u003ci\u003eB\u003c/i\u003e rise through the arc\r\n\u003ci\u003eBD\u003c/i\u003e almost to the level\r\nof the line \u003ci\u003eCD\u003c/i\u003e, being\r\nprevented from reaching\r\nit exactly by the resistance\r\nof the air and\r\nof the thread. From\r\nthis we may truly conclude\r\nthat its impetus at\r\nthe point \u003ci\u003eB\u003c/i\u003e, acquired by\r\nits descent through the\r\narc \u003ci\u003eCB\u003c/i\u003e, is sufficient to\r\nurge it through a similar arc \u003ci\u003eBD\u003c/i\u003e to the same height. Having\r\nperformed this experiment and repeated it several times, let us\r\ndrive in the wall, in the projection of the vertical \u003ci\u003eAB\u003c/i\u003e, as at \u003ci\u003eE\u003c/i\u003e or\r\nat \u003ci\u003eF\u003c/i\u003e, a nail five or six inches long, so that the thread \u003ci\u003eAC\u003c/i\u003e, carrying\r\nas before the ball through the arc \u003ci\u003eCB\u003c/i\u003e, at the moment it reaches\r\nthe position \u003ci\u003eAB\u003c/i\u003e, shall strike the nail \u003ci\u003eE\u003c/i\u003e, and the ball be thus compelled\r\nto move up the arc \u003ci\u003eBG\u003c/i\u003e described about \u003ci\u003eE\u003c/i\u003e as centre.\r\nThen we shall see what the same impetus will here accomplish,\r\nacquired now as before at the same point \u003ci\u003eB\u003c/i\u003e, which then drove the\r\nsame moving body through the arc \u003ci\u003eBD\u003c/i\u003e to the height of the horizontal\r\n\u003ci\u003eCD\u003c/i\u003e. Now gentlemen, you will be pleased to see the ball\r\nrise to the horizontal line at the point \u003ci\u003eG\u003c/i\u003e, and the same thing also\r\nhappen if the nail be placed lower as at \u003ci\u003eF\u003c/i\u003e, in which case the ball\r\nwould describe the arc \u003ci\u003eBJ\u003c/i\u003e, always terminating its ascent precisely\r\nat the line \u003ci\u003eCD\u003c/i\u003e. If the nail be placed so low that the length of\r\nthread below it does not reach to the height of \u003ci\u003eCD\u003c/i\u003e (which would\r\nhappen if \u003ci\u003eF\u003c/i\u003e were nearer \u003ci\u003eB\u003c/i\u003e than to the intersection of \u003ci\u003eAB\u003c/i\u003e with the\r\nhorizontal \u003ci\u003eCD\u003c/i\u003e), then the thread will wind itself about the nail.\r\nThis experiment leaves no room for doubt as to the truth of the\r\nsupposition. For as the two arcs \u003ci\u003eCB\u003c/i\u003e, \u003ci\u003eDB\u003c/i\u003e are equal and similarly\r\nsituated, the momentum acquired in the descent of the arc \u003ci\u003eCB\u003c/i\u003e is\r\nthe same as that acquired in the descent of the arc \u003ci\u003eDB\u003c/i\u003e; but the\r\nmomentum acquired at \u003ci\u003eB\u003c/i\u003e by the descent through the arc \u003ci\u003eCB\u003c/i\u003e is capable\r\nof driving up the same moving body through the arc \u003ci\u003eBD\u003c/i\u003e;\r\nhence also the momentum acquired in the descent \u003ci\u003eDB\u003c/i\u003e is equal to\r\nthat which drives the same moving body through the same arc\r\nfrom \u003ci\u003eB\u003c/i\u003e to \u003ci\u003eD\u003c/i\u003e, so that in general every momentum acquired in the\r\ndescent of an arc is equal to that which causes the same moving\r\nbody to ascend through the same arc; but all the momenta which\r\ncause the ascent of all the arcs \u003ci\u003eBD\u003c/i\u003e, \u003ci\u003eBG\u003c/i\u003e, \u003ci\u003eBJ\u003c/i\u003e, are equal since they\r\nare made by the same momentum acquired in the descent \u003ci\u003eCB\u003c/i\u003e, as\r\nthe experiment shows: therefore all the momenta acquired in the\r\ndescent of the arcs \u003ci\u003eDB\u003c/i\u003e, \u003ci\u003eGB\u003c/i\u003e, \u003ci\u003eJB\u003c/i\u003e are equal.\"\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_145\" id=\"Page_145\"\u003e[Pg 145]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cdiv class=\"figcenter\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-155.jpg\" width=\"300\" height=\"246\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 43.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_146\" id=\"Page_146\"\u003e[Pg 146]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe remark relative to the pendulum may be applied\r\nto the inclined plane and leads to the law of inertia.\r\nWe read on page 124:\u003ca name=\"FNanchor_45_45\" id=\"FNanchor_45_45\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_45_45\" class=\"fnanchor\"\u003e[45]\u003c/a\u003e\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_147\" id=\"Page_147\"\u003e[Pg 147]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cblockquote\u003e\u003cp\u003e\"It is plain now that a movable body, starting from rest at \u003ci\u003eA\u003c/i\u003e\r\nand descending down the inclined plane \u003ci\u003eAB\u003c/i\u003e, acquires a velocity\r\nproportional to the increment of its time: the velocity possessed\r\nat \u003ci\u003eB\u003c/i\u003e is the greatest of the velocities acquired, and by its nature\r\nimmutably impressed, provided all causes of new acceleration or\r\nretardation are taken away: I say acceleration, having in view its\r\npossible further progress along the plane extended; retardation, in\r\nview of the possibility of its being reversed and made to mount the\r\nascending plane \u003ci\u003eBC\u003c/i\u003e. But in the horizontal plane \u003ci\u003eGH\u003c/i\u003e its equable\r\nmotion, according to its velocity as acquired in the descent from \u003ci\u003eA\u003c/i\u003e\r\nto \u003ci\u003eB\u003c/i\u003e, will be continued \u003ci\u003ead infinitum\u003c/i\u003e.\" (Fig. 44.)\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 400px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-157.jpg\" width=\"400\" height=\"156\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 44.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eHuygens, upon whose shoulders the mantel of Galileo\r\nfell, forms a sharper conception of the law of inertia\r\nand generalises the principle respecting the heights of\r\nascent which was so fruitful in Galileo\u0027s hands. He\r\nemploys the latter principle in the solution of the problem\r\nof the centre of oscillation and is perfectly clear in\r\nthe statement that the principle respecting the heights\r\nof ascent is identical with the principle of the excluded\r\nperpetual motion.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe following important passages then occur (Hugenii,\r\n\u003ci\u003eHorologium oscillatorium, pars secunda\u003c/i\u003e). \u003ci\u003eHypotheses\u003c/i\u003e:\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_148\" id=\"Page_148\"\u003e[Pg 148]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cblockquote\u003e\u003cp\u003e\"If gravity did not exist, nor the atmosphere obstruct the motions\r\nof bodies, a body would keep up forever the motion once impressed\r\nupon it, with equable velocity, in a straight line.\"\u003ca name=\"FNanchor_46_46\" id=\"FNanchor_46_46\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_46_46\" class=\"fnanchor\"\u003e[46]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eIn part four of the \u003ci\u003eHorologium de centro oscillationis\u003c/i\u003e\r\nwe read:\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"If any number of weights be set in motion by the force of\r\ngravity, the common centre of gravity of the weights as a whole\r\ncannot possibly rise higher than the place which it occupied when\r\nthe motion began.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"That this hypothesis of ours may arouse no scruples, we\r\nwill state that it simply imports, what no one has ever denied, that\r\nheavy bodies do not move \u003ci\u003eupwards\u003c/i\u003e.\u0026mdash;And truly if the devisers of\r\nthe new machines who make such futile attempts to construct a\r\nperpetual motion would acquaint themselves with this principle,\r\nthey could easily be brought to see their errors and to understand\r\nthat the thing is utterly impossible by mechanical means.\"\u003ca name=\"FNanchor_47_47\" id=\"FNanchor_47_47\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_47_47\" class=\"fnanchor\"\u003e[47]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eThere is possibly a Jesuitical mental reservation\r\ncontained in the words \"mechanical means.\" One\r\nmight be led to believe from them that Huygens held\r\na non-mechanical perpetual motion for possible.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe generalisation of Galileo\u0027s principle is still\r\nmore clearly put in Prop. IV of the same chapter:\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"If a pendulum, composed of several weights, set in motion\r\nfrom rest, complete any part of its full oscillation, and from that\r\npoint onwards, the individual weights, with their common connexions\r\ndissolved, change their acquired velocities upwards and ascend\r\nas far as they can, the common centre of gravity of all will be carried\r\nup to the same altitude with that which it occupied before the\r\nbeginning of the oscillation.\"\u003ca name=\"FNanchor_48_48\" id=\"FNanchor_48_48\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_48_48\" class=\"fnanchor\"\u003e[48]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_149\" id=\"Page_149\"\u003e[Pg 149]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003eOn this last principle now, which is a generalisation,\r\napplied to a system of masses, of one of Galileo\u0027s\r\nideas respecting a single mass and which from Huygens\u0027s\r\nexplanation we recognise as the principle of excluded\r\nperpetual motion, Huygens grounds his theory\r\nof the centre of oscillation. Lagrange characterises\r\nthis principle as precarious and is rejoiced at James\r\nBernoulli\u0027s successful attempt, in 1681, to reduce the\r\ntheory of the centre of oscillation to the laws of the\r\nlever, which appeared to him clearer. All the great\r\ninquirers of the seventeenth and eighteenth centuries\r\nbroke a lance on this problem, and it led ultimately,\r\nin conjunction with the principle of virtual velocities,\r\nto the principle enunciated by D\u0027Alembert in 1743 in\r\nhis \u003ci\u003eTraité de dynamique\u003c/i\u003e, though previously employed\r\nin a somewhat different form by Euler and Hermann.\u003c/p\u003e\r\n\r\n\u003cp\u003eFurthermore, the Huygenian principle respecting\r\nthe heights of ascent became the foundation of the\r\n\"law of the conservation of living force,\" as that was\r\nenunciated by John and Daniel Bernoulli and employed\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_150\" id=\"Page_150\"\u003e[Pg 150]\u003c/a\u003e\u003c/span\u003e\r\nwith such signal success by the latter in his\r\n\u003ci\u003eHydrodynamics\u003c/i\u003e. The theorems of the Bernoullis differ\r\nin form only from Lagrange\u0027s expression in the \u003ci\u003eAnalytical\r\nMechanics\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe manner in which Torricelli reached his famous\r\nlaw of efflux for liquids leads again to our principle.\r\nTorricelli assumed that the liquid which flows out of\r\nthe basal orifice of a vessel cannot by its velocity of\r\nefflux ascend to a greater height than its level in the\r\nvessel.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us next consider a point which belongs to pure\r\nmechanics, the history of the principle of \u003ci\u003evirtual motions\u003c/i\u003e\r\nor \u003ci\u003evirtual velocities\u003c/i\u003e. This principle was not first\r\nenunciated, as is usually stated, and as Lagrange also\r\nasserts, by Galileo, but earlier, by Stevinus. In his\r\n\u003ci\u003eTrochleostatica\u003c/i\u003e of the above-cited work, page 72, he\r\nsays:\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"Observe that this axiom of statics holds good here:\u003c/p\u003e\r\n\r\n\u003cp\u003e\"As the space of the body acting is to the space of the body\r\nacted upon, so is the power of the body acted upon to the power of\r\nthe body acting.\"\u003ca name=\"FNanchor_49_49\" id=\"FNanchor_49_49\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_49_49\" class=\"fnanchor\"\u003e[49]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eGalileo, as we know, recognised the truth of the\r\nprinciple in the consideration of the simple machines,\r\nand also deduced the laws of the equilibrium of liquids\r\nfrom it.\u003c/p\u003e\r\n\r\n\u003cp\u003eTorricelli carries the principle back to the properties\r\nof the centre of gravity. The condition controlling\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_151\" id=\"Page_151\"\u003e[Pg 151]\u003c/a\u003e\u003c/span\u003e\r\nequilibrium in a simple machine, in which power\r\nand load are represented by weights, is that the common\r\ncentre of gravity of the weights shall not sink.\r\nConversely, if the centre of gravity cannot sink equilibrium\r\nobtains, because heavy bodies of themselves\r\ndo not move upwards. In this form the principle of\r\nvirtual velocities is identical with Huygens\u0027s principle\r\nof the impossibility of a perpetual motion.\u003c/p\u003e\r\n\r\n\u003cp\u003eJohn Bernoulli, in 1717, first perceived the universal\r\nimport of the principle of virtual movements for all\r\nsystems; a discovery stated in a letter to Varignon.\r\nFinally, Lagrange gives a general demonstration of\r\nthe principle and founds upon it his whole \u003ci\u003eAnalytical\r\nMechanics\u003c/i\u003e. But this general demonstration is based\r\nafter all upon Huygens and Torricelli\u0027s remarks. Lagrange,\r\nas is known, conceives simple pulleys arranged\r\nin the directions of the forces of the system, passes a\r\ncord through these pulleys, and appends to its free\r\nextremity a weight which is a common measure of all\r\nthe forces of the system. With no difficulty, now, the\r\nnumber of elements of each pulley may be so chosen\r\nthat the forces in question shall be replaced by them.\r\nIt is then clear that if the weight at the extremity cannot\r\nsink, equilibrium subsists, because heavy bodies\r\ncannot of themselves move upwards. If we do not go\r\nso far, but wish to abide by Torricelli\u0027s idea, we may\r\nconceive every individual force of the system replaced\r\nby a special weight suspended from a cord passing\r\nover a pulley in the direction of the force and attached\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_152\" id=\"Page_152\"\u003e[Pg 152]\u003c/a\u003e\u003c/span\u003e\r\nat its point of application. Equilibrium subsists then\r\nwhen the common centre of gravity of all the weights\r\ntogether cannot sink. The fundamental supposition\r\nof this demonstration is plainly the impossibility of a\r\nperpetual motion.\u003c/p\u003e\r\n\r\n\u003cp\u003eLagrange tried in every way to supply a proof free\r\nfrom extraneous elements and fully satisfactory, but\r\nwithout complete success. Nor were his successors\r\nmore fortunate.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe whole of mechanics, thus, is based upon an\r\nidea, which, though unequivocal, is yet unwonted and\r\nnot coequal with the other principles and axioms of\r\nmechanics. Every student of mechanics, at some stage\r\nof his progress, feels the uncomfortableness of this\r\nstate of affairs; every one wishes it removed; but seldom\r\nis the difficulty stated in words. Accordingly, the\r\nzealous pupil of the science is highly rejoiced when he\r\nreads in a master like Poinsot (\u003ci\u003eThéorie générale de\r\nl\u0027équilibre et du mouvement des systèmes\u003c/i\u003e) the following\r\npassage, in which that author is giving his opinion of\r\nthe \u003ci\u003eAnalytical Mechanics\u003c/i\u003e:\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"In the meantime, because our attention in that work was first\r\nwholly engrossed with the consideration of its beautiful development\r\nof mechanics, which seemed to spring complete from a single\r\nformula, we naturally believed that the science was completed or\r\nthat it only remained to seek the demonstration of the principle of\r\nvirtual velocities. But that quest brought back all the difficulties\r\nthat we had overcome by the principle itself. That law so general,\r\nwherein are mingled the vague and unfamiliar ideas of infinitely\r\nsmall movements and of perturbations of equilibrium, only grew\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_153\" id=\"Page_153\"\u003e[Pg 153]\u003c/a\u003e\u003c/span\u003e\r\nobscure upon examination; and the work of Lagrange supplying\r\nnothing clearer than the march of analysis, we saw plainly that the\r\nclouds had only appeared lifted from the course of mechanics because\r\nthey had, so to speak, been gathered at the very origin of that\r\nscience.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"At bottom, a general demonstration of the principle of virtual\r\nvelocities would be equivalent to the establishment of the whole\r\nof mechanics upon a different basis: for the demonstration of a\r\nlaw which embraces a whole science is neither more nor less than\r\nthe reduction of that science to another law just as general, but\r\nevident, or at least more simple than the first, and which, consequently,\r\nwould render that useless.\"\u003ca name=\"FNanchor_50_50\" id=\"FNanchor_50_50\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_50_50\" class=\"fnanchor\"\u003e[50]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eAccording to Poinsot, therefore, a proof of the\r\nprinciple of virtual movements is tantamount to a total\r\nrehabilitation of mechanics.\u003c/p\u003e\r\n\r\n\u003cp\u003eAnother circumstance of discomfort to the mathematician\r\nis, that in the historical form in which mechanics\r\nat present exists, dynamics is founded on\r\nstatics, whereas it is desirable that in a science which\r\npretends to deductive completeness the more special\r\nstatical theorems should be deducible from the more\r\ngeneral dynamical principles.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_154\" id=\"Page_154\"\u003e[Pg 154]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eIn fact, a great master, Gauss, gave expression to\r\nthis desire in his presentment of the principle of least\r\nconstraint (Crelle\u0027s \u003ci\u003eJournal für reine und angewandte\r\nMathematik\u003c/i\u003e, Vol. IV, p. 233) in the following words:\r\n\"Proper as it is that in the gradual development of a\r\nscience, and in the instruction of individuals, the easy\r\nshould precede the difficult, the simple the complex,\r\nthe special the general, yet the mind, when once it has\r\nreached a higher point of view, demands the contrary\r\ncourse, in which all statics shall appear simply as a\r\nspecial case of mechanics.\" Gauss\u0027s own principle,\r\nnow, possesses all the requisites of universality, but\r\nits difficulty is that it is not immediately intelligible\r\nand that Gauss deduced it with the help of D\u0027Alembert\u0027s\r\nprinciple, a procedure which left matters where\r\nthey were before.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhence, now, is derived this strange part which\r\nthe principle of virtual motion plays in mechanics?\r\nFor the present I shall only make this reply. It would\r\nbe difficult for me to tell the difference of impression\r\nwhich Lagrange\u0027s proof of the principle made on me\r\nwhen I first took it up as a student and when I subsequently\r\nresumed it after having made historical researches.\r\nIt first appeared to me insipid, chiefly on\r\naccount of the pulleys and the cords which did not fit\r\nin with the mathematical view, and whose action I\r\nwould much rather have discovered from the principle\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_155\" id=\"Page_155\"\u003e[Pg 155]\u003c/a\u003e\u003c/span\u003e\r\nitself than have taken for granted. But now that I\r\nhave studied the history of the science I cannot imagine\r\na more beautiful demonstration.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn fact, through all mechanics it is this self-same\r\nprinciple of excluded perpetual motion which accomplishes\r\nalmost all, which displeased Lagrange, but\r\nwhich he still had to employ, at least tacitly, in his own\r\ndemonstration. If we give this principle its proper\r\nplace and setting, the paradox is explained.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe principle of excluded perpetual motion is thus\r\nno new discovery; it has been the guiding idea, for\r\nthree hundred years, of all the great inquirers. But\r\nthe principle cannot properly be \u003ci\u003ebased\u003c/i\u003e upon mechanical\r\nperceptions. For long before the development of\r\nmechanics the conviction of its truth existed and even\r\ncontributed to that development. Its power of conviction,\r\ntherefore, must have more universal and\r\ndeeper roots. We shall revert to this point.\u003c/p\u003e\r\n\r\n\r\n\u003ch3\u003eII. MECHANICAL PHYSICS.\u003c/h3\u003e\r\n\r\n\u003cp\u003eIt cannot be denied that an unmistakable tendency\r\nhas prevailed, from Democritus to the present day, to\r\nexplain \u003ci\u003eall\u003c/i\u003e physical events \u003ci\u003emechanically\u003c/i\u003e. Not to mention\r\nearlier obscure expressions of that tendency we\r\nread in Huygens the following:\u003ca name=\"FNanchor_51_51\" id=\"FNanchor_51_51\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_51_51\" class=\"fnanchor\"\u003e[51]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"There can be no doubt that light consists of the \u003ci\u003emotion\u003c/i\u003e of a\r\ncertain substance. For if we examine its production, we find that\r\nhere on earth it is principally fire and flame which engender it, both\r\nof which contain beyond doubt bodies which are in rapid movement,\r\nsince they dissolve and destroy many other bodies more solid\r\nthan they: while if we regard its effects, we see that when light is\r\naccumulated, say by concave mirrors, it has the property of combustion\r\njust as fire has, that is to say, it disunites the parts of\r\nbodies, which is assuredly a proof of \u003ci\u003emotion\u003c/i\u003e, at least in the \u003ci\u003etrue\r\nphilosophy\u003c/i\u003e, in which the causes of all natural effects are conceived\r\nas \u003ci\u003emechanical\u003c/i\u003e causes. Which in my judgment must be accomplished\r\nor all hope of ever understanding physics renounced.\"\u003ca name=\"FNanchor_52_52\" id=\"FNanchor_52_52\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_52_52\" class=\"fnanchor\"\u003e[52]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_156\" id=\"Page_156\"\u003e[Pg 156]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eS. Carnot,\u003ca name=\"FNanchor_53_53\" id=\"FNanchor_53_53\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_53_53\" class=\"fnanchor\"\u003e[53]\u003c/a\u003e in introducing the principle of excluded\r\nperpetual motion into the theory of heat, makes the\r\nfollowing apology:\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"It will be objected here, perhaps, that a perpetual motion\r\nproved impossible for \u003ci\u003epurely mechanical actions\u003c/i\u003e, is perhaps not so\r\nwhen the influence of \u003ci\u003eheat\u003c/i\u003e or of electricity is employed. But can\r\nphenomena of heat or electricity be thought of as due to anything\r\nelse than to \u003ci\u003ecertain motions of bodies\u003c/i\u003e, and as such must they not be\r\nsubject to the general laws of mechanics?\"\u003ca name=\"FNanchor_54_54\" id=\"FNanchor_54_54\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_54_54\" class=\"fnanchor\"\u003e[54]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_157\" id=\"Page_157\"\u003e[Pg 157]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003eThese examples, which might be multiplied by\r\nquotations from recent literature indefinitely, show\r\nthat a tendency to explain all things mechanically\r\nactually exists. This tendency is also intelligible.\r\nMechanical events as simple motions in space and\r\ntime best admit of observation and pursuit by the help\r\nof our highly organised senses. We reproduce mechanical\r\nprocesses almost without effort in our imagination.\r\nPressure as a circumstance that produces motion\r\nis very familiar to us from daily experience. All\r\nchanges which the individual personally produces in\r\nhis environment, or humanity brings about by means\r\nof the arts in the world, are effected through the instrumentality\r\nof \u003ci\u003emotions\u003c/i\u003e. Almost of necessity, therefore,\r\nmotion appears to us as the most important\r\nphysical factor. Moreover, mechanical properties may\r\nbe discovered in all physical events. The sounding\r\nbell trembles, the heated body expands, the electrified\r\nbody attracts other bodies. Why, therefore, should\r\nwe not attempt to grasp all events under their mechanical\r\naspect, since that is so easily apprehended and\r\nmost accessible to observation and measurement? In\r\nfact, no objection \u003ci\u003eis\u003c/i\u003e to be made to the attempt to elucidate\r\nthe properties of physical events by mechanical\r\n\u003ci\u003eanalogies\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut modern physics has proceeded \u003ci\u003every far\u003c/i\u003e in this\r\ndirection. The point of view which Wundt represents\r\nin his excellent treatise \u003ci\u003eOn the Physical Axioms\u003c/i\u003e is probably\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_158\" id=\"Page_158\"\u003e[Pg 158]\u003c/a\u003e\u003c/span\u003e\r\nshared by the majority of physicists. The axioms\r\nof physics which Wundt sets up are as follows:\u003c/p\u003e\r\n\r\n\u003cp\u003e1. All natural causes are motional causes.\u003c/p\u003e\r\n\r\n\u003cp\u003e2. Every motional cause lies outside the object\r\nmoved.\u003c/p\u003e\r\n\r\n\u003cp\u003e3. All motional causes act in the direction of the\r\nstraight line of junction, and so forth.\u003c/p\u003e\r\n\r\n\u003cp\u003e4. The effect of every cause persists.\u003c/p\u003e\r\n\r\n\u003cp\u003e5. Every effect involves an equal countereffect.\u003c/p\u003e\r\n\r\n\u003cp\u003e6. Every effect is equivalent to its cause.\u003c/p\u003e\r\n\r\n\u003cp\u003eThese principles might be studied properly enough\r\nas fundamental principles of mechanics. But when\r\nthey are set up as axioms of physics, their enunciation\r\nis simply tantamount to a negation of all events except\r\nmotion.\u003c/p\u003e\r\n\r\n\u003cp\u003eAccording to Wundt, all changes of nature are\r\nmere changes of place. All causes are motional causes\r\n(page 26). Any discussion of the philosophical grounds\r\non which Wundt supports his theory would lead us\r\ndeep into the speculations of the Eleatics and the\r\nHerbartians. Change of place, Wundt holds, is the\r\n\u003ci\u003eonly\u003c/i\u003e change of a thing in which a thing remains identical\r\nwith itself. If a thing changed \u003ci\u003equalitatively\u003c/i\u003e, we\r\nshould be obliged to imagine that something was annihilated\r\nand something else created in its place, which\r\nis not to be reconciled with our idea of the identity of\r\nthe object observed and of the indestructibility of\r\nmatter. But we have only to remember that the Eleatics\r\nencountered difficulties of exactly the same sort\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_159\" id=\"Page_159\"\u003e[Pg 159]\u003c/a\u003e\u003c/span\u003e\r\nin motion. Can we not also imagine that a thing is\r\ndestroyed in \u003ci\u003eone\u003c/i\u003e place and in \u003ci\u003eanother\u003c/i\u003e an exactly similar\r\nthing created? After all, do we really know \u003ci\u003emore\u003c/i\u003e\r\nwhy a body leaves one place and appears in another,\r\nthan why a \u003ci\u003ecold\u003c/i\u003e body grows \u003ci\u003ewarm\u003c/i\u003e? Granted that we\r\nhad a perfect knowledge of the mechanical processes\r\nof nature, could we and should we, for that reason,\r\n\u003ci\u003eput out of the world\u003c/i\u003e all other processes that we do not\r\nunderstand? On this principle it would really be the\r\nsimplest course to deny the existence of the whole\r\nworld. This is the point at which the Eleatics ultimately\r\narrived, and the school of Herbart stopped\r\nlittle short of the same goal.\u003c/p\u003e\r\n\r\n\u003cp\u003ePhysics treated in this sense supplies us simply\r\nwith a diagram of the world, in which we do not know\r\nreality again. It happens, in fact, to men who give\r\nthemselves up to this view for many years, that the\r\nworld of sense from which they start as a province of\r\nthe greatest familiarity, suddenly becomes, in their\r\neyes, the supreme \"world-riddle.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eIntelligible as it is, therefore, that the efforts of\r\nthinkers have always been bent upon the \"reduction\r\nof all physical processes to the motions of atoms,\" it\r\nmust yet be affirmed that this is a chimerical ideal.\r\nThis ideal has often played an effective part in popular\r\nlectures, but in the workshop of the serious inquirer\r\nit has discharged scarcely the least function.\r\nWhat has really been achieved in mechanical physics\r\nis either the \u003ci\u003eelucidation\u003c/i\u003e of physical processes by more\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_160\" id=\"Page_160\"\u003e[Pg 160]\u003c/a\u003e\u003c/span\u003e\r\nfamiliar \u003ci\u003emechanical analogies\u003c/i\u003e, (for example, the theories\r\nof light and of electricity,) or the exact \u003ci\u003equantitative\u003c/i\u003e\r\nascertainment of the connexion of mechanical processes\r\nwith other physical processes, for example, the\r\nresults of thermodynamics.\u003c/p\u003e\r\n\r\n\r\n\u003ch3\u003eIII. THE PRINCIPLE OF ENERGY IN PHYSICS.\u003c/h3\u003e\r\n\r\n\u003cp\u003eWe can know only from \u003ci\u003eexperience\u003c/i\u003e that mechanical\r\nprocesses produce other physical transformations, or\r\n\u003ci\u003evice versa\u003c/i\u003e. The attention was first directed to the connexion\r\nof mechanical processes, especially the performance\r\nof work, with changes of thermal conditions\r\nby the invention of the steam-engine, and by its great\r\ntechnical importance. Technical interests and the\r\nneed of scientific lucidity meeting in the mind of S.\r\nCarnot led to the remarkable development from which\r\nthermodynamics flowed. It is simply \u003ci\u003ean accident of\r\nhistory\u003c/i\u003e that the development in question was not connected\r\nwith the practical applications of \u003ci\u003eelectricity\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the determination of the maximum quantity of\r\n\u003ci\u003ework\u003c/i\u003e that, generally, a heat-machine, or, to take a\r\nspecial case, a steam-engine, can perform with the\r\nexpenditure of a \u003ci\u003egiven\u003c/i\u003e amount of heat of combustion,\r\nCarnot is guided by mechanical analogies. A body can\r\ndo work on being heated, by expanding under pressure.\r\nBut to do this the body must receive heat from a \u003ci\u003ehotter\u003c/i\u003e\r\nbody. Heat, therefore, to do work, must pass from a\r\nhotter body to a colder body, just as water must fall\r\nfrom a higher level to a lower level to put a mill-wheel\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_161\" id=\"Page_161\"\u003e[Pg 161]\u003c/a\u003e\u003c/span\u003e\r\nin motion. Differences of temperature, accordingly,\r\nrepresent forces able to do work exactly as do differences\r\nof height in heavy bodies. Carnot pictures to\r\nhimself an ideal process in which no heat flows away\r\nunused, that is, without doing work. With a given expenditure\r\nof heat, accordingly, this process furnishes\r\nthe maximum of work. An analogue of the process\r\nwould be a mill-wheel which scooping its water out of\r\na higher level would slowly carry it to a lower level\r\nwithout the loss of a drop. A peculiar property of the\r\nprocess is, that with the expenditure of the same work\r\nthe water can be raised again exactly to its original\r\nlevel. This property of \u003ci\u003ereversibility\u003c/i\u003e is also shared by\r\nthe process of Carnot. His process also can be reversed\r\nby the expenditure of the same amount of work,\r\nand the heat again brought back to its original temperature\r\nlevel.\u003c/p\u003e\r\n\r\n\u003cp\u003eSuppose, now, we had \u003ci\u003etwo\u003c/i\u003e different reversible processes\r\n\u003ci\u003eA\u003c/i\u003e, \u003ci\u003eB\u003c/i\u003e, such that in \u003ci\u003eA\u003c/i\u003e a quantity of heat, \u003ci\u003eQ\u003c/i\u003e,\r\nflowing off from the temperature \u003ci\u003et\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e to the lower temperature\r\n\u003ci\u003et\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e should perform the work \u003ci\u003eW\u003c/i\u003e, but in \u003ci\u003eB\u003c/i\u003e under\r\nthe same circumstances it should perform a greater\r\nquantity of work \u003ci\u003eW\u003c/i\u003e + \u003ci\u003eW\u0027\u003c/i\u003e; then, we could join \u003ci\u003eB\u003c/i\u003e in\r\nthe sense assigned and \u003ci\u003eA\u003c/i\u003e in the reverse sense into a\r\n\u003ci\u003esingle\u003c/i\u003e process. Here \u003ci\u003eA\u003c/i\u003e would reverse the transformation\r\nof heat produced by \u003ci\u003eB\u003c/i\u003e and would leave a surplus\r\nof work \u003ci\u003eW\u0027\u003c/i\u003e, produced, so to speak, from nothing.\r\nThe combination would present a perpetual motion.\u003c/p\u003e\r\n\r\n\u003cp\u003eWith the feeling, now, that it makes little difference\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_162\" id=\"Page_162\"\u003e[Pg 162]\u003c/a\u003e\u003c/span\u003e\r\nwhether the mechanical laws are broken directly\r\nor indirectly (by processes of heat), and convinced of\r\nthe existence of a \u003ci\u003euniversal\u003c/i\u003e law-ruled connexion of nature,\r\nCarnot here excludes for the first time from the\r\nprovince of \u003ci\u003egeneral\u003c/i\u003e physics the possibility of a perpetual\r\nmotion. \u003ci\u003eBut it follows, then, that the quantity\r\nof work W, produced by the passage of a quantity of heat\r\nQ from a temperature t\u003csub\u003e1\u003c/sub\u003e to a temperature t\u003csub\u003e2\u003c/sub\u003e, is independent\r\nof the nature of the substances as also of the character\r\nof the process, so far as that is unaccompanied by\r\nloss, but is wholly dependent upon the temperature t\u003csub\u003e1\u003c/sub\u003e, t\u003csub\u003e2\u003c/sub\u003e.\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThis important principle has been fully confirmed\r\nby the special researches of Carnot himself (1824), of\r\nClapeyron (1834), and of Sir William Thomson (1849),\r\nnow Lord Kelvin. The principle was reached \u003ci\u003ewithout\r\nany assumption whatever\u003c/i\u003e concerning the nature of heat,\r\nsimply by the exclusion of a perpetual motion. Carnot,\r\nit is true, was an adherent of the theory of Black, according\r\nto which the sum-total of the quantity of heat\r\nin the world is constant, but so far as his investigations\r\nhave been hitherto considered the decision on\r\nthis point is of no consequence. Carnot\u0027s principle\r\nled to the most remarkable results. W. Thomson\r\n(1848) founded upon it the ingenious idea of an \"absolute\"\r\nscale of temperature. James Thomson (1849)\r\nconceived a Carnot process to take place with water\r\nfreezing under pressure and, therefore, performing\r\nwork. He discovered, thus, that the freezing point is\r\nlowered 0·0075° Celsius by every additional atmosphere\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_163\" id=\"Page_163\"\u003e[Pg 163]\u003c/a\u003e\u003c/span\u003e\r\nof pressure. This is mentioned merely as an\r\nexample.\u003c/p\u003e\r\n\r\n\u003cp\u003eAbout twenty years after the publication of Carnot\u0027s\r\nbook a further advance was made by J. R. Mayer\r\nand J. P. Joule. Mayer, while engaged as a physician\r\nin the service of the Dutch, observed, during a\r\nprocess of bleeding in Java, an unusual redness of the\r\nvenous blood. In agreement with Liebig\u0027s theory of\r\nanimal heat he connected this fact with the diminished\r\nloss of heat in warmer climates, and with the diminished\r\nexpenditure of organic combustibles. The total\r\nexpenditure of heat of a man at rest must be equal to\r\nthe total heat of combustion. But since \u003ci\u003eall\u003c/i\u003e organic actions,\r\neven the mechanical actions, must be set down\r\nto the credit of the heat of combustion, some connexion\r\nmust exist between mechanical work and expenditure\r\nof heat.\u003c/p\u003e\r\n\r\n\u003cp\u003eJoule started from quite similar convictions concerning\r\nthe galvanic battery. A heat of association\r\nequivalent to the consumption of the zinc can be made\r\nto appear in the galvanic cell. If a current is set up,\r\na part of this heat appears in the conductor of the\r\ncurrent. The interposition of an apparatus for the\r\ndecomposition of water causes a part of this heat to\r\ndisappear, which on the burning of the explosive gas\r\nformed, is reproduced. If the current runs an electromotor,\r\na portion of the heat again disappears, which,\r\non the consumption of the work by friction, again\r\nmakes its appearance. Accordingly, both the heat\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_164\" id=\"Page_164\"\u003e[Pg 164]\u003c/a\u003e\u003c/span\u003e\r\nproduced and the work produced, appeared to Joule\r\nalso as connected with the consumption of material.\r\nThe thought was therefore present, both to Mayer and\r\nto Joule, of regarding heat and work as equivalent\r\nquantities, so connected with each other that what is\r\nlost in one form universally appears in another. The\r\nresult of this was a \u003ci\u003esubstantial\u003c/i\u003e conception of heat and\r\nof work, and \u003ci\u003eultimately a substantial conception of energy\u003c/i\u003e.\r\nHere every physical change of condition is regarded\r\nas energy, the destruction of which generates\r\nwork or equivalent heat. An electric charge, for example,\r\nis energy.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn 1842 Mayer had calculated from the physical\r\nconstants then universally accepted that by the disappearance\r\nof one kilogramme-calorie 365 kilogramme-metres\r\nof work could be performed, and \u003ci\u003evice versa\u003c/i\u003e.\r\nJoule, on the other hand, by a long series of delicate\r\nand varied experiments beginning in 1843 ultimately\r\ndetermined the mechanical equivalent of the kilogramme-calorie,\r\nmore exactly, as 425 kilogramme-metres.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we estimate every change of physical condition\r\nby the \u003ci\u003emechanical work\u003c/i\u003e which can be performed upon\r\nthe \u003ci\u003edisappearance\u003c/i\u003e of that condition, and call this measure\r\n\u003ci\u003eenergy\u003c/i\u003e, then we can measure all physical changes\r\nof condition, no matter how different they may be,\r\nwith the same common measure, and say: \u003ci\u003ethe sum-total\r\nof all energy remains constant\u003c/i\u003e. This is the form that\r\nthe principle of excluded perpetual motion received at\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_165\" id=\"Page_165\"\u003e[Pg 165]\u003c/a\u003e\u003c/span\u003e\r\nthe hands of Mayer, Joule, Helmholtz, and W. Thomson\r\nin its extension to the whole domain of physics.\u003c/p\u003e\r\n\r\n\u003cp\u003eAfter it had been proved that heat must \u003ci\u003edisappear\u003c/i\u003e\r\nif mechanical work was to be done at its expense,\r\nCarnot\u0027s principle could no longer be regarded as a\r\ncomplete expression of the facts. Its improved form\r\nwas first given, in 1850, by Clausius, whom Thomson\r\nfollowed in 1851. It runs thus: \"If a quantity of heat\r\n\u003ci\u003eQ\u0027\u003c/i\u003e is transformed into work in a reversible process,\r\n\u003ci\u003eanother\u003c/i\u003e quantity of heat \u003ci\u003eQ\u003c/i\u003e of the absolute\u003ca name=\"FNanchor_55_55\" id=\"FNanchor_55_55\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_55_55\" class=\"fnanchor\"\u003e[55]\u003c/a\u003e temperature\r\n\u003ci\u003eT\u003csub\u003e1\u003c/sub\u003e\u003c/i\u003e is lowered to the absolute temperature \u003ci\u003eT\u003csub\u003e2\u003c/sub\u003e\u003c/i\u003e.\"\r\nHere \u003ci\u003eQ\u0027\u003c/i\u003e is dependent only on \u003ci\u003eQ\u003c/i\u003e, \u003ci\u003eT\u003csub\u003e1\u003c/sub\u003e\u003c/i\u003e, \u003ci\u003eT\u003csub\u003e2\u003c/sub\u003e\u003c/i\u003e, but is independent\r\nof the substances used and of the character of\r\nthe process, so far as that is unaccompanied by loss.\r\nOwing to this last fact, it is sufficient to find the relation\r\nwhich obtains for some one well-known physical\r\nsubstance, say a gas, and some definite simple process.\r\nThe relation found will be the one that holds\r\ngenerally. We get, thus,\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003ci\u003eQ\u0027/(Q\u0027 + Q)\u003c/i\u003e = \u003ci\u003e(T\u003csub\u003e1\u003c/sub\u003e-T\u003csub\u003e2\u003c/sub\u003e)/T\u003csub\u003e1\u003c/sub\u003e\u003c/i\u003e (1)\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003ethat is, the quotient of the available heat \u003ci\u003eQ\u0027\u003c/i\u003e transformed\r\ninto work divided by the sum of the transformed\r\nand transferred heats (the total sum used), the\r\nso-called \u003ci\u003eeconomical coefficient\u003c/i\u003e of the process, is,\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003ci\u003e(T\u003csub\u003e1\u003c/sub\u003e-T\u003csub\u003e2\u003c/sub\u003e)/T\u003csub\u003e1\u003c/sub\u003e\u003c/i\u003e.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_166\" id=\"Page_166\"\u003e[Pg 166]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003ch3\u003eIV. THE CONCEPTIONS OF HEAT.\u003c/h3\u003e\r\n\r\n\u003cp\u003eWhen a cold body is put in contact with a warm\r\nbody it is observed that the first body is warmed and\r\nthat the second body is cooled. We may say that the\r\nfirst body is warmed \u003ci\u003eat the expense of\u003c/i\u003e the second body.\r\nThis suggests the notion of a thing, or heat-substance,\r\nwhich passes from the one body to the other. If two\r\nmasses of water \u003ci\u003em\u003c/i\u003e, \u003ci\u003em\u0027\u003c/i\u003e, of unequal temperatures, be\r\nput together, it will be found, upon the rapid equalisation\r\nof the temperatures, that the respective changes\r\nof temperatures \u003ci\u003eu\u003c/i\u003e and \u003ci\u003eu\u0027\u003c/i\u003e are inversely proportional to\r\nthe masses and of opposite signs, so that the algebraical\r\nsum of the products is,\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003ci\u003emu\u003c/i\u003e + \u003ci\u003em\u0027u\u0027\u003c/i\u003e = 0.\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eBlack called the products \u003ci\u003emu\u003c/i\u003e, \u003ci\u003em\u0027u\u0027\u003c/i\u003e, which are decisive\r\nfor our knowledge of the process, \u003ci\u003equantities of heat\u003c/i\u003e.\r\nWe may form a very clear \u003ci\u003epicture\u003c/i\u003e of these products\r\nby conceiving them with Black as measures of the\r\nquantities of some substance. But the essential thing\r\nis not this picture but the \u003ci\u003econstancy\u003c/i\u003e of the sum of these\r\nproducts in simple processes of conduction. If a quantity\r\nof heat disappears at one point, an equally large\r\nquantity will make its appearance at some other point.\r\nThe retention of this idea leads to the discovery of\r\nspecific heat. Black, finally, perceives that also something\r\nelse may appear for a vanished quantity of heat,\r\nnamely: the fusion or vaporisation of a definite quantity\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_167\" id=\"Page_167\"\u003e[Pg 167]\u003c/a\u003e\u003c/span\u003e\r\nof matter. He adheres here still to this favorite\r\nview, though with some freedom, and considers the\r\nvanished quantity of heat as still present, but as \u003ci\u003elatent\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe generally accepted notion of a caloric, or heat-stuff,\r\nwas strongly shaken by the work of Mayer and\r\nJoule. If the quantity of heat can be increased and\r\ndiminished, people said, heat cannot be a substance,\r\nbut must be a \u003ci\u003emotion\u003c/i\u003e. The subordinate part of this\r\nstatement has become much more popular than all the\r\nrest of the doctrine of energy. But we may convince\r\nourselves that the motional conception of heat is now\r\nas unessential as was formerly its conception as a substance.\r\nBoth ideas were favored or impeded solely\r\nby accidental historical circumstances. It does not\r\nfollow that heat is not a substance from the fact that\r\na mechanical equivalent exists for quantity of heat.\r\nWe will make this clear by the following question\r\nwhich bright students have sometimes put to me. Is\r\nthere a mechanical equivalent of electricity as there is\r\na mechanical equivalent of heat? Yes, and no. There\r\nis no mechanical equivalent of \u003ci\u003equantity\u003c/i\u003e of electricity\r\nas there is an equivalent of \u003ci\u003equantity\u003c/i\u003e of heat, because\r\nthe same quantity of electricity has a very different\r\ncapacity for work, according to the circumstances in\r\nwhich it is placed; but there \u003ci\u003eis\u003c/i\u003e a mechanical equivalent\r\nof electrical energy.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us ask another question. Is there a mechanical\r\nequivalent of water? No, there is no mechanical\r\nequivalent of quantity of water, but there is a mechanical\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_168\" id=\"Page_168\"\u003e[Pg 168]\u003c/a\u003e\u003c/span\u003e\r\nequivalent of weight of water multiplied by\r\nits distance of descent.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen a Leyden jar is discharged and work thereby\r\nperformed, we do not picture to ourselves that the\r\nquantity of electricity disappears as work is done, but\r\nwe simply assume that the electricities come into different\r\npositions, equal quantities of positive and negative\r\nelectricity being united with one another.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat, now, is the reason of this difference of view\r\nin our treatment of heat and of electricity? The reason\r\nis purely historical, wholly conventional, and, what\r\nis still more important, is wholly indifferent. I may\r\nbe allowed to establish this assertion.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn 1785 Coulomb constructed his torsion balance,\r\nby which he was enabled to measure the repulsion of\r\nelectrified bodies. Suppose we have two small balls,\r\n\u003ci\u003eA\u003c/i\u003e, \u003ci\u003eB\u003c/i\u003e, which over their whole extent are similarly\r\nelectrified. These two balls will exert on one another,\r\nat a certain distance \u003ci\u003er\u003c/i\u003e of their centres, a certain repulsion\r\n\u003ci\u003ep\u003c/i\u003e. We bring into contact with \u003ci\u003eB\u003c/i\u003e now a ball\r\n\u003ci\u003eC\u003c/i\u003e, suffer both to be equally electrified, and then measure\r\nthe repulsion of \u003ci\u003eB\u003c/i\u003e from \u003ci\u003eA\u003c/i\u003e and of \u003ci\u003eC\u003c/i\u003e from \u003ci\u003eA\u003c/i\u003e at the\r\nsame distance \u003ci\u003er\u003c/i\u003e. The sum of these repulsions is again\r\n\u003ci\u003ep\u003c/i\u003e. Accordingly something has remained constant.\r\nIf we ascribe this effect to a substance, then we infer\r\nnaturally its constancy. But the essential point of the\r\nexposition is the divisibility of the electric force \u003ci\u003ep\u003c/i\u003e and\r\nnot the simile of substance.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn 1838 Riess constructed his electrical air-thermometer\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_169\" id=\"Page_169\"\u003e[Pg 169]\u003c/a\u003e\u003c/span\u003e\r\n(the thermoelectrometer). This gives a measure\r\nof the quantity of heat produced by the discharge of\r\njars. This quantity of heat is not proportional to the\r\nquantity of electricity contained in the jar by Coulomb\u0027s\r\nmeasure, but if \u003ci\u003eQ\u003c/i\u003e be this quantity and \u003ci\u003eC\u003c/i\u003e be the\r\ncapacity, is proportional to \u003ci\u003eQ\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e/2\u003ci\u003eC\u003c/i\u003e, or, more simply\r\nstill, to the energy of the charged jar. If, now, we\r\ndischarge the jar completely through the thermometer,\r\nwe obtain a certain quantity of heat, \u003ci\u003eW\u003c/i\u003e. But if\r\nwe make the discharge through the thermometer into\r\na second jar, we obtain a quantity less than \u003ci\u003eW\u003c/i\u003e. But we\r\nmay obtain the remainder by completely discharging\r\nboth jars through the air-thermometer, when it will\r\nagain be proportional to the energy of the two jars. On\r\nthe first, incomplete discharge, accordingly, a part of\r\nthe electricity\u0027s capacity for work was lost.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen the charge of a jar produces heat its energy\r\nis changed and its value by Riess\u0027s thermometer is decreased.\r\nBut by Coulomb\u0027s measure the quantity remains\r\nunaltered.\u003c/p\u003e\r\n\r\n\u003cp\u003eNow let us imagine that Riess\u0027s thermometer had\r\nbeen invented before Coulomb\u0027s torsion balance, which\r\nis not a difficult feat, since both inventions are independent\r\nof each other; what would be more natural than\r\nthat the \"quantity\" of electricity contained in a jar\r\nshould be measured by the heat produced in the thermometer?\r\nBut then, this so-called quantity of electricity\r\nwould decrease on the production of heat or on\r\nthe performance of work, whereas it now remains unchanged;\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_170\" id=\"Page_170\"\u003e[Pg 170]\u003c/a\u003e\u003c/span\u003e\r\nin that case, therefore, electricity would not\r\nbe a \u003ci\u003esubstance\u003c/i\u003e but a \u003ci\u003emotion\u003c/i\u003e, whereas now it is still a\r\nsubstance. The reason, therefore, why we have other\r\nnotions of electricity than we have of heat, is purely\r\nhistorical, accidental, and conventional.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis is also the case with other physical things.\r\nWater does not disappear when work is done. Why?\r\nBecause we measure quantity of water with scales, just\r\nas we do electricity. But suppose the capacity of\r\nwater for work were called quantity, and had to be\r\nmeasured, therefore, by a mill instead of by scales;\r\nthen this quantity also would disappear as it performed\r\nthe work. It may, now, be easily conceived\r\nthat many substances are not so easily got at as water.\r\nIn that case we should be unable to carry out the one\r\nkind of measurement with the scales whilst many other\r\nmodes of measurement would still be left us.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the case of heat, now, the historically established\r\nmeasure of \"quantity\" is accidentally the work-value\r\nof the heat. Accordingly, its quantity disappears when\r\nwork is done. But that heat is not a substance follows\r\nfrom this as little as does the opposite conclusion that\r\nit is a substance. In Black\u0027s case the quantity of heat\r\nremains constant because the heat passes into no \u003ci\u003eother\u003c/i\u003e\r\nform of energy.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf any one to-day should still wish to think of heat\r\nas a substance, we might allow that person this liberty\r\nwith little ado. He would only have to assume that\r\nthat which we call quantity of heat was the energy of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_171\" id=\"Page_171\"\u003e[Pg 171]\u003c/a\u003e\u003c/span\u003e\r\na substance whose quantity remained unaltered, but\r\nwhose energy changed. In point of fact we might\r\nmuch better say, in analogy with the other terms of\r\nphysics, energy of heat, instead of quantity of heat.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen we wonder, therefore, at the discovery that\r\nheat is motion, we wonder at something that was never\r\ndiscovered. It is perfectly indifferent and possesses\r\nnot the slightest scientific value, whether we think of\r\nheat as a substance or not. The fact is, heat behaves\r\nin some connexions like a substance, in others not.\r\nHeat is latent in steam as oxygen is latent in water.\u003c/p\u003e\r\n\r\n\r\n\u003ch3\u003eV. THE CONFORMITY IN THE DEPORTMENT OF THE\r\nENERGIES.\u003c/h3\u003e\r\n\r\n\u003cp\u003eThe foregoing reflexions will gain in lucidity from\r\na consideration of the conformity which obtains in the\r\nbehavior of all energies, a point to which I called attention\r\nlong ago.\u003ca name=\"FNanchor_56_56\" id=\"FNanchor_56_56\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_56_56\" class=\"fnanchor\"\u003e[56]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eA weight \u003ci\u003eP\u003c/i\u003e at a height \u003ci\u003eH\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e represents an energy\r\n\u003ci\u003eW\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e = \u003ci\u003ePH\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e. If we suffer the weight to sink to a lower\r\nheight \u003ci\u003eH\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, during which work is done, and the work\r\ndone is employed in the production of living force,\r\nheat, or an electric charge, in short, is transformed,\r\nthen the energy \u003ci\u003eW\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e = \u003ci\u003ePH\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e is still \u003ci\u003eleft\u003c/i\u003e. The equation\r\nsubsists\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_172\" id=\"Page_172\"\u003e[Pg 172]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003ci\u003eW\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e/\u003ci\u003eH\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e = \u003ci\u003eW\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e/\u003ci\u003eH\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, (2)\r\nor, denoting the \u003ci\u003etransformed\u003c/i\u003e energy by \u003ci\u003eW\u003c/i\u003e\u0027 = \u003ci\u003eW\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e-\u003ci\u003eW\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e\r\nand the \u003ci\u003etransferred\u003c/i\u003e energy, that transported to the\r\nlower level, by \u003ci\u003eW\u003c/i\u003e = \u003ci\u003eW\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e,\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003ci\u003eW\u003c/i\u003e\u0027/(\u003ci\u003eW\u003c/i\u003e\u0027 + \u003ci\u003eW\u003c/i\u003e) = (\u003ci\u003eH\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e-\u003ci\u003eH\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e)/\u003ci\u003eH\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, (3)\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003ean equation in all respects analogous to equation (1)\r\nat page 165. The property in question, therefore, is\r\nby no means peculiar to heat. Equation (2) gives the\r\nrelation between the energy taken from the higher\r\nlevel and that deposited on the lower level (the energy\r\nleft behind); it says that these \u003ci\u003eenergies\u003c/i\u003e are proportional\r\nto the \u003ci\u003eheights of the levels\u003c/i\u003e. An equation analogous\r\nto equation (2) may be set up for \u003ci\u003eevery\u003c/i\u003e form of\r\nenergy; hence the equation which corresponds to\r\nequation (3), and so to equation (1), may be regarded\r\nas valid for every form. For electricity, for example,\r\n\u003ci\u003eH\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003eH\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e signify the potentials.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen we observe for the first time the agreement\r\nhere indicated in the transformative law of the energies,\r\nit appears surprising and unexpected, for we do\r\nnot perceive at once its reason. But to him who pursues\r\nthe comparative historical method that reason\r\nwill not long remain a secret.\u003c/p\u003e\r\n\r\n\u003cp\u003eSince Galileo, mechanical work, though long under\r\na different name, has been a \u003ci\u003efundamental concept\u003c/i\u003e of\r\nmechanics, as also a very important notion in the applied\r\nsciences. The transformation of work into living\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_173\" id=\"Page_173\"\u003e[Pg 173]\u003c/a\u003e\u003c/span\u003e\r\nforce, and of living force into work, suggests directly\r\nthe notion of energy\u0026mdash;the idea having been first\r\nfruitfully employed by Huygens, although Thomas\r\nYoung first called it by the \u003ci\u003ename\u003c/i\u003e of \"energy.\" Let\r\nus add to this the constancy of weight (really the constancy\r\nof mass) and we shall see that with respect to\r\nmechanical energy it is involved in the very definition\r\nof the term that the capacity for work or the potential\r\nenergy of a weight is proportional to the height of the\r\nlevel at which it is, in the geometrical sense, and that\r\nit decreases on the lowering of the weight, on transformation,\r\nproportionally to the height of the level.\r\nThe zero level here is wholly arbitrary. With this,\r\nequation (2) is given, from which all the other forms\r\nfollow.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen we reflect on the tremendous start which\r\nmechanics had over the other branches of physics, it\r\nis not to be wondered at that the attempt was always\r\nmade to apply the notions of that science wherever\r\nthis was possible. Thus the notion of mass, for example,\r\nwas imitated by Coulomb in the notion of\r\nquantity of electricity. In the further development\r\nof the theory of electricity, the notion of work was\r\nlikewise immediately introduced in the theory of potential,\r\nand heights of electrical level were measured\r\nby the work of unit of quantity raised to that level.\r\nBut with this the preceding equation with all its consequences\r\nis given for electrical energy. The case with\r\nthe other energies was similar.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_174\" id=\"Page_174\"\u003e[Pg 174]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003ci\u003eThermal\u003c/i\u003e energy, however, appears as a special\r\ncase. Only by the peculiar experiments mentioned\r\ncould it be discovered that heat is an energy. But the\r\nmeasure of this energy by Black\u0027s quantity of heat is\r\nthe outcome of fortuitous circumstances. In the first\r\nplace, the accidental slight variability of the capacity\r\nfor heat \u003ci\u003ec\u003c/i\u003e with the temperature, and the accidental\r\nslight deviation of the usual thermometrical scales\r\nfrom the scale derived from \u003ci\u003ethe tensions of gases\u003c/i\u003e, brings\r\nit about that the notion \"quantity of heat\" can be set\r\nup and that the quantity of heat \u003ci\u003ect\u003c/i\u003e corresponding to a\r\ndifference of temperature \u003ci\u003et\u003c/i\u003e is nearly proportional to\r\nthe energy of the heat. It is a quite accidental historical\r\ncircumstance that Amontons hit upon the idea\r\nof measuring temperature by the tension of a gas. It\r\nis certain in this that he did not think of the work of\r\nthe heat.\u003ca name=\"FNanchor_57_57\" id=\"FNanchor_57_57\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_57_57\" class=\"fnanchor\"\u003e[57]\u003c/a\u003e But the numbers standing for temperature,\r\nthus, are made proportional to the tensions of\r\ngases, that is, to the work done by gases, with otherwise\r\nequal changes of volume. It thus happens that\r\n\u003ci\u003etemperature heights\u003c/i\u003e and \u003ci\u003elevel heights of work\u003c/i\u003e are proportional\r\nto one another.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf properties of the thermal condition varying\r\ngreatly from the tensions of gases had been chosen,\r\nthis relation would have assumed very complicated\r\nforms, and the agreement between heat and the other\r\nenergies above considered would not subsist. It is\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_175\" id=\"Page_175\"\u003e[Pg 175]\u003c/a\u003e\u003c/span\u003e\r\nvery instructive to reflect upon this point. A \u003ci\u003enatural\r\nlaw\u003c/i\u003e, therefore, is not implied in the conformity of the\r\nbehavior of the energies, but this conformity is rather\r\nconditioned by the uniformity of our modes of conception\r\nand is also partly a matter of good fortune.\u003c/p\u003e\r\n\r\n\r\n\u003ch3\u003eVI. THE DIFFERENCES OF THE ENERGIES AND THE\r\nLIMITS OF THE PRINCIPLE OF ENERGY.\u003c/h3\u003e\r\n\r\n\u003cp\u003eOf every quantity of heat \u003ci\u003eQ\u003c/i\u003e which does work in a\r\nreversible process (one unaccompanied by loss) between\r\nthe absolute temperatures \u003ci\u003eT\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003eT\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e, only the portion\u003c/p\u003e\r\n\r\n\u003cp\u003e(\u003ci\u003eT\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e-\u003ci\u003eT\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e)/\u003ci\u003eT\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eis transformed into work, while the remainder is transferred\r\nto the lower temperature-level \u003ci\u003eT\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e. This transferred\r\nportion can, upon the reversal of the process,\r\nwith the same expenditure of work, again be brought\r\nback to the level \u003ci\u003eT\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e. But if the process is not reversible,\r\nthen more heat than in the foregoing case flows\r\nto the lower level, and the surplus can no longer be\r\nbrought back to the higher level \u003ci\u003eT\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e without some \u003ci\u003especial\u003c/i\u003e\r\nexpenditure. W. Thomson (1852), accordingly,\r\ndrew attention to the fact, that in all non-reversible,\r\nthat is, in all real thermal processes, quantities of heat\r\nare lost for mechanical work, and that accordingly a\r\ndissipation or waste of mechanical energy is taking\r\nplace. In all cases, heat is only partially transformed\r\ninto work, but frequently work is wholly transformed\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_176\" id=\"Page_176\"\u003e[Pg 176]\u003c/a\u003e\u003c/span\u003e\r\ninto heat. Hence, a tendency exists towards a diminution\r\nof the \u003ci\u003emechanical\u003c/i\u003e energy and towards an increase\r\nof the \u003ci\u003ethermal\u003c/i\u003e energy of the world.\u003c/p\u003e\r\n\r\n\u003cp\u003eFor a simple, closed cyclical process, accompanied\r\nby no loss, in which the quantity of heat \u003ci\u003eQ_\u003c/i\u003e{1} is taken\r\nfrom the level \u003ci\u003eT_\u003c/i\u003e{1}, and the quantity \u003ci\u003eQ_\u003c/i\u003e{2} is deposited\r\nupon the level \u003ci\u003eT_\u003c/i\u003e{2}, the following relation, agreeably to\r\nequation (2), exists,\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e-(\u003ci\u003eQ\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e/\u003ci\u003eT\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e) + (\u003ci\u003eQ\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e/\u003ci\u003eT\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e) = 0.\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eSimilarly, for any number of compound reversible\r\ncycles Clausius finds the algebraical sum\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u0026#931;\u003ci\u003eQ\u003c/i\u003e/\u003ci\u003eT\u003c/i\u003e = 0,\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eand supposing the temperature to change continuously,\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u0026#8747;\u003ci\u003edQ\u003c/i\u003e/\u003ci\u003eT\u003c/i\u003e = 0 (4)\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003eHere the elements of the quantities of heat deducted\r\nfrom a given level are reckoned negative, and the elements\r\nimparted to it, positive. If the process is not\r\nreversible, then expression (4), which Clausius calls\r\n\u003ci\u003eentropy\u003c/i\u003e, increases. In actual practice this is always\r\nthe case, and Clausius finds himself led to the statement:\u003c/p\u003e\r\n\r\n\u003cp\u003e1. That the energy of the world remains constant.\u003c/p\u003e\r\n\r\n\u003cp\u003e2. That the entropy of the world tends toward a\r\nmaximum.\u003c/p\u003e\r\n\r\n\u003cp\u003eOnce we have noted the above-indicated conformity\r\nin the behavior of different energies, the \u003ci\u003epeculiarity\u003c/i\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_177\" id=\"Page_177\"\u003e[Pg 177]\u003c/a\u003e\u003c/span\u003e\r\nof thermal energy here mentioned must strike us.\r\nWhence is this peculiarity derived, for, generally every\r\nenergy passes only partly into another form, which is\r\nalso true of thermal energy? The explanation will be\r\nfound in the following.\u003c/p\u003e\r\n\r\n\u003cp\u003eEvery transformation of a special kind of energy \u003ci\u003eA\u003c/i\u003e\r\nis accompanied with a fall of potential of that particular\r\nkind of energy, including heat. But whilst for the\r\nother kinds of energy a transformation and therefore a\r\nloss of energy on the part of the kind sinking in potential\r\nis connected with the fall of the potential, with\r\nheat the case is different. Heat can suffer a fall of\r\npotential without sustaining a loss of energy, at least\r\naccording to the customary mode of estimation. If a\r\nweight sinks, it must create perforce kinetic energy,\r\nor heat, or some other form of energy. Also, an electrical\r\ncharge cannot suffer a fall of potential without\r\nloss of energy, i. e., without transformation. But heat\r\ncan pass with a fall of temperature to a body of greater\r\ncapacity and the same thermal energy still be preserved,\r\nso long as we regard \u003ci\u003eevery quantity\u003c/i\u003e of heat as\r\nenergy. This it is that gives to heat, besides its\r\nproperty of energy, in many cases the character of a\r\nmaterial \u003ci\u003esubstance\u003c/i\u003e, or quantity.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we look at the matter in an unprejudiced light,\r\nwe must ask if there is any scientific sense or purpose\r\nin still considering as energy a quantity of heat that\r\ncan no longer be transformed into mechanical work,\r\n(for example, the heat of a closed equably warmed\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_178\" id=\"Page_178\"\u003e[Pg 178]\u003c/a\u003e\u003c/span\u003e\r\nmaterial system). The principle of energy certainly\r\nplays in this case a wholly superfluous rôle, which is\r\nassigned to it only from habit.\u003ca name=\"FNanchor_58_58\" id=\"FNanchor_58_58\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_58_58\" class=\"fnanchor\"\u003e[58]\u003c/a\u003e To maintain the principle\r\nof energy in the face of a knowledge of the dissipation\r\nor waste of mechanical energy, in the face of\r\nthe increase of entropy is equivalent almost to the\r\nliberty which Black took when he regarded the heat\r\nof liquefaction as still present but latent.\u003ca name=\"FNanchor_59_59\" id=\"FNanchor_59_59\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_59_59\" class=\"fnanchor\"\u003e[59]\u003c/a\u003e It is to be\r\nremarked further, that the expressions \"energy of the\r\nworld\" and \"entropy of the world\" are slightly permeated\r\nwith scholasticism. Energy and entropy are\r\n\u003ci\u003emetrical\u003c/i\u003e notions. What meaning can there be in applying\r\nthese notions to a case in which they are not\r\napplicable, in which their values are not determinable?\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we could really determine the entropy of the\r\nworld it would represent a true, absolute measure of\r\ntime. In this way is best seen the utter tautology of\r\na statement that the entropy of the world increases\r\nwith the time. Time, and the fact that certain changes\r\ntake place only in a definite sense, are one and the\r\nsame thing.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_179\" id=\"Page_179\"\u003e[Pg 179]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003ch3\u003eVII. THE SOURCES OF THE PRINCIPLE OF ENERGY.\u003c/h3\u003e\r\n\r\n\u003cp\u003eWe are now prepared to answer the question, What\r\nare the sources of the principle of energy? All knowledge\r\nof nature is derived in the last instance from experience.\r\nIn this sense they are right who look upon\r\nthe principle of energy as a result of experience.\u003c/p\u003e\r\n\r\n\u003cp\u003eExperience teaches that the sense-elements \u0026#945;\u0026#946;\u0026#947;\u0026#948;…\r\ninto which the world may be decomposed, are subject\r\nto change. It tells us further, that certain of these\r\nelements are \u003ci\u003econnected\u003c/i\u003e with other elements, so that they\r\nappear and disappear together; or, that the appearance\r\nof the elements of one class is connected with the\r\ndisappearance of the elements of the other class. We\r\nwill avoid here the notions of cause and effect because\r\nof their obscurity and equivocalness. The result\r\nof experience may be expressed as follows: \u003ci\u003eThe\r\nsensuous elements of the world (\u0026#945;\u0026#946;\u0026#947;\u0026#948;…) show themselves\r\nto be interdependent.\u003c/i\u003e This interdependence is\r\nbest represented by some such conception as is in\r\ngeometry that of the mutual dependence of the sides\r\nand angles of a triangle, only much more varied and\r\ncomplex.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs an example, we may take a mass of gas enclosed\r\nin a cylinder and possessed of a definite volume (\u0026#945;),\r\nwhich we change by a pressure (\u0026#946;) on the piston, at\r\nthe same time feeling the cylinder with our hand and\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_180\" id=\"Page_180\"\u003e[Pg 180]\u003c/a\u003e\u003c/span\u003e\r\nreceiving a sensation of heat (\u0026#947;). Increase of pressure\r\ndiminishes the volume and increases the sensation\r\nof heat.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe various facts of experience are not in all respects\r\nalike. Their common sensuous elements are\r\nplaced in relief by a process of abstraction and thus\r\nimpressed upon the memory. In this way the expression\r\nis obtained of the features of \u003ci\u003eagreement\u003c/i\u003e of extensive\r\ngroups of facts. The simplest sentence which we can\r\nutter is, by the very nature of language, an abstraction\r\nof this kind. But account must also be taken of the\r\n\u003ci\u003edifferences\u003c/i\u003e of related facts. Facts may be so nearly related\r\nas to contain the same kind of a \u0026#945;\u0026#946;\u0026#947;…, but the\r\nrelation be such that the \u0026#945;\u0026#946;\u0026#947;… of the one differ\r\nfrom the \u0026#945;\u0026#946;\u0026#947;… of the other only by the number of\r\nequal parts into which they can be divided. Such\r\nbeing the case, if rules can be given for deducing \u003ci\u003efrom\r\none another\u003c/i\u003e the numbers which are the measures of\r\nthese \u0026#945;\u0026#946;\u0026#947;…, then we possess in such rules the \u003ci\u003emost\r\ngeneral\u003c/i\u003e expression of a group of facts, as also that expression\r\nwhich corresponds to all its differences. This\r\nis the goal of quantitative investigation.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf this goal be reached what we have found is that\r\nbetween the \u0026#945;\u0026#946;\u0026#947;… of a group of facts, or better, between\r\nthe numbers which are their measures, a number\r\nof equations exists. The simple fact of change\r\nbrings it about that the number of these equations\r\nmust be smaller than the number of the \u0026#945;\u0026#946;\u0026#947;…. If\r\nthe former be smaller by one than the latter, then one\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_181\" id=\"Page_181\"\u003e[Pg 181]\u003c/a\u003e\u003c/span\u003e\r\nportion of the \u0026#945;\u0026#946;\u0026#947;… is \u003ci\u003euniquely\u003c/i\u003e determined by the\r\nother portion.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe quest of relations of this last kind is the most\r\nimportant function of special experimental research,\r\nbecause we are enabled by it to complete in thought\r\nfacts that are only partly given. It is self-evident that\r\nonly experience can ascertain that between the \u0026#945;\u0026#946;\u0026#947;…\r\nrelations exist and of what kind they are. Further,\r\nonly experience can tell that the relations that exist\r\nbetween the \u0026#945;\u0026#946;\u0026#947;… are such that changes of them\r\ncan be reversed. If this were not the fact all occasion\r\nfor the enunciation of the principle of energy, as is\r\neasily seen, would be wanting. In experience, therefore,\r\nis buried the ultimate well-spring of all knowledge\r\nof nature, and consequently, in this sense, also\r\nthe ultimate source of the principle of energy.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut this does not exclude the fact that the principle\r\nof energy has also a logical root, as will now be\r\nshown. Let us assume on the basis of experience that\r\none group of sensuous elements \u0026#945;\u0026#946;\u0026#947;… determines\r\n\u003ci\u003euniquely\u003c/i\u003e another group \u0026#955;\u0026#956;\u0026#957;…. Experience further\r\nteaches that changes of \u0026#945;\u0026#946;\u0026#947;… can be \u003ci\u003ereversed\u003c/i\u003e. It\r\nis then a logical consequence of this observation, that\r\nevery time that \u0026#945;\u0026#946;\u0026#947;… assume the same values this\r\nis also the case with \u0026#955;\u0026#956;\u0026#957;…. Or, that purely \u003ci\u003eperiodical\u003c/i\u003e\r\nchanges of \u0026#945;\u0026#946;\u0026#947;… can produce no \u003ci\u003epermanent\u003c/i\u003e\r\nchanges of \u0026#955;\u0026#956;\u0026#957;…. If the group \u0026#955;\u0026#956;\u0026#957;… is a mechanical\r\ngroup, then a perpetual motion is excluded.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_182\" id=\"Page_182\"\u003e[Pg 182]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will be said that this is a vicious circle, which\r\nwe will grant. But psychologically, the situation is\r\nessentially different, whether I think simply of the\r\nunique determination and reversibility of events, or\r\nwhether I exclude a perpetual motion. The attention\r\ntakes in the two cases different directions and diffuses\r\nlight over different sides of the question, which logically\r\nof course are necessarily connected.\u003c/p\u003e\r\n\r\n\u003cp\u003eSurely that firm, logical setting of the thoughts noticeable\r\nin the great inquirers, Stevinus, Galileo, and\r\nthe rest, which, consciously or instinctively, was supported\r\nby a fine feeling for the slightest contradictions,\r\nhas no other purpose than to limit the bounds of\r\nthought and so exempt it from the possibility of error.\r\nIn this, therefore, the logical root of the principle of\r\nexcluded perpetual motion is given, namely, in that\r\nuniversal conviction which existed even before the development\r\nof mechanics and co-operated in that development.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is perfectly natural that the principle of excluded\r\nperpetual motion should have been first developed in\r\nthe simple domain of pure mechanics. Towards the\r\ntransference of that principle into the domain of general\r\nphysics the idea contributed much that all physical\r\nphenomena are mechanical phenomena. But the\r\nforegoing discussion shows how little essential this\r\nnotion is. The issue really involved is the recognition\r\nof a general interconnexion of nature. This once established,\r\nwe see with Carnot that it is indifferent\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_183\" id=\"Page_183\"\u003e[Pg 183]\u003c/a\u003e\u003c/span\u003e\r\nwhether the mechanical laws are broken directly or\r\ncircuitously.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe principle of the excluded perpetual motion is\r\nvery closely related to the modern principle of energy,\r\nbut it is not identical with it, for the latter is to be\r\ndeduced from the former only by means of a definite\r\n\u003ci\u003eformal conception\u003c/i\u003e. As may be seen from the preceding\r\nexposition, the perpetual motion can be excluded without\r\nour employing or possessing the notion of \u003ci\u003ework\u003c/i\u003e.\r\nThe modern principle of energy results primarily from\r\na \u003ci\u003esubstantial\u003c/i\u003e conception of work and of every change\r\nof physical condition which by being reversed produces\r\nwork. The strong need of such a conception,\r\nwhich is by no means necessary, but in a formal sense\r\nis very convenient and lucid, is exhibited in the case\r\nof J. R. Mayer and Joule. It was before remarked\r\nthat this conception was suggested to both inquirers\r\nby the observation that both the production of heat\r\nand the production of mechanical work were connected\r\nwith an expenditure of substance. Mayer says: \"Ex\r\nnihilo nil fit,\" and in another place, \"The creation or\r\ndestruction of a force (work) lies without the province\r\nof human activity.\" In Joule we find this passage:\r\n\"It is manifestly \u003ci\u003eabsurd\u003c/i\u003e to suppose that the powers\r\nwith which God has endowed matter can be destroyed.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eSome writers have observed in such statements the\r\nattempt at a \u003ci\u003emetaphysical\u003c/i\u003e establishment of the doctrine\r\nof energy. But we see in them simply the formal need\r\nof a simple, clear, and living grasp of the facts, which\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_184\" id=\"Page_184\"\u003e[Pg 184]\u003c/a\u003e\u003c/span\u003e\r\nreceives its development in practical and technical life,\r\nand which we carry over, as best we can, into the\r\nprovince of science. As a fact, Mayer writes to Griesinger:\r\n\"If, finally, you ask me how I became involved\r\nin the whole affair, my answer is simply this: Engaged\r\nduring a sea voyage almost exclusively with the study\r\nof physiology, I discovered the new theory for the\r\nsufficient reason that I \u003ci\u003evividly felt the need of it\u003c/i\u003e.\"\u003c/p\u003e\r\n\r\n\u003cp\u003eThe substantial conception of work (energy) is by\r\nno means a necessary one. And it is far from true that\r\nthe problem is solved with the recognition of the need\r\nof such a conception. Rather let us see how Mayer\r\ngradually endeavored to satisfy that need. He first\r\nregards quantity of motion, or momentum, \u003ci\u003emv\u003c/i\u003e, as the\r\nequivalent of work, and did not light, until later, on\r\nthe notion of living force (\u003ci\u003emv\u003csup\u003e2\u003c/sup\u003e/2\u003c/i\u003e). In the province\r\nof electricity he was unable to assign the expression\r\nwhich is the equivalent of work. This was done later\r\nby Helmholtz. The formal need, therefore, is \u003ci\u003efirst\u003c/i\u003e\r\npresent, and our conception of nature is subsequently\r\ngradually \u003ci\u003eadapted\u003c/i\u003e to it.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe laying bare of the experimental, logical, and\r\nformal root of the present principle of energy will perhaps\r\ncontribute much to the removal of the mysticism\r\nwhich still clings to this principle. With respect to\r\nour formal need of a very simple, palpable, substantial\r\nconception of the processes in our environment, it\r\nremains an open question how far nature corresponds\r\nto that need, or how far we can satisfy it. In one\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_185\" id=\"Page_185\"\u003e[Pg 185]\u003c/a\u003e\u003c/span\u003e\r\nphase of the preceding discussions it would seem as\r\nif the substantial notion of the principle of energy, like\r\nBlack\u0027s material conception of heat, has its natural\r\nlimits in facts, beyond which it can only be artificially\r\nadhered to.\u003c/p\u003e\u003chr class=\"chap\" /\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_186\" id=\"Page_186\"\u003e[Pg 186]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"THE_ECONOMICAL_NATURE_OF\" id=\"THE_ECONOMICAL_NATURE_OF\"\u003eTHE ECONOMICAL NATURE OF\r\nPHYSICAL INQUIRY.\u003c/a\u003e\u003ca name=\"FNanchor_60_60\" id=\"FNanchor_60_60\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_60_60\" class=\"fnanchor\"\u003e[60]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eWhen the human mind, with its limited powers,\r\nattempts to mirror in itself the rich life of the\r\nworld, of which it is itself only a small part, and which\r\nit can never hope to exhaust, it has every reason for\r\nproceeding economically. Hence that tendency, expressed\r\nin the philosophy of all times, to compass by\r\na few organic thoughts the fundamental features of\r\nreality. \"Life understands not death, nor death life.\"\r\nSo spake an old Chinese philosopher. Yet in his unceasing\r\ndesire to diminish the boundaries of the incomprehensible,\r\nman has always been engaged in attempts\r\nto understand death by life and life by death.\u003c/p\u003e\r\n\r\n\u003cp\u003eAmong the ancient civilised peoples, nature was\r\nfilled with demons and spirits having the feelings and\r\ndesires of men. In all essential features, this animistic\r\nview of nature, as Tylor\u003ca name=\"FNanchor_61_61\" id=\"FNanchor_61_61\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_61_61\" class=\"fnanchor\"\u003e[61]\u003c/a\u003e has aptly termed it, is shared\r\nin common by the fetish-worshipper of modern Africa\r\nand the most advanced nations of antiquity. As a\r\ntheory of the world it has never completely disappeared.\r\nThe monotheism of the Christians never fully\r\novercame it, no more than did that of the Jews. In\r\nthe belief in witchcraft and in the superstitions of the\r\nsixteenth and seventeenth centuries, the centuries of\r\nthe rise of natural science, it assumed frightful pathological\r\ndimensions. Whilst Stevinus, Kepler, and\r\nGalileo were slowly rearing the fabric of modern physical\r\nscience, a cruel and relentless war was waged\r\nwith firebrand and rack against the devils that glowered\r\nfrom every corner. To-day even, apart from all survivals\r\nof that period, apart from the traces of fetishism\r\nwhich still inhere in our physical concepts,\u003ca name=\"FNanchor_62_62\" id=\"FNanchor_62_62\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_62_62\" class=\"fnanchor\"\u003e[62]\u003c/a\u003e those\r\nvery ideas still covertly lurk in the practices of modern\r\nspiritualism.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_187\" id=\"Page_187\"\u003e[Pg 187]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eBy the side of this animistic conception of the\r\nworld, we meet from time to time, in different forms,\r\nfrom Democritus to the present day, another view,\r\nwhich likewise claims exclusive competency to comprehend\r\nthe universe. This view may be characterised\r\nas the \u003ci\u003ephysico-mechanical\u003c/i\u003e view of the world. To-day,\r\nthat view holds, indisputably, the first place in the\r\nthoughts of men, and determines the ideals and the\r\ncharacter of our times. The coming of the mind of\r\nman into the full consciousness of its powers, in the\r\neighteenth century, was a period of genuine disillusionment.\r\nIt produced the splendid precedent of a life\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_188\" id=\"Page_188\"\u003e[Pg 188]\u003c/a\u003e\u003c/span\u003e\r\nreally worthy of man, competent to overcome the old\r\nbarbarism in the practical fields of life; it created the\r\n\u003ci\u003eCritique of Pure Reason\u003c/i\u003e, which banished into the realm\r\nof shadows the sham-ideas of the old metaphysics; it\r\npressed into the hands of the mechanical philosophy\r\nthe reins which it now holds.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe oft-quoted words of the great Laplace,\u003ca name=\"FNanchor_63_63\" id=\"FNanchor_63_63\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_63_63\" class=\"fnanchor\"\u003e[63]\u003c/a\u003e which\r\nI will now give, have the ring of a jubilant toast to\r\nthe scientific achievements of the eighteenth century:\r\n\"A mind to which were given for a single instant all\r\nthe forces of nature and the mutual positions of all its\r\nmasses, if it were otherwise powerful enough to subject\r\nthese problems to analysis, could grasp, with a\r\nsingle formula, the motions of the largest masses as\r\nwell as of the smallest atoms; nothing would be uncertain\r\nfor it; the future and the past would lie revealed\r\nbefore its eyes.\" In writing these words, Laplace,\r\nas we know, had also in mind the atoms of the\r\nbrain. That idea has been expressed more forcibly\r\nstill by some of his followers, and it is not too much\r\nto say that Laplace\u0027s ideal is substantially that of the\r\ngreat majority of modern scientists.\u003c/p\u003e\r\n\r\n\u003cp\u003eGladly do we accord to the creator of the \u003ci\u003eMécanique\r\ncéleste\u003c/i\u003e the sense of lofty pleasure awakened in\r\nhim by the great success of the Enlightenment, to\r\nwhich we too owe our intellectual freedom. But to-day,\r\nwith minds undisturbed and before \u003ci\u003enew\u003c/i\u003e tasks, it\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_189\" id=\"Page_189\"\u003e[Pg 189]\u003c/a\u003e\u003c/span\u003e\r\nbecomes physical science to secure itself against self-deception\r\nby a careful study of its character, so that\r\nit can pursue with greater sureness its true objects.\r\nIf I step, therefore, beyond the narrow precincts of my\r\nspecialty in this discussion, to trespass on friendly\r\nneighboring domains, I may plead in my excuse that\r\nthe subject-matter of knowledge is common to all domains\r\nof research, and that fixed, sharp lines of demarcation\r\ncannot be drawn.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe belief in occult magic powers of nature has\r\ngradually died away, but in its place a new belief has\r\narisen, the belief in the magical power of science.\r\nScience throws her treasures, not like a capricious\r\nfairy into the laps of a favored few, but into the laps\r\nof all humanity, with a lavish extravagance that no\r\nlegend ever dreamt of! Not without apparent justice,\r\ntherefore, do her distant admirers impute to her the\r\npower of opening up unfathomable abysses of nature,\r\nto which the senses cannot penetrate. Yet she who\r\ncame to bring light into the world, can well dispense\r\nwith the darkness of mystery, and with pompous show,\r\nwhich she needs neither for the justification of her\r\naims nor for the adornment of her plain achievements.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe homely beginnings of science will best reveal\r\nto us its simple, unchangeable character. Man acquires\r\nhis first knowledge of nature half-consciously\r\nand automatically, from an instinctive habit of mimicking\r\nand forecasting facts in thought, of supplementing\r\nsluggish experience with the swift wings of thought,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_190\" id=\"Page_190\"\u003e[Pg 190]\u003c/a\u003e\u003c/span\u003e\r\nat first only for his material welfare. When he hears\r\na noise in the underbrush he constructs there, just as\r\nthe animal does, the enemy which he fears; when he\r\nsees a certain rind he forms mentally the image of the\r\nfruit which he is in search of; just as we mentally associate\r\na certain kind of matter with a certain line in\r\nthe spectrum or an electric spark with the friction of a\r\npiece of glass. A knowledge of causality in this form\r\ncertainly reaches far below the level of Schopenhauer\u0027s\r\npet dog, to whom it was ascribed. It probably exists\r\nin the whole animal world, and confirms that great\r\nthinker\u0027s statement regarding the will which created\r\nthe intellect for its purposes. These primitive psychical\r\nfunctions are rooted in the economy of our organism\r\nnot less firmly than are motion and digestion.\r\nWho would deny that we feel in them, too, the elemental\r\npower of a long practised logical and physiological\r\nactivity, bequeathed to us as an heirloom from\r\nour forefathers?\u003c/p\u003e\r\n\r\n\u003cp\u003eSuch primitive acts of knowledge constitute to-day\r\nthe solidest foundation of scientific thought. Our instinctive\r\nknowledge, as we shall briefly call it, by virtue\r\nof the conviction that we have consciously and\r\nintentionally contributed nothing to its formation, confronts\r\nus with an authority and logical power which\r\nconsciously acquired knowledge even from familiar\r\nsources and of easily tested fallibility can never possess.\r\nAll so-called axioms are such instinctive knowledge.\r\nNot consciously gained knowledge alone, but powerful\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_191\" id=\"Page_191\"\u003e[Pg 191]\u003c/a\u003e\u003c/span\u003e\r\nintellectual instinct, joined with vast conceptive powers,\r\nconstitute the great inquirer. The greatest advances\r\nof science have always consisted in some successful\r\nformulation, in clear, abstract, and communicable terms,\r\nof what was instinctively known long before, and of\r\nthus making it the permanent property of humanity.\r\nBy Newton\u0027s principle of the equality of pressure and\r\ncounterpressure, whose truth all before him had felt, but\r\nwhich no predecessor had abstractly formulated, mechanics\r\nwas placed by a single stroke on a higher level.\r\nOur statement might also be historically justified by\r\nexamples from the scientific labors of Stevinus, S.\r\nCarnot, Faraday, J. R. Mayer, and others.\u003c/p\u003e\r\n\r\n\u003cp\u003eAll this, however, is merely the soil from which\r\nscience starts. The first real beginnings of science\r\nappear in society, particularly in the manual arts,\r\nwhere the necessity for the communication of experience\r\narises. Here, where some new discovery is to\r\nbe described and related, the compulsion is first felt of\r\nclearly defining in consciousness the important and\r\nessential features of that discovery, as many writers\r\ncan testify. The aim of instruction is simply the saving\r\nof experience; the labor of one man is made to\r\ntake the place of that of another.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe most wonderful economy of communication is\r\nfound in language. Words are comparable to type,\r\nwhich spare the repetition of written signs and thus\r\nserve a multitude of purposes; or to the few sounds\r\nof which our numberless different words are composed.\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_192\" id=\"Page_192\"\u003e[Pg 192]\u003c/a\u003e\u003c/span\u003e\r\nLanguage, with its helpmate, conceptual thought, by\r\nfixing the essential and rejecting the unessential, constructs\r\nits rigid pictures of the fluid world on the plan\r\nof a mosaic, at a sacrifice of exactness and fidelity but\r\nwith a saving of tools and labor. Like a piano-player\r\nwith previously prepared sounds, a speaker excites in\r\nhis listener thoughts previously prepared, but fitting\r\nmany cases, which respond to the speaker\u0027s summons\r\nwith alacrity and little effort.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe principles which a prominent political economist,\r\nE. Hermann,\u003ca name=\"FNanchor_64_64\" id=\"FNanchor_64_64\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_64_64\" class=\"fnanchor\"\u003e[64]\u003c/a\u003e has formulated for the economy of\r\nthe industrial arts, are also applicable to the ideas of\r\ncommon life and of science. The economy of language\r\nis augmented, of course, in the terminology of science.\r\nWith respect to the economy of written intercourse\r\nthere is scarcely a doubt that science itself will realise\r\nthat grand old dream of the philosophers of a Universal\r\nReal Character. That time is not far distant.\r\nOur numeral characters, the symbols of mathematical\r\nanalysis, chemical symbols, and musical notes, which\r\nmight easily be supplemented by a system of color-signs,\r\ntogether with some phonetic alphabets now in\r\nuse, are all beginnings in this direction. The logical\r\nextension of what we have, joined with a use of the\r\nideas which the Chinese ideography furnishes us, will\r\nrender the special invention and promulgation of a\r\nUniversal Character wholly superfluous.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe communication of scientific knowledge always\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_193\" id=\"Page_193\"\u003e[Pg 193]\u003c/a\u003e\u003c/span\u003e\r\ninvolves description, that is, a mimetic reproduction\r\nof facts in thought, the object of which is to replace\r\nand save the trouble of new experience. Again, to\r\nsave the labor of instruction and of acquisition, concise,\r\nabridged description is sought. This is really all\r\nthat natural laws are. Knowing the value of the acceleration\r\nof gravity, and Galileo\u0027s laws of descent, we\r\npossess simple and compendious directions for reproducing\r\nin thought all possible motions of falling bodies.\r\nA formula of this kind is a complete substitute\r\nfor a full table of motions of descent, because by means\r\nof the formula the data of such a table can be easily\r\nconstructed at a moment\u0027s notice without the least\r\nburdening of the memory.\u003c/p\u003e\r\n\r\n\u003cp\u003eNo human mind could comprehend all the individual\r\ncases of refraction. But knowing the index of refraction\r\nfor the two media presented, and the familiar\r\nlaw of the sines, we can easily reproduce or fill out in\r\nthought every conceivable case of refraction. The advantage\r\nhere consists in the disburdening of the memory;\r\nan end immensely furthered by the written preservation\r\nof the natural constants. More than this comprehensive\r\nand condensed report about facts is not\r\ncontained in a natural law of this sort. In reality, the\r\nlaw always contains less than the fact itself, because it\r\ndoes not reproduce the fact as a whole but only in\r\nthat aspect of it which is important for us, the rest being\r\neither intentionally or from necessity omitted.\r\nNatural laws may be likened to intellectual type of a\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_194\" id=\"Page_194\"\u003e[Pg 194]\u003c/a\u003e\u003c/span\u003e\r\nhigher order, partly movable, partly stereotyped, which\r\nlast on new editions of experience may become downright\r\nimpediments.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen we look over a province of facts for the first\r\ntime, it appears to us diversified, irregular, confused,\r\nfull of contradictions. We first succeed in grasping\r\nonly single facts, unrelated with the others. The\r\nprovince, as we are wont to say, is not \u003ci\u003eclear\u003c/i\u003e. By and\r\nby we discover the simple, permanent elements of the\r\nmosaic, out of which we can mentally construct the\r\nwhole province. When we have reached a point where\r\nwe can discover everywhere the same facts, we no\r\nlonger feel lost in this province; we comprehend it\r\nwithout effort; it is \u003ci\u003eexplained\u003c/i\u003e for us.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet me illustrate this by an example. As soon as\r\nwe have grasped the fact of the rectilinear propagation\r\nof light, the regular course of our thoughts stumbles\r\nat the phenomena of refraction and diffraction. As soon\r\nas we have cleared matters up by our index of refraction\r\nwe discover that a special index is necessary for\r\neach color. Soon after we have accustomed ourselves\r\nto the fact that light added to light increases its intensity,\r\nwe suddenly come across a case of total darkness\r\nproduced by this cause. Ultimately, however,\r\nwe see everywhere in the overwhelming multifariousness\r\nof optical phenomena the fact of the spatial and\r\ntemporal periodicity of light, with its velocity of propagation\r\ndependent on the medium and the period. This\r\ntendency of obtaining a survey of a given province\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_195\" id=\"Page_195\"\u003e[Pg 195]\u003c/a\u003e\u003c/span\u003e\r\nwith the least expenditure of thought, and of representing\r\nall its facts by some one single mental process,\r\nmay be justly termed an economical one.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe greatest perfection of mental economy is attained\r\nin that science which has reached the highest\r\nformal development, and which is widely employed in\r\nphysical inquiry, namely, in mathematics. Strange as\r\nit may sound, the power of mathematics rests upon\r\nits evasion of all unnecessary thought and on its wonderful\r\nsaving of mental operations. Even those arrangement-signs\r\nwhich we call numbers are a system\r\nof marvellous simplicity and economy. When we employ\r\nthe multiplication-table in multiplying numbers\r\nof several places, and so use the results of old operations\r\nof counting instead of performing the whole of\r\neach operation anew; when we consult our table of\r\nlogarithms, replacing and saving thus new calculations\r\nby old ones already performed; when we employ\r\ndeterminants instead of always beginning afresh the\r\nsolution of a system of equations; when we resolve\r\nnew integral expressions into familiar old integrals;\r\nwe see in this simply a feeble reflexion of the intellectual\r\nactivity of a Lagrange or a Cauchy, who, with\r\nthe keen discernment of a great military commander,\r\nsubstituted for new operations whole hosts of old ones.\r\nNo one will dispute me when I say that the most elementary\r\nas well as the highest mathematics are economically-ordered\r\nexperiences of counting, put in forms\r\nready for use.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_196\" id=\"Page_196\"\u003e[Pg 196]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eIn algebra we perform, as far as possible, all numerical\r\noperations which are identical in form once\r\nfor all, so that only a remnant of work is left for the\r\nindividual case. The use of the signs of algebra and\r\nanalysis, which are merely symbols of operations to\r\nbe performed, is due to the observation that we can\r\nmaterially disburden the mind in this way and spare\r\nits powers for more important and more difficult duties,\r\nby imposing all mechanical operations upon the\r\nhand. One result of this method, which attests its\r\neconomical character, is the construction of calculating\r\nmachines. The mathematician Babbage, the inventor\r\nof the difference-engine, was probably the first who\r\nclearly perceived this fact, and he touched upon it,\r\nalthough only cursorily, in his work, \u003ci\u003eThe Economy of\r\nManufactures and Machinery\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe student of mathematics often finds it hard to\r\nthrow off the uncomfortable feeling that his science, in\r\nthe person of his pencil, surpasses him in intelligence,\u0026mdash;an\r\nimpression which the great Euler confessed he\r\noften could not get rid of. This feeling finds a sort of\r\njustification when we reflect that the majority of the\r\nideas we deal with were conceived by others, often\r\ncenturies ago. In great measure it is really the intelligence\r\nof other people that confronts us in science.\r\nThe moment we look at matters in this light, the uncanniness\r\nand magical character of our impressions\r\ncease, especially when we remember that we can think\r\nover again at will any one of those alien thoughts.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_197\" id=\"Page_197\"\u003e[Pg 197]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003ePhysics is experience, arranged in economical order.\r\nBy this order not only is a broad and comprehensive\r\nview of what we have rendered possible, but also\r\nthe defects and the needful alterations are made manifest,\r\nexactly as in a well-kept household. Physics\r\nshares with mathematics the advantages of succinct\r\ndescription and of brief, compendious definition, which\r\nprecludes confusion, even in ideas where, with no apparent\r\nburdening of the brain, hosts of others are contained.\r\nOf these ideas the rich contents can be produced\r\nat any moment and displayed in their full perceptual\r\nlight. Think of the swarm of well-ordered notions\r\npent up in the idea of the potential. Is it wonderful\r\nthat ideas containing so much finished labor should\r\nbe easy to work with?\u003c/p\u003e\r\n\r\n\u003cp\u003eOur first knowledge, thus, is a product of the\r\neconomy of self-preservation. By communication, the\r\nexperience of \u003ci\u003emany\u003c/i\u003e persons, individually acquired at\r\nfirst, is collected in \u003ci\u003eone\u003c/i\u003e. The communication of\r\nknowledge and the necessity which every one feels of\r\nmanaging his stock of experience with the least expenditure\r\nof thought, compel us to put our knowledge in\r\neconomical forms. But here we have a clue which\r\nstrips science of all its mystery, and shows us what its\r\npower really is. With respect to specific results it\r\nyields us nothing that we could not reach in a sufficiently\r\nlong time without methods. There is no problem\r\nin all mathematics that cannot be solved by direct\r\ncounting. But with the present implements of mathematics\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_198\" id=\"Page_198\"\u003e[Pg 198]\u003c/a\u003e\u003c/span\u003e\r\nmany operations of counting can be performed\r\nin a few minutes which without mathematical methods\r\nwould take a lifetime. Just as a single human being,\r\nrestricted wholly to the fruits of his own labor, could\r\nnever amass a fortune, but on the contrary the accumulation\r\nof the labor of many men in the hands of one is\r\nthe foundation of wealth and power, so, also, no knowledge\r\nworthy of the name can be gathered up in a\r\nsingle human mind limited to the span of a human life\r\nand gifted only with finite powers, except by the most\r\nexquisite economy of thought and by the careful\r\namassment of the economically ordered experience of\r\nthousands of co-workers. What strikes us here as the\r\nfruits of sorcery are simply the rewards of excellent\r\nhousekeeping, as are the like results in civil life. But\r\nthe business of science has this advantage over every\r\nother enterprise, that from \u003ci\u003eits\u003c/i\u003e amassment of wealth no\r\none suffers the least loss. This, too, is its blessing,\r\nits freeing and saving power.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe recognition of the economical character of\r\nscience will now help us, perhaps, to understand better\r\ncertain physical notions.\u003c/p\u003e\r\n\r\n\u003cp\u003eThose elements of an event which we call \"cause\r\nand effect\" are certain salient features of it, which are\r\nimportant for its mental reproduction. Their importance\r\nwanes and the attention is transferred to fresh\r\ncharacters the moment the event or experience in\r\nquestion becomes familiar. If the connexion of such\r\nfeatures strikes us as a necessary one, it is simply because\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_199\" id=\"Page_199\"\u003e[Pg 199]\u003c/a\u003e\u003c/span\u003e\r\nthe interpolation of certain intermediate links\r\nwith which we are very familiar, and which possess,\r\ntherefore, higher authority for us, is often attended\r\nwith success in our explanations. That \u003ci\u003eready\u003c/i\u003e experience\r\nfixed in the mosaic of the mind with which we meet\r\nnew events, Kant calls an innate concept of the understanding\r\n(\u003ci\u003eVerstandesbegriff\u003c/i\u003e).\u003c/p\u003e\r\n\r\n\u003cp\u003eThe grandest principles of physics, resolved into\r\ntheir elements, differ in no wise from the descriptive\r\nprinciples of the natural historian. The question,\r\n\"Why?\" which is always appropriate where the explanation\r\nof a contradiction is concerned, like all proper\r\nhabitudes of thought, can overreach itself and be asked\r\nwhere nothing remains to be understood. Suppose we\r\nwere to attribute to nature the property of producing\r\nlike effects in like circumstances; just these like circumstances\r\nwe should not know how to find. Nature\r\nexists once only. Our schematic mental imitation alone\r\nproduces like events. Only in the mind, therefore, does\r\nthe mutual dependence of certain features exist.\u003c/p\u003e\r\n\r\n\u003cp\u003eAll our efforts to mirror the world in thought would\r\nbe futile if we found nothing permanent in the varied\r\nchanges of things. It is this that impels us to form the\r\nnotion of substance, the source of which is not different\r\nfrom that of the modern ideas relative to the conservation\r\nof energy. The history of physics furnishes\r\nnumerous examples of this impulse in almost all fields,\r\nand pretty examples of it may be traced back to the\r\nnursery. \"Where does the light go to when it is put\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_200\" id=\"Page_200\"\u003e[Pg 200]\u003c/a\u003e\u003c/span\u003e\r\nout?\" asks the child. The sudden shrivelling up of a\r\nhydrogen balloon is inexplicable to a child; it looks\r\neverywhere for the large body which was just there\r\nbut is now gone.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhere does heat come from? Where does heat\r\ngo to? Such childish questions in the mouths of mature\r\nmen shape the character of a century.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn mentally separating a body from the changeable\r\nenvironment in which it moves, what we really do\r\nis to extricate a group of sensations on which our\r\nthoughts are fastened and which is of relatively greater\r\nstability than the others, from the stream of all our\r\nsensations. Absolutely unalterable this group is not.\r\nNow this, now that member of it appears and disappears,\r\nor is altered. In its full identity it never recurs.\r\nYet the sum of its constant elements as compared\r\nwith the sum of its changeable ones, especially if we\r\nconsider the continuous character of the transition, is\r\nalways so great that for the purpose in hand the former\r\nusually appear sufficient to determine the body\u0027s identity.\r\nBut because we can separate from the group\r\nevery single member without the body\u0027s ceasing to be\r\nfor us the same, we are easily led to believe that after\r\nabstracting all the members something additional\r\nwould remain. It thus comes to pass that we form\r\nthe notion of a substance distinct from its attributes,\r\nof a thing-in-itself, whilst our sensations are regarded\r\nmerely as symbols or indications of the properties of\r\nthis thing-in-itself. But it would be much better to\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_201\" id=\"Page_201\"\u003e[Pg 201]\u003c/a\u003e\u003c/span\u003e\r\nsay that bodies or things are compendious mental symbols\r\nfor groups of sensations\u0026mdash;symbols that do not exist\r\noutside of thought. Thus, the merchant regards\r\nthe labels of his boxes merely as indexes of their contents,\r\nand not the contrary. He invests their contents,\r\nnot their labels, with real value. The same\r\neconomy which induces us to analyse a group and to\r\nestablish special signs for its component parts, parts\r\nwhich also go to make up other groups, may likewise\r\ninduce us to mark out by some single symbol a whole\r\ngroup.\u003c/p\u003e\r\n\r\n\u003cp\u003eOn the old Egyptian monuments we see objects\r\nrepresented which do not reproduce a single visual\r\nimpression, but are composed of various impressions.\r\nThe heads and the legs of the figures appear in profile,\r\nthe head-dress and the breast are seen from the\r\nfront, and so on. We have here, so to speak, a mean\r\nview of the objects, in forming which the sculptor has\r\nretained what he deemed essential, and neglected what\r\nhe thought indifferent. We have living exemplifications\r\nof the processes put into stone on the walls of\r\nthese old temples, in the drawings of our children, and\r\nwe also observe a faithful analogue of them in the formation\r\nof ideas in our own minds. Only in virtue of\r\nsome such facility of view as that indicated, are we\r\nallowed to speak of a body. When we speak of a cube\r\nwith trimmed corners\u0026mdash;a figure which is not a cube\u0026mdash;we\r\ndo so from a natural instinct of economy, which\r\nprefers to add to an old familiar conception a correction\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_202\" id=\"Page_202\"\u003e[Pg 202]\u003c/a\u003e\u003c/span\u003e\r\ninstead of forming an entirely new one. This is\r\nthe process of all judgment.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe crude notion of \"body\" can no more stand\r\nthe test of analysis than can the art of the Egyptians\r\nor that of our little children. The physicist who sees\r\na body flexed, stretched, melted, and vaporised, cuts\r\nup this body into smaller permanent parts; the chemist\r\nsplits it up into elements. Yet even an element is\r\nnot unalterable. Take sodium. When warmed, the\r\nwhite, silvery mass becomes a liquid, which, when the\r\nheat is increased and the air shut out, is transformed\r\ninto a violet vapor, and on the heat being still more\r\nincreased glows with a yellow light. If the name sodium\r\nis still retained, it is because of the continuous\r\ncharacter of the transitions and from a necessary instinct\r\nof economy. By condensing the vapor, the\r\nwhite metal may be made to reappear. Indeed, even\r\nafter the metal is thrown into water and has passed\r\ninto sodium hydroxide, the vanished properties may\r\nby skilful treatment still be made to appear; just as a\r\nmoving body which has passed behind a column and\r\nis lost to view for a moment may make its appearance\r\nafter a time. It is unquestionably very convenient\r\nalways to have ready the name and thought for a\r\ngroup of properties wherever that group by any possibility\r\ncan appear. But more than a compendious economical\r\nsymbol for these phenomena, that name and\r\nthought is not. It would be a mere empty word for\r\none in whom it did not awaken a large group of well-ordered\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_203\" id=\"Page_203\"\u003e[Pg 203]\u003c/a\u003e\u003c/span\u003e\r\nsense-impressions. And the same is true of\r\nthe molecules and atoms into which the chemical element\r\nis still further analysed.\u003c/p\u003e\r\n\r\n\u003cp\u003eTrue, it is customary to regard the conservation of\r\nweight, or, more precisely, the conservation of mass,\r\nas a direct proof of the constancy of matter. But this\r\nproof is dissolved, when we go to the bottom of it,\r\ninto such a multitude of instrumental and intellectual\r\noperations, that in a sense it will be found to constitute\r\nsimply an equation which our ideas in imitating\r\nfacts have to satisfy. That obscure, mysterious lump\r\nwhich we involuntarily add in thought, we seek for in\r\nvain outside the mind.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is always, thus, the crude notion of substance\r\nthat is slipping unnoticed into science, proving itself\r\nconstantly insufficient, and ever under the necessity of\r\nbeing reduced to smaller and smaller world-particles.\r\nHere, as elsewhere, the lower stage is not rendered\r\nindispensable by the higher which is built upon it, no\r\nmore than the simplest mode of locomotion, walking,\r\nis rendered superfluous by the most elaborate means of\r\ntransportation. Body, as a compound of light and\r\ntouch sensations, knit together by sensations of space,\r\nmust be as familiar to the physicist who seeks it, as to\r\nthe animal who hunts its prey. But the student of the\r\ntheory of knowledge, like the geologist and the astronomer,\r\nmust be permitted to reason back from the forms\r\nwhich are created before his eyes to others which he\r\nfinds ready made for him.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_204\" id=\"Page_204\"\u003e[Pg 204]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eAll physical ideas and principles are succinct directions,\r\nfrequently involving subordinate directions,\r\nfor the employment of economically classified experiences,\r\nready for use. Their conciseness, as also the\r\nfact that their contents are rarely exhibited in full,\r\noften invests them with the semblance of independent\r\nexistence. Poetical myths regarding such ideas,\u0026mdash;for\r\nexample, that of Time, the producer and devourer of\r\nall things,\u0026mdash;do not concern us here. We need only\r\nremind the reader that even Newton speaks of an \u003ci\u003eabsolute\u003c/i\u003e\r\ntime independent of all phenomena, and of an\r\nabsolute space\u0026mdash;views which even Kant did not shake\r\noff, and which are often seriously entertained to-day.\r\nFor the natural inquirer, determinations of time are\r\nmerely abbreviated statements of the dependence of\r\none event upon another, and nothing more. When\r\nwe say the acceleration of a freely falling body is 9·810\r\nmetres per second, we mean the velocity of the body\r\nwith respect to the centre of the earth is 9·810 metres\r\ngreater when the earth has performed an additional\r\n86400th part of its rotation\u0026mdash;a fact which itself can be\r\ndetermined only by the earth\u0027s relation to other heavenly\r\nbodies. Again, in velocity is contained simply a\r\nrelation of the position of a body to the position of\r\nthe earth.\u003ca name=\"FNanchor_65_65\" id=\"FNanchor_65_65\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_65_65\" class=\"fnanchor\"\u003e[65]\u003c/a\u003e Instead of referring events to the earth\r\nwe may refer them to a clock, or even to our internal\r\nsensation of time. Now, because all are connected,\r\nand each may be made the measure of the rest, the illusion\r\neasily arises that time has significance independently\r\nof all.\u003ca name=\"FNanchor_66_66\" id=\"FNanchor_66_66\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_66_66\" class=\"fnanchor\"\u003e[66]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_205\" id=\"Page_205\"\u003e[Pg 205]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003eThe aim of research is the discovery of the equations\r\nwhich subsist between the elements of phenomena.\r\nThe equation of an ellipse expresses the universal\r\n\u003ci\u003econceivable\u003c/i\u003e relation between its co-ordinates, of which\r\nonly the real values have \u003ci\u003egeometrical\u003c/i\u003e significance.\r\nSimilarly, the equations between the elements of \u003ci\u003ephenomena\u003c/i\u003e\r\nexpress a universal, mathematically conceivable\r\nrelation. Here, however, for many values only\r\ncertain directions of change are \u003ci\u003ephysically\u003c/i\u003e admissible.\r\nAs in the ellipse only certain \u003ci\u003evalues\u003c/i\u003e satisfying the\r\nequation are realised, so in the physical world only\r\ncertain \u003ci\u003echanges\u003c/i\u003e of value occur. Bodies are always accelerated\r\ntowards the earth. Differences of temperature,\r\nleft to themselves, always grow less; and so on.\r\nSimilarly, with respect to space, mathematical and\r\nphysiological researches have shown that the space of\r\nexperience is simply an \u003ci\u003eactual\u003c/i\u003e case of many conceivable\r\ncases, about whose peculiar properties experience\r\nalone can instruct us. The elucidation which this idea\r\ndiffuses cannot be questioned, despite the absurd uses\r\nto which it has been put.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us endeavor now to summarise the results of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_206\" id=\"Page_206\"\u003e[Pg 206]\u003c/a\u003e\u003c/span\u003e\r\nour survey. In the economical schematism of science\r\nlie both its strength and its weakness. Facts are always\r\nrepresented at a sacrifice of completeness and\r\nnever with greater precision than fits the needs of the\r\nmoment. The incongruence between thought and experience,\r\ntherefore, will continue to subsist as long as\r\nthe two pursue their course side by side; but it will\r\nbe continually diminished.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn reality, the point involved is always the completion\r\nof some partial experience; the derivation of\r\none portion of a phenomenon from some other. In\r\nthis act our ideas must be based directly upon sensations.\r\nWe call this measuring.\u003ca name=\"FNanchor_67_67\" id=\"FNanchor_67_67\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_67_67\" class=\"fnanchor\"\u003e[67]\u003c/a\u003e The condition of\r\nscience, both in its origin and in its application, is a\r\n\u003ci\u003egreat relative stability\u003c/i\u003e of our environment. What it\r\nteaches us is interdependence. Absolute forecasts,\r\nconsequently, have no significance in science. With\r\ngreat changes in celestial space we should lose our\r\nco-ordinate systems of space and time.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen a geometer wishes to understand the form of\r\na curve, he first resolves it into small rectilinear elements.\r\nIn doing this, however, he is fully aware that\r\nthese elements are only provisional and arbitrary devices\r\nfor comprehending in parts what he cannot comprehend\r\nas a whole. When the law of the curve is\r\nfound he no longer thinks of the elements. Similarly,\r\nit would not become physical science to see in its self-created,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_207\" id=\"Page_207\"\u003e[Pg 207]\u003c/a\u003e\u003c/span\u003e\r\nchangeable, economical tools, molecules and\r\natoms, realities behind phenomena, forgetful of the\r\nlately acquired sapience of her older sister, philosophy,\r\nin substituting a mechanical mythology for the old\r\nanimistic or metaphysical scheme, and thus creating\r\nno end of suppositious problems. The atom must remain\r\na tool for representing phenomena, like the\r\nfunctions of mathematics. Gradually, however, as\r\nthe intellect, by contact with its subject-matter, grows\r\nin discipline, physical science will give up its mosaic\r\nplay with stones and will seek out the boundaries and\r\nforms of the bed in which the living stream of phenomena\r\nflows. The goal which it has set itself is the\r\n\u003ci\u003esimplest\u003c/i\u003e and \u003ci\u003emost economical\u003c/i\u003e abstract expression of facts.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_208\" id=\"Page_208\"\u003e[Pg 208]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_209\" id=\"Page_209\"\u003e[Pg 209]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_210\" id=\"Page_210\"\u003e[Pg 210]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_211\" id=\"Page_211\"\u003e[Pg 211]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_212\" id=\"Page_212\"\u003e[Pg 212]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_213\" id=\"Page_213\"\u003e[Pg 213]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_214\" id=\"Page_214\"\u003e[Pg 214]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eThe question now remains, whether the same\r\nmethod of research which till now we have tacitly restricted\r\nto physics, is also applicable in the psychical\r\ndomain. This question will appear superfluous to the\r\nphysical inquirer. Our physical and psychical views\r\nspring in exactly the same manner from instinctive\r\nknowledge. We read the thoughts of men in their\r\nacts and facial expressions without knowing how.\r\nJust as we predict the behavior of a magnetic needle\r\nplaced near a current by imagining Ampère\u0027s swimmer\r\nin the current, similarly we predict in thought the\r\nacts and behavior of men by assuming sensations, feelings,\r\nand wills similar to our own connected with their\r\nbodies. What we here instinctively perform would\r\nappear to us as one of the subtlest achievements of\r\nscience, far outstripping in significance and ingenuity\r\nAmpère\u0027s rule of the swimmer, were it not that every\r\nchild unconsciously accomplished it. The question\r\nsimply is, therefore, to grasp scientifically, that is, by\r\nconceptional thought, what we are already familiar\r\nwith from other sources. And here much is to be\r\naccomplished. A long sequence of facts is to be disclosed\r\nbetween the physics of expression and movement\r\nand feeling and thought.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe hear the question, \"But how is it possible to\r\nexplain feeling by the motions of the atoms of the\r\nbrain?\" Certainly this will never be done, no more\r\nthan light or heat will ever be deduced from the law\r\nof refraction. We need not deplore, therefore, the\r\nlack of ingenious solutions of this question. The problem\r\nis not a problem. A child looking over the walls\r\nof a city or of a fort into the moat below sees with\r\nastonishment living people in it, and not knowing of\r\nthe portal which connects the wall with the moat, cannot\r\nunderstand how they could have got down from\r\nthe high ramparts. So it is with the notions of physics.\r\nWe cannot climb up into the province of psychology\r\nby the ladder of our abstractions, but we can climb\r\ndown into it.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us look at the matter without bias. The world\r\nconsists of colors, sounds, temperatures, pressures,\r\nspaces, times, and so forth, which now we shall not\r\ncall sensations, nor phenomena, because in either term\r\nan arbitrary, one-sided theory is embodied, but simply\r\n\u003ci\u003eelements\u003c/i\u003e. The fixing of the flux of these elements,\r\nwhether mediately or immediately, is the real object of\r\nphysical research. As long as, neglecting our own\r\nbody, we employ ourselves with the interdependence\r\nof those groups of elements which, including men and\r\nanimals, make up \u003ci\u003eforeign\u003c/i\u003e bodies, we are physicists.\r\nFor example, we investigate the change of the red\r\ncolor of a body as produced by a change of illumination.\r\nBut the moment we consider the special influence\r\non the red of the elements constituting our\r\nbody, outlined by the well-known perspective with\r\nhead invisible, we are at work in the domain of physiological\r\npsychology. We close our eyes, and the red\r\ntogether with the whole visible world disappears.\r\nThere exists, thus, in the perspective field of every sense\r\na portion which exercises on all the rest a different\r\nand more powerful influence than the rest upon one\r\nanother. With this, however, all is said. In the light\r\nof this remark, we call \u003ci\u003eall\u003c/i\u003e elements, in so far as we regard\r\nthem as dependent on this special part (our body),\r\n\u003ci\u003esensations\u003c/i\u003e. That the world is our sensation, in this\r\nsense, cannot be questioned. But to make a system\r\nof conduct out of this provisional conception, and to\r\nabide its slaves, is as unnecessary for us as would be\r\na similar course for a mathematician who, in varying a\r\nseries of variables of a function which were previously\r\nassumed to be constant, or in interchanging the independent\r\nvariables, finds his method to be the source\r\nof some very surprising ideas for him.\u003ca name=\"FNanchor_68_68\" id=\"FNanchor_68_68\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_68_68\" class=\"fnanchor\"\u003e[68]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we look at the matter in this unbiassed light it\r\nwill appear indubitable that the method of physiological\r\npsychology is none other than that of physics;\r\nwhat is more, that this science is a part of physics.\r\nIts subject-matter is not different from that of physics.\r\nIt will unquestionably determine the relations\r\nthe sensations bear to the physics of our body. We\r\nhave already learned from a member of this academy\r\n(Hering) that in all probability a sixfold manifoldness\r\nof the chemical processes of the visual substance corresponds\r\nto the sixfold manifoldness of color-sensation,\r\nand a threefold manifoldness of the physiological processes\r\nto the threefold manifoldness of space-sensations.\r\nThe paths of reflex actions and of the will are\r\nfollowed up and disclosed; it is ascertained what region\r\nof the brain subserves the function of speech,\r\nwhat region the function of locomotion, etc. That\r\nwhich still clings to our body, namely, our thoughts,\r\nwill, when those investigations are finished, present no\r\ndifficulties new in principle. When experience has\r\nonce clearly exhibited these facts and science has\r\nmarshalled them in economic and perspicuous order,\r\nthere is no doubt that we shall \u003ci\u003eunderstand\u003c/i\u003e them. For\r\nother \"understanding\" than a mental mastery of facts\r\nnever existed. Science does not create facts from facts,\r\nbut simply \u003ci\u003eorders\u003c/i\u003e known facts.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us look, now, a little more closely into the modes\r\nof research of physiological psychology. We have a\r\nvery clear idea of how a body moves in the space encompassing\r\nit. With our optical field of sight we are\r\nvery familiar. But we are unable to state, as a rule,\r\nhow we have come by an idea, from what corner of\r\nour intellectual field of sight it has entered, or by what\r\nregion the impulse to a motion is sent forth. Moreover,\r\nwe shall never get acquainted with this mental\r\nfield of view from self-observation alone. Self-observation,\r\nin conjunction with physiological research,\r\nwhich seeks out physical connexions, can put this field\r\nof vision in a clear light before us, and will thus first\r\nreally reveal to us our inner man.\u003c/p\u003e\r\n\r\n\u003cp\u003ePrimarily, natural science, or physics, in its widest\r\nsense, makes us acquainted with only the firmest connexions\r\nof groups of elements. Provisorily, we may\r\nnot bestow too much attention on the single constituents\r\nof those groups, if we are desirous of retaining a\r\ncomprehensible whole. Instead of equations between\r\nthe primitive variables, physics gives us, as much the\r\neasiest course, equations between \u003ci\u003efunctions\u003c/i\u003e of those\r\nvariables. Physiological psychology teaches us how\r\nto separate the visible, the tangible, and the audible\r\nfrom bodies\u0026mdash;a labor which is subsequently richly requited,\r\nas the division of the subjects of physics well\r\nshows. Physiology further analyses the visible into\r\nlight and space sensations; the first into colors, the\r\nlast also into their component parts; it resolves noises\r\ninto sounds, these into tones, and so on. Unquestionably\r\nthis analysis can be carried much further than it\r\nhas been. It will be possible in the end to exhibit the\r\ncommon elements at the basis of very abstract but\r\ndefinite logical acts of like form,\u0026mdash;elements which the\r\nacute jurist and mathematician, as it were, \u003ci\u003efeels\u003c/i\u003e out,\r\nwith absolute certainty, where the uninitiated hears\r\nonly empty words. Physiology, in a word, will reveal\r\nto us the true real elements of the world. Physiological\r\npsychology bears to physics in its widest sense a relation\r\nsimilar to that which chemistry bears to physics\r\nin its narrowest sense. But far greater than the mutual\r\nsupport of physics and chemistry will be that\r\nwhich natural science and psychology will render each\r\nother. And the results that shall spring from this\r\nunion will, in all likelihood, far outstrip those of the\r\nmodern mechanical physics.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat those ideas are with which we shall comprehend\r\nthe world when the closed circuit of physical and\r\npsychological facts shall lie complete before us, (that\r\ncircuit of which we now see only two disjoined parts,)\r\ncannot be foreseen at the outset of the work. The\r\nmen will be found who will see what is right and\r\nwill have the courage, instead of wandering in the\r\nintricate paths of logical and historical accident, to\r\nenter on the straight ways to the heights from which\r\nthe mighty stream of facts can be surveyed. Whether\r\nthe notion which we now call matter will continue to\r\nhave a scientific significance beyond the crude purposes\r\nof common life, we do not know. But we certainly\r\nshall wonder how colors and tones which were\r\nsuch innermost parts of us could suddenly get lost in\r\nour physical world of atoms; how we could be suddenly\r\nsurprised that something which outside us simply\r\nclicked and beat, in our heads should make light\r\nand music; and how we could ask whether matter can\r\nfeel, that is to say, whether a mental symbol for a\r\ngroup of sensations can feel?\u003c/p\u003e\r\n\r\n\u003cp\u003eWe cannot mark out in hard and fast lines the\r\nscience of the future, but we can foresee that the rigid\r\nwalls which now divide man from the world will gradually\r\ndisappear; that human beings will not only confront\r\neach other, but also the entire organic and so-called\r\nlifeless world, with less selfishness and with livelier\r\nsympathy. Just such a presentiment as this perhaps\r\npossessed the great Chinese philosopher Licius\r\nsome two thousand years ago when, pointing to a heap\r\nof mouldering human bones, he said to his scholars in\r\nthe rigid, lapidary style of his tongue: \"These and I\r\nalone have the knowledge that we neither live nor are\r\ndead.\"\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_TRANSFORMATION_AND_ADAPTATION\" id=\"ON_TRANSFORMATION_AND_ADAPTATION\"\u003eON TRANSFORMATION AND ADAPTATION\r\nIN SCIENTIFIC THOUGHT.\u003c/a\u003e\u003ca name=\"FNanchor_69_69\" id=\"FNanchor_69_69\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_69_69\" class=\"fnanchor\"\u003e[69]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eIt was towards the close of the sixteenth century\r\nthat Galileo with a superb indifference to the dialectic\r\narts and sophistic subtleties of the Schoolmen of\r\nhis time, turned the attention of his brilliant mind\r\nto nature. By nature his ideas were transformed and\r\nreleased from the fetters of inherited prejudice. At\r\nonce the mighty revolution was felt, that was therewith\r\neffected in the realm of human thought\u0026mdash;felt indeed in\r\ncircles far remote and wholly unrelated to the sphere\r\nof science, felt in strata of society that hitherto had\r\nonly indirectly recognised the influence of scientific\r\nthought.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_215\" id=\"Page_215\"\u003e[Pg 215]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eAnd how great and how far-reaching that revolution\r\nwas! From the beginning of the seventeenth century\r\ntill its close we see arising, at least in embryo,\r\nalmost all that plays a part in the natural and technical\r\nscience of to-day, almost all that in the two centuries\r\nfollowing so wonderfully transformed the facial\r\nappearance of the earth, and all that is moving onward\r\nin process of such mighty evolution to-day. And all\r\nthis, the direct result of Galilean ideas, the direct outcome\r\nof that freshly awakened sense for the investigation\r\nof natural phenomena which taught the Tuscan\r\nphilosopher to form the concept and the law of falling\r\nbodies from the \u003ci\u003eobservation\u003c/i\u003e of a falling stone! Galileo\r\nbegan his investigations without an implement worthy\r\nof the name; he measured time in the most primitive\r\nway, by the efflux of water. Yet soon afterwards the\r\ntelescope, the microscope, the barometer, the thermometer,\r\nthe air-pump, the steam engine, the pendulum,\r\nand the electrical machine were invented in rapid\r\nsuccession. The fundamental theorems of dynamical\r\nscience, of optics, of heat, and of electricity were all\r\ndisclosed in the century that followed Galileo.\u003c/p\u003e\r\n\r\n\u003cp\u003eOf scarcely less importance, it seems, was that\r\nmovement which was prepared for by the illustrious\r\nbiologists of the hundred years just past, and formally\r\nbegun by the late Mr. Darwin. Galileo quickened the\r\nsense for the simpler phenomena of \u003ci\u003einorganic\u003c/i\u003e nature.\r\nAnd with the same simplicity and frankness that\r\nmarked the efforts of Galileo, and without the aid of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_216\" id=\"Page_216\"\u003e[Pg 216]\u003c/a\u003e\u003c/span\u003e\r\ntechnical or scientific instruments, without physical or\r\nchemical experiment, but solely by the power of\r\nthought and observation, Darwin grasps a new property\r\nof \u003ci\u003eorganic\u003c/i\u003e nature\u0026mdash;which we may briefly call its\r\n\u003ci\u003eplasticity\u003c/i\u003e.\u003ca name=\"FNanchor_70_70\" id=\"FNanchor_70_70\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_70_70\" class=\"fnanchor\"\u003e[70]\u003c/a\u003e With the same directness of purpose, Darwin,\r\ntoo, pursues his way. With the same candor\r\nand love of truth, he points out the strength and the\r\nweakness of his demonstrations. With masterly equanimity\r\nhe holds aloof from the discussion of irrelevant\r\nsubjects and wins alike the admiration of his adherents\r\nand of his adversaries.\u003c/p\u003e\r\n\r\n\u003cp\u003eScarcely thirty years have elapsed\u003ca name=\"FNanchor_71_71\" id=\"FNanchor_71_71\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_71_71\" class=\"fnanchor\"\u003e[71]\u003c/a\u003e since Darwin first\r\npropounded the principles of his theory of evolution.\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_217\" id=\"Page_217\"\u003e[Pg 217]\u003c/a\u003e\u003c/span\u003e\r\nYet, already we see his ideas firmly rooted in every\r\nbranch of human thought, however remote. Everywhere,\r\nin history, in philosophy, even in the physical\r\nsciences, we hear the watchwords: heredity, adaptation,\r\nselection. We speak of the struggle for existence\r\namong the heavenly bodies and of the struggle for existence\r\nin the world of molecules.\u003ca name=\"FNanchor_72_72\" id=\"FNanchor_72_72\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_72_72\" class=\"fnanchor\"\u003e[72]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe impetus given by Galileo to scientific thought\r\nwas marked in every direction; thus, his pupil, Borelli,\r\nfounded the school of exact medicine, from\r\nwhence proceeded even distinguished mathematicians.\r\nAnd now Darwinian ideas, in the same way, are animating\r\nall provinces of research. It is true, nature is\r\nnot made up of two distinct parts, the inorganic and\r\nthe organic; nor must these two divisions be treated\r\nperforce by totally distinct methods. Many \u003ci\u003esides\u003c/i\u003e, however,\r\nnature has. Nature is like a thread in an intricate\r\ntangle, which must be followed and traced, now from\r\nthis point, now from that. But we must never imagine,\u0026mdash;and\r\nthis physicists have learned from Faraday and\r\nJ. R. Mayer,\u0026mdash;that progress along paths once entered\r\nupon is the \u003ci\u003eonly\u003c/i\u003e means of reaching the truth.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will devolve upon the specialists of the future to\r\ndetermine the relative tenability and fruitfulness of the\r\nDarwinian ideas in the different provinces. Here I\r\nwish simply to consider the growth of natural \u003ci\u003eknowledge\u003c/i\u003e\r\nin the light of the theory of evolution. For knowledge,\r\ntoo, is a product of organic nature. And although\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_218\" id=\"Page_218\"\u003e[Pg 218]\u003c/a\u003e\u003c/span\u003e\r\nideas, as such, do not comport themselves in all respects\r\nlike independent organic individuals, and although\r\nviolent comparisons should be avoided, still, if Darwin\r\nreasoned rightly, the general imprint of evolution and\r\ntransformation must be noticeable in ideas also.\u003c/p\u003e\r\n\r\n\u003cp\u003eI shall waive here the consideration of the fruitful\r\ntopic of the transmission of ideas or rather of the\r\ntransmission of the aptitude for certain ideas.\u003ca name=\"FNanchor_73_73\" id=\"FNanchor_73_73\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_73_73\" class=\"fnanchor\"\u003e[73]\u003c/a\u003e Nor\r\nwould it come within my province to discuss psychical\r\nevolution in any form, as Spencer\u003ca name=\"FNanchor_74_74\" id=\"FNanchor_74_74\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_74_74\" class=\"fnanchor\"\u003e[74]\u003c/a\u003e and many other\r\nmodern psychologists have done, with varying success.\r\nNeither shall I enter upon a discussion of the\r\nstruggle for existence and of natural selection among\r\nscientific theories.\u003ca name=\"FNanchor_75_75\" id=\"FNanchor_75_75\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_75_75\" class=\"fnanchor\"\u003e[75]\u003c/a\u003e We shall consider here only such\r\nprocesses of transformation as every student can easily\r\nobserve in his own mind.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_219\" id=\"Page_219\"\u003e[Pg 219]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_220\" id=\"Page_220\"\u003e[Pg 220]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_221\" id=\"Page_221\"\u003e[Pg 221]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_222\" id=\"Page_222\"\u003e[Pg 222]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_223\" id=\"Page_223\"\u003e[Pg 223]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_224\" id=\"Page_224\"\u003e[Pg 224]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_225\" id=\"Page_225\"\u003e[Pg 225]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_226\" id=\"Page_226\"\u003e[Pg 226]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_227\" id=\"Page_227\"\u003e[Pg 227]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_228\" id=\"Page_228\"\u003e[Pg 228]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_229\" id=\"Page_229\"\u003e[Pg 229]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_230\" id=\"Page_230\"\u003e[Pg 230]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_231\" id=\"Page_231\"\u003e[Pg 231]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_232\" id=\"Page_232\"\u003e[Pg 232]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_233\" id=\"Page_233\"\u003e[Pg 233]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eThe child of the forest picks out and pursues with\r\nmarvellous acuteness the trails of animals. He outwits\r\nand overreaches his foes with surpassing cunning.\r\nHe is perfectly at home in the sphere of his peculiar\r\nexperience. But confront him with an unwonted phenomenon;\r\nplace him face to face with a technical product\r\nof modern civilisation, and he will lapse into impotency\r\nand helplessness. Here are facts which he\r\ndoes not comprehend. If he endeavors to grasp their\r\nmeaning, he misinterprets them. He fancies the moon,\r\nwhen eclipsed, to be tormented by an evil spirit. To\r\nhis mind a puffing locomotive is a living monster. The\r\nletter accompanying a commission with which he is\r\nentrusted, having once revealed his thievishness, is in\r\nhis imagination a conscious being, which he must hide\r\nbeneath a stone, before venturing to commit a fresh\r\ntrespass. Arithmetic to him is like the art of the\r\ngeomancers in the Arabian Nights,\u0026mdash;an art which is\r\nable to accomplish every imaginable impossibility.\r\nAnd, like Voltaire\u0027s \u003ci\u003eingénu\u003c/i\u003e, when placed in our social\r\nworld, he plays, as we think, the maddest pranks.\u003c/p\u003e\r\n\r\n\u003cp\u003eWith the man who has made the achievements of\r\nmodern science and civilisation his own, the case is\r\nquite different. He sees the moon pass temporarily\r\ninto the shadow of the earth. He feels in his thoughts\r\nthe water growing hot in the boiler of the locomotive;\r\nhe feels also the increase of the tension which pushes\r\nthe piston forward. Where he is not able to trace the\r\ndirect relation of things he has recourse to his yard-stick\r\nand table of logarithms, which aid and facilitate\r\nhis thought without predominating over it. Such opinions\r\nas he cannot concur in, are at least known to him,\r\nand he knows how to meet them in argument.\u003c/p\u003e\r\n\r\n\u003cp\u003eNow, wherein does the difference between these\r\ntwo men consist? The train of thought habitually\r\nemployed by the first one does not correspond to the\r\nfacts that he sees. He is surprised and nonplussed\r\nat every step. But the thoughts of the second man\r\nfollow and anticipate events, his thoughts have become\r\nadapted or accommodated to the larger field of\r\nobservation and activity in which he is located; he conceives\r\nthings as they are. The Indian\u0027s sphere of experience,\r\nhowever, is quite different; his bodily organs\r\nof sense are in constant activity; he is ever intensely\r\nalert and on the watch for his foes; or, his entire attention\r\nand energy are engaged in procuring sustenance.\r\nNow, how can such a creature project his mind\r\ninto futurity, foresee or prophesy? This is not possible\r\nuntil our fellow-beings have, in a measure, relieved\r\nus of our concern for existence. It is then that we\r\nacquire freedom for observation, and not infrequently\r\ntoo that narrowness of thought which society helps and\r\nteaches us to disregard.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we move for a time within a fixed circle of phenomena\r\nwhich recur with unvarying uniformity, our\r\nthoughts gradually adapt themselves to our environment;\r\nour ideas reflect unconsciously our surroundings.\r\nThe stone we hold in our hand, when dropped,\r\nnot only falls to the ground in reality; it also falls in\r\nour thoughts. Iron-filings dart towards a magnet in\r\nimagination as well as in fact, and, when thrown into\r\na fire, they grew hot in conception as well.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe impulse to complete mentally a phenomenon\r\nthat has been only partially observed, has not its origin\r\nin the phenomenon itself; of this fact, we are fully\r\nsensible. And we well know that it does not lie within\r\nthe sphere of our volition. It seems to confront us\r\nrather as a power and a law imposed from without\r\nand controlling both thought and facts.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fact that we are able by the help of this law to\r\nprophesy and forecast, merely proves a sameness or\r\nuniformity of environment sufficient to effect a mental\r\nadaptation of this kind. A necessity of fulfilment,\r\nhowever, is not contained in this compulsory principle\r\nwhich controls our thoughts; nor is it in any way determined\r\nby the possibility of prediction. We are always\r\nobliged, in fact, to await the completion of what\r\nhas been predicted. Errors and departures are constantly\r\ndiscernible, and are slight only in provinces of\r\ngreat rigid constancy, as in astronomy.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn cases where our thoughts follow the connexion\r\nof events with ease, and in instances where we positively\r\nforefeel the course of a phenomenon, it is natural\r\nto fancy that the latter is determined by and must\r\nconform to our thoughts. But the belief in that mysterious\r\nagency called \u003ci\u003ecausality\u003c/i\u003e, which holds thought and\r\nevent in unison, is violently shaken when a person first\r\nenters a province of inquiry in which he has previously\r\nhad no experience. Take for instance the strange\r\ninteraction of electric currents and magnets, or the\r\nreciprocal action of currents, which seem to defy all\r\nthe resources of mechanical science. Let him be confronted\r\nwith such phenomena and he will immediately\r\nfeel himself forsaken by his power of prediction; he\r\nwill bring nothing with him into this strange field of\r\nevents but the hope of soon being able to adapt his\r\nideas to the new conditions there presented.\u003c/p\u003e\r\n\r\n\u003cp\u003eA person constructs from a bone the remaining\r\nanatomy of an animal; or from the visible part of a\r\nhalf-concealed wing of a butterfly he infers and reconstructs\r\nthe part concealed. He does so with a feeling\r\nof highest confidence in the accuracy of his results;\r\nand in these processes we find nothing preternatural\r\nor transcendent. But when physicists adapt their\r\nthoughts to conform to the dynamical course of events\r\nin time, we invariably surround their investigations\r\nwith a metaphysical halo; yet these latter adaptations\r\nbear quite the same character as the former, and our\r\nonly reason for investing them with a metaphysical\r\ngarb, perhaps, is their high practical value.\u003ca name=\"FNanchor_76_76\" id=\"FNanchor_76_76\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_76_76\" class=\"fnanchor\"\u003e[76]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us consider for a moment what takes place\r\nwhen the field of observation to which our ideas have\r\nbeen adapted and now conform, becomes enlarged.\r\nWe had, let us say, always seen heavy bodies sink\r\nwhen their support was taken away; we had also seen,\r\nperhaps, that the sinking of heavier bodies forced\r\nlighter bodies upwards. But now we see a lever in\r\naction, and we are suddenly struck with the fact that\r\na lighter body is lifting another of much greater weight.\r\nOur customary train of thought demands its rights;\r\nthe new and unwonted event likewise demands its\r\nrights. From this conflict between thought and fact\r\nthe \u003ci\u003eproblem\u003c/i\u003e arises; out of this partial contrariety springs\r\nthe question, \"Why?\" With the new adaptation to the\r\nenlarged field of observation, the problem disappears,\r\nor, in other words, is solved. In the instance cited,\r\nwe must adopt the habit of always considering the\r\nmechanical work performed.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe child just awakening into consciousness of the\r\nworld, knows no problem. The bright flower, the\r\nringing bell, are all new to it; yet it is surprised at\r\nnothing. The out and out Philistine, whose only\r\nthoughts lie in the beaten path of his every-day pursuits,\r\nlikewise has no problems. Everything goes its\r\nwonted course, and if perchance a thing go wrong at\r\ntimes, it is at most a mere object of curiosity and\r\nnot worth serious consideration. In fact, the question\r\n\"Why?\" loses all warrant in relations where we are\r\nfamiliar with every aspect of events. But the capable\r\nand talented young man has his head full of problems;\r\nhe has acquired, to a greater or less degree, certain\r\nhabitudes of thought, and at the same time he is constantly\r\nobserving what is new and unwonted, and in\r\nhis case there is no end to the questions, \"Why?\"\u003c/p\u003e\r\n\r\n\u003cp\u003eThus, the factor which most promotes scientific\r\nthought is the gradual widening of the field of experience.\r\nWe scarcely notice events we are accustomed\r\nto; the latter do not really develop their intellectual\r\nsignificance until placed in contrast with something to\r\nwhich we are unaccustomed. Things that at home\r\nare passed by unnoticed, delight us when abroad,\r\nthough they may appear in only slightly different forms.\r\nThe sun shines with heightened radiance, the flowers\r\nbloom in brighter colors, our fellow-men accost us\r\nwith lighter and happier looks. And, returning home,\r\nwe find even the old familiar scenes more inspiring\r\nand suggestive than before.\u003c/p\u003e\r\n\r\n\u003cp\u003eEvery motive that prompts and stimulates us to\r\nmodify and transform our thoughts, proceeds from\r\nwhat is new, uncommon, and not understood. Novelty\r\nexcites wonder in persons whose fixed habits of thought\r\nare shaken and disarranged by what they see. But the\r\nelement of wonder never lies in the phenomenon or\r\nevent observed; its place is in the person observing.\r\nPeople of more vigorous mental type aim at once at an\r\n\u003ci\u003eadaptation of thought\u003c/i\u003e that will conform to what they\r\nhave observed. Thus does science eventually become\r\nthe natural foe of the wonderful. The sources of the\r\nmarvellous are unveiled, and surprise gives way to\r\ncalm interpretation.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us consider such a mental transformative process\r\nin detail. The circumstance that heavy bodies\r\nfall to the earth appears perfectly natural and regular.\r\nBut when a person observes that wood floats upon\r\nwater, and that flames and smoke rise in the air, then\r\nthe contrary of the first phenomenon is presented.\r\nAn olden theory endeavors to explain these facts by imputing\r\nto substances the power of volition, as that attribute\r\nwhich is most familiar to man. It asserted\r\nthat every substance seeks its proper place, heavy\r\nbodies tending downwards and light ones upwards.\r\nIt soon turned out, however, that even smoke had\r\nweight, that it, too, sought its place below, and that\r\nit was forced upwards only because of the downward\r\ntendency of the air, as wood is forced to the surface of\r\nwater because the water exerts the greater downward\r\npressure.\u003c/p\u003e\r\n\r\n\u003cp\u003eAgain, we see a body thrown into the air. It ascends.\r\nHow is it that it does not seek its proper place? Why\r\ndoes the velocity of its \"violent\" motion decrease as\r\nit rises, while that of its \"natural\" fall increases as it\r\ndescends. If we mark closely the relation between\r\nthese two facts, the problem will solve itself. We shall\r\nsee, as Galileo did, that the decrease of velocity in\r\nrising and the increase of velocity in falling are one\r\nand the same phenomenon, viz., an increase of velocity\r\ntowards the earth. Accordingly, it is not a place\r\nthat is assigned to the body, but an increase of velocity\r\ntowards the earth.\u003c/p\u003e\r\n\r\n\u003cp\u003eBy this idea the movements of heavy bodies are\r\nrendered perfectly familiar. Newton, now, firmly\r\ngrasping this new way of thinking, sees the moon and\r\nthe planets moving in their paths upon principles similar\r\nto those which determine the motion of a projectile\r\nthrown into the air. Yet the movements of the\r\nplanets were marked by peculiarities which compelled\r\nhim once more to modify slightly his customary mode\r\nof thought. The heavenly bodies, or rather the parts\r\ncomposing them, do not move with constant accelerations\r\ntowards each other, but \"attract each other,\"\r\ndirectly as the mass and inversely as the square of the\r\ndistance.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis latter notion, which includes the one applying\r\nto terrestrial bodies as a special case, is, as we see,\r\nquite different from the conception from which we\r\nstarted. How limited in scope was the original idea\r\nand to what a multitude of phenomena is not the present\r\none applicable! Yet there is a trace, after all,\r\nof the \"search for place\" in the expression \"attraction.\"\r\nAnd it would be folly, indeed, for us to avoid,\r\nwith punctilious dread, this conception of \"attraction\"\r\nas bearing marks of its pedigree. It is the historical\r\nbase of the Newtonian conception and it still continues\r\nto direct our thoughts in the paths so long familiar to\r\nus. Thus, the happiest ideas do not fall from heaven,\r\nbut spring from notions already existing.\u003c/p\u003e\r\n\r\n\u003cp\u003eSimilarly, a ray of light was first regarded as a continuous\r\nand homogeneous straight line. It then became\r\nthe path of projection for minute missiles; then\r\nan aggregate of the paths of countless different kinds\r\nof missiles. It became periodic; it acquired various\r\nsides; and ultimately it even lost its motion in a\r\nstraight line.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe electric current was conceived originally as\r\nthe flow of a hypothetical fluid. To this conception\r\nwas soon added the notion of a chemical current, the\r\nnotion of an electric, magnetic, and anisotropic optical\r\nfield, intimately connected with the path of the current.\r\nAnd the richer a conception becomes in following\r\nand keeping pace with facts, the better adapted it\r\nis to anticipate them.\u003c/p\u003e\r\n\r\n\u003cp\u003eAdaptive processes of this kind have no assignable\r\nbeginning, inasmuch as every problem that incites\r\nto new adaptation, presupposes a fixed habitude of\r\nthought. Moreover, they have no visible end; in so\r\nfar as experience never ceases. Science, accordingly,\r\nstands midway in the evolutionary process; and science\r\nmay advantageously direct and promote this process,\r\nbut it can never take its place. That science is inconceivable\r\nthe principles of which would enable a person\r\nwith no experience to construct the world of experience,\r\nwithout a knowledge of it. One might just as\r\nwell expect to become a great musician, solely by the\r\naid of theory, and without musical experience; or to\r\nbecome a painter by following the directions of a text-book.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn glancing over the history of an idea with which\r\nwe have become perfectly familiar, we are no longer\r\nable to appreciate the full significance of its growth.\r\nThe deep and vital changes that have been effected in\r\nthe course of its evolution, are recognisable only from\r\nthe astounding narrowness of view with which great\r\ncontemporary scientists have occasionally opposed\r\neach other. Huygens\u0027s wave-theory of light was incomprehensible\r\nto Newton, and Newton\u0027s idea of universal\r\ngravity was unintelligible to Huygens. But a\r\ncentury afterwards both notions were reconcilable,\r\neven in ordinary minds.\u003c/p\u003e\r\n\r\n\u003cp\u003eOn the other hand, the original creations of pioneer\r\nintellects, unconsciously formed, do not assume\r\na foreign garb; their form is their own. In them,\r\nchildlike simplicity is joined to the maturity of manhood,\r\nand they are not to be compared with processes\r\nof thought in the average mind. The latter are carried\r\non as are the acts of persons in the state of mesmerism,\r\nwhere actions involuntarily follow the images which\r\nthe words of other persons suggest to their minds.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe ideas that have become most familiar through\r\nlong experience, are the very ones that intrude themselves\r\ninto the conception of every new fact observed.\r\nIn every instance, thus, they become involved in a\r\nstruggle for self-preservation, and it is just they that\r\nare seized by the inevitable process of transformation.\u003c/p\u003e\r\n\r\n\u003cp\u003eUpon this process rests substantially the method\r\nof explaining by hypothesis new and uncomprehended\r\nphenomena. Thus, instead of forming entirely new\r\nnotions to explain the movements of the heavenly\r\nbodies and the phenomena of the tides, we imagine the\r\nmaterial particles composing the bodies of the universe\r\nto possess weight or gravity with respect to one another.\r\nSimilarly, we imagine electrified bodies to be\r\nfreighted with fluids that attract and repel, or we conceive\r\nthe space between them to be in a state of elastic\r\ntension. In so doing, we substitute for new ideas\r\ndistinct and more familiar notions of old experience\u0026mdash;notions\r\nwhich to a great extent run unimpeded in their\r\ncourses, although they too must suffer partial transformation.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe animal cannot construct new members to perform\r\nevery new function that circumstances and fate\r\ndemand of it. On the contrary it is obliged to make\r\nuse of those it already possesses. When a vertebrate\r\nanimal chances into an environment where it must\r\nlearn to fly or swim, an additional pair of extremities is\r\nnot grown for the purpose. On the contrary, the animal\r\nmust adapt and transform a pair that it already\r\nhas.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe construction of hypotheses, therefore, is not\r\nthe product of artificial scientific methods. This process\r\nis unconsciously carried on in the very infancy of\r\nscience. Even later, hypotheses do not become detrimental\r\nand dangerous to progress except when more\r\nreliance is placed on them than on the facts themselves;\r\nwhen the contents of the former are more\r\nhighly valued than the latter, and when, rigidly adhering\r\nto hypothetical notions, we overestimate the\r\nideas we possess as compared with those we have to\r\nacquire.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe extension of our sphere of experience always\r\ninvolves a transformation of our ideas. It matters not\r\nwhether the face of nature becomes actually altered,\r\npresenting new and strange phenomena, or whether\r\nthese phenomena are brought to light by an intentional\r\nor accidental turn of observation. In fact, all the varied\r\nmethods of scientific inquiry and of purposive\r\nmental adaptation enumerated by John Stuart Mill,\r\nthose of observation as well as those of experiment,\r\nare ultimately recognisable as forms of one fundamental\r\nmethod, the method of change, or variation. It is\r\nthrough change of circumstances that the natural philosopher\r\nlearns. This process, however, is by no means\r\nconfined to the investigator of nature. The historian,\r\nthe philosopher, the jurist, the mathematician, the\r\nartist, the æsthetician,\u003ca name=\"FNanchor_77_77\" id=\"FNanchor_77_77\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_77_77\" class=\"fnanchor\"\u003e[77]\u003c/a\u003e all illuminate and unfold their\r\nideas by producing from the rich treasures of memory\r\nsimilar, but different, cases; thus, they observe and\r\nexperiment in their thoughts. Even if all sense-experience\r\nshould suddenly cease, the events of the days\r\npast would meet in different attitudes in the mind\r\nand the process of adaptation would still continue\u0026mdash;a\r\nprocess which, in contradistinction to the adaptation\r\nof thoughts to facts in practical spheres, would be\r\nstrictly theoretical, being an adaptation of thoughts to\r\nthoughts.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe method of change or variation brings before us\r\nlike cases of phenomena, having partly the same and\r\npartly different elements. It is only by comparing\r\ndifferent cases of refracted light at changing angles of\r\nincidence that the common factor, the constancy of\r\nthe refractive index, is disclosed. And only by comparing\r\nthe refractions of light of different colors, does\r\nthe difference, the inequality of the indices of refraction,\r\narrest the attention. Comparison based upon\r\nchange leads the mind simultaneously to the highest\r\nabstractions and to the finest distinctions.\u003c/p\u003e\r\n\r\n\u003cp\u003eUndoubtedly, the animal also is able to distinguish\r\nbetween the similar and dissimilar of two cases. Its\r\nconsciousness is aroused by a noise or a rustling, and\r\nits motor centre is put in readiness. The sight of the\r\ncreature causing the disturbance, will, according to its\r\nsize, provoke flight or prompt pursuit; and in the latter\r\ncase, the more exact distinctions will determine the\r\nmode of attack. But man alone attains to the faculty\r\nof voluntary and conscious comparison. Man alone\r\ncan, by his power of abstraction, rise, in one moment,\r\nto the comprehension of principles like the conservation\r\nof mass or the conservation of energy, and in the\r\nnext observe and mark the arrangement of the iron\r\nlines in the spectrum. In thus dealing with the objects\r\nof his conceptual life, his ideas unfold and expand,\r\nlike his nervous system, into a widely ramified\r\nand organically articulated tree, on which he may follow\r\nevery limb to its farthermost branches, and, when\r\noccasion demands, return to the trunk from which he\r\nstarted.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe English philosopher Whewell has remarked\r\nthat two things are requisite to the formation of science:\r\nfacts and ideas. Ideas alone lead to empty\r\nspeculation; mere facts can yield no organic knowledge.\r\nWe see that all depends upon the capacity of\r\nadapting existing notions to fresh facts.\u003c/p\u003e\r\n\r\n\u003cp\u003eOver-readiness to yield to every new fact prevents\r\nfixed habits of thought from arising. Excessively rigid\r\nhabits of thought impede freedom of observation. In\r\nthe struggle, in the compromise between judgment\r\nand prejudgment (prejudice), if we may use the term,\r\nour understanding of things broadens.\u003c/p\u003e\r\n\r\n\u003cp\u003eHabitual judgment, applied to a new case without\r\nantecedent tests, we call prejudgment or prejudice.\r\nWho does not know its terrible power! But we think\r\nless often of the importance and utility of prejudice.\r\nPhysically, no one could exist, if he had to guide and\r\nregulate the circulation, respiration, and digestion of\r\nhis body by conscious and purposive acts. So, too,\r\nno one could exist intellectually if he had to form judgments\r\non every passing experience, instead of allowing\r\nhimself to be controlled by the judgments he has\r\nalready formed. Prejudice is a sort of reflex motion\r\nin the province of intelligence.\u003c/p\u003e\r\n\r\n\u003cp\u003eOn prejudices, that is, on habitual judgments not\r\ntested in every case to which they are applied, reposes\r\na goodly portion of the thought and work of the natural\r\nscientist. On prejudices reposes most of the conduct\r\nof society. With the sudden disappearance of\r\nprejudice society would hopelessly dissolve. That\r\nprince displayed a deep insight into the power of intellectual\r\nhabit, who quelled the loud menaces and\r\ndemands of his body-guard for arrears of pay and compelled\r\nthem to turn about and march, by simply pronouncing\r\nthe regular word of command; he well knew\r\nthat they would be unable to resist that.\u003c/p\u003e\r\n\r\n\u003cp\u003eNot until the discrepancy between habitual judgments\r\nand facts becomes great is the investigator implicated\r\nin appreciable illusion. Then tragic complications\r\nand catastrophes occur in the practical life of\r\nindividuals and nations\u0026mdash;crises where man, placing\r\ncustom above life, instead of pressing it into the service\r\nof life, becomes the victim of his error. The very\r\npower which in intellectual life advances, fosters, and\r\nsustains us, may in other circumstances delude and\r\ndestroy us.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_234\" id=\"Page_234\"\u003e[Pg 234]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_235\" id=\"Page_235\"\u003e[Pg 235]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_236\" id=\"Page_236\"\u003e[Pg 236]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eIdeas are not all of life. They are only momentary\r\nefflorescences of light, designed to illuminate the paths\r\nof the will. But as delicate reagents on our organic\r\nevolution our ideas are of paramount importance. No\r\ntheory can gainsay the vital transformation which we\r\nfeel taking place within us through their agency. Nor\r\nis it necessary that we should have a proof of this process.\r\nWe are immediately assured of it.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe transformation of ideas thus appears as a part\r\nof the general evolution of life, as a part of its adaptation\r\nto a constantly widening sphere of action. A\r\ngranite boulder on a mountain-side tends towards the\r\nearth below. It must abide in its resting-place for\r\nthousands of years before its support gives way. The\r\nshrub that grows at its base is farther advanced; it\r\naccommodates itself to summer and winter. The fox\r\nwhich, overcoming the force of gravity, creeps to the\r\nsummit where he has scented his prey, is freer in his\r\nmovements than either. The arm of man reaches\r\nfurther still; and scarcely anything of note happens\r\nin Africa or Asia that does not leave an imprint upon\r\nhis life. What an immense portion of the life of\r\nother men is reflected in ourselves; their joys, their\r\naffections, their happiness and misery! And this too,\r\nwhen we survey only our immediate surroundings,\r\nand confine our attention to modern literature. How\r\nmuch more do we experience when we travel through\r\nancient Egypt with Herodotus, when we stroll through\r\nthe streets of Pompeii, when we carry ourselves back\r\nto the gloomy period of the crusades or to the golden\r\nage of Italian art, now making the acquaintance of a\r\nphysician of Molière, and now that of a Diderot or of\r\na D\u0027Alembert. What a great part of the life of others,\r\nof their character and their purpose, do we not absorb\r\nthrough poetry and music! And although they only\r\ngently touch the chords of our emotions, like the memory\r\nof youth softly breathing upon the spirit of an\r\naged man, we have nevertheless lived them over again\r\nin part. How great and comprehensive does self become\r\nin this conception; and how insignificant the\r\nperson! Egoistical systems both of optimism and pessimism\r\nperish with their narrow standard of the import\r\nof intellectual life. We feel that the real pearls\r\nof life lie in the ever changing contents of consciousness,\r\nand that the person is merely an indifferent symbolical\r\nthread on which they are strung.\u003ca name=\"FNanchor_78_78\" id=\"FNanchor_78_78\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_78_78\" class=\"fnanchor\"\u003e[78]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eWe are prepared, thus, to regard ourselves and\r\nevery one of our ideas as a product and a subject of\r\nuniversal evolution; and in this way we shall advance\r\nsturdily and unimpeded along the paths which the\r\nfuture will throw open to us.\u003ca name=\"FNanchor_79_79\" id=\"FNanchor_79_79\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_79_79\" class=\"fnanchor\"\u003e[79]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_THE_PRINCIPLE_OF_COMPARISON\" id=\"ON_THE_PRINCIPLE_OF_COMPARISON\"\u003eON THE PRINCIPLE OF COMPARISON\r\nIN PHYSICS.\u003c/a\u003e\u003ca name=\"FNanchor_80_80\" id=\"FNanchor_80_80\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_80_80\" class=\"fnanchor\"\u003e[80]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eTwenty years ago when Kirchhoff defined the object\r\nof mechanics as the \"description, in complete\r\nand very simple terms, of the motions occurring in nature,\"\r\nhe produced by the statement a peculiar impression.\r\nFourteen years subsequently, Boltzmann, in the\r\nlife-like picture which he drew of the great inquirer,\r\ncould still speak of the universal astonishment at this\r\nnovel method of treating mechanics, and we meet with\r\nepistemological treatises to-day, which plainly show\r\nhow difficult is the acceptance of this point of view. A\r\nmodest and small band of inquirers there were, however,\r\nto whom Kirchhoff\u0027s few words were tidings of a\r\nwelcome and powerful ally in the epistemological field.\u003c/p\u003e\r\n\r\n\u003cp\u003eNow, how does it happen that we yield our assent\r\nso reluctantly to the philosophical opinion of an inquirer\r\nfor whose scientific achievements we have only\r\nwords of praise? One reason probably is that few inquirers\r\ncan find time and leisure, amid the exacting\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_237\" id=\"Page_237\"\u003e[Pg 237]\u003c/a\u003e\u003c/span\u003e\r\nemployments demanded for the acquisition of new\r\nknowledge, to inquire closely into that tremendous\r\npsychical process by which science is formed. Further,\r\nit is inevitable that much should be put into Kirchhoff\u0027s\r\nrigid words that they were not originally intended to\r\nconvey, and that much should be found wanting in\r\nthem that had always been regarded as an essential\r\nelement of scientific knowledge. What can mere description\r\naccomplish? What has become of explanation,\r\nof our insight into the causal connexion of things?\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_238\" id=\"Page_238\"\u003e[Pg 238]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_239\" id=\"Page_239\"\u003e[Pg 239]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003ePermit me, for a moment, to contemplate not the\r\nresults of science, but the mode of its \u003ci\u003egrowth\u003c/i\u003e, in a\r\nfrank and unbiassed manner. We know of only \u003ci\u003eone\u003c/i\u003e\r\nsource of \u003ci\u003eimmediate revelation\u003c/i\u003e of scientific facts\u0026mdash;\u003ci\u003eour\r\nsenses\u003c/i\u003e. Restricted to this source alone, thrown wholly\r\nupon his own resources, obliged to start always anew,\r\nwhat could the isolated individual accomplish? Of a\r\nstock of knowledge so acquired the science of a distant\r\nnegro hamlet in darkest Africa could hardly give\r\nus a sufficiently humiliating conception. For there\r\nthat veritable miracle of thought-transference has already\r\nbegun its work, compared with which the miracles\r\nof the spiritualists are rank monstrosities\u0026mdash;\u003ci\u003ecommunication\r\nby language\u003c/i\u003e. Reflect, too, that by means\r\nof the magical characters which our libraries contain\r\nwe can raise the spirits of the \"the sovereign dead of\r\nold\" from Faraday to Galileo and Archimedes, through\r\nages of time\u0026mdash;spirits who do not dismiss us with ambiguous\r\nand derisive oracles, but tell us the best they\r\nknow; then shall we feel what a stupendous and indispensable\r\nfactor in the formation of science \u003ci\u003ecommunication\u003c/i\u003e\r\nis. Not the dim, half-conscious \u003ci\u003esurmises\u003c/i\u003e\r\nof the acute observer of nature or critic of humanity\r\nbelong to science, but only that which they possess\r\nclearly enough to \u003ci\u003ecommunicate\u003c/i\u003e to others.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut how, now, do we go about this communication\r\nof a newly acquired experience, of a newly observed\r\nfact? As the different calls and battle-cries of gregarious\r\nanimals are unconsciously formed signs for\r\na common observation or action, irrespective of the\r\ncauses which produce such action\u0026mdash;a fact that already\r\ninvolves the germ of the concept; so also the words\r\nof human language, which is only more highly specialised,\r\nare names or signs for universally known\r\nfacts, which all can observe or have observed. If the\r\nmental representation, accordingly, follows the new\r\nfact at once and \u003ci\u003epassively\u003c/i\u003e, then that new fact must, of\r\nitself, immediately be constituted and represented in\r\nthought by facts already universally known and commonly\r\nobserved. Memory is always ready to put forward\r\nfor \u003ci\u003ecomparison\u003c/i\u003e known facts which resemble the\r\nnew event, or agree with it in certain features, and\r\nso renders possible that elementary internal judgment\r\nwhich the mature and definitively formulated judgment\r\nsoon follows.\u003c/p\u003e\r\n\r\n\u003cp\u003eComparison, as the fundamental condition of communication,\r\nis the most powerful inner vital element\r\nof science. The zoölogist sees in the bones of the\r\nwing-membranes of bats, fingers; he compares the\r\nbones of the cranium with the vertebræ, the embryos\r\nof different organisms with one another, and the different\r\nstages of development of the same organism\r\nwith one another. The geographer sees in Lake Garda\r\na fjord, in the Sea of Aral a lake in process of drying\r\nup. The philologist compares different languages with\r\none another, and the formations of the same language\r\nas well. If it is not customary to speak of comparative\r\nphysics in the same sense that we speak of comparative\r\nanatomy, the reason is that in a science of\r\nsuch great experimental activity the attention is turned\r\naway too much from the \u003ci\u003econtemplative\u003c/i\u003e element. But\r\nlike all other sciences, physics lives and grows by\r\ncomparison.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_240\" id=\"Page_240\"\u003e[Pg 240]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_241\" id=\"Page_241\"\u003e[Pg 241]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eThe manner in which the result of the comparison\r\nfinds expression in the communication, varies of course\r\nvery much. When we say that the colors of the spectrum\r\nare red, yellow, green, blue, and violet, the designations\r\nemployed may possibly have been derived\r\nfrom the technology of tattooing, or they may subsequently\r\nhave acquired the significance of standing for\r\nthe colors of the rose, the lemon, the leaf, the corn-flower,\r\nand the violet. From the frequent repetition\r\nof such comparisons, however, made under the most\r\nmanifold circumstances, the inconstant features, as\r\ncompared with the permanent congruent features, get\r\nso obliterated that the latter acquire a fixed significance\r\nindependent of every object and connexion, or take on\r\nas we say an \u003ci\u003eabstract\u003c/i\u003e or \u003ci\u003econceptual\u003c/i\u003e import. No one\r\nthinks at the word \"red\" of any other agreement with\r\nthe rose than that of color, or at the word \"straight\"\r\nof any other property of a stretched cord than the\r\nsameness of direction. Just so, too, numbers, originally\r\nthe names of the fingers of the hands and feet,\r\nfrom being used as arrangement-signs for all kinds of\r\nobjects, were lifted to the plane of abstract concepts.\r\nA verbal report (communication) of a fact that uses\r\nonly these purely abstract implements, we call a \u003ci\u003edirect\r\ndescription\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe direct description of a fact of any great extent\r\nis an irksome task, even where the requisite notions\r\nare already completely developed. What a simplification\r\nit involves if we can say, the fact \u003ci\u003eA\u003c/i\u003e now\r\nconsidered comports itself, not in \u003ci\u003eone\u003c/i\u003e, but in \u003ci\u003emany\u003c/i\u003e or\r\nin \u003ci\u003eall\u003c/i\u003e its features, like an old and well-known fact \u003ci\u003eB\u003c/i\u003e.\r\nThe moon comports itself as a heavy body does with\r\nrespect to the earth; light like a wave-motion or an\r\nelectric vibration; a magnet, as if it were laden with\r\ngravitating fluids, and so on. We call such a description,\r\nin which we appeal, as it were, to a description\r\nalready and elsewhere formulated, or perhaps still to\r\nbe precisely formulated, an \u003ci\u003eindirect description\u003c/i\u003e. We\r\nare at liberty to supplement this description, gradually,\r\nby direct description, to correct it, or to replace it altogether.\r\nWe see, thus, without difficulty, that what is\r\ncalled a \u003ci\u003etheory\u003c/i\u003e or a \u003ci\u003etheoretical idea\u003c/i\u003e, falls under the\r\ncategory of what is here termed indirect description.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_242\" id=\"Page_242\"\u003e[Pg 242]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_243\" id=\"Page_243\"\u003e[Pg 243]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_244\" id=\"Page_244\"\u003e[Pg 244]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_245\" id=\"Page_245\"\u003e[Pg 245]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_246\" id=\"Page_246\"\u003e[Pg 246]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_247\" id=\"Page_247\"\u003e[Pg 247]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_248\" id=\"Page_248\"\u003e[Pg 248]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_249\" id=\"Page_249\"\u003e[Pg 249]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_250\" id=\"Page_250\"\u003e[Pg 250]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_251\" id=\"Page_251\"\u003e[Pg 251]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_252\" id=\"Page_252\"\u003e[Pg 252]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eWhat, now, is a theoretical idea? Whence do we\r\nget it? What does it accomplish for us? Why does it\r\noccupy a higher place in our judgment than the mere\r\nholding fast to a fact or an observation? Here, too,\r\nmemory and comparison alone are in play. But instead\r\nof \u003ci\u003ea single\u003c/i\u003e feature of resemblance culled from\r\nmemory, in this case \u003ci\u003ea great system\u003c/i\u003e of resemblances\r\nconfronts us, a well-known physiognomy, by means of\r\nwhich the new fact is immediately transformed into an\r\nold acquaintance. Besides, it is in the power of the\r\nidea to offer us more than we actually see in the new\r\nfact, at the first moment; it can extend the fact, and\r\nenrich it with features which we are first induced to\r\n\u003ci\u003eseek\u003c/i\u003e from such suggestions, and which are often actually\r\nfound. It is this \u003ci\u003erapidity\u003c/i\u003e in extending knowledge\r\nthat gives to theory a preference over simple observation.\r\nBut that preference is wholly \u003ci\u003equantitative\u003c/i\u003e.\r\nQualitatively, and in real essential points, theory differs\r\nfrom observation neither in the mode of its origin\r\nnor in its last results.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe adoption of a theory, however, always involves\r\na danger. For a theory puts in the place of a fact \u003ci\u003eA\u003c/i\u003e\r\nin thought, always a \u003ci\u003edifferent\u003c/i\u003e, but simpler and more\r\nfamiliar fact \u003ci\u003eB\u003c/i\u003e, which in \u003ci\u003esome\u003c/i\u003e relations can mentally\r\nrepresent \u003ci\u003eA\u003c/i\u003e, but for the very reason that it is different,\r\nin other relations cannot represent it. If now, as\r\nmay readily happen, sufficient care is not exercised,\r\nthe most fruitful theory may, in special circumstances,\r\nbecome a downright obstacle to inquiry. Thus, the\r\nemission-theory of light, in accustoming the physicist\r\nto think of the projectile path of the \"light-particles\"\r\nas an undifferentiated straight-line, demonstrably impeded\r\nthe discovery of the periodicity of light. By\r\nputting in the place of light the more familiar phenomena\r\nof sound, Huygens renders light in many of\r\nits features a familiar event, but with respect to polarisation,\r\nwhich lacks the longitudinal waves with which\r\nalone he was acquainted, it had for him a doubly\r\nstrange aspect. He is unable thus to grasp in abstract\r\nthought the fact of polarisation, which is before his\r\neyes, whilst Newton, merely by adapting to the observation\r\nhis thoughts, and putting this question, \"\u003ci\u003eAnnon\r\nradiorum luminis diversa sunt latera?\u003c/i\u003e\" abstractly\r\ngrasped polarisation, that is, directly described it, a\r\ncentury before Malus. On the other hand, if the\r\nagreement of the fact with the idea theoretically representing\r\nit, extends further than its inventor originally\r\nanticipated, then we may be led by it to unexpected\r\ndiscoveries, of which conical refraction, circular polarisation\r\nby total reflexion, Hertz\u0027s waves offer ready\r\nexamples, in contrast to the illustrations given above.\u003c/p\u003e\r\n\r\n\u003cp\u003eOur insight into the conditions indicated will be\r\nimproved, perhaps, by contemplating the development\r\nof some theory or other more in detail. Let us consider\r\na magnetised bar of steel by the side of a second\r\nunmagnetised bar, in all other respects the same. The\r\nsecond bar gives no indication of the presence of iron-filings;\r\nthe first attracts them. Also, when the iron-filings\r\nare absent, we must think of the magnetised\r\nbar as in a different condition from that of the unmagnetised.\r\nFor, that the mere presence of the iron-filings\r\ndoes not induce the phenomenon of attraction is proved\r\nby the second unmagnetised bar. The ingenuous man,\r\nwho finds in his will, as his most familiar source of\r\npower, the best facilities for comparison, conceives a\r\nspecies of \u003ci\u003espirit\u003c/i\u003e in the magnet. The behavior of a\r\nwarm body or of an \u003ci\u003eelectrified\u003c/i\u003e body suggests similar\r\nideas. This is the point of view of the oldest theory,\r\n\u003ci\u003efetishism\u003c/i\u003e, which the inquirers of the early Middle\r\nAges had not yet overcome, and which in its last vestiges,\r\nin the conception of forces, still flourishes in\r\nmodern physics. We see, thus, the \u003ci\u003edramatic\u003c/i\u003e element\r\nneed no more be absent in a scientific description, than\r\nin a thrilling novel.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf, on subsequent examination, it be observed that\r\na cold body, in contact with a hot body, warms itself,\r\nso to speak, \u003ci\u003eat the expense\u003c/i\u003e of the hot body; further,\r\nthat when the substances are the same, the cold body,\r\nwhich, let us say, has twice the mass of the other,\r\ngains only half the number of degrees of temperature\r\nthat the other loses, a wholly new impression arises.\r\nThe demoniac character of the event vanishes, for the\r\nsupposed spirit acts not by caprice, but according to\r\nfixed laws. In its place, however, \u003ci\u003einstinctively\u003c/i\u003e the\r\nnotion of a \u003ci\u003esubstance\u003c/i\u003e is substituted, part of which flows\r\nover from the one body to the other, but the total\r\namount of which, representable by the sum of the products\r\nof the masses into the respective changes of\r\ntemperature, remains constant. Black was the first to\r\nbe \u003ci\u003epowerfully\u003c/i\u003e struck with this resemblance of thermal\r\nprocesses to the motion of a substance, and under its\r\nguidance discovered the specific heat, the heat of fusion,\r\nand the heat of vaporisation of bodies. Gaining\r\nstrength and fixity, however, from these successes,\r\nthis notion of substance subsequently stood in the way\r\nof scientific advancement. It blinded the eyes of the\r\nsuccessors of Black, and prevented them from seeing\r\nthe manifest fact, which every savage knows, that heat\r\nis \u003ci\u003eproduced\u003c/i\u003e by friction. Fruitful as that notion was\r\nfor Black, helpful as it still is to the learner to-day in\r\nBlack\u0027s special field, permanent and universal validity\r\nas a \u003ci\u003etheory\u003c/i\u003e it could never maintain. But what is essential,\r\nconceptually, in it, viz., the constancy of the product-sum\r\nabove mentioned, retains its value and may\r\nbe regarded as a \u003ci\u003edirect description\u003c/i\u003e of Black\u0027s facts.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt stands to reason that those theories which push\r\nthemselves forward unsought, instinctively, and wholly\r\nof their own accord, should have the greatest power,\r\nshould carry our thoughts most with them, and exhibit\r\nthe staunchest powers of self-preservation. On the\r\nother hand, it may also be observed that when critically\r\nscrutinised such theories are extremely apt to\r\nlose their cogency. We are constantly busied with\r\n\"substance,\" its modes of action have stamped themselves\r\nindelibly upon our thoughts, our vividest and\r\nclearest reminiscences are associated with it. It should\r\ncause us no surprise, therefore, that Robert Mayer and\r\nJoule, who gave the final blow to Black\u0027s substantial\r\nconception of heat, should have re-introduced the\r\nsame notion of substance in a more abstract and modified\r\nform, only applying to a much more extensive\r\nfield.\u003c/p\u003e\r\n\r\n\u003cp\u003eHere, too, the psychological circumstances which\r\nimpart to the new conception its power, lie clearly before\r\nus. By the unusual redness of the venous blood\r\nin tropical climates Mayer\u0027s attention is directed to\r\nthe lessened expenditure of internal heat and to the\r\nproportionately lessened \u003ci\u003econsumption of material\u003c/i\u003e by the\r\nhuman body in those climates. But as every effort of\r\nthe human organism, including its mechanical work,\r\nis connected with the consumption of material, and as\r\nwork by friction can engender heat, therefore heat and\r\nwork appear in kind equivalent, and between them a\r\nproportional relation must subsist. Not \u003ci\u003eevery\u003c/i\u003e quantity,\r\nbut the appropriately calculated \u003ci\u003esum\u003c/i\u003e of the two, as\r\nconnected with a proportionate consumption of material,\r\nappears \u003ci\u003esubstantial\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eBy exactly similar considerations, relative to the\r\neconomy of the galvanic element, Joule arrived at his\r\nview; he found experimentally that the sum of the\r\nheat evolved in the circuit, of the heat consumed in the\r\ncombustion of the gas developed, of the electro-magnetic\r\nwork of the current, properly calculated,\u0026mdash;in\r\nshort, the sum of all the effects of the battery,\u0026mdash;is connected\r\nwith a proportionate consumption of zinc. Accordingly,\r\nthis sum itself has a substantial character.\u003c/p\u003e\r\n\r\n\u003cp\u003eMayer was so absorbed with the view attained,\r\nthat the indestructibility of \u003ci\u003eforce\u003c/i\u003e, in our phraseology\r\n\u003ci\u003ework\u003c/i\u003e, appeared to him \u003ci\u003ea priori\u003c/i\u003e evident. \"The creation\r\nor annihilation of a force,\" he says, \"lies without\r\nthe province of human thought and power.\" Joule\r\nexpressed himself to a similar effect: \"It is manifestly\r\nabsurd to suppose that the powers with which God\r\nhas endowed matter can be destroyed.\" Strange to\r\nsay, on the basis of such utterances, not Joule, but\r\nMayer, was stamped as a metaphysician. We may\r\nbe sure, however, that both men were merely giving\r\nexpression, and that half-unconsciously, to a powerful\r\n\u003ci\u003eformal\u003c/i\u003e need of the new simple view, and that both\r\nwould have been extremely surprised if it had been\r\nproposed to them that their principle should be submitted\r\nto a philosophical congress or ecclesiastical\r\nsynod for a decision upon its validity. But with all\r\nagreements, the attitude of these two men, in other\r\nrespects, was totally different. Whilst Mayer represented\r\nthis \u003ci\u003eformal\u003c/i\u003e need with all the stupendous instinctive\r\nforce of genius, we might say almost with the\r\nardor of fanaticism, yet was withal not wanting in the\r\nconceptive ability to compute, prior to all other inquirers,\r\nthe mechanical equivalent of heat from old\r\nphysical constants long known and at the disposal of\r\nall, and so to set up for the new doctrine a programme\r\nembracing all physics and physiology; Joule, on the\r\nother hand, applied himself to the exact verification of\r\nthe doctrine by beautifully conceived and masterfully\r\nexecuted experiments, extending over all departments\r\nof physics. Soon Helmholtz too attacked the problem,\r\nin a totally independent and characteristic manner.\r\nAfter the professional virtuosity with which this physicist\r\ngrasped and disposed of all the points unsettled\r\nby Mayer\u0027s programme and more besides, what especially\r\nstrikes us is the consummate critical lucidity of\r\nthis young man of twenty-six years. In his exposition\r\nis wanting that vehemence and impetuosity which\r\nmarked Mayer\u0027s. The principle of the conservation\r\nof energy is no self-evident or \u003ci\u003ea priori\u003c/i\u003e proposition for\r\nhim. What follows, on the assumption that that proposition\r\nobtains? In this hypothetical form, he subjugates\r\nhis matter.\u003c/p\u003e\r\n\r\n\u003cp\u003eI must confess, I have always marvelled at the\r\næsthetic and ethical taste of many of our contemporaries\r\nwho have managed to fabricate out of this relation\r\nof things, odious national and personal questions,\r\ninstead of praising the good fortune that made \u003ci\u003eseveral\u003c/i\u003e\r\nsuch men work together and of rejoicing at the instructive\r\ndiversity and idiosyncrasies of great minds\r\nfraught with such rich consequences for us.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe know that still another theoretical conception\r\nplayed a part in the development of the principle of\r\nenergy, which Mayer held aloof from, namely, the conception\r\nthat heat, as also the other physical processes,\r\nare due to motion. But once the principle of energy\r\nhas been reached, these auxiliary and transitional theories\r\ndischarge no essential function, and we may regard\r\nthe principle, like that which Black gave, as a\r\ncontribution to the \u003ci\u003edirect description\u003c/i\u003e of a widely extended\r\ndomain of facts.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt would appear from such considerations not only\r\nadvisable, but even necessary, with all due recognition\r\nof the helpfulness of theoretic ideas in research,\r\nyet gradually, as the new facts grow familiar, to substitute\r\nfor indirect description \u003ci\u003edirect\u003c/i\u003e description, which\r\ncontains nothing that is unessential and restricts itself\r\nabsolutely to the abstract apprehension of facts. We\r\nmight almost say, that the descriptive sciences, so\r\ncalled with a tincture of condescension, have, in respect\r\nof scientific character, outstripped the physical\r\nexpositions lately in vogue. Of course, a virtue has\r\nbeen made of necessity here.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe must admit, that it is not in our power to describe\r\ndirectly every fact, on the moment. Indeed,\r\nwe should succumb in utter despair if the whole wealth\r\nof facts which we come step by step to know, were\r\npresented to us all at once. Happily, only detached\r\nand unusual features first strike us, and such we bring\r\nnearer to ourselves by \u003ci\u003ecomparison\u003c/i\u003e with every-day\r\nevents. Here the notions of the common speech are\r\nfirst developed. The comparisons then grow more\r\nmanifold and numerous, the fields of facts compared\r\nmore extensive, the concepts that make direct description\r\npossible, proportionately more general and more\r\nabstract.\u003c/p\u003e\r\n\r\n\u003cp\u003eFirst we become familiar with the motion of freely\r\nfalling bodies. The concepts of force, mass, and work\r\nare then carried over, with appropriate modifications,\r\nto the phenomena of electricity and magnetism. A\r\nstream of water is said to have suggested to Fourier\r\nthe first distinct picture of currents of heat. A special\r\ncase of vibrations of strings investigated by Taylor,\r\ncleared up for him a special case of the conduction of\r\nheat. Much in the same way that Daniel Bernoulli\r\nand Euler constructed the most diverse forms of vibrations\r\nof strings from Taylor\u0027s cases, so Fourier constructs\r\nout of simple cases of conduction the most\r\nmultifarious motions of heat; and that method has\r\nextended itself over the whole of physics. Ohm forms\r\nhis conception of the electric current in imitation of\r\nFourier\u0027s. The latter, also, adopts Fick\u0027s theory of\r\ndiffusion. In an analogous manner a conception of\r\nthe magnetic current is developed. All sorts of stationary\r\ncurrents are thus made to exhibit common\r\nfeatures, and even the condition of complete equilibrium\r\nin an extended medium shares these features\r\nwith the dynamical condition of equilibrium of a stationary\r\ncurrent. Things as remote as the magnetic\r\nlines of force of an electric current and the stream-lines\r\nof a frictionless liquid vortex enter in this way\r\ninto a peculiar relationship of similarity. The concept\r\nof potential, originally enunciated for a restricted\r\nprovince, acquires a wide-reaching applicability.\r\nThings as dissimilar as pressure, temperature,\r\nand electromotive force, now show points of agreement\r\nin relation to ideas derived by definite methods\r\nfrom that concept: viz., fall of pressure, fall of temperature,\r\nfall of potential, as also with the further notions\r\nof liquid, thermal, and electric strength of current.\r\nThat relationship between systems of ideas in\r\nwhich the dissimilarity of every two homologous concepts\r\nas well as the agreement in logical relations\r\nof every two homologous pairs of concepts, is clearly\r\nbrought to light, is called an \u003ci\u003eanalogy\u003c/i\u003e. It is an effective\r\nmeans of mastering heterogeneous fields of facts in\r\nunitary comprehension. The path is plainly shown in\r\nwhich \u003ci\u003ea universal physical phenomenology\u003c/i\u003e embracing all\r\ndomains, will be developed.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the process described we attain for the first time\r\nto what is indispensable in the direct description of\r\nbroad fields of fact\u0026mdash;the wide-reaching \u003ci\u003eabstract concept\u003c/i\u003e.\r\nAnd now I must put a question smacking of the school-master,\r\nbut unavoidable: What is a concept? Is it a\r\nhazy representation, admitting withal of mental visualisation?\r\nNo. Mental visualisation accompanies it\r\nonly in the simplest cases, and then merely as an adjunct.\r\nThink, for example, of the \"coefficient of self-induction,\"\r\nand seek for its visualised mental image.\r\nOr is, perhaps, the concept a mere word? The adoption\r\nof this forlorn idea, which has been actually proposed\r\nof late by a reputed mathematician would only\r\nthrow us back a thousand years into the deepest scholasticism.\r\nWe must, therefore, reject it.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe solution is not far to seek. We must not think\r\nthat sensation, or representation, is a purely passive\r\nprocess. The lowest organisms respond to it with a\r\nsimple reflex motion, by engulfing the prey which approaches\r\nthem. In higher organisms the centripetal\r\nstimulus encounters in the nervous system obstacles\r\nand aids which modify the centrifugal process. In still\r\nhigher organisms, where prey is pursued and examined,\r\nthe process in question may go through extensive\r\npaths of circular motions before it comes to relative\r\nrest. Our own life, too, is enacted in such\r\nprocesses; all that we call science may be regarded\r\nas parts, or middle terms, of such activities.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt will not surprise us now if I say: the definition\r\nof a concept, and, when it is very familiar, even its\r\nname, is an \u003ci\u003eimpulse\u003c/i\u003e to some accurately determined,\r\noften complicated, critical, comparative, or constructive\r\n\u003ci\u003eactivity\u003c/i\u003e, the usually sense-perceptive result of\r\nwhich is a term or member of the concept\u0027s scope. It\r\nmatters not whether the concept draws the attention\r\nonly to one certain sense (as sight) or to a phase of a\r\nsense (as color, form), or is the starting-point of a\r\ncomplicated action; nor whether the activity in question\r\n(chemical, anatomical, and mathematical operations)\r\nis muscular or technical, or performed wholly\r\nin the imagination, or only intimated. The concept is\r\nto the physicist what a musical note is to a piano-player.\r\nA trained physicist or mathematician reads a\r\nmemoir like a musician reads a score. But just as the\r\npiano-player must first learn to move his fingers singly\r\nand collectively, before he can follow his notes without\r\neffort, so the physicist or mathematician must go\r\nthrough a long apprenticeship before he gains control,\r\nso to speak, of the manifold delicate innervations\r\nof his muscles and imagination. Think of how frequently\r\nthe beginner in physics or mathematics performs\r\nmore, or less, than is required, or of how frequently\r\nhe conceives things differently from what they\r\nare! But if, after having had sufficient discipline, he\r\nlights upon the phrase \"coefficient of self-induction,\"\r\nhe knows immediately what that term requires of him.\r\nLong and thoroughly practised \u003ci\u003eactions\u003c/i\u003e, which have\r\ntheir origin in the necessity of comparing and representing\r\nfacts by other facts, are thus the very kernel\r\nof concepts. In fact, positive and philosophical philology\r\nboth claim to have established that all roots\r\nrepresent concepts and stood originally for muscular\r\nactivities alone. The slow assent of physicists to\r\nKirchhoff\u0027s dictum now becomes intelligible. They\r\nbest could feel the vast amount of individual labor,\r\ntheory, and skill required before the ideal of direct\r\ndescription could be realised.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_253\" id=\"Page_253\"\u003e[Pg 253]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_254\" id=\"Page_254\"\u003e[Pg 254]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_255\" id=\"Page_255\"\u003e[Pg 255]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_256\" id=\"Page_256\"\u003e[Pg 256]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_257\" id=\"Page_257\"\u003e[Pg 257]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_258\" id=\"Page_258\"\u003e[Pg 258]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_259\" id=\"Page_259\"\u003e[Pg 259]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eSuppose, now, the ideal of a given province of\r\nfacts is reached. Does description accomplish all that\r\nthe inquirer can ask? In my opinion, it does. Description\r\nis a building up of facts in thought, and this\r\nbuilding up is, in the experimental sciences, often the\r\ncondition of actual execution. For the physicist, to\r\ntake a special case, the metrical units are the building-stones,\r\nthe concepts the directions for building, and\r\nthe facts the result of the building. Our mental\r\nimagery is almost a complete substitute for the fact,\r\nand by means of it we can ascertain all the fact\u0027s properties.\r\nWe do not know that worst which we ourselves\r\nhave made.\u003c/p\u003e\r\n\r\n\u003cp\u003ePeople require of science that it should \u003ci\u003eprophesy\u003c/i\u003e,\r\nand Hertz uses that expression in his posthumous\r\n\u003ci\u003eMechanics\u003c/i\u003e. But, natural as it is, the expression is too\r\nnarrow. The geologist and the palæontologist, at times\r\nthe astronomer, and always the historian and the philologist,\r\nprophesy, so to speak, \u003ci\u003ebackwards\u003c/i\u003e. The descriptive\r\nsciences, like geometry and mathematics, prophesy\r\nneither forward or backwards, but seek from given\r\nconditions the conditioned. Let us say rather: \u003ci\u003eScience\r\ncompletes in thought facts that are only partly given\u003c/i\u003e.\r\nThis is rendered possible by description, for description\r\npresupposes the interdependence of the descriptive\r\nelements: otherwise nothing would be described.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is said, description leaves the sense of causality\r\nunsatisfied. In fact, many imagine they understand\r\nmotions better when they picture to themselves the\r\npulling forces; and yet the \u003ci\u003eaccelerations\u003c/i\u003e, the facts,\r\naccomplish more, without superfluous additions. I\r\nhope that the science of the future will discard the\r\nidea of cause and effect, as being formally obscure;\r\nand in my feeling that these ideas contain a strong\r\ntincture of fetishism, I am certainly not alone. The\r\nmore proper course is, \u003ci\u003eto regard the abstract determinative\r\nelements of a fact as interdependent\u003c/i\u003e, in a purely logical\r\nway, as the mathematician or geometer does.\r\nTrue, by comparison with the will, forces are brought\r\nnearer to our feeling; but it may be that ultimately the\r\nwill itself will be made clearer by comparison with the\r\naccelerations of masses.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we are asked, candidly, when is a fact \u003ci\u003eclear\u003c/i\u003e to\r\nus, we must say \"when we can reproduce it by very\r\n\u003ci\u003esimple\u003c/i\u003e and very familiar intellectual operations, such\r\nas the construction of accelerations, or the geometrical\r\nsummation of accelerations, and so forth.\" The\r\nrequirement of \u003ci\u003esimplicity\u003c/i\u003e is of course to the expert\r\na different matter from what it is to the novice. For\r\nthe first, description by a system of differential equations\r\nis sufficient; for the second, a gradual construction\r\nout of elementary laws is required. The first\r\ndiscerns at once the connexion of the two expositions.\r\nOf course, it is not disputed that the \u003ci\u003eartistic\u003c/i\u003e value of\r\nmaterially equivalent descriptions may not be different.\u003c/p\u003e\r\n\r\n\u003cp\u003eMost difficult is it to persuade strangers that the\r\ngrand universal laws of physics, such as apply indiscriminately\r\nto material, electrical, magnetic, and other\r\nsystems, are not essentially different from descriptions.\r\nAs compared with many sciences, physics occupies in\r\nthis respect a position of vantage that is easily explained.\r\nTake, for example, anatomy. As the anatomist\r\nin his quest for agreements and differences in\r\nanimals ascends to ever higher and higher \u003ci\u003eclassifications\u003c/i\u003e,\r\nthe individual facts that represent the ultimate\r\nterms of the system, are still so different that they\r\nmust be \u003ci\u003esingly\u003c/i\u003e noted. Think, for example, of the common\r\nmarks of the Vertebrates, of the class-characters\r\nof Mammals and Birds on the one hand and of Fishes\r\non the other, of the double circulation of the blood on\r\nthe one hand and of the single on the other. In the\r\nend, always \u003ci\u003eisolated\u003c/i\u003e facts remain, which show only a\r\n\u003ci\u003eslight\u003c/i\u003e likeness to one another.\u003c/p\u003e\r\n\r\n\u003cp\u003eA science still more closely allied to physics, chemistry,\r\nis often in the same strait. The abrupt change\r\nof the qualitative properties, in all likelihood conditioned\r\nby the slight stability of the intermediate states,\r\nthe remote resemblance of the co-ordinated facts of\r\nchemistry render the treatment of its data difficult.\r\nPairs of bodies of different qualitative properties unite\r\nin different mass-ratios; but no connexion between\r\nthe first and the last is to be noted, at first.\u003c/p\u003e\r\n\r\n\u003cp\u003ePhysics, on the other hand, reveals to us wide domains\r\nof \u003ci\u003equalitatively homogeneous\u003c/i\u003e facts, differing from\r\none another only in the number of equal parts into\r\nwhich their characteristic marks are divisible, that is,\r\ndiffering only \u003ci\u003equantitatively\u003c/i\u003e. Even where we have to\r\ndeal with qualities (colors and sounds), quantitative\r\ncharacters of those qualities are at our disposal. Here\r\nthe classification is so simple a task that it rarely impresses\r\nus as such, whilst in infinitely fine gradations,\r\nin a \u003ci\u003econtinuum of facts\u003c/i\u003e, our number-system is ready beforehand\r\nto follow as far as we wish. The co-ordinated\r\nfacts are here extremely similar and very closely affined,\r\nas are also their descriptions which consist in\r\nthe determination of the numerical measures of one\r\ngiven set of characters from those of a different set by\r\nmeans of familiar mathematical operations\u0026mdash;methods\r\nof derivation. Thus, the common characteristics of\r\nall descriptions can be found here; and with them a\r\nsuccinct, comprehensive description, or a rule for the\r\nconstruction of all single descriptions, is assigned,\u0026mdash;and\r\nthis we call \u003ci\u003elaw\u003c/i\u003e. Well-known examples are the\r\nformulæ for freely falling bodies, for projectiles, for\r\ncentral motion, and so forth. If physics apparently\r\naccomplishes more by its methods than other sciences,\r\nwe must remember that in a sense it has presented to\r\nit much simpler problems.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe remaining sciences, whose facts also present a\r\nphysical side, need not be envious of physics for this\r\nsuperiority; for all its acquisitions ultimately redound\r\nto their benefit as well. But also in other ways this\r\nmutual help shall and must change. Chemistry has advanced\r\nvery far in making the methods of physics her\r\nown. Apart from older attempts, the periodical series\r\nof Lothar Meyer and Mendelejeff are a brilliant and\r\nadequate means of producing an easily surveyed system\r\nof facts, which by gradually becoming complete,\r\nwill take the place almost of a continuum of facts.\r\nFurther, by the study of solutions, of dissociation, in\r\nfact generally of phenomena which present a continuum\r\nof cases, the methods of thermodynamics have\r\nfound entrance into chemistry. Similarly we may hope\r\nthat, at some future day, a mathematician, letting the\r\nfact-continuum of embryology play before his mind,\r\nwhich the palæontologists of the future will supposedly\r\nhave enriched with more intermediate and derivative\r\nforms between Saurian and Bird than the isolated\r\nPterodactyl, Archæopteryx, Ichthyornis, and so forth,\r\nwhich we now have\u0026mdash;that such a mathematician shall\r\ntransform, by the variation of a few parameters, as in\r\na dissolving view, one form into another, just as we\r\ntransform one conic section into another.\u003c/p\u003e\r\n\r\n\u003cp\u003eReverting now to Kirchhoff\u0027s words, we can come\r\nto some agreement regarding their import. Nothing\r\ncan be built without building-stones, mortar, scaffolding,\r\nand a builder\u0027s skill. Yet assuredly the wish is\r\nwell founded, that will show to posterity the complete\r\nstructure in its finished form, bereft of unsightly scaffolding.\r\nIt is the pure logical and æsthetic sense of the\r\nmathematician that speaks out of Kirchhoff\u0027s words.\r\nModern expositions of physics aspire after his ideal;\r\nthat, too, is intelligible. But it would be a poor didactic\r\nshift, for one whose business it was to train\r\narchitects, to say: \"Here is a splendid edifice; if thou\r\nwouldst really build, go thou and do likewise\".\u003c/p\u003e\r\n\r\n\u003cp\u003eThe barriers between the special sciences, which\r\nmake division of work and concentration possible, but\r\nwhich appear to us after all as cold and conventional\r\nrestrictions, will gradually disappear. Bridge upon\r\nbridge is thrown over the gaps. Contents and methods,\r\neven of the remotest branches, are compared.\r\nWhen the Congress of Natural Scientists shall meet a\r\nhundred years hence, we may expect that they will\r\nrepresent a unity in a higher sense than is possible to-day,\r\nnot in sentiment and aim alone, but in method\r\nalso. In the meantime, this great change will be\r\nhelped by our keeping constantly before our minds the\r\nfact of the intrinsic relationship of all research, which\r\nKirchhoff characterised with such classical simplicity.\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"THE_PART_PLAYED_BY_ACCIDENT_IN\" id=\"THE_PART_PLAYED_BY_ACCIDENT_IN\"\u003eTHE PART PLAYED BY ACCIDENT IN\r\nINVENTION AND DISCOVERY.\u003c/a\u003e\u003ca name=\"FNanchor_81_81\" id=\"FNanchor_81_81\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_81_81\" class=\"fnanchor\"\u003e[81]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eIt is characteristic of the naïve and sanguine\r\nbeginnings of thought in youthful men and\r\nnations, that all problems are held to be soluble and\r\nfundamentally intelligible on the first appearance of\r\nsuccess. The sage of Miletus, on seeing plants take\r\ntheir rise from moisture, believed he had comprehended\r\nthe whole of nature, and he of Samos, on discovering\r\nthat definite numbers corresponded to the\r\nlengths of harmonic strings, imagined he could exhaust\r\nthe nature of the world by means of numbers.\r\nPhilosophy and science in such periods are blended.\r\nWider experience, however, speedily discloses the\r\nerror of such a course, gives rise to criticism, and\r\nleads to the division and ramification of the sciences.\u003c/p\u003e\r\n\r\n\u003cp\u003eAt the same time, the necessity of a broad and\r\ngeneral view of the world remains; and to meet this\r\nneed philosophy parts company with special inquiry.\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_260\" id=\"Page_260\"\u003e[Pg 260]\u003c/a\u003e\u003c/span\u003e\r\nIt is true, the two are often found united in gigantic\r\npersonalities. But as a rule their ways diverge more\r\nand more widely from each other. And if the estrangement\r\nof philosophy from science can reach a point\r\nwhere data unworthy of the nursery are not deemed too\r\nscanty as foundations of the world, on the other hand\r\nthe thorough-paced specialist may go to the extreme\r\nof rejecting point-blank the possibility of a broader\r\nview, or at least of deeming it superfluous, forgetful\r\nof Voltaire\u0027s apophthegm, nowhere more applicable\r\nthan here, \u003ci\u003eLe superflu\u0026mdash;chose très nécessaire\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is true, the history of philosophy, owing to the\r\ninsufficiency of its constructive data, is and must be\r\nlargely a history of error. But it would be the height\r\nof ingratitude on our part to forget that the seeds of\r\nthoughts which still fructify the soil of special research,\r\nsuch as the theory of irrationals, the conceptions\r\nof conservation, the doctrine of evolution, the\r\nidea of specific energies, and so forth, may be traced\r\nback in distant ages to philosophical sources. Furthermore,\r\nto have deferred or abandoned the attempt\r\nat a broad philosophical view of the world from a full\r\nknowledge of the insufficiency of our materials, is\r\nquite a different thing from never having undertaken\r\nit at all. The revenge of its neglect, moreover, is\r\nconstantly visited upon the specialist by his committal\r\nof the very errors which philosophy long ago exposed.\r\nAs a fact, in physics and physiology, particularly\r\nduring the first half of this century, are to be\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_261\" id=\"Page_261\"\u003e[Pg 261]\u003c/a\u003e\u003c/span\u003e\r\nmet intellectual productions which for naïve simplicity\r\nare not a jot inferior to those of the Ionian school, or\r\nto the Platonic ideas, or to that much reviled ontological\r\nproof.\u003c/p\u003e\r\n\r\n\u003cp\u003eLatterly, there has been evidence of a gradual\r\nchange in the situation. Recent philosophy has set\r\nitself more modest and more attainable ends; it is\r\nno longer inimical to special inquiry; in fact, it is\r\nzealously taking part in that inquiry. On the other\r\nhand, the special sciences, mathematics and physics,\r\nno less than philology, have become eminently philosophical.\r\nThe material presented is no longer accepted\r\nuncritically. The glance of the inquirer is\r\nbent upon neighboring fields, whence that material\r\nhas been derived. The different special departments\r\nare striving for closer union, and gradually the conviction\r\nis gaining ground that philosophy can consist\r\nonly of mutual, complemental criticism, interpenetration,\r\nand union of the special sciences into a consolidated\r\nwhole. As the blood in nourishing the body\r\nseparates into countless capillaries, only to be collected\r\nagain and to meet in the heart, so in the science\r\nof the future all the rills of knowledge will gather\r\nmore and more into a common and undivided stream.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is this view\u0026mdash;not an unfamiliar one to the present\r\ngeneration\u0026mdash;that I purpose to advocate. Entertain\r\nno hope, or rather fear, that I shall construct\r\nsystems for you. I shall remain a natural inquirer.\r\nNor expect that it is my intention to skirt all the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_262\" id=\"Page_262\"\u003e[Pg 262]\u003c/a\u003e\u003c/span\u003e\r\nfields of natural inquiry. I can attempt to be your\r\nguide only in that branch which is familiar to me, and\r\neven there I can assist in the furtherment of only a\r\nsmall portion of the allotted task. If I shall succeed\r\nin rendering plain to you the relations of physics,\r\npsychology, and the theory of knowledge, so that you\r\nmay draw from each profit and light, redounding to\r\nthe advantage of each, I shall regard my work as not\r\nhaving been in vain. Therefore, to illustrate by an\r\nexample how, consonantly with my powers and views,\r\nI conceive such inquiries should be conducted, I shall\r\ntreat to-day, in the form of a brief sketch, of the following\r\nspecial and limited subject\u0026mdash;of \u003ci\u003ethe part which\r\naccidental circumstances play in the development of inventions\r\nand discoveries\u003c/i\u003e.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_263\" id=\"Page_263\"\u003e[Pg 263]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_264\" id=\"Page_264\"\u003e[Pg 264]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_265\" id=\"Page_265\"\u003e[Pg 265]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_266\" id=\"Page_266\"\u003e[Pg 266]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_267\" id=\"Page_267\"\u003e[Pg 267]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_268\" id=\"Page_268\"\u003e[Pg 268]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_269\" id=\"Page_269\"\u003e[Pg 269]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_270\" id=\"Page_270\"\u003e[Pg 270]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_271\" id=\"Page_271\"\u003e[Pg 271]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_272\" id=\"Page_272\"\u003e[Pg 272]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_273\" id=\"Page_273\"\u003e[Pg 273]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_274\" id=\"Page_274\"\u003e[Pg 274]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_275\" id=\"Page_275\"\u003e[Pg 275]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_276\" id=\"Page_276\"\u003e[Pg 276]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_277\" id=\"Page_277\"\u003e[Pg 277]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_278\" id=\"Page_278\"\u003e[Pg 278]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_279\" id=\"Page_279\"\u003e[Pg 279]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_280\" id=\"Page_280\"\u003e[Pg 280]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_281\" id=\"Page_281\"\u003e[Pg 281]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_282\" id=\"Page_282\"\u003e[Pg 282]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eWhen we Germans say of a man that he was not\r\nthe inventor of gunpowder,\u003ca name=\"FNanchor_82_82\" id=\"FNanchor_82_82\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_82_82\" class=\"fnanchor\"\u003e[82]\u003c/a\u003e we impliedly cast a grave\r\nsuspicion on his abilities. But the expression is not\r\na felicitous one, as there is probably no invention in\r\nwhich deliberate thought had a smaller, and pure luck\r\na larger, share than in this. It is well to ask, Are we\r\njustified in placing a low estimate on the achievement\r\nof an inventor because accident has assisted him in\r\nhis work? Huygens, whose discoveries and inventions\r\nare justly sufficient to entitle him to an opinion\r\nin such matters, lays great emphasis on this factor.\r\nHe asserts that a man capable of inventing the telescope\r\nwithout the concurrence of accident must have\r\nbeen gifted with superhuman genius.\u003ca name=\"FNanchor_83_83\" id=\"FNanchor_83_83\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_83_83\" class=\"fnanchor\"\u003e[83]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eA man living in the midst of civilisation finds himself\r\nsurrounded by a host of marvellous inventions,\r\nconsidering none other than the means of satisfying\r\nthe needs of daily life. Picture such a man transported\r\nto the epoch preceding the invention of these\r\ningenious appliances, and imagine him undertaking\r\nin a serious manner to comprehend their origin. At\r\nfirst the intellectual power of the men capable of producing\r\nsuch marvels will strike him as incredible, or,\r\nif we adopt the ancient view, as divine. But his astonishment\r\nis considerably allayed by the disenchanting\r\nyet elucidative revelations of the history of primitive\r\nculture, which to a large extent prove that these\r\ninventions took their rise very slowly and by imperceptible\r\ndegrees.\u003c/p\u003e\r\n\r\n\u003cp\u003eA small hole in the ground with fire kindled in it\r\nconstituted the primitive stove. The flesh of the\r\nquarry, wrapped with water in its skin, was boiled by\r\ncontact with heated stones. Cooking by stones was\r\nalso done in wooden vessels. Hollow gourds were\r\nprotected from the fire by coats of clay. Thus, from\r\nthe burned clay accidentally originated the enveloping\r\npot, which rendered the gourd superfluous, although\r\nfor a long time thereafter the clay was still spread\r\nover the gourd, or pressed into woven wicker-work\r\nbefore the potter\u0027s art assumed its final independence.\r\nEven then the wicker-work ornament was retained, as\r\na sort of attest of its origin.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe see, thus, it is by accidental circumstances, or\r\nby such as lie without our purpose, foresight, and\r\npower, that man is gradually led to the acquaintance\r\nof improved means of satisfying his wants. Let the\r\nreader picture to himself the genius of a man who\r\ncould have foreseen without the help of accident that\r\nclay handled in the ordinary manner would produce a\r\nuseful cooking utensil! The majority of the inventions\r\nmade in the early stages of civilisation, including\r\nlanguage, writing, money, and the rest, could not\r\nhave been the product of deliberate methodical reflexion\r\nfor the simple reason that no idea of their\r\nvalue and significance could have been had except\r\nfrom practical use. The invention of the bridge may\r\nhave been suggested by the trunk of a tree which had\r\nfallen athwart a mountain-torrent; that of the tool by\r\nthe use of a stone accidentally taken into the hand to\r\ncrack nuts. The use of fire probably started in and\r\nwas disseminated from regions where volcanic eruptions,\r\nhot springs, and burning jets of natural gas\r\nafforded opportunity for quietly observing and turning\r\nto practical account the properties of fire. Only\r\nafter that had been done could the significance of the\r\nfire-drill be appreciated, an instrument which was\r\nprobably discovered from boring a hole through a\r\npiece of wood. The suggestion of a distinguished inquirer\r\nthat the invention of the fire-drill originated on\r\nthe occasion of a religious ceremony is both fantastic\r\nand incredible. And as to the use of fire, we should\r\nno more attempt to derive that from the invention of\r\nthe fire-drill than we should from the invention of sulphur\r\nmatches. Unquestionably the opposite course\r\nwas the real one.\u003ca name=\"FNanchor_84_84\" id=\"FNanchor_84_84\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_84_84\" class=\"fnanchor\"\u003e[84]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eSimilar phenomena, though still largely veiled in\r\nobscurity, mark the initial transition of nations from\r\na hunting to a nomadic life and to agriculture.\u003ca name=\"FNanchor_85_85\" id=\"FNanchor_85_85\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_85_85\" class=\"fnanchor\"\u003e[85]\u003c/a\u003e We\r\nshall not multiply examples, but content ourselves\r\nwith the remark that the same phenomena recur in\r\nhistorical times, in the ages of great technical inventions,\r\nand, further, that regarding them the most\r\nwhimsical notions have been circulated\u0026mdash;notions which\r\nascribe to accident an unduly exaggerated part, and\r\none which in a psychological respect is absolutely impossible.\r\nThe observation of steam escaping from a\r\ntea-kettle and of the clattering of the lid is supposed\r\nto have led to the invention of the steam-engine. Just\r\nthink of the gap between this spectacle and the conception\r\nof the performance of great mechanical work\r\nby steam, for a man totally ignorant of the steam-engine!\r\nLet us suppose, however, that an engineer,\r\nversed in the practical construction of pumps, should\r\naccidentally dip into water an inverted bottle that had\r\nbeen filled with steam for drying and still retained its\r\nsteam. He would see the water rush violently into\r\nthe bottle, and the idea would very naturally suggest\r\nitself of founding on this experience a convenient and\r\nuseful atmospheric steam-pump, which by imperceptible\r\ndegrees, both psychologically possible and immediate,\r\nwould then undergo a natural and gradual transformation\r\ninto Watt\u0027s steam-engine.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut granting that the most important inventions\r\nare brought to man\u0027s notice accidentally and in ways\r\nthat are beyond his foresight, yet it does not follow\r\nthat accident alone is sufficient to produce an invention.\r\nThe part which man plays is by no means a\r\npassive one. Even the first potter in the primeval\r\nforest must have felt some stirrings of genius within\r\nhim. In all such cases, the inventor is obliged \u003ci\u003eto take\r\nnote\u003c/i\u003e of the new fact, he must discover and grasp its\r\nadvantageous feature, and must have the power to\r\nturn that feature to account in the realisation of his\r\npurpose. He must \u003ci\u003eisolate\u003c/i\u003e the new feature, impress it\r\nupon his memory, unite and interweave it with the\r\nrest of his thought; in short, he must possess the capacity\r\n\u003ci\u003eto profit by experience\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe capacity to profit by experience might well be\r\nset up as a test of intelligence. This power varies\r\nconsiderably in men of the same race, and increases\r\nenormously as we advance from the lower animals to\r\nman. The former are limited in this regard almost\r\nentirely to the reflex actions which they have inherited\r\nwith their organism, they are almost totally incapable\r\nof individual experience, and considering their simple\r\nwants are scarcely in need of it. The ivory-snail\r\n(\u003ci\u003eEburna spirata\u003c/i\u003e) never learns to avoid the carnivorous\r\nActinia, no matter how often it may wince under the\r\nlatter\u0027s shower of needles, apparently having no memory\r\nfor pain whatever.\u003ca name=\"FNanchor_86_86\" id=\"FNanchor_86_86\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_86_86\" class=\"fnanchor\"\u003e[86]\u003c/a\u003e A spider can be lured forth\r\nrepeatedly from its hole by touching its web with a\r\ntuning-fork. The moth plunges again and again into\r\nthe flame which has burnt it. The humming-bird\r\nhawk-moth\u003ca name=\"FNanchor_87_87\" id=\"FNanchor_87_87\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_87_87\" class=\"fnanchor\"\u003e[87]\u003c/a\u003e dashes repeatedly against the painted\r\nroses of the wall-paper, like the unhappy and desperate\r\nthinker who never wearies of attacking the same\r\ninsoluble chimerical problem. As aimlessly almost as\r\nMaxwell\u0027s gaseous molecules and in the same unreasoning\r\nmanner common flies in their search for light\r\nand air stream against the glass pane of a half-opened\r\nwindow and remain there from sheer inability to find\r\ntheir way around the narrow frame. But a pike separated\r\nfrom the minnows of his aquarium by a glass\r\npartition, learns after the lapse of a few months,\r\nthough only after having butted himself half to death,\r\nthat he cannot attack these fishes with impunity.\r\nWhat is more, he leaves them in peace even after the\r\nremoval of the partition, though he will bolt a strange\r\nfish at once. Considerable memory must be attributed\r\nto birds of passage, a memory which, probably\r\nowing to the absence of disturbing thoughts, acts with\r\nthe precision of that of some idiots. Finally, the\r\nsusceptibility to training evinced by the higher vertebrates\r\nis indisputable proof of the ability of these animals\r\nto profit by experience.\u003c/p\u003e\r\n\r\n\u003cp\u003eA powerfully developed \u003ci\u003emechanical\u003c/i\u003e memory, which\r\nrecalls vividly and faithfully old situations, is sufficient\r\nfor avoiding definite particular dangers, or for taking\r\nadvantage of definite particular opportunities. But\r\nmore is required for the development of \u003ci\u003einventions\u003c/i\u003e.\r\nMore extensive chains of images are necessary here,\r\nthe excitation by mutual contact of widely different\r\ntrains of ideas, a more powerful, more manifold, and\r\nricher connexion of the contents of memory, a more\r\npowerful and impressionable psychical life, heightened\r\nby use. A man stands on the bank of a mountain-torrent,\r\nwhich is a serious obstacle to him. He remembers\r\nthat he has crossed just such a torrent before\r\non the trunk of a fallen tree. Hard by trees are\r\ngrowing. He has often moved the trunks of fallen\r\ntrees. He has also felled trees before, and then moved\r\nthem. To fell trees he has used sharp stones. He\r\ngoes in search of such a stone, and as the old situations\r\nthat crowd into his memory and are held there in living\r\nreality by the definite powerful interest which he\r\nhas in crossing just this torrent,\u0026mdash;as these impressions\r\nare made to pass before his mind in the \u003ci\u003einverse order\u003c/i\u003e in\r\nwhich they were here evoked, he invents the bridge.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere can be no doubt but the higher vertebrates\r\nadapt their actions in some moderate degree to circumstances.\r\nThe fact that they give no appreciable\r\nevidence of advance by the accumulation of inventions,\r\nis satisfactorily explained by a difference of degree\r\nor intensity of intelligence as compared with\r\nman; the assumption of a difference of kind is not\r\nnecessary. A person who saves a little every day, be\r\nit ever so little, has an incalculable advantage over\r\nhim who daily squanders that amount, or is unable to\r\nkeep what he has accumulated. A slight quantitative\r\ndifference in such things explains enormous differences\r\nof advancement.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe rules which hold good in prehistoric times\r\nalso hold good in historical times, and the remarks\r\nmade on invention may be applied almost without\r\nmodification to discovery; for the two are distinguished\r\nsolely by the use to which the new knowledge\r\nis put. In both cases the investigator is concerned\r\nwith some \u003ci\u003enewly observed\u003c/i\u003e relation of new or old properties,\r\nabstract or concrete. It is observed, for example,\r\nthat a substance which gives a chemical reaction\r\n\u003ci\u003eA\u003c/i\u003e is also the cause of a chemical reaction \u003ci\u003eB\u003c/i\u003e. If this\r\nobservation fulfils no purpose but that of furthering\r\nthe scientist\u0027s insight, or of removing a source of intellectual\r\ndiscomfort, we have a discovery; but an invention,\r\nif in using the substance giving the reaction\r\n\u003ci\u003eA\u003c/i\u003e to produce the desired reaction \u003ci\u003eB\u003c/i\u003e, we have a practical\r\nend in view, and seek to remove a source of material\r\ndiscomfort. The phrase, \u003ci\u003edisclosure of the connexion\r\nof reactions\u003c/i\u003e, is broad enough to cover discoveries\r\nand inventions in all departments. It embraces the\r\nPythagorean proposition, which is a combination of a\r\ngeometrical and an arithmetical reaction, Newton\u0027s\r\ndiscovery of the connexion of Kepler\u0027s motions with\r\nthe law of the inverse squares, as perfectly as it does\r\nthe detection of some minute but appropriate alteration\r\nin the construction of a tool, or of some appropriate\r\nchange in the methods of a dyeing establishment.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe disclosure of new provinces of facts before\r\nunknown can only be brought about by accidental circumstances,\r\nunder which are \u003ci\u003eremarked\u003c/i\u003e facts that commonly\r\ngo unnoticed. The achievement of the discoverer\r\nhere consists in his \u003ci\u003esharpened attention\u003c/i\u003e, which\r\ndetects the uncommon features of an occurrence and\r\ntheir determining conditions from their most evanescent\r\nmarks,\u003ca name=\"FNanchor_88_88\" id=\"FNanchor_88_88\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_88_88\" class=\"fnanchor\"\u003e[88]\u003c/a\u003e and discovers means of submitting them\r\nto exact and full observation. Under this head belong\r\nthe first disclosures of electrical and magnetic\r\nphenomena, Grimaldi\u0027s observation of interference,\r\nArago\u0027s discovery of the increased check suffered by a\r\nmagnetic needle vibrating in a copper envelope as\r\ncompared with that observed in a bandbox, Foucault\u0027s\r\nobservation of the stability of the plane of vibration\r\nof a rod accidentally struck while rotating in a turning-lathe,\r\nMayer\u0027s observation of the increased redness\r\nof venous blood in the tropics, Kirchhoff\u0027s observation\r\nof the augmentation of the \u003ci\u003eD\u003c/i\u003e-line in the solar\r\nspectrum by the interposition of a sodium lamp,\r\nSchönbein\u0027s discovery of ozone from the phosphoric\r\nsmell emitted on the disruption of air by electric\r\nsparks, and a host of others. All these facts, of which\r\nunquestionably many were \u003ci\u003eseen\u003c/i\u003e numbers of times before\r\nthey were \u003ci\u003enoticed\u003c/i\u003e, are examples of the inauguration\r\nof momentous discoveries by accidental circumstances,\r\nand place the importance of strained attention\r\nin a brilliant light.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut not only is a significant part played in the beginning\r\nof an inquiry by co-operative circumstances\r\nbeyond the foresight of the investigator; their influence\r\nis also active in its prosecution. Dufay, thus, whilst\r\nfollowing up the behavior of \u003ci\u003eone\u003c/i\u003e electrical state which\r\nhe had assumed, discovers the existence of \u003ci\u003etwo\u003c/i\u003e. Fresnel\r\nlearns by accident that the interference-bands received\r\non ground glass are seen to better advantage\r\nin the open air. The diffraction-phenomenon of two\r\nslits proved to be considerably different from what\r\nFraunhofer had anticipated, and in following up this\r\ncircumstance he was led to the important discovery of\r\ngrating-spectra. Faraday\u0027s induction-phenomenon departed\r\nwidely from the initial conception which occasioned\r\nhis experiments, and it is precisely this deviation\r\nthat constitutes his real discovery.\u003c/p\u003e\r\n\r\n\u003cp\u003eEvery man has pondered on some subject. Every\r\none of us can multiply the examples cited, by less illustrious\r\nones from his own experience. I shall cite\r\nbut one. On rounding a railway curve once, I accidentally\r\nremarked a striking apparent inclination of\r\nthe houses and trees. I inferred that the direction of\r\nthe total resultant \u003ci\u003ephysical\u003c/i\u003e acceleration of the body\r\nreacts \u003ci\u003ephysiologically\u003c/i\u003e as the vertical. Afterwards, in\r\nattempting to inquire more carefully into this phenomenon,\r\nand this only, in a large whirling machine,\r\nthe collateral phenomena conducted me to the sensation\r\nof angular acceleration, vertigo, Flouren\u0027s experiments\r\non the section of the semi-circular canals\r\netc., from which gradually resulted views relating to\r\nsensations of direction which are also held by Breuer\r\nand Brown, which were at first contested on all hands,\r\nbut are now regarded on many sides as correct, and\r\nwhich have been recently enriched by the interesting\r\ninquiries of Breuer concerning the \u003ci\u003emacula acustica\u003c/i\u003e, and\r\nKreidel\u0027s experiments with magnetically orientable\r\ncrustacea.\u003ca name=\"FNanchor_89_89\" id=\"FNanchor_89_89\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_89_89\" class=\"fnanchor\"\u003e[89]\u003c/a\u003e Not disregard of accident but a direct and\r\npurposeful employment of it advances research.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe more powerful the psychical connexion of the\r\nmemory pictures is,\u0026mdash;and it varies with the individual\r\nand the mood,\u0026mdash;the more apt is the same accidental\r\nobservation to be productive of results. Galileo knows\r\nthat the air has weight; he also knows of the \"resistance\r\nto a vacuum,\" expressed both in weight and\r\nin the height of a column of water. But the two ideas\r\ndwelt asunder in his mind. It remained for Torricelli\r\nto vary the specific gravity of the liquid measuring the\r\npressure, and not till then was the air included in the\r\nlist of pressure-exerting fluids. The reversal of the\r\nlines of the spectrum was seen repeatedly before\r\nKirchhoff, and had been mechanically explained. But\r\nit was left for his penetrating vision to discern the\r\nevidence of the connexion of this phenomenon with\r\nquestions of heat, and to him alone through persistent\r\nlabor was revealed the sweeping significance of the\r\nfact for the mobile equilibrium of heat. Supposing,\r\nthen, that such a rich organic connexion of the elements\r\nof memory exists, and is the prime distinguishing\r\nmark of the inquirer, next in importance certainly\r\nis that \u003ci\u003eintense interest\u003c/i\u003e in a definite object, in a definite\r\nidea, which fashions advantageous combinations of\r\nthought from elements before disconnected, and obtrudes\r\nthat idea into every observation made, and into\r\nevery thought formed, making it enter into relationship\r\nwith all things. Thus Bradley, deeply engrossed\r\nwith the subject of aberration, is led to its solution\r\nby an exceedingly unobtrusive experience in crossing\r\nthe Thames. It is permissible, therefore, to ask\r\nwhether accident leads the discoverer, or the discoverer\r\naccident, to a successful outcome in scientific\r\nquests.\u003c/p\u003e\r\n\r\n\u003cp\u003eNo man should dream of solving a great problem\r\nunless he is so thoroughly saturated with his subject\r\nthat everything else sinks into comparative insignificance.\r\nDuring a hurried meeting with Mayer in Heidelberg\r\nonce, Jolly remarked, with a rather dubious\r\nimplication, that if Mayer\u0027s theory were correct water\r\ncould be warmed by shaking. Mayer went away without\r\na word of reply. Several weeks later, and now\r\nunrecognised by Jolly, he rushed into the latter\u0027s presence\r\nexclaiming: \"Es ischt aso!\" (It is so, it is\r\nso!) It was only after considerable explanation that\r\nJolly found out what Mayer wanted to say. The incident\r\nneeds no comment.\u003ca name=\"FNanchor_90_90\" id=\"FNanchor_90_90\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_90_90\" class=\"fnanchor\"\u003e[90]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eA person deadened to sensory impressions and\r\ngiven up solely to the pursuit of his own thoughts,\r\nmay also light on an idea that will divert his mental\r\nactivity into totally new channels. In such cases it is\r\na psychical accident, an intellectual experience, as\r\ndistinguished from a physical accident, to which the\r\nperson owes his discovery\u0026mdash;a discovery which is here\r\nmade \"deductively\" by means of mental copies of the\r\nworld, instead of experimentally. \u003ci\u003ePurely\u003c/i\u003e experimental\r\ninquiry, moreover, does not exist, for, as Gauss says,\r\nvirtually we always experiment with our thoughts.\r\nAnd it is precisely that constant, corrective interchange\r\nor intimate union of experiment and deduction,\r\nas it was cultivated by Galileo in his \u003ci\u003eDialogues\u003c/i\u003e\r\nand by Newton in his \u003ci\u003eOptics\u003c/i\u003e, that is the foundation of\r\nthe benign fruitfulness of modern scientific inquiry as\r\ncontrasted with that of antiquity, where observation\r\nand reflexion ofttimes pursued their respective courses\r\nlike two strangers.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe have to wait for the appearance of a favorable\r\nphysical accident. The movement of our thoughts\r\nobeys the law of association. In the case of meagre\r\nexperience the result of this law is simply the mechanical\r\nreproduction of definite sensory experiences. On\r\nthe other hand, if the psychical life is subjected to the\r\nincessant influences of a powerful and rich experience,\r\nthen every representative element in the mind is connected\r\nwith so many others that the actual and natural\r\ncourse of the thoughts is easily influenced and determined\r\nby insignificant circumstances, which accidentally\r\nare decisive. Hereupon, the process termed imagination\r\nproduces its protean and infinitely diversified\r\nforms. Now what can we do to guide this process,\r\nseeing that the combinatory law of the images is without\r\nour reach? Rather let us ask, what influence can\r\na powerful and constantly recurring idea exert on the\r\nmovement of our thoughts? According to what has\r\npreceded, the answer is involved in the question itself.\r\nThe \u003ci\u003eidea\u003c/i\u003e dominates the thought of the inquirer, not\r\nthe latter the former.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us see, now, if we can acquire a profounder\r\ninsight into the process of discovery. The condition\r\nof the discoverer is, as James has aptly remarked, not\r\nunlike the situation of a person who is trying to remember\r\nsomething that he has forgotten. Both are\r\nsensible of a gap, and have only a remote presentiment\r\nof what is missing. Suppose I meet in a company\r\na well-known and affable gentleman whose name\r\nI have forgotten, and who to my horror asks to be introduced\r\nto some one. I set to work according to\r\nLichtenberg\u0027s rule, and run down the alphabet in\r\nsearch of the initial letter of his name. A vague sympathy\r\nholds me at the letter \u003ci\u003eG\u003c/i\u003e. Tentatively I add the\r\nsecond letter and am arrested at \u003ci\u003ee\u003c/i\u003e, and long before I\r\nhave tried the third letter \u003ci\u003er\u003c/i\u003e, the name \"Gerson\" sounds\r\nsonorously upon my ear, and my anguish is gone.\r\nWhile taking a walk I meet a gentleman from whom\r\nI receive a communication. On returning home, and\r\nin attending to weightier affairs, the matter slips my\r\nmind. Moodily, but in vain, I ransack my memory.\r\nFinally I observe that I am going over my walk again\r\nin thought. On the street corner in question the self-same\r\ngentleman stands before me and repeats his\r\ncommunication. In this process are successively recalled\r\nto consciousness all the percepts which were\r\nconnected with the percept that was lost, and with\r\nthem, finally, that, too, is brought to light. In the\r\nfirst case\u0026mdash;where the experience had already been\r\nmade and is permanently impressed on our thought\u0026mdash;a\r\n\u003ci\u003esystematic\u003c/i\u003e procedure is both possible and easy, for\r\nwe know that a name must be composed of a limited\r\nnumber of sounds. But at the same time it should be\r\nobserved that the labor involved in such a combinatorial\r\ntask would be enormous if the name were long\r\nand the responsiveness of the mind weaker.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is often said, and not wholly without justification,\r\nthat the scientist has solved a \u003ci\u003eriddle\u003c/i\u003e. Every problem\r\nin geometry may be clothed in the garb of a \u003ci\u003eriddle\u003c/i\u003e.\r\nThus: \"What thing is that \u003ci\u003eM\u003c/i\u003e which has the properties\r\n\u003ci\u003eA\u003c/i\u003e, \u003ci\u003eB\u003c/i\u003e, \u003ci\u003eC\u003c/i\u003e?\" \"What circle is that which touches\r\nthe straight lines \u003ci\u003eA\u003c/i\u003e, \u003ci\u003eB\u003c/i\u003e, but touches \u003ci\u003eB\u003c/i\u003e in the point \u003ci\u003eC\u003c/i\u003e?\"\r\nThe first two conditions marshal before the imagination\r\nthe group of circles whose centres lie in the line\r\nof symmetry of \u003ci\u003eA\u003c/i\u003e, \u003ci\u003eB\u003c/i\u003e. The third condition reminds\r\nus of all the circles having centres in the straight line\r\nthat stands at right angles to \u003ci\u003eB\u003c/i\u003e in \u003ci\u003eC\u003c/i\u003e. The \u003ci\u003ecommon\u003c/i\u003e\r\nterm, or common terms, of the two groups of images\r\nsolves the riddle\u0026mdash;satisfies the problem. Puzzles dealing\r\nwith things or words induce similar processes, but\r\nthe memory in such cases is exerted in many directions\r\nand more varied and less clearly ordered provinces\r\nof ideas are surveyed. The difference between\r\nthe situation of a geometer who has a construction to\r\nmake, and that of an engineer, or a scientist, confronted\r\nwith a problem, is simply this, that the first\r\nmoves in a field with which he is thoroughly acquainted,\r\nwhereas the two latter are obliged to familiarise\r\nthemselves with this field subsequently, and in\r\na measure far transcending what is commonly required.\r\nIn this process the mechanical engineer has\r\nat least always a definite goal before him and definite\r\nmeans to accomplish his aim, whilst in the case of the\r\nscientist that aim is in many instances presented only\r\nin vague and general outlines. Often the very formulation\r\nof the riddle devolves on him. Frequently it\r\nis not until the aim has been reached that the broader\r\noutlook requisite for systematic procedure is obtained.\r\nBy far the larger portion of his success, therefore, is\r\ncontingent on luck and instinct. It is immaterial, so\r\nfar as its character is concerned, whether the process\r\nin question is brought rapidly to a conclusion in the\r\nbrain of one man, or whether it is spun out for centuries\r\nin the minds of a long succession of thinkers.\r\nThe same relation that a word solving a riddle bears\r\nto that riddle is borne by the modern conception of\r\nlight to the facts discovered by Grimaldi, Römer,\r\nHuygens, Newton, Young, Malus, and Fresnel, and\r\nonly by the help of this slowly developed conception\r\nis our mental vision enabled to embrace the broad\r\ndomain of facts in question.\u003c/p\u003e\r\n\r\n\u003cp\u003eA welcome complement to the discoveries which\r\nthe history of civilisation and comparative psychology\r\nhave furnished, is to be found in the confessions of\r\ngreat scientists and artists. Scientists \u003ci\u003eand\u003c/i\u003e artists, we\r\nmight say, for Liebig boldly declared there was no\r\nessential difference between the two. Are we to regard\r\nLeonardo da Vinci as a scientist or as an artist?\r\nIf the artist builds up his work from a few motives,\r\nthe scientist discovers the motives which permeate\r\nreality. If scientists like Lagrange or Fourier are in\r\na certain measure artists in the presentation of their\r\nresults, on the other hand, artists like Shakespeare or\r\nRuysdael are scientists in the insight which must\r\nhave preceded their creations.\u003c/p\u003e\r\n\r\n\u003cp\u003eNewton, when questioned about his methods of\r\nwork, could give no other answer but that he was\r\nwont to ponder again and again on a subject; and\r\nsimilar utterances are accredited to D\u0027Alembert and\r\nHelmholtz. Scientists and artists both recommend\r\npersistent labor. After the repeated survey of a field\r\nhas afforded opportunity for the interposition of advantageous\r\naccidents, has rendered all the traits that\r\nsuit with the mood or the dominant thought more\r\nvivid, and has gradually relegated to the background\r\nall things that are inappropriate, making their future\r\nappearance impossible; then from the teeming, swelling\r\nhost of fancies which a free and high-flown imagination\r\ncalls forth, suddenly that particular form\r\narises to the light which harmonises perfectly with\r\nthe ruling idea, mood, or design. Then it is that that\r\nwhich has resulted slowly as the result of a gradual\r\nselection, appears as if it were the outcome of a deliberate\r\nact of creation. Thus are to be explained the\r\nstatements of Newton, Mozart, Richard Wagner, and\r\nothers, when they say that thoughts, melodies, and\r\nharmonies had poured in upon them, and that they\r\nhad simply retained the right ones. Undoubtedly,\r\nthe man of genius, too, consciously or instinctively,\r\npursues systematic methods wherever it is possible;\r\nbut in his delicate presentiment he will omit many a\r\ntask or abandon it after a hasty trial on which a less\r\nendowed man would squander his energies in vain.\r\nThus, the genius accomplishes\u003ca name=\"FNanchor_91_91\" id=\"FNanchor_91_91\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_91_91\" class=\"fnanchor\"\u003e[91]\u003c/a\u003e in a brief space of\r\ntime undertakings for which the life of an ordinary\r\nman would far from suffice. We shall hardly go astray\r\nif we regard genius as only a slight deviation from\r\nthe average mental endowment\u0026mdash;as possessing simply\r\na greater sensitiveness of cerebral reaction and a\r\ngreater swiftness of reaction. The men who, obeying\r\ntheir inner impulses, make sacrifices for an idea instead\r\nof advancing their material welfare, may appear\r\nto the full-blooded Philistine as fools; yet we shall\r\nscarcely adopt Lombroso\u0027s view, that genius is to be\r\nregarded as a disease, although it is unfortunately\r\ntrue that the sensitive brains and fragile constitutions\r\nsuccumb most readily to sickness.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe remark of C. G. J. Jacobi that mathematics\r\nis slow of growth and only reaches the truth by long\r\nand devious paths, that the way to its discovery must\r\nbe prepared for long beforehand, and that then the\r\ntruth will make its long-deferred appearance as if impelled\r\nby some divine necessity\u003ca name=\"FNanchor_92_92\" id=\"FNanchor_92_92\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_92_92\" class=\"fnanchor\"\u003e[92]\u003c/a\u003e\u0026mdash;all this holds true\r\nof every science. We are astounded often to note\r\nthat it required the combined labors of many eminent\r\nthinkers for a full century to reach a truth which it\r\ntakes us only a few hours to master and which once\r\nacquired seems extremely easy to reach under the\r\nright sort of circumstances. To our humiliation we\r\nlearn that even the greatest men are born more for\r\nlife than for science. The extent to which even they\r\nare indebted to accident\u0026mdash;to that singular conflux of\r\nthe physical and the psychical life in which the continuous\r\nbut yet imperfect and never-ending adaptation\r\nof the latter to the former finds its distinct expression\u0026mdash;that\r\nhas been the subject of our remarks to-day.\r\nJacobi\u0027s poetical thought of a divine necessity acting\r\nin science will lose none of its loftiness for us if we\r\ndiscover in this necessity the same power that destroys\r\nthe unfit and fosters the fit. For loftier, nobler,\r\nand more romantic than poetry is the truth and the\r\nreality.\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_SENSATIONS_OF_ORIENTATION93\" id=\"ON_SENSATIONS_OF_ORIENTATION93\"\u003eON SENSATIONS OF ORIENTATION.\u003c/a\u003e\u003ca name=\"FNanchor_93_93\" id=\"FNanchor_93_93\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_93_93\" class=\"fnanchor\"\u003e[93]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eThrough the co-operation of a succession of inquirers,\r\namong whom are particularly to be mentioned\r\nGoltz of Strassburg and Breuer of Vienna,\r\nconsiderable advances have been made during the\r\nlast twenty-five years in our knowledge of the means\r\nby which we ascertain our position in space and the\r\ndirection of our motion, or orient ourselves, as the\r\nphrase goes. I presume that you are already acquainted\r\nwith the physiological part of the processes\r\nwith which our sensations of movement, or, more generally\r\nspeaking, our sensations of orientation, are connected.\r\nHere I shall consider more particularly the\r\nphysical side of the matter. In fact, I was originally\r\nled to the consideration of these questions by the\r\nobservation of extremely simple and perfectly well-known\r\nphysical facts, before I had any great acquaintance\r\nwith physiology and while pursuing unbiasedly\r\nmy natural thoughts; and I am of the conviction that\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_283\" id=\"Page_283\"\u003e[Pg 283]\u003c/a\u003e\u003c/span\u003e\r\nthe way which I have pursued, and which is entirely\r\nfree from hypotheses, will, if you will follow my exposition,\r\nbe that of easiest acquisition for the most of\r\nyou.\u003c/p\u003e\r\n\r\n\u003cp\u003eNo man of sound common sense could ever have\r\ndoubted that a pressure or force is requisite to set a\r\nbody in motion in a given direction and that a contrary\r\npressure is required to stop suddenly a body in\r\nmotion. Though the law of inertia was first formulated\r\nwith anything like exactness by Galileo, the\r\nfacts at the basis of it were known long previously to\r\nmen of the stamp of Leonardo da Vinci, Rabelais,\r\nand others, and were illustrated by them with appropriate\r\nexperiments. Leonardo knew that by a swift\r\nstroke with a ruler one can knock out from a vertical\r\ncolumn of checkers a single checker without over-throwing\r\nthe column. The experiment with a coin\r\nresting on a piece of pasteboard covering a goblet,\r\nwhich falls into the goblet when the pasteboard is\r\njerked away, like all experiments of the kind, is certainly\r\nvery old.\u003c/p\u003e\r\n\r\n\u003cp\u003eWith Galileo the experience in question assumes\r\ngreater clearness and force. In the famous dialogue\r\non the Copernican system which cost him his freedom,\r\nhe explains the tides in an unfelicitous, though\r\nin principle correct manner, by the analogue of a\r\nplatter of water swung to and fro. In opposition to\r\nthe Aristotelians of his time, who believed the descent\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_284\" id=\"Page_284\"\u003e[Pg 284]\u003c/a\u003e\u003c/span\u003e\r\nof a heavy body could be accelerated by the\r\nsuperposition of another heavy body, he asserted that\r\na body could never be accelerated by one lying upon\r\nit unless the first in some way impeded the superposed\r\nbody in its descent. To seek to press a falling\r\nbody by means of another placed upon it, is as senseless\r\nas trying to prod a man with a lance when the man\r\nis speeding away from one with the same velocity as\r\nthe lance. Even this little excursion into physics can\r\nexplain much to us. You know the peculiar sensation\r\nwhich one has in falling, as when one jumps from a\r\nhigh springboard into the water, and which is also\r\nexperienced in some measure at the beginning of the\r\ndescent of elevators and swings. The reciprocal gravitational\r\npressure of the different parts of our body,\r\nwhich is certainly felt in some manner, vanishes in\r\nfree descent, or, in the case of the elevator, is diminished\r\non the beginning of the descent. A similar sensation\r\nwould be experienced if we were suddenly\r\ntransported to the moon where the acceleration of\r\ngravity is much less than upon the earth. I was led\r\nto these considerations in 1866 by a suggestion in\r\nphysics, and having also taken into account the alterations\r\nof the blood-pressure in the cases in question,\r\nI found I coincided without knowing it with Wollaston\r\nand Purkinje. The first as early as 1810 in his Croonian\r\nlecture had touched on the subject of sea-sickness\r\nand explained it by alterations of the blood-pressure,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_285\" id=\"Page_285\"\u003e[Pg 285]\u003c/a\u003e\u003c/span\u003e\r\nand later had laid similar considerations at the\r\nbasis of his explanation of vertigo (1820-1826).\u003ca name=\"FNanchor_94_94\" id=\"FNanchor_94_94\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_94_94\" class=\"fnanchor\"\u003e[94]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eNewton was the first to enunciate with perfect\r\ngenerality that a body can change the velocity and\r\ndirection of its motion only by the action of a force,\r\nor the action of a second body. A corollary of this\r\nlaw which was first expressly deduced by Euler is\r\nthat a body can never be set \u003ci\u003erotating\u003c/i\u003e or made to cease\r\nrotating of itself but only by forces and other bodies.\r\nFor example, turn an open watch which has run down\r\nfreely backwards and forwards in your hand. The\r\nbalance-wheel will not fully catch the rapid rotations,\r\nit does not even respond fully to the elastic force of\r\nthe spring which proves too weak to carry the wheel\r\nentirely with it.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us consider now that whether we move ourselves\r\nby means of our legs, or whether we are\r\nmoved by a vehicle or a boat, at first only a part\r\nof our body is directly moved and the rest of it is\r\nafterwards set in motion by the first part. We see\r\nthat pressures, pulls, and tensions are always produced\r\nbetween the parts of the body in this action,\r\nwhich pressures, pulls, and tensions give rise to sensations\r\nby which the forward or rotary movements in\r\nwhich we are engaged are made perceptible.\u003ca name=\"FNanchor_95_95\" id=\"FNanchor_95_95\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_95_95\" class=\"fnanchor\"\u003e[95]\u003c/a\u003e But it\r\nis quite natural that sensations so familiar should be\r\nlittle noticed and that attention should be drawn to\r\nthem only under special circumstances when they occur\r\nunexpectedly or with unusual strength.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_286\" id=\"Page_286\"\u003e[Pg 286]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cdiv class=\"figcenter\" style=\"width: 450px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-296.jpg\" width=\"450\" height=\"330\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 45.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThus my attention was drawn to this point by the\r\nsensation of falling and subsequently by another singular\r\noccurrence. I was rounding a sharp railway\r\ncurve once when I suddenly saw all the trees, houses,\r\nand factory chimneys along the track swerve from the\r\nvertical and assume a strikingly inclined position.\r\nWhat had hitherto appeared to me perfectly natural,\r\nnamely, the fact that we distinguish the vertical so\r\nperfectly and sharply from every other direction, now\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_287\" id=\"Page_287\"\u003e[Pg 287]\u003c/a\u003e\u003c/span\u003e\r\nstruck me as enigmatical. Why is it that the same\r\ndirection can now appear vertical to me and now cannot?\r\nBy what is the vertical distinguished for us?\r\n(Compare Figure 45.)\u003c/p\u003e\r\n\r\n\u003cp\u003eThe rails are raised on the convex or outward side\r\nof the track in order to insure the stability of the carriage\r\nas against the action of the centrifugal force, the\r\nwhole being so arranged that the combination of the\r\nforce of gravity with the centrifugal force of the train\r\nshall give rise to a force perpendicular to the plane\r\nof the rails.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us assume, now, that under all circumstances\r\nwe somehow sense the direction of the total resultant\r\nmass-acceleration whencesoever it may arise as the\r\nvertical. Then both the ordinary and the extraordinary\r\nphenomena will be alike rendered intelligible.\u003ca name=\"FNanchor_96_96\" id=\"FNanchor_96_96\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_96_96\" class=\"fnanchor\"\u003e[96]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eI was now desirous of putting the view I had\r\nreached to a more convenient and exact test than was\r\npossible on a railway journey where one has no control\r\nover the determining circumstances and cannot\r\nalter them at will. I accordingly had the simple apparatus\r\nconstructed which is represented in Figure 46.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn a large frame \u003ci\u003eBB\u003c/i\u003e, which is fastened to the walls,\r\nrotates about a vertical axis \u003ci\u003eAA\u003c/i\u003e a second frame \u003ci\u003eRR\u003c/i\u003e,\r\nand within the latter a third one \u003ci\u003err\u003c/i\u003e, which can be set\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_288\" id=\"Page_288\"\u003e[Pg 288]\u003c/a\u003e\u003c/span\u003e\r\nat any distance and position from the axis, made stationary\r\nor movable, and is provided with a chair for\r\nthe observer.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 600px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-298.jpg\" width=\"600\" height=\"385\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 46.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eFrom Mach\u0027s \u003ci\u003eBewegungsempfindungen\u003c/i\u003e, Leipsic, Engelmann, 1875.]\u003c/p\u003e\r\n\r\n\u003cp\u003eThe observer takes his seat in the chair and to\r\nprevent disturbances of judgment is enclosed in a paper\r\nbox. If the observer together with the frame \u003ci\u003err\u003c/i\u003e\r\nbe then set in uniform rotation, he will feel and see\r\nthe beginning of the rotation both as to direction and\r\namount very distinctly although every outward visible\r\nor tangible point of reference is wanting. If the motion\r\nbe uniformly continued the sensation of rotation\r\nwill gradually cease entirely and the observer will imagine\r\nhimself at rest. But if \u003ci\u003err\u003c/i\u003e be placed outside the\r\naxis of rotation, at once on the rotation beginning, a\r\nstrikingly apparent, palpable, actually visible inclination\r\nof the entire paper box is produced, slight when\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_289\" id=\"Page_289\"\u003e[Pg 289]\u003c/a\u003e\u003c/span\u003e\r\nthe rotation is slow, strong when the rotation is rapid,\r\nand continuing as long as the rotation lasts. It is absolutely\r\nimpossible for the observer to escape perceiving\r\nthe inclination, although here also all outward\r\npoints of reference are wanting. If the observer, for\r\nexample, is seated so as to look towards the axis, he\r\nwill feel the box strongly tipped backwards, as it necessarily\r\nmust be if the direction of the total resultant\r\nforce is perceived as the vertical. For other positions\r\nof the observer the situation is similar.\u003ca name=\"FNanchor_97_97\" id=\"FNanchor_97_97\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_97_97\" class=\"fnanchor\"\u003e[97]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eOnce, while performing one of these experiments,\r\nand after rotating so long that I was no longer conscious\r\nof the movement, I suddenly caused the apparatus\r\nto be stopped, whereupon I immediately felt\r\nand saw myself with the whole box rapidly flung round\r\nin rotation in the opposite direction, although I knew\r\nthat the whole apparatus was at rest and every outward\r\npoint of reference for the perception of motion\r\nwas wanting. Every one who disbelieves in sensations\r\nof movement should be made acquainted with\r\nthese phenomena. Had Newton known them and had\r\nhe ever observed how we may actually imagine ourselves\r\nturned and displaced in space without the assistance\r\nof stationary bodies as points of reference, he\r\nwould certainly have been confirmed more than ever\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_290\" id=\"Page_290\"\u003e[Pg 290]\u003c/a\u003e\u003c/span\u003e\r\nin his unfortunate speculations regarding absolute\r\nspace.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe sensation of rotation in the opposite direction\r\nafter the apparatus has been stopped, slowly and gradually\r\nceases. But on accidentally inclining my head\r\nonce during this occurrence, the axis of apparent rotation\r\nwas also observed to incline in exactly the same\r\nmanner both as to direction and as to amount. It is\r\naccordingly clear that the acceleration or retardation\r\nof rotation is felt. The acceleration operates as a\r\nstimulus. The sensation, however, like almost all\r\nsensations, though it gradually decreases, lasts perceptibly\r\nlonger than the stimulus. Hence the long\r\ncontinued apparent rotation after the stopping of the\r\napparatus. The organ, however, which causes the\r\npersistence of this sensation must have its seat in the\r\n\u003ci\u003ehead\u003c/i\u003e, since otherwise the axis of apparent rotation\r\ncould not assume the same motion as the head.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf I were to say, now, that a light had flashed\r\nupon me in making these last observations, the expression\r\nwould be a feeble one. I ought to say I experienced\r\na perfect illumination. My juvenile experiences\r\nof vertigo occurred to me. I remembered\r\nFlourens\u0027s experiments relative to the section of the\r\nsemi-circular canals of the labyrinths of doves and\r\nrabbits, where this inquirer had observed phenomena\r\nsimilar to vertigo, but which he preferred to interpret,\r\nfrom his bias to the acoustic theory of the labyrinth,\r\nas the expression of painful auditive disturbances. I\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_291\" id=\"Page_291\"\u003e[Pg 291]\u003c/a\u003e\u003c/span\u003e\r\nsaw that Goltz had nearly but not quite hit the bull\u0027s\r\neye with his theory of the semi-circular canals. This\r\ninquirer, who, from his happy habit of following his\r\nown natural thoughts without regard for tradition,\r\nhas cleared up so much in science, spoke, as early as\r\n1870, on the ground of experiments, as follows: \"It\r\nis uncertain whether the semi-circular canals are auditive\r\norgans or not. In any event they form an apparatus\r\nwhich serves for the preservation of equilibrium.\r\nThey are, so to speak, the sense-organs of equilibrium\r\nof the head and indirectly of the whole body.\" I\r\nremembered the galvanic dizziness which had been\r\nobserved by Ritter and Purkinje on the passage of a\r\ncurrent through the head, when the persons experimented\r\nupon imagined they were falling towards the\r\ncathode. The experiment was immediately repeated,\r\nand sometime later (1874) I was enabled to demonstrate\r\nthe same objectively with fishes, all of which\r\nplaced themselves sidewise and in the same direction\r\nin the field of the current as if at command.\u003ca name=\"FNanchor_98_98\" id=\"FNanchor_98_98\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_98_98\" class=\"fnanchor\"\u003e[98]\u003c/a\u003e Müller\u0027s\r\ndoctrine of specific energies now appeared to me\r\nto bring all these new and old observations into a simple,\r\nconnected unity.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 600px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-302.jpg\" width=\"600\" height=\"406\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 47.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eThe labyrinth of a dove (stereoscopically reproduced), from R. Ewald,\r\n\u003ci\u003eNervus Octavus\u003c/i\u003e, Wiesbaden, Bergmann, 1892.]\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us picture to ourselves the labyrinth of the\r\near with its three semi-circular canals lying in three\r\nmutually perpendicular planes (Comp. Fig. 47), the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_292\" id=\"Page_292\"\u003e[Pg 292]\u003c/a\u003e\u003c/span\u003e\r\nmysterious position of which inquirers have endeavored\r\nto explain in every possible and impossible way.\r\nLet us conceive the nerves of the ampullæ, or the dilated\r\nextensions of the semi-circular canals, equipped\r\nwith a capacity for responding to every imaginable\r\nstimulus with a sensation of rotation just as the nerves\r\nof the retina of the eye when excited by pressures,\r\nby electrical or chemical stimuli always respond with\r\nthe sensation of light; let us picture to ourselves,\r\nfurther, that the usual excitation of the ampullæ\r\nnerves is produced by the inertia of the contents of\r\nthe semi-circular canals, which contents on suitable\r\nrotations in the plane of the semi-circular canal are\r\nleft behind in the motion, or at least have a tendency\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_293\" id=\"Page_293\"\u003e[Pg 293]\u003c/a\u003e\u003c/span\u003e\r\nto remain behind and consequently exert a pressure.\r\nIt will be seen that on this supposition all the single\r\nfacts which without the theory appear as so many\r\ndifferent individual phenomena, become from this single\r\npoint of view clear and intelligible.\u003c/p\u003e\r\n\r\n\u003cp\u003eI had the satisfaction, immediately after the communication\r\nin which I set forth this idea,\u003ca name=\"FNanchor_99_99\" id=\"FNanchor_99_99\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_99_99\" class=\"fnanchor\"\u003e[99]\u003c/a\u003e of seeing a\r\npaper by Breuer appear\u003ca name=\"FNanchor_100_100\" id=\"FNanchor_100_100\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_100_100\" class=\"fnanchor\"\u003e[100]\u003c/a\u003e in which this author had\r\narrived by entirely different methods at results that\r\nagreed in all essential points with my own. A few\r\nweeks later appeared the researches of Crum Brown\r\nof Edinburgh, whose methods were even still nearer\r\nmine. Breuer\u0027s paper was far richer in physiological\r\nrespects than mine, and he had particularly gone\r\ninto greater detail in his investigation of the collateral\r\neffects of the reflex motions and orientation of\r\nthe eyes in the phenomena under consideration.\u003ca name=\"FNanchor_101_101\" id=\"FNanchor_101_101\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_101_101\" class=\"fnanchor\"\u003e[101]\u003c/a\u003e In\r\naddition certain experiments which I had suggested in\r\nmy paper as a test of the correctness of the view\r\nin question had already been performed by Breuer.\r\nBreuer has also rendered services of the highest order\r\nin the further elaboration of this field. But in a\r\nphysical regard, my paper was, of course, more complete.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn order to portray to the eye the behavior of the\r\nsemi-circular canals, I have constructed here a little\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_294\" id=\"Page_294\"\u003e[Pg 294]\u003c/a\u003e\u003c/span\u003e\r\napparatus. (See Fig. 48.) The large rotatable disc\r\nrepresents the osseous semi-circular canal, which is\r\ncontinuous with the bones of the head; the small disc,\r\nwhich is free to rotate on the axis of the first, represents\r\nthe mobile and partly liquid contents of the semi-circular\r\ncanal. On rotating the large disc, the small\r\ndisc as you see remains\r\nbehind. I\r\nhave to turn some\r\ntime before the\r\nsmall disc is carried\r\nalong with the large\r\none by friction. But\r\nif I now stop the\r\nlarge disc the small\r\ndisc as you see continues\r\nto rotate.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 350px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-304.jpg\" width=\"350\" height=\"497\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 48.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eModel representing the action of the semi-circular\r\ncanals.]\u003c/p\u003e\r\n\r\n\u003cp\u003eSimply assume\r\nnow that the rotation\r\nof the small\r\ndisc, say in the direction\r\nof the hands\r\nof a watch, would\r\ngive rise to a sensation of rotation in the opposite\r\ndirection, and conversely, and you already understand\r\na good portion of the facts above set forth.\r\nThe explanation still holds, even if the small disc\r\ndoes not perform appreciable rotations but is checked\r\nby a contrivance similar to an elastic spring, the tension\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_295\" id=\"Page_295\"\u003e[Pg 295]\u003c/a\u003e\u003c/span\u003e\r\nof which disengages a sensation. Conceive, now,\r\nthree such contrivances with their mutually perpendicular\r\nplanes of rotation joined together so as to\r\nform a single apparatus; then to this apparatus as a\r\nwhole, no rotation can be imparted without its being\r\nindicated by the small mobile discs or by the springs\r\nwhich are attached to them. Conceive both the right\r\nand the left ear equipped with such an apparatus, and\r\nyou will find that it answers all the purposes of the\r\nsemi-circular canals, which you see represented stereoscopically\r\nin Fig. 47 for the ear of a dove.\u003c/p\u003e\r\n\r\n\u003cp\u003eOf the many experiments which I have made on\r\nmy own person, and the results of which could be\r\npredicted by the new view according to the behavior\r\nof the model and consequently according to the rules\r\nof mechanics, I shall cite but one. I fasten a horizontal\r\nboard in the frame \u003ci\u003eRR\u003c/i\u003e of my rotatory apparatus,\r\nlie down upon the same with my right ear upon the\r\nboard, and cause the apparatus to be uniformly rotated.\r\nAs soon as I no longer perceive the rotation,\r\nI turn around upon my left ear and immediately the\r\nsensation of rotation again starts up with marked vividness.\r\nThe experiment can be repeated as often as\r\none wishes. A slight turn of the head even is sufficient\r\nfor reviving the sensation of rotation which in\r\nthe perfectly quiescent state at once disappears altogether.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe will imitate the experiment on the model. I\r\nturn the large disc until finally the small disc is carried\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_296\" id=\"Page_296\"\u003e[Pg 296]\u003c/a\u003e\u003c/span\u003e\r\nalong with it. If, now, while the rotation continues\r\nuniform, I burn off a little thread which you\r\nsee here, the small disc will be flipped round by a\r\nspring into its own plane 180°, so as now to present\r\nits opposite side to you, when the rotation at once begins\r\nin the opposite direction.\u003c/p\u003e\r\n\r\n\u003cp\u003eWe have consequently a very simple means for determining\r\nwhether one is actually the subject or not\r\nof uniform and imperceptible rotations. If the earth\r\nrotated much more rapidly than it really does, or if\r\nour semi-circular canals were much more sensitive, a\r\nNansen sleeping at the North Pole would be waked\r\nby a sensation of rotation every time he turned over.\r\nFoucault\u0027s pendulum experiment as a demonstration\r\nof the earth\u0027s rotation would be superfluous under\r\nsuch circumstances. The only reason we cannot prove\r\nthe rotation of the earth with the help of our model,\r\nlies in the small angular velocity of the earth and in\r\nthe consequent liability to great experimental errors.\u003ca name=\"FNanchor_102_102\" id=\"FNanchor_102_102\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_102_102\" class=\"fnanchor\"\u003e[102]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eAristotle has said that \"The sweetest of all\r\nthings is knowledge.\" And he is right. But if you\r\nwere to suppose that the \u003ci\u003epublication\u003c/i\u003e of a new view\r\nwere productive of unbounded sweetness, you would\r\nbe mightily mistaken. No one disturbs his fellow-men\r\nwith a new view unpunished. Nor should the fact be\r\nmade a subject of reproach to these fellow-men. To\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_297\" id=\"Page_297\"\u003e[Pg 297]\u003c/a\u003e\u003c/span\u003e\r\npresume to revolutionise the current way of thinking\r\nwith regard to any question, is no pleasant task, and\r\nabove all not an easy one. They who have advanced\r\nnew views know best what serious difficulties stand in\r\ntheir way. With honest and praiseworthy zeal, men\r\nset to work in search of everything that does not\r\nsuit with them. They seek to discover whether they\r\ncannot explain the facts better or as well, or approximately\r\nas well, by the traditional views. And that,\r\ntoo, is justified. But at times some extremely artless\r\nanimadversions are heard that almost nonplus us.\r\n\"If a sixth sense existed it could not fail to have\r\nbeen discovered thousands of years ago.\" Indeed;\r\nthere was a time, then, when only seven planets could\r\nhave existed! But I do not believe that any one will\r\nlay any weight on the philological question whether\r\nthe set of phenomena which we have been considering\r\nshould be called a sense. The phenomena will not\r\ndisappear when the name disappears. It was further\r\nsaid to me that animals exist which have no labyrinth,\r\nbut which can yet orientate themselves, and that consequently\r\nthe labyrinth has nothing to do with orientation.\r\nWe do not walk forsooth with our legs, because\r\nsnakes propel themselves without them!\u003c/p\u003e\r\n\r\n\u003cp\u003eBut if the promulgator of a new idea cannot hope\r\nfor any great pleasure from its publication, yet the\r\ncritical process which his views undergo is extremely\r\nhelpful to the subject-matter of them. All the defects\r\nwhich necessarily adhere to the new view are gradually\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_298\" id=\"Page_298\"\u003e[Pg 298]\u003c/a\u003e\u003c/span\u003e\r\ndiscovered and eliminated. Over-rating and exaggeration\r\ngive way to more sober estimates. And\r\nso it came about that it was found unpermissible to\r\nattribute all functions of orientation exclusively to the\r\nlabyrinth. In these critical labors Delage, Aubert,\r\nBreuer, Ewald, and others have rendered distinguished\r\nservices. It can also not fail to happen that\r\nfresh facts become known in this process which could\r\nhave been predicted by the new view, which actually\r\nwere predicted in part, and which consequently furnish\r\na support for the new view. Breuer and Ewald\r\nsucceeded in electrically and mechanically exciting\r\nthe labyrinth, and even single parts of the labyrinth,\r\nand thus in producing the movements that belong to\r\nsuch stimuli. It was shown that when the semi-circular\r\ncanals were absent vertigo could not be produced,\r\nwhen the entire labyrinth was removed the orientation\r\nof the head was no longer possible, that without\r\nthe labyrinth galvanic vertigo could not be induced. I\r\nmyself constructed as early as 1875 an apparatus for\r\nobserving animals in rotation, which was subsequently\r\nreinvented in various forms and has since received the\r\nname of \"cyclostat.\"\u003ca name=\"FNanchor_103_103\" id=\"FNanchor_103_103\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_103_103\" class=\"fnanchor\"\u003e[103]\u003c/a\u003e In experiments with the most\r\nvaried kinds of animals it was shown that, for example,\r\nthe larvæ of frogs are not subject to vertigo until\r\ntheir semi-circular canals which at the start are wanting\r\nare developed (K. Schäfer). A large percentage\r\nof the deaf and dumb are afflicted with grave affections\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_299\" id=\"Page_299\"\u003e[Pg 299]\u003c/a\u003e\u003c/span\u003e\r\nof the labyrinth. The American psychologist,\r\nWilliam James, has made whirling experiments with\r\nmany deaf and dumb subjects, and in a large number\r\nof them found that susceptibility to giddiness is wanting.\r\nHe also found that many deaf and dumb people\r\non being ducked under water, whereby they lose their\r\nweight and consequently have no longer the full assistance\r\nof their muscular sense, utterly lose their\r\nsense of position in space, do not know which is up\r\nand which is down, and are thrown into the greatest\r\nconsternation,\u0026mdash;results which do not occur in normal\r\nmen. Such facts are convincing proof that we do not\r\norientate ourselves entirely by means of the labyrinth,\r\nimportant as it is for us. Dr. Kreidl has made experiments\r\nsimilar to those of James and found that\r\nnot only is vertigo absent in deaf and dumb people\r\nwhen whirled about, but that also the reflex movements\r\nof the eyes which are normally induced by the\r\nlabyrinth are wanting. Finally, Dr. Pollak has found\r\nthat galvanic vertigo does not exist in a large percentage\r\nof the deaf and dumb. Neither the jerking\r\nmovements nor the uniform movements of the eyes\r\nwere observed which normal human beings exhibit in\r\nthe Ritter and Purkinje experiment.\u003c/p\u003e\r\n\r\n\u003cp\u003eAfter the physicist has arrived at the idea that the\r\nsemi-circular canals are the organ of sensation of rotation\r\nor of angular acceleration, he is next constrained\r\nto ask for the organs that mediate the sensation\r\nof acceleration noticed in forward movements.\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_300\" id=\"Page_300\"\u003e[Pg 300]\u003c/a\u003e\u003c/span\u003e\r\nIn searching for an organ for this function, he of\r\ncourse is not apt to select one that stands in no anatomical\r\nand spatial relation with the semi-circular\r\ncanals. And in addition there are physiological considerations\r\nto be weighed. The preconceived opinion\r\nonce having been abandoned that the \u003ci\u003eentire\u003c/i\u003e labyrinth\r\nis auditory in its function, there remains after the\r\ncochlea is reserved for sensations of tone and the\r\nsemi-circular canals for the sensation of angular acceleration,\r\nthe vestibule for the discharge of additional\r\nfunctions. The vestibule, particularly the part of it\r\nknown as the sacculus, appeared to me, by reason of\r\nthe so-called otoliths which it contains, eminently\r\nadapted for being the organ of sensation of forward\r\nacceleration or of the position of the head. In this\r\nconjecture I again closely coincided with Breuer.\u003c/p\u003e\r\n\r\n\u003cp\u003eThat a sensation of position, of direction and\r\namount of mass-acceleration exists, our experience in\r\nelevators as well as of movement in curved paths is\r\nsufficient proof. I have also attempted to produce and\r\ndestroy suddenly great velocities of forward movement\r\nby means of various contrivances of which I\r\nshall mention only one here. If, while enclosed in\r\nthe paper box of my large whirling apparatus at some\r\ndistance from the axis, my body is in uniform rotation\r\nwhich I no longer feel, and I then loosen the connexions\r\nof the frame \u003ci\u003err\u003c/i\u003e with \u003ci\u003eR\u003c/i\u003e thus making the former\r\nmoveable and I then suddenly stop the larger frame,\r\nmy forward motion is abruptly impeded while the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_301\" id=\"Page_301\"\u003e[Pg 301]\u003c/a\u003e\u003c/span\u003e\r\nframe \u003ci\u003err\u003c/i\u003e continues to rotate. I imagine now that I\r\nam speeding on in a straight line in a direction opposite\r\nto that of the checked motion. Unfortunately, for\r\nmany reasons it cannot be proved convincingly that\r\nthe organ in question has its seat in the head. According\r\nto the opinion of Delage, the labyrinth has\r\nnothing to do with this particular sensation of movement.\r\nBreuer, on the other hand, is of the opinion\r\nthat the organ of forward movement in man is stunted\r\nand the persistence of the sensation in question is too\r\nbrief to permit our instituting experiments as obvious\r\nas in the case of rotation. In fact, Crum Brown once\r\nobserved while in an irritated condition peculiar vertical\r\nphenomena in his own person, which were all\r\nsatisfactorily explained by an abnormally long persistence\r\nof the sensation of rotation, and I myself in an\r\nanalogous case on the stopping of a railway train felt\r\nthe apparent backward motion in striking intensity\r\nand for an unusual length of time.\u003c/p\u003e\r\n\r\n\u003cp\u003eThere is no doubt whatever that we feel changes\r\nof vertical acceleration, and it will appear from the\r\nfollowing extremely probable that the otoliths of the\r\nvestibule are the sense-organ for the \u003ci\u003edirection\u003c/i\u003e of the\r\nmass-acceleration. It will then be incompatible with\r\na really logical view to regard the latter as incapable\r\nof sensing horizontal accelerations.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the lower animals the analogue of the labyrinth\r\nis shrunk to a little vesicle filled with a liquid and\r\ncontaining tiny crystals, auditive stones, or otoliths, of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_302\" id=\"Page_302\"\u003e[Pg 302]\u003c/a\u003e\u003c/span\u003e\r\ngreater specific gravity, suspended on minute hairs.\r\nThese crystals appear physically well adapted for indicating\r\nboth the direction of gravity and the direction\r\nof incipient movements. That they discharge the former\r\nfunction, Delage was the first to convince himself\r\nby experiments with lower animals which on the removal\r\nof the otoliths utterly lost their bearings and\r\ncould no longer regain their normal position. Loeb\r\nalso found that fishes without labyrinths swim now on\r\ntheir bellies and now on their backs. But the most\r\nremarkable, most beautiful, and most convincing experiment\r\nis that which Dr. Kreidl instituted with\r\ncrustaceans. According to Hensen, certain Crustacea\r\non sloughing spontaneously introduce fine grains of\r\nsand as auditive stones into their otolith vesicle. At\r\nthe ingenious suggestion of S. Exner, Dr. Kreidl constrained\r\nsome of these animals to put up with iron\r\nfilings (\u003ci\u003eferrum limatum\u003c/i\u003e). If the pole of an electro-magnet\r\nbe brought near the animal, it will at once\r\nturn its back away from the pole accompanying the\r\nmovement with appropriate reflex motions of the eye\r\nthe moment the current is closed, exactly as if gravity\r\nhad been brought to bear upon the animal in the\r\nsame direction as the magnetic force.\u003ca name=\"FNanchor_104_104\" id=\"FNanchor_104_104\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_104_104\" class=\"fnanchor\"\u003e[104]\u003c/a\u003e This, in fact,\r\nis what should be expected from the function ascribed\r\nto the otoliths. If the eyes be covered with asphalt\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_303\" id=\"Page_303\"\u003e[Pg 303]\u003c/a\u003e\u003c/span\u003e\r\nvarnish, and the auditive sacs removed, the crustaceans\r\nlose their sense of direction utterly, tumble\r\nhead over heels, lie on their side or their back indifferently.\r\nThis does not happen when the eyes only\r\nare covered. For vertebrates, Breuer has demonstrated\r\nby searching investigations that the otoliths,\r\nor better, statoliths, slide in three planes parallel to\r\nthe planes of the semi-circular canals, and are consequently\r\nperfectly adapted for indicating changes\r\nboth in the amount and the direction of the mass-acceleration.\u003ca name=\"FNanchor_105_105\" id=\"FNanchor_105_105\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_105_105\" class=\"fnanchor\"\u003e[105]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eI have already remarked that not every function\r\nof orientation can be ascribed exclusively to the labyrinth.\r\nThe deaf and dumb who have to be immersed\r\nin water, and the crustaceans who must have their\r\neyes closed if they are to be perfectly disorientated, are\r\nproof of this fact. I saw a blind cat at Hering\u0027s laboratory\r\nwhich to one who was not a very attentive observer\r\nbehaved exactly like a seeing cat. It played\r\nnimbly with objects rolling on the floor, stuck its head\r\ninquisitively into open drawers, sprang dexterously\r\nupon chairs, ran with perfect accuracy through open\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_304\" id=\"Page_304\"\u003e[Pg 304]\u003c/a\u003e\u003c/span\u003e\r\ndoors, and never bumped against closed ones. The\r\nvisual sense had here been rapidly replaced by the\r\ntactual and auditive senses. And it appears from\r\nEwald\u0027s investigations that even after the labyrinths\r\nhave been removed, animals gradually learn to move\r\nabout again quite in the normal fashion, presumably\r\nbecause the eliminated function of the labyrinth is\r\nnow performed by some part of the brain. A certain\r\npeculiar weakness of the muscles alone is perceptible\r\nwhich Ewald ascribes to the absence of the stimulus\r\nwhich is otherwise constantly emitted by the labyrinth\r\n(the labyrinth-tonus). But if the part of the\r\nbrain which discharges the deputed function be removed,\r\nthe animals are again completely disorientated\r\nand absolutely helpless.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt may be said that the views enunciated by Breuer,\r\nCrum Brown and myself in 1873 and 1874, and which\r\nare substantially a fuller and richer development of\r\nGoltz\u0027s idea, have upon the whole been substantiated.\r\nAt least they have exercised a helpful and stimulative\r\ninfluence. New problems have of course arisen in the\r\ncourse of the investigation which still await solution,\r\nand much work remains to be done. At the same\r\ntime we see how fruitful the renewed co-operation of\r\nthe various special departments of science may become\r\nafter a period of isolation and invigorating labor\r\napart.\u003c/p\u003e\r\n\r\n\u003cp\u003eI may be permitted, therefore, to consider the relation\r\nbetween hearing and orientation from another\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_305\" id=\"Page_305\"\u003e[Pg 305]\u003c/a\u003e\u003c/span\u003e\r\nand more general point of view. What we call the\r\nauditive organ is in the lower animals simply a sac\r\ncontaining auditive stones. As we ascend the scale,\r\n1, 2, 3 semi-circular canals gradually develop from\r\nthem, whilst the structure of the otolith organ itself\r\nbecomes more complicated. Finally, in the higher\r\nvertebrates, and particularly in the mammals, a part\r\nof the latter organ (the lagena) becomes the cochlea,\r\nwhich Helmholtz explained as the organ for sensations\r\nof tone. In the belief that the entire labyrinth\r\nwas an auditive organ, Helmholtz, contrary to the results\r\nof his own masterly analysis, originally sought\r\nto interpret another part of the labyrinth as the organ\r\nof noises. I showed a long time ago (1873) that every\r\ntonal stimulus by shortening the duration of the excitation\r\nto a few vibrations, gradually loses its character\r\nof pitch and takes on that of a sharp, dry report or\r\nnoise.\u003ca name=\"FNanchor_106_106\" id=\"FNanchor_106_106\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_106_106\" class=\"fnanchor\"\u003e[106]\u003c/a\u003e All the intervening stages between tones and\r\nnoises can be exhibited. Such being the case, it will\r\nhardly be assumed that one organ is suddenly and at\r\nsome given point replaced in function by another. On\r\nthe basis of different experiments and reasonings S.\r\nExner also regards the assumption of a special organ\r\nfor the sensing of noises as unnecessary.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf we will but reflect how small a portion of the\r\nlabyrinth of higher animals is apparently in the service\r\nof the sense of hearing, and how large, on the other\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_306\" id=\"Page_306\"\u003e[Pg 306]\u003c/a\u003e\u003c/span\u003e\r\nhand, the portion is which very likely serves the purposes\r\nof orientation, how much the first anatomical\r\nbeginnings of the auditive sac of lower animals resemble\r\nthat part of the fully developed labyrinth which\r\ndoes not hear, the view is irresistibly suggested which\r\nBreuer and I (1874, 1875) expressed, that the auditive\r\norgan took its development from an organ for sensing\r\nmovements by adaptation to weak periodic motional\r\nstimuli, and that many apparatuses in the lower animals\r\nwhich are held to be organs of hearing are not\r\nauditive organs at all.\u003ca name=\"FNanchor_107_107\" id=\"FNanchor_107_107\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_107_107\" class=\"fnanchor\"\u003e[107]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThis view appears to be perceptibly gaining\r\nground. Dr. Kreidl by skilfully-planned experiments\r\nhas arrived at the conclusion that even fishes do not\r\nhear, whereas E. H. Weber, in his day, regarded the\r\nossicles which unite the air-bladder of fishes with the\r\nlabyrinth as organs expressly designed for conducting\r\nsound from the former to the latter.\u003ca name=\"FNanchor_108_108\" id=\"FNanchor_108_108\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_108_108\" class=\"fnanchor\"\u003e[108]\u003c/a\u003e Störensen has\r\ninvestigated the excitation of sounds by the air-bladder\r\nof fishes, as also the conduction of shocks through\r\nWeber\u0027s ossicles. He regards the air-bladder as particularly\r\nadapted for receiving the noises made by\r\nother fishes and conducting them to the labyrinth.\r\nHe has heard the loud grunting tones of the fishes\r\nin South American rivers, and is of the opinion that\r\nthey allure and find each other in this manner. According\r\nto these views certain fishes are neither deaf\r\nnor dumb.\u003ca name=\"FNanchor_109_109\" id=\"FNanchor_109_109\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_109_109\" class=\"fnanchor\"\u003e[109]\u003c/a\u003e The question here involved might be\r\nsolved perhaps by sharply distinguishing between the\r\nsensation of hearing proper, and the perception of\r\nshocks. The first-mentioned sensation may, even in\r\nthe case of many vertebrates, be extremely restricted,\r\nor perhaps even absolutely wanting. But besides the\r\nauditive function, Weber\u0027s ossicles may perfectly well\r\ndischarge some other function. Although, as Moreau\r\nhas shown, the air-bladder itself is not an organ of\r\nequilibrium in the simple physical sense of Borelli,\r\nyet doubtless some function of this character is still\r\nreserved for it. The union with the labyrinth favors\r\nthis conception, and so a host of new problems rises\r\nhere before us.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_307\" id=\"Page_307\"\u003e[Pg 307]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eI should like to close with a reminiscence from the\r\nyear 1863. Helmholtz\u0027s \u003ci\u003eSensations of Tone\u003c/i\u003e had just\r\nbeen published and the function of the cochlea now\r\nappeared clear to the whole world. In a private conversation\r\nwhich I had with a physician, the latter declared\r\nit to be an almost hopeless undertaking to seek\r\nto fathom the function of the other parts of the labyrinth,\r\nwhereas I in youthful boldness maintained that\r\nthe question could hardly fail to be solved, and that\r\nvery soon, although of course I had then no glimmering\r\nof how it was to be done. Ten years later the\r\nquestion was substantially solved.\u003c/p\u003e\r\n\r\n\u003cp\u003eTo-day, after having tried my powers frequently\r\nand in vain on many questions, I no longer believe\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_308\" id=\"Page_308\"\u003e[Pg 308]\u003c/a\u003e\u003c/span\u003e\r\nthat we can make short work of the problems of science.\r\nNevertheless, I should not consider an \"ignorabimus\"\r\nas an expression of modesty, but rather as\r\nthe opposite. That expression is a suitable one only\r\nwith regard to problems which are wrongly formulated\r\nand which are therefore not problems at all.\r\nEvery real problem can and will be solved in due\r\ncourse of time without supernatural divination, entirely\r\nby accurate observation and close, searching\r\nthought.\u003c/p\u003e\u003chr class=\"chap\" /\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_309\" id=\"Page_309\"\u003e[Pg 309]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_SOME_PHENOMENA_ATTENDING\" id=\"ON_SOME_PHENOMENA_ATTENDING\"\u003eON SOME PHENOMENA ATTENDING\r\nTHE FLIGHT OF PROJECTILES.\u003c/a\u003e\u003ca name=\"FNanchor_110_110\" id=\"FNanchor_110_110\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_110_110\" class=\"fnanchor\"\u003e[110]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"I have led my ragamuffins where they were\r\npeppered.\"\u0026mdash;\u003ci\u003eFalstaff.\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\"He goes but to see a noise that he heard.\"\u0026mdash;\u003ci\u003eMidsummer\r\nNight\u0027s Dream.\u003c/i\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eTo shoot, in the shortest time possible, as many\r\nholes as possible in one another\u0027s bodies, and\r\nnot always for exactly pardonable objects and ideals,\r\nseems to have risen to the dignity of a duty with modern\r\nmen, who, by a singular inconsistency, and in\r\nsubservience to a diametrically contrary ideal, are\r\nbound by the equally holy obligation of making these\r\nholes as small as possible, and, when made, of stopping\r\nthem up and of healing them as speedily as\r\npossible. Since, then, shooting and all that appertains\r\nthereto, is a very important, if not the most important,\r\naffair of modern life, you will doubtless not be averse\r\nto giving your attention for an hour to some experiments\r\nwhich have been undertaken, not for advancing\r\nthe ends of war, but for promoting the ends of science,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_310\" id=\"Page_310\"\u003e[Pg 310]\u003c/a\u003e\u003c/span\u003e\r\nand which throw some light on the phenomena\r\nattending the flight of projectiles.\u003c/p\u003e\r\n\r\n\u003cp\u003eModern science strives to construct its picture of\r\nthe world not from speculations but so far as possible\r\nfrom facts. It verifies its constructs by recourse to\r\nobservation. Every newly observed fact completes\r\nits world-picture, and every divergence of a construct\r\nfrom observation points to some imperfection, to some\r\nlacuna in it. What is seen is put to the test of, and\r\nsupplemented by, what is thought, which is again\r\nnaught but the result of things previously seen. It\r\nis always peculiarly fascinating, therefore, to subject\r\nto direct verification by observation, that is, to render\r\npalpable to the senses, something which we have only\r\ntheoretically excogitated or theoretically surmised.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn 1881, on hearing in Paris the lecture of the Belgian\r\nartillerist Melsens, who hazarded the conjecture\r\nthat projectiles travelling at a high rate of speed carry\r\nmasses of compressed air before them which are instrumental\r\nin producing in bodies struck by the projectiles\r\ncertain well-known facts of the nature of explosions,\r\nthe desire arose in me of experimentally testing\r\nhis conjecture and of rendering the phenomenon,\r\nif it really existed, perceptible. The desire was the\r\nstronger as I could say that all the means for realising\r\nit existed, and that I had in part already used and\r\ntested them for other purposes.\u003c/p\u003e\r\n\r\n\u003cp\u003eAnd first let us get clear regarding the difficulties\r\nwhich have to be surmounted. Our task is that of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_311\" id=\"Page_311\"\u003e[Pg 311]\u003c/a\u003e\u003c/span\u003e\r\nobserving a bullet or other projectile which is rushing\r\nthrough space at a velocity of many hundred yards a\r\nsecond, together with the disturbances which the bullet\r\ncauses in the surrounding atmosphere. Even the\r\nopaque solid body itself, the projectile, is only exceptionally\r\nvisible under such circumstances\u0026mdash;only when\r\nit is of considerable size and when we see its line of\r\nflight in strong perspective abridgement so that the\r\nvelocity is apparently diminished. We see a large\r\nprojectile quite clearly when we stand behind the cannon\r\nand look steadily along its line of flight or in the\r\nless pleasant case when the projectile is speeding towards\r\nus. There is, however, a very simple and effective\r\nmethod of observing swiftly moving bodies with as\r\nlittle trouble as if they were held at rest at some point\r\nin their path. The method is that of illumination by\r\na brilliant electric spark of extremely short duration\r\nin a dark room. But since, for the full intellectual\r\ncomprehension of a picture presented to the eye, a\r\ncertain, not inconsiderable interval of time is necessary,\r\nthe method of instantaneous photography will\r\nnaturally also be employed. The pictures, which are\r\nof extremely minute duration, are thus permanently\r\nrecorded and can be examined and analysed at one\u0027s\r\nconvenience and leisure.\u003c/p\u003e\r\n\r\n\u003cp\u003eWith the difficulty just mentioned is associated\r\nstill another and greater difficulty which is due to the\r\nair. The atmosphere in its usual condition is generally\r\nnot visible even when at rest. But the task presented\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_312\" id=\"Page_312\"\u003e[Pg 312]\u003c/a\u003e\u003c/span\u003e\r\nto us is to render visible masses of air which\r\nin addition are moving with a high velocity.\u003c/p\u003e\r\n\r\n\u003cp\u003eTo be visible, a body must either emit light itself,\r\nmust shine, or must affect in some way the light which\r\nfalls upon it, must take up that light entirely or partly,\r\nabsorb it, or must have a deflective effect upon it, that\r\nis, reflect or refract it. We cannot see the air as we\r\ncan a flame, for it shines only exceptionally, as in a\r\nGeissler\u0027s tube. The atmosphere is extremely transparent\r\nand colorless; it cannot be seen, therefore, as\r\na dark or colored body can, or as chlorine gas can,\r\nor vapor of bromine or iodine. Air, finally, has so\r\nsmall an index of refraction and so small a deflective\r\ninfluence upon light, that the refractive effect is commonly\r\nimperceptible altogether.\u003c/p\u003e\r\n\r\n\u003cp\u003eA glass rod is visible in air or in water, but it is\r\nalmost invisible in a mixture of benzol and bisulphuret\r\nof carbon, which has the same mean index of refraction\r\nas the glass. Powdered glass in the same mixture\r\nhas a vivid coloring, because owing to the decomposition\r\nof the colors the indices are the same\r\nfor only one color which traverses the mixture unimpeded,\r\nwhilst the other colors undergo repeated reflexions.\u003ca name=\"FNanchor_111_111\" id=\"FNanchor_111_111\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_111_111\" class=\"fnanchor\"\u003e[111]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eWater is invisible in water, alcohol in alcohol. But\r\nif alcohol be mixed with water the flocculent streaks\r\nof the alcohol in the water will be seen at once and\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_313\" id=\"Page_313\"\u003e[Pg 313]\u003c/a\u003e\u003c/span\u003e\r\n\u003ci\u003evice versa\u003c/i\u003e. And in like manner the air, too, under\r\nfavorable circumstances, may be seen. Over a roof\r\nheated by the burning sun, a tremulous wavering of\r\nobjects is noticeable, as there is also over red-hot\r\nstoves, radiators, and registers. In all these cases\r\ntiny flocculent masses of hot and cold air, of slightly\r\ndiffering refrangibility, are mingled together.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn like manner the more highly refracting parts of\r\nnon-homogeneous masses of glass, the so-called striæ\r\nor imperfections of the glass, are readily detectible\r\namong the less refracting parts which constitute the\r\nbulk of the same. Such glasses are unserviceable for\r\noptical purposes, and special attention has been devoted\r\nto the investigation of the methods for eliminating\r\nor avoiding these defects. The result has been\r\nthe development of an extremely delicate method for\r\ndetecting optical faults\u0026mdash;the so-called method of Foucault\r\nand Toepler\u0026mdash;which is suitable also for our\r\npresent purpose.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 600px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-324.jpg\" width=\"600\" height=\"169\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 49.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eEven Huygens when trying to detect the presence\r\nof striæ in polished glasses viewed them under oblique\r\nillumination, usually at a considerable distance, so as\r\nto give full scope to the aberrations, and had recourse\r\nfor greater exactitude to a telescope. But the method\r\nwas carried to its highest pitch of perfection in 1867\r\nby Toepler who employed the following procedure:\r\nA small luminous source \u003ci\u003ea\u003c/i\u003e (Fig. 49) illuminates a lens\r\n\u003ci\u003eL\u003c/i\u003e which throws an image \u003ci\u003eb\u003c/i\u003e of the luminous source.\r\nIf the eye be so placed that the image falls on the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_314\" id=\"Page_314\"\u003e[Pg 314]\u003c/a\u003e\u003c/span\u003e\r\npupil, the entire lens, if perfect, will appear equally\r\nilluminated, for the reason that all points of it send\r\nout rays to the eye. Coarse imperfections of form or\r\nof homogeneity are rendered visible only in case the\r\naberrations are so large that the light from many spots\r\npasses by the pupil of the eye. But if the image \u003ci\u003eb\u003c/i\u003e be\r\npartly intercepted by the edge of a small slide, then\r\nthose spots in the lens as thus partly darkened will\r\nappear brighter whose light by its greater aberrations\r\nstill reaches the eye in spite of the intercepting slide,\r\nwhile those spots will appear darker which in consequence\r\nof aberration in the other direction throw their\r\nlight entirely upon the slide. This artifice of the intercepting\r\nslide which had previously been employed\r\nby Foucault for the investigation of the optical imperfections\r\nof mirrors enhances enormously the delicacy\r\nof the method, which is still further augmented by\r\nToepler\u0027s employment of a telescope behind the slide.\r\nToepler\u0027s method, accordingly, enjoys all the advantages\r\nof the Huygens and the Foucault procedure\r\ncombined. It is so delicate that the minutest irregularities\r\nin the air surrounding the lens can be rendered\r\ndistinctly visible, as I shall show by an example. I\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_315\" id=\"Page_315\"\u003e[Pg 315]\u003c/a\u003e\u003c/span\u003e\r\nplace a candle before the lens \u003ci\u003eL\u003c/i\u003e (Fig. 50) and so arrange\r\na second lens \u003ci\u003eM\u003c/i\u003e that the flame of the candle is\r\nimaged upon the screen \u003ci\u003eS\u003c/i\u003e. As soon as the intercepting\r\nslide is pushed into the focus, \u003ci\u003eb\u003c/i\u003e, of the light issuing\r\nfrom \u003ci\u003ea\u003c/i\u003e, you see the images of the changes of\r\ndensity and the images of the movements induced in\r\nthe air by the flame quite distinctly upon the screen.\r\nThe distinctness of the phenomenon as a whole depends\r\nupon the position of the intercepting slide \u003ci\u003eb\u003c/i\u003e.\r\nThe removal of \u003ci\u003eb\u003c/i\u003e increases the illumination but decreases\r\nthe distinctness. If the luminous source \u003ci\u003ea\u003c/i\u003e be\r\nremoved, we see the image of the candle flame only\r\nupon the screen \u003ci\u003eS\u003c/i\u003e. If we remove the flame and allow\r\n\u003ci\u003ea\u003c/i\u003e to continue shining, the screen \u003ci\u003eS\u003c/i\u003e will appear uniformly\r\nilluminated.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 700px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-325.jpg\" width=\"700\" height=\"265\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 50.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eAfter Toepler had sought long and in vain to render\r\nthe irregularities produced in air by sound-waves\r\nvisible by this principle, he was at last conducted to\r\nhis goal by the favorable circumstances attending the\r\nproduction of electric sparks. The waves generated\r\nin the air by electric sparks and accompanying the\r\nexplosive snapping of the same, are of sufficiently\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_316\" id=\"Page_316\"\u003e[Pg 316]\u003c/a\u003e\u003c/span\u003e\r\nshort period and sufficiently powerful to be rendered\r\nvisible by these methods. Thus we see how by a\r\ncareful regard for the merest and most shadowy indications\r\nof a phenomenon and by slight progressive\r\nand appropriate alterations of the circumstances and\r\nthe methods, ultimately the most astounding results\r\ncan be attained. Consider, for example, two such\r\nphenomena as the rubbing of amber and the electric\r\nlighting of modern streets. A person ignorant of the\r\nmyriad minute links that join these two things together,\r\nwill be absolutely nonplussed at their connexion,\r\nand will comprehend it no more than the ordinary\r\nobserver who is unacquainted with embryology, anatomy,\r\nand paleontology will understand the connexion\r\nbetween a saurian and a bird. The high value and\r\nsignificance of the co-operation of inquirers through\r\ncenturies, where each has but to take up the thread of\r\nwork of his predecessors and spin it onwards, is rendered\r\nforcibly evident by such examples. And such\r\nknowledge destroys, too, in the clearest manner imaginable\r\nthat impression of the marvellous which the\r\nspectator may receive from science, and at the same\r\ntime is a most salutary admonishment to the worker\r\nin science against superciliousness. I have also to\r\nadd the sobering remark that all our art would be in\r\nvain did not nature herself afford at least some slight\r\nguiding threads leading from a hidden phenomenon\r\ninto the domain of the observable. And so it need\r\nnot surprise us that once under particularly favorable\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_317\" id=\"Page_317\"\u003e[Pg 317]\u003c/a\u003e\u003c/span\u003e\r\ncircumstances an extremely powerful sound-wave\r\nwhich had been caused by the explosion of several\r\nhundred pounds of dynamite threw a directly visible\r\nshadow in the sunlight, as Boys has recently told us.\r\nIf the sound-waves were absolutely without influence\r\nupon the light, this could not have occurred, and all\r\nour artifices would then, too, be in vain. And so,\r\nsimilarly, the phenomenon accompanying projectiles\r\nwhich I am about to show you was once in a very imperfect\r\nmanner incidentally seen by a French artillerist,\r\nJournée, while that observer was simply following\r\nthe line of flight of a projectile with a telescope, just\r\nas also the undulations produced by candle flames are\r\nin a weak degree directly visible and in the bright sunlight\r\nare imaged in shadowy waves upon a uniform\r\nwhite background.\u003c/p\u003e\r\n\r\n\u003cp\u003e\u003ci\u003eInstantaneous illumination\u003c/i\u003e by the electric spark,\r\nthe method of rendering visible small optical differences\r\nor striæ, which may hence be called the \u003ci\u003estriate\u003c/i\u003e,\r\nor \u003ci\u003edifferential\u003c/i\u003e, method,\u003ca name=\"FNanchor_112_112\" id=\"FNanchor_112_112\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_112_112\" class=\"fnanchor\"\u003e[112]\u003c/a\u003e invented by Foucault and\r\nToepler, and finally the \u003ci\u003erecording\u003c/i\u003e of the image by a \u003ci\u003ephotographic\u003c/i\u003e\r\nplate,\u0026mdash;these therefore are the chief means\r\nwhich are to lead us to our goal.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_318\" id=\"Page_318\"\u003e[Pg 318]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eI instituted my first experiments in the summer of\r\n1884 with a target-pistol, shooting the bullet through\r\na striate field as described above, and taking care that\r\nthe projectile whilst in the field should disengage an\r\nilluminating electric spark from a Leyden jar or Franklin\u0027s\r\npane, which spark produced a photographic impression\r\nof the projectile upon a plate, especially arranged\r\nfor the purpose. I obtained the image of the\r\nprojectile at once and without difficulty. I also readily\r\nobtained, with the still rather defective dry plate which\r\nI was using, exceedingly delicate images of the sound-waves\r\n(spark-waves). But no atmospheric condensation\r\nproduced by the projectile was visible. I now\r\ndetermined the velocity of my projectile and found it\r\nto be only 240 metres per second, or considerably less\r\nthan the velocity of sound (which is 340 metres per\r\nsecond). I saw immediately that under such circumstances\r\nno noticeable compression of the air could be\r\nproduced, for any atmospheric compression must of\r\nnecessity travel forward at the same speed with sound\r\n(340 metres per second) and consequently would be\r\nalways ahead of and speeding away from the projectile.\u003c/p\u003e\r\n\r\n\u003cp\u003eI was so thoroughly convinced, however, of the\r\nexistence of the supposed phenomenon at a velocity\r\nexceeding 340 metres per second, that I requested\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_319\" id=\"Page_319\"\u003e[Pg 319]\u003c/a\u003e\u003c/span\u003e\r\nProfessor Salcher, of Fiume, an Austrian port on the\r\nGulf of Quarnero, to undertake the experiment with\r\nprojectiles travelling at a high rate of speed. In the\r\nsummer of 1886 Salcher in conjunction with Professor\r\nRiegler conducted in a spacious and suitable apartment\r\nplaced at their disposal by the Directors of the\r\nRoyal Imperial Naval Academy, experiments of the\r\nkind indicated and conforming in method exactly to\r\nthose which I had instituted, with the precise results\r\nexpected. The phenomenon, in fact, accorded perfectly\r\nwith the \u003ci\u003ea priori\u003c/i\u003e sketch of it which I had drafted\r\npreviously to the experiment. As the experimenting\r\nwas continued, new and unforeseen features made their\r\nappearance.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt would be unfair, of course, to expect from the\r\nvery first experiments faultless and highly distinct photographs.\r\nIt was sufficient that success was secured\r\nand that I had convinced myself that further labor\r\nand expenditure would not be vain. And on this\r\nscore I am greatly indebted to the two gentlemen\r\nabove mentioned.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe Austrian Naval Department subsequently\r\nplaced a cannon at Salcher\u0027s disposal in Pola, an\r\nAdriatic seaport, and I myself, together with my son,\r\nthen a student of medicine, having received and accepted\r\na courteous invitation from Krupp, repaired to\r\nMeppen, a town in Hanover, where we conducted\r\nwith only the necessary apparatus several experiments\r\non the open artillery range. All these experiments\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_320\" id=\"Page_320\"\u003e[Pg 320]\u003c/a\u003e\u003c/span\u003e\r\nfurnished tolerably good and complete pictures. Some\r\nlittle progress, too, was made. The outcome of our\r\nexperience on both artillery ranges, however, was the\r\nsettled conviction that really good results could be\r\nobtained only by the most careful conduct of the experiments\r\nin a laboratory especially adapted to the\r\npurpose. The expensiveness of the experiments on\r\na large scale was not the determining consideration\r\nhere, for the size of the projectile is indifferent. Given\r\nthe same velocity and the results are quite similar,\r\nwhether the projectiles are large or small. On the\r\nother hand, in a laboratory the experimenter has perfect\r\ncontrol over the initial velocity, which, provided\r\nthe proper equipment is at hand, can be altered at\r\nwill simply by altering the charge and the weight of\r\nthe projectile. The requisite experiments were accordingly\r\nconducted by me in my laboratory at Prague,\r\npartly in conjunction with my son and partly afterwards\r\nby him alone. The latter are the most perfect\r\nand I shall accordingly speak in detail here of\r\nthese only.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 600px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-331.jpg\" width=\"600\" height=\"341\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 51.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003ePicture to yourself an apparatus for detecting optical\r\nstriæ set up in a dark room. In order not to\r\nmake the description too complicated, I shall give the\r\nessential features only of the apparatus, leaving out\r\nof account altogether the minuter details which are\r\nrather of consequence for the technical performance\r\nof the experiment than for its understanding. We\r\nsuppose the projectile speeding on its path, accordingly,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_321\" id=\"Page_321\"\u003e[Pg 321]\u003c/a\u003e\u003c/span\u003e\r\nthrough the field of our differential optical apparatus.\r\nOn reaching the centre of the field (Fig. 51)\r\nthe projectile disengages an illuminating electric spark\r\n\u003ci\u003ea\u003c/i\u003e, and the image of the projectile, so produced, is photographically\r\nimpressed upon the plate of the camera\r\nbehind the intercepting slide \u003ci\u003eb\u003c/i\u003e. In the last and\r\nbest experiments the lens \u003ci\u003eL\u003c/i\u003e was replaced by a spherical\r\nsilvered-glass mirror made by K. Fritsch (formerly\r\nProkesch) of Vienna, whereby the apparatus was\r\nnaturally more complicated than it appears in our diagram.\r\nThe projectile having been carefully aimed\r\npasses in crossing the differential field between two\r\nvertical isolated wires which are connected with the\r\ntwo coatings of a Leyden jar, and completely filling\r\nthe space between the wires discharges the jar. In\r\nthe axis of the differential apparatus the circuit has a\r\nsecond gap \u003ci\u003ea\u003c/i\u003e which furnishes the illuminating spark,\r\nthe image of which falls on the intercepting slide \u003ci\u003eb\u003c/i\u003e.\r\nThe wires in the differential field having occasioned\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_322\" id=\"Page_322\"\u003e[Pg 322]\u003c/a\u003e\u003c/span\u003e\r\nmanifold disturbances were subsequently done away\r\nwith. In the new arrangement the projectile passes\r\nthrough a ring (see dotted line, Fig. 51), to the air in\r\nwhich it imparts a sharp impulse which travels forward\r\nin the tube \u003ci\u003er\u003c/i\u003e as a sound-wave having the approximate\r\nvelocity of 340 metres per second, topples\r\nover through the aperture of an electric screen the\r\nflame of a candle situated at the other opening of the\r\ntube, and so discharges the jar. The length of the\r\ntube \u003ci\u003er\u003c/i\u003e is so adjusted that the discharge occurs the\r\nmoment the projectile enters the centre of the now\r\nfully clear and free field of vision. We will also leave\r\nout of account the fact that to secure fully the success\r\nof the experiment, a large jar is first discharged\r\nby the flame, and that by the agency of this first discharge\r\nthe discharge of a second small jar having a\r\nspark of very short period which furnishes the spark\r\nreally illuminating the projectile is effected. Sparks\r\nfrom large jars have an appreciable duration, and\r\nowing to the great velocity of the projectiles furnish\r\nblurred photographs only. By carefully husbanding\r\nthe light of the differential apparatus, and owing to\r\nthe fact that much more light reaches the photographic\r\nplate in this way than would otherwise reach\r\nit, we can obtain beautiful, strong, and sharp photographs\r\nwith incredibly small sparks. The contours of\r\nthe pictures appear as very delicate and very sharp,\r\nclosely adjacent double lines. From their distance\r\nfrom one another, and from the velocity of the projectile,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_323\" id=\"Page_323\"\u003e[Pg 323]\u003c/a\u003e\u003c/span\u003e\r\nthe duration of the illumination, or of the spark,\r\nis found to be 1/800000 of a second. It is evident,\r\ntherefore, that experiments with mechanical snap\r\nslides can furnish no results worthy of the name.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 400px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-333.jpg\" width=\"400\" height=\"517\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 52.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eLet us consider now first the picture of a projectile\r\nin the rough, as represented in Figure 52, and\r\nthen let us examine it in its photographic form as seen\r\nin Figure 53. The latter picture is of a shot from an\r\nAustrian Mannlicher rifle. If I were not to tell you\r\nwhat the picture represented you would very likely\r\nimagine it to be a bird\u0027s eye view of a boat \u003ci\u003eb\u003c/i\u003e moving\r\nswiftly through the water. In front you see the bow-wave\r\nand behind the body a phenomenon \u003ci\u003ek\u003c/i\u003e which\r\nclosely resembles the eddies formed in the wake of a\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_324\" id=\"Page_324\"\u003e[Pg 324]\u003c/a\u003e\u003c/span\u003e\r\nship. And as a matter of fact the dark hyperboloid\r\narc which streams from the tip of the projectile really\r\nis a compressed wave of air exactly analogous to the\r\nbow-wave produced by a ship moving through the\r\nwater, with the exception that the wave of air is not\r\na surface-wave. The air-wave is produced in atmospheric\r\nspace and encompasses the projectile in the\r\nform of a shell on all sides. The wave is visible for\r\nthe same reason that the heated shell of air surrounding\r\nthe candle flame of our former experiments is visible.\r\nAnd the cylinder of friction-heated air which the\r\nprojectile throws off in the form of vortex rings really\r\ndoes answer to the water in the wake of a vessel.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-334.jpg\" width=\"300\" height=\"363\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 53. Photograph of a blunted projectile.]\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_325\" id=\"Page_325\"\u003e[Pg 325]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eNow just as a slowly moving boat produces no\r\nbow-wave, but the bow-wave is seen only when the\r\nboat moves with a speed which is greater than the\r\nvelocity of propagation of surface-waves in water, so,\r\nin like manner, no wave of compression is visible in\r\nfront of a projectile so long as the speed of the projectile\r\nis less than the velocity of sound. But if the\r\nspeed of the projectile reaches and exceeds the velocity\r\nof sound, then the head-wave, as we shall call it,\r\naugments noticeably in power, and is more and more\r\nextended, that is, the angle made by the contours of\r\nthe wave with the direction of flight is more and more\r\ndiminished, just as when the speed of a boat is increased\r\na similar phenomenon is noticed in connexion\r\nwith the bow-wave. In fact, we can from an instantaneous\r\nphotograph so taken approximately estimate\r\nthe speed with which the projectile is travelling.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe explanation of the bow-wave of a ship and\r\nthat of the head-wave of a body travelling in atmospheric\r\nspace both repose upon the same principle,\r\nlong ago employed by Huygens. Conceive a number\r\nof pebbles to be cast into a pond of water at regular\r\nintervals in such wise that all the spots struck are situate\r\nin the same straight line, and that every spot\r\nsubsequently struck lies a short space farther to the\r\nright. The spots first struck will furnish then the\r\nwave-circles which are widest, and all of them together\r\nwill, at the points where they are thickest,\r\nform a sort of cornucopia closely resembling the bow-wave.\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_326\" id=\"Page_326\"\u003e[Pg 326]\u003c/a\u003e\u003c/span\u003e\r\n(Fig. 54.) The resemblance is greater the\r\nsmaller the pebbles are, and the more quickly they\r\nsucceed each other. If a rod be dipped into the water\r\nand quickly carried along its surface, the falling of\r\nthe pebbles will then take place, so to speak, uninterruptedly,\r\nand we shall have a real bow-wave. If we\r\nput the compressed air-wave in the place of the surface-waves\r\nof the water, we shall have the head-wave\r\nof the projectile.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figcenter\" style=\"width: 600px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-336.jpg\" width=\"600\" height=\"265\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 54.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eYou may be disposed to say now, it is all very\r\npretty and interesting to observe a projectile in its\r\nflight, but of what practical use is it?\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is true, I reply, one cannot \u003ci\u003ewage war\u003c/i\u003e with photographed\r\nprojectiles. And I have likewise often had\r\nto say to medical students attending my lectures on\r\nphysics, when they inquired for the practical value of\r\nsome physical observation, \"You cannot, gentlemen,\r\ncure diseases with it.\" I had also once to give my\r\nopinion regarding how much physics should be taught\r\nat a school for millers, supposing the instruction\r\nthere to be confined \u003ci\u003eexactly\u003c/i\u003e to what was necessary for\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_327\" id=\"Page_327\"\u003e[Pg 327]\u003c/a\u003e\u003c/span\u003e\r\na miller. I was obliged to reply: \"A miller always\r\n\u003ci\u003eneeds\u003c/i\u003e exactly as much physics as he \u003ci\u003eknows\u003c/i\u003e.\" Knowledge\r\nwhich one does not possess one cannot use.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us forego entirely the consideration that as a\r\ngeneral thing every scientific advance, every new\r\nproblem elucidated, every extension or enrichment of\r\nour knowledge of facts, affords a better foundation for\r\npractical pursuits. Let us rather put the special\r\nquestion, Is it not possible to derive some really practical\r\nknowledge from our theoretical acquaintance\r\nwith the phenomena which take place in the space\r\nsurrounding a projectile?\u003c/p\u003e\r\n\r\n\u003cp\u003eNo physicist who has ever studied waves of sound\r\nor photographed them will have the least doubt regarding\r\nthe sound-wave character of the atmospheric\r\ncondensation encompassing the head of a flying projectile.\r\nWe have therefore, without ado, called this\r\ncondensation the head-wave.\u003c/p\u003e\r\n\r\n\u003cp\u003eKnowing this, it follows that the view of Melsens\r\naccording to which the projectile carries along with\r\nit masses of air which it forces into the bodies struck,\r\nis untenable. A forward-moving sound-wave is not a\r\nforward-moving mass of matter but a forward-moving\r\nform of motion, just as a water-wave or the waves of\r\na field of wheat are only forward-moving forms of motion\r\nand not movements of masses of water or masses\r\nof wheat.\u003c/p\u003e\r\n\r\n\u003cp\u003eBy interference-experiments, on which I cannot\r\ntouch here but which will be found roughly represented\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_328\" id=\"Page_328\"\u003e[Pg 328]\u003c/a\u003e\u003c/span\u003e\r\nin Figure 55, it was found that the bell-shaped\r\nhead-wave in question is an extremely thin shell and\r\nthat the condensations of the same are quite moderate,\r\nscarcely exceeding two-tenths of an atmosphere.\r\nThere can be no question, therefore, of explosive effects\r\nin the body struck by the projectile through so\r\nslight a degree of atmospheric compression. The\r\nphenomena attending wounds from rifle balls, for example,\r\nare not to be explained as Melsens and Busch\r\nexplain them, but are due, as Kocher and Reger maintain,\r\nto the effects of the impact of the projectile itself.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 400px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-338.jpg\" width=\"400\" height=\"394\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 55.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eA simple experiment will show how insignificant is\r\nthe part played by the friction of the air, or the supposed\r\nconveyance of the air along with the moving\r\nprojectile. If the photograph of the projectile be\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_329\" id=\"Page_329\"\u003e[Pg 329]\u003c/a\u003e\u003c/span\u003e\r\ntaken while passing through a flame, i. e., a visible\r\ngas, the flame will be seen to be, not torn and deformed,\r\nbut smoothly and cleanly perforated, like any\r\nsolid body. Within and around the flame the contours\r\nof the head-wave will be seen. The flickering,\r\nthe extinction of the flame, etc., take place only after\r\nthe projectile has travelled on a considerable distance\r\nin its path, and is then affected by the powder gases\r\nwhich hurry after the bullet or by the air preceding\r\nthe powder-gases.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe physicist who examines the head-wave and\r\nrecognises its sound-wave character also sees that the\r\nwave in question is of the same kind with the short\r\nsharp waves produced by electric sparks, that it is a\r\n\u003ci\u003enoise\u003c/i\u003e-wave. Hence, whenever any portion of the head-wave\r\nstrikes the ear it will be heard as a report. Appearances\r\npoint to the conclusion that the projectile\r\ncarries this report along with it. In addition to this\r\nreport, which advances with the velocity of the projectile\r\nand so usually travels at a speed greater than the\r\nvelocity of sound, there is also to be heard the report\r\nof the exploding powder which travels forward with\r\nthe ordinary velocity of sound. Hence two explosions\r\nwill be heard, each distinct in time. The circumstance\r\nthat this fact was long misconstrued by\r\npractical observers but when actually noticed frequently\r\nreceived grotesque explanations and that ultimately\r\nmy view was accepted as the correct one, appears\r\nto me in itself a sufficient justification that\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_330\" id=\"Page_330\"\u003e[Pg 330]\u003c/a\u003e\u003c/span\u003e\r\nresearches such as we are here speaking of are not utterly\r\nsuperfluous even in practical directions. That\r\nthe flashes and sounds of discharging artillery are\r\nused for estimating the distances of batteries is well\r\nknown, and it stands to reason that any unclear theoretical\r\nconception of the facts here involved will seriously\r\naffect the correctness of practical calculations.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt may appear astonishing to a person hearing it\r\nfor the first time, that a single shot has a double report\r\ndue to two different velocities of propagation.\r\nBut the reflexion that projectiles whose velocity is less\r\nthan the velocity of sound produce no head-waves (because\r\nevery impulse imparted to the air travels forward,\r\nthat is, ahead, with exactly the velocity of\r\nsound), throws full light when logically developed\r\nupon the peculiar circumstance above mentioned. If\r\nthe projectile moves faster than sound, the air ahead\r\nof it cannot recede from it quickly enough. The air\r\nis condensed and warmed, and thereupon, as all know,\r\nthe velocity of sound is augmented until the head-wave\r\ntravels forward as rapidly as the projectile itself, so\r\nthat there is no need whatever of any additional augmentation\r\nof the velocity of propagation. If such a\r\nwave were left entirely to itself, it would increase in\r\nlength and soon pass into an ordinary sound-wave,\r\ntravelling with less velocity. But the projectile is always\r\nbehind it and so maintains it at its proper density\r\nand velocity. Even if the projectile penetrates a\r\npiece of cardboard or a board of wood, which catches\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_331\" id=\"Page_331\"\u003e[Pg 331]\u003c/a\u003e\u003c/span\u003e\r\nand obstructs the head-wave, there will, as Figure 56\r\nshows, immediately appear at the emerging apex a\r\nnewly formed, not to say newly born, head-wave. We\r\nmay observe on the cardboard the reflexion and diffraction\r\nof the head-wave, and by means of a flame\r\nits refraction, so that no doubt as to its nature can remain.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 350px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-341.jpg\" width=\"350\" height=\"411\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 56.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003ePermit me, now, to illustrate the most essential of\r\nthe points that I have just adduced, by means of a few\r\nrough drawings taken from older and less perfect photographs.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the sketch of Figure 57 you see the projectile,\r\nwhich has just left the barrel of the rifle, touch a wire\r\nand disengage the illuminating spark. At the apex of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_332\" id=\"Page_332\"\u003e[Pg 332]\u003c/a\u003e\u003c/span\u003e\r\nthe projectile you already see the beginnings of a\r\npowerful head-wave, and in front of the wave a transparent\r\nfungiform cluster. This latter is the air which\r\nhas been forced out of the barrel by the projectile.\r\nCircular sound-waves, noise-waves, which are soon\r\novertaken by the projectile, also issue from the barrel.\r\nBut behind the projectile opaque puffs of powder-gas\r\nrush forth. It is scarcely necessary to add that many\r\nother questions in ballistics may be studied by this\r\nmethod, as, for example, the movement of the gun-carriage.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 450px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-342.jpg\" width=\"450\" height=\"354\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 57.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eA distinguished French artillerist, M. Gossot, has\r\napplied the views of the head-wave here given in quite\r\na different manner. The practice in measuring the\r\nvelocity of projectiles is to cause the projectile to pass\r\nthrough wire screens placed at different points in its\r\npath, and by the tearing of these screens to give rise\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_333\" id=\"Page_333\"\u003e[Pg 333]\u003c/a\u003e\u003c/span\u003e\r\nto electro-magnetic time-signals on falling slabs or\r\nrotating drums. Gossot caused these signals to be\r\nmade directly by the impact of the head-wave, did\r\naway thus with the wire screens, and carried the\r\nmethod so far as to be able to measure the velocities\r\nof projectiles travelling in high altitudes, where the\r\nuse of wire screens was quite out of the question.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe laws of the resistance of fluids and of air to\r\nbodies travelling in them form an extremely complicated\r\nproblem, which can be reasoned out very simply\r\nand prettily as a matter of pure philosophy but\r\npractice offers not a few difficulties. The same\r\nbody having the velocity 2, 3, 4 … displaces in the\r\nsame interval 2, 3, 4 … times the same mass of air,\r\nor the same mass of fluid, and imparts to it \u003ci\u003ein addition\u003c/i\u003e\r\n2, 3, 4 … times the same velocity. But for this,\r\nplainly, 4, 9, 16 … times the original force is required.\r\nHence, the resistance, it is said, increases\r\nwith the square of the velocity. This is all very pretty\r\nand simple and obvious. But practice and theory are\r\nat daggers\u0027 points here. Practice tells us that when\r\nwe increase the velocity, the law of the resistance\r\nchanges. For every portion of the velocity the law is\r\ndifferent.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe studies of the talented English naval architect,\r\nFroude, have thrown light upon this question.\r\nFroude has shown that the resistance is conditioned\r\nby a combination of the most multifarious phenomena.\r\nA ship in motion is subjected to the friction of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_334\" id=\"Page_334\"\u003e[Pg 334]\u003c/a\u003e\u003c/span\u003e\r\nthe water. It causes eddies and it generates in addition\r\nwaves which radiate outward from it. Every one\r\nof these phenomena are dependent upon the velocity\r\nin some different manner, and it is consequently not\r\nastonishing that the law of the resistance should be a\r\ncomplicated one.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe preceding observations suggest quite analogous\r\nreflexions for projectiles. Here also we have friction,\r\nthe formation of eddies, and the generation of\r\nwaves. Here, also, therefore, we should not be surprised\r\nat finding the law of the resistance of the air a\r\ncomplicated one, nor puzzled at learning that in actuality\r\nthe law of resistance changes as soon as the\r\nspeed of the projectile exceeds the velocity of sound,\r\nfor this is the precise point at which one important\r\nelement of the resistance, namely, the formation of\r\nwaves, first comes into play.\u003c/p\u003e\r\n\r\n\u003cp\u003eNo one doubts that a pointed bullet pierces the\r\nair with less resistance than a blunt bullet. The\r\nphotographs themselves show that the head-wave is\r\nweaker for a pointed projectile. It is not impossible,\r\nsimilarly, that forms of bullets will be invented which\r\ngenerate fewer eddies, etc., and that we shall study\r\nthese phenomena also by photography. I am of opinion\r\nfrom the few experiments which I have made in\r\nthis direction that not much more can be done by\r\nchanging the form of the projectile when the velocity\r\nis very great, but I have not gone into the question\r\nthoroughly. Researches of the kind we are considering\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_335\" id=\"Page_335\"\u003e[Pg 335]\u003c/a\u003e\u003c/span\u003e\r\ncan certainly not be detrimental to practical artillery,\r\nand it is no less certain that experiments by artillerists\r\non a large scale will be of undoubted benefit\r\nto physics.\u003c/p\u003e\r\n\r\n\u003cp\u003eNo one who has had the opportunity of studying\r\nmodern guns and projectiles in their marvellous perfection,\r\ntheir power and precision, can help confessing\r\nthat a high technical and scientific achievement has\r\nfound its incarnation in these objects. We may surrender\r\nourselves so completely to this impression as\r\nto forget for a moment the terrible purposes they\r\nserve.\u003c/p\u003e\r\n\r\n\u003cp\u003ePermit me, therefore, before we separate, to say a\r\nfew words on this glaring contrast. The greatest man\r\nof war and of silence which the present age has produced\r\nonce asserted that perpetual peace is a dream,\r\nand not a beautiful dream at that. We may accord\r\nto this profound student of mankind a judgment in\r\nthese matters and can also appreciate the soldier\u0027s\r\nhorror of stagnation from all too lengthy peace. But\r\nit requires a strong belief in the insuperableness of\r\nmediæval barbarism to hope for and to expect no\r\ngreat improvement in international relations. Think\r\nof our forefathers and of the times when club law\r\nruled supreme, when within the same country and the\r\nsame state brutal assaults and equally brutal self-defence\r\nwere universal and self-evident. This state\r\nof affairs grew so oppressive that finally a thousand\r\nand one circumstances compelled people to put an\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_336\" id=\"Page_336\"\u003e[Pg 336]\u003c/a\u003e\u003c/span\u003e\r\nend to it, and the cannon had most to say in accomplishing\r\nthe work. Yet the rule of club law was not\r\nabolished so quickly after all. It had simply passed\r\nto other clubs. We must not abandon ourselves to\r\ndreams of the Rousseau type. Questions of law will\r\nin a sense forever remain questions of might. Even\r\nin the United States where every one is as a matter\r\nof principle entitled to the same privileges, the ballot\r\naccording to Stallo\u0027s pertinent remark is but a milder\r\nsubstitute for the club. Nor need I tell you that\r\nmany of our own fellow-citizens are still enamored of\r\nthe old original methods. Very, very gradually, however,\r\nas civilisation progresses, the intercourse of men\r\ntakes on gentler forms, and no one who really knows\r\nthe good old times will ever honestly wish them back\r\nagain, however beautifully they may be painted and\r\nrhymed about.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn the intercourse of the nations, however, the old\r\nclub law still reigns supreme. But since its rule is\r\ntaxing the intellectual, the moral, and the material resources\r\nof the nations to the utmost and constitutes\r\nscarcely less a burden in peace than in war, scarcely\r\nless a yoke for the victor than for the vanquished, it\r\nmust necessarily grow more and more unendurable.\r\nReason, fortunately, is no longer the exclusive possession\r\nof those who modestly call themselves the\r\nupper ten thousand. Here, as everywhere, the evil\r\nitself will awaken the intellectual and ethical forces\r\nwhich are destined to mitigate it. Let the hate of\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_337\" id=\"Page_337\"\u003e[Pg 337]\u003c/a\u003e\u003c/span\u003e\r\nraces and of nationalities run riot as it may, the intercourse\r\nof nations will still increase and grow more intimate.\r\nBy the side of the problems which separate\r\nnations, the great and common ideals which claim the\r\nexclusive powers of the men of the future appear one\r\nafter another in greater distinctness and in greater\r\nmight.\u003c/p\u003e\u003chr class=\"chap\" /\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_338\" id=\"Page_338\"\u003e[Pg 338]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"ON_INSTRUCTION_IN_THE_CLASSICS\" id=\"ON_INSTRUCTION_IN_THE_CLASSICS\"\u003eON INSTRUCTION IN THE CLASSICS\r\nAND THE SCIENCES.\u003c/a\u003e\u003ca name=\"FNanchor_113_113\" id=\"FNanchor_113_113\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_113_113\" class=\"fnanchor\"\u003e[113]\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003ePerhaps the most fantastic proposition that Maupertuis,\u003ca name=\"FNanchor_114_114\" id=\"FNanchor_114_114\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_114_114\" class=\"fnanchor\"\u003e[114]\u003c/a\u003e\r\nthe renowned president of the Berlin\r\nAcademy, ever put forward for the approval of his\r\ncontemporaries was that of founding a city in which,\r\nto instruct and discipline young students, only Latin\r\nshould be spoken. Maupertuis\u0027s Latin city remained\r\nan idle wish. But for centuries Latin and Greek \u003ci\u003einstitutions\u003c/i\u003e\r\nexist in which our children spend a goodly\r\nportion of their days, and whose atmosphere constantly\r\nsurrounds them, even when without their walls.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_339\" id=\"Page_339\"\u003e[Pg 339]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003cp\u003eFor centuries instruction in the ancient languages\r\nhas been zealously cultivated. For centuries its necessity\r\nhas been alternately championed and contested.\r\nMore strongly than ever are authoritative voices now\r\nraised against the preponderance of instruction in the\r\nclassics and in favor of an education more suited to\r\nthe needs of the time, especially for a more generous\r\ntreatment of mathematics and the natural sciences.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn accepting your invitation to speak here on the\r\nrelative educational value of the classical and the\r\nmathematico-physical sciences in colleges and high\r\nschools, I find my justification in the duty and the\r\nnecessity laid upon every teacher of forming from his\r\nown experiences an opinion upon this important question,\r\nas partly also in the special circumstance that in\r\nmy youth I was personally under the influence of\r\nschool-life for only a short time, just previous to my\r\nentering the university, and had, therefore, ample opportunity\r\nto observe the effects of widely different\r\nmethods upon my own person.\u003c/p\u003e\r\n\r\n\u003cp\u003ePassing now, to a review of the arguments which\r\nthe advocates of instruction in the classics advance,\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_340\" id=\"Page_340\"\u003e[Pg 340]\u003c/a\u003e\u003c/span\u003e\r\nand of what the adherents of instruction in the physical\r\nsciences in their turn adduce, we find ourselves in\r\nrather a perplexing position with respect to the arguments\r\nof the first named. For these have been different\r\nat different times, and they are even now of a very\r\nmultifarious character, as must be where men advance,\r\nin favor of an institution that exists and which they are\r\ndetermined to retain at any cost, everything they can\r\npossibly think of. We shall find here much that has\r\nevidently been brought forward only to impress the\r\nminds of the ignorant; much, too, that was advanced\r\nin good faith and which is not wholly without foundation.\r\nWe shall get a fair idea of the reasoning employed\r\nby considering, first, the arguments that have grown\r\nout of the historical circumstances connected with the\r\noriginal introduction of the classics, and, lastly, those\r\nwhich were subsequently adduced as accidental afterthoughts.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_341\" id=\"Page_341\"\u003e[Pg 341]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_342\" id=\"Page_342\"\u003e[Pg 342]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_343\" id=\"Page_343\"\u003e[Pg 343]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_344\" id=\"Page_344\"\u003e[Pg 344]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_345\" id=\"Page_345\"\u003e[Pg 345]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_346\" id=\"Page_346\"\u003e[Pg 346]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_347\" id=\"Page_347\"\u003e[Pg 347]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eInstruction in Latin, as Paulsen\u003ca name=\"FNanchor_115_115\" id=\"FNanchor_115_115\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_115_115\" class=\"fnanchor\"\u003e[115]\u003c/a\u003e has minutely\r\nshown, was introduced by the Roman Church along\r\nwith Christianity. With the Latin language were also\r\ntransmitted the scant and meagre remnants of ancient\r\nscience. Whoever wished to acquire this ancient education,\r\nthen the only one worthy of the name, for him\r\nthe Latin language was the only and indispensable\r\nmeans; such a person had to learn Latin to rank\r\namong educated people.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe wide-spread influence of the Roman Church\r\nwrought many and various results. Among those for\r\nwhich all are glad, we may safely count the establishment\r\nof a sort of \u003ci\u003euniformity\u003c/i\u003e among the nations and of a\r\nregular international intercourse by means of the Latin\r\nlanguage, which did much to unite the nations in the\r\ncommon work of civilisation, carried on from the fifteenth\r\nto the eighteenth century. The Latin language\r\nwas thus long the language of scholars, and instruction\r\nin Latin the road to a liberal education\u0026mdash;a shibboleth\r\nstill employed, though long inappropriate.\u003c/p\u003e\r\n\r\n\u003cp\u003eFor scholars as a class, it is to be regretted, perhaps,\r\nthat Latin has ceased to be the medium of international\r\ncommunication. But the attributing of the\r\nloss of this function by the Latin language to its incapacity\r\nto accommodate itself to the numerous new\r\nideas and conceptions which have arisen in the course\r\nof the development of science is, in my opinion, wholly\r\nerroneous. It would be difficult to find a modern\r\nscientist who had enriched science with as many new\r\nideas as Newton has, yet Newton knew how to express\r\nthose ideas very correctly and precisely in the\r\nLatin language. If this view were correct, it would\r\nalso hold true of every living language. Originally\r\nevery language has to adapt itself to new ideas.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is far more likely that Latin was displaced as\r\nthe literary vehicle of science by the influence of the\r\nnobility. By their desire to enjoy the fruits of literature\r\nand science, through a less irksome medium than\r\nLatin, the nobility performed for the people at large\r\nan undeniable service. For the days were now past\r\nwhen acquaintance with the language and literature of\r\nscience was restricted to a caste, and in this step, perhaps,\r\nwas made the most important advance of modern\r\ntimes. To-day, when international intercourse is firmly\r\nestablished in spite of the many languages employed,\r\nno one would think of reintroducing Latin.\u003ca name=\"FNanchor_116_116\" id=\"FNanchor_116_116\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_116_116\" class=\"fnanchor\"\u003e[116]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eThe facility with which the ancient languages lend\r\nthemselves to the expression of new ideas is evidenced\r\nby the fact that the great majority of our scientific\r\nideas, as survivals of this period of Latin intercourse,\r\nbear Latin and Greek designations, while in great\r\nmeasure scientific ideas are even now invested with\r\nnames from these sources. But to deduce from the\r\nexistence and use of such terms the necessity of still\r\nlearning Latin and Greek on the part of all who employ\r\nthem is carrying the conclusion too far. All terms,\r\nappropriate and inappropriate,\u0026mdash;and there are a large\r\nnumber of inappropriate and monstrous combinations\r\nin science,\u0026mdash;rest on convention. The essential thing\r\nis, that people should associate with the sign the precise\r\nidea that is designated by it. It matters little\r\nwhether a person can correctly derive the words \u003ci\u003etelegraph\u003c/i\u003e,\r\n\u003ci\u003etangent\u003c/i\u003e, \u003ci\u003eellipse\u003c/i\u003e, \u003ci\u003eevolute\u003c/i\u003e, etc., if the correct idea\r\nis present in his mind when he uses them. On the\r\nother hand, no matter how well he may know their etymology,\r\nhis knowledge will be of little use to him if\r\nthe correct idea is absent. Ask the average and fairly\r\neducated classical scholar to translate a few lines for\r\nyou from Newton\u0027s \u003ci\u003ePrincipia\u003c/i\u003e, or from Huygens\u0027s \u003ci\u003eHorologium\u003c/i\u003e,\r\nand you will discover at once what an extremely\r\nsubordinate rôle the mere knowledge of language\r\nplays in such things. Without its associated\r\nthought a word remains a mere sound. The fashion of\r\nemploying Greek and Latin designations\u0026mdash;for it can\r\nbe termed nothing else\u0026mdash;has a natural root in history;\r\nit is impossible for the practice to disappear suddenly,\r\nbut it has fallen of late considerably into disuse. The\r\nterms \u003ci\u003egas\u003c/i\u003e, \u003ci\u003eohm\u003c/i\u003e, \u003ci\u003eAmpère\u003c/i\u003e, \u003ci\u003evolt\u003c/i\u003e, etc., are in international\r\nuse, but they are not Latin nor Greek. Only the person\r\nwho rates the unessential and accidental husk\r\nhigher than its contents, can speak of the necessity of\r\nlearning Latin or Greek for such reasons, to say nothing\r\nof spending eight or ten years on the task. Will\r\nnot a dictionary supply in a few seconds all the information\r\nwe wish on such subjects?\u003ca name=\"FNanchor_117_117\" id=\"FNanchor_117_117\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_117_117\" class=\"fnanchor\"\u003e[117]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is indisputable that our modern civilisation took\r\nup the threads of the ancient civilisation, that at\r\nmany points it begins where the latter left off, and\r\nthat centuries ago the remains of the ancient culture\r\nwere the only culture existing in Europe. Then, of\r\ncourse, a classical education really was the liberal education,\r\nthe higher education, the ideal education, for\r\nit was the \u003ci\u003esole\u003c/i\u003e education. But when the same claim\r\nis now raised in behalf of a classical education, it must\r\nbe uncompromisingly contested as bereft of all foundation.\r\nFor our civilisation has gradually attained\r\nits independence; it has lifted itself far above the ancient\r\ncivilisation, and has entered generally new directions\r\nof progress. Its note, its characteristic feature,\r\nis the enlightenment that has come from the great\r\nmathematical and physical researches of the last centuries,\r\nand which has permeated not only the practical\r\narts and industries but is also gradually finding\r\nits way into all fields of thought, including philosophy\r\nand history, sociology and linguistics. Those traces\r\nof ancient views that are still discoverable in philosophy,\r\nlaw, art, and science, operate more as hindrances\r\nthan helps, and will not long stand before the development\r\nof independent and more natural views.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt ill becomes classical scholars, therefore, to regard\r\nthemselves, at this day, as the educated class\r\n\u003ci\u003epar excellence\u003c/i\u003e, to condemn as uneducated all persons\r\nwho do not understand Latin and Greek, to complain\r\nthat with such people profitable conversations are not\r\nto be carried on, etc. The most delectable stories\r\nhave got into circulation, illustrative of the defective\r\neducation of scientists and engineers. A renowned\r\ninquirer, for example, is said to have once announced\r\nhis intention of holding a free course of university lectures,\r\nwith the word \"frustra\"; an engineer who spent\r\nhis leisure hours in collecting insects is said to have\r\ndeclared that he was studying \"etymology.\" It is\r\ntrue, incidents of this character make us shudder or\r\nsmile, according to our mood or temperament. But\r\nwe must admit, the next moment, that in giving way\r\nto such feelings we have merely succumbed to a childish\r\nprejudice. A lack of tact but certainly no lack of\r\neducation is displayed in the use of such half-understood\r\nexpressions. Every candid person will confess\r\nthat there are many branches of knowledge about which\r\nhe had better be silent. We shall not be so uncharitable\r\nas to turn the tables and discuss the impression\r\nthat classical scholars might make on a scientist or\r\nengineer, in speaking of science. Possibly many ludicrous\r\nstories might be told of them, and of far more\r\nserious import, which should fully compensate for the\r\nblunders of the other party.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe mutual severity of judgment which we have\r\nhere come upon, may also forcibly bring home to us\r\nhow really scarce a true liberal culture is. We may\r\ndetect in this mutual attitude, too, something of that\r\nnarrow, mediæval arrogance of caste, where a man\r\nbegan, according to the special point of view of the\r\nspeaker, with the scholar, the soldier, or the nobleman.\r\nLittle sense or appreciation is to be found in it for the\r\n\u003ci\u003ecommon\u003c/i\u003e task of humanity, little feeling for the need of\r\nmutual assistance in the great work of civilisation,\r\nlittle breadth of mind, little truly liberal culture.\u003c/p\u003e\r\n\r\n\u003cp\u003eA knowledge of Latin, and partly, also, a knowledge\r\nof Greek, is still a necessity for the members of\r\na few professions by nature more or less directly concerned\r\nwith the civilisations of antiquity, as for lawyers,\r\ntheologians, philologists, historians, and generally\r\nfor a small number of persons, among whom\r\nfrom time to time I count myself, who are compelled\r\nto seek for information in the Latin literature of the\r\ncenturies just past.\u003ca name=\"FNanchor_118_118\" id=\"FNanchor_118_118\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_118_118\" class=\"fnanchor\"\u003e[118]\u003c/a\u003e But that all young persons in\r\nsearch of a higher education should pursue for this\r\nreason Latin and Greek to such excess; that persons\r\nintending to become physicians and scientists should\r\ncome to the universities defectively educated, or even\r\nmiseducated; and that they should be compelled to\r\ncome only from schools that do \u003ci\u003enot\u003c/i\u003e supply them with\r\nthe proper preparatory knowledge is going a little bit\r\ntoo far.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_348\" id=\"Page_348\"\u003e[Pg 348]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_349\" id=\"Page_349\"\u003e[Pg 349]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_350\" id=\"Page_350\"\u003e[Pg 350]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_351\" id=\"Page_351\"\u003e[Pg 351]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_352\" id=\"Page_352\"\u003e[Pg 352]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eAfter the conditions which had given to the study\r\nof Latin and Greek their high import had ceased to\r\nexist, the traditional curriculum, naturally, was retained.\r\nThen, the different effects of this method of\r\neducation, good and bad, which no one had thought of\r\nat its introduction, were realised and noted. As natural,\r\ntoo, was it that those who had strong interests\r\nin the preservation of these studies, from knowing no\r\nothers or from living by them, or for still other reasons,\r\nshould emphasise the \u003ci\u003egood\u003c/i\u003e results of such instruction.\r\nThey pointed to the good effects as if they\r\nhad been consciously aimed at by the method and could\r\nbe attained only through its agency.\u003c/p\u003e\r\n\r\n\u003cp\u003eOne real benefit that students might derive from\r\na rightly conducted course in the classics would be\r\nthe opening up of the rich literary treasures of antiquity,\r\nand intimacy with the conceptions and views\r\nof the world held by two advanced nations. A person\r\nwho has read and understood the Greek and Roman\r\nauthors has felt and experienced more than one who is\r\nrestricted to the impressions of the present. He sees\r\nhow men placed in different circumstances judge quite\r\ndifferently of the same things from what we do to-day.\r\nHis own judgments will be rendered thus more independent.\r\nAgain, the Greek and Latin authors are indisputably\r\na rich fountain of recreation, of enlightenment,\r\nand of intellectual pleasure after the day\u0027s toil, and\r\nthe individual, not less than civilised humanity generally,\r\nwill remain grateful to them for all time. Who\r\ndoes not recall with pleasure the wanderings of Ulysses,\r\nwho does not listen joyfully to the simple narratives\r\nof Herodotus, who would ever repent of having\r\nmade the acquaintance of Plato\u0027s Dialogues, or of\r\nhaving tasted Lucian\u0027s divine humor? Who would\r\ngive up the glances he has obtained into the private\r\nlife of antiquity from Cicero\u0027s letters, from Plautus or\r\nTerence? To whom are not the portraits of Suetonius\r\nundying reminiscences? Who, in fact, would throw\r\naway \u003ci\u003eany\u003c/i\u003e knowledge he had once gained?\u003c/p\u003e\r\n\r\n\u003cp\u003eYet people who draw from these sources only, who\r\nknow only this culture, have surely no right to dogmatise\r\nabout the value of some other culture. As objects\r\nof research for individuals, this literature is extremely\r\nvaluable, but it is a different question whether\r\nit is equally valuable as the almost exclusive means of\r\neducation of our youth.\u003c/p\u003e\r\n\r\n\u003cp\u003eDo not other nations and other literatures exist\r\nfrom which we ought to learn? Is not nature herself\r\nour first school-mistress? Are our highest models always\r\nto be the Greeks, with their narrow provinciality\r\nof mind, that divided the world into \"Greeks and barbarians,\"\r\nwith their superstitions, with their eternal\r\nquestioning of oracles? Aristotle with his incapacity\r\nto learn from facts, with his word-science; Plato with\r\nhis heavy, interminable dialogues, with his barren, at\r\ntimes childish, dialectics\u0026mdash;are they unsurpassable?\u003ca name=\"FNanchor_119_119\" id=\"FNanchor_119_119\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_119_119\" class=\"fnanchor\"\u003e[119]\u003c/a\u003e\r\nThe Romans with their apathy, their pompous externality,\r\nset off by fulsome and bombastic phrases, with\r\ntheir narrow-minded, philistine philosophy, with their\r\nfrenzied sensuality, with their cruel and bestial indulgence\r\nin animal and man baiting, with their outrageous\r\nmaltreatment and plundering of their subjects\u0026mdash;are\r\nthey patterns worthy of imitation? Or shall, perhaps,\r\nour science edify itself with the works of Pliny who\r\ncites midwives as authorities and himself stands on\r\ntheir point of view?\u003c/p\u003e\r\n\r\n\u003cp\u003eBesides, if an acquaintance with the ancient world\r\nreally were attained, we might come to some settlement\r\nwith the advocates of classical education. But it\r\nis words and forms, and forms and words only, that\r\nare supplied to our youth; and even collateral subjects\r\nare forced into the strait-jacket of the same\r\nrigid method and made a science of words, sheer feats\r\nof mechanical memory. Really, we feel ourselves set\r\nback a thousand years into the dull cloister-cells of the\r\nMiddle Ages.\u003c/p\u003e\r\n\r\n\u003cp\u003eThis must be changed. It is possible to get acquainted\r\nwith the views of the Greeks and Romans by\r\na shorter road than the intellect deadening process\r\nof eight or ten years of declining, conjugating, analysing,\r\nand extemporisation. There are to-day plenty of\r\neducated persons who have acquired through good\r\ntranslations vivider, clearer, and more just views of\r\nclassical antiquity than the graduates of our gymnasiums\r\nand colleges.\u003ca name=\"FNanchor_120_120\" id=\"FNanchor_120_120\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_120_120\" class=\"fnanchor\"\u003e[120]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eFor us moderns, the Greeks and the Romans are\r\nsimply two objects of archæological and historical research\r\nlike all others. If we put them before our\r\nyouth in fresh and living pictures, and not merely in\r\nwords and syllables, the effect will be assured. We\r\nderive a totally different enjoyment from the Greeks\r\nwhen we approach them after a study of the results\r\nof modern research in the history of civilisation. We\r\nread many a chapter of Herodotus differently when we\r\nattack his works equipped with a knowledge of natural\r\nscience, and with information about the stone age and\r\nthe lake-dwellers. What our classical institutions \u003ci\u003epretend\u003c/i\u003e\r\nto give can and actually will be given to our youth\r\nwith much more fruitful results by competent \u003ci\u003ehistorical\u003c/i\u003e\r\ninstruction, which must supply, not names and numbers\r\nalone, nor the mere history of dynasties and wars,\r\nbut be in every sense of the word a true history of\r\ncivilisation.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe view still widely prevails that although all\r\n\"higher, ideal culture,\" all extension of our view of\r\nthe world, is acquired by philological and in a lesser\r\ndegree by historical studies, still the mathematics and\r\nnatural sciences should not be neglected on account\r\nof their usefulness. This is an opinion to which I must\r\nrefuse my assent. It were strange if man could learn\r\nmore, could draw more intellectual nourishment, from\r\nthe shards of a few old broken jugs, from inscribed\r\nstones, or yellow parchments, than from all the rest\r\nof nature. True, man is man\u0027s first concern, but he\r\nis not his sole concern.\u003c/p\u003e\r\n\r\n\u003cp\u003eIn ceasing to regard man as the centre of the world;\r\nin discovering that the earth is a top whirled about\r\nthe sun, which speeds off with it into infinite space;\r\nin finding that in the fixed stars the same elements\r\nexist as on earth; in meeting everywhere the same\r\nprocesses of which the life of man is merely a vanishingly\r\nsmall part\u0026mdash;in such things, too, is a widening of\r\nour view of the world, and edification, and poetry.\r\nThere are here perhaps grander and more significant\r\nfacts than the bellowing of the wounded Ares, or the\r\ncharming island of Calypso, or the ocean-stream engirdling\r\nthe earth. He only should speak of the relative\r\nvalue of these two domains of thought, of their\r\npoetry, who knows both.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe \"utility\" of physical science is, in a measure,\r\nonly a \u003ci\u003ecollateral\u003c/i\u003e product of that flight of the intellect\r\nwhich produced science. No one, however, should\r\nunderrate the utility of science who has shared in the\r\nrealisation by modern industrial art of the Oriental\r\nworld of fables, much less one upon whom those treasures\r\nhave been poured, as it were, from the fourth dimension,\r\nwithout his aid or understanding.\u003c/p\u003e\r\n\r\n\u003cp\u003eNor may we believe that science is useful only to\r\nthe practical man. Its influence permeates all our affairs,\r\nour whole life; everywhere its ideas are decisive.\r\nHow differently does the jurist, the legislator, or the\r\npolitical economist think, who knows, for example,\r\nthat a square mile of the most fertile soil can support\r\nwith the solar heat annually consumed only a definite\r\nnumber of human beings, which no art or science can\r\nincrease. Many economical theories, which open new\r\nair-paths of progress, air-paths in the literal sense of\r\nthe word, would be made impossible by such knowledge.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_353\" id=\"Page_353\"\u003e[Pg 353]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_354\" id=\"Page_354\"\u003e[Pg 354]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eThe eulogists of classical education love to emphasise\r\nthe cultivation of taste which comes from employment\r\nwith the ancient models. I candidly confess\r\nthat there is something absolutely revolting in this to\r\nme. To form the taste, then, our youths must sacrifice\r\nten years of their life! Luxury takes precedence over\r\nnecessity. Have the future generations, in the face\r\nof the difficult problems, the great social questions,\r\nwhich they must meet, and that with strengthened\r\nmind and heart, no more important duties to fulfil than\r\nthese?\u003c/p\u003e\r\n\r\n\u003cp\u003eBut let us assume that this end were desirable.\r\nCan taste be formed by rules and precepts? Do not\r\nideals of beauty change? Is it not a stupendous absurdity\r\nto force one\u0027s self artificially to admire things\r\nwhich, with all their historical interest, with all their\r\nbeauty in individual points, are for the most part\r\nforeign to the rest of our thoughts and feelings, provided\r\nwe have such of \u003ci\u003eour own\u003c/i\u003e. A nation that is\r\ntruly such, has its own taste and will not go to others\r\nfor it. And every individual perfect man has his own\r\ntaste.\u003ca name=\"FNanchor_121_121\" id=\"FNanchor_121_121\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_121_121\" class=\"fnanchor\"\u003e[121]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eAnd what, after all, does this cultivation of taste\r\nconsist in? In the acquisition of the personal literary\r\nstyle of a few select authors! What should we think\r\nof a people that would force its youth a thousand\r\nyears from now, by years of practice, to master the\r\ntortuous or bombastic style of some successful lawyer\r\nor politician of to-day? Should we not justly accuse\r\nthem of a woful lack of taste?\u003c/p\u003e\r\n\r\n\u003cp\u003eThe evil effects of this imagined cultivation of the\r\ntaste find expression often enough. The young \u003ci\u003esavant\u003c/i\u003e\r\nwho regards the composition of a scientific essay as a\r\nrhetorical exercise instead of a simple and unadorned\r\npresentation of the facts and the truth, still sits unconsciously\r\non the school-bench, and still unwittingly represents\r\nthe point of view of the Romans, by whom the\r\nelaboration of speeches was regarded as a serious scientific (!)\r\nemployment.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_355\" id=\"Page_355\"\u003e[Pg 355]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_356\" id=\"Page_356\"\u003e[Pg 356]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_357\" id=\"Page_357\"\u003e[Pg 357]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eFar be it from me to underrate the value of the development\r\nof the instinct of speech and of the increased\r\ncomprehension of our own language which comes from\r\nphilological studies. By the study of a foreign language,\r\nespecially of one which differs widely from ours,\r\nthe signs and forms of words are first clearly distinguished\r\nfrom the thoughts which they express. Words\r\nof the closest possible correspondence in different languages\r\nnever coincide absolutely with the ideas they\r\nstand for, but place in relief slightly different aspects\r\nof the same thing, and by the study of language the\r\nattention is directed to these shades of difference. But\r\nit would be far from admissible to contend that the\r\nstudy of Latin and Greek is the most fruitful and natural,\r\nlet alone the \u003ci\u003eonly\u003c/i\u003e, means of attaining this end.\r\nAny one who will give himself the pleasure of a few\r\nhours\u0027 companionship with a Chinese grammar; who\r\nwill seek to make clear to himself the mode of speech\r\nand thought of a people who never advanced as far as\r\nthe analysis of articulate sounds, but stopped at the\r\nanalysis of syllables, to whom our alphabetical characters,\r\ntherefore, are an inexplicable puzzle, and who\r\nexpress all their rich and profound thoughts by means\r\nof a few syllables with variable emphasis and position,\u0026mdash;such\r\na person, perhaps, will acquire new, and extremely\r\nelucidative ideas upon the relation of language\r\nand thought. But should our children, therefore,\r\nstudy Chinese? Certainly not. No more, then,\r\nshould they be burdened with Latin, at least in the\r\nmeasure they are.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is a beautiful achievement to reproduce a Latin\r\nthought in a modern language with the maximum fidelity\r\nof meaning and expression\u0026mdash;for the \u003ci\u003etranslator\u003c/i\u003e.\r\nMoreover, we shall be very grateful to the translator\r\nfor his performance. But to demand this feat of every\r\neducated man, without consideration of the sacrifice of\r\ntime and labor which it entails, is unreasonable. And\r\nfor this very reason, as classical teachers admit, that\r\nideal is never perfectly attained, except in rare cases\r\nwith scholars possessed of special talents and great\r\nindustry. Without slurring, therefore, the high importance\r\nof the study of the ancient languages as a\r\nprofession, we may yet feel sure that the instinct for\r\nspeech which is part of every liberal education can,\r\nand must, be acquired in a different way. Should we,\r\nindeed, be forever lost if the Greeks had not lived before\r\nus?\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fact is, we must carry our demands further\r\nthan the representatives of classical philology. We\r\nmust ask of every educated man a fair scientific conception\r\nof the nature and value of language, of the\r\nformation of language, of the alteration of the meaning\r\nof roots, of the degeneration of fixed forms of\r\nspeech to grammatical forms, in brief, of all the main\r\nresults of modern comparative philology. We should\r\njudge that this were attainable by a careful study of\r\nour mother tongue and of the languages next allied to\r\nit, and subsequently of the more ancient tongues from\r\nwhich the former are derived. If any one object that\r\nthis is too difficult and entails too much labor, I should\r\nadvise such a person to place side by side an English,\r\na Dutch, a Danish, a Swedish, and a German Bible, and\r\nto compare a few lines of them; he will be amazed at\r\nthe multitude of suggestions that offer themselves.\u003ca name=\"FNanchor_122_122\" id=\"FNanchor_122_122\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_122_122\" class=\"fnanchor\"\u003e[122]\u003c/a\u003e\r\nIn fact, I believe that a really progressive, fruitful, rational,\r\nand instructive study of languages can be conducted\r\nonly on this plan. Many of my audience will\r\nremember, perhaps, the bright and encouraging effect,\r\nlike that of a ray of sunlight on a gloomy day, which\r\nthe meagre and furtive remarks on comparative philology\r\nin Curtius\u0027s Greek grammar wrought in that\r\nbarren and lifeless desert of verbal quibbles.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_358\" id=\"Page_358\"\u003e[Pg 358]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_359\" id=\"Page_359\"\u003e[Pg 359]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eThe principal result obtained by the present method\r\nof studying the ancient languages is that which comes\r\nfrom the student\u0027s employment with their complicated\r\ngrammars. It consists in the sharpening of the attention\r\nand in the exercise of the judgment by the practice\r\nof subsuming special cases under general rules,\r\nand of distinguishing between different cases. Obviously,\r\nthe same result can be reached by many other\r\nmethods; for example, by difficult games of cards.\r\nEvery science, the mathematics and the physical sciences\r\nincluded, accomplish as much, if not more, in\r\nthis disciplining of the judgment. In addition, the\r\nmatter treated by those sciences has a much higher intrinsic\r\ninterest for young people, and so engages spontaneously\r\ntheir attention; while on the other hand they\r\nare elucidative and useful in other directions in which\r\ngrammar can accomplish nothing.\u003c/p\u003e\r\n\r\n\u003cp\u003eWho cares, so far as the matter of it is concerned,\r\nwhether we say \u003ci\u003ehominum\u003c/i\u003e or \u003ci\u003ehominorum\u003c/i\u003e in the genitive\r\nplural, interesting as the fact may be for the philologist?\r\nAnd who would dispute that the intellectual\r\nneed of causal insight is awakened not by grammar\r\nbut by the natural sciences?\u003c/p\u003e\r\n\r\n\u003cp\u003eIt is not our intention, therefore, to gainsay in the\r\nleast the good influence which the study of Latin and\r\nGreek grammar \u003ci\u003ealso\u003c/i\u003e exercises on the sharpening of the\r\njudgment. In so far as the study of words as such\r\nmust greatly promote lucidity and accuracy of expression,\r\nin so far as Latin and Greek are not yet\r\nwholly indispensable to many branches of knowledge,\r\nwe willingly concede to them a place in our schools,\r\nbut would demand that the disproportionate amount of\r\ntime allotted to them, wrongly withdrawn from other\r\nuseful studies, should be considerably curtailed. That\r\nin the end Latin and Greek will not be employed as\r\nthe universal means of education, we are fully convinced.\r\nThey will be relegated to the closet of the\r\nscholar or professional philologist, and gradually make\r\nway for the modern languages and the modern science\r\nof language.\u003c/p\u003e\r\n\r\n\u003cp\u003eLong ago Locke reduced to their proper limits the\r\nexaggerated notions which obtained of the close connexion\r\nof thought and speech, of logic and grammar,\r\nand recent investigators have established on still surer\r\nfoundations his views. How little a complicated grammar\r\nis necessary for expressing delicate shades of\r\nthought is demonstrated by the Italians and French,\r\nwho, although they have almost totally discarded the\r\ngrammatical redundancies of the Romans, are yet not\r\nsurpassed by the latter in accuracy of thought, and\r\nwhose poetical, but especially whose scientific literature,\r\nas no one will dispute, can bear favorable comparison\r\nwith the Roman.\u003c/p\u003e\r\n\r\n\u003cp\u003eReviewing again the arguments advanced in favor\r\nof the study of the ancient languages, we are obliged\r\nto say that in the main and as applied to the present,\r\nthey are wholly devoid of force. In so far as the\r\naims which this study theoretically pursues are still\r\nworthy of attainment, they appear to us as altogether\r\ntoo narrow, and are surpassed in this only by the\r\nmeans employed. As almost the sole, indisputable result\r\nof this study we must count the increase of the\r\nstudent\u0027s skill and precision in expression. One inclined\r\nto be uncharitable might say that our gymnasiums\r\nand classical academies turn out men who can\r\nspeak and write, but, unfortunately, have little to write\r\nor speak about. Of that broad, liberal view, of that\r\nfamed universal culture, which the classical curriculum\r\nis supposed to yield, serious words need not be lost.\r\nThis culture might, perhaps, more properly be termed\r\nthe contracted or lopsided culture.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_360\" id=\"Page_360\"\u003e[Pg 360]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_361\" id=\"Page_361\"\u003e[Pg 361]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_362\" id=\"Page_362\"\u003e[Pg 362]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_363\" id=\"Page_363\"\u003e[Pg 363]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_364\" id=\"Page_364\"\u003e[Pg 364]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_365\" id=\"Page_365\"\u003e[Pg 365]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_366\" id=\"Page_366\"\u003e[Pg 366]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_367\" id=\"Page_367\"\u003e[Pg 367]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_368\" id=\"Page_368\"\u003e[Pg 368]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_369\" id=\"Page_369\"\u003e[Pg 369]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_370\" id=\"Page_370\"\u003e[Pg 370]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_371\" id=\"Page_371\"\u003e[Pg 371]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eWhile considering the study of languages we threw\r\na few side glances at mathematics and the natural sciences.\r\nLet us now inquire whether these, as branches\r\nof study, cannot accomplish much that is to be attained\r\nin no other way. I shall meet with no contradiction\r\nwhen I say that without at least an elementary mathematical\r\nand scientific education a man remains a total\r\nstranger in the world in which he lives, a stranger in\r\nthe civilisation of the time that bears him. Whatever\r\nhe meets in nature, or in the industrial world, either\r\ndoes not appeal to him at all, from his having neither\r\neye nor ear for it, or it speaks to him in a totally unintelligible\r\nlanguage.\u003c/p\u003e\r\n\r\n\u003cp\u003eA real understanding of the world and its civilisation,\r\nhowever, is not the only result of the study of\r\nmathematics and the physical sciences. Much more\r\nessential for the preparatory school is the \u003ci\u003eformal\u003c/i\u003e cultivation\r\nwhich comes from these studies, the strengthening\r\nof the reason and the judgment, the exercise\r\nof the imagination. Mathematics, physics, chemistry,\r\nand the so-called descriptive sciences are so much\r\nalike in this respect, that, apart from a few points, we\r\nneed not separate them in our discussion.\u003c/p\u003e\r\n\r\n\u003cp\u003eLogical sequence and continuity of ideas, so necessary\r\nfor fruitful thought, are \u003ci\u003epar excellence\u003c/i\u003e the results of\r\nmathematics; the ability to follow facts with thoughts,\r\nthat is, to observe or collect experiences, is chiefly developed\r\nby the natural sciences. Whether we notice\r\nthat the sides and the angles of a triangle are connected\r\nin a definite way, that an equilateral triangle possesses\r\ncertain definite properties of symmetry, or whether we\r\nnotice the deflexion of a magnetic needle by an electric\r\ncurrent, the dissolution of zinc in diluted sulphuric\r\nacid, whether we remark that the wings of a butterfly\r\nare slightly colored on the under, and the fore-wings\r\nof the moth on the upper, surface: indiscriminately\r\nhere we proceed from \u003ci\u003eobservations\u003c/i\u003e, from individual\r\nacts of immediate intuitive knowledge. The field of\r\nobservation is more restricted and lies closer at hand\r\nin mathematics; it is more varied and broader but\r\nmore difficult to compass in the natural sciences. The\r\nessential thing, however, is for the student to learn to\r\nmake observations in all these fields. The philosophical\r\nquestion whether our acts of knowledge in mathematics\r\nare of a special kind is here of no importance\r\nfor us. It is true, of course, that the observation can\r\nbe practised by languages also. But no one, surely,\r\nwill deny, that the concrete, living pictures presented\r\nin the fields just mentioned possess different\r\nand more powerful attractions for the mind of the\r\nyouth than the abstract and hazy figures which language\r\noffers, and on which the attention is certainly not\r\nso spontaneously bestowed, nor with such good results.\u003ca name=\"FNanchor_123_123\" id=\"FNanchor_123_123\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_123_123\" class=\"fnanchor\"\u003e[123]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eObservation having revealed the different properties\r\nof a given geometrical or physical object, it is discovered\r\nthat in many cases these properties \u003ci\u003edepend\u003c/i\u003e in\r\nsome way upon one another. This interdependence\r\nof properties (say that of equal sides and equal angles\r\nat the base of a triangle, the relation of pressure to\r\nmotion,) is nowhere so distinctly marked, nowhere is\r\nthe necessity and permanency of the interdependence\r\nso plainly noticeable, as in the fields mentioned.\r\nHence the continuity and logical consequence of the\r\nideas which we acquire in those fields. The relative\r\nsimplicity and perspicuity of geometrical and physical\r\nrelations supply here the conditions of natural and\r\neasy progress. Relations of equal simplicity are not\r\nmet with in the fields which the study of language\r\nopens up. Many of you, doubtless, have often wondered\r\nat the little respect for the notions of cause and\r\neffect and their connexion that is sometimes found\r\namong professed representatives of the classical studies.\r\nThe explanation is probably to be sought in the\r\nfact that the analogous relation of motive and action\r\nfamiliar to them from their studies, presents nothing\r\nlike the clear simplicity and determinateness that the\r\nrelation of cause and effect does.\u003c/p\u003e\r\n\r\n\u003cp\u003eThat perfect mental grasp of all possible cases,\r\nthat economical order and organic union of the thoughts\r\nwhich comes from it, which has grown for every one\r\nwho has ever tasted it a permanent need which he\r\nseeks to satisfy in every new province, can be developed\r\nonly by employment with the relative simplicity of\r\nmathematical and scientific investigations.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhen a set of facts comes into apparent conflict\r\nwith another set of facts, and a problem is presented,\r\nits solution consists ordinarily in a more refined distinction\r\nor in a more extended view of the facts, as\r\nmay be aptly illustrated by Newton\u0027s solution of the\r\nproblem of dispersion. When a new mathematical or\r\nscientific fact is \u003ci\u003edemonstrated\u003c/i\u003e, or \u003ci\u003eexplained\u003c/i\u003e, such demonstration\r\nalso rests simply upon showing the connexion\r\nof the new fact with the facts already known; for\r\nexample, that the radius of a circle can be laid off as\r\nchord exactly six times in the circle is explained or\r\nproved by dividing the regular hexagon inscribed in\r\nthe circle into equilateral triangles. That the quantity\r\nof heat developed in a second in a wire conveying an\r\nelectric current is quadrupled on the doubling of the\r\nstrength of the current, we explain from the doubling of\r\nthe fall of the potential due to the doubling of the\r\ncurrent\u0027s intensity, as also from the doubling of the\r\nquantity flowing through, in a word, from the quadrupling\r\nof the work done. In point of principle, explanation\r\nand direct proof do not differ much.\u003c/p\u003e\r\n\r\n\u003cp\u003eHe who solves scientifically a geometrical, physical,\r\nor technical problem, easily remarks that his\r\nprocedure is a \u003ci\u003emethodical\u003c/i\u003e mental quest, rendered possible\r\nby the economical order of the province\u0026mdash;a simplified\r\npurposeful quest as contrasted with unmethodical,\r\nunscientific guess-work. The geometer, for example,\r\nwho has to construct a circle touching two given\r\nstraight lines, casts his eye over the relations of symmetry\r\nof the desired construction, and seeks the centre\r\nof his circle solely in the line of symmetry of the two\r\nstraight lines. The person who wants a triangle of\r\nwhich two angles and the sum of the sides are given,\r\ngrasps in his mind the determinateness of the form of\r\nthis triangle and restricts his search for it to a certain\r\ngroup of triangles of the \u003ci\u003esame form\u003c/i\u003e. Under very different\r\ncircumstances, therefore, the simplicity, the intellectual\r\nperviousness, of the subject-matter of mathematics\r\nand natural science is felt, and promotes both\r\nthe discipline and the self-confidence of the reason.\u003c/p\u003e\r\n\r\n\u003cp\u003eUnquestionably, much more will be attained by instruction\r\nin the mathematics and the natural sciences\r\nthan now is, when more natural methods are adopted.\r\nOne point of importance here is that young students\r\nshould not be spoiled by premature abstraction, but\r\nshould be made acquainted with their material from\r\nliving pictures of it before they are made to work with\r\nit by purely ratiocinative methods. A good stock of\r\ngeometrical experience could be obtained, for example,\r\nfrom geometrical drawing and from the practical\r\nconstruction of models. In the place of the unfruitful\r\nmethod of Euclid, which is only fit for special, restricted\r\nuses, a broader and more conscious method\r\nmust be adopted, as Hankel has pointed out.\u003ca name=\"FNanchor_124_124\" id=\"FNanchor_124_124\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_124_124\" class=\"fnanchor\"\u003e[124]\u003c/a\u003e Then,\r\nif, on reviewing geometry, and after it presents no\r\nsubstantial difficulties, the more general points of view,\r\nthe principles of scientific method are placed in relief\r\nand brought to consciousness, as Von Nagel,\u003ca name=\"FNanchor_125_125\" id=\"FNanchor_125_125\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_125_125\" class=\"fnanchor\"\u003e[125]\u003c/a\u003e J. K.\r\nBecker,\u003ca name=\"FNanchor_126_126\" id=\"FNanchor_126_126\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_126_126\" class=\"fnanchor\"\u003e[126]\u003c/a\u003e Mann,\u003ca name=\"FNanchor_127_127\" id=\"FNanchor_127_127\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_127_127\" class=\"fnanchor\"\u003e[127]\u003c/a\u003e and others have well done, fruitful\r\nresults will be surely attained. In the same way,\r\nthe subject-matter of the natural sciences should be\r\nmade familiar by pictures and experiment before a\r\nprofounder and reasoned grasp of these subjects is\r\nattempted. Here the emphasis of the more general\r\npoints of view is to be postponed.\u003c/p\u003e\r\n\r\n\u003cp\u003eBefore my present audience it would be superfluous\r\nfor me to contend further that mathematics and natural\r\nscience are justified constituents of a sound education,\u0026mdash;a\r\nclaim that even philologists, after some\r\nresistance, have conceded. Here I may count upon\r\nassent when I say that mathematics and the natural\r\nsciences pursued alone as means of instruction yield a\r\nricher education in matter and form, a more general\r\neducation, an education better adapted to the needs\r\nand spirit of the time,\u0026mdash;than the philological branches\r\npursued alone would yield.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut how shall this idea be realised in the curricula\r\nof our intermediate educational institutions? It is unquestionable\r\nin my mind that the German \u003ci\u003eRealschulen\u003c/i\u003e\r\nand \u003ci\u003eRealgymnasien\u003c/i\u003e, where the exclusive classical course\r\nis for the most part replaced by mathematics, science,\r\nand modern languages, give the \u003ci\u003eaverage\u003c/i\u003e man a more\r\ntimely education than the gymnasium proper, although\r\nthey are not yet regarded as fit preparatory schools for\r\nfuture theologians and professional philologists. The\r\nGerman gymnasiums are too one-sided. With these\r\nthe first changes are to be made; of these alone we\r\nshall speak here. Possibly a \u003ci\u003esingle\u003c/i\u003e preparatory school,\r\nsuitably planned, might serve all purposes.\u003c/p\u003e\r\n\r\n\u003cp\u003eShall we, then, in our gymnasiums fill out the hours\r\nof study which stand at our disposal, or are still to be\r\nwrested from the classicists, with as great and as varied\r\na quantity of mathematical and scientific matter\r\nas possible? Expect no such proposition from me.\r\nNo one will suggest such a course who has himself\r\nbeen actively engaged in scientific thought. Thoughts\r\ncan be awakened and fructified as a field is fructified\r\nby sunshine and rain. But thoughts cannot be juggled\r\nout and worried out by heaping up materials and\r\nthe hours of instruction, nor by any sort of precepts:\r\nthey must grow naturally of their own free accord.\r\nFurthermore, thoughts cannot be accumulated beyond\r\na certain limit in a single head, any more than the produce\r\nof a field can be increased beyond certain limits.\u003c/p\u003e\r\n\r\n\u003cp\u003eI believe that the amount of matter necessary for a\r\nuseful education, such as should be offered to \u003ci\u003eall\u003c/i\u003e the\r\npupils of a preparatory school, is very small. If I had\r\nthe requisite influence, I should, in all composure, and\r\nfully convinced that I was doing what was best, first\r\ngreatly curtail in the lower classes the amount of matter\r\nin both the classical and the scientific courses; I\r\nshould cut down considerably the number of the school\r\nhours and the work done outside the school. I am\r\nnot with many teachers of opinion that ten hours work\r\na day for a child is not too much. I am convinced\r\nthat the mature men who offer this advice so lightly\r\nare themselves unable to give their attention successfully\r\nfor as long a time to any subject that is new to\r\nthem, (for example, to elementary mathematics or\r\nphysics,) and I would ask every one who thinks the\r\ncontrary to make the experiment upon himself. Learning\r\nand teaching are not routine office-work that can\r\nbe kept up mechanically for long periods. But even\r\nsuch work tires in the end. If our young men are\r\nnot to enter the universities with blunted and impoverished\r\nminds, if they are not to leave in the preparatory\r\nschools their vital energy, which they should\r\nthere gather, great changes must be made. Waiving\r\nthe injurious effects of overwork upon the body, the\r\nconsequences of it for the mind seem to me positively\r\ndreadful.\u003c/p\u003e\r\n\r\n\u003cp\u003eI know of nothing more terrible than the poor creatures\r\nwho have learned too much. Instead of that\r\nsound powerful judgment which would probably have\r\ngrown up if they had learned nothing, their thoughts\r\ncreep timidly and hypnotically after words, principles,\r\nand formulæ, constantly by the same paths. What\r\nthey have acquired is a spider\u0027s web of thoughts too\r\nweak to furnish sure supports, but complicated enough\r\nto produce confusion.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut how shall better methods of mathematical and\r\nscientific education be combined with the decrease of\r\nthe subject-matter of instruction? I think, by abandoning\r\nsystematic instruction altogether, at least in so\r\nfar as that is required of \u003ci\u003eall\u003c/i\u003e young pupils. I see no\r\nnecessity whatever that the graduates of our high\r\nschools and preparatory schools should be little philologists,\r\nand at the same time little mathematicians,\r\nphysicists, and botanists; in fact, I do not see the possibility\r\nof such a result. I see in the endeavor to attain\r\nthis result, in which every instructor seeks for his\r\nown branch a place apart from the others, the main\r\nmistake of our whole system. I should be satisfied if\r\nevery young student could come into living contact\r\nwith and pursue to their ultimate logical consequences\r\nmerely a \u003ci\u003efew\u003c/i\u003e mathematical or scientific discoveries.\r\nSuch instruction would be mainly and naturally associated\r\nwith selections from the great scientific classics.\r\nA few powerful and lucid ideas could thus be made\r\nto take root in the mind and receive thorough elaboration.\r\nThis accomplished, our youth would make a\r\ndifferent showing from what they do to-day.\u003ca name=\"FNanchor_128_128\" id=\"FNanchor_128_128\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_128_128\" class=\"fnanchor\"\u003e[128]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eWhat need is there, for example, of burdening the\r\nhead of a young student with all the details of botany?\r\nThe student who has botanised under the guidance of\r\na teacher finds on all hands, not indifferent things, but\r\nknown or unknown things, by which he is stimulated,\r\nand his gain made permanent. I express here, not my\r\nown, but the opinion of a friend, a practical teacher.\r\nAgain, it is not at all necessary that all the matter that\r\nis offered in the schools should be learned. The best\r\nthat we have learned, that which has remained with\r\nus for life, outlived the test of examination. How can\r\nthe mind thrive when matter is heaped on matter, and\r\nnew materials piled constantly on old, undigested materials?\r\nThe question here is not so much that of the\r\naccumulation of positive knowledge as of intellectual\r\ndiscipline. It seems also unnecessary that \u003ci\u003eall\u003c/i\u003e branches\r\nshould be treated at school, and that exactly the same\r\nstudies should be pursued in all schools. A single\r\nphilological, a single historical, a single mathematical,\r\na single scientific branch, pursued as common subjects\r\nof instruction for all pupils, are sufficient to accomplish\r\nall that is necessary for the intellectual development.\r\nOn the other hand, a wholesome mutual stimulus\r\nwould be produced by this greater variety in the\r\npositive culture of men. Uniforms are excellent for\r\nsoldiers, but they will not fit heads. Charles V. learned\r\nthis, and it should never be forgotten. On the contrary,\r\nteachers and pupils both need considerable latitude, if\r\nthey are to yield good results.\u003c/p\u003e\r\n\r\n\u003cp\u003eWith John Karl Becker I am of the opinion that\r\nthe utility and amount for individuals of every study\r\nshould be precisely determined. All that exceeds this\r\namount should be unconditionally banished from the\r\nlower classes. With respect to mathematics, Becker,\u003ca name=\"FNanchor_129_129\" id=\"FNanchor_129_129\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_129_129\" class=\"fnanchor\"\u003e[129]\u003c/a\u003e\r\nin my judgment, has admirably solved this question.\u003c/p\u003e\r\n\r\n\u003cp\u003eWith respect to the upper classes the demand assumes\r\na different form. Here also the amount of matter\r\nobligatory on all pupils ought not to exceed a certain\r\nlimit. But in the great mass of knowledge that a\r\nyoung man must acquire to-day for his profession it is\r\nno longer just that ten years of his youth should be\r\nwasted with mere preludes. The upper classes should\r\nsupply a truly useful preparation for the professions,\r\nand should not be modelled upon the wants merely of\r\nfuture lawyers, ministers, and philologists. Again, it\r\nwould be both foolish and impossible to attempt to\r\nprepare the same person properly for all the different\r\nprofessions. In such case the function of the schools\r\nwould be, as Lichtenberg feared, simply to select the\r\npersons best fitted for being drilled, whilst precisely the\r\nfinest special talents, which do not submit to indiscriminate\r\ndiscipline, would be excluded from the contest.\r\nHence, a certain amount of liberty in the choice\r\nof studies must be introduced in the upper classes, by\r\nmeans of which it will be free for every one who is clear\r\nabout the choice of his profession to devote his chief\r\nattention either to the study of the philologico-historical\r\nor to that of the mathematico-scientific branches.\r\nThen the matter now treated could be retained, and in\r\nsome branches, perhaps, judiciously extended,\u003ca name=\"FNanchor_130_130\" id=\"FNanchor_130_130\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_130_130\" class=\"fnanchor\"\u003e[130]\u003c/a\u003e without\r\nburdening the scholar with many branches or increasing\r\nthe number of the hours of study. With more\r\nhomogeneous work the student\u0027s capacity for work increases,\r\none part of his labor supporting the other\r\ninstead of obstructing it. If, however, a young man\r\nshould subsequently choose a different profession, then\r\nit is \u003ci\u003ehis\u003c/i\u003e business to make up what he has lost. No\r\nharm certainly will come to society from this change,\r\nnor could it be regarded as a misfortune if philologists\r\nand lawyers with mathematical educations or physical\r\nscientists with classical educations should now and\r\nthen appear.\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_372\" id=\"Page_372\"\u003e[Pg 372]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_373\" id=\"Page_373\"\u003e[Pg 373]\u003c/a\u003e\u003c/span\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_374\" id=\"Page_374\"\u003e[Pg 374]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_375\" id=\"Page_375\"\u003e[Pg 375]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp\u003eThe view is now wide-spread that a Latin and\r\nGreek education no longer meets the general wants of\r\nthe times, that a more opportune, a more \"liberal\"\r\neducation exists. The phrase, \"a liberal education,\"\r\nhas been greatly misused. A truly liberal education is\r\nunquestionably very rare. The \u003ci\u003eschools\u003c/i\u003e can hardly offer\r\nsuch; at best they can only bring home to the student\r\nthe necessity of it. It is, then, his business to acquire,\r\nas best he can, a more or less liberal education. It\r\nwould be very difficult, too, at any one time to give a\r\ndefinition of a \"liberal\" education which would satisfy\r\nevery one, still more difficult to give one which would\r\nhold good for a hundred years. The educational\r\nideal, in fact, varies much. To one, a knowledge of\r\nclassical antiquity appears not too dearly bought \"with\r\nearly death.\" We have no objection to this person,\r\nor to those who think like him, pursuing their ideal\r\nafter their own fashion. But we may certainly protest\r\nstrongly against the realisation of such ideals on our\r\nown children. Another,\u0026mdash;Plato, for example,\u0026mdash;puts\r\nmen ignorant of geometry on a level with animals.\u003ca name=\"FNanchor_131_131\" id=\"FNanchor_131_131\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_131_131\" class=\"fnanchor\"\u003e[131]\u003c/a\u003e\r\nIf such narrow views had the magical powers of the\r\nsorceress Circe, many a man who perhaps justly\r\nthought himself well educated would become conscious\r\nof a not very flattering transformation of himself.\r\nLet us seek, therefore, in our educational system\r\nto meet the wants of the present, and not establish\r\nprejudices for the future.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut how does it come, we must ask, that institutions\r\nso antiquated as the German gymnasiums could\r\nsubsist so long in opposition to public opinion? The\r\nanswer is simple. The schools were first organised by\r\nthe Church; since the Reformation they have been in\r\nthe hands of the State. On so large a scale, the plan\r\npresents many advantages. Means can be placed at\r\nthe disposal of education such as no private source, at\r\nleast in Europe, could furnish. Work can be conducted\r\nupon the same plan in many schools, and so\r\nexperiments made of extensive scope which would be\r\notherwise impossible. A single man with influence\r\nand ideas can under such circumstances do great\r\nthings for the promotion of education.\u003c/p\u003e\r\n\r\n\u003cp\u003eBut the matter has also its reverse aspect. The\r\nparty in power works for its own interests, uses the\r\nschools for its special purposes. Educational competition\r\nis excluded, for all successful attempts at improvement\r\nare impossible unless undertaken or permitted\r\nby the State. By the uniformity of the people\u0027s\r\neducation, a prejudice once in vogue is permanently\r\nestablished. The highest intelligences, the strongest\r\nwills cannot overthrow it suddenly. In fact, as everything\r\nis adapted to the view in question, a sudden\r\nchange would be physically impossible. The two\r\nclasses which virtually hold the reins of power in the\r\nState, the jurists and theologians, know only the one-sided,\r\npredominantly classical culture which they have\r\nacquired in the State schools, and would have this culture\r\nalone valued. Others accept this opinion from\r\ncredulity; others, underestimating their true worth for\r\nsociety, bow before the power of the prevalent opinion;\r\nothers, again, affect the opinion of the ruling\r\nclasses even against their better judgment, so as to\r\nabide on the same plane of respect with the latter. I\r\nwill make no charges, but I must confess that the deportment\r\nof medical men with respect to the question\r\nof the qualification of graduates of your \u003ci\u003eRealschulen\u003c/i\u003e\r\nhas frequently made that impression upon me. Let\r\nus remember, finally, that an influential statesman,\r\neven within the boundaries which the law and public\r\nopinion set him, can do serious harm to the cause\r\nof education by considering his own one-sided views\r\ninfallible, and in enforcing them recklessly and inconsiderately\u0026mdash;which\r\nnot only \u003ci\u003ecan\u003c/i\u003e happen, but has, repeatedly,\r\nhappened.\u003ca name=\"FNanchor_132_132\" id=\"FNanchor_132_132\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_132_132\" class=\"fnanchor\"\u003e[132]\u003c/a\u003e The monopoly of education by\r\nthe State\u003ca name=\"FNanchor_133_133\" id=\"FNanchor_133_133\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_133_133\" class=\"fnanchor\"\u003e[133]\u003c/a\u003e thus assumes in our eyes a somewhat different\r\naspect. And to revert to the question above asked,\r\nthere is not the slightest doubt that the German gymnasiums\r\nin their present form would have ceased to\r\nexist long ago if the State had not supported them.\u003c/p\u003e\r\n\r\n\u003cp\u003eAll this must be changed. But the change will\r\nnot be made of itself, nor without our energetic interference,\r\nand it will be made slowly. But the path is\r\nmarked out for us, the will of the people must acquire\r\nand exert upon our school legislation a greater and\r\nmore powerful influence. Furthermore, the questions\r\nat issue must be publicly and candidly discussed that\r\nthe views of the people may be clarified. All who feel\r\nthe insufficiency of the existing \u003ci\u003erégime\u003c/i\u003e must combine\r\ninto a powerful organisation that their views may\r\nacquire impressiveness and the opinions of the individual\r\nnot die away unheard.\u003c/p\u003e\r\n\r\n\u003cp\u003eI recently read, gentlemen, in an excellent book of\r\ntravels, that the Chinese speak with unwillingness of\r\npolitics. Conversations of this sort are usually cut\r\nshort with the remark that they may bother about such\r\nthings whose business it is and who are paid for it.\r\nNow it seems to me that it is not only the business of\r\nthe State, but a very serious concern of all of us, how\r\nour children shall be educated in the public schools\r\nat \u003ci\u003eour\u003c/i\u003e cost.\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"APPENDIX\" id=\"APPENDIX\"\u003eAPPENDIX.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\u003cp class=\"center\"\u003eI.\u003c/p\u003e\r\n\r\n\u003ch3\u003e\u003ca id=\"A_CONTRIBUTION_TO_THE_HISTORY_OF_ACOUSTICS\"\u003e\u003c/a\u003eA CONTRIBUTION TO THE HISTORY OF ACOUSTICS.\u003ca name=\"FNanchor_134_134\" id=\"FNanchor_134_134\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_134_134\" class=\"fnanchor\"\u003e[134]\u003c/a\u003e\u003c/h3\u003e\r\n\r\n\r\n\u003cp\u003eWhile searching for papers by Amontons, several\r\nvolumes of the Memoirs of the Paris Academy\r\nfor the first years of the eighteenth century, fell\r\ninto my hands. It is difficult to portray the delight\r\nwhich one experiences in running over the leaves of\r\nthese volumes. One sees as an actual spectator almost\r\nthe rise of the most important discoveries and witnesses\r\nthe progress of many fields of knowledge from\r\nalmost total ignorance to relatively perfect clearness.\u003c/p\u003e\r\n\r\n\u003cp\u003eI propose to discuss here the fundamental researches\r\nof Sauveur in Acoustics. It is astonishing\r\nhow extraordinarily near Sauveur was to the view\r\nwhich Helmholtz was the first to adopt in its full extent\r\na hundred and fifty years later.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe \u003ci\u003eHistoire de l\u0027Académie\u003c/i\u003e for 1700, p. 131, tells\r\nus that Sauveur had succeeded in making music an\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_376\" id=\"Page_376\"\u003e[Pg 376]\u003c/a\u003e\u003c/span\u003e\r\nobject of scientific research, and that he had invested\r\nthe new science with the name of \"acoustics.\" On\r\nfive successive pages a number of discoveries are recorded\r\nwhich are more fully discussed in the volume\r\nfor the year following.\u003c/p\u003e\r\n\r\n\u003cp\u003eSauveur regards the \u003ci\u003esimplicity\u003c/i\u003e of the ratios obtaining\r\nbetween the rates of vibration of consonances as\r\nsomething universally known.\u003ca name=\"FNanchor_135_135\" id=\"FNanchor_135_135\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_135_135\" class=\"fnanchor\"\u003e[135]\u003c/a\u003e He is in hope, by\r\nfurther research, of determining the chief rules of musical\r\ncomposition and of fathoming the \"metaphysics\r\nof the agreeable,\" the main law of which he asserts\r\nto be the union of \"simplicity with multiplicity.\"\r\nPrecisely as Euler\u003ca name=\"FNanchor_136_136\" id=\"FNanchor_136_136\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_136_136\" class=\"fnanchor\"\u003e[136]\u003c/a\u003e did a number of years later, he\r\nregards a consonance as more perfect according as\r\nthe ratio of its vibrational rates is expressed in smaller\r\nwhole numbers, because the smaller these whole numbers\r\nare the oftener the vibrations of the two tones\r\ncoincide, and hence the more readily they are apprehended.\r\nAs the limit of consonance, he takes the\r\nratio 5:6, although he does not conceal the fact that\r\npractice, sharpened attention, habit, taste, and even\r\nprejudice play collateral rôles in the matter, and that\r\nconsequently the question is not a purely scientific\r\none.\u003c/p\u003e\r\n\r\n\u003cp\u003eSauveur\u0027s ideas took their development from his\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_377\" id=\"Page_377\"\u003e[Pg 377]\u003c/a\u003e\u003c/span\u003e\r\nhaving instituted at all points more exact quantitative\r\ninvestigations than his predecessors. He is first desirous\r\nof determining as the foundation of musical\r\ntuning a fixed note of one hundred vibrations which\r\ncan be reproduced at any time; the fixing of the notes\r\nof musical instruments by the common tuning pipes\r\nthen in use with rates of vibration unknown, appearing\r\nto him inadequate. According to Mersenne (\u003ci\u003eHarmonie\r\nUniverselle\u003c/i\u003e, 1636), a given cord seventeen feet\r\nlong and weighted with eight pounds executes eight\r\nvisible vibrations in a second. By diminishing its\r\nlength then in a given proportion we obtain a proportionately\r\naugmented rate of vibration. But this procedure\r\nappears too uncertain to Sauveur, and he employs\r\nfor his purpose the beats (\u003ci\u003ebattemens\u003c/i\u003e), which were\r\nknown to the organ-makers of his day, and which he\r\ncorrectly explains as due to the alternate coincidence\r\nand non-coincidence of the same vibrational phases of\r\ndifferently pitched notes.\u003ca name=\"FNanchor_137_137\" id=\"FNanchor_137_137\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_137_137\" class=\"fnanchor\"\u003e[137]\u003c/a\u003e At every coincidence there\r\nis a swelling of the sound, and hence the number of\r\nbeats per second will be equal to the difference of the\r\nrates of vibration. If we tune two of three organ-pipes\r\nto the remaining one in the ratio of the minor and major\r\nthird, the mutual ratio of the rates of vibration of\r\nthe first two will be as 24: 25, that is to say, for every\r\n24 vibrations to the lower note there will be 25 to the\r\nhigher, and one beat. If the two pipes give together\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_378\" id=\"Page_378\"\u003e[Pg 378]\u003c/a\u003e\u003c/span\u003e\r\nfour beats in a second, then the higher has the fixed\r\ntone of 100 vibrations. The open pipe in question\r\nwill consequently be five feet in length. We also determine\r\nby this procedure the absolute rates of vibration\r\nof all the other notes.\u003c/p\u003e\r\n\r\n\u003cp\u003eIt follows at once that a pipe eight times as long\r\nor 40 feet in length will yield a vibrational rate of\r\n12-1/2, which Sauveur ascribes to the lowest audible\r\ntone, and further also that a pipe 64 times as small\r\nwill execute 6,400 vibrations, which Sauveur took for\r\nthe highest audible limit. The author\u0027s delight at his\r\nsuccessful enumeration of the \"imperceptible vibrations\"\r\nis unmistakably asserted here, and it is justified\r\nwhen we reflect that to-day even Sauveur\u0027s principle,\r\nslightly modified, constitutes the simplest and most\r\ndelicate means we have for exactly determining rates\r\nof vibration. Far more important still, however, is a\r\nsecond observation which Sauveur made while studying\r\nbeats, and to which we shall revert later.\u003c/p\u003e\r\n\r\n\u003cp\u003eStrings whose lengths can be altered by movable\r\nbridges are much easier to handle than pipes in such\r\ninvestigations, and it was natural that Sauveur should\r\nsoon resort to their use.\u003c/p\u003e\r\n\r\n\u003cp\u003eOne of his bridges accidentally not having been\r\nbrought into full and hard contact with the string,\r\nand consequently only imperfectly impeding the vibrations,\r\nSauveur discovered the harmonic overtones of\r\nthe string, at first by the unaided ear, and concluded\r\nfrom this fact that the string was divided into aliquot\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_379\" id=\"Page_379\"\u003e[Pg 379]\u003c/a\u003e\u003c/span\u003e\r\nparts. The string when plucked, and when the bridge\r\nstood at the third division for example, yielded the\r\ntwelfth of its fundamental note. At the suggestion\r\nof some academician\u003ca name=\"FNanchor_138_138\" id=\"FNanchor_138_138\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_138_138\" class=\"fnanchor\"\u003e[138]\u003c/a\u003e probably, variously colored\r\npaper riders were placed at the nodes (\u003ci\u003enoeuds\u003c/i\u003e) and\r\nventral segments (\u003ci\u003eventres\u003c/i\u003e), and the division of the\r\nstring due to the excitation of the overtones (\u003ci\u003esons\r\nharmoniques\u003c/i\u003e) belonging to its fundamental note (\u003ci\u003eson\r\nfondamental\u003c/i\u003e) thus rendered visible. For the clumsy\r\nbridge the more convenient feather or brush was soon\r\nsubstituted.\r\n.\r\nWhile engaged in these investigations Sauveur also\r\nobserved the sympathetic vibration of a string induced\r\nby the excitation of a second one in unison with it.\r\nHe also discovered that the overtone of a string can\r\nrespond to another string tuned to its note. He even\r\nwent further and discovered that on exciting one string\r\nthe overtone which it has in common with another,\r\ndifferently pitched string can be produced on that\r\nother; for example, on strings having for their vibrational\r\nratio 3:4, the fourth of the lower and the third\r\nof the higher may be made to respond. It follows indisputably\r\nfrom this that the excited string yields\r\novertones simultaneously with its fundamental tone.\r\nPreviously to this Sauveur\u0027s attention had been drawn\r\nby other observers to the fact that the overtones of\r\nmusical instruments can be picked out by attentive\r\nlistening, particularly in the night.\u003ca name=\"FNanchor_139_139\" id=\"FNanchor_139_139\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_139_139\" class=\"fnanchor\"\u003e[139]\u003c/a\u003e He himself mentions\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_380\" id=\"Page_380\"\u003e[Pg 380]\u003c/a\u003e\u003c/span\u003e\r\nthe simultaneous sounding of the overtones and\r\nthe fundamental tone.\u003ca name=\"FNanchor_140_140\" id=\"FNanchor_140_140\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_140_140\" class=\"fnanchor\"\u003e[140]\u003c/a\u003e That he did not give the\r\nproper consideration to this circumstance was, as will\r\nafterwards be seen, fatal to his theory.\u003c/p\u003e\r\n\r\n\u003cp\u003eWhile studying beats Sauveur makes the remark\r\nthat they are \u003ci\u003edispleasing\u003c/i\u003e to the ear. He held the beats\r\nwere distinctly audible only when less than six occurred\r\nin a second. Larger numbers were not distinctly\r\nperceptible and gave rise accordingly to no\r\ndisturbance. He then attempts to reduce the difference\r\nbetween consonance and dissonance to a question\r\nof beats. Let us hear his own words.\u003ca name=\"FNanchor_141_141\" id=\"FNanchor_141_141\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_141_141\" class=\"fnanchor\"\u003e[141]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"Beats are unpleasing to the ear because of the unevenness\r\nof the sound, and it may be held with much plausibility that the\r\nreason why octaves are so pleasing is that we never hear their\r\nbeats.\u003ca name=\"FNanchor_142_142\" id=\"FNanchor_142_142\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_142_142\" class=\"fnanchor\"\u003e[142]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\"In following out this idea, we find that the chords whose\r\nbeats we cannot hear are precisely those which the musicians call\r\nconsonances and that those whose beats are heard are the dissonances,\r\nand that when a chord is a dissonance in one octave and a\r\nconsonance in another, it beats in the one and does not beat in the\r\nother. Consequently it is called an imperfect consonance. It is\r\nvery easy by the principles of M. Sauveur, here established, to ascertain\r\nwhat chords beat and in what octaves, above or below the\r\nfixed note. If this hypothesis be correct, it will disclose the true\r\nsource of the rules of composition, hitherto unknown to science,\r\nand given over almost entirely to judgment by the ear. These\r\nsorts of natural judgment, marvellous though they may sometimes\r\nappear, are not so but have very real causes, the knowledge of\r\nwhich belongs to science, provided it can gain possession thereof.\"\u003ca name=\"FNanchor_143_143\" id=\"FNanchor_143_143\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_143_143\" class=\"fnanchor\"\u003e[143]\u003c/a\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_381\" id=\"Page_381\"\u003e[Pg 381]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003eSauveur thus correctly discerns in beats the cause\r\nof the disturbance of consonance, to which all disharmony\r\nis \"probably\" to be referred. It will be seen,\r\nhowever, that according to his view all distant intervals\r\nmust necessarily be consonances and all near intervals\r\ndissonances. He also overlooks the absolute\r\ndifference in point of principle between his old view,\r\nmentioned at the outset, and his new view, rather attempting\r\nto obliterate it.\u003c/p\u003e\r\n\r\n\u003cp\u003eR. Smith\u003ca name=\"FNanchor_144_144\" id=\"FNanchor_144_144\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_144_144\" class=\"fnanchor\"\u003e[144]\u003c/a\u003e takes note of the theory of Sauveur and\r\ncalls attention to the first of the above-mentioned defects.\r\nBeing himself essentially involved in the old\r\nview of Sauveur, which is usually attributed to Euler,\r\nhe yet approaches in his criticism a brief step nearer\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_382\" id=\"Page_382\"\u003e[Pg 382]\u003c/a\u003e\u003c/span\u003e\r\nto the modern theory, as appears from the following\r\npassage.\u003ca name=\"FNanchor_145_145\" id=\"FNanchor_145_145\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_145_145\" class=\"fnanchor\"\u003e[145]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\"The truth is, this gentleman confounds the distinction between\r\nperfect and imperfect consonances, by comparing imperfect\r\nconsonances which beat because the succession of their short cycles\u003ca name=\"FNanchor_146_146\" id=\"FNanchor_146_146\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_146_146\" class=\"fnanchor\"\u003e[146]\u003c/a\u003e\r\nis periodically confused and interrupted, with perfect ones\r\nwhich cannot beat, because the succession of their short cycles is\r\nnever confused nor interrupted.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The \u003ci\u003efluttering roughness\u003c/i\u003e above mentioned is perceivable\r\nin all other perfect consonances, in a smaller degree in proportion\r\nas their cycles are shorter and simpler, and their pitch is higher;\r\nand is of a \u003ci\u003edifferent kind\u003c/i\u003e from the \u003ci\u003esmoother beats\u003c/i\u003e and undulations\r\nof \u003ci\u003etempered consonances\u003c/i\u003e; because we can alter the rate of\r\nthe latter by altering the temperament, but not of the former, the\r\nconsonance being perfect at a given pitch: And because a judicious\r\near can often hear, at the same time, both the flutterings and the\r\nbeats of a tempered consonance; sufficiently distinct from each\r\nother.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"For nothing gives greater offence to the hearer, though ignorant\r\nof the cause of it, than those rapid, piercing beats of high\r\nand loud sounds, which make imperfect consonances with one another.\r\nAnd yet a few slow beats, like the slow undulations of a\r\nclose shake now and then introduced, are far from being disagreeable.\"\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eSmith is accordingly clear that other \"roughnesses\"\r\nexist besides the beats which Sauveur considered,\r\nand if the investigations had been continued\r\non the basis of Sauveur\u0027s idea, these additional roughnesses\r\nwould have turned out to be the beats of the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_383\" id=\"Page_383\"\u003e[Pg 383]\u003c/a\u003e\u003c/span\u003e\r\novertones, and the theory thus have attained the\r\npoint of view of Helmholtz.\u003c/p\u003e\r\n\r\n\u003cp\u003eReviewing the differences between Sauveur\u0027s and\r\nHelmholtz\u0027s theories, we find the following:\u003c/p\u003e\r\n\r\n\u003cp\u003e1. The theory according to which consonance depends\r\non the frequent and regular coincidence of vibrations\r\nand their ease of enumeration, appears from\r\nthe new point of view inadmissible. The simplicity\r\nof the ratios obtaining between the rates of vibration\r\nis indeed a \u003ci\u003emathematical\u003c/i\u003e characteristic of consonance\r\nas well as a \u003ci\u003ephysical\u003c/i\u003e condition thereof, for the reason\r\nthat the coincidence of the overtones as also their\r\nfurther physical and physiological consequences is\r\nconnected with this fact. But no \u003ci\u003ephysiological\u003c/i\u003e or \u003ci\u003epsychological\u003c/i\u003e\r\nexplanation of consonance is given by this\r\nfact, for the simple reason that in the acoustic nerve-process\r\nnothing corresponding to the periodicity of\r\nthe sonant stimulus is discoverable.\u003c/p\u003e\r\n\r\n\u003cp\u003e2. In the recognition of beats as a disturbance of\r\nconsonance, both theories agree. Sauveur\u0027s theory,\r\nhowever, does not take into account the fact that\r\nclangs, or musical sounds generally, are composite\r\nand that the disturbance in the consonances of distant\r\nintervals principally arise from the beats of the overtones.\r\nFurthermore, Sauveur was wrong in asserting\r\nthat the number of beats must be less than six in a\r\nsecond in order to produce disturbances. Even Smith\r\nknows that very slow beats are not a cause of disturbance,\r\nand Helmholtz found a much higher number\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_384\" id=\"Page_384\"\u003e[Pg 384]\u003c/a\u003e\u003c/span\u003e\r\n(33) for the maximum of disturbance. Finally, Sauveur\r\ndid not consider that although the number of\r\nbeats increases with the recession from unison, yet\r\ntheir \u003ci\u003estrength\u003c/i\u003e is diminished. On the basis of the\r\nprinciple of specific energies and of the laws of sympathetic\r\nvibration the new theory finds that two atmospheric\r\nmotions of like amplitude but different periods,\r\n\u003ci\u003ea\u003c/i\u003e sin(\u003ci\u003ert\u003c/i\u003e) and \u003ci\u003ea\u003c/i\u003e sin[(\u003ci\u003er\u003c/i\u003e + \u0026#961;)(\u003ci\u003et\u003c/i\u003e + \u0026#964;)], cannot be\r\ncommunicated with the same amplitude to the same\r\nnervous end-organ. On the contrary, an end-organ\r\nthat reacts best to the period \u003ci\u003er\u003c/i\u003e responds more weakly\r\nto the period \u003ci\u003er\u003c/i\u003e + \u0026#961;, the two amplitudes bearing to each\r\nother the proportion \u003ci\u003ea\u003c/i\u003e: \u0026#966;\u003ci\u003ea\u003c/i\u003e. Here \u0026#966; decreases when\r\n\u0026#961; increases, and when \u0026#961; = 0 it becomes equal to 1, so\r\nthat only the portion of the stimulus \u0026#966;\u003ci\u003ea\u003c/i\u003e is subject to\r\nbeats, and the portion (1-\u0026#966;)\u003ci\u003ea\u003c/i\u003e continues smoothly\r\nonward without disturbance.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf there is any moral to be drawn from the history\r\nof this theory, it is that considering how near Sauveur\u0027s\r\nerrors were to the truth, it behooves us to exercise\r\nsome caution also with regard to the new theory.\r\nAnd in reality there seems to be reason for\r\ndoing so.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe fact that a musician will never confound a\r\nmore perfectly consonant chord on a poorly tuned\r\npiano with a less perfectly consonant chord on a well\r\ntuned piano, although the roughness in the two cases\r\nmay be the same, is sufficient indication that the degree\r\nof roughness is not the only characteristic of a\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_385\" id=\"Page_385\"\u003e[Pg 385]\u003c/a\u003e\u003c/span\u003e\r\nharmony. As the musician knows, even the harmonic\r\nbeauties of a Beethoven sonata are not easily effaced\r\non a poorly tuned piano; they scarcely suffer more\r\nthan a Raphael drawing executed in rough unfinished\r\nstrokes. The \u003ci\u003epositive physiologico-psychological\u003c/i\u003e characteristic\r\nwhich distinguishes one harmony from another\r\nis not given by the beats. Nor is this characteristic\r\nto be found in the fact that, for example, in sounding\r\na major third the fifth partial tone of the lower note\r\ncoincides with the fourth of the higher note. This\r\ncharacteristic comes into consideration only for the\r\ninvestigating and abstracting reason. If we should\r\nregard it also as characteristic of the sensation, we\r\nshould lapse into a fundamental error which would\r\nbe quite analogous to that cited in (1).\u003c/p\u003e\r\n\r\n\u003cp\u003eThe \u003ci\u003epositive physiological\u003c/i\u003e characteristics of the intervals\r\nwould doubtless be speedily revealed if it were\r\npossible to conduct aperiodic, for example galvanic,\r\nstimuli to the single sound-sensing organs, in which\r\ncase the beats would be totally eliminated. Unfortunately\r\nsuch an experiment can hardly be regarded as\r\npracticable. The employment of acoustic stimuli of\r\nshort duration and consequently also free from beats,\r\ninvolves the additional difficulty of a pitch not precisely\r\ndeterminable.\u003c/p\u003e\u003chr class=\"chap\" /\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_386\" id=\"Page_386\"\u003e[Pg 386]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003cp class=\"center\"\u003eII.\u003c/p\u003e\r\n\r\n\u003ch3\u003e\u003ca id=\"REMARKS_ON_THE_THEORY_OF_SPATIAL_VISION\"\u003e\u003c/a\u003eREMARKS ON THE THEORY OF SPATIAL VISION.\u003ca name=\"FNanchor_147_147\" id=\"FNanchor_147_147\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_147_147\" class=\"fnanchor\"\u003e[147]\u003c/a\u003e\u003c/h3\u003e\r\n\r\n\r\n\u003cp\u003eAccording to Herbart, spatial vision rests on reproduction-series.\r\nIn such an event, of course, and\r\nif the supposition is correct, the magnitudes of the\r\nresidua with which the percepts or representations\r\nare coalesced (the helps to coalescence) are of cardinal\r\ninfluence. Furthermore, since the coalescences\r\nmust first be fully perfected before they make their\r\nappearance, and since upon their appearance the inhibitory\r\nratios are brought into play, ultimately, then,\r\nif we leave out of account the accidental order of time\r\nin which the percepts are given, everything in spatial\r\nvision depends on the oppositions and affinities, or,\r\nin brief, on the qualities of the percepts, which enter\r\ninto series.\u003c/p\u003e\r\n\r\n\u003cp\u003eLet us see how the theory stands with respect to\r\nthe special facts involved.\u003c/p\u003e\r\n\r\n\u003cp\u003e1. If intersecting series only, running anteriorly\r\nand posteriorly, are requisite for the production of\r\nspatial sensation, why are not analogues of them found\r\nin all the senses?\u003c/p\u003e\r\n\r\n\u003cp\u003e2. Why do we measure differently colored objects\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_387\" id=\"Page_387\"\u003e[Pg 387]\u003c/a\u003e\u003c/span\u003e\r\nand variegated objects with one and the same spatial\r\nmeasure? How do we recognise differently colored\r\nobjects as the same in size? Where do we get our\r\nmeasure of space from and what is it?\u003c/p\u003e\r\n\r\n\u003cp\u003e3. Why is it that differently colored figures of the\r\nsame form reproduce one another and are recognised\r\nas the same?\u003c/p\u003e\r\n\r\n\u003cp\u003eHere are difficulties enough. Herbart is unable to\r\nsolve them by his theory. The unprejudiced student\r\nsees at once that his \"inhibition by reason of form\"\r\nand \"preference by reason of form\" are absolutely\r\nimpossible. Think of Herbart\u0027s example of the red\r\nand black letters.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe \"help to coalescence\" is a passport, so to\r\nspeak, made out to the name and person of the percept.\r\nA percept which is coalesced with another cannot\r\nreproduce all others qualitatively different from it\r\nfor the simple reason that the latter are in like manner\r\ncoalesced with one another. Two qualitatively different\r\nseries certainly do not reproduce themselves because\r\nthey present the same order of degree of coalescence.\u003c/p\u003e\r\n\r\n\u003cp\u003eIf it is certain that only things simultaneous and\r\nthings which are alike are reproduced, a basic principle\r\nof Herbart\u0027s psychology which even the most\r\nabsolute empiricists will not deny, nothing remains\r\nbut to modify the theory of spatial perception or to\r\ninvent in its place a new principle in the manner indicated,\r\na step which hardly any one would seriously\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_388\" id=\"Page_388\"\u003e[Pg 388]\u003c/a\u003e\u003c/span\u003e\r\nundertake. The new principle could not fail to throw\r\nall psychology into the most dreadful confusion.\u003c/p\u003e\r\n\r\n\u003cp\u003eAs to the modification which is needed there can\r\nbe hardly any doubt as to how in the face of the facts\r\nand conformably to Herbart\u0027s own principles it is to\r\nbe carried out. If two differently colored figures of\r\nequal size reproduce each other and are recognised as\r\nequal, the result can be due to nothing but to the existence\r\nin both series of presentations of a presentation\r\nor percept which is qualitatively \u003ci\u003ethe same\u003c/i\u003e. The\r\ncolors are different. Consequently, like or equal percepts\r\nmust be connected with the colors which are\r\nyet independent of the colors. We have not to look\r\nlong for them, for they are the like effects of the muscular\r\nfeelings of the eye when confronted by the two\r\nfigures. We might say we reach the vision of space\r\nby the registering of light-sensations in a schedule of\r\ngraduated muscle-sensations.\u003ca name=\"FNanchor_148_148\" id=\"FNanchor_148_148\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_148_148\" class=\"fnanchor\"\u003e[148]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eA few considerations will show the likelihood of\r\nthe rôle of the muscle-sensations. The muscular apparatus\r\nof \u003ci\u003eone\u003c/i\u003e eye is unsymmetrical. The two eyes\r\ntogether form a system which is vertical in symmetry.\r\nThis already explains much.\u003c/p\u003e\r\n\r\n\u003cp\u003e1. The \u003ci\u003eposition\u003c/i\u003e of a figure influences its view. According\r\nto the position in which objects are viewed\r\ndifferent muscle-sensations come into play and the\r\nimpression is altered. To recognise inverted letters\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_389\" id=\"Page_389\"\u003e[Pg 389]\u003c/a\u003e\u003c/span\u003e\r\nas such long experience is required. The best proof\r\nof this are the letters d, b, p, q, which are represented\r\nby the same figure in different positions and yet are\r\nalways distinguished as different.\u003ca name=\"FNanchor_149_149\" id=\"FNanchor_149_149\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_149_149\" class=\"fnanchor\"\u003e[149]\u003c/a\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e2. It will not escape the attentive observer that for\r\nthe same reasons and even with the same figure and\r\nin the same position the fixation point is also decisive.\r\nThe figure seems to change \u003ci\u003eduring\u003c/i\u003e the act of vision.\r\nFor example, an eight-pointed star constructed by\r\nsuccessively joining in a regular octagon the first corner\r\nwith the fourth, the fourth with the seventh, etc.,\r\nskipping in every case two corners, assumes alternately,\r\naccording to where we suffer the centre of vision\r\nto rest, a predominantly architectonic or a freer\r\nand more open character. Vertical and horizontal\r\nlines are always differently apprehended from what\r\noblique lines are.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figleft\" style=\"width: 300px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-399.jpg\" width=\"300\" height=\"130\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 58.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003e3. The reason why we prefer vertical symmetry\r\nand regard it as something special in its kind, whereas\r\nwe do not recognise\r\nhorizontal symmetry\r\nat all immediately, is\r\ndue to the vertical\r\nsymmetry of the muscular\r\napparatus of the eye. The left-hand side \u003ci\u003ea\u003c/i\u003e of\r\nthe accompanying vertically-symmetrical figure induces\r\nin the left eye the same muscular feelings as the\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_390\" id=\"Page_390\"\u003e[Pg 390]\u003c/a\u003e\u003c/span\u003e\r\nright-hand side \u003ci\u003eb\u003c/i\u003e does in the right eye. The pleasing\r\neffect of symmetry has its cause primarily in the repetition\r\nof muscular feelings. That a repetition actually\r\noccurs here, sometimes sufficiently marked in character\r\nas to lead to the confounding of objects, is\r\nproved apart from the theory by the fact which is\r\nfamiliar to every one \u003ci\u003equem dii oderunt\u003c/i\u003e that children\r\nfrequently reverse figures from the right to the left,\r\nbut never from above downwards; for example, write\r\nε instead of 3 until they finally come to notice the\r\nslight difference. Figure 50 shows how pleasing the\r\nrepetition of muscular\r\nfeelings may be. As\r\nwill be readily understood,\r\nvertical and horizontal lines exhibit relations\r\nsimilar to symmetrical figures which are immediately\r\ndisturbed when oblique positions are chosen for the\r\nlines. Compare what Helmholtz says regarding the\r\nrepetition and coincidence of partial tones.\u003c/p\u003e\r\n\r\n\u003cdiv class=\"figright\" style=\"width: 400px;\"\u003e\r\n\u003cimg src=\"https://chrisdeasy.com/wp-content/uploads/gutenberg-popular-scientific-lectures-i-400.jpg\" width=\"400\" height=\"88\" alt=\"\" /\u003e\r\n\u003cspan class=\"caption\"\u003eFig. 59.\u003c/span\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cp\u003eI may be permitted to add a general remark. It\r\nis a quite universal phenomenon in psychology that\r\ncertain qualitatively quite different series of percepts\r\nmutually awaken and reproduce one another and in a\r\ncertain aspect produce the appearance of sameness or\r\nsimilarity. We say of such series that they are of\r\nlike or of similar form, naming their abstracted likeness\r\n\u003ci\u003eform\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e1. Of spatial figures we have already spoken.\u003c/p\u003e\r\n\r\n\u003cp\u003e2. We call two melodies like melodies when they\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_391\" id=\"Page_391\"\u003e[Pg 391]\u003c/a\u003e\u003c/span\u003e\r\npresent the same succession of pitch-ratios;\r\nthe absolute pitch (or key) may be as different\r\nas can be. We can so select the melodies that\r\nnot even two partial tones of the notes in each\r\nare common. Yet we recognise the melodies\r\nas alike. And, what is more, we notice the\r\nform of the melody more readily and recognise\r\nit again more easily than the key (the absolute\r\npitch) in which it was played.\u003c/p\u003e\r\n\r\n\u003cp\u003e3. We recognise in two different melodies the\r\nsame rhythm no matter how different the melodies\r\nmay be otherwise. We know and recognise\r\nthe rhythm more easily even than the absolute\r\nduration (the tempo).\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eThese examples will suffice. In all these and in\r\nall similar cases the recognition and likeness cannot\r\ndepend upon the qualities of the percepts, for these\r\nare different. On the other hand recognition, conformably\r\nto the principles of psychology, is possible\r\nonly with percepts which are the same in quality.\r\nConsequently there is no other escape than to imagine\r\nthe qualitatively unlike percepts of the two series as\r\nnecessarily connected with other percepts which are\r\nqualitatively alike.\u003c/p\u003e\r\n\r\n\u003cp\u003eSince in differently colored figures of like form, like\r\nmuscular feelings are necessarily induced if the figures\r\nare recognised as alike, so there must necessarily lie\r\nat the basis of all forms also, and we might even say\r\nat the basis of all abstractions, percepts of a peculiar\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_392\" id=\"Page_392\"\u003e[Pg 392]\u003c/a\u003e\u003c/span\u003e\r\nquality. And this holds true for space and form as\r\nwell as for time, rhythm, pitch, the form of melodies,\r\nintensity, etc. But whence is psychology to derive all\r\nthese qualities? Have no fear, they will all be found,\r\nas were the sensations of muscles for the theory of\r\nspace. The organism is at present still rich enough\r\nto meet all the requirements of psychology in this direction,\r\nand it is even time to give serious ear to the\r\nquestion of \"corporeal resonance\" which psychology\r\nso loves to dwell on.\u003c/p\u003e\r\n\r\n\u003cp\u003eDifferent psychical qualities appear to bear a very\r\nintimate mutual relation to one another. Special research\r\non the subject, as well also as the demonstration\r\nthat this remark may be generally employed in\r\nphysics, will follow later.\u003ca name=\"FNanchor_150_150\" id=\"FNanchor_150_150\"\u003e\u003c/a\u003e\u003ca href=\"#Footnote_150_150\" class=\"fnanchor\"\u003e[150]\u003c/a\u003e\u003c/p\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_393\" id=\"Page_393\"\u003e[Pg 393]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"INDEX\" id=\"INDEX\"\u003eINDEX.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eAbsolute, temperature, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etime, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eforecasts, have no signification in science, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAbstract, meaning of the term, \u003ca href=\"#Page_240\"\u003e240\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAbstraction, \u003ca href=\"#Page_180\"\u003e180\u003c/a\u003e, \u003ca href=\"#Page_200\"\u003e200\u003c/a\u003e, \u003ca href=\"#Page_208\"\u003e208\u003c/a\u003e, \u003ca href=\"#Page_231\"\u003e231\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAcceleration, organ for forward, \u003ca href=\"#Page_299\"\u003e299\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eAccelerations, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e, footnote, \u003ca href=\"#Page_225\"\u003e225\u003c/a\u003e-\u003ca href=\"#Page_226\"\u003e226\u003c/a\u003e, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAccident, logical and historical, in science, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e, \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e, \u003ca href=\"#Page_170\"\u003e170\u003c/a\u003e, \u003ca href=\"#Page_213\"\u003e213\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein inventions and discoveries, \u003ca href=\"#Page_262\"\u003e262\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAccord, the pure triple, \u003ca href=\"#Page_46\"\u003e46\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAccumulators, electrical, \u003ca href=\"#Page_125\"\u003e125\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003e\u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e, footnote.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAcoustic color, \u003ca href=\"#Page_36\"\u003e36\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAcoustics, Sauveur on, \u003ca href=\"#Page_375\"\u003e375\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eAction and reaction, importance of the principle of, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAdaptation, in organic and inorganic matter, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e, \u003ca href=\"#Page_229\"\u003e229\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein scientific thought, \u003ca href=\"#Page_214\"\u003e214\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eÆsthetics, computation as a principle of, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eresearches in, \u003ca href=\"#Page_89\"\u003e89\u003c/a\u003e, footnote;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erepetition, a principle of, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAfrica, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAgreeable effects, due to repetition of sensations, \u003ca href=\"#Page_92\"\u003e92\u003c/a\u003e, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eAgriculture, transition to, \u003ca href=\"#Page_265\"\u003e265\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAir-gun, \u003ca href=\"#Page_135\"\u003e135\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAlcohol and water, mixture of oil and, in Plateau\u0027s experiments, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAlgebra, economy of, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAlien thoughts in science, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAll, the, \u003ca href=\"#Page_88\"\u003e88\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAmontons, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e, \u003ca href=\"#Page_346\"\u003e346\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAmpère, the word, \u003ca href=\"#Page_314\"\u003e314\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAmpère\u0027s swimmer, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAnalogies, mechanical, \u003ca href=\"#Page_157\"\u003e157\u003c/a\u003e, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egenerally, \u003ca href=\"#Page_236\"\u003e236\u003c/a\u003e-\u003ca href=\"#Page_258\"\u003e258\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAnalogy, defined, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAnalysis, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAnalytical geometry, not necessary to physicians, \u003ca href=\"#Page_370\"\u003e370\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eAnatomic structures, transparent stereoscopic views of, \u003ca href=\"#Page_74\"\u003e74\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAnatomy, character of research in, \u003ca href=\"#Page_255\"\u003e255\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAndrieu, Jules, \u003ca href=\"#Page_49\"\u003e49\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eAnimals, the psychical activity of, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e, \u003ca href=\"#Page_231\"\u003e231\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe language of, \u003ca href=\"#Page_238\"\u003e238\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir capacity for experience, \u003ca href=\"#Page_266\"\u003e266\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAnimism, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e, \u003ca href=\"#Page_254\"\u003e254\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAnisotropic optical fields, \u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eApparatus for producing movements of rotation, \u003ca href=\"#Page_287\"\u003e287\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eArabesque, an inverted, \u003ca href=\"#Page_95\"\u003e95\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArabian Nights, \u003ca href=\"#Page_219\"\u003e219\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArago, \u003ca href=\"#Page_270\"\u003e270\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAral, the Sea of, \u003ca href=\"#Page_239\"\u003e239\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArchæopteryx, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArchimedes, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArcimboldo, Giuseppe, \u003ca href=\"#Page_36\"\u003e36\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArea, principle of least superficial, \u003ca href=\"#Page_10\"\u003e10\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eAres, the bellowing of the wounded, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAristotelians, \u003ca href=\"#Page_283\"\u003e283\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAristotle, \u003ca href=\"#Page_348\"\u003e348\u003c/a\u003e, \u003ca href=\"#Page_296\"\u003e296\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArt, development of, \u003ca href=\"#Page_28\"\u003e28\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eArtillery, practical, \u003ca href=\"#Page_334\"\u003e334\u003c/a\u003e-\u003ca href=\"#Page_335\"\u003e335\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArtistic value of scientific descriptions, \u003ca href=\"#Page_254\"\u003e254\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eArts, practical, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAscent, heights of, \u003ca href=\"#Page_143\"\u003e143\u003c/a\u003e-\u003ca href=\"#Page_151\"\u003e151\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_394\" id=\"Page_394\"\u003e[Pg 394]\u003c/a\u003e\u003c/span\u003eAsia, 234.\u003c/li\u003e\r\n\r\n\u003cli\u003eAssyrians, the art of, \u003ca href=\"#Page_79\"\u003e79\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAstronomer, measures celestial by terrestrial distances, \u003ca href=\"#Page_136\"\u003e136\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAstronomy, antecedent to psychology, \u003ca href=\"#Page_90\"\u003e90\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erigidity of its truths, \u003ca href=\"#Page_221\"\u003e221\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAtomic theories, \u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAtoms, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAttention, the rôle of, in sensuous perception, \u003ca href=\"#Page_35\"\u003e35\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eAttraction, generally, \u003ca href=\"#Page_226\"\u003e226\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof liquid particles, \u003ca href=\"#Page_13\"\u003e13\u003c/a\u003e-\u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein electricity, \u003ca href=\"#Page_109\"\u003e109\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eAubert, \u003ca href=\"#Page_298\"\u003e298\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAudition. See \u003ci\u003eEar\u003c/i\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eAustrian gymnasiums, \u003ca href=\"#Page_370\"\u003e370\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eAxioms, instinctive knowledge, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eBabbage, on the economy of machinery, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBach, \u003ca href=\"#Page_20\"\u003e20\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBackwards, prophesying, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBacon, Lord, \u003ca href=\"#Page_48\"\u003e48\u003c/a\u003e, \u003ca href=\"#Page_280\"\u003e280\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBaer, C. E. von, \u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBalance, electrical, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e, footnote;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etorsion, \u003ca href=\"#Page_109\"\u003e109\u003c/a\u003e, \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBalloon, a hydrogen, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBarbarism and civilisation, \u003ca href=\"#Page_335\"\u003e335\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eBass-clef, \u003ca href=\"#Page_101\"\u003e101\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBass, fundamental, \u003ca href=\"#Page_44\"\u003e44\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBeats, \u003ca href=\"#Page_40\"\u003e40\u003c/a\u003e-\u003ca href=\"#Page_45\"\u003e45\u003c/a\u003e, \u003ca href=\"#Page_377\"\u003e377\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eBeautiful, our notions of, variable, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBeauty, objects of, in nature, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBecker, J. K., \u003ca href=\"#Page_364\"\u003e364\u003c/a\u003e, \u003ca href=\"#Page_369\"\u003e369\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBeethoven, \u003ca href=\"#Page_39\"\u003e39\u003c/a\u003e, \u003ca href=\"#Page_44\"\u003e44\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBeginnings of science, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBelvedere Gallery at Vienna, \u003ca href=\"#Page_36\"\u003e36\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBernoulli, Daniel, on the conservation of living force, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the vibrations of strings, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBernoulli, James, on the centre of oscillation, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBernoulli, John, on the conservation of living force, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the principle of virtual velocities, \u003ca href=\"#Page_151\"\u003e151\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBible, parallel passages from, for language study, \u003ca href=\"#Page_356\"\u003e356\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBinocular vision, \u003ca href=\"#Page_66\"\u003e66\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eBlack, his theory of caloric, \u003ca href=\"#Page_138\"\u003e138\u003c/a\u003e, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon quantity of heat, \u003ca href=\"#Page_166\"\u003e166\u003c/a\u003e, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon latent heat, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eresearches in heat generally, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBlind cat, \u003ca href=\"#Page_303\"\u003e303\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBodies, heavy, seek their places, \u003ca href=\"#Page_224\"\u003e224\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erotating, \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBody, a mental symbol for groups of sensations, \u003ca href=\"#Page_200\"\u003e200\u003c/a\u003e-\u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe human, our knowledge of, \u003ca href=\"#Page_90\"\u003e90\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBoltzmann, \u003ca href=\"#Page_236\"\u003e236\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBooth, Mr., \u003ca href=\"#Page_77\"\u003e77\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBorelli, \u003ca href=\"#Page_217\"\u003e217\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBoulder, a granite, \u003ca href=\"#Page_233\"\u003e233\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBow-wave of ships and moving projectiles, \u003ca href=\"#Page_323\"\u003e323\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eBoys, \u003ca href=\"#Page_317\"\u003e317\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBradley, \u003ca href=\"#Page_273\"\u003e273\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBrahman, the, \u003ca href=\"#Page_63\"\u003e63\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBrain, localisation of functions in, \u003ca href=\"#Page_210\"\u003e210\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBreuer, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e, \u003ca href=\"#Page_282\"\u003e282\u003c/a\u003e et seq., \u003ca href=\"#Page_293\"\u003e293\u003c/a\u003e, \u003ca href=\"#Page_298\"\u003e298\u003c/a\u003e, \u003ca href=\"#Page_300\"\u003e300\u003c/a\u003e, \u003ca href=\"#Page_301\"\u003e301\u003c/a\u003e, \u003ca href=\"#Page_303\"\u003e303\u003c/a\u003e, \u003ca href=\"#Page_306\"\u003e306\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBrewster, his stereoscope, \u003ca href=\"#Page_73\"\u003e73\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBridge, invention of the, \u003ca href=\"#Page_264\"\u003e264\u003c/a\u003e, \u003ca href=\"#Page_268\"\u003e268\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBritish Association, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBrooklyn Bridge, \u003ca href=\"#Page_75\"\u003e75\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eBrown, Crum, \u003ca href=\"#Page_293\"\u003e293\u003c/a\u003e, \u003ca href=\"#Page_301\"\u003e301\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBuilding, our concepts directions for, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efacts the result of, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003escience compared to, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eBuilding-stones, metrical units are, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBusch, \u003ca href=\"#Page_328\"\u003e328\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eBusiness of a merchant, science compared to the, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eButterfly, a, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eCalculating machines, their economical character, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCaloric, theory of, stood in the way of scientific advancement, \u003ca href=\"#Page_138\"\u003e138\u003c/a\u003e, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCalypso, the island of, \u003ca href=\"#Page_351\"\u003e351\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCanterbury, Archbishop of, \u003ca href=\"#Page_39\"\u003e39\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCantor, M., \u003ca href=\"#Page_361\"\u003e361\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eCapacity, electrical, \u003ca href=\"#Page_116\"\u003e116\u003c/a\u003e et seq., \u003ca href=\"#Page_123\"\u003e123\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethermal, \u003ca href=\"#Page_123\"\u003e123\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003especific inductive, \u003ca href=\"#Page_117\"\u003e117\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCapulets and Montagues, \u003ca href=\"#Page_87\"\u003e87\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCards, difficult games of, \u003ca href=\"#Page_357\"\u003e357\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCarnot, S., excludes perpetual motion in heat, \u003ca href=\"#Page_156\"\u003e156\u003c/a\u003e, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis mechanical view of physics, \u003ca href=\"#Page_156\"\u003e156\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_395\" id=\"Page_395\"\u003e[Pg 395]\u003c/a\u003e\u003c/span\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon thermodynamics, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis principle, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCarus, Dr. Paul, \u003ca href=\"#Page_265\"\u003e265\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eCasselli\u0027s telegraph, \u003ca href=\"#Page_26\"\u003e26\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCassini, \u003ca href=\"#Page_51\"\u003e51\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCauchy, character of the intellectual activity of a, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCausal insight, awakened by science, \u003ca href=\"#Page_357\"\u003e357\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCausality, \u003ca href=\"#Page_157\"\u003e157\u003c/a\u003e-\u003ca href=\"#Page_159\"\u003e159\u003c/a\u003e, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e et seq., \u003ca href=\"#Page_221\"\u003e221\u003c/a\u003e et seq., \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e, \u003ca href=\"#Page_254\"\u003e254\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCause and effect, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e et seq. See also \u003ci\u003eCausality\u003c/i\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCentimetre-gramme-second system, \u003ca href=\"#Page_111\"\u003e111\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCentre of gravity, must lie as low as possible for equilibrium to subsist, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eTorricelli\u0027s principle of, \u003ca href=\"#Page_150\"\u003e150\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCentre of oscillation, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChange, method of, in science, \u003ca href=\"#Page_230\"\u003e230\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChangeable character of bodies, \u003ca href=\"#Page_202\"\u003e202\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChanges, physical, how they occur, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCharacter, a Universal Real, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCharacter, like the forms of liquids, \u003ca href=\"#Page_3\"\u003e3\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003epersons of, \u003ca href=\"#Page_24\"\u003e24\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCharles the Fifth, \u003ca href=\"#Page_369\"\u003e369\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChemical, elements, \u003ca href=\"#Page_202\"\u003e202\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esymbols, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecurrent, \u003ca href=\"#Page_118\"\u003e118\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eChemistry, character of research in, \u003ca href=\"#Page_255\"\u003e255\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe method of thermodynamics in, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eChild, a, modes of thought of, \u003ca href=\"#Page_223\"\u003e223\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elooking into a moat, \u003ca href=\"#Page_208\"\u003e208\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eChild of the forest, his interpretation of new events, \u003ca href=\"#Page_218\"\u003e218\u003c/a\u003e-\u003ca href=\"#Page_219\"\u003e219\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChildish questions, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e-\u003ca href=\"#Page_200\"\u003e200\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChildren, the drawings of, \u003ca href=\"#Page_201\"\u003e201\u003c/a\u003e-\u003ca href=\"#Page_202\"\u003e202\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChinese language, economy of, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003estudy of, \u003ca href=\"#Page_354\"\u003e354\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eChinese philosopher, an old, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChinese, speak with unwillingness of politics, \u003ca href=\"#Page_374\"\u003e374\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe art of, \u003ca href=\"#Page_79\"\u003e79\u003c/a\u003e-\u003ca href=\"#Page_80\"\u003e80\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eChosen, many are called but few are, \u003ca href=\"#Page_65\"\u003e65\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChrist, saying of, \u003ca href=\"#Page_65\"\u003e65\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChristianity, Latin introduced with, \u003ca href=\"#Page_311\"\u003e311\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChristians and Jews, monotheism of the, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eChurch and State, \u003ca href=\"#Page_88\"\u003e88\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCicero, \u003ca href=\"#Page_318\"\u003e318\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCirce, \u003ca href=\"#Page_372\"\u003e372\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCircle, the figure of least area with given periphery, \u003ca href=\"#Page_12\"\u003e12\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCircular polarisation, \u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCivilisation and barbarism, \u003ca href=\"#Page_335\"\u003e335\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eCivilisation, some phenomena of, explained by binocular vision, \u003ca href=\"#Page_74\"\u003e74\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCivilised man, his modes of conception and interpretation, \u003ca href=\"#Page_219\"\u003e219\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eClapeyron, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eClass-characters of animals, \u003ca href=\"#Page_255\"\u003e255\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eClassical, culture, the good and bad effects of, \u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003escholars, not the only educated people, \u003ca href=\"#Page_345\"\u003e345\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eClassics, on instruction in, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e-\u003ca href=\"#Page_374\"\u003e374\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe scientific, \u003ca href=\"#Page_368\"\u003e368\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eClassification in science, \u003ca href=\"#Page_255\"\u003e255\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eClausius, on thermodynamics, \u003ca href=\"#Page_165\"\u003e165\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon reversible cycles, \u003ca href=\"#Page_176\"\u003e176\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eClaviatur, Mach\u0027s, \u003ca href=\"#Page_42\"\u003e42\u003c/a\u003e-\u003ca href=\"#Page_43\"\u003e43\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eClub-law, \u003ca href=\"#Page_335\"\u003e335\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCochlea, the, a species of piano-forte, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCockchafer, \u003ca href=\"#Page_86\"\u003e86\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCoefficient of self-induction, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e, \u003ca href=\"#Page_252\"\u003e252\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eColophonium, solution of, \u003ca href=\"#Page_7\"\u003e7\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eColor, acoustic, \u003ca href=\"#Page_36\"\u003e36\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eColor-sensation, \u003ca href=\"#Page_210\"\u003e210\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eColor-signs, their economy, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eColors, origin of the names of, \u003ca href=\"#Page_239\"\u003e239\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eColumn, body moving behind a, \u003ca href=\"#Page_202\"\u003e202\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCommunication, its functions, import and fruits, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e, \u003ca href=\"#Page_238\"\u003e238\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eby language, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehigh importance of, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eComparative physics, \u003ca href=\"#Page_239\"\u003e239\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eComparison in science, \u003ca href=\"#Page_231\"\u003e231\u003c/a\u003e, \u003ca href=\"#Page_238\"\u003e238\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eComputation, a principle of æsthetics, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConcepts, abstract, defined, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e-\u003ca href=\"#Page_252\"\u003e252\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emetrical, in electricity, \u003ca href=\"#Page_107\"\u003e107\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eConceptual, meaning of the term, \u003ca href=\"#Page_240\"\u003e240\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConceptual thought, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConcha, \u003ca href=\"#Page_18\"\u003e18\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCondensers, electrical, \u003ca href=\"#Page_125\"\u003e125\u003c/a\u003e et seq. \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_396\" id=\"Page_396\"\u003e[Pg 396]\u003c/a\u003e\u003c/span\u003eConductors and non-conductors. See \u003ci\u003eElectrical\u003c/i\u003e, etc.\u003c/li\u003e\r\n\r\n\u003cli\u003eConformity in the deportment of the energies, \u003ca href=\"#Page_171\"\u003e171\u003c/a\u003e-\u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConfusion of objects, cause of, \u003ca href=\"#Page_95\"\u003e95\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConic sections, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConical refraction, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e, \u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConservation of energy, \u003ca href=\"#Page_137\"\u003e137\u003c/a\u003e et seq. See \u003ci\u003eEnergy\u003c/i\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConservation of weight or mass, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConsonance, connexion of the simple natural numbers with, \u003ca href=\"#Page_33\"\u003e33\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eEuclid\u0027s definition of, \u003ca href=\"#Page_33\"\u003e33\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eexplanation of, \u003ca href=\"#Page_42\"\u003e42\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003escientific definition of, \u003ca href=\"#Page_44\"\u003e44\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eand dissonance reduced to beats, \u003ca href=\"#Page_376\"\u003e376\u003c/a\u003e, \u003ca href=\"#Page_370\"\u003e370\u003c/a\u003e, \u003ca href=\"#Page_383\"\u003e383\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eConsonant intervals, \u003ca href=\"#Page_43\"\u003e43\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConstancy of matter, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConstant, the dielectric, \u003ca href=\"#Page_117\"\u003e117\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eConstants, the natural, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eContinuum of facts, \u003ca href=\"#Page_256\"\u003e256\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eCornelius, \u003ca href=\"#Page_388\"\u003e388\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eCorti, the Marchese, his discovery of minute rods in the labyrinth of the ear, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCoulomb, his electrical researches, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e, \u003ca href=\"#Page_109\"\u003e109\u003c/a\u003e, \u003ca href=\"#Page_113\"\u003e113\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis notion of quantity of electricity, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis torsion-balance, \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCrew, Prof. Henry, \u003ca href=\"#Page_317\"\u003e317\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eCriticism, Socrates the father of scientific, \u003ca href=\"#Page_1\"\u003e1\u003c/a\u003e, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003ci\u003eCritique of Pure Reason\u003c/i\u003e, Kant\u0027s, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCrucible, derivation of the word, \u003ca href=\"#Page_49\"\u003e49\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eCrustacea, auditory filaments of, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e, \u003ca href=\"#Page_302\"\u003e302\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCube of oil, \u003ca href=\"#Page_5\"\u003e5\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCulture, ancient and modern, \u003ca href=\"#Page_344\"\u003e344\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCurrents, chemical, \u003ca href=\"#Page_118\"\u003e118\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eelectrical, \u003ca href=\"#Page_118\"\u003e118\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egalvanic, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emeasurement of electrical, \u003ca href=\"#Page_135\"\u003e135\u003c/a\u003e-\u003ca href=\"#Page_136\"\u003e136\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof heat, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e-\u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003estrength of, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eCurtius, \u003ca href=\"#Page_356\"\u003e356\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCurved lines, their asymmetry, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCurves, how their laws are investigated, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCycles, reversible, Clausius on, \u003ca href=\"#Page_176\"\u003e176\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCyclical processes, closed, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCyclops, \u003ca href=\"#Page_67\"\u003e67\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCyclostat, \u003ca href=\"#Page_298\"\u003e298\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eCylinder, of oil, \u003ca href=\"#Page_6\"\u003e6\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emass of gas enclosed in a, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eD\u0027Alembert, on the causes of harmony, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis principle, \u003ca href=\"#Page_142\"\u003e142\u003c/a\u003e, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e, \u003ca href=\"#Page_154\"\u003e154\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e, \u003ca href=\"#Page_279\"\u003e279\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDanish schools, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eDarwin, his study of organic nature, \u003ca href=\"#Page_215\"\u003e215\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis methods of research, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDeaf and dumb, not subject to giddiness, \u003ca href=\"#Page_299\"\u003e299\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDeaf person, with a piano, analyses sounds, \u003ca href=\"#Page_27\"\u003e27\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDeath and life, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDefinition, compendious, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDeiters, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDelage, \u003ca href=\"#Page_298\"\u003e298\u003c/a\u003e, \u003ca href=\"#Page_301\"\u003e301\u003c/a\u003e, \u003ca href=\"#Page_302\"\u003e302\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDemocritus, his mechanical conception of the world, \u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDemonstration, character of, \u003ca href=\"#Page_362\"\u003e362\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDeportment of the energies, conformity in the, \u003ca href=\"#Page_171\"\u003e171\u003c/a\u003e-\u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDerivation, laws only methods of, \u003ca href=\"#Page_256\"\u003e256\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDescent, Galileo\u0027s laws of, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egenerally, \u003ca href=\"#Page_143\"\u003e143\u003c/a\u003e et seq., \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e, \u003ca href=\"#Page_215\"\u003e215\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDescription, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e, \u003ca href=\"#Page_236\"\u003e236\u003c/a\u003e, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ea condition of scientific knowledge, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edirect and indirect, \u003ca href=\"#Page_240\"\u003e240\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein physics, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDescriptive sciences, their resemblance to the abstract, \u003ca href=\"#Page_248\"\u003e248\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDeterminants, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDiderot, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDielectric constant, the, \u003ca href=\"#Page_117\"\u003e117\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDifference-engine, the, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDifferential coefficients, their relation to symmetry, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDifferential laws, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDifferential method, for detecting optical imperfections, \u003ca href=\"#Page_317\"\u003e317\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDiffraction, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e, \u003ca href=\"#Page_194\"\u003e194\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDiffusion, Fick\u0027s theory of, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDischarge of Leyden jars, \u003ca href=\"#Page_114\"\u003e114\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eDiscoveries, the gist of, \u003ca href=\"#Page_270\"\u003e270\u003c/a\u003e, \u003ca href=\"#Page_375\"\u003e375\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDiscovery and invention, distinction between, \u003ca href=\"#Page_269\"\u003e269\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDissonance, explanation of, \u003ca href=\"#Page_42\"\u003e42\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edefinition of, \u003ca href=\"#Page_33\"\u003e33\u003c/a\u003e, \u003ca href=\"#Page_44\"\u003e44\u003c/a\u003e. See \u003ci\u003eConsonance\u003c/i\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDistances, estimation of, by the eye, \u003ca href=\"#Page_68\"\u003e68\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eDogs, like tuning-forks, \u003ca href=\"#Page_23\"\u003e23\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_397\" id=\"Page_397\"\u003e[Pg 397]\u003c/a\u003e\u003c/span\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir mentality, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDomenech, Abbé, \u003ca href=\"#Page_92\"\u003e92\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDramatic element in science, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDrop of water, on a greased plate, \u003ca href=\"#Page_8\"\u003e8\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the end of a stick, \u003ca href=\"#Page_8\"\u003e8\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein free descent, \u003ca href=\"#Page_8\"\u003e8\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eDubois, \u003ca href=\"#Page_218\"\u003e218\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDubois-Reymond, \u003ca href=\"#Page_370\"\u003e370\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eDufay, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eDynamics, foundations of, \u003ca href=\"#Page_153\"\u003e153\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eEar, researches in the theory of, \u003ca href=\"#Page_17\"\u003e17\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ediagram of, \u003ca href=\"#Page_18\"\u003e18\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits analysis of sounds, \u003ca href=\"#Page_20\"\u003e20\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ea puzzle-lock, \u003ca href=\"#Page_28\"\u003e28\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ereflected in a mirror, \u003ca href=\"#Page_93\"\u003e93\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eno symmetry in its sensation, \u003ca href=\"#Page_103\"\u003e103\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEarth, its oblateness not due to its original fluid condition, \u003ca href=\"#Page_2\"\u003e2\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erotation of, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003einternal disturbances of, \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEconomical, nature of physical inquiry, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eprocedure of the human mind, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eorder of physics, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eschematism of science, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etools of science, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecoefficient of dynamos, \u003ca href=\"#Page_133\"\u003e133\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEconomy, of the actions of nature, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe purpose of science, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof language, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof the industrial arts, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof mathematics, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e-\u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof machinery, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof self-preservation, our first knowledge derived from, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egenerally, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e et seq., \u003ca href=\"#Page_269\"\u003e269\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEducation, higher, \u003ca href=\"#Page_86\"\u003e86\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eliberal, \u003ca href=\"#Page_341\"\u003e341\u003c/a\u003e et seq., \u003ca href=\"#Page_371\"\u003e371\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEfflux, liquid, \u003ca href=\"#Page_150\"\u003e150\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEgo, its nature, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEgypt, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEgyptians, art of, \u003ca href=\"#Page_78\"\u003e78\u003c/a\u003e et seq., \u003ca href=\"#Page_201\"\u003e201\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEighteenth century, the scientific achievements of, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEleatics, on motion, \u003ca href=\"#Page_158\"\u003e158\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eElectrical, attraction and repulsion, \u003ca href=\"#Page_109\"\u003e109\u003c/a\u003e et seq., \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecapacity, \u003ca href=\"#Page_116\"\u003e116\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eforce, \u003ca href=\"#Page_110\"\u003e110\u003c/a\u003e, \u003ca href=\"#Page_119\"\u003e119\u003c/a\u003e, \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003espark, \u003ca href=\"#Page_117\"\u003e117\u003c/a\u003e, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e, \u003ca href=\"#Page_133\"\u003e133\u003c/a\u003e, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eenergy, measurement of, \u003ca href=\"#Page_128\"\u003e128\u003c/a\u003e et seq., \u003ca href=\"#Page_169\"\u003e169\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecurrents, conceptions of, \u003ca href=\"#Page_118\"\u003e118\u003c/a\u003e, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e, \u003ca href=\"#Page_135\"\u003e135\u003c/a\u003e-\u003ca href=\"#Page_136\"\u003e136\u003c/a\u003e, \u003ca href=\"#Page_226\"\u003e226\u003c/a\u003e-\u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efluids, \u003ca href=\"#Page_112\"\u003e112\u003c/a\u003e et seq., \u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ependulums, \u003ca href=\"#Page_110\"\u003e110\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elevels, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003epotential, \u003ca href=\"#Page_121\"\u003e121\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003equantity, \u003ca href=\"#Page_111\"\u003e111\u003c/a\u003e, \u003ca href=\"#Page_118\"\u003e118\u003c/a\u003e, \u003ca href=\"#Page_119\"\u003e119\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eElectricity, as a substance and as a motion, \u003ca href=\"#Page_170\"\u003e170\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edifference between the conceptions of heat and, \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e et seq.,\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erôle of work in, \u003ca href=\"#Page_120\"\u003e120\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egalvanic, \u003ca href=\"#Page_134\"\u003e134\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eSee \u003ci\u003eElectrical\u003c/i\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eElectrometer, W. Thomson\u0027s absolute, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eElectrometers, \u003ca href=\"#Page_122\"\u003e122\u003c/a\u003e, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eElectrostatic unit, \u003ca href=\"#Page_111\"\u003e111\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eElectrostatics, concepts of, \u003ca href=\"#Page_107\"\u003e107\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eElements, interdependence of the sensuous, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof bodies, \u003ca href=\"#Page_202\"\u003e202\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof phenomena, equations between, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof sensations, \u003ca href=\"#Page_200\"\u003e200\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eused instead of sensations, \u003ca href=\"#Page_208\"\u003e208\u003c/a\u003e-\u003ca href=\"#Page_209\"\u003e209\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEllipse, equation of, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe word, \u003ca href=\"#Page_342\"\u003e342\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEmbryology, possible future state of, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEnergies, conformity in the deportment of, \u003ca href=\"#Page_171\"\u003e171\u003c/a\u003e-\u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edifferences of, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEnergy, a metrical notion, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003econservation of, \u003ca href=\"#Page_137\"\u003e137\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edefined, \u003ca href=\"#Page_139\"\u003e139\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emetaphysical establishment of the doctrine of, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ekinetic, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003epotential, \u003ca href=\"#Page_128\"\u003e128\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esubstantial conception of, \u003ca href=\"#Page_164\"\u003e164\u003c/a\u003e, \u003ca href=\"#Page_185\"\u003e185\u003c/a\u003e, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003econservation of, in electrical phenomena, \u003ca href=\"#Page_131\"\u003e131\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elimits of principle of, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eprinciple of, in physics, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e-\u003ca href=\"#Page_166\"\u003e166\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esources of principle of, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethermal, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eThomas Young on, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEnergy-value of heat, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eEnlightenment, the, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEntropy, a metrical notion, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEnvironment, stability of our, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEquations for obtaining facts, \u003ca href=\"#Page_180\"\u003e180\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ebetween the elements of phenomena, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEquilibrium, conditions of, in simple machines, \u003ca href=\"#Page_151\"\u003e151\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efigures of liquid, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egeneral condition of, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein the State, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEtymology, the word, misused for entomology, \u003ca href=\"#Page_316\"\u003e316\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEuclid, on consonance and dissonance, \u003ca href=\"#Page_33\"\u003e33\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis geometry, \u003ca href=\"#Page_364\"\u003e364\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_398\" id=\"Page_398\"\u003e[Pg 398]\u003c/a\u003e\u003c/span\u003eEuler, on the causes of harmony, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eimpression of the mathematical processes on, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the vibrations of strings, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e, \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e, \u003ca href=\"#Page_376\"\u003e376\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEuler and Hermann\u0027s principle, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEuthyphron, questioned by Socrates, \u003ca href=\"#Page_1\"\u003e1\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEvolute, the word, \u003ca href=\"#Page_342\"\u003e342\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEvolution, theory of, as applied to ideas, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eEwald, \u003ca href=\"#Page_298\"\u003e298\u003c/a\u003e, \u003ca href=\"#Page_304\"\u003e304\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eExcluded perpetual motion, logical root of the principle of, \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eExner, S., \u003ca href=\"#Page_302\"\u003e302\u003c/a\u003e, \u003ca href=\"#Page_305\"\u003e305\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eExperience, communication of, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eour ready, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe principle of energy derived from, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe wellspring of all knowledge of nature, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eincongruence between thought and, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eExperimental research, function of, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eExplanation, nature of, \u003ca href=\"#Page_194\"\u003e194\u003c/a\u003e, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e, \u003ca href=\"#Page_362\"\u003e362\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eEye, cannot analyse colors, \u003ca href=\"#Page_20\"\u003e20\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eresearches in the theory of the, \u003ca href=\"#Page_18\"\u003e18\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eloss of, as affecting vision, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eEyes, purpose of, \u003ca href=\"#Page_66\"\u003e66\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir structure symmetrical not identical, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eFace, human, inverted, \u003ca href=\"#Page_95\"\u003e95\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFacts and ideas, necessary to science, \u003ca href=\"#Page_231\"\u003e231\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFacts, description of, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eagreement of, \u003ca href=\"#Page_180\"\u003e180\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erelations of, \u003ca href=\"#Page_180\"\u003e180\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehow represented, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ereflected in imagination, \u003ca href=\"#Page_220\"\u003e220\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe result of constructions, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ea continuum of, \u003ca href=\"#Page_256\"\u003e256\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eequations for obtaining, \u003ca href=\"#Page_180\"\u003e180\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eFalling bodies, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e, \u003ca href=\"#Page_215\"\u003e215\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eGalileo on the law of, \u003ca href=\"#Page_143\"\u003e143\u003c/a\u003e et seq., \u003ca href=\"#Page_284\"\u003e284\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eFalling, cats, \u003ca href=\"#Page_303\"\u003e303\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eFalstaff, \u003ca href=\"#Page_309\"\u003e309\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFamiliar intermediate links of thought, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFaraday, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e, \u003ca href=\"#Page_217\"\u003e217\u003c/a\u003e, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis conception of electricity, \u003ca href=\"#Page_114\"\u003e114\u003c/a\u003e, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eFechner, theory of Corti\u0027s fibres, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eFeeling, cannot be explained by motions of atoms, \u003ca href=\"#Page_208\"\u003e208\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eFetishism, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e, \u003ca href=\"#Page_254\"\u003e254\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein our physical concepts, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eFibres of Corti, \u003ca href=\"#Page_17\"\u003e17\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eFick, his theory of diffusion, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFigures, symmetry of, \u003ca href=\"#Page_92\"\u003e92\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eFigures of liquid equilibrium, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eFire, use of, \u003ca href=\"#Page_264\"\u003e264\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFishes, \u003ca href=\"#Page_306\"\u003e306\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFixed note, determining of a, \u003ca href=\"#Page_377\"\u003e377\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFizeau, his determination of the velocity of light, \u003ca href=\"#Page_55\"\u003e55\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eFlats, reversed into sharps, \u003ca href=\"#Page_101\"\u003e101\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFlouren\u0027s experiments, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e, \u003ca href=\"#Page_290\"\u003e290\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFlower-girl, the baskets of a, \u003ca href=\"#Page_95\"\u003e95\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFluids, electrical, \u003ca href=\"#Page_112\"\u003e112\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eForce, electric, \u003ca href=\"#Page_110\"\u003e110\u003c/a\u003e, \u003ca href=\"#Page_119\"\u003e119\u003c/a\u003e, \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eunit of \u003ca href=\"#Page_111\"\u003e111\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eliving, \u003ca href=\"#Page_137\"\u003e137\u003c/a\u003e, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egenerally \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eSee the related headings.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eForces, will compared to, \u003ca href=\"#Page_254\"\u003e254\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eForeseeing events, \u003ca href=\"#Page_220\"\u003e220\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eFormal conceptions, rôle of, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFormal need of a clear view of facts, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e, \u003ca href=\"#Page_246\"\u003e246\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehow far it corresponds to nature, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eFormative forces of liquids, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eForms of liquids, \u003ca href=\"#Page_3\"\u003e3\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eForward movement, sensation of, \u003ca href=\"#Page_300\"\u003e300\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eForwards, prophesying, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFoucault, \u003ca href=\"#Page_57\"\u003e57\u003c/a\u003e, \u003ca href=\"#Page_70\"\u003e70\u003c/a\u003e, \u003ca href=\"#Page_296\"\u003e296\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFoucault and Toepler, method of, for detecting optical faults, \u003ca href=\"#Page_313\"\u003e313\u003c/a\u003e et seq., \u003ca href=\"#Page_320\"\u003e320\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFoundation of scientific thought, primitive acts of knowledge, the, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFourier, on processes of heat, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e, \u003ca href=\"#Page_278\"\u003e278\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFox, a, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFranklin\u0027s pane, \u003ca href=\"#Page_116\"\u003e116\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFrary, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eFraunhofer, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFreezing-point, lowered by pressure, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFresnel, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFritsch, \u003ca href=\"#Page_321\"\u003e321\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFrogs, larvæ of, not subject to vertigo, \u003ca href=\"#Page_298\"\u003e298\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFroude, \u003ca href=\"#Page_333\"\u003e333\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFrustra, misuse of the word, \u003ca href=\"#Page_345\"\u003e345\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eFuture, science of the, \u003ca href=\"#Page_213\"\u003e213\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eGalileo, on the motion of pendulums, \u003ca href=\"#Page_21\"\u003e21\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis attempted measurement of the velocity of light, \u003ca href=\"#Page_50\"\u003e50\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis exclusion of a perpetual motion, \u003ca href=\"#Page_143\"\u003e143\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon velocities acquired in free descent, \u003ca href=\"#Page_143\"\u003e143\u003c/a\u003e-\u003ca href=\"#Page_147\"\u003e147\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the law of inertia, \u003ca href=\"#Page_146\"\u003e146\u003c/a\u003e-\u003ca href=\"#Page_147\"\u003e147\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon virtual velocities, \u003ca href=\"#Page_150\"\u003e150\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon work, \u003ca href=\"#Page_172\"\u003e172\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis laws of descent, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon falling bodies, \u003ca href=\"#Page_225\"\u003e225\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egreat results of his study of nature, \u003ca href=\"#Page_214\"\u003e214\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis rude scientific implements, \u003ca href=\"#Page_215\"\u003e215\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eselections from his works for use in instruction, \u003ca href=\"#Page_368\"\u003e368\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_399\" id=\"Page_399\"\u003e[Pg 399]\u003c/a\u003e\u003c/span\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e, \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e, \u003ca href=\"#Page_274\"\u003e274\u003c/a\u003e, \u003ca href=\"#Page_283\"\u003e283\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGalle, observes the planet Neptune, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGalvanic, electricity, \u003ca href=\"#Page_134\"\u003e134\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecurrent, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edizziness, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003evertigo, \u003ca href=\"#Page_298\"\u003e298\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGalvanoscope, \u003ca href=\"#Page_135\"\u003e135\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGalvanotropism, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGarda, Lake, \u003ca href=\"#Page_239\"\u003e239\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGas, the word, \u003ca href=\"#Page_264\"\u003e264\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emass of, enclosed in a cylinder, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGases, tensions of, for scales of temperature, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGauss, on the foundations of dynamics, \u003ca href=\"#Page_154\"\u003e154\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis principle, \u003ca href=\"#Page_154\"\u003e154\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e, \u003ca href=\"#Page_274\"\u003e274\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGenius, \u003ca href=\"#Page_279\"\u003e279\u003c/a\u003e, \u003ca href=\"#Page_280\"\u003e280\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGeography, comparison in, \u003ca href=\"#Page_239\"\u003e239\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGeometers, in our eyes, \u003ca href=\"#Page_72\"\u003e72\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGeotropism, \u003ca href=\"#Page_289\"\u003e289\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGerman schools and gymnasiums, \u003ca href=\"#Page_372\"\u003e372\u003c/a\u003e, \u003ca href=\"#Page_373\"\u003e373\u003c/a\u003e, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eGhosts, photographic, \u003ca href=\"#Page_73\"\u003e73\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGlass, invisible in a mixture of the same refrangibility, \u003ca href=\"#Page_312\"\u003e312\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003epowdered, visible in a mixture of the same refrangibility, \u003ca href=\"#Page_312\"\u003e312\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGlove, in a mirror, \u003ca href=\"#Page_93\"\u003e93\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGoethe, quotations from, \u003ca href=\"#Page_9\"\u003e9\u003c/a\u003e, \u003ca href=\"#Page_31\"\u003e31\u003c/a\u003e, \u003ca href=\"#Page_49\"\u003e49\u003c/a\u003e, \u003ca href=\"#Page_88\"\u003e88\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the cause of harmony, \u003ca href=\"#Page_35\"\u003e35\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGoltz, \u003ca href=\"#Page_282\"\u003e282\u003c/a\u003e, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGossot, \u003ca href=\"#Page_332\"\u003e332\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGothic cathedral, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGravitation, discovery of, \u003ca href=\"#Page_225\"\u003e225\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eGravity, how to get rid of the effects of, in liquids, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGray, Elisha, his telautograph, \u003ca href=\"#Page_26\"\u003e26\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGreased plate, drop of water on a, \u003ca href=\"#Page_8\"\u003e8\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGreat minds, idiosyncrasies of, \u003ca href=\"#Page_247\"\u003e247\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGreek language, scientific terms derivedfrom, \u003ca href=\"#Page_342\"\u003e342\u003c/a\u003e-\u003ca href=\"#Page_343\"\u003e343\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecommon words derived from, \u003ca href=\"#Page_343\"\u003e343\u003c/a\u003e, footnote;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003estill necessary for some professions, \u003ca href=\"#Page_346\"\u003e346\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits literary wealth, \u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e-\u003ca href=\"#Page_348\"\u003e348\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003enarrowness and one-sidedness of its literature, \u003ca href=\"#Page_348\"\u003e348\u003c/a\u003e-\u003ca href=\"#Page_349\"\u003e349\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits excessive study useless, \u003ca href=\"#Page_349\"\u003e349\u003c/a\u003e-\u003ca href=\"#Page_350\"\u003e350\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits study sharpens the judgment, \u003ca href=\"#Page_357\"\u003e357\u003c/a\u003e-\u003ca href=\"#Page_358\"\u003e358\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ea knowledge of it not necessary to a liberal education, \u003ca href=\"#Page_371\"\u003e371\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGreeks, their provinciality and narrow-mindedness, \u003ca href=\"#Page_349\"\u003e349\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003enow only objects of historical research, \u003ca href=\"#Page_350\"\u003e350\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eGriesinger, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGrimaldi, \u003ca href=\"#Page_270\"\u003e270\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eGrimm, \u003ca href=\"#Page_344\"\u003e344\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eGrunting fishes, \u003ca href=\"#Page_306\"\u003e306\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eHabitudes of thought, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e, \u003ca href=\"#Page_224\"\u003e224\u003c/a\u003e, \u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e, \u003ca href=\"#Page_232\"\u003e232\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHaeckel, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e, \u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHamilton, deduction of the conical refraction of light, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHankel, \u003ca href=\"#Page_364\"\u003e364\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHarmonics, \u003ca href=\"#Page_38\"\u003e38\u003c/a\u003e, \u003ca href=\"#Page_40\"\u003e40\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHarmony, on the causes of, \u003ca href=\"#Page_32\"\u003e32\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elaws of the theory of, explained, \u003ca href=\"#Page_30\"\u003e30\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe investigation of the ancients concerning, \u003ca href=\"#Page_32\"\u003e32\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egenerally, \u003ca href=\"#Page_103\"\u003e103\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eSee \u003ci\u003eConsonance\u003c/i\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHarris, electrical balance of, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eHartwich, Judge, \u003ca href=\"#Page_343\"\u003e343\u003c/a\u003e, \u003ca href=\"#Page_353\"\u003e353\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eHat, a high silk, \u003ca href=\"#Page_24\"\u003e24\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHats, ladies\u0027, development of, \u003ca href=\"#Page_64\"\u003e64\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHead-wave of a projectile, \u003ca href=\"#Page_323\"\u003e323\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eHearing and orientation, relation between, \u003ca href=\"#Page_304\"\u003e304\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eHeat, a material substance, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edifference between the conceptions of electricity and, \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esubstantial conception of, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eCarnot on, \u003ca href=\"#Page_156\"\u003e156\u003c/a\u003e, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eFourier on the conduction of, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003enot necessarily a motion, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e, \u003ca href=\"#Page_170\"\u003e170\u003c/a\u003e, \u003ca href=\"#Page_171\"\u003e171\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emechanical equivalent of, \u003ca href=\"#Page_164\"\u003e164\u003c/a\u003e, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof liquefaction, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003equantity of, \u003ca href=\"#Page_166\"\u003e166\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elatent, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003especific, \u003ca href=\"#Page_166\"\u003e166\u003c/a\u003e, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe conceptions of, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e-\u003ca href=\"#Page_171\"\u003e171\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emachine, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ea measure of electrical energy, \u003ca href=\"#Page_133\"\u003e133\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_400\" id=\"Page_400\"\u003e[Pg 400]\u003c/a\u003e\u003c/span\u003e\u003cspan style=\"margin-left: 1em;\"\u003emechanical theory of, \u003ca href=\"#Page_133\"\u003e133\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ewhere does it come from? \u003ca href=\"#Page_200\"\u003e200\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHeavy bodies, sinking of, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHeights of ascent, \u003ca href=\"#Page_143\"\u003e143\u003c/a\u003e-\u003ca href=\"#Page_151\"\u003e151\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHelm, \u003ca href=\"#Page_172\"\u003e172\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHelmholtz, applies the principle of energy to electricity, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis telestereoscope, \u003ca href=\"#Page_84\"\u003e84\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis theory of Corti\u0027s fibres, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon harmony, \u003ca href=\"#Page_35\"\u003e35\u003c/a\u003e, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the conservation of energy, \u003ca href=\"#Page_165\"\u003e165\u003c/a\u003e, \u003ca href=\"#Page_247\"\u003e247\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis method of thought, \u003ca href=\"#Page_247\"\u003e247\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_138\"\u003e138\u003c/a\u003e, \u003ca href=\"#Page_305\"\u003e305\u003c/a\u003e, \u003ca href=\"#Page_307\"\u003e307\u003c/a\u003e, \u003ca href=\"#Page_375\"\u003e375\u003c/a\u003e, \u003ca href=\"#Page_383\"\u003e383\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHensen, V., on the auditory function of the filaments of Crustacea, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e, \u003ca href=\"#Page_302\"\u003e302\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHerbart, \u003ca href=\"#Page_386\"\u003e386\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eHerbartians, on motion, \u003ca href=\"#Page_158\"\u003e158\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHerculaneum, art in, \u003ca href=\"#Page_80\"\u003e80\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHeredity, in organic and inorganic matter, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eHering, on development, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon vision, \u003ca href=\"#Page_210\"\u003e210\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHermann, E., on the economy of the industrial arts, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHermann, L., \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHerodotus, \u003ca href=\"#Page_26\"\u003e26\u003c/a\u003e, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e, \u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e, \u003ca href=\"#Page_350\"\u003e350\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHertz, his waves, \u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis use of the phrase \"prophesy,\" \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHerzen, \u003ca href=\"#Page_361\"\u003e361\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eHindu mathematicians, their beautiful problems, \u003ca href=\"#Page_30\"\u003e30\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHoltz\u0027s electric machine, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHorse, \u003ca href=\"#Page_63\"\u003e63\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHousehold, physics compared to a well-kept, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHousekeeping in science and civil life, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHudson, the, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHuman beings, puzzle-locks, \u003ca href=\"#Page_27\"\u003e27\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHuman body, our knowledge of, \u003ca href=\"#Page_90\"\u003e90\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHuman mind, must proceed economically, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHumanity, likened to a polyp-plant, \u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHuygens, his mechanical view of physics, \u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the nature of light and heat, \u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e-\u003ca href=\"#Page_156\"\u003e156\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis principle of the heights of ascent, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the law of inertia and the motion of a compound pendulum, \u003ca href=\"#Page_147\"\u003e147\u003c/a\u003e-\u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the impossible perpetual motion, \u003ca href=\"#Page_147\"\u003e147\u003c/a\u003e-\u003ca href=\"#Page_148\"\u003e148\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon work, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eselections from his works for use in instruction, \u003ca href=\"#Page_368\"\u003e368\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis view of light, \u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e-\u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e, \u003ca href=\"#Page_262\"\u003e262\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eHuygens, optical method for detecting imperfections in optical glasses \u003ca href=\"#Page_313\"\u003e313\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHydrogen balloon, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHydrostatics, Stevinus\u0027s principle of, \u003ca href=\"#Page_141\"\u003e141\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eHypotheses, their rôle in explanation, \u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eIchthyornis, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIchthyosaurus, \u003ca href=\"#Page_63\"\u003e63\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIdea? what is a theoretical, \u003ca href=\"#Page_241\"\u003e241\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIdealism, \u003ca href=\"#Page_209\"\u003e209\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIdeas, a product of organic nature, \u003ca href=\"#Page_217\"\u003e217\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eand facts, necessary to science, \u003ca href=\"#Page_231\"\u003e231\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003enot all of life, \u003ca href=\"#Page_233\"\u003e233\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir growth and importance, \u003ca href=\"#Page_233\"\u003e233\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ea product of universal evolution, \u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe history of, \u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein great minds, \u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe rich contents of, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir unsettled character in common life, their clarification in science, \u003ca href=\"#Page_1\"\u003e1\u003c/a\u003e-\u003ca href=\"#Page_2\"\u003e2\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eIdeography, the Chinese, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eImagery, mental, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eImagination, facts reflected in, \u003ca href=\"#Page_220\"\u003e220\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eInclined plane, law of, \u003ca href=\"#Page_140\"\u003e140\u003c/a\u003e-\u003ca href=\"#Page_141\"\u003e141\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIncomprehensible, the, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIndian, his modes of conception and interpretation, \u003ca href=\"#Page_218\"\u003e218\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eIndividual, a thread on which pearls are strung, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIndustrial arts, economy of the, E. Hermann on, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInertia, law of, \u003ca href=\"#Page_143\"\u003e143\u003c/a\u003e et seq., \u003ca href=\"#Page_146\"\u003e146\u003c/a\u003e et seq., \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e, footnote, \u003ca href=\"#Page_283\"\u003e283\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eInnate concepts of the understanding, Kant on, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInnervation, visual, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInquirer, his division of labor, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecompared to a shoemaker, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e-\u003ca href=\"#Page_106\"\u003e106\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ewhat constitutes the great, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe true, seeks the truth everywhere, \u003ca href=\"#Page_63\"\u003e63\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe, compared to a wooer, \u003ca href=\"#Page_45\"\u003e45\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eInstinctive knowledge, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_401\" id=\"Page_401\"\u003e[Pg 401]\u003c/a\u003e\u003c/span\u003eInstruction, aim of, the saving of experience, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein the classics, mathematics, and sciences, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e-\u003ca href=\"#Page_374\"\u003e374\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elimitation of matter of, \u003ca href=\"#Page_365\"\u003e365\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eInsulators, \u003ca href=\"#Page_130\"\u003e130\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIntegrals, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eIntellectual development, conditions of, \u003ca href=\"#Page_286\"\u003e286\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eIntentions, acts of nature compared to, \u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e-\u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInterconnexion of nature, \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInterdependence, of properties, \u003ca href=\"#Page_361\"\u003e361\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof the sensuous elements of the world, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eInterference experiments with the head-wave of moving projectiles, \u003ca href=\"#Page_327\"\u003e327\u003c/a\u003e-\u003ca href=\"#Page_328\"\u003e328\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInternational intercourse, established by Latin, \u003ca href=\"#Page_341\"\u003e341\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInternational measures, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInvention, discovery and, distinction between, \u003ca href=\"#Page_269\"\u003e269\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eInventions, requisites for the development of, \u003ca href=\"#Page_266\"\u003e266\u003c/a\u003e, \u003ca href=\"#Page_268\"\u003e268\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eIron-filings, \u003ca href=\"#Page_220\"\u003e220\u003c/a\u003e, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eItalian art, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eJacobi, C. G. J., on mathematics, \u003ca href=\"#Page_280\"\u003e280\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eJames, W., \u003ca href=\"#Page_275\"\u003e275\u003c/a\u003e, \u003ca href=\"#Page_299\"\u003e299\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eJava, \u003ca href=\"#Page_163\"\u003e163\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eJews and Christians, monotheism of the, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eJolly, Professor von, \u003ca href=\"#Page_112\"\u003e112\u003c/a\u003e, \u003ca href=\"#Page_274\"\u003e274\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eJoule, J. P., on the conservation of energy, \u003ca href=\"#Page_163\"\u003e163\u003c/a\u003e-\u003ca href=\"#Page_165\"\u003e165\u003c/a\u003e, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis conception of energy, \u003ca href=\"#Page_245\"\u003e245\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis metaphysics, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e, \u003ca href=\"#Page_246\"\u003e246\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis method of thought, \u003ca href=\"#Page_247\"\u003e247\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_137\"\u003e137\u003c/a\u003e, \u003ca href=\"#Page_138\"\u003e138\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eJournée, \u003ca href=\"#Page_317\"\u003e317\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eJudge, criminal, the natural philosopher compared to a, \u003ca href=\"#Page_48\"\u003e48\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eJudgment, essentially economy of thought, \u003ca href=\"#Page_201\"\u003e201\u003c/a\u003e-\u003ca href=\"#Page_202\"\u003e202\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esharpened by languages and sciences, \u003ca href=\"#Page_357\"\u003e357\u003c/a\u003e-\u003ca href=\"#Page_358\"\u003e358\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_232\"\u003e232\u003c/a\u003e-\u003ca href=\"#Page_233\"\u003e233\u003c/a\u003e, \u003ca href=\"#Page_238\"\u003e238\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eJuliet, Romeo and, \u003ca href=\"#Page_87\"\u003e87\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eJupiter, its satellites employed in the determination of the velocity of light, \u003ca href=\"#Page_51\"\u003e51\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eJurisprudence, Latin and Greek unnecessary for the study of, \u003ca href=\"#Page_346\"\u003e346\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eKant, his hypothesis of the origin of the planetary system, \u003ca href=\"#Page_5\"\u003e5\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis \u003ci\u003eCritique of Pure Reason\u003c/i\u003e, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon innate concepts of the understanding, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon time, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso footnote, \u003ca href=\"#Page_93\"\u003e93\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eKepler, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e, \u003ca href=\"#Page_270\"\u003e270\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eKinetic energy, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eKirchhoff, his epistemological ideas, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e-\u003ca href=\"#Page_258\"\u003e258\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis definition of mechanics, \u003ca href=\"#Page_236\"\u003e236\u003c/a\u003e, \u003ca href=\"#Page_258\"\u003e258\u003c/a\u003e, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e, \u003ca href=\"#Page_273\"\u003e273\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eKnight, \u003ca href=\"#Page_289\"\u003e289\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eKnowledge, a product of organic nature, \u003ca href=\"#Page_217\"\u003e217\u003c/a\u003e et seq., \u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003einstinctive, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emade possible by economy of thought, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eour first, derived from the economy of self-preservation, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe theory of, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eour primitive acts of the foundation of science, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eKocher, \u003ca href=\"#Page_328\"\u003e328\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eKoenig, measurement of the velocity of sound, \u003ca href=\"#Page_57\"\u003e57\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eKölliker, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eKopisch, \u003ca href=\"#Page_61\"\u003e61\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eKreidl, \u003ca href=\"#Page_299\"\u003e299\u003c/a\u003e, \u003ca href=\"#Page_302\"\u003e302\u003c/a\u003e, \u003ca href=\"#Page_306\"\u003e306\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis experiments, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eKrupp, \u003ca href=\"#Page_319\"\u003e319\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eLabels, the value of, \u003ca href=\"#Page_201\"\u003e201\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLabor, the accumulation of, the foundation of wealth and power, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003einquirer\u0027s division of, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e, \u003ca href=\"#Page_258\"\u003e258\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLabyrinth, of the ear, \u003ca href=\"#Page_18\"\u003e18\u003c/a\u003e, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e, \u003ca href=\"#Page_305\"\u003e305\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLactantius, on the study of moral and physical science, \u003ca href=\"#Page_89\"\u003e89\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLadder of our abstraction, the, \u003ca href=\"#Page_208\"\u003e208\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLadies, their eyes, \u003ca href=\"#Page_71\"\u003e71\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elike tuning-forks, \u003ca href=\"#Page_23\"\u003e23\u003c/a\u003e-\u003ca href=\"#Page_24\"\u003e24\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLagrange, on Huygens\u0027s principle, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the principle of virtual velocities, \u003ca href=\"#Page_150\"\u003e150\u003c/a\u003e-\u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003echaracter of the intellectual activity of a, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e, \u003ca href=\"#Page_278\"\u003e278\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLake-dwellers, \u003ca href=\"#Page_46\"\u003e46\u003c/a\u003e, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLamp-shade, \u003ca href=\"#Page_70\"\u003e70\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLane\u0027s unit jar, \u003ca href=\"#Page_115\"\u003e115\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLanguage, knowledge of the nature of, demanded by a liberal education, \u003ca href=\"#Page_356\"\u003e356\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erelationship between, and thought, \u003ca href=\"#Page_358\"\u003e358\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecommunication by \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eeconomy of, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehuman its character, \u003ca href=\"#Page_238\"\u003e238\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_402\" id=\"Page_402\"\u003e[Pg 402]\u003c/a\u003e\u003c/span\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof animals, \u003ca href=\"#Page_238\"\u003e238\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003einstruction in, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits methods, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLaplace, on the atoms of the brain, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the scientific achievements of the eighteenth century, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis hypothesis of the origin of the planetary system, \u003ca href=\"#Page_5\"\u003e5\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLatent heat, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLatin city of Maupertuis, \u003ca href=\"#Page_339\"\u003e339\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLatin, instruction in, \u003ca href=\"#Page_311\"\u003e311\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eintroduced with the Christian Church, \u003ca href=\"#Page_340\"\u003e340\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe language of scholars, the medium of international intercourse, its power, utility, and final abandonment, \u003ca href=\"#Page_341\"\u003e341\u003c/a\u003e-\u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe wealth of its literature, \u003ca href=\"#Page_348\"\u003e348\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe excessive study of, \u003ca href=\"#Page_346\"\u003e346\u003c/a\u003e, \u003ca href=\"#Page_349\"\u003e349\u003c/a\u003e, \u003ca href=\"#Page_354\"\u003e354\u003c/a\u003e, \u003ca href=\"#Page_355\"\u003e355\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits power to sharpen the judgment, \u003ca href=\"#Page_357\"\u003e357\u003c/a\u003e-\u003ca href=\"#Page_358\"\u003e358\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLavish extravagance of science, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLaw, a, defined, \u003ca href=\"#Page_256\"\u003e256\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ea natural, not contained in the conformity of the energies, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLaw-maker, motives of not always discernible, \u003ca href=\"#Page_9\"\u003e9\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLayard, \u003ca href=\"#Page_79\"\u003e79\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLearning, its nature, \u003ca href=\"#Page_366\"\u003e366\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eLeast superficial area, principle of, accounted for by the mutual attractions of liquid particles, \u003ca href=\"#Page_13\"\u003e13\u003c/a\u003e-\u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eillustrated by a pulley arrangement, \u003ca href=\"#Page_12\"\u003e12\u003c/a\u003e-\u003ca href=\"#Page_13\"\u003e13\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_9\"\u003e9\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLeibnitz, on harmony, \u003ca href=\"#Page_33\"\u003e33\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon international intercourse, \u003ca href=\"#Page_342\"\u003e342\u003c/a\u003e, footnote.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLessing, quotation from, \u003ca href=\"#Page_47\"\u003e47\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLetters of the alphabet, their symmetry, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e, \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLevel heights of work, \u003ca href=\"#Page_172\"\u003e172\u003c/a\u003e-\u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLever, a, in action, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLeverrier, prediction of the planet Neptune, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLeyden jar, \u003ca href=\"#Page_114\"\u003e114\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLiberal education, a, \u003ca href=\"#Page_341\"\u003e341\u003c/a\u003e et seq., \u003ca href=\"#Page_359\"\u003e359\u003c/a\u003e, \u003ca href=\"#Page_371\"\u003e371\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLibraries, thoughts stored up in, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLichtenberg, on instruction, \u003ca href=\"#Page_276\"\u003e276\u003c/a\u003e, \u003ca href=\"#Page_370\"\u003e370\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLicius, a Chinese philosopher, \u003ca href=\"#Page_213\"\u003e213\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLiebig, \u003ca href=\"#Page_163\"\u003e163\u003c/a\u003e, \u003ca href=\"#Page_278\"\u003e278\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLife and death, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLight, history of as elucidating how theories obstruct research, \u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eHuygens\u0027s and Newton\u0027s views of, \u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e-\u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits different conceptions, \u003ca href=\"#Page_226\"\u003e226\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erectilinear propagation of, \u003ca href=\"#Page_194\"\u003e194\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erôle of, in vision, \u003ca href=\"#Page_81\"\u003e81\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003espatial and temporal periodicity of, explains optical phenomena, \u003ca href=\"#Page_194\"\u003e194\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003enumerical velocity of, \u003ca href=\"#Page_58\"\u003e58\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ewhere does it go to? \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egenerally, \u003ca href=\"#Page_48\"\u003e48\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLike effects in like circumstances, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLikeness, \u003ca href=\"#Page_388\"\u003e388\u003c/a\u003e, \u003ca href=\"#Page_391\"\u003e391\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLilliput, \u003ca href=\"#Page_84\"\u003e84\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLines, straight, their symmetry, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecurved, their asymmetry, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof force, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLinks of thought, intermediate, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLiquefaction, latent heat of, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLiquid, efflux, law of, \u003ca href=\"#Page_150\"\u003e150\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eequilibrium, figures of, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe latter produced in open air, \u003ca href=\"#Page_7\"\u003e7\u003c/a\u003e-\u003ca href=\"#Page_8\"\u003e8\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir beauty and multiplicity of form, \u003ca href=\"#Page_7\"\u003e7\u003c/a\u003e, \u003ca href=\"#Page_8\"\u003e8\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emade permanent by melted colophonium, \u003ca href=\"#Page_7\"\u003e7\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLiquids, forms of, \u003ca href=\"#Page_1\"\u003e1\u003c/a\u003e-\u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edifference between, and solids, \u003ca href=\"#Page_2\"\u003e2\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir mobility and adaptiveness of form, \u003ca href=\"#Page_3\"\u003e3\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe courtiers \u003ci\u003epar excellence\u003c/i\u003e of the natural bodies, \u003ca href=\"#Page_3\"\u003e3\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003epossess under certain circumstances forms of their own, \u003ca href=\"#Page_3\"\u003e3\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLiving force, \u003ca href=\"#Page_137\"\u003e137\u003c/a\u003e, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elaw of the conservation of, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLloyd, observation of the conical refraction of light, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLobster, of Lake Mohrin, the, \u003ca href=\"#Page_61\"\u003e61\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLocalisation, cerebral, \u003ca href=\"#Page_210\"\u003e210\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLocke, on language and thought, \u003ca href=\"#Page_358\"\u003e358\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLocomotive, steam in the boiler of, \u003ca href=\"#Page_219\"\u003e219\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLoeb, J., \u003ca href=\"#Page_289\"\u003e289\u003c/a\u003e, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e, \u003ca href=\"#Page_302\"\u003e302\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLogarithms, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e, \u003ca href=\"#Page_219\"\u003e219\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein music, \u003ca href=\"#Page_103\"\u003e103\u003c/a\u003e-\u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLogical root, of the principle of energy, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof the principle of excluded perpetual motion, \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eLombroso, \u003ca href=\"#Page_280\"\u003e280\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eLucian, \u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003e\u003ci\u003eMacula acustica\u003c/i\u003e, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMagic lantern, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMagic powers of nature, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_403\" id=\"Page_403\"\u003e[Pg 403]\u003c/a\u003e\u003c/span\u003eMagical power of science, belief in the, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMagnet, a, \u003ca href=\"#Page_220\"\u003e220\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ewill compared to the pressure of a, \u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecoercive force of a, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMagnetic needle, near a current, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMagnetised bar of steel, \u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e-\u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMajor and minor keys in music, \u003ca href=\"#Page_100\"\u003e100\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eMalus, \u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMan, a fragment of nature\u0027s life, \u003ca href=\"#Page_49\"\u003e49\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis life embraces others, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMann, \u003ca href=\"#Page_364\"\u003e364\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eManuscript in a mirror, \u003ca href=\"#Page_93\"\u003e93\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMaple syrup, statues of, on Moon, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMarx, \u003ca href=\"#Page_35\"\u003e35\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMaterial, the relations of work with heat and the consumption of, \u003ca href=\"#Page_245\"\u003e245\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eMathematical methods, their character, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e-\u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMathematics, economy of, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon instruction in, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e-\u003ca href=\"#Page_374\"\u003e374\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eC. G. J. Jacobi on, \u003ca href=\"#Page_280\"\u003e280\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMatter, constancy of, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits nature, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe notion of, \u003ca href=\"#Page_213\"\u003e213\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMaupertuis, his Latin city, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMaximal and minimal problems, their rôle in physics, \u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eMayer, J. R., his conception of energy, \u003ca href=\"#Page_245\"\u003e245\u003c/a\u003e, \u003ca href=\"#Page_246\"\u003e246\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis methods of thought, \u003ca href=\"#Page_247\"\u003e247\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the conservation of energy, \u003ca href=\"#Page_163\"\u003e163\u003c/a\u003e, \u003ca href=\"#Page_164\"\u003e164\u003c/a\u003e, \u003ca href=\"#Page_165\"\u003e165\u003c/a\u003e, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis metaphysical utterances, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e, \u003ca href=\"#Page_246\"\u003e246\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_138\"\u003e138\u003c/a\u003e, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e, \u003ca href=\"#Page_217\"\u003e217\u003c/a\u003e, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e, \u003ca href=\"#Page_274\"\u003e274\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMeasurement, definition of, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMeasures, international, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMécanique céleste, \u003ca href=\"#Page_90\"\u003e90\u003c/a\u003e, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esociale, and morale, the, \u003ca href=\"#Page_90\"\u003e90\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMechanical, conception of the world, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e, \u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e et seq., \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eenergy, W. Thomson on waste of, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eanalogies between \u0026mdash;\u0026mdash; and thermal energy, \u003ca href=\"#Page_17\"\u003e17\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eequivalent of heat, electricity, etc., \u003ca href=\"#Page_164\"\u003e164\u003c/a\u003e, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emythology, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ephenomena, physical events as, \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ephilosophy, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ephysics, \u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e-\u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e, \u003ca href=\"#Page_212\"\u003e212\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esubstitution-value of heat, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e, footnote.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMechanics, Kirchhoff\u0027s definition of, \u003ca href=\"#Page_236\"\u003e236\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMedicine, students of, \u003ca href=\"#Page_326\"\u003e326\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMelody, \u003ca href=\"#Page_101\"\u003e101\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMelsens, \u003ca href=\"#Page_310\"\u003e310\u003c/a\u003e, \u003ca href=\"#Page_327\"\u003e327\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMemory, a treasure-house for comparison, \u003ca href=\"#Page_230\"\u003e230\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecommon elements impressed upon the, \u003ca href=\"#Page_180\"\u003e180\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits importance, \u003ca href=\"#Page_238\"\u003e238\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003escience disburdens the, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMendelejeff, his periodical series, \u003ca href=\"#Page_256\"\u003e256\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMental, adaptation, \u003ca href=\"#Page_214\"\u003e214\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecompletion of phenomena, \u003ca href=\"#Page_220\"\u003e220\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eimagery, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eimitation, our schematic, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eprocesses, economical, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ereproduction, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003evisualisation, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMephistopheles, \u003ca href=\"#Page_88\"\u003e88\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMercantile principle, a miserly, at the basis of science, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMersenne, \u003ca href=\"#Page_377\"\u003e377\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMesmerism, the mental state of ordinary minds, \u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMetaphysical establishment of doctrine of energy, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMetaphysical spooks, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMetrical, concepts of electricity, \u003ca href=\"#Page_107\"\u003e107\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003enotions, energy and entropy are, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eunits, the building-stones of the physicist, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMetronomes, \u003ca href=\"#Page_41\"\u003e41\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMeyer, Lothar, his periodical series, \u003ca href=\"#Page_256\"\u003e256\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMiddle Ages, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e, \u003ca href=\"#Page_349\"\u003e349\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMidsummer Night\u0027s Dream, \u003ca href=\"#Page_309\"\u003e309\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMill, John Stuart, \u003ca href=\"#Page_230\"\u003e230\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMillers, school for, \u003ca href=\"#Page_326\"\u003e326\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMill-wheel, doing work, \u003ca href=\"#Page_161\"\u003e161\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMimicking facts in thought, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMinor and major keys in music, \u003ca href=\"#Page_100\"\u003e100\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eMirror, symmetrical reversion of objects in, \u003ca href=\"#Page_92\"\u003e92\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eMiserly mercantile principle at the basis of science, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMoat, child looking into, \u003ca href=\"#Page_208\"\u003e208\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eModern scientists, adherents of the mechanical philosophy, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMolecular theories, \u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMolecules, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMolière, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMomentum, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMonocular vision, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_404\" id=\"Page_404\"\u003e[Pg 404]\u003c/a\u003e\u003c/span\u003eMonotheism of the Christians and Jews, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMontagues and Capulets, \u003ca href=\"#Page_87\"\u003e87\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMoon, eclipse of, \u003ca href=\"#Page_219\"\u003e219\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elightness of bodies on, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe study of the, \u003ca href=\"#Page_90\"\u003e90\u003c/a\u003e, \u003ca href=\"#Page_284\"\u003e284\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMoreau, \u003ca href=\"#Page_307\"\u003e307\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMosaic of thought, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMotion, a perpetual, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003equantity of, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe Eleatics on, \u003ca href=\"#Page_158\"\u003e158\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eWundt on, \u003ca href=\"#Page_158\"\u003e158\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe Herbartians on, \u003ca href=\"#Page_158\"\u003e158\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMotions, natural and violent, \u003ca href=\"#Page_226\"\u003e226\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir familiar character, \u003ca href=\"#Page_157\"\u003e157\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMountains of the earth, would crumble if very large, \u003ca href=\"#Page_3\"\u003e3\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eweight of bodies on, \u003ca href=\"#Page_112\"\u003e112\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMozart, \u003ca href=\"#Page_44\"\u003e44\u003c/a\u003e, \u003ca href=\"#Page_279\"\u003e279\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMüller, Johann, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMultiplication-table, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMultiplier, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMusic, band of, its \u003ci\u003etempo\u003c/i\u003e accelerated and retarded, \u003ca href=\"#Page_53\"\u003e53\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe principle of repetition in, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits notation, mathematically illustrated, \u003ca href=\"#Page_103\"\u003e103\u003c/a\u003e-\u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMusical notes, reversion of, \u003ca href=\"#Page_101\"\u003e101\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir economy, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMusical scale, a species of one-dimensional space, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eMystery, in physics, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003escience can dispense with, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMysticism, numerical, \u003ca href=\"#Page_33\"\u003e33\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein the principle of energy, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eMythology, the mechanical, of philosophy, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eNagel, von, \u003ca href=\"#Page_364\"\u003e364\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNansen, \u003ca href=\"#Page_296\"\u003e296\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNapoleon, picture representing the tomb of, \u003ca href=\"#Page_36\"\u003e36\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNations, intercourse and ideas of, \u003ca href=\"#Page_336\"\u003e336\u003c/a\u003e-\u003ca href=\"#Page_337\"\u003e337\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNatural constants, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNatural law, a, not contained in the conformity of the energies, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNatural laws, abridged descriptions, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elikened to type, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eNatural motions, \u003ca href=\"#Page_225\"\u003e225\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNatural selection in scientific theories, \u003ca href=\"#Page_63\"\u003e63\u003c/a\u003e, \u003ca href=\"#Page_218\"\u003e218\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNature, experience the well-spring of all knowledge of, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efashions of, \u003ca href=\"#Page_64\"\u003e64\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efirst knowledge of, instinctive, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egeneral interconnexion of, \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehas many sides, \u003ca href=\"#Page_217\"\u003e217\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eher forces compared to purposes, \u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e-\u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elikened to a good man of business, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe economy of her actions, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehow she appears to other animals, \u003ca href=\"#Page_83\"\u003e83\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003einquiry of, viewed as a torture, \u003ca href=\"#Page_48\"\u003e48\u003c/a\u003e-\u003ca href=\"#Page_49\"\u003e49\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eview of, as something designedly concealed from man, \u003ca href=\"#Page_49\"\u003e49\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elike a covetous tailor, \u003ca href=\"#Page_9\"\u003e9\u003c/a\u003e-\u003ca href=\"#Page_10\"\u003e10\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emagic powers of, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eour view of, modified by binocular vision, \u003ca href=\"#Page_82\"\u003e82\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe experimental method a questioning of, \u003ca href=\"#Page_48\"\u003e48\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eNegro hamlet, the science of a, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNeptune, prediction and discovery of the planet, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNew views, \u003ca href=\"#Page_296\"\u003e296\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eNewton, describes polarisation, \u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eexpresses his wealth of thought in Latin, \u003ca href=\"#Page_341\"\u003e341\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis discovery of gravitation, \u003ca href=\"#Page_225\"\u003e225\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis solution of dispersion, \u003ca href=\"#Page_362\"\u003e362\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis principle of the equality of pressure and counterpressure, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis view of light, \u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e-\u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon absolute time, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eselections from his works for use in instruction, \u003ca href=\"#Page_368\"\u003e368\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_270\"\u003e270\u003c/a\u003e, \u003ca href=\"#Page_274\"\u003e274\u003c/a\u003e, \u003ca href=\"#Page_279\"\u003e279\u003c/a\u003e, \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e, \u003ca href=\"#Page_289\"\u003e289\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eNobility, they displace Latin, \u003ca href=\"#Page_342\"\u003e342\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNotation, musical, mathematically illustrated, \u003ca href=\"#Page_103\"\u003e103\u003c/a\u003e-\u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNumbers, economy of, \u003ca href=\"#Page_195\"\u003e195\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir connexion with consonance, \u003ca href=\"#Page_32\"\u003e32\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eNumerical mysticism, \u003ca href=\"#Page_33\"\u003e33\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eNursery, the questions of the, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eObservation, \u003ca href=\"#Page_310\"\u003e310\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eObservation, in science, \u003ca href=\"#Page_261\"\u003e261\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOcean-stream, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOettingen, Von, \u003ca href=\"#Page_103\"\u003e103\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOhm, on electric currents, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOhm, the word, \u003ca href=\"#Page_343\"\u003e343\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOil, alcohol, water, and, employed in Plateau\u0027s experiments, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efree mass of, assumes the shape of a sphere, \u003ca href=\"#Page_12\"\u003e12\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egeometrical figures of, \u003ca href=\"#Page_5\"\u003e5\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eOne-eyed people, vision of, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOphthalmoscope, \u003ca href=\"#Page_18\"\u003e18\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOptic nerves, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_405\" id=\"Page_405\"\u003e[Pg 405]\u003c/a\u003e\u003c/span\u003eOptimism and pessimism, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOrder of physics, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOrgan, bellows of an, \u003ca href=\"#Page_135\"\u003e135\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOrganic nature, results of Darwin\u0027s studies of, \u003ca href=\"#Page_215\"\u003e215\u003c/a\u003e et seq.\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eSee \u003ci\u003eAdaptation\u003c/i\u003e and \u003ci\u003eHeredity\u003c/i\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eOriental world of fables, \u003ca href=\"#Page_273\"\u003e273\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOrientation, sensations of, \u003ca href=\"#Page_282\"\u003e282\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eOscillation, centre of, \u003ca href=\"#Page_147\"\u003e147\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eOstwald, \u003ca href=\"#Page_172\"\u003e172\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOtoliths, \u003ca href=\"#Page_301\"\u003e301\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eOvertones, \u003ca href=\"#Page_28\"\u003e28\u003c/a\u003e, \u003ca href=\"#Page_40\"\u003e40\u003c/a\u003e, \u003ca href=\"#Page_349\"\u003e349\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eOzone, Schöbein\u0027s discovery of, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003ePainted things, the difference between real and, \u003ca href=\"#Page_68\"\u003e68\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePalestrina, \u003ca href=\"#Page_44\"\u003e44\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eParameter, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePartial tones, \u003ca href=\"#Page_390\"\u003e390\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eParticles, smallest, \u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePascheles, Dr. W., \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePaulsen, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e, \u003ca href=\"#Page_340\"\u003e340\u003c/a\u003e, \u003ca href=\"#Page_373\"\u003e373\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePearls of life, strung on the individual as on a thread, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePencil surpasses the mathematician in intelligence, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePendulum, motion of a, \u003ca href=\"#Page_144\"\u003e144\u003c/a\u003e et seq.,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eincreased motion of, due to slight impulses, \u003ca href=\"#Page_21\"\u003e21\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eelectrical, \u003ca href=\"#Page_110\"\u003e110\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePercepts, of like form, \u003ca href=\"#Page_390\"\u003e390\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePeriodical, changes, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eseries, \u003ca href=\"#Page_256\"\u003e256\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePermanent, changes, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eelements of the world, \u003ca href=\"#Page_194\"\u003e194\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePerpetual motion, a, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edefined, \u003ca href=\"#Page_139\"\u003e139\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eimpossibility of, \u003ca href=\"#Page_139\"\u003e139\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe principle of the, excluded, \u003ca href=\"#Page_140\"\u003e140\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eexcluded from general physics, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePersonality, its nature, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePerspective, \u003ca href=\"#Page_76\"\u003e76\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003econtraction of, \u003ca href=\"#Page_74\"\u003e74\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edistortion of, \u003ca href=\"#Page_77\"\u003e77\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePessimism and optimism, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePharaohs, \u003ca href=\"#Page_85\"\u003e85\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhenomenology, a universal physical, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhilistine, modes of thought of, \u003ca href=\"#Page_223\"\u003e223\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhilology, comparison in, \u003ca href=\"#Page_239\"\u003e239\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhilosopher, an ancient, on the moral and physical sciences, \u003ca href=\"#Page_89\"\u003e89\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhilosophy, its character at all times, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emechanical, \u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e et seq., \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e, \u003ca href=\"#Page_259\"\u003e259\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePhonetic alphabets, their economy, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhotography, by the electric spark, \u003ca href=\"#Page_318\"\u003e318\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhotography of projectiles, \u003ca href=\"#Page_309\"\u003e309\u003c/a\u003e-\u003ca href=\"#Page_337\"\u003e337\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhotography, stupendous advances of, \u003ca href=\"#Page_74\"\u003e74\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhysical, concepts, fetishism in our, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eideas and principles, their nature, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003einquiry, the economical nature of, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eresearch, object of \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e, \u003ca href=\"#Page_209\"\u003e209\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePhysical phenomena, as mechanical phenomena, \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erelations between, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePhysico-mechanical view of the world, \u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e, \u003ca href=\"#Page_188\"\u003e188\u003c/a\u003e, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhysics, compared to a well-kept household, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eeconomical experience, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe principles of, descriptive, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe methods of, \u003ca href=\"#Page_209\"\u003e209\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits method characterised, \u003ca href=\"#Page_211\"\u003e211\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecomparison in, \u003ca href=\"#Page_239\"\u003e239\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe facts of, qualitatively homogeneous, \u003ca href=\"#Page_255\"\u003e255\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehow it began, \u003ca href=\"#Page_37\"\u003e37\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehelped by psychology, \u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003estudy of its own character, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe goal of, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e, \u003ca href=\"#Page_209\"\u003e209\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePhysiological psychology, its methods, \u003ca href=\"#Page_211\"\u003e211\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003ePhysiology, its scope, \u003ca href=\"#Page_212\"\u003e212\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePiano, its mirrored counterpart, \u003ca href=\"#Page_100\"\u003e100\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eused to illustrate the facts of sympathetic vibration, \u003ca href=\"#Page_25\"\u003e25\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePiano-player, a speaker compared to, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePicture, physical, a, \u003ca href=\"#Page_110\"\u003e110\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePike, learns by experience, \u003ca href=\"#Page_267\"\u003e267\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePillars of Corti, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePlaces, heavy bodies seek their, \u003ca href=\"#Page_224\"\u003e224\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003ePlanetary system, origin of, illustrated, \u003ca href=\"#Page_5\"\u003e5\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePlasticity of organic nature, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePlateau, his law of free liquid equilibrium, \u003ca href=\"#Page_9\"\u003e9\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis method of getting rid of the effects of gravity, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePlates of oil, thin, \u003ca href=\"#Page_6\"\u003e6\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePlato, \u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e, \u003ca href=\"#Page_371\"\u003e371\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePlautus, \u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePlayfair, \u003ca href=\"#Page_138\"\u003e138\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_406\" id=\"Page_406\"\u003e[Pg 406]\u003c/a\u003e\u003c/span\u003ePleasant effects, cause of, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003ePliny, \u003ca href=\"#Page_349\"\u003e349\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePoetry and science, \u003ca href=\"#Page_30\"\u003e30\u003c/a\u003e, \u003ca href=\"#Page_31\"\u003e31\u003c/a\u003e, \u003ca href=\"#Page_351\"\u003e351\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePoinsot, on the foundations of mechanics, \u003ca href=\"#Page_152\"\u003e152\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003ePolarisation, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eabstractly described by Newton, \u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePolitics, Chinese speak with unwillingness of, \u003ca href=\"#Page_374\"\u003e374\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePollak, \u003ca href=\"#Page_299\"\u003e299\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePolyp plant, humanity likened to a, \u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePompeii, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eart in, \u003ca href=\"#Page_80\"\u003e80\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePopper J., \u003ca href=\"#Page_172\"\u003e172\u003c/a\u003e, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePotential, social, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eelectrical, \u003ca href=\"#Page_121\"\u003e121\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emeasurement of, \u003ca href=\"#Page_126\"\u003e126\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efall of, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eswarm of notions in the idea of, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits wide scope, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePottery, invention of, \u003ca href=\"#Page_263\"\u003e263\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePrediction, \u003ca href=\"#Page_221\"\u003e221\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003ePrejudice, the function, power, and dangers of, \u003ca href=\"#Page_232\"\u003e232\u003c/a\u003e-\u003ca href=\"#Page_233\"\u003e233\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePreparatory schools, the defects of the German, \u003ca href=\"#Page_346\"\u003e346\u003c/a\u003e-\u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ewhat they should teach, \u003ca href=\"#Page_364\"\u003e364\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePressure of a stone or of a magnet, will compared to, \u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_157\"\u003e157\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePrimitive acts of knowledge the foundation of scientific thought, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eProblem, nature of a, \u003ca href=\"#Page_223\"\u003e223\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eProblems which are wrongly formulated, \u003ca href=\"#Page_308\"\u003e308\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eProcess, Carnot\u0027s, \u003ca href=\"#Page_161\"\u003e161\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eProjectiles, the effects of the impact of, \u003ca href=\"#Page_310\"\u003e310\u003c/a\u003e, \u003ca href=\"#Page_327\"\u003e327\u003c/a\u003e-\u003ca href=\"#Page_328\"\u003e328\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eseen with the naked eye, \u003ca href=\"#Page_311\"\u003e311\u003c/a\u003e, \u003ca href=\"#Page_317\"\u003e317\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emeasuring the velocity of, \u003ca href=\"#Page_332\"\u003e332\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ephotography of, \u003ca href=\"#Page_309\"\u003e309\u003c/a\u003e-\u003ca href=\"#Page_337\"\u003e337\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eProny\u0027s brake, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eProof, nature of, \u003ca href=\"#Page_284\"\u003e284\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eProphesying events, \u003ca href=\"#Page_220\"\u003e220\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003ePsalms, quotation from the, \u003ca href=\"#Page_89\"\u003e89\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePseudoscope, Wheatstone\u0027s, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePsychology, preceded by astronomy, \u003ca href=\"#Page_90\"\u003e90\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehow reached, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehelps physical science, \u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits method the same as that of physics, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePully arrangement, illustrating principle of least superficial area, \u003ca href=\"#Page_12\"\u003e12\u003c/a\u003e-\u003ca href=\"#Page_13\"\u003e13\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePurkinje, \u003ca href=\"#Page_284\"\u003e284\u003c/a\u003e, \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e, \u003ca href=\"#Page_299\"\u003e299\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePurposes, the acts of nature compared to, \u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e-\u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003enature pursues no, \u003ca href=\"#Page_66\"\u003e66\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003ePuzzle-lock, a, \u003ca href=\"#Page_26\"\u003e26\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePuzzles, \u003ca href=\"#Page_277\"\u003e277\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePyramid of oil, \u003ca href=\"#Page_6\"\u003e6\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePythagoras, his discovery of the laws of harmony, \u003ca href=\"#Page_32\"\u003e32\u003c/a\u003e, \u003ca href=\"#Page_259\"\u003e259\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eQuality of tones, \u003ca href=\"#Page_36\"\u003e36\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eQuantitative investigation, the goal of, \u003ca href=\"#Page_180\"\u003e180\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eQuantity of electricity, \u003ca href=\"#Page_111\"\u003e111\u003c/a\u003e, \u003ca href=\"#Page_118\"\u003e118\u003c/a\u003e, \u003ca href=\"#Page_119\"\u003e119\u003c/a\u003e, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e-\u003ca href=\"#Page_170\"\u003e170\u003c/a\u003e, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof heat, \u003ca href=\"#Page_166\"\u003e166\u003c/a\u003e, \u003ca href=\"#Page_167\"\u003e167\u003c/a\u003e-\u003ca href=\"#Page_171\"\u003e171\u003c/a\u003e, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof motion, \u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eQuests made of the inquirer, not by him, \u003ca href=\"#Page_30\"\u003e30\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eQuételet, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eRabelais, \u003ca href=\"#Page_283\"\u003e283\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRaindrop, form of, \u003ca href=\"#Page_3\"\u003e3\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRameau, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eReaction and action, principle of, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eReactions, disclosure of the connexion of, \u003ca href=\"#Page_270\"\u003e270\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eRealgymnasien, \u003ca href=\"#Page_365\"\u003e365\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRealschulen, \u003ca href=\"#Page_365\"\u003e365\u003c/a\u003e, \u003ca href=\"#Page_373\"\u003e373\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eReason, stands above the senses, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eReflex action, \u003ca href=\"#Page_210\"\u003e210\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eReflexion, produces symmetrical reversion of objects, \u003ca href=\"#Page_93\"\u003e93\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eRefraction, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e, \u003ca href=\"#Page_194\"\u003e194\u003c/a\u003e, \u003ca href=\"#Page_208\"\u003e208\u003c/a\u003e, \u003ca href=\"#Page_230\"\u003e230\u003c/a\u003e, \u003ca href=\"#Page_231\"\u003e231\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eReger, \u003ca href=\"#Page_328\"\u003e328\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eReliefs, photographs of, \u003ca href=\"#Page_68\"\u003e68\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRepetition, its rôle in æsthetics, \u003ca href=\"#Page_89\"\u003e89\u003c/a\u003e, footnote, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e et seq., \u003ca href=\"#Page_97\"\u003e97\u003c/a\u003e, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e et seq., \u003ca href=\"#Page_390\"\u003e390\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eReproduction of facts in thought, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRepulsion, electric, \u003ca href=\"#Page_109\"\u003e109\u003c/a\u003e et seq., \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eResearch, function of experimental \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe aim of, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eResemblances between facts, \u003ca href=\"#Page_255\"\u003e255\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eResin, solution of, \u003ca href=\"#Page_7\"\u003e7\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eResistance, laws of, for bodies travelling in air and fluids, \u003ca href=\"#Page_333\"\u003e333\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eResonance, corporeal, \u003ca href=\"#Page_392\"\u003e392\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eResponse of sonorous bodies, \u003ca href=\"#Page_25\"\u003e25\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRetina, the corresponding spots of \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_407\" id=\"Page_407\"\u003e[Pg 407]\u003c/a\u003e\u003c/span\u003e\u003cspan style=\"margin-left: 1em;\"\u003enerves of compared to fingers of a hand, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eReversible processes, \u003ca href=\"#Page_161\"\u003e161\u003c/a\u003e et seq., \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e, \u003ca href=\"#Page_176\"\u003e176\u003c/a\u003e, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e, \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRhine, the, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRichard the Third, \u003ca href=\"#Page_77\"\u003e77\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRiddles, \u003ca href=\"#Page_277\"\u003e277\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRiders, \u003ca href=\"#Page_379\"\u003e379\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRiegler, \u003ca href=\"#Page_319\"\u003e319\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRiess, experiment with the thermo-electrometer, \u003ca href=\"#Page_133\"\u003e133\u003c/a\u003e et seq., \u003ca href=\"#Page_169\"\u003e169\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRigid connexions, \u003ca href=\"#Page_142\"\u003e142\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRind of a fruit, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRings of oil, illustrating formation of rings of Saturn, \u003ca href=\"#Page_5\"\u003e5\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRitter, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e, \u003ca href=\"#Page_299\"\u003e299\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRods of Corti, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRolph, W. H., \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRoman Church, Latin introduced with the, \u003ca href=\"#Page_340\"\u003e340\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eRomans, their provinciality and narrow-mindedness, \u003ca href=\"#Page_270\"\u003e270\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRomeo and Juliet, \u003ca href=\"#Page_87\"\u003e87\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRömer, Olaf, \u003ca href=\"#Page_51\"\u003e51\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eRoots, the nature of, in language, \u003ca href=\"#Page_252\"\u003e252\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRosetti, his experiment on the work required to develop electricity, \u003ca href=\"#Page_131\"\u003e131\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRotating bodies, \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRotation, apparatus of, in physics, \u003ca href=\"#Page_59\"\u003e59\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esensations of, \u003ca href=\"#Page_288\"\u003e288\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eRousseau, \u003ca href=\"#Page_336\"\u003e336\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRubber pyramid, illustrating the principle of least superficial area, \u003ca href=\"#Page_10\"\u003e10\u003c/a\u003e-\u003ca href=\"#Page_11\"\u003e11\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eRuysdael, \u003ca href=\"#Page_279\"\u003e279\u003c/a\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\r\n\u003cli\u003eSachs, Hans, \u003ca href=\"#Page_106\"\u003e106\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSalcher, Prof. \u003ca href=\"#Page_319\"\u003e319\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSalviati, \u003ca href=\"#Page_144\"\u003e144\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSaturn, rings of, their formation illustrated, \u003ca href=\"#Page_5\"\u003e5\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSaurians, \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSauveur, on acoustics, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e, \u003ca href=\"#Page_375\"\u003e375\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eSavage, modes of conception and interpretation of a, \u003ca href=\"#Page_218\"\u003e218\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eSchäfer, K., \u003ca href=\"#Page_298\"\u003e298\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003ci\u003eSchlierenmethode\u003c/i\u003e, \u003ca href=\"#Page_317\"\u003e317\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSchönbein\u0027s discovery of ozone, \u003ca href=\"#Page_271\"\u003e271\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSchool-boy, copy-book of, \u003ca href=\"#Page_92\"\u003e92\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSchoolmen, \u003ca href=\"#Page_214\"\u003e214\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSchools, State-control of, \u003ca href=\"#Page_372\"\u003e372\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eSchopenhauer, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSchultze, Max, \u003ca href=\"#Page_19\"\u003e19\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eScience, a miserly mercantile principle at its basis, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecompared to a business, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eviewed as a maximum or minimum problem, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e, footnote;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits process not greatly different from the intellectual activity of ordinary life, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e, footnote;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eeconomy of its task, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erelation of, to poetry, \u003ca href=\"#Page_30\"\u003e30\u003c/a\u003e, \u003ca href=\"#Page_31\"\u003e31\u003c/a\u003e, \u003ca href=\"#Page_351\"\u003e351\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe church of, \u003ca href=\"#Page_67\"\u003e67\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ebeginnings of, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ebelief in the magical power of, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecan dispense with mystery, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003elavish extravagance of, \u003ca href=\"#Page_189\"\u003e189\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eeconomy of the terminology of, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003epartly made up of the intelligence of others, \u003ca href=\"#Page_196\"\u003e196\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003estripped of mystery, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits true power, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe economical schematism of, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe object of, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe tools of, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edoes not create facts, \u003ca href=\"#Page_211\"\u003e211\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof the future, \u003ca href=\"#Page_213\"\u003e213\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erevolution in, dating from Galileo, \u003ca href=\"#Page_214\"\u003e214\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe natural foe of the marvellous, \u003ca href=\"#Page_224\"\u003e224\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003echaracterised, \u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egrowth of, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edramatic element in, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edescribed, \u003ca href=\"#Page_251\"\u003e251\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eits function, \u003ca href=\"#Page_253\"\u003e253\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eclassification in, \u003ca href=\"#Page_255\"\u003e255\u003c/a\u003e, \u003ca href=\"#Page_259\"\u003e259\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe way of discovery in, \u003ca href=\"#Page_316\"\u003e316\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eSee also \u003ci\u003ePhysics\u003c/i\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSciences, partition of the, \u003ca href=\"#Page_86\"\u003e86\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe barriers and relations between the \u003ca href=\"#Page_257\"\u003e257\u003c/a\u003e-\u003ca href=\"#Page_258\"\u003e258\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon instruction in the, \u003ca href=\"#Page_338\"\u003e338\u003c/a\u003e-\u003ca href=\"#Page_374\"\u003e374\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eScientific, criticism, Socrates the father of, \u003ca href=\"#Page_1\"\u003e1\u003c/a\u003e, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ediscoveries, their fate, \u003ca href=\"#Page_138\"\u003e138\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eknowledge, involves description, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethought, transformation and adaptation in, \u003ca href=\"#Page_214\"\u003e214\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethought, advanced by new experiences, \u003ca href=\"#Page_223\"\u003e223\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethought, the difficulty of, \u003ca href=\"#Page_366\"\u003e366\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eterms, \u003ca href=\"#Page_342\"\u003e342\u003c/a\u003e-\u003ca href=\"#Page_343\"\u003e343\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efounded on primitive acts of knowledge, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eScientists, stories about their ignorance, \u003ca href=\"#Page_342\"\u003e342\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eScrew, the, \u003ca href=\"#Page_62\"\u003e62\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSea-sickness, \u003ca href=\"#Page_284\"\u003e284\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSecret computation, Leibnitz\u0027s, \u003ca href=\"#Page_33\"\u003e33\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSeek their places, bodies, \u003ca href=\"#Page_226\"\u003e226\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSelf-induction, coefficient of, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e, \u003ca href=\"#Page_252\"\u003e252\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSelf-observation, \u003ca href=\"#Page_211\"\u003e211\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_408\" id=\"Page_408\"\u003e[Pg 408]\u003c/a\u003e\u003c/span\u003eSelf-preservation, our first knowledge derived from the economy of, \u003ca href=\"#Page_197\"\u003e197\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003estruggle for, among ideas, \u003ca href=\"#Page_228\"\u003e228\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSemi-circular canals, \u003ca href=\"#Page_290\"\u003e290\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eSensation of rounding a railway curve, \u003ca href=\"#Page_286\"\u003e286\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSensations, analysed, \u003ca href=\"#Page_251\"\u003e251\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ewhen similar, produce agreeable effects, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etheir character, \u003ca href=\"#Page_200\"\u003e200\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edefined, \u003ca href=\"#Page_209\"\u003e209\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof orientation, \u003ca href=\"#Page_282\"\u003e282\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSense-elements, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSenses, theory of, \u003ca href=\"#Page_104\"\u003e104\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe source of our knowledge of facts, \u003ca href=\"#Page_237\"\u003e237\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSeventh, the troublesome, \u003ca href=\"#Page_46\"\u003e46\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eShadow method, \u003ca href=\"#Page_313\"\u003e313\u003c/a\u003e et seq., \u003ca href=\"#Page_317\"\u003e317\u003c/a\u003e footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eShadows, rôle of, in vision, \u003ca href=\"#Page_81\"\u003e81\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eShakespeare, \u003ca href=\"#Page_278\"\u003e278\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSharps, reversed into flats, \u003ca href=\"#Page_101\"\u003e101\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eShell, spherical, law of attraction for a, \u003ca href=\"#Page_124\"\u003e124\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eShoemaker, inquirer compared to, \u003ca href=\"#Page_105\"\u003e105\u003c/a\u003e-\u003ca href=\"#Page_106\"\u003e106\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eShooting, \u003ca href=\"#Page_309\"\u003e309\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eShots, double report of, \u003ca href=\"#Page_229\"\u003e229\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eSimilarity, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSimony, \u003ca href=\"#Page_280\"\u003e280\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSimplicity, a varying element in description, \u003ca href=\"#Page_254\"\u003e254\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSines, law of the, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSinking of heavy bodies, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSixth sense, \u003ca href=\"#Page_297\"\u003e297\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSmith, R., on acoustics, \u003ca href=\"#Page_34\"\u003e34\u003c/a\u003e, \u003ca href=\"#Page_381\"\u003e381\u003c/a\u003e, \u003ca href=\"#Page_383\"\u003e383\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSoap-films, Van der Mensbrugghe\u0027s experiment with, \u003ca href=\"#Page_11\"\u003e11\u003c/a\u003e-\u003ca href=\"#Page_12\"\u003e12\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSoapsuds, films and figures of, \u003ca href=\"#Page_7\"\u003e7\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSocial potential, \u003ca href=\"#Page_15\"\u003e15\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSocrates, the father of scientific criticism, \u003ca href=\"#Page_1\"\u003e1\u003c/a\u003e, \u003ca href=\"#Page_16\"\u003e16\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSodium, \u003ca href=\"#Page_202\"\u003e202\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSodium-light, vibrations of, as a measure of time, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSolidity, conception of, by the eye, \u003ca href=\"#Page_71\"\u003e71\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003espatial, photographs of, \u003ca href=\"#Page_73\"\u003e73\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSolids, and liquids, their difference merely one of degree, \u003ca href=\"#Page_2\"\u003e2\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSonorous bodies, \u003ca href=\"#Page_24\"\u003e24\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eSoret, J. P., \u003ca href=\"#Page_89\"\u003e89\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSounds, symmetry of, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003egenerally, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e-\u003ca href=\"#Page_47\"\u003e47\u003c/a\u003e, \u003ca href=\"#Page_212\"\u003e212\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSound-waves rendered visible, \u003ca href=\"#Page_315\"\u003e315\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eSources of the principle of energy, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpace, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esensation of, \u003ca href=\"#Page_210\"\u003e210\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSpark, electric, \u003ca href=\"#Page_117\"\u003e117\u003c/a\u003e, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e, \u003ca href=\"#Page_133\"\u003e133\u003c/a\u003e, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpatial vision, \u003ca href=\"#Page_386\"\u003e386\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpecies, stability of, a theory, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpecific energies, \u003ca href=\"#Page_291\"\u003e291\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpecific heat, \u003ca href=\"#Page_166\"\u003e166\u003c/a\u003e, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpecific inductive capacity, \u003ca href=\"#Page_117\"\u003e117\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpectral analysis of sound, \u003ca href=\"#Page_27\"\u003e27\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpectrum, mental associations of the, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpeech, the instinct of, cultivated by languages, \u003ca href=\"#Page_354\"\u003e354\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpencer, \u003ca href=\"#Page_218\"\u003e218\u003c/a\u003e, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSphere, a soft rotating, \u003ca href=\"#Page_2\"\u003e2\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe figure of least surface, \u003ca href=\"#Page_12\"\u003e12\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eelectrical capacity of, \u003ca href=\"#Page_123\"\u003e123\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSpherical shell, law of attraction for \u003ca href=\"#Page_124\"\u003e124\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpiders, the eyes of, \u003ca href=\"#Page_67\"\u003e67\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpirits, as explanation of the world \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpiritualism, modern, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpooks, metaphysical, \u003ca href=\"#Page_222\"\u003e222\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSquinting, \u003ca href=\"#Page_72\"\u003e72\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStability of our environment, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStallo, \u003ca href=\"#Page_336\"\u003e336\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStars, the fixed, \u003ca href=\"#Page_90\"\u003e90\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eState, benefits and evils of its control of the schools, \u003ca href=\"#Page_372\"\u003e372\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe Church and, \u003ca href=\"#Page_88\"\u003e88\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eStatical electricity, \u003ca href=\"#Page_134\"\u003e134\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStationary currents, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStatoliths, \u003ca href=\"#Page_303\"\u003e303\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSteam-engine, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e, \u003ca href=\"#Page_265\"\u003e265\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSteeple-jacks, \u003ca href=\"#Page_75\"\u003e75\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStereoscope, Wheatstone and Brewster\u0027s, \u003ca href=\"#Page_73\"\u003e73\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStevinus, on the inclined plane, \u003ca href=\"#Page_140\"\u003e140\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon hydrostatics, \u003ca href=\"#Page_141\"\u003e141\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the equilibrium of systems, \u003ca href=\"#Page_142\"\u003e142\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ediscovers the principle of virtual velocities, \u003ca href=\"#Page_150\"\u003e150\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003echaracterisation of his thought, \u003ca href=\"#Page_142\"\u003e142\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eStone Age, \u003ca href=\"#Page_46\"\u003e46\u003c/a\u003e, \u003ca href=\"#Page_321\"\u003e321\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStörensen, \u003ca href=\"#Page_306\"\u003e306\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStove, primitive, \u003ca href=\"#Page_263\"\u003e263\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStraight line, a, its symmetry, \u003ca href=\"#Page_98\"\u003e98\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStraight, meaning of the word, \u003ca href=\"#Page_240\"\u003e240\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_409\" id=\"Page_409\"\u003e[Pg 409]\u003c/a\u003e\u003c/span\u003eStreet, vista into a, \u003ca href=\"#Page_75\"\u003e75\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStriae, in glass, \u003ca href=\"#Page_313\"\u003e313\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStriate method, for detecting optical imperfections, \u003ca href=\"#Page_317\"\u003e317\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStriking distance, \u003ca href=\"#Page_115\"\u003e115\u003c/a\u003e, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStrings, vibrations of, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eStruggle for existence among ideas, \u003ca href=\"#Page_217\"\u003e217\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSubstance, heat conceived as a, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eelectricity as a, \u003ca href=\"#Page_170\"\u003e170\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ethe source of our notion of, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erôle of the notion of, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eenergy conceived as a, \u003ca href=\"#Page_164\"\u003e164\u003c/a\u003e, \u003ca href=\"#Page_185\"\u003e185\u003c/a\u003e, \u003ca href=\"#Page_244\"\u003e244\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSubstitution-value of heat, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eSuetonius, \u003ca href=\"#Page_348\"\u003e348\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSulphur, specific inductive capacity of, \u003ca href=\"#Page_117\"\u003e117\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSun, human beings could not exist on, \u003ca href=\"#Page_3\"\u003e3\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSwift, \u003ca href=\"#Page_84\"\u003e84\u003c/a\u003e, \u003ca href=\"#Page_280\"\u003e280\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSwimmer, Ampère\u0027s, \u003ca href=\"#Page_207\"\u003e207\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eSymmetry, definition of, \u003ca href=\"#Page_92\"\u003e92\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efigures of, \u003ca href=\"#Page_92\"\u003e92\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eplane of, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003evertical and horizontal, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein music, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e et seq.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eSympathetic vibration, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e et seq., \u003ca href=\"#Page_379\"\u003e379\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eTailor, nature like a covetous, \u003ca href=\"#Page_9\"\u003e9\u003c/a\u003e-\u003ca href=\"#Page_10\"\u003e10\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTangent, the word, \u003ca href=\"#Page_263\"\u003e263\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTaste, doubtful cultivation of, by the classics, \u003ca href=\"#Page_352\"\u003e352\u003c/a\u003e-\u003ca href=\"#Page_353\"\u003e353\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof the ancients, \u003ca href=\"#Page_353\"\u003e353\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eTaylor, on the vibration of strings, \u003ca href=\"#Page_249\"\u003e249\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTeaching, its nature, \u003ca href=\"#Page_366\"\u003e366\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eTelegraph, the word, \u003ca href=\"#Page_263\"\u003e263\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTelescope, \u003ca href=\"#Page_262\"\u003e262\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTelestereoscope, the, \u003ca href=\"#Page_84\"\u003e84\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTemperament, even, in tuning, \u003ca href=\"#Page_47\"\u003e47\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTemperature, absolute, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edifferences of, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edifferences of, viewed as level surfaces, \u003ca href=\"#Page_161\"\u003e161\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eheights of, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003escale of, derived from tensions of gases, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eTerence, \u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTerms, scientific, \u003ca href=\"#Page_342\"\u003e342\u003c/a\u003e-\u003ca href=\"#Page_343\"\u003e343\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eThales, \u003ca href=\"#Page_259\"\u003e259\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTheories, their scope, function, and power, \u003ca href=\"#Page_241\"\u003e241\u003c/a\u003e-\u003ca href=\"#Page_242\"\u003e242\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emust be replaced by direct description, \u003ca href=\"#Page_248\"\u003e248\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eThermal, energy, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e, \u003ca href=\"#Page_177\"\u003e177\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecapacity, \u003ca href=\"#Page_123\"\u003e123\u003c/a\u003e, footnote.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eThermodynamics, \u003ca href=\"#Page_160\"\u003e160\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eThermoelectrometer, Riess\u0027s, \u003ca href=\"#Page_133\"\u003e133\u003c/a\u003e, \u003ca href=\"#Page_169\"\u003e169\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eThing-in-itself, the, \u003ca href=\"#Page_200\"\u003e200\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eThings, mental symbols for groups of sensations, \u003ca href=\"#Page_200\"\u003e200\u003c/a\u003e-\u003ca href=\"#Page_201\"\u003e201\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eThomson, James, on the lowering of the freezing-point of water by pressure, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eThomson, W., his absolute electrometer, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e, footnote;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon thermodynamics, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the conservation of energy, \u003ca href=\"#Page_165\"\u003e165\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the mechanical measures of temperature, \u003ca href=\"#Page_174\"\u003e174\u003c/a\u003e, footnote;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon waste of mechanical energy, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e, footnote.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eThought, habitudes of, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e, \u003ca href=\"#Page_224\"\u003e224\u003c/a\u003e, \u003ca href=\"#Page_227\"\u003e227\u003c/a\u003e, \u003ca href=\"#Page_232\"\u003e232\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erelationship between language and, \u003ca href=\"#Page_329\"\u003e329\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eincongruence between experience and, \u003ca href=\"#Page_206\"\u003e206\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eluxuriance of a fully developed, \u003ca href=\"#Page_58\"\u003e58\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003etransformation in scientific, \u003ca href=\"#Page_214\"\u003e214\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eThoughts, their development and the struggle for existence among them, \u003ca href=\"#Page_63\"\u003e63\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eimportance of erroneous, \u003ca href=\"#Page_65\"\u003e65\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eas reproductions of facts, \u003ca href=\"#Page_107\"\u003e107\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eThread, the individual a, on which pearls are strung, \u003ca href=\"#Page_234\"\u003e234\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTides, \u003ca href=\"#Page_283\"\u003e283\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTimbre, \u003ca href=\"#Page_37\"\u003e37\u003c/a\u003e, \u003ca href=\"#Page_38\"\u003e38\u003c/a\u003e, \u003ca href=\"#Page_39\"\u003e39\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTime, \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e, \u003ca href=\"#Page_205\"\u003e205\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eToepler and Foucault, method of, for detecting optical faults, \u003ca href=\"#Page_313\"\u003e313\u003c/a\u003e et seq., \u003ca href=\"#Page_320\"\u003e320\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTone-figures, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTones, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e-\u003ca href=\"#Page_47\"\u003e47\u003c/a\u003e, \u003ca href=\"#Page_99\"\u003e99\u003c/a\u003e et seq., \u003ca href=\"#Page_212\"\u003e212\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTorsion, moment of, \u003ca href=\"#Page_132\"\u003e132\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTorsion-balance, Coulomb\u0027s, \u003ca href=\"#Page_109\"\u003e109\u003c/a\u003e, \u003ca href=\"#Page_168\"\u003e168\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTorricelli, on virtual velocities, \u003ca href=\"#Page_150\"\u003e150\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis law of liquid efflux, \u003ca href=\"#Page_150\"\u003e150\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eon the atmosphere, \u003ca href=\"#Page_273\"\u003e273\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eTourist, journey of, work of the inquirer compared to, \u003ca href=\"#Page_17\"\u003e17\u003c/a\u003e, \u003ca href=\"#Page_29\"\u003e29\u003c/a\u003e, \u003ca href=\"#Page_30\"\u003e30\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTransatlantic cable, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTransformation and adaptation in scientific thought, \u003ca href=\"#Page_214\"\u003e214\u003c/a\u003e-\u003ca href=\"#Page_235\"\u003e235\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTransformation of ideas, \u003ca href=\"#Page_63\"\u003e63\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTransformative law of the energies, \u003ca href=\"#Page_172\"\u003e172\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_410\" id=\"Page_410\"\u003e[Pg 410]\u003c/a\u003e\u003c/span\u003eTranslation, difficulties of, \u003ca href=\"#Page_354\"\u003e354\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTree, conceptual life compared to a, \u003ca href=\"#Page_231\"\u003e231\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTriangle, mutual dependence of the sides and angles of a, \u003ca href=\"#Page_179\"\u003e179\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTriple accord, \u003ca href=\"#Page_46\"\u003e46\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTruth, wooed by the inquirer, \u003ca href=\"#Page_45\"\u003e45\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003edifficulty of its acquisition, \u003ca href=\"#Page_46\"\u003e46\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eTumblers, resounding, \u003ca href=\"#Page_23\"\u003e23\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTuning-forks, explanation of their motion, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eTylor, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eTympanum, \u003ca href=\"#Page_18\"\u003e18\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eType, natural laws likened to, \u003ca href=\"#Page_193\"\u003e193\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ewords compared to, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eUlysses, \u003ca href=\"#Page_347\"\u003e347\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eUnderstanding, what it means, \u003ca href=\"#Page_211\"\u003e211\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eUniforms, do not fit heads, \u003ca href=\"#Page_369\"\u003e369\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eUnique determination, \u003ca href=\"#Page_181\"\u003e181\u003c/a\u003e-\u003ca href=\"#Page_182\"\u003e182\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eUnison, \u003ca href=\"#Page_43\"\u003e43\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eUnit, electrostatic, \u003ca href=\"#Page_111\"\u003e111\u003c/a\u003e.\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eSee \u003ci\u003eForce\u003c/i\u003e and \u003ci\u003eWork\u003c/i\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eUnited States, \u003ca href=\"#Page_336\"\u003e336\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eUniversal Real Character, a, \u003ca href=\"#Page_192\"\u003e192\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eUtility of physical science, \u003ca href=\"#Page_351\"\u003e351\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eVariation, the method of, in science, \u003ca href=\"#Page_230\"\u003e230\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein biology, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eVelocity, of light, \u003ca href=\"#Page_48\"\u003e48\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eof the descent of bodies, \u003ca href=\"#Page_143\"\u003e143\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emeaning of, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003evirtual, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e-\u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003ci\u003eVerstandesbegriffe\u003c/i\u003e, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVertical, perception of the, \u003ca href=\"#Page_272\"\u003e272\u003c/a\u003e, \u003ca href=\"#Page_286\"\u003e286\u003c/a\u003e et seq.;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esymmetry, \u003ca href=\"#Page_389\"\u003e389\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eVertigo, \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e, \u003ca href=\"#Page_290\"\u003e290\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVestibule of the ear, \u003ca href=\"#Page_300\"\u003e300\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVibration, \u003ca href=\"#Page_22\"\u003e22\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eVibration-figures, \u003ca href=\"#Page_91\"\u003e91\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVinci, Leonardo da, \u003ca href=\"#Page_278\"\u003e278\u003c/a\u003e, \u003ca href=\"#Page_283\"\u003e283\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eViolent motions, \u003ca href=\"#Page_225\"\u003e225\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVirtual velocities, \u003ca href=\"#Page_149\"\u003e149\u003c/a\u003e-\u003ca href=\"#Page_155\"\u003e155\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVisibility, general conditions of, \u003ca href=\"#Page_312\"\u003e312\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVision, symmetry of our apparatus of, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e.\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eSee \u003ci\u003eEye\u003c/i\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eVisual nerves, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVisualisation, mental, \u003ca href=\"#Page_250\"\u003e250\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVolt, the word, \u003ca href=\"#Page_343\"\u003e343\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVolta, \u003ca href=\"#Page_127\"\u003e127\u003c/a\u003e, footnote, \u003ca href=\"#Page_134\"\u003e134\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVoltaire, \u003ca href=\"#Page_260\"\u003e260\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVoltaire\u0027s ingènu, \u003ca href=\"#Page_219\"\u003e219\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eVowels, composed of simple musical notes, \u003ca href=\"#Page_26\"\u003e26\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eWagner, Richard, \u003ca href=\"#Page_279\"\u003e279\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWald, F., \u003ca href=\"#Page_178\"\u003e178\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eWallace, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWar, and peace, reflexions upon, \u003ca href=\"#Page_309\"\u003e309\u003c/a\u003e, \u003ca href=\"#Page_335\"\u003e335\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eWaste of mechanical energy, W. Thomson on, \u003ca href=\"#Page_175\"\u003e175\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWatches, experiment with, \u003ca href=\"#Page_41\"\u003e41\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein a mirror, \u003ca href=\"#Page_93\"\u003e93\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eWater, jet of, resolved into drops, \u003ca href=\"#Page_60\"\u003e60\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003efree, solid figures of, \u003ca href=\"#Page_8\"\u003e8\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eobjects reflected in, \u003ca href=\"#Page_94\"\u003e94\u003c/a\u003e, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003epossible modes of measurement of, \u003ca href=\"#Page_170\"\u003e170\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eWatt, \u003ca href=\"#Page_266\"\u003e266\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWealth, the foundation of, \u003ca href=\"#Page_198\"\u003e198\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWeapons, modern, \u003ca href=\"#Page_335\"\u003e335\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWeber, \u003ca href=\"#Page_108\"\u003e108\u003c/a\u003e, \u003ca href=\"#Page_306\"\u003e306\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWeight of bodies, varies with their distance from the centre of the earth, \u003ca href=\"#Page_112\"\u003e112\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWeismann, \u003ca href=\"#Page_216\"\u003e216\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWheatstone, his stereoscope, \u003ca href=\"#Page_73\"\u003e73\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ehis pseudoscope, \u003ca href=\"#Page_96\"\u003e96\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ealso \u003ca href=\"#Page_59\"\u003e59\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eWheel, history and importance of, \u003ca href=\"#Page_61\"\u003e61\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eWhewell, on the formation of science, \u003ca href=\"#Page_231\"\u003e231\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWhole, the, \u003ca href=\"#Page_204\"\u003e204\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003cli\u003eWhy, the question, \u003ca href=\"#Page_199\"\u003e199\u003c/a\u003e, \u003ca href=\"#Page_223\"\u003e223\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWill, Schopenhauer on the, \u003ca href=\"#Page_190\"\u003e190\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eman\u0027s most familiar source of power, \u003ca href=\"#Page_243\"\u003e243\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eused to explain the world, \u003ca href=\"#Page_186\"\u003e186\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eforces compared to, \u003ca href=\"#Page_254\"\u003e254\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ecompared to pressure, \u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eWindmill, a rotating, \u003ca href=\"#Page_53\"\u003e53\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWire frames and nets, for constructing liquid figures of equilibrium, \u003ca href=\"#Page_4\"\u003e4\u003c/a\u003e et seq.\u003c/li\u003e\r\n\r\n\u003cli\u003eWitchcraft, \u003ca href=\"#Page_187\"\u003e187\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWollaston, \u003ca href=\"#Page_284\"\u003e284\u003c/a\u003e, \u003ca href=\"#Page_285\"\u003e285\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWonderful, science the natural foe of the, \u003ca href=\"#Page_224\"\u003e224\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWoods, the relative distance of trees in, \u003ca href=\"#Page_68\"\u003e68\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWooer, inquirer compared to a, \u003ca href=\"#Page_45\"\u003e45\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWords and sounds, \u003ca href=\"#Page_343\"\u003e343\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWords, compared to type, \u003ca href=\"#Page_191\"\u003e191\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_411\" id=\"Page_411\"\u003e[Pg 411]\u003c/a\u003e\u003c/span\u003eWork, of liquid forces of attraction, \u003ca href=\"#Page_14\"\u003e14\u003c/a\u003e;\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003ein electricity, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003emeasure of, \u003ca href=\"#Page_119\"\u003e119\u003c/a\u003e et seq., \u003ca href=\"#Page_130\"\u003e130\u003c/a\u003e, \u003ca href=\"#Page_223\"\u003e223\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003erelation of, with heat, \u003ca href=\"#Page_162\"\u003e162\u003c/a\u003e, \u003ca href=\"#Page_245\"\u003e245\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eamount required to develop electricity, \u003ca href=\"#Page_131\"\u003e131\u003c/a\u003e et seq.;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eproduces various physical changes, \u003ca href=\"#Page_139\"\u003e139\u003c/a\u003e;\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003esubstantial conception of, \u003ca href=\"#Page_183\"\u003e183\u003c/a\u003e-\u003ca href=\"#Page_184\"\u003e184\u003c/a\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cspan style=\"margin-left: 1em;\"\u003eSee \u003ci\u003eEnergy\u003c/i\u003e.\u003c/span\u003e\u003c/li\u003e\r\n\r\n\u003cli\u003eWorld, the, what it consists of, \u003ca href=\"#Page_208\"\u003e208\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWorld-particles, \u003ca href=\"#Page_203\"\u003e203\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWronsky, \u003ca href=\"#Page_172\"\u003e172\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eWundt, on causality and the axioms of physics, \u003ca href=\"#Page_157\"\u003e157\u003c/a\u003e-\u003ca href=\"#Page_159\"\u003e159\u003c/a\u003e; \u003ca href=\"#Page_359\"\u003e359\u003c/a\u003e footnote.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eXenophon, \u003ca href=\"#Page_49\"\u003e49\u003c/a\u003e, footnote.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eYoung, Thomas, on energy, \u003ca href=\"#Page_173\"\u003e173\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003c/ul\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eZelter, \u003ca href=\"#Page_35\"\u003e35\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eZeuner, \u003ca href=\"#Page_171\"\u003e171\u003c/a\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003eZoölogy, comparison in, \u003ca href=\"#Page_239\"\u003e239\u003c/a\u003e.\u003c/li\u003e\u003c/ul\u003e\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_412\" id=\"Page_412\"\u003e[Pg 412]\u003c/a\u003e\u003cbr /\u003e\u003ca name=\"Page_413\" id=\"Page_413\"\u003e[Pg 413]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003chr class=\"chap\" /\u003e\r\n\r\n\r\n\u003ch2\u003eTHE SCIENCE OF MECHANICS.\u003c/h2\u003e\r\n\r\n\u003cp class=\"center\"\u003eA CRITICAL AND HISTORICAL EXPOSITION OF ITS\r\nPRINCIPLES.\u003c/p\u003e\r\n\r\n\u003cp class=\"center bold\"\u003eBy DR. ERNST MACH.\u003c/p\u003e\r\n\r\n\u003cp class=\"center small\"\u003ePROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE\r\nUNIVERSITY OF VIENNA.\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003eTranslated from the Second German Edition\u003cbr /\u003e\r\n\u003cspan class=\"bold\"\u003eBy THOMAS J. McCORMACK.\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003chr/\u003e\r\n\u003cp class=\"center\"\u003e250 Cuts. 534 Pages. Half Morocco, Gilt Top, Marginal Analyses.\u003cbr/\u003e\r\nExhaustive Index. Price $2.50.\u003c/p\u003e\r\n\r\n\r\n\u003chr/\u003e\r\n\r\n\u003ch3\u003e\u003ca name=\"TABLE_OF_CONTENTS2\" id=\"TABLE_OF_CONTENTS2\"\u003eTABLE OF CONTENTS.\u003c/a\u003e\u003c/h3\u003e\r\n\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003eStatics.\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eThe Lever.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Inclined Plane.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Composition of Forces.\u003c/li\u003e\r\n\r\n\u003cli\u003eVirtual Velocities.\u003c/li\u003e\r\n\r\n\u003cli\u003eStatics in Their Application to Fluids.\u003c/li\u003e\r\n\r\n\u003cli\u003eStatics in Their Application to Gases.\u003c/li\u003e\u003c/ul\u003e\r\n\r\n\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003eDynamics.\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eGalileo\u0027s Achievements.\u003c/li\u003e\r\n\r\n\u003cli\u003eAchievements of Huygens.\u003c/li\u003e\r\n\r\n\u003cli\u003eAchievements of Newton.\u003c/li\u003e\r\n\r\n\u003cli\u003ePrinciple of Reaction.\u003c/li\u003e\r\n\r\n\u003cli\u003eCriticism of the Principle of Reaction\r\nand of the Concept of Mass.\u003c/li\u003e\r\n\r\n\u003cli\u003eNewton\u0027s Views of Time, Space, and\r\nMotion.\u003c/li\u003e\r\n\r\n\u003cli\u003eCritique of the Newtonian Enunciations.\u003c/li\u003e\r\n\r\n\u003cli\u003eRetrospect of the Development of\r\nDynamics.\u003c/li\u003e\u003c/ul\u003e\r\n\r\n\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003eThe Extension of the Principles of Mechanics.\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eScope of the Newtonian Principles.\u003c/li\u003e\r\n\r\n\u003cli\u003eFormulæ and Units of Mechanics.\u003c/li\u003e\r\n\r\n\u003cli\u003eConservation of Momentum, Conservation\r\nof the Centre of Gravity,\r\nand Conservation of Areas.\u003c/li\u003e\r\n\r\n\u003cli\u003eLaws of Impact.\u003c/li\u003e\r\n\r\n\u003cli\u003eD\u0027Alembert\u0027s Principle.\u003c/li\u003e\r\n\r\n\u003cli\u003ePrinciple of \u003ci\u003eVis Viva\u003c/i\u003e.\u003c/li\u003e\r\n\r\n\u003cli\u003ePrinciple of Least Constraint.\u003c/li\u003e\r\n\r\n\u003cli\u003ePrinciple of Least Action.\u003c/li\u003e\r\n\r\n\u003cli\u003eHamilton\u0027s Principle.\u003c/li\u003e\r\n\r\n\u003cli\u003eHydrostatic and Hydrodynamic\r\nQuestions.\u003c/li\u003e\u003c/ul\u003e\r\n\r\n\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003eFormal Development of Mechanics.\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eThe Isoperimetrical Problems.\u003c/li\u003e\r\n\r\n\u003cli\u003eTheological, Animistic, and Mystical\r\nPoints of View in Mechanics.\u003c/li\u003e\r\n\r\n\u003cli\u003eAnalytical Mechanics.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Economy of Science.\u003c/li\u003e\u003c/ul\u003e\r\n\r\n\r\n\u003cp\u003e\u003cspan class=\"smcap\"\u003eThe Relation of Mechanics to Other Departments of Knowledge.\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\r\n\u003cli\u003eRelations of Mechanics to Physics.\u003c/li\u003e\r\n\r\n\u003cli\u003eRelations of Mechanics to Physiology.\u003c/li\u003e\u003c/ul\u003e\r\n\r\n\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_414\" id=\"Page_414\"\u003e[Pg 414]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"PRESS_NOTICES\" id=\"PRESS_NOTICES\"\u003ePRESS NOTICES.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003e\"The appearance of a translation into English of this remarkable book\r\nshould serve to revivify in this country [England] the somewhat stagnating\r\ntreatment of its subject, and should call up the thoughts which puzzle us when\r\nwe think of them, and that is not sufficiently often…. Professor Mach is a\r\nstriking instance of the combination of great mathematical knowledge with\r\nexperimental skill, as exemplified not only by the elegant illustrations of mechanical\r\nprinciples which abound in this treatise, but also from his brilliant\r\nexperiments on the photography of bullets…. A careful study of Professor\r\nMach\u0027s work, and a treatment with more experimental illustration, on the\r\nlines laid down in the interesting diagrams of his \u003ci\u003eScience of Mechanics\u003c/i\u003e, will\r\ndo much to revivify theoretical mechanical science, as developed from the\r\nelements by rigorous logical treatment.\"\u0026mdash;Prof. A. G. Greenhill, in \u003ci\u003eNature\u003c/i\u003e,\r\nLondon.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Those who are curious to learn how the principles of mechanics have\r\nbeen evolved, from what source they take their origin, and how far they can\r\nbe deemed of positive and permanent value, will find Dr. Mach\u0027s able treatise\r\nentrancingly interesting…. The book is a remarkable one in many respects,\r\nwhile the mixture of history with the latest scientific principles and\r\nabsolute mathematical deductions makes it exceedingly attractive.\"\u0026mdash;\u003ci\u003eMechanical\r\nWorld\u003c/i\u003e, Manchester and London, England.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Mach\u0027s Mechanics is unique. It is not a text-book, but forms a useful\r\nsupplement to the ordinary text-book. The latter is usually a skeleton outline,\r\nfull of mathematical symbols and other abstractions. Mach\u0027s book has\r\n\u0027muscle and clothing,\u0027 and being written from the historical standpoint, introduces\r\nthe leading contributors in succession, tells what they did and how\r\nthey did it, and often what manner of men they were. Thus it is that the\r\npages glow, as it were, with a certain humanism, quite delightful in a scientific\r\nbook…. The book is handsomely printed, and deserves a warm reception\r\nfrom all interested in the progress of science.\"\u0026mdash;\u003ci\u003eThe Physical Review\u003c/i\u003e, New\r\nYork and London.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Mr. T. J. McCormack, by his effective translation, where translation\r\nwas no light task, of this masterly treatise upon the earliest and most fundamental\r\nof the sciences, has rendered no slight service to the English speaking\r\nstudent. The German and English languages are generally accounted\r\nsecond to none in their value as instruments for the expression of scientific\r\nthought; but the conversion bodily of an abstruse work from one into the\r\nother, so as to preserve all the meaning and spirit of the original and to set it\r\neasily and naturally into its new form, is a task of the greatest difficulty, and\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_415\" id=\"Page_415\"\u003e[Pg 415]\u003c/a\u003e\u003c/span\u003e\r\nwhen performed so well as in the present instance, merits great commendation.\r\nDr. Mach has created for his own works the severest possible standard\r\nof judgment. To expect no more from the books of such a master than from\r\nthe elementary productions of an ordinary teacher in the science would be\r\nundue moderation. Our author has lifted what, to many of us, was at one\r\ntime a course of seemingly unprofitable mental gymnastics, encompassed\r\nonly at vast expenditure of intellectual effort, into a study possessing a deep\r\nphilosophical value and instinct with life and interest. \u0027No profit grows\r\nwhere is no pleasure ta\u0027en,\u0027 and the emancipated collegian will turn with\r\npleasure from the narrow methods of the text-book to where the science is\r\nmade to illustrate, by a treatment at once broad and deep, the fundamental\r\nconnexion between all the physical sciences, taken together.\"\u0026mdash;\u003ci\u003eThe Mining\r\nJournal\u003c/i\u003e, London, England.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"As a history of mechanics, the work is admirable.\"\u0026mdash;\u003ci\u003eThe Nation\u003c/i\u003e, New\r\nYork.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"An excellent book, admirably illustrated.\"\u0026mdash;\u003ci\u003eThe Literary World\u003c/i\u003e, London,\r\nEngland.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Sets forth the elements of its subject with a lucidity, clearness, and\r\nforce unknown in the mathematical text-books … is admirably fitted to\r\nserve students as an introduction on historical lines to the principles of mechanical\r\nscience.\"\u0026mdash;\u003ci\u003eCanadian Mining and Mechanical Review\u003c/i\u003e, Ottawa, Can.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"A masterly book…. To any one who feels that he does not know as\r\nmuch as he ought to about physics, we can commend it most heartily as a\r\nscholarly and able treatise … both interesting and profitable.\"\u0026mdash;A. M.\r\nWellington, in \u003ci\u003eEngineering News\u003c/i\u003e, New York.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The book as a whole is unique, and is a valuable addition to any library\r\nof science or philosophy…. Reproductions of quaint old portraits and\r\nvignettes give piquancy to the pages. The numerous marginal titles form a\r\ncomplete epitome of the work; and there is that invaluable adjunct, a good\r\nindex. Altogether the publishers are to be congratulated upon producing a\r\ntechnical work that is thoroughly attractive in its make-up.\"\u0026mdash;Prof. D. W.\r\nHering, in \u003ci\u003eScience\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"There is one other point upon which this volume should be commended,\r\nand that is the perfection of the translation. It is a common fault that books\r\nof the greatest interest and value in the original are oftenest butchered or\r\nmade ridiculous by a clumsy translator. The present is a noteworthy exception.\"\u0026mdash;\u003ci\u003eRailway\r\nAge\u003c/i\u003e.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_416\" id=\"Page_416\"\u003e[Pg 416]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The book is admirably printed and bound…. The presswork is unexcelled\r\nby any technical books that have come to our hands for some time,\r\nand the engravings and figures are all clearly and well executed.\"\u0026mdash;\u003ci\u003eRailroad\r\nGazette\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"TESTIMONIALS_OF_PROMINENT_EDUCATORS\" id=\"TESTIMONIALS_OF_PROMINENT_EDUCATORS\"\u003eTESTIMONIALS OF PROMINENT EDUCATORS.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003e\"I am delighted with Professor Mach\u0027s \u003ci\u003eScience of Mechanics\u003c/i\u003e.\"\u0026mdash;\u003ci\u003eM. E.\r\nCooley\u003c/i\u003e, Professor of Mechanical Engineering, Ann Arbor, Mich.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"You have done a good service to science in publishing Mach\u0027s \u003ci\u003eScience\r\nof Mechanics\u003c/i\u003e in English. I shall take every opportunity to recommend it to\r\nyoung students as a source of much interesting information and inspiration.\"\u0026mdash;\u003ci\u003eM.\r\nI. Pupin\u003c/i\u003e, Professor of Mechanics, Columbia College, New York.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Mach\u0027s \u003ci\u003eScience of Mechanics\u003c/i\u003e is an admirable … book.\"\u0026mdash;\u003ci\u003eProf. E. A.\r\nFuertes\u003c/i\u003e, Director of the College of Civil Engineering of Cornell University,\r\nIthaca, N. Y.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"I congratulate you upon producing the work in such good style and in\r\nso good a translation. I bought a copy of it a year ago, very shortly after you\r\nissued it. The book itself is deserving of the highest admiration; and you\r\nare entitled to the thanks of all English-speaking physicists for the publication\r\nof this translation.\"\u0026mdash;\u003ci\u003eD. W. Hering\u003c/i\u003e, Professor of Physics, University of\r\nthe City of New York, New York.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"I have read Mach\u0027s \u003ci\u003eScience of Mechanics\u003c/i\u003e with great pleasure. The book\r\nis exceedingly interesting.\"\u0026mdash;\u003ci\u003eW. F. Magie\u003c/i\u003e, Professor of Physics, Princeton\r\nUniversity, Princeton, N. J.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The \u003ci\u003eScience of Mechanics\u003c/i\u003e by Mach, translated by T. J. McCormack, I\r\nregard as a most valuable work, not only for acquainting the student with the\r\nhistory of the development of Mechanics, but as serving to present to him\r\nmost favorably the fundamental ideas of Mechanics and their rational connexion\r\nwith the highest mathematical developments. It is a most profitable\r\nbook to read along with the study of a text-book of Mechanics, and I shall\r\ntake pleasure in recommending its perusal by my students.\"\u0026mdash;\u003ci\u003eS. W. Robinson\u003c/i\u003e,\r\nProfessor of Mechanical Engineering, Ohio State University, Columbus, Ohio.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"I am delighted with Mach\u0027s \u0027Mechanics.\u0027 I will call the attention to\r\nit of students and instructors who have the Mechanics or Physics to study or\r\nteach.\"\u0026mdash;\u003ci\u003eJ. E. Davies\u003c/i\u003e, University of Wisconsin, Madison, Wis.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"There can be but one opinion as to the value of Mach\u0027s work in this\r\ntranslation. No instructor in physics should be without a copy of it.\"\u0026mdash;\u003ci\u003eHenry\r\nCrew\u003c/i\u003e, Professor of Physics in the Northwestern University, Evanston, Ill.\u003c/p\u003e\u003chr class=\"chap\" /\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_417\" id=\"Page_417\"\u003e[Pg 417]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"POPULAR_SCIENTIFIC_LECTURES\" id=\"POPULAR_SCIENTIFIC_LECTURES\"\u003ePOPULAR SCIENTIFIC LECTURES.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\u003cp class=\"center\"\u003eA PORTRAYAL OF THE SPIRIT AND METHODS\r\nOF SCIENCE.\u003c/p\u003e\r\n\r\n\u003cp class=\"center bold\"\u003eBy DR. ERNST MACH.\u003c/p\u003e\r\n\r\n\u003cp class=\"small center\"\u003ePROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE\r\nUNIVERSITY OF VIENNA.\u003c/p\u003e\r\n\r\n\u003cp class=\"center bold\"\u003eTranslated by THOMAS J. McCORMACK.\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003ci\u003eThird Edition, Revised Throughout and Greatly Enlarged.\u003c/i\u003e\u003c/p\u003e\r\n\r\n\u003chr/\u003e\r\n\r\n\u003cp class=\"center\"\u003eCloth, Gilt Top. Exhaustively Indexed. Pages, 415. Cuts, 59. Price, $1.50.\u003c/p\u003e\r\n\r\n\u003chr/\u003e\r\n\r\n\r\n\u003ch3\u003e\u003ca name=\"TITLES_OF_THE_LECTURES\" id=\"TITLES_OF_THE_LECTURES\"\u003eTITLES OF THE LECTURES.\u003c/a\u003e\u003c/h3\u003e\r\n\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eThe Forms of Liquids.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Fibres of Corti.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn the Causes of Harmony.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn the Velocity of Light.\u003c/li\u003e\r\n\r\n\u003cli\u003eWhy Has Man Two Eyes?\u003c/li\u003e\r\n\r\n\u003cli\u003eOn Symmetry.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn the Fundamental Concepts of Static Electricity.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn the Principle of the Conservation of Energy.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn the Economical Nature of Physical Inquiry.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn the Principle of Comparison in Physics.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn the Part Played by Accident in Invention and Discovery.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn Sensations of Orientation.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn the Relative Educational Value of the Classics and the Mathematico-Physical Sciences.\u003c/li\u003e\r\n\r\n\u003cli\u003eA Contribution to the History of Acoustics.\u003c/li\u003e\r\n\r\n\u003cli\u003eRemarks on the Theory of Spatial Vision.\u003c/li\u003e\r\n\r\n\u003cli\u003eOn Transformation and Adaptation in Scientific Thought.\u003c/li\u003e\u003c/ul\u003e\r\n\r\n\r\n\r\n\u003ch2\u003ePRESS NOTICES.\u003c/h2\u003e\r\n\r\n\u003cp\u003e\"A most fascinating volume, treating of phenomena in which all are interested,\r\nin a delightful style and with wonderful clearness. For lightness\r\nof touch and yet solid value of information the chapter \u0027Why Has Man Two\r\nEyes?\u0027 has scarcely a rival in the whole realm of popular scientific writing.\"\u0026mdash;\u003ci\u003eThe\r\nBoston Traveller\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Truly remarkable in the insight they give into the relationship of the\r\nvarious fields cultivated under the name of Physics…. A vein of humor is\r\nmet here and there reminding the reader of Heaviside, never offending one\u0027s\r\ntaste. These features, together with the lightness of touch with which Mr.\r\nMcCormack has rendered them, make the volume one that may be fairly\r\ncalled rare. The spirit of the author is preserved in such attractive, really\r\ndelightful, English that one is assured nothing has been lost by translation.\"\u0026mdash;Prof.\r\nHenry Crew, in \u003ci\u003eThe Astrophysical Journal\u003c/i\u003e.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_418\" id=\"Page_418\"\u003e[Pg 418]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\"A very delightful and useful book…. The author treats some of the\r\nmost recondite problems of natural science, in so charmingly untechnical a\r\nway, with such a wealth of bright illustration, as makes his meaning clear to\r\nthe person of ordinary intelligence and education…. This is a work that\r\nshould find a place in every library, and that people should be encouraged to\r\nread.\"\u0026mdash;\u003ci\u003eDaily Picayune\u003c/i\u003e, New Orleans.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"In his translation Mr. McCormack has well preserved the frank, simple,\r\nand pleasing style of this famous lecturer on scientific topics. Professor\r\nMach deals with the live facts, the salient points of science, and not with its\r\nmysticism or dead traditions. He uses the simplest of illustrations and expresses\r\nhimself clearly, tersely, and with a delightful freshness that makes\r\nentertaining reading of what in other hands would be dull and prosy.\"\u0026mdash;\u003ci\u003eEngineering\r\nNews\u003c/i\u003e, N. Y.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The general reader is led by plain and easy steps along a delightful way\r\nthrough what would be to him without such a help a complicated maze of\r\ndifficulties. Marvels are invented and science is revealed as the natural foe\r\nto mysteries.\"\u0026mdash;\u003ci\u003eThe Chautauquan\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The beautiful quality of the work is not marred by abstruse discussions\r\nwhich would require a scientist to fathom, but is so simple and so clear that\r\nit brings us into direct contact with the matter treated.\"\u0026mdash;\u003ci\u003eThe Boston Post\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"A masterly exposition of important scientific truths.\"\u0026mdash;\u003ci\u003eScotsman\u003c/i\u003e, Edinburgh.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"These lectures by Dr. Mach are delightfully simple and frank; there is\r\nno dryness or darkness of technicalities, and science and common life do not\r\nseem separated by a gulf…. The style is admirable, and the whole volume\r\nseems gloriously alive and human.\"\u0026mdash;\u003ci\u003eProvidence Journal\u003c/i\u003e, R. I.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The non-scientific reader who desires to learn something of modern\r\nscientific theories, and the reasons for their existence, cannot do better than\r\ncarefully study these lectures. The English is excellent throughout, and reflects\r\ngreat credit on the translator.\"\u0026mdash;\u003ci\u003eManufacturer and Builder\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"We like the quiet, considerate intelligence of these lectures.\"\u0026mdash;\u003ci\u003eIndependent\u003c/i\u003e,\r\nNew York.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Professor Mach\u0027s lectures are so pleasantly written and illumined with\r\nsuch charm of illustration that they have all the interest of lively fiction.\"\u0026mdash;\u003ci\u003eNew\r\nYork Com. Advertiser\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The literary and philosophical suggestiveness of the book is very rich.\"\r\n\u003ci\u003eHartford Seminary Record\u003c/i\u003e.\u003c/p\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_419\" id=\"Page_419\"\u003e[Pg 419]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003e\"All are presented so skilfully that one can imagine that Professor Mach\u0027s\r\nhearers departed from his lecture-room with the conviction that science was\r\na matter for abecedarians. Will please those who find the fairy tales of\r\nscience more absorbing than fiction.\"\u0026mdash;\u003ci\u003eThe Pilot\u003c/i\u003e, Boston.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Professor Mach … is a master in physics…. His book is a good one\r\nand will serve a good purpose, both for instruction and suggestion.\"\u0026mdash;Prof.\r\nA. E. Dolbear, in \u003ci\u003eThe Dial\u003c/i\u003e.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"The most beautiful ideas are unfolded in the exposition.\"\u0026mdash;\u003ci\u003eCatholic\r\nWorld\u003c/i\u003e, New York.\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"THE_ANALYSIS_OF_THE_SENSATIONS\" id=\"THE_ANALYSIS_OF_THE_SENSATIONS\"\u003eTHE ANALYSIS OF THE SENSATIONS\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\u003cp class=\"center bold\"\u003eBy DR. ERNST MACH.\u003c/p\u003e\r\n\r\n\u003cp class=\"center small\"\u003ePROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE\r\nUNIVERSITY OF VIENNA.\u003c/p\u003e\r\n\r\n\u003chr/\u003e\r\n\r\n\u003cp class=\"center\"\u003ePages, 208. Illustrations, 37. Indexed.\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e(Price, Cloth, $1.25.)\u003c/p\u003e\r\n\r\n\u003chr/\u003e\r\n\r\n\r\n\u003ch3\u003e\u003ca name=\"CONTENTS\" id=\"CONTENTS\"\u003eCONTENTS.\u003c/a\u003e\u003c/h3\u003e\r\n\r\n\r\n\u003cul class=\"IX\"\u003e\u003cli\u003eIntroductory: Antimetaphysical.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Chief Points of View for the Investigation\r\nof the Senses.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Space-Sensations of the Eye.\u003c/li\u003e\r\n\r\n\u003cli\u003eSpace-Sensation, Continued.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Relations of the Sight-Sensations\r\nto One Another and to the\r\nOther Psychical Elements.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Sensation of Time.\u003c/li\u003e\r\n\r\n\u003cli\u003eThe Sensation of Sound.\u003c/li\u003e\r\n\r\n\u003cli\u003eInfluence of the Preceding Investigations\r\non the Mode of Conceiving\r\nPhysics.\u003c/li\u003e\u003c/ul\u003e\r\n\r\n\u003chr/\u003e\r\n\r\n\u003cp\u003e\"A wonderfully original little book. Like everything he writes a work of\r\ngenius.\"\u0026mdash;\u003ci\u003eProf. W. James\u003c/i\u003e of Harvard.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"I consider each work of Professor Mach a distinct acquisition to a\r\nlibrary of science.\"\u0026mdash;\u003ci\u003eProf. D. W. Hering\u003c/i\u003e, New York University.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"There is no work known to the writer which, in its general scientific\r\nbearings, is more likely to repay richly thorough study. We are all interested\r\nin nature in one way or another, and our interests can only be heightened\r\nand clarified by Mach\u0027s wonderfully original and wholesome book. It is not\r\nsaying too much to maintain that every intelligent person should have a copy\r\nof it,\u0026mdash;and should study that copy.\"\u0026mdash;\u003ci\u003eProf. J. E. Trevor\u003c/i\u003e, Cornell.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"Students may here make the acquaintance of some of the open questions\r\nof sensation and at the same time take a lesson in the charm of scientific\r\nmodesty that can hardly be excelled.\"\u0026mdash;\u003ci\u003eProf. E. C. Sanford\u003c/i\u003e, Clark University.\u003c/p\u003e\r\n\r\n\u003cp\u003e\"It exhibits keen observation and acute thought, with many new and interesting\r\nexperiments by way of illustration. Moreover, the style is light\r\nand even lively\u0026mdash;a rare merit in a German prose work, and still rarer in a\r\ntranslation of one.\"\u0026mdash;\u003ci\u003eThe Literary World\u003c/i\u003e, London.\u003c/p\u003e\r\n\r\n\u003chr/\u003e\r\n\r\n\u003cp class=\"center\"\u003eCHICAGO:\u003cbr /\u003e\r\n\u003cspan class=\"bold\"\u003eThe Open Court Publishing Company\u003c/span\u003e\u003cbr /\u003e\r\n324 DEARBORN STREET.\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003eLONDON: Kegan Paul, Trench, Trübner, \u0026amp; Company.\u003c/p\u003e\u003chr class=\"chap\" /\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_420\" id=\"Page_420\"\u003e[Pg 420]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"CATALOGUE_OF_PUBLICATIONS\" id=\"CATALOGUE_OF_PUBLICATIONS\"\u003eCATALOGUE OF PUBLICATIONS\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\u003cp class=\"center small\"\u003eOF THE\u003cbr /\u003e\r\n\u003cspan class=\"big\"\u003eOPEN COURT PUBLISHING CO.\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003chr/\u003e\r\n\r\n\u003cp\u003eCOPE, E. D.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE PRIMARY FACTORS OF ORGANIC EVOLUTION.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e121 cuts. Pp., xvi, 547. Cloth, $2.00, net.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eMÜLLER, F. MAX.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHREE INTRODUCTORY LECTURES ON THE SCIENCE OF THOUGHT.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eWith a correspondence on \"Thought Without Words,\" between F. Max Müller and Francis Galton, the Duke of Argyll, George J. Romanes and others. 128 pages. Cloth, 75 cents. Paper, 25 cents.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHREE LECTURES ON THE SCIENCE OF LANGUAGE.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eThe Oxford University Extension Lectures, with a Supplement, \"My Predecessors.\" 112 pages. 2nd Edition. Cloth, 75 cents. Paper, 25c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eROMANES, GEORGE JOHN.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eDARWIN AND AFTER DARWIN.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eAn Exposition of the Darwinian Theory and a Discussion of Post-Darwinian Questions. Three Vols., $4.00. Singly, as follows:\u003c/p\u003e\r\n\r\n\u003cp\u003e1. \u003cspan class=\"smcap\"\u003eThe Darwinian Theory.\u003c/span\u003e 460 pages. 125 illustrations. Cloth, $2.00.\u003c/p\u003e\r\n\r\n\u003cp\u003e2. \u003cspan class=\"smcap\"\u003ePost-Darwinian Questions.\u003c/span\u003e Heredity and Utility. Pp. 338. $1.50.\u003c/p\u003e\r\n\r\n\u003cp\u003e3. \u003cspan class=\"smcap\"\u003ePost-Darwinian Questions.\u003c/span\u003e Isolation and Physiological Selection. Pp. 181. $1.00.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eAN EXAMINATION OF WEISMANNISM.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e236 pages. Cloth, $1.00. Paper, 35c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHOUGHTS ON RELIGION.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eEdited by Charles Gore, M. A., Canon of Westminster. Third Edition, Pages, 184. Cloth, gilt top, $1.25.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eRIBOT, TH.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE PSYCHOLOGY OF ATTENTION.\u003c/p\u003e\r\n\r\n\u003cp\u003eTHE DISEASES OF PERSONALITY.\u003c/p\u003e\r\n\r\n\u003cp\u003eTHE DISEASES OF THE WILL.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eAuthorised translations. Cloth, 75 cents each. Paper, 25 cents. \u003ci\u003eFull set, cloth, $1.75, net.\u003c/i\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eMACH, ERNST.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE SCIENCE OF MECHANICS.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e\u003cspan class=\"smcap\"\u003eA Critical and Historical Exposition of its Principles.\u003c/span\u003e Translated by \u003cspan class=\"smcap\"\u003eT. J. McCormack\u003c/span\u003e. 250 cuts. 534 pages. 1/2 m., gilt top. $2.50.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePOPULAR SCIENTIFIC LECTURES.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eThird Edition. 415 pages. 59 cuts. Cloth, gilt top. Net, $1.50.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE ANALYSIS OF THE SENSATIONS.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePp. 208. 37 cuts. Cloth, $1.25, net.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eGOODWIN, REV. T. A.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eLOVERS THREE THOUSAND YEARS AGO.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eAs Indicated by the Song of Solomon. Pp. 41. Boards, 50c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eHOLYOAKE, G. J.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eENGLISH SECULARISM. \u003cspan class=\"smcap\"\u003eA Confession of Belief.\u003c/span\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePp. 146. Cloth, 50c., net.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eCORNILL, CARL HEINRICH.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE PROPHETS OF ISRAEL.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePopular Sketches from Old Testament History. Pp., 200. Cloth, $1.00.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE RISE OF THE PEOPLE OF ISRAEL.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eSee \u003ci\u003eEpitomes of Three Sciences\u003c/i\u003e, below.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eBINET, ALFRED.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE PSYCHIC LIFE OF MICRO-ORGANISMS.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eAuthorised translation. 135 pages. Cloth, 75 cents; Paper, 25 cents.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eON DOUBLE CONSCIOUSNESS.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eStudies in Experimental Psychology. 93 pages. Paper, 15 cents.\u003c/p\u003e\u003c/blockquote\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_421\" id=\"Page_421\"\u003e[Pg 421]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\u003cp\u003eWAGNER, RICHARD\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eA PILGRIMAGE TO BEETHOVEN.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eA Novelette. Frontispiece, portrait of Beethoven. Pp. 40. Boards, 50c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eWEISMANN, AUGUST.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eGERMINAL SELECTION. \u003cspan class=\"smcap\"\u003eAs a Source of Definite Variation.\u003c/span\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePp. 73. Paper, 25c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eNOIRÉ, LUDWIG.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eON THE ORIGIN OF LANGUAGE. Pp. 57. Paper, 15c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eFREYTAG, GUSTAV.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE LOST MANUSCRIPT. A Novel.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e2 vols. 953 pages. Extra cloth, $4.00. One vol., cl., $1.00; paper, 75c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eMARTIN LUTHER.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eIllustrated. Pp. 130. Cloth, $1.00. Paper, 25c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eHERING, EWALD.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eON MEMORY, and THE SPECIFIC ENERGIES OF THE NERVOUS\r\nSYSTEM. Pp. 50. Paper, 15c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eTRUMBULL, M. 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Price, 10 cents.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eGOETHE AND SCHILLER\u0027S XENIONS.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eSelected and translated by Paul Carus. Album form. Pp., 162. Cl., $1.00\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eOLDENBERG, H.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eANCIENT INDIA: ITS LANGUAGE AND RELIGIONS.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePp. 100. Cloth, 50c. Paper, 25c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eCARUS, PAUL.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE ETHICAL PROBLEM.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e90 pages. Cloth, 50 cents; Paper, 30 cents.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eFUNDAMENTAL PROBLEMS.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eSecond edition, enlarged and revised. 372 pp. Cl., $1.50. Paper, 50c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eHOMILIES OF SCIENCE.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e317 pages. Cloth, Gilt Top, $1.50.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE IDEA OF GOD.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eFourth edition. 32 pages. Paper, 15 cents.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE SOUL OF MAN.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eWith 152 cuts and diagrams. 458 pages. Cloth, $3.00.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTRUTH IN FICTION. \u003cspan class=\"smcap\"\u003eTwelve Tales with a Moral.\u003c/span\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eFine laid paper, white and gold binding, gilt edges. Pp. 111. $1.00.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE RELIGION OF SCIENCE.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eSecond, extra edition. Price, 50 cents. R. S. L. edition, 25c. Pp. 103.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePRIMER OF PHILOSOPHY.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e240 pages. Second Edition. Cloth, $1.00. Paper, 25c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHREE LECTURES: (1) \u003cspan class=\"smcap\"\u003eThe Philosophy of the Tool.\u003c/span\u003e Pages, 24. Paper,\r\n10c. (2) \u003cspan class=\"smcap\"\u003eOur Need of Philosophy.\u003c/span\u003e Pages, 14. Paper, 5c. (3) \u003cspan class=\"smcap\"\u003eScience\r\na Religious Revelation.\u003c/span\u003e Pages, 21. Paper, 5c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE GOSPEL OF BUDDHA. According to Old Records.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e4th Edition. Pp., 275. Cloth, $1.00. Paper, 35 cents. In German, $1.25.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eBUDDHISM AND ITS CHRISTIAN CRITICS.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePages, 311. Cloth, $1.25.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eKARMA. \u003cspan class=\"smcap\"\u003eA Story of Early Buddhism.\u003c/span\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eIllustrated by Japanese artists. 2nd Edition. Crêpe paper, 75 cents.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eGARBE, RICHARD.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE REDEMPTION OF THE BRAHMAN. \u003cspan class=\"smcap\"\u003eA Tale of Hindu Life.\u003c/span\u003e\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eLaid paper. Gilt top. 96 pages. Price, 75c. Paper, 25c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eTHE PHILOSOPHY OF ANCIENT INDIA.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003ePp. 89. Cloth, 50c. Paper, 25c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\r\n\u003cp\u003eEPITOMES OF THREE SCIENCES.\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003e1. \u003cspan class=\"smcap\"\u003eThe Study of Sanskrit.\u003c/span\u003e By \u003ci\u003eH. Oldenberg\u003c/i\u003e. 2. \u003cspan class=\"smcap\"\u003eExperimental Psychology.\u003c/span\u003e\r\nBy \u003ci\u003eJoseph Jastrow\u003c/i\u003e. 3. \u003cspan class=\"smcap\"\u003eThe Rise of the People of Israel.\u003c/span\u003e By\r\n\u003ci\u003eC. H. Cornill\u003c/i\u003e. 140 pages. Cloth, reduced to 50 cents.\u003c/p\u003e\u003c/blockquote\u003e\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_422\" id=\"Page_422\"\u003e[Pg 422]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\r\n\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"The_Religion_of_Science_Library\" id=\"The_Religion_of_Science_Library\"\u003eThe Religion of Science Library.\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\r\n\u003cp\u003eA collection of bi-monthly publications, most of which are reprints of\r\nbooks published by The Open Court Publishing Company. Yearly, $1.50.\r\nSeparate copies according to prices quoted. The books are printed upon\r\ngood paper, from large type.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe Religion of Science Library, by its extraordinarily reasonable price,\r\nwill place a large number of valuable books within the reach of all readers.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe following have already appeared in the series:\u003c/p\u003e\r\n\r\n\u003cblockquote\u003e\u003cp\u003eNo. 1. \u003ci\u003eThe Religion of Science.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003ePaul Carus\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e2. \u003ci\u003eThree Introductory Lectures on the Science of Thought.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eF. Max Müller\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e3. \u003ci\u003eThree Lectures on the Science of Language.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eF. Max Müller\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e4. \u003ci\u003eThe Diseases of Personality.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eTh. Ribot\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e5. \u003ci\u003eThe Psychology of Attention.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eTh. Ribot\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e6. \u003ci\u003eThe Psychic Life of Micro-Organisms.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eAlfred Binet\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e7. \u003ci\u003eThe Nature of the State.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003ePaul Carus\u003c/span\u003e. 15c.\u003c/p\u003e\r\n\r\n\u003cp\u003e8. \u003ci\u003eOn Double Consciousness.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eAlfred Binet\u003c/span\u003e. 15c.\u003c/p\u003e\r\n\r\n\u003cp\u003e9. \u003ci\u003eFundamental Problems.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003ePaul Carus\u003c/span\u003e. 50c.\u003c/p\u003e\r\n\r\n\u003cp\u003e10. \u003ci\u003eThe Diseases of the Will.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eTh. Ribot\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e11. \u003ci\u003eThe Origin of Language.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eLudwig Noire\u003c/span\u003e. 15c.\u003c/p\u003e\r\n\r\n\u003cp\u003e12. \u003ci\u003eThe Free Trade Struggle in England.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eM. M. Trumbull\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e13. \u003ci\u003eWheelbarrow on the Labor Question.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eM. M. Trumbull\u003c/span\u003e. 35c.\u003c/p\u003e\r\n\r\n\u003cp\u003e14. \u003ci\u003eThe Gospel of Buddha.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003ePaul Carus\u003c/span\u003e. 35c.\u003c/p\u003e\r\n\r\n\u003cp\u003e15. \u003ci\u003eThe Primer of Philosophy.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003ePaul Carus\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e16. \u003ci\u003eOn Memory\u003c/i\u003e, and \u003ci\u003eThe Specific Energies of the Nervous System\u003c/i\u003e. By \u003cspan class=\"smcap\"\u003eProf. Ewald Hering\u003c/span\u003e. 15c.\u003c/p\u003e\r\n\r\n\u003cp\u003e17. \u003ci\u003eThe Redemption of the Brahman.\u003c/i\u003e A Tale of Hindu Life. By \u003cspan class=\"smcap\"\u003eRichard Garbe\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e18. \u003ci\u003eAn Examination of Weismannism.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eG. J. Romanes\u003c/span\u003e. 35c.\u003c/p\u003e\r\n\r\n\u003cp\u003e19. \u003ci\u003eOn Germinal Selection.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eAugust Weismann\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e20. \u003ci\u003eLovers Three Thousand Years Ago.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eT. A. Goodwin\u003c/span\u003e. 15c.\u003c/p\u003e\r\n\r\n\u003cp\u003e21. \u003ci\u003ePopular Scientific Lectures.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eErnst Mach\u003c/span\u003e. 50c.\u003c/p\u003e\r\n\r\n\u003cp\u003e22. \u003ci\u003eAncient India: Its Language and Religions.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eH. Oldenberg\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e23. \u003ci\u003eThe Prophets of Ancient Israel.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eProf. C. H. Cornill\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e24. \u003ci\u003eHomilies of Science.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003ePaul Carus\u003c/span\u003e. 35c.\u003c/p\u003e\r\n\r\n\u003cp\u003e25. \u003ci\u003eThoughts on Religion.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eG. J. Romanes\u003c/span\u003e. 50 cents.\u003c/p\u003e\r\n\r\n\u003cp\u003e26. \u003ci\u003eThe Philosophy of Ancient India.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eProf. Richard Garbe\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e27. \u003ci\u003eMartin Luther.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eGustav Freytag\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e28. \u003ci\u003eEnglish Secularism.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eGeorge Jacob Holyoake\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e29. \u003ci\u003eOn Orthogenesis.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eTh. Eimer\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e30. \u003ci\u003eChinese Philosophy.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003ePaul Carus\u003c/span\u003e. 25c.\u003c/p\u003e\r\n\r\n\u003cp\u003e31. \u003ci\u003eThe Lost Manuscript.\u003c/i\u003e By \u003cspan class=\"smcap\"\u003eGustav Freytag\u003c/span\u003e. 60c.\u003c/p\u003e\u003c/blockquote\u003e\r\n\u003cp\u003e\u003cspan class=\"pagenum\"\u003e\u003ca name=\"Page_423\" id=\"Page_423\"\u003e[Pg 423]\u003c/a\u003e\u003c/span\u003e\u003c/p\u003e\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp class=\"center\"\u003eTHE OPEN COURT PUBLISHING CO.\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003e\u003cspan class=\"smcap\"\u003e324 Dearborn Street, Chicago, Ill.\u003c/span\u003e\u003cbr /\u003e\r\nLONDON: Kegan Paul, Trench, Trübner \u0026amp; Co\u003c/p\u003e\r\n\r\n\u003chr class=\"chap\" /\u003e\r\n\r\n\r\n\u003ch2\u003e\u003ca name=\"THE_OPEN_COURT\" id=\"THE_OPEN_COURT\"\u003eTHE OPEN COURT\u003c/a\u003e\u003c/h2\u003e\r\n\r\n\u003cp class=\"center small\"\u003eA MONTHLY MAGAZINE\u003c/p\u003e\r\n\r\n\u003cp class=\"center bold\"\u003eDevoted to the Science of Religion, the Religion of Science, and\r\nthe Extension of the Religious Parliament Idea.\u003c/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003ci\u003eTHE OPEN COURT\u003c/i\u003e does not understand by religion any creed or dogmatic\r\nbelief, but man\u0027s world-conception in so far as it regulates his conduct.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe old dogmatic conception of religion is based upon the science of past\r\nages; to base religion upon the maturest and truest thought of the present\r\ntime is the object of \u003ci\u003eThe Open Court\u003c/i\u003e. Thus, the religion of \u003ci\u003eThe Open Court\u003c/i\u003e is\r\nthe Religion of Science, that is, the religion of verified and verifiable truth.\u003c/p\u003e\r\n\r\n\u003cp\u003eAlthough opposed to irrational orthodoxy and narrow bigotry, \u003ci\u003eThe Open\r\nCourt\u003c/i\u003e does not attack the properly religious element of the various religions.\r\nIt criticises their errors unflinchingly but without animosity, and endeavors\r\nto preserve of them all that is true and good.\u003c/p\u003e\r\n\r\n\u003cp\u003eThe current numbers of \u003ci\u003eThe Open Court\u003c/i\u003e contain valuable original articles\r\nfrom the pens of distinguished thinkers. Accurate and authorised translations\r\nare made in Philosophy, Science, and Criticism from the literature of\r\nContinental Europe, and reviews of noteworthy recent investigations are presented.\r\nPortraits of eminent philosophers and scientists are published, and\r\nappropriate illustrations accompany some of the articles.\u003c/p\u003e\r\n\r\n\u003cp\u003eTerms: $1.00 a year; $1.35 to foreign countries in the Postal Union.\r\nSingle Copies, 10 cents.\u003c/p\u003e\r\n\r\n\r\n\u003ch2\u003eTHE MONIST\u003c/h2\u003e\r\n\r\n\u003cp class=\"center smalL\"\u003eA QUARTERLY MAGAZINE OF\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003ePHILOSOPHY AND SCIENCE.\u003c/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003ci\u003eTHE MONIST\u003c/i\u003e discusses the fundamental problems of Philosophy in\r\ntheir practical relations to the religious, ethical, and sociological questions\r\nof the day. The following have contributed to its columns:\u003c/p\u003e\r\n\r\n\u003cul class=\"IX\"\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. Joseph Le Conte\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eDr. W. T. Harris\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eM. D. Conway\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eCharles S. Peirce\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. F. Max Müller\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. E. D. Cope\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eCarus Sterne\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eMrs. C. Ladd Franklin\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. Max Verworn\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. Felix Klein\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. G. J. Romanes\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. C. Lloyd Morgan\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eJames Sully\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eB. Bosanquet\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eDr. A. Binet\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. Ernst Mach\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eRabbi Emil Hirsch\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eLester F. Ward\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. H. Schubert\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eDr. Edm. Montgomery\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. C. Lombroso\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. E. Haeckel\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. H. Höffding\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eDr. F. Oswald\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. J. Delb\u0026oelig;uf\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. F. Jodl\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. H. M. Stanley\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eG. Ferrero\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eJ. Venn\u003c/span\u003e,\u003c/li\u003e\r\n\u003cli\u003e\u003cspan class=\"smcap\"\u003eProf. H. von Holst\u003c/span\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\r\n\r\n\u003cp\u003ePer Copy, 50 cents; Yearly, $2.00. In England and all countries in U.P.U.\r\nper Copy, 2s 6d; Yearly, 9s 6d.\u003c/p\u003e\r\n\r\n\u003chr class=\"tb\" /\u003e\r\n\r\n\u003cp class=\"center\"\u003eCHICAGO\u003c/p\u003e\r\n\r\n\u003cp class=\"center big\"\u003eTHE OPEN COURT PUBLISHING CO.,\u003c/p\u003e\r\n\r\n\u003cp class=\"center\"\u003eMonon Building, 324 Dearborn St.,\u003cbr /\u003e\r\nLONDON: Kegan Paul, Trench, Trübner \u0026amp; Co.\u003c/p\u003e\r\n\r\n\u003chr class=\"tb\" /\u003e\r\n\u003cp\u003eFOOTNOTES:\u003c/p\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_1_1\" id=\"Footnote_1_1\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_1_1\"\u003e\u003cspan class=\"label\"\u003e[1]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eStatique expérimentale et théorique des liquids\u003c/i\u003e, 1873. See also \u003ci\u003eThe Science\r\nof Mechanics\u003c/i\u003e, p. 384 et seqq., The Open Court Publishing Co., Chicago, 1893.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_2_2\" id=\"Footnote_2_2\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_2_2\"\u003e\u003cspan class=\"label\"\u003e[2]\u003c/span\u003e\u003c/a\u003e Compare Mach, \u003ci\u003eUeber die Molecularwirkung der Flüssigkeiten\u003c/i\u003e, Reports\r\nof the Vienna Academy, 1862.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_3_3\" id=\"Footnote_3_3\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_3_3\"\u003e\u003cspan class=\"label\"\u003e[3]\u003c/span\u003e\u003c/a\u003e In almost all branches of physics that are well worked out such maximal\r\nand minimal problems play an important part.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_4_4\" id=\"Footnote_4_4\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_4_4\"\u003e\u003cspan class=\"label\"\u003e[4]\u003c/span\u003e\u003c/a\u003e Compare Mach, \u003ci\u003eVorträge über Psychophysik\u003c/i\u003e, Vienna, 1863, page 41; \u003ci\u003eCompendium\r\nder Physik für Mediciner\u003c/i\u003e, Vienna, 1863, page 234; and also \u003ci\u003eThe Science\r\nof Mechanics\u003c/i\u003e, Chicago, 1893, pp. 84 and 464.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_5_5\" id=\"Footnote_5_5\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_5_5\"\u003e\u003cspan class=\"label\"\u003e[5]\u003c/span\u003e\u003c/a\u003e Like reflexions are found in Quételet, \u003ci\u003eDu système sociale\u003c/i\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_6_6\" id=\"Footnote_6_6\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_6_6\"\u003e\u003cspan class=\"label\"\u003e[6]\u003c/span\u003e\u003c/a\u003e For the full development of this idea see the essay \"On the Economical\r\nNature of Physical Inquiry,\" p. 186, and the chapter on \"The Economy of\r\nScience,\" in my \u003ci\u003eMechanics\u003c/i\u003e (Chicago: The Open Court Publishing Company,\r\n1893), p. 481.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_7_7\" id=\"Footnote_7_7\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_7_7\"\u003e\u003cspan class=\"label\"\u003e[7]\u003c/span\u003e\u003c/a\u003e Science may be regarded as a maximum or minimum problem, exactly\r\nas the business of the merchant. In fact, the intellectual activity of natural\r\ninquiry is not so greatly different from that exercised in ordinary life as is\r\nusually supposed.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_8_8\" id=\"Footnote_8_8\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_8_8\"\u003e\u003cspan class=\"label\"\u003e[8]\u003c/span\u003e\u003c/a\u003e This experiment, with its associated reflexions, is due to Galileo.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_9_9\" id=\"Footnote_9_9\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_9_9\"\u003e\u003cspan class=\"label\"\u003e[9]\u003c/span\u003e\u003c/a\u003e A development of the theory of musical audition differing in many\r\npoints from the theory of Helmholtz here expounded, will be found in my\r\n\u003ci\u003eContributions to the Analysis of the Sensations\u003c/i\u003e (English translation by C. M.\r\nWilliams), Chicago, The Open Court Publishing Company, 1897.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_10_10\" id=\"Footnote_10_10\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_10_10\"\u003e\u003cspan class=\"label\"\u003e[10]\u003c/span\u003e\u003c/a\u003e Sauveur also set out from Leibnitz\u0027s idea, but arrived by independent\r\nresearches at a different theory, which was very near to that of Helmholtz.\r\nCompare on this point Sauveur, \u003ci\u003eMémoires de l\u0027Académie des Sciences\u003c/i\u003e, Paris,\r\n1700-1705, and R. Smith, \u003ci\u003eHarmonics\u003c/i\u003e, Cambridge, 1749. (See \u003ci\u003eAppendix\u003c/i\u003e, p. 346.)\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_11_11\" id=\"Footnote_11_11\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_11_11\"\u003e\u003cspan class=\"label\"\u003e[11]\u003c/span\u003e\u003c/a\u003e According to Mr. Jules Andrieu, the idea that nature must be tortured\r\nto reveal her secrets is preserved in the name \u003ci\u003ecrucible\u003c/i\u003e\u0026mdash;from the Latin \u003ci\u003ecrux\u003c/i\u003e,\r\na cross. But, more probably, \u003ci\u003ecrucible\u003c/i\u003e is derived from some Old French or\r\nTeutonic form, as \u003ci\u003ecruche\u003c/i\u003e, \u003ci\u003ekroes\u003c/i\u003e, \u003ci\u003ekrus\u003c/i\u003e, etc., a pot or jug (cf. Modern English\r\n\u003ci\u003ecrock\u003c/i\u003e, \u003ci\u003ecruse\u003c/i\u003e, and German \u003ci\u003eKrug\u003c/i\u003e).\u0026mdash;\u003ci\u003eTrans.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_12_12\" id=\"Footnote_12_12\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_12_12\"\u003e\u003cspan class=\"label\"\u003e[12]\u003c/span\u003e\u003c/a\u003e Xenophon, Memorabilia iv, 7, puts into the mouth of Socrates these\r\nwords: \u0026#959;\u0026#8020;\u0026#964;\u0026#949; \u0026#947;\u0026#8048;\u0026#961; \u0026#949;\u0026#8017;\u0026#961;\u0026#949;\u0026#964;\u0026#8048; \u0026#7936;\u0026#957;\u0026#952;\u0026#961;\u0026#8061;\u0026#960;\u0026#959;\u0026#953;\u0026#962; \u0026#945;\u0026#8016;\u0026#964;\u0026#8048; \u0026#7952;\u0026#957;\u0026#8057;\u0026#956;\u0026#953;\u0026#950;\u0026#949;\u0026#957; \u0026#949;\u0026#7990;\u0026#957;\u0026#945;\u0026#953;, \u0026#959;\u0026#8020;\u0026#964;\u0026#949; \u0026#967;\u0026#945;\u0026#961;\u0026#8055;\u0026#950;\u0026#949;\u0026#963;\u0026#952;\u0026#945;\u0026#953;\r\n\u0026#952;\u0026#949;\u0026#959;\u0026#8150;\u0026#962; \u0026#7938;\u0026#957; \u0026#7969;\u0026#947;\u0026#949;\u0026#8150;\u0026#964;\u0026#959; \u0026#964;\u0026#8056;\u0026#957; \u0026#950;\u0026#951;\u0026#964;\u0026#959;\u0026#8166;\u0026#957;\u0026#964;\u0026#945; \u0026#7939; \u0026#7952;\u0026#954;\u0026#949;\u0026#8150;\u0026#957;\u0026#959;\u0026#953; \u0026#963;\u0026#945;\u0026#966;\u0026#951;\u0026#957;\u0026#8055;\u0026#963;\u0026#945;\u0026#953; \u0026#959;\u0026#8016;\u0026#954; \u0026#7952;\u0026#946;\u0026#959;\u0026#965;\u0026#955;\u0026#8053;\u0026#952;\u0026#951;\u0026#963;\u0026#945;\u0026#957;.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_13_13\" id=\"Footnote_13_13\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_13_13\"\u003e\u003cspan class=\"label\"\u003e[13]\u003c/span\u003e\u003c/a\u003e Galilei, \u003ci\u003eDiscorsi e dimostrazione matematiche\u003c/i\u003e. Leyden, 1638. \u003ci\u003eDialogo\r\nPrimo.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_14_14\" id=\"Footnote_14_14\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_14_14\"\u003e\u003cspan class=\"label\"\u003e[14]\u003c/span\u003e\u003c/a\u003e In the same way, the pitch of a locomotive-whistle is higher as the\r\nlocomotive rapidly approaches an observer, and lower when rapidly leaving\r\nhim than if the locomotive were at rest.\u0026mdash;\u003ci\u003eTrans.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_15_15\" id=\"Footnote_15_15\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_15_15\"\u003e\u003cspan class=\"label\"\u003e[15]\u003c/span\u003e\u003c/a\u003e A kilometre is 0.621 or nearly five-eighths of a statute mile.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_16_16\" id=\"Footnote_16_16\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_16_16\"\u003e\u003cspan class=\"label\"\u003e[16]\u003c/span\u003e\u003c/a\u003e Observe, also, the respect in which the wheel is held in India, Japan\r\nand other Buddhistic countries, as the emblem of power, order, and law, and\r\nof the superiority of mind over matter. The consciousness of the importance of\r\nthis invention seems to have lingered long in the minds of these nations.\u0026mdash;\u003ci\u003eTr.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_17_17\" id=\"Footnote_17_17\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_17_17\"\u003e\u003cspan class=\"label\"\u003e[17]\u003c/span\u003e\u003c/a\u003e This effect is particularly noticeable in the size of workmen on high\r\nchimneys and church-steeples\u0026mdash;\"steeple Jacks.\" When the cables were slung\r\nfrom the towers of the Brooklyn bridge (277 feet high), the men sent out in\r\nbaskets to paint them, appeared, against the broad background of heaven and\r\nwater, like flies.\u0026mdash;\u003ci\u003eTrans.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_18_18\" id=\"Footnote_18_18\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_18_18\"\u003e\u003cspan class=\"label\"\u003e[18]\u003c/span\u003e\u003c/a\u003e See Joh. Müller, \u003ci\u003eVergleichende Physiologie des Gesichtssinnes\u003c/i\u003e, Leipsic,\r\n1826.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_19_19\" id=\"Footnote_19_19\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_19_19\"\u003e\u003cspan class=\"label\"\u003e[19]\u003c/span\u003e\u003c/a\u003e Delivered before the German Casino of Prague, in the winter of 1871.\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\nA fuller treatment of the problems of this lecture will be found in my \u003ci\u003eContributions\r\nto the Analysis of the Sensations\u003c/i\u003e (Jena, 1886), English Translation,\r\nChicago, 1895. J. P. Soret, \u003ci\u003eSur la perception du beau\u003c/i\u003e (Geneva, 1892), also regards\r\nrepetition as a principle of æsthetics. His discussions of the \u003ci\u003eæsthetical\u003c/i\u003e\r\nside of the subject are much more detailed than mine. But with respect to\r\nthe psychological and physiological foundation of the principle, I am convinced\r\nthat the \u003ci\u003eContributions to the Analysis of the Sensations\u003c/i\u003e go deeper.\u0026mdash;\u003cspan class=\"smcap\"\u003eMach\u003c/span\u003e\r\n(1894).\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_20_20\" id=\"Footnote_20_20\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_20_20\"\u003e\u003cspan class=\"label\"\u003e[20]\u003c/span\u003e\u003c/a\u003e Kant, in his \u003ci\u003eProlegomena zu jeder künftigen Metaphysik\u003c/i\u003e, also refers to\r\nthis fact, but for a different purpose.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_21_21\" id=\"Footnote_21_21\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_21_21\"\u003e\u003cspan class=\"label\"\u003e[21]\u003c/span\u003e\u003c/a\u003e Compare Mach, \u003ci\u003eFichte\u0027s Zeitschrift für Philosophie\u003c/i\u003e, 1864, p. 1.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_22_22\" id=\"Footnote_22_22\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_22_22\"\u003e\u003cspan class=\"label\"\u003e[22]\u003c/span\u003e\u003c/a\u003e The fact that the first and second differential coefficients of a curve are\r\ndirectly seen, but the higher coefficients not, is very simply explained. The\r\nfirst gives the position of the tangent, the declination of the straight line from\r\nthe position of symmetry, the second the declination of the curve from the\r\nstraight line. It is, perhaps, not unprofitable to remark here that the ordinary\r\nmethod of testing rulers and plane surfaces (by reversed applications)\r\nascertains the deviation of the object from symmetry to itself.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_23_23\" id=\"Footnote_23_23\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_23_23\"\u003e\u003cspan class=\"label\"\u003e[23]\u003c/span\u003e\u003c/a\u003e See the lecture \u003ci\u003eOn the Causes of Harmony\u003c/i\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_24_24\" id=\"Footnote_24_24\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_24_24\"\u003e\u003cspan class=\"label\"\u003e[24]\u003c/span\u003e\u003c/a\u003e A. von Oettingen, \u003ci\u003eHarmoniesystem in dualer Entwicklung\u003c/i\u003e. Leipsic and\r\nDorpat, 1866.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_25_25\" id=\"Footnote_25_25\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_25_25\"\u003e\u003cspan class=\"label\"\u003e[25]\u003c/span\u003e\u003c/a\u003e Compare Mach\u0027s \u003ci\u003eZur Theorie des Gehörorgans\u003c/i\u003e, Vienna Academy, 1863.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_26_26\" id=\"Footnote_26_26\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_26_26\"\u003e\u003cspan class=\"label\"\u003e[26]\u003c/span\u003e\u003c/a\u003e A lecture delivered at the International Electrical Exhibition, in Vienna,\r\non September 4, 1883.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_27_27\" id=\"Footnote_27_27\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_27_27\"\u003e\u003cspan class=\"label\"\u003e[27]\u003c/span\u003e\u003c/a\u003e If the two bodies were oppositely electrified they would exert attractions\r\nupon each other.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_28_28\" id=\"Footnote_28_28\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_28_28\"\u003e\u003cspan class=\"label\"\u003e[28]\u003c/span\u003e\u003c/a\u003e The quantity which flows off is in point of fact less than \u003ci\u003eq\u003c/i\u003e. It would be\r\nequal to the quantity \u003ci\u003eq\u003c/i\u003e only if the inner coating of the jar were wholly encompassed\r\nby the outer coating.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_29_29\" id=\"Footnote_29_29\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_29_29\"\u003e\u003cspan class=\"label\"\u003e[29]\u003c/span\u003e\u003c/a\u003e Rigorously, of course, this is not correct. First, it is to be noted that the\r\njar \u003ci\u003eL\u003c/i\u003e is discharged simultaneously with the electrode of the machine. The\r\njar \u003ci\u003eF\u003c/i\u003e, on the other hand, is always discharged simultaneously with the outer\r\ncoating of the jar \u003ci\u003eL\u003c/i\u003e. Hence, if we call the capacity of the electrode of the\r\nmachine \u003ci\u003eE\u003c/i\u003e, that of the unit jar \u003ci\u003eL\u003c/i\u003e, that of the outer coating of \u003ci\u003eL\u003c/i\u003e, \u003ci\u003eA\u003c/i\u003e, and that of\r\nthe principal jar \u003ci\u003eF\u003c/i\u003e, then this equation would exist for the example in the text:\r\n(\u003ci\u003eF\u003c/i\u003e + \u003ci\u003eA\u003c/i\u003e)/(\u003ci\u003eL\u003c/i\u003e + \u003ci\u003eE\u003c/i\u003e) = 5. A cause of further departure from absolute exactness is\r\nthe residual charge.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_30_30\" id=\"Footnote_30_30\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_30_30\"\u003e\u003cspan class=\"label\"\u003e[30]\u003c/span\u003e\u003c/a\u003e Making allowance for the corrections indicated in the preceding footnote,\r\nI have obtained for the dielectric constant of sulphur the number 3.2,\r\nwhich agrees practically with the results obtained by more delicate methods.\r\nFor the highest attainable precision one should by rights immerse the two\r\nplates of the condenser first wholly in air and then wholly in sulphur, if the\r\nratio of the capacities is to correspond to the dielectric constant. In point of\r\nfact, however, the error which arises from inserting simply a plate of sulphur\r\nthat exactly fills the space between the two plates, is of no consequence.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_31_31\" id=\"Footnote_31_31\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_31_31\"\u003e\u003cspan class=\"label\"\u003e[31]\u003c/span\u003e\u003c/a\u003e As this definition in its simple form is apt to give rise to misunderstandings,\r\nelucidations are usually added to it. It is clear that we cannot lift a\r\nquantity of electricity to \u003ci\u003eK\u003c/i\u003e, without changing the distribution on \u003ci\u003eK\u003c/i\u003e and the\r\npotential on \u003ci\u003eK\u003c/i\u003e. Hence, the charges on \u003ci\u003eK\u003c/i\u003e must be conceived as fixed, and so\r\nsmall a quantity raised that no appreciable change is produced by it. Taking\r\nthe work thus expended as many times as the small quantity in question is\r\ncontained in the unit of quantity, we shall obtain the potential. The potential\r\nof a body \u003ci\u003eK\u003c/i\u003e may be briefly and precisely defined as follows: If we expend\r\nthe element of work \u003ci\u003edW\u003c/i\u003e to raise the element of positive quantity \u003ci\u003edQ\u003c/i\u003e from the\r\nearth to the conductor, the potential of a conductor \u003ci\u003eK\u003c/i\u003e will be given by \u003ci\u003eV\u003c/i\u003e =\r\n\u003ci\u003edW\u003c/i\u003e/\u003ci\u003edQ\u003c/i\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_32_32\" id=\"Footnote_32_32\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_32_32\"\u003e\u003cspan class=\"label\"\u003e[32]\u003c/span\u003e\u003c/a\u003e In this article the solidus or slant stroke is used for the usual fractional\r\nsign of division. Where plus or minus signs occur in the numerator or denominator,\r\nbrackets or a vinculum is used.\u0026mdash;\u003ci\u003eTr.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_33_33\" id=\"Footnote_33_33\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_33_33\"\u003e\u003cspan class=\"label\"\u003e[33]\u003c/span\u003e\u003c/a\u003e A sort of agreement exists between the notions of thermal and electrical\r\ncapacity, but the difference between the two ideas also should be carefully\r\nborne in mind. The thermal capacity of a body depends solely upon that body\r\nitself. The electrical capacity of a body \u003ci\u003eK\u003c/i\u003e is influenced by all bodies in its\r\nvicinity, inasmuch as the charge of these bodies is able to alter the potential\r\nof \u003ci\u003eK\u003c/i\u003e. To give, therefore, an unequivocal significance to the notion of the capacity\r\n(\u003ci\u003eC\u003c/i\u003e) of a body \u003ci\u003eK\u003c/i\u003e, \u003ci\u003eC\u003c/i\u003e is defined as the relation \u003ci\u003eQ\u003c/i\u003e/\u003ci\u003eV\u003c/i\u003e for the body \u003ci\u003eK\u003c/i\u003e in a\r\ncertain given position of all neighboring bodies, and during connexion of all\r\nneighboring conductors with the earth. In practice the situation is much\r\nsimpler. The capacity, for example, of a jar, the inner coating of which is\r\nalmost enveloped by its outer coating, communicating with the ground, is not\r\nsensibly affected by charged or uncharged adjacent conductors.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_34_34\" id=\"Footnote_34_34\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_34_34\"\u003e\u003cspan class=\"label\"\u003e[34]\u003c/span\u003e\u003c/a\u003e These formulæ easily follow from Newton\u0027s theorem that a homogeneous\r\nspherical shell, whose elements obey the law of the inverse squares, exerts no\r\nforce whatever on points within it but acts on points without as if the whole\r\nmass were concentrated at its centre. The formulæ next adduced also flow\r\nfrom this proposition.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_35_35\" id=\"Footnote_35_35\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_35_35\"\u003e\u003cspan class=\"label\"\u003e[35]\u003c/span\u003e\u003c/a\u003e The energy of a sphere of radius \u003ci\u003er\u003c/i\u003e charged with the quantity \u003ci\u003eq\u003c/i\u003e is\r\n1/2(\u003ci\u003eq\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e/\u003ci\u003er\u003c/i\u003e). If the radius increase by the space \u003ci\u003edr\u003c/i\u003e a loss of energy occurs, and\r\nthe work done is 1/2(\u003ci\u003eq\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e/\u003ci\u003er\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e)\u003ci\u003edr\u003c/i\u003e. Letting \u003ci\u003ep\u003c/i\u003e denote the uniform electrical pressure\r\non unit of surface of the sphere, the work done is also 4\u003ci\u003er\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e\u0026#960;\u003ci\u003epdr\u003c/i\u003e. Hence\r\n\u003ci\u003ep\u003c/i\u003e = (1/8\u003ci\u003er\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e\u0026#960;)(\u003ci\u003eq\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e/\u003ci\u003er\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e). Subjected to the same superficial pressure on all sides,\r\nsay in a fluid, our half sphere would be an equilibrium. Hence we must make\r\nthe pressure \u003ci\u003ep\u003c/i\u003e act on the surface of the great circle to obtain the effect on the\r\nbalance, which is \u003ci\u003er\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e\u0026#960;\u003ci\u003ep\u003c/i\u003e = 1/8(\u003ci\u003eq\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e/\u003ci\u003er\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e) = 1/8\u003ci\u003eV\u003c/i\u003e\u003csup\u003e2\u003c/sup\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_36_36\" id=\"Footnote_36_36\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_36_36\"\u003e\u003cspan class=\"label\"\u003e[36]\u003c/span\u003e\u003c/a\u003e The arrangement described is for several reasons not fitted for the actual\r\nmeasurement of potential. Thomson\u0027s absolute electrometer is based upon\r\nan ingenious modification of the electrical balance of Harris and Volta. Of\r\ntwo large plane parallel plates, one communicates with the earth, while the\r\nother is brought to the potential to be measured. A small movable superficial\r\nportion \u003ci\u003ef\u003c/i\u003e of this last hangs from the balance for the determination of the\r\nattraction \u003ci\u003eP\u003c/i\u003e. The distance of the plates from each other being \u003ci\u003eD\u003c/i\u003e we get \u003ci\u003eV\u003c/i\u003e =\r\n\u003ci\u003eD\u003c/i\u003e\u0026#8730;(8\u0026#960;\u003ci\u003eP\u003c/i\u003e/\u003ci\u003ef\u003c/i\u003e).\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_37_37\" id=\"Footnote_37_37\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_37_37\"\u003e\u003cspan class=\"label\"\u003e[37]\u003c/span\u003e\u003c/a\u003e This moment of torsion needs a supplementary correction, on account of\r\nthe vertical electric attraction of the excited disks. This is done by changing\r\nthe weight of the disk by means of additional weights and by making a second\r\nreading of the angles of deflexion.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_38_38\" id=\"Footnote_38_38\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_38_38\"\u003e\u003cspan class=\"label\"\u003e[38]\u003c/span\u003e\u003c/a\u003e The jar in our experiment acts like an accumulator, being charged by a\r\ndynamo machine. The relation which obtains between the expended and the\r\navailable work may be gathered from the following simple exposition. A\r\nHoltz machine \u003ci\u003eH\u003c/i\u003e (Fig. 40) is charging a unit jar \u003ci\u003eL\u003c/i\u003e, which after \u003ci\u003en\u003c/i\u003e discharges\r\nof quantity \u003ci\u003eq\u003c/i\u003e and potential \u003ci\u003ev\u003c/i\u003e, charges the jar \u003ci\u003eF\u003c/i\u003e with the quantity \u003ci\u003eQ\u003c/i\u003e at the potential\r\n\u003ci\u003eV\u003c/i\u003e. The energy of the unit-jar discharges is lost and that of the jar \u003ci\u003eF\u003c/i\u003e\r\nalone is left. Hence the ratio of the available work to the total work expended\r\nis\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\n\u003ci\u003e½QV/[½QV + (n/2)qv]\u003c/i\u003e and as \u003ci\u003eQ\u003c/i\u003e = \u003ci\u003enq\u003c/i\u003e, also \u003ci\u003eV/(V + v)\u003c/i\u003e.\r\n\u003c/p\u003e\r\n\r\n\u003cp\u003e\r\nIf, now, we interpose no unit jar, still the parts of the machine and the wires\r\nof conduction are themselves virtually such unit jars and the formula still\r\nsubsists \u003ci\u003eV\u003c/i\u003e/(\u003ci\u003eV\u003c/i\u003e + \u0026#931;\u003ci\u003ev\u003c/i\u003e), in which \u0026#931;\u003ci\u003ev\u003c/i\u003e represents the sum of all the successively introduced\r\ndifferences of potential in the circuit of connexion.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_39_39\" id=\"Footnote_39_39\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_39_39\"\u003e\u003cspan class=\"label\"\u003e[39]\u003c/span\u003e\u003c/a\u003e Published in Vol. 5, No. I, of \u003ci\u003eThe Monist\u003c/i\u003e, October, 1894, being in part\r\na re-elaboration of the treatise \u003ci\u003eUeber die Erhaltung der Arbeit\u003c/i\u003e, Prague, 1872.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_40_40\" id=\"Footnote_40_40\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_40_40\"\u003e\u003cspan class=\"label\"\u003e[40]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eOn Matter, Living Force, and Heat\u003c/i\u003e, Joule: \u003ci\u003eScientific Papers\u003c/i\u003e, London,\r\n1884, I, p. 265.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_41_41\" id=\"Footnote_41_41\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_41_41\"\u003e\u003cspan class=\"label\"\u003e[41]\u003c/span\u003e\u003c/a\u003e \"Atqui hoc si sit, globorum series sive corona eundem situm cum priore\r\nhabebit, eademque de causa octo globi sinistri ponderosiores erunt sex dextris,\r\nideoque rursus octo illi descendent, sex illi ascendent, istique globi ex sese\r\n\u003ci\u003econtinuum et aeternum motum efficient, quod est falsum\u003c/i\u003e.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_42_42\" id=\"Footnote_42_42\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_42_42\"\u003e\u003cspan class=\"label\"\u003e[42]\u003c/span\u003e\u003c/a\u003e \"A igitur, (si ullo modo per naturam fieri possit) locum sibi tributum\r\nnon servato, ac delabatur in \u003ci\u003eD\u003c/i\u003e; quibus positis aqua quae ipsi \u003ci\u003eA\u003c/i\u003e succedit eandem\r\nob causam deffluet in \u003ci\u003eD\u003c/i\u003e, eademque ab alia istinc expelletur, atque adeo\r\naqua haec (cum ubique eadem ratio sit) \u003ci\u003emotum instituet perpetuum, quod absurdum\r\nfuerit\u003c/i\u003e.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_43_43\" id=\"Footnote_43_43\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_43_43\"\u003e\u003cspan class=\"label\"\u003e[43]\u003c/span\u003e\u003c/a\u003e \"Accipio, gradus velocitatis ejusdem mobilis super diversas planorum\r\ninclinationes acquisitos tunc esse aequales, cum eorundum planorum elevationes\r\naequales sint.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_44_44\" id=\"Footnote_44_44\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_44_44\"\u003e\u003cspan class=\"label\"\u003e[44]\u003c/span\u003e\u003c/a\u003e \"Voi molto probabilmente discorrete, ma oltre al veri simile voglio con\r\nuna esperienza crescer tanto la probabilità, che poco gli manchi all\u0027agguagliarsi\r\nad una ben necessaria dimostrazione. Figuratevi questo foglio essere\r\nuna parete eretta all\u0027orizzonte, e da un chiodo fitto in essa pendere una palla\r\ndi piombo d\u0027un\u0027oncia, o due, sospesa dal sottil filo \u003ci\u003eAB\u003c/i\u003e lungo due, o tre braccia\r\nperpendicolare all\u0027orizzonte, e nella parete segnate una linea orizontale \u003ci\u003eDC\u003c/i\u003e\r\nsegante a squadra il perpendicolo \u003ci\u003eAB\u003c/i\u003e, il quale sia lontano dalla parete due\r\ndita in circa, trasferendo poi il filo \u003ci\u003eAB\u003c/i\u003e colla palla in \u003ci\u003eAC\u003c/i\u003e, lasciata essa palla in\r\nlibertà, la quale primieramente vedrete scendere descrivendo l\u0027arco \u003ci\u003eCBD\u003c/i\u003e, e\r\ndi tanto trapassare il termine \u003ci\u003eB\u003c/i\u003e, che scorrendo per l\u0027arco \u003ci\u003eBD\u003c/i\u003e sormonterà fino\r\nquasi alla segnata parallela \u003ci\u003eCD\u003c/i\u003e, restando di per vernirvi per piccolissimo intervallo,\r\ntoltogli il precisamente arrivarvi dall\u0027impedimento dell\u0027aria, e del\r\nfilo. Dal che possiamo veracemente concludere, che l\u0027impeto acquistato nel\r\npunto \u003ci\u003eB\u003c/i\u003e dalla palla nello scendere per l\u0027arco \u003ci\u003eCB\u003c/i\u003e, fu tanto, che bastò a risospingersi\r\nper un simile arco \u003ci\u003eBD\u003c/i\u003e alla medesima altezza; fatta, e più volte reiterata\r\ncotale esperienza, voglio, che fiechiamo nella parete rasente al perpendicolo\r\n\u003ci\u003eAB\u003c/i\u003e un chiodo come in \u003ci\u003eE\u003c/i\u003e, ovvero in \u003ci\u003eF\u003c/i\u003e, che sporga in fuori cinque, o\r\nsei dita, e questo acciocchè il filo \u003ci\u003eAC\u003c/i\u003e tornando come prima a riportar la palla\r\n\u003ci\u003eC\u003c/i\u003e per l\u0027arco \u003ci\u003eCB\u003c/i\u003e, giunta che ella sia in \u003ci\u003eB\u003c/i\u003e, inoppando il filo nel chiodo \u003ci\u003eE\u003c/i\u003e, sia\r\ncostretta a camminare per la circonferenza \u003ci\u003eBG\u003c/i\u003e descritta in torno al centro \u003ci\u003eE\u003c/i\u003e,\r\ndal che vedremo quello, che potrà far quel medesimo impeto, che dianzi concepizo\r\nnel medesimo termine \u003ci\u003eB\u003c/i\u003e, sospinse l\u0027istesso mobile per l\u0027arco \u003ci\u003eED\u003c/i\u003e all\u0027altezza\r\ndell\u0027orizzonale \u003ci\u003eCD\u003c/i\u003e. Ora, Signori, voi vedrete con gusto condursi la\r\npalla all\u0027orizzontale nel punto \u003ci\u003eG\u003c/i\u003e, e l\u0027istesso accadere, l\u0027intoppo si metesse\r\npiù basso, come in \u003ci\u003eF\u003c/i\u003e, dove la palla descriverebbe l\u0027arco \u003ci\u003eBJ\u003c/i\u003e, terminando sempre\r\nla sua salita precisamente nella linea \u003ci\u003eCD\u003c/i\u003e, e quando l\u0027intoppe del chiodo\r\nfusse tanto basso, che l\u0027avanzo del filo sotto di lui non arivasse all\u0027altezza di\r\n\u003ci\u003eCD\u003c/i\u003e (il che accaderebbe, quando fusse più vicino al punto \u003ci\u003eB\u003c/i\u003e, che al segamento\r\ndell\u0027 \u003ci\u003eAB\u003c/i\u003e coll\u0027orizzontale \u003ci\u003eCD\u003c/i\u003e), allora il filo cavalcherebbe il chiodo, e\r\nsegli avolgerebbe intorno. Questa esperienza non lascia luogo di dubitare\r\ndella verità del supposto: imperocchè essendo li due archi \u003ci\u003eCB\u003c/i\u003e, \u003ci\u003eDB\u003c/i\u003e equali e\r\nsimilmento posti, l\u0027acquisto di momento fatto per la scesa nell\u0027arco \u003ci\u003eCB\u003c/i\u003e, è il\r\nmedesimo, che il fatto per la scesa dell\u0027arco \u003ci\u003eDB\u003c/i\u003e; ma il momento acquistato\r\nin \u003ci\u003eB\u003c/i\u003e per l\u0027arco \u003ci\u003eCB\u003c/i\u003e è potente a risospingere in su il medesimo mobile per l\u0027arco\r\n\u003ci\u003eBD\u003c/i\u003e; adunque anco il momento acquistato nella scesa \u003ci\u003eDB\u003c/i\u003e è eguale a quello,\r\nche sospigne l\u0027istesso mobile pel medesimo arco da \u003ci\u003eB\u003c/i\u003e in \u003ci\u003eD\u003c/i\u003e, sicche universal-mente\r\nogni memento acquistato per la scesa d\u0027un arco è eguale a quello, che\r\npuò far risalire l\u0027istesso mobile pel medesimo arco: ma i momenti tutti che\r\nfanno resalire per tutti gli archi \u003ci\u003eBD\u003c/i\u003e, \u003ci\u003eBG\u003c/i\u003e, \u003ci\u003eBJ\u003c/i\u003e sono eguali, poichè son fatti\r\ndal istesso medesimo momento acquistato per la scesa \u003ci\u003eCB\u003c/i\u003e, come mostra\r\nl\u0027esperienza: adunque tutti i momenti, che si acquistano per le scese negli\r\narchi \u003ci\u003eDB\u003c/i\u003e, \u003ci\u003eGB\u003c/i\u003e, \u003ci\u003eJB\u003c/i\u003e sono eguali.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_45_45\" id=\"Footnote_45_45\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_45_45\"\u003e\u003cspan class=\"label\"\u003e[45]\u003c/span\u003e\u003c/a\u003e \"Constat jam, quod mobile ex quiete in \u003ci\u003eA\u003c/i\u003e descendens per \u003ci\u003eAB\u003c/i\u003e, gradus\r\nacquirit velocitatis juxta temporis ipsius incrementum: gradum vero in \u003ci\u003eB\u003c/i\u003e\r\nesse maximum acquisitorum, et suapte natura immutabiliter impressum, sublatis\r\nscilicet causis accelerationis novae, aut retardationis: accelerationis inquam,\r\nsi adhuc super extenso plano ulterius progrederetur; retardationis\r\nvero, dum super planum acclive \u003ci\u003eBC\u003c/i\u003e fit reflexio: in horizontali autem \u003ci\u003eGH\u003c/i\u003e\r\naequabilis motus juxta gradum velocitatis ex \u003ci\u003eA\u003c/i\u003e in \u003ci\u003eB\u003c/i\u003e acquisitae in infinitum\r\nextenderetur.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_46_46\" id=\"Footnote_46_46\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_46_46\"\u003e\u003cspan class=\"label\"\u003e[46]\u003c/span\u003e\u003c/a\u003e \"Si gravitas non esset, neque aër motui corporum officeret, unumquodque\r\neorum, acceptum semel motum continuaturum velocitate aequabili, secundum\r\nlineam rectam.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_47_47\" id=\"Footnote_47_47\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_47_47\"\u003e\u003cspan class=\"label\"\u003e[47]\u003c/span\u003e\u003c/a\u003e \"Si pondera quotlibet, vi gravitatis suae, moveri incipiant; non posse\r\ncentrum gravitatis ex ipsis compositae altius, quam ubi incipiente motu reperiebatur,\r\nascendere.\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\n\"Ipsa vero hypothesis nostra quominus scrupulum moveat, nihil aliud\r\nsibi velle ostendemus, quam, quod nemo unquam negavit, gravia nempe sursum\r\nnon ferri.\u0026mdash;Et sane, si hac eadem uti scirent novorum operum machinatores,\r\nqui motum perpetuum irrito conatu moliuntur, facile suos ipsi errores\r\ndeprehenderent, intelligerentque rem eam mechanica ratione haud quaquam\r\npossibilem esse.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_48_48\" id=\"Footnote_48_48\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_48_48\"\u003e\u003cspan class=\"label\"\u003e[48]\u003c/span\u003e\u003c/a\u003e \"Si pendulum e pluribus ponderibus compositum, atque e quiete dimissum,\r\npartem quamcunque oscillationis integrae confecerit, atque inde porro\r\nintelligantur pondera ejus singula, relicto communi vinculo, celeritates acquisitas\r\nsursum convertere, ac quousque possunt ascendere; hoc facto centrum\r\ngravitatis ex omnibus compositae, ad eandem altitudinem reversum erit, quam\r\nante inceptam oscillationem obtinebat.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_49_49\" id=\"Footnote_49_49\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_49_49\"\u003e\u003cspan class=\"label\"\u003e[49]\u003c/span\u003e\u003c/a\u003e \"Notato autem hic illud staticum axioma etiam locum habere:\r\n\u003c/p\u003e\r\n\r\n\u003cdiv class=\"poem\"\u003e\u003cdiv class=\"stanza\"\u003e\r\n\u003cspan class=\"i0\"\u003e\"Ut spatium agentis ad spatium patientis\u003cbr /\u003e\u003c/span\u003e\r\n\u003cspan class=\"i0\"\u003eSic potentia patientis ad potentiam agentis.\"\u003cbr /\u003e\u003c/span\u003e\r\n\u003c/div\u003e\u003c/div\u003e\r\n\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_50_50\" id=\"Footnote_50_50\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_50_50\"\u003e\u003cspan class=\"label\"\u003e[50]\u003c/span\u003e\u003c/a\u003e \"Cependant, comme dans cet ouvrage on ne fut d\u0027abord attentif qu\u0027à\r\nconsidérer ce beau développement de la mécanique qui semblait sortir tout\r\nentière d\u0027une seule et même formule, on crut naturellement que la science etait\r\nfaite, et qu\u0027il ne restait plus qu\u0027à chercher la démonstration du principe des\r\nvitesses virtuelles. Mais cette recherche ramena toutes les difficultés qu\u0027on\r\navait franchies par le principe même. Cette loi si générale, où se mêlent des\r\nidées vagues et étrangères de mouvements infinement petits et de perturbation\r\nd\u0027équilibre, ne fit en quelque sorte que s\u0027obsurcir à l\u0027examen; et le livre de\r\nLagrange n\u0027offrant plus alors rien de clair que la marche des calculs, on vit\r\nbien que les nuages n\u0027avaient paru levé sur le cours de la mécanique que\r\nparcequ\u0027ils étaient, pour ainsi dire, rassemblés à l\u0027origine même do cette\r\nscience.\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\n\"Une démonstration générale du principe des vitesses virtuelles devait\r\nau fond revenir a établir le mécanique entière sur une autre base: car la demonstration\r\nd\u0027une loi qui embrasse toute une science ne peut être autre chose\r\nqua la reduction de cette science à une autre loi aussi générale, mais évidente,\r\nou du moins plus simple que la première, et qui partant la rende inutile.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_51_51\" id=\"Footnote_51_51\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_51_51\"\u003e\u003cspan class=\"label\"\u003e[51]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eTraité de la lumière\u003c/i\u003e, Leyden, 1690, p. 2.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_52_52\" id=\"Footnote_52_52\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_52_52\"\u003e\u003cspan class=\"label\"\u003e[52]\u003c/span\u003e\u003c/a\u003e \"L\u0027on ne sçaurait douter que la lumière ne consiste dans le \u003ci\u003emouvement\u003c/i\u003e de\r\ncertaine matière. Car soit qu\u0027on regarde sa production, on trouve qu\u0027içy sur\r\nla terre c\u0027est principalement le feu et la flamme qui l\u0027engendrent, lesquels\r\ncontient sans doute des corps qui sont dans un mouvement rapide, puis qu\u0027ils\r\ndissolvent et fondent plusieurs autres corps des plus solides: soit qu\u0027on regarde\r\nses effets, on voit que quand la lumière est ramasseé, comme par des\r\nmiroires concaves, elle a la vertu de brûler comme le feu. c-est-à-dire qu\u0027elle\r\ndesunit les parties des corps; ce qui marque assurément du \u003ci\u003emouvement\u003c/i\u003e, au\r\nmoins dans la \u003ci\u003evraye Philosophie\u003c/i\u003e, dans laquelle on conçoit la cause de tous les\r\neffets naturels par des raisons de \u003ci\u003emechanique\u003c/i\u003e. Ce qu\u0027il faut faire à mon avis,\r\nou bien renoncer à tout espérance de jamais rien comprendre dans la Physique.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_53_53\" id=\"Footnote_53_53\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_53_53\"\u003e\u003cspan class=\"label\"\u003e[53]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eSur la puissance motrice du feu\u003c/i\u003e. (Paris, 1824.)\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_54_54\" id=\"Footnote_54_54\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_54_54\"\u003e\u003cspan class=\"label\"\u003e[54]\u003c/span\u003e\u003c/a\u003e \"On objectra peut-être ici que le mouvement perpétuel, démontré impossible\r\npar les \u003ci\u003eseules actions mécaniques\u003c/i\u003e, ne l\u0027est peut-être pas lorsqu\u0027on\r\nemploie l\u0027influence soit de la \u003ci\u003echaleur\u003c/i\u003e, soit de l\u0027électricité; mais pent-on concevoir\r\nles phénomènes de la chaleur et de l\u0027électricité comme dus à autre\r\nchose qu\u0027à des \u003ci\u003emouvements quelconques des corps\u003c/i\u003e et comme tels ne doivent-ils\r\npas être soumis aux lois générales de la mécanique?\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_55_55\" id=\"Footnote_55_55\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_55_55\"\u003e\u003cspan class=\"label\"\u003e[55]\u003c/span\u003e\u003c/a\u003e By this is meant the temperature of a Celsius scale, the zero of which is\r\n273° below the melting-point of ice.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_56_56\" id=\"Footnote_56_56\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_56_56\"\u003e\u003cspan class=\"label\"\u003e[56]\u003c/span\u003e\u003c/a\u003e I first drew attention to this fact in my treatise \u003ci\u003eUeber die Erhaltung der\r\nArbeit\u003c/i\u003e, Prague, 1872. Before this, Zeuner had pointed out the analogy between\r\nmechanical and thermal energy. I have given a more extensive development\r\nof this idea in a communication to the \u003ci\u003eSitzungsberichte der Wiener\u003c/i\u003e\r\n\u003ci\u003eAkademie\u003c/i\u003e, December, 1892, entitled \u003ci\u003eGeschichte und Kritik des Carnot\u0027schen\r\nWärmegesetzes\u003c/i\u003e. Compare also the works of Popper (1884), Helm (1887),\r\nWronsky (1888), and Ostwald (1892).\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_57_57\" id=\"Footnote_57_57\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_57_57\"\u003e\u003cspan class=\"label\"\u003e[57]\u003c/span\u003e\u003c/a\u003e Sir William Thomson first consciously and intentionally introduced\r\n(1848, 1851) a \u003ci\u003emechanical\u003c/i\u003e measure of temperature similar to the electric measure\r\nof potential.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_58_58\" id=\"Footnote_58_58\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_58_58\"\u003e\u003cspan class=\"label\"\u003e[58]\u003c/span\u003e\u003c/a\u003e Compare my \u003ci\u003eAnalysis of the Sensations\u003c/i\u003e, Jena, 1886: English translation,\r\nChicago, 1897.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_59_59\" id=\"Footnote_59_59\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_59_59\"\u003e\u003cspan class=\"label\"\u003e[59]\u003c/span\u003e\u003c/a\u003e A better terminology appears highly desirable in the place of the usual\r\nmisleading one. Sir William Thomson (1852) appears to have felt this need,\r\nand it has been clearly expressed by F. Wald (1889). We should call the work\r\nwhich corresponds to a vanished quantity of heat its mechanical substitution-value;\r\nwhile that work which can be \u003ci\u003eactually\u003c/i\u003e performed in the passage of a\r\nthermal condition \u003ci\u003eA\u003c/i\u003e to a condition \u003ci\u003eB\u003c/i\u003e, alone deserves the name of the \u003ci\u003eenergy-value\u003c/i\u003e\r\nof this change of condition. In this way the \u003ci\u003earbitrary\u003c/i\u003e substantial conception\r\nof the processes would be preserved and misapprehensions forestalled.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_60_60\" id=\"Footnote_60_60\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_60_60\"\u003e\u003cspan class=\"label\"\u003e[60]\u003c/span\u003e\u003c/a\u003e An address delivered before the anniversary meeting of the Imperial\r\nAcademy of Sciences, at Vienna, May 25, 1882.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_61_61\" id=\"Footnote_61_61\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_61_61\"\u003e\u003cspan class=\"label\"\u003e[61]\u003c/span\u003e\u003c/a\u003e \u003ci\u003ePrimitive Culture.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_62_62\" id=\"Footnote_62_62\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_62_62\"\u003e\u003cspan class=\"label\"\u003e[62]\u003c/span\u003e\u003c/a\u003e Tylor, \u003ci\u003eloc. cit.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_63_63\" id=\"Footnote_63_63\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_63_63\"\u003e\u003cspan class=\"label\"\u003e[63]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eEssai philosophique sur les probabilités\u003c/i\u003e. 6th Ed. Paris, 1840, p. 4. The\r\nnecessary consideration of the initial velocities is lacking in this formulation.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_64_64\" id=\"Footnote_64_64\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_64_64\"\u003e\u003cspan class=\"label\"\u003e[64]\u003c/span\u003e\u003c/a\u003e \u003ci\u003ePrincipien der Wirthschaftslehre\u003c/i\u003e, Vienna, 1873.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_65_65\" id=\"Footnote_65_65\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_65_65\"\u003e\u003cspan class=\"label\"\u003e[65]\u003c/span\u003e\u003c/a\u003e It is clear from this that all so-called elementary (differential) laws involve\r\na relation to the whole.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_66_66\" id=\"Footnote_66_66\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_66_66\"\u003e\u003cspan class=\"label\"\u003e[66]\u003c/span\u003e\u003c/a\u003e If it be objected, that in the case of perturbations of the velocity of rotation\r\nof the earth, we could be sensible of such perturbations, and being obliged\r\nto have some measure of time, we should resort to the period of vibration of\r\nthe waves of sodium light,\u0026mdash;all that this would show is that for practical reasons\r\nwe should select that event which best served us as the \u003ci\u003esimplest\u003c/i\u003e common\r\nmeasure of the others.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_67_67\" id=\"Footnote_67_67\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_67_67\"\u003e\u003cspan class=\"label\"\u003e[67]\u003c/span\u003e\u003c/a\u003e Measurement, in fact, is the definition of one phenomenon by another\r\n(standard) phenomenon.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_68_68\" id=\"Footnote_68_68\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_68_68\"\u003e\u003cspan class=\"label\"\u003e[68]\u003c/span\u003e\u003c/a\u003e I have represented the point of view here taken for more than thirty\r\nyears and developed it in various writings (\u003ci\u003eErhaltung der Arbeit\u003c/i\u003e, 1872, parts\r\nof which are published in the article on \u003ci\u003eThe Conservation of Energy\u003c/i\u003e in this\r\ncollection; \u003ci\u003eThe Forms of Liquids\u003c/i\u003e, 1872, also published in this collection; and\r\nthe \u003ci\u003eBewegungsempfindungen\u003c/i\u003e, 1875). The idea, though known to philosophers,\r\nis unfamiliar to the majority of physicists. It is a matter of deep regret to me,\r\ntherefore, that the title and author of a small tract which accorded with my\r\nviews in numerous details and which I remember having caught a glance of\r\nin a very busy period (1879-1880), have so completely disappeared from my\r\nmemory that all efforts to obtain a clue to them have hitherto been fruitless.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_69_69\" id=\"Footnote_69_69\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_69_69\"\u003e\u003cspan class=\"label\"\u003e[69]\u003c/span\u003e\u003c/a\u003e Inaugural Address, delivered on assuming the Rectorate of the University\r\nof Prague, October 18, 1883.\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\nThe idea presented in this essay is neither new nor remote. I have touched\r\nupon it myself on several occasions (first in 1867), but have never made it the\r\nsubject of a formal disquisition. Doubtless, others, too, have treated it; it\r\nlies, so to speak, in the air. However, as many of my illustrations were well\r\nreceived, although known only in an imperfect form from the lecture itself\r\nand the newspapers, I have, contrary to my original intention, decided to\r\npublish it. It is not my intention to trespass here upon the domain of biology.\r\nMy statements are to be taken merely as the expression of the fact that no one\r\ncan escape the influence of a great and far-reaching idea.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_70_70\" id=\"Footnote_70_70\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_70_70\"\u003e\u003cspan class=\"label\"\u003e[70]\u003c/span\u003e\u003c/a\u003e At first sight an apparent contradiction arises from the admission of both\r\nheredity and adaptation; and it is undoubtedly true that a strong disposition\r\nto heredity precludes great capability of adaptation. But imagine the organism\r\nto be a plastic mass which retains the form transmitted to it by former\r\ninfluences until new influences modify it; the \u003ci\u003eone\u003c/i\u003e property of \u003ci\u003eplasticity\u003c/i\u003e will\r\nthen represent capability of adaptation as well as power of heredity. Analogous\r\nto this is the case of a bar of magnetised steel of high coercive force:\r\nthe steel retains its magnetic properties until a new force displaces them.\r\nTake also a body in motion: the body retains the velocity acquired in (\u003ci\u003einherited\u003c/i\u003e\r\nfrom) the interval of time just preceding, except it be changed in the\r\nnext moment by an accelerating force. In the case of the body in motion the\r\n\u003ci\u003echange\u003c/i\u003e of velocity (\u003ci\u003eAbänderung\u003c/i\u003e) was looked upon as a matter of course, while\r\nthe discovery of the principle of \u003ci\u003einertia\u003c/i\u003e (or persistence) created surprise; in\r\nDarwin\u0027s case, on the contrary, \u003ci\u003eheredity\u003c/i\u003e (or persistence) was taken for granted,\r\nwhile the principle of \u003ci\u003evariation\u003c/i\u003e (\u003ci\u003eAbänderung\u003c/i\u003e) appeared novel.\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\nFully adequate views are, of course, to be reached only by a study of the\r\noriginal facts emphasised by Darwin, and not by these analogies. The example\r\nreferring to motion, if I am not mistaken, I first heard, in conversation,\r\nfrom my friend J. Popper, Esq., of Vienna.\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\nMany inquirers look upon the stability of the species as something settled,\r\nand oppose to it the Darwinian theory. But the stability of the species is itself\r\na \"theory.\" The essential modifications which Darwin\u0027s views also are\r\nundergoing will be seen from the works of Wallace [and Weismann], but more\r\nespecially from a book of W. H. Rolph, \u003ci\u003eBiologische Probleme\u003c/i\u003e, Leipsic, 1882.\r\nUnfortunately, this last talented investigator is no longer numbered among\r\nthe living.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_71_71\" id=\"Footnote_71_71\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_71_71\"\u003e\u003cspan class=\"label\"\u003e[71]\u003c/span\u003e\u003c/a\u003e Written in 1883.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_72_72\" id=\"Footnote_72_72\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_72_72\"\u003e\u003cspan class=\"label\"\u003e[72]\u003c/span\u003e\u003c/a\u003e See Pfaundler, \u003ci\u003ePogg. Ann., Jubelband\u003c/i\u003e, p. 182.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_73_73\" id=\"Footnote_73_73\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_73_73\"\u003e\u003cspan class=\"label\"\u003e[73]\u003c/span\u003e\u003c/a\u003e See the beautiful discussions of this point in Hering\u0027s \u003ci\u003eMemory as a General\r\nFunction of Organised Matter\u003c/i\u003e (1870), Chicago, The Open Court Publishing\r\nCo., 1887. Compare also Dubois, \u003ci\u003eUeber die Uebung\u003c/i\u003e, Berlin, 1881.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_74_74\" id=\"Footnote_74_74\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_74_74\"\u003e\u003cspan class=\"label\"\u003e[74]\u003c/span\u003e\u003c/a\u003e Spencer, \u003ci\u003eThe Principles of Psychology\u003c/i\u003e. London, 1872.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_75_75\" id=\"Footnote_75_75\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_75_75\"\u003e\u003cspan class=\"label\"\u003e[75]\u003c/span\u003e\u003c/a\u003e See the article \u003ci\u003eThe Velocity of Light\u003c/i\u003e, page 63.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_76_76\" id=\"Footnote_76_76\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_76_76\"\u003e\u003cspan class=\"label\"\u003e[76]\u003c/span\u003e\u003c/a\u003e I am well aware that the endeavor to confine oneself in natural research\r\nto \u003ci\u003efacts\u003c/i\u003e is often censured as an exaggerated fear of metaphysical spooks.\r\nBut I would observe, that, judged by the mischief which they have wrought,\r\nthe metaphysical, of all spooks, are the least fabulous. It is not to be denied\r\nthat many forms of thought were not originally acquired by the individual, but\r\nwere antecedently formed, or rather prepared for, in the development of the\r\nspecies, in some such way as Spencer, Haeckel, Hering, and others have\r\nsupposed, and as I myself have hinted on various occasions.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_77_77\" id=\"Footnote_77_77\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_77_77\"\u003e\u003cspan class=\"label\"\u003e[77]\u003c/span\u003e\u003c/a\u003e Compare, for example, \u003ci\u003eSchiller, Zerstreute Betrachtungen über verschiedene\r\nästhetische Gegenstände\u003c/i\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_78_78\" id=\"Footnote_78_78\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_78_78\"\u003e\u003cspan class=\"label\"\u003e[78]\u003c/span\u003e\u003c/a\u003e We must not be deceived in imagining that the happiness of other people\r\nis not a very considerable and essential portion of our own. It is common\r\ncapital, which cannot be created by the individual, and which does not perish\r\nwith him. The formal and material limitation of the \u003ci\u003eego\u003c/i\u003e is necessary and sufficient\r\nonly for the crudest practical objects, and cannot subsist in a broad conception.\r\nHumanity in its entirety may be likened to a polyp-plant. The\r\nmaterial and organic bonds of individual union have, indeed, been severed;\r\nthey would only have impeded freedom of movement and evolution. But the\r\nultimate aim, the psychical connexion of the whole, has been attained in a\r\nmuch higher degree through the richer development thus made possible.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_79_79\" id=\"Footnote_79_79\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_79_79\"\u003e\u003cspan class=\"label\"\u003e[79]\u003c/span\u003e\u003c/a\u003e C. E. von Baer, the subsequent opponent of Darwin and Haeckel, has\r\ndiscussed in two beautiful addresses (\u003ci\u003eDas allgemeinste Gesetz der Natur in\r\naller Entwickelung\u003c/i\u003e, and \u003ci\u003eWelche Auffassung der lebenden Natur ist die richtige,\r\nund wie ist diese Auffassung auf die Entomologie anzuwenden\u003c/i\u003e?) the\r\nnarrowness of the view which regards an animal in its existing state as\r\nfinished and complete, instead of conceiving it as a phase in the series of evolutionary\r\nforms and regarding the species itself as a phase of the development\r\nof the animal world in general.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_80_80\" id=\"Footnote_80_80\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_80_80\"\u003e\u003cspan class=\"label\"\u003e[80]\u003c/span\u003e\u003c/a\u003e An address delivered before the General Session of the German Association\r\nof Naturalists and Physicians, at Vienna, Sept. 24, 1894.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_81_81\" id=\"Footnote_81_81\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_81_81\"\u003e\u003cspan class=\"label\"\u003e[81]\u003c/span\u003e\u003c/a\u003e Inaugural lecture delivered on assuming the Professorship of the History\r\nand Theory of Inductive Science in the University of Vienna, October\r\n21, 1895.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_82_82\" id=\"Footnote_82_82\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_82_82\"\u003e\u003cspan class=\"label\"\u003e[82]\u003c/span\u003e\u003c/a\u003e The phrase is, \u003ci\u003eEr hat das Pulver nicht erfunden\u003c/i\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_83_83\" id=\"Footnote_83_83\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_83_83\"\u003e\u003cspan class=\"label\"\u003e[83]\u003c/span\u003e\u003c/a\u003e \"Quod si quis tanta industria exstitisset, ut ex naturae principiis at geometria\r\nhanc rem eruere potuisset, eum ego supra mortalium sortem ingenio\r\nvaluisse dicendum crederem. Sed hoc tantum abest, ut fortuito reperti artificii\r\nrationem non adhuc satis explicari potuerint viri doctissimi.\"\u0026mdash;Hugenii\r\nDioptrica (de telescopiis).\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_84_84\" id=\"Footnote_84_84\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_84_84\"\u003e\u003cspan class=\"label\"\u003e[84]\u003c/span\u003e\u003c/a\u003e I must not be understood as saying that the fire-drill has played no part\r\nin the worship of fire or of the sun.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_85_85\" id=\"Footnote_85_85\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_85_85\"\u003e\u003cspan class=\"label\"\u003e[85]\u003c/span\u003e\u003c/a\u003e Compare on this point the extremely interesting remarks of Dr. Paul\r\nCarus in his \u003ci\u003ePhilosophy of the Tool\u003c/i\u003e, Chicago, 1893.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_86_86\" id=\"Footnote_86_86\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_86_86\"\u003e\u003cspan class=\"label\"\u003e[86]\u003c/span\u003e\u003c/a\u003e Möbius, \u003ci\u003eNaturwissenschaftlicher Verein für Schleswig-Holstein\u003c/i\u003e, Kiel,\r\n1893, p. 113 et seq.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_87_87\" id=\"Footnote_87_87\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_87_87\"\u003e\u003cspan class=\"label\"\u003e[87]\u003c/span\u003e\u003c/a\u003e I am indebted for this observation to Professor Hatscheck.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_88_88\" id=\"Footnote_88_88\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_88_88\"\u003e\u003cspan class=\"label\"\u003e[88]\u003c/span\u003e\u003c/a\u003e Cf. Hoppe, \u003ci\u003eEntdecken und Finden\u003c/i\u003e, 1870.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_89_89\" id=\"Footnote_89_89\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_89_89\"\u003e\u003cspan class=\"label\"\u003e[89]\u003c/span\u003e\u003c/a\u003e See the lecture \"Sensations of Orientation,\" p. 282 et seq.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_90_90\" id=\"Footnote_90_90\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_90_90\"\u003e\u003cspan class=\"label\"\u003e[90]\u003c/span\u003e\u003c/a\u003e This story was related to me by Jolly, and subsequently repeated in a\r\nletter from him.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_91_91\" id=\"Footnote_91_91\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_91_91\"\u003e\u003cspan class=\"label\"\u003e[91]\u003c/span\u003e\u003c/a\u003e I do not know whether Swift\u0027s academy of schemers in Lagado, in\r\nwhich great discoveries and inventions were made by a sort of verbal game\r\nof dice, was intended as a satire on Francis Bacon\u0027s method of making discoveries\r\nby means of huge synoptic tables constructed by scribes. It certainly\r\nwould not have been ill-placed.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_92_92\" id=\"Footnote_92_92\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_92_92\"\u003e\u003cspan class=\"label\"\u003e[92]\u003c/span\u003e\u003c/a\u003e \"Crescunt disciplinae lente tardeque; per varios errores sero pervenitur\r\nad veritatem. Omnia praeparata esse debent diuturno et assiduo labore\r\nad introitum veritatis novae. Jam illa certo temporis momento divina quadam\r\nnecessitate coacta emerget.\"\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\nQuoted by Simony, \u003ci\u003eIn ein ringförmiges Band einen Knoten zu machen\u003c/i\u003e,\r\nVienna, 1881, p. 41.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_93_93\" id=\"Footnote_93_93\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_93_93\"\u003e\u003cspan class=\"label\"\u003e[93]\u003c/span\u003e\u003c/a\u003e A lecture delivered on February 24, 1897, before the \u003ci\u003eVerein zur Verbreitung\r\nnaturwissenschaftlicher Kenntnisse in Wien\u003c/i\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_94_94\" id=\"Footnote_94_94\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_94_94\"\u003e\u003cspan class=\"label\"\u003e[94]\u003c/span\u003e\u003c/a\u003e Wollaston, \u003ci\u003ePhilosophical Transactions, Royal Society\u003c/i\u003e, 1810. In the same\r\nplace Wollaston also describes and explains the creaking of the muscles.\r\nMy attention was recently called to this work by Dr. W. Pascheles.\u0026mdash;Cf. also\r\nPurkinje, \u003ci\u003ePrager medicin\u003c/i\u003e. \u003ci\u003eJahrbücher\u003c/i\u003e, Bd. 6, Wien, 1820.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_95_95\" id=\"Footnote_95_95\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_95_95\"\u003e\u003cspan class=\"label\"\u003e[95]\u003c/span\u003e\u003c/a\u003e Similarly many external forces do not act at once on all parts of the\r\nearth, and the internal forces which produce deformations act at first immediately\r\nonly upon limited parts. If the earth were a feeling being, the tides\r\nand other terrestrial events would provoke in it similar sensations to those\r\nof our movements. Perhaps the slight alterations of the altitude of the\r\npole which are at present being studied are connected with the continual\r\nslight deformations of the central ellipsoid occasioned by seismical happenings.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_96_96\" id=\"Footnote_96_96\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_96_96\"\u003e\u003cspan class=\"label\"\u003e[96]\u003c/span\u003e\u003c/a\u003e For the popular explanation by unconscious inference the matter is extremely\r\nsimple. We regard the railway carriage as vertical and unconsciously\r\ninfer the inclination of the trees. Of course the opposite conclusion that we\r\nregard the trees as vertical and infer the inclination of the carriage, unfortunately,\r\nis equally clear on this theory.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_97_97\" id=\"Footnote_97_97\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_97_97\"\u003e\u003cspan class=\"label\"\u003e[97]\u003c/span\u003e\u003c/a\u003e It will be observed that my way of thinking and experimenting here is\r\nrelated to that which led Knight to the discovery and investigation of the\r\ngeotropism of plants. \u003ci\u003ePhilosophical Transactions\u003c/i\u003e, January 9, 1806. The relations\r\nbetween vegetable and animal geotropism have been more recently investigated\r\nby J. Loeb.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_98_98\" id=\"Footnote_98_98\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_98_98\"\u003e\u003cspan class=\"label\"\u003e[98]\u003c/span\u003e\u003c/a\u003e This experiment is doubtless related to the galvanotropic experiment\r\nwith the larvæ of frogs described ten years later by L. Hermann. Compare\r\non this point my remarks in the \u003ci\u003eAnzeiger der Wiener Akademie\u003c/i\u003e, 1886, No. 21.\r\nRecent experiments in galvanotropism are due to J. Loeb.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_99_99\" id=\"Footnote_99_99\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_99_99\"\u003e\u003cspan class=\"label\"\u003e[99]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eWiener Akad.\u003c/i\u003e, 6 November, 1873.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_100_100\" id=\"Footnote_100_100\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_100_100\"\u003e\u003cspan class=\"label\"\u003e[100]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eWiener Gesellschaft der Aerzte\u003c/i\u003e, 14 November, 1874.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_101_101\" id=\"Footnote_101_101\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_101_101\"\u003e\u003cspan class=\"label\"\u003e[101]\u003c/span\u003e\u003c/a\u003e I have made a contribution to this last question in my \u003ci\u003eAnalysis of the\r\nSensations\u003c/i\u003e, (1886), English translation, 1897.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_102_102\" id=\"Footnote_102_102\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_102_102\"\u003e\u003cspan class=\"label\"\u003e[102]\u003c/span\u003e\u003c/a\u003e In my \u003ci\u003eGrundlinien der Lehre von den Bewegungsempfindungen\u003c/i\u003e, 1875,\r\nthe matter occupying lines 4 to 13 of page 20 from below, which rests on an\r\nerror, is, as I have also elsewhere remarked, to be stricken out. For another\r\nexperiment related to that of Foucault, compare my \u003ci\u003eMechanics\u003c/i\u003e, p. 303.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_103_103\" id=\"Footnote_103_103\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_103_103\"\u003e\u003cspan class=\"label\"\u003e[103]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eAnzeiger der Wiener Akad.\u003c/i\u003e, 30 December, 1875.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_104_104\" id=\"Footnote_104_104\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_104_104\"\u003e\u003cspan class=\"label\"\u003e[104]\u003c/span\u003e\u003c/a\u003e The experiment was specially interesting for me as I had already attempted\r\nin 1874, although with very little confidence and without success, to\r\nexcite electromagnetically my own labyrinth through which I had caused a\r\ncurrent to pass.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_105_105\" id=\"Footnote_105_105\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_105_105\"\u003e\u003cspan class=\"label\"\u003e[105]\u003c/span\u003e\u003c/a\u003e Perhaps the discussion concerning the peculiarity of cats always falling\r\non their feet, which occupied the Parisian Academy, and, incidentally, Parisian\r\nsociety a few years ago, will be remembered here. I believe that the\r\nquestions which arose are disposed of by the considerations advanced in my\r\n\u003ci\u003eBewegungsempfindungen\u003c/i\u003e (1875). I also partly gave, as early as 1866, the apparatus\r\nconceived by the Parisian scientists to illustrate the phenomena in\r\nquestion. One difficulty was left untouched in the Parisian debate. The\r\notolith apparatus of the cat can render it no service in \u003ci\u003efree\u003c/i\u003e descent. The\r\ncat, however, while at rest, doubtless knows its position in space and is instinctively\r\nconscious of the amount of movement which will put it on its feet.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_106_106\" id=\"Footnote_106_106\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_106_106\"\u003e\u003cspan class=\"label\"\u003e[106]\u003c/span\u003e\u003c/a\u003e See the Appendix to the English edition of my \u003ci\u003eAnalysis of the Sensations\u003c/i\u003e,\r\nChicago, 1897.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_107_107\" id=\"Footnote_107_107\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_107_107\"\u003e\u003cspan class=\"label\"\u003e[107]\u003c/span\u003e\u003c/a\u003e Compare my \u003ci\u003eAnalysis of Sensations\u003c/i\u003e, p. 123 ff.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_108_108\" id=\"Footnote_108_108\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_108_108\"\u003e\u003cspan class=\"label\"\u003e[108]\u003c/span\u003e\u003c/a\u003e E. H. Weber, \u003ci\u003eDe aure et auditu hominis et animalium\u003c/i\u003e, Lipsiae, 1820.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_109_109\" id=\"Footnote_109_109\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_109_109\"\u003e\u003cspan class=\"label\"\u003e[109]\u003c/span\u003e\u003c/a\u003e Störensen, \u003ci\u003eJourn. Anat. Phys.\u003c/i\u003e, London, Vol. 29 (1895).\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_110_110\" id=\"Footnote_110_110\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_110_110\"\u003e\u003cspan class=\"label\"\u003e[110]\u003c/span\u003e\u003c/a\u003e A lecture delivered on Nov. 10, 1897.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_111_111\" id=\"Footnote_111_111\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_111_111\"\u003e\u003cspan class=\"label\"\u003e[111]\u003c/span\u003e\u003c/a\u003e Christiansen, \u003ci\u003eWiedemann\u0027s Annalen\u003c/i\u003e, XXIII. S. 298, XXIV., p. 439 (1884-1885).\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_112_112\" id=\"Footnote_112_112\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_112_112\"\u003e\u003cspan class=\"label\"\u003e[112]\u003c/span\u003e\u003c/a\u003e The German phrase is \u003ci\u003eSchlierenmethode\u003c/i\u003e, by which term the method is\r\nknown even by American physicists. It is also called in English the \"shadow-method.\"\r\nBut a term is necessary which will cover all the derivatives, and\r\nso we have employed alternatively the words \u003ci\u003estriate\u003c/i\u003e and \u003ci\u003edifferential\u003c/i\u003e. The\r\netymology of \u003ci\u003eschlieren\u003c/i\u003e, it would seem, is uncertain. Its present use is derived\r\nfrom its technological signification in glass-manufacturing, where by \u003ci\u003edie\r\nSchlieren\u003c/i\u003e are meant the wavy streaks and imperfections in glass. Hence its\r\napplication to the method for detecting small optical \u003ci\u003edifferences\u003c/i\u003e and faults\r\ngenerally. Professor Crew of Evanston suggests to the translator that \u003ci\u003eschlieren\u003c/i\u003e\r\nmay be related to our \u003ci\u003eslur\u003c/i\u003e (L. G., \u003ci\u003eslüren\u003c/i\u003e, to trail, to draggle), a conjecture\r\nwhich is doubtless correct and agrees both with the meaning of \u003ci\u003eschlieren\u003c/i\u003e as\r\ngiven in the large German dictionaries and with the intransitive use of our\r\nown verb \u003ci\u003eslur\u003c/i\u003e, the faults in question being conceived as \"trailings,\" \"streakings,\"\r\netc.\u0026mdash;\u003ci\u003eTrans.\u003c/i\u003e\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_113_113\" id=\"Footnote_113_113\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_113_113\"\u003e\u003cspan class=\"label\"\u003e[113]\u003c/span\u003e\u003c/a\u003e An address delivered before the Congress of Delegates of the German\r\nRealschulmännerverein, at Dortmund, April 16, 1886. The full title of the\r\naddress reads: \"On the Relative Educational Value of the Classics and the\r\nMathematico-Physical Sciences in Colleges and High Schools.\"\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\nAlthough substantially contained in an address which I was to have made\r\nat the meeting of Natural Scientists at Salzburg in 1881 (deferred on account\r\nof the Paris Exposition), and in the Introduction to a course of lectures on\r\n\"Physical Instruction in Preparatory Schools,\" which I delivered in 1883, the\r\ninvitation of the German Realschulmännerverein afforded me the first opportunity\r\nof putting my views upon this subject before a large circle of readers.\r\nOwing to the place and circumstances of delivery, my remarks apply of course,\r\nprimarily, only to German schools, but, with slight modifications, made in\r\nthis translation, are not without force for the institutions of other countries.\r\nIn giving here expression to a strong personal conviction formed long ago, it\r\nis a matter of deep satisfaction to me to find that they agree in many points\r\nwith the views recently advanced in independent form by Paulsen (\u003ci\u003eGeschichte\r\ndes gelehrten Unterrichts\u003c/i\u003e, Leipsic, 1885) and Frary (\u003ci\u003eLa question du latin\u003c/i\u003e,\r\nParis, Cerf, 1885). It is not my desire nor effort here to say much that is new,\r\nbut merely to contribute my mite towards bringing about the inevitable revolution\r\nnow preparing in the world of elementary instruction. In the opinion\r\nof experienced educationists the first result of that revolution will be to make\r\nGreek and mathematics alternately optional subjects in the higher classes of\r\nthe German Gymnasium and in the corresponding institutions of other countries,\r\nas has been done in the splendid system of instruction in Denmark. The\r\ngap between the German classical Gymnasium and the German Realgymnasium,\r\nor between classical and scientific schools generally, can thus be bridged\r\nover, and the remaining inevitable transformations will then be accomplished\r\nin relative peace and quiet. (Prague, May, 1886.)\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_114_114\" id=\"Footnote_114_114\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_114_114\"\u003e\u003cspan class=\"label\"\u003e[114]\u003c/span\u003e\u003c/a\u003e Maupertuis, \u003ci\u003e\u0026OElig;uvres\u003c/i\u003e, Dresden, 1752, p. 339.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_115_115\" id=\"Footnote_115_115\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_115_115\"\u003e\u003cspan class=\"label\"\u003e[115]\u003c/span\u003e\u003c/a\u003e F. Paulsen, \u003ci\u003eGeschichte des gelehrten Unterrichts\u003c/i\u003e, Leipsic, 1885.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_116_116\" id=\"Footnote_116_116\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_116_116\"\u003e\u003cspan class=\"label\"\u003e[116]\u003c/span\u003e\u003c/a\u003e There is a peculiar irony of fate in the fact that while Leibnitz was casting\r\nabout for a new vehicle of universal linguistic intercourse, the Latin language\r\nwhich still subserved this purpose the best of all, was dropping more\r\nand more out of use, and that Leibnitz himself contributed not the least to\r\nthis result.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_117_117\" id=\"Footnote_117_117\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_117_117\"\u003e\u003cspan class=\"label\"\u003e[117]\u003c/span\u003e\u003c/a\u003e As a rule, the human brain is too much, and wrongly, burdened with\r\nthings which might be more conveniently and accurately preserved in books\r\nwhere they could be found at a moment\u0027s notice. In a recent letter to me\r\nfrom Düsseldorf, Judge Hartwich writes:\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\n\"A host of words exist which are out and out Latin or Greek, yet are employed\r\nwith perfect correctness by people of good education who never had\r\nthe good luck to be taught the ancient languages. For example, words like\r\n\u0027dynasty.\u0027 … The child learns such words as parts of the common stock of\r\nspeech, or even as parts of his mother-tongue, just as he does the words\r\n\u0027father,\u0027 \u0027mother,\u0027 \u0027bread,\u0027 \u0027milk.\u0027 Does the ordinary mortal know the etymology\r\nof these Saxon words? Did it not require the almost incredible\r\nindustry of the Grimms and other Teutonic philologists to throw the merest\r\nglimmerings of light upon the origin and growth of our own mother-tongue?\r\nBesides, do not thousands of people of so-called classical education use\r\nevery moment hosts of words of foreign origin whose derivation they do not\r\nknow? Very few of them think it worth while to look up such words in the\r\ndictionaries, although they love to maintain that people should study the\r\nancient languages for the sake of etymology alone.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_118_118\" id=\"Footnote_118_118\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_118_118\"\u003e\u003cspan class=\"label\"\u003e[118]\u003c/span\u003e\u003c/a\u003e Standing remote from the legal profession I should not have ventured to\r\ndeclare that the study of Greek was not necessary for the jurists; yet this\r\nview was taken in the debate that followed this lecture by professional jurists\r\nof high standing. According to this opinion, the preparatory education obtained\r\nin the German Realgymnasium would also be sufficient for the future\r\njurists and insufficient only for theologians and philologists. [In England and\r\nAmerica not only is Greek not necessary, but the law-Latin is so peculiar that\r\neven persons of \u003ci\u003egood\u003c/i\u003e classical education cannot understand it.\u0026mdash;\u003ci\u003eTr.\u003c/i\u003e]\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_119_119\" id=\"Footnote_119_119\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_119_119\"\u003e\u003cspan class=\"label\"\u003e[119]\u003c/span\u003e\u003c/a\u003e In emphasising here the weak sides of the writings of Plato and Aristotle,\r\nforced on my attention while reading them in German translations, I, of\r\ncourse, have no intention of underrating the great merits and the high historical\r\nimportance of these two men. Their importance must not be measured\r\nby the fact that our speculative philosophy still moves to a great extent\r\nin their paths of thought. The more probable conclusion is that this branch\r\nhas made very little progress in the last two thousand years. Natural science\r\nalso was implicated for centuries in the meshes of the Aristotelian thought,\r\nand owes its rise mainly to having thrown off those fetters.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_120_120\" id=\"Footnote_120_120\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_120_120\"\u003e\u003cspan class=\"label\"\u003e[120]\u003c/span\u003e\u003c/a\u003e I would not for a moment contend that we derive exactly the same profit\r\nfrom reading a Greek author in a translation as from reading him in the original;\r\nbut the difference, the excess of gain in the second case, appears to me,\r\nand probably will to most men who are not professional philologists, to be\r\ntoo dearly bought with the expenditure of eight years of valuable time.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_121_121\" id=\"Footnote_121_121\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_121_121\"\u003e\u003cspan class=\"label\"\u003e[121]\u003c/span\u003e\u003c/a\u003e \"The temptation,\" Judge Hartwich writes, \"to regard the \u0027taste\u0027 of the\r\nancients as so lofty and unsurpassable appears to me to have its chief origin\r\nin the fact that the ancients were unexcelled in the representation of the\r\nnude. First, by their unremitting care of the human body they produced\r\nsplendid models; and secondly, in their gymnasiums and in their athletic\r\ngames they had these models constantly before their eyes. No wonder, then,\r\nthat their statues still excite our admiration! For the form, the ideal of the\r\nhuman body has not changed in the course of the centuries. But with intellectual\r\nmatters it is totally different; they change from century to century,\r\nnay, from decennium to decennium. It is very natural now, that people\r\nshould unconsciously apply what is thus so easily seen, namely, the works of\r\nsculpture, as a universal criterion of the highly developed taste of the ancients\u0026mdash;a\r\nfallacy against which people cannot, in my judgment, be too strongly\r\nwarned.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_122_122\" id=\"Footnote_122_122\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_122_122\"\u003e\u003cspan class=\"label\"\u003e[122]\u003c/span\u003e\u003c/a\u003e English: \"In the beginning God created the heaven and the earth.\r\nAnd the earth was without form and void; and darkness was upon the face\r\nof the deep. And the spirit of God moved upon the face of the waters.\"\u0026mdash;Dutch:\r\n\"In het begin schiep God den hemel en de aarde. De aarde nu was\r\nwoest en ledig, en duisternis was op den afgrond; en de Geest Gods zwefde\r\nop de wateren.\"\u0026mdash;Danish: \"I Begyndelsen skabte Gud Himmelen og Jorden.\r\nOg Jorden var ode og tom, og der var morkt ovenover Afgrunden, og\r\nGuds Aand svoevede ovenover Vandene.\"\u0026mdash;Swedish: \"I begynnelsen skapade\r\nGud Himmel och Jord. Och Jorden war öde och tom, och mörker war\r\npä djupet, och Gods Ande swäfde öfwer wattnet.\"\u0026mdash;German: \"Am Anfang\r\nschuf Gott Himmel und Erde. Und die Erde war wüst und leer, und es war\r\nfinster auf der Tiefe; und der Geist Gottes schwebte auf dem Wasser.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_123_123\" id=\"Footnote_123_123\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_123_123\"\u003e\u003cspan class=\"label\"\u003e[123]\u003c/span\u003e\u003c/a\u003e Compare Herzen\u0027s excellent remarks, \u003ci\u003eDe l\u0027enseignement secondaire dans\r\nla Suisse romande\u003c/i\u003e, Lausanne, 1886.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_124_124\" id=\"Footnote_124_124\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_124_124\"\u003e\u003cspan class=\"label\"\u003e[124]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eGeschichte der Mathematik\u003c/i\u003e, Leipsic, 1874.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_125_125\" id=\"Footnote_125_125\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_125_125\"\u003e\u003cspan class=\"label\"\u003e[125]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eGeometrische Analyse\u003c/i\u003e, Ulm, 1886.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_126_126\" id=\"Footnote_126_126\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_126_126\"\u003e\u003cspan class=\"label\"\u003e[126]\u003c/span\u003e\u003c/a\u003e In his text-books of elementary mathematics\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_127_127\" id=\"Footnote_127_127\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_127_127\"\u003e\u003cspan class=\"label\"\u003e[127]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eAbhandlungen aus dem Gebiete der Mathematik\u003c/i\u003e, Würzburg, 1883.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_128_128\" id=\"Footnote_128_128\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_128_128\"\u003e\u003cspan class=\"label\"\u003e[128]\u003c/span\u003e\u003c/a\u003e My idea here is an appropriate selection of readings from Galileo, Huygens,\r\nNewton, etc. The choice is so easily made that there can be no question\r\nof difficulties. The contents would be discussed with the students, and\r\nthe original experiments performed with them. Those scholars alone should\r\nreceive this instruction in the upper classes who did not look forward to systematical\r\ninstruction in the physical sciences. I do not make this proposition\r\nof reform here for the first time. I have no doubt, moreover, that such radical\r\nchanges will only be slowly introduced.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_129_129\" id=\"Footnote_129_129\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_129_129\"\u003e\u003cspan class=\"label\"\u003e[129]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eDie Mathematik als Lehrgegenstand des Gymnasiums\u003c/i\u003e, Berlin, 1883.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_130_130\" id=\"Footnote_130_130\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_130_130\"\u003e\u003cspan class=\"label\"\u003e[130]\u003c/span\u003e\u003c/a\u003e Wrong as it is to burden future physicians and scientists with Greek for\r\nthe sake of the theologians and philologists, it would be just as wrong to compel\r\ntheologians and philologists, on account of the physicians, to study such\r\nsubjects as analytical geometry. Moreover, I cannot believe that ignorance\r\nof analytical geometry would be a serious hindrance to a physician that was\r\notherwise well versed in quantitative thought. No special advantage generally\r\nis observable in the graduates of the Austrian gymnasiums, all of whom have\r\nstudied analytical geometry. [Refers to an assertion of Dubois-Reymond.]\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_131_131\" id=\"Footnote_131_131\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_131_131\"\u003e\u003cspan class=\"label\"\u003e[131]\u003c/span\u003e\u003c/a\u003e Compare M. Cantor, \u003ci\u003eGeschichte der Mathematik\u003c/i\u003e, Leipsic, 1880, Vol. I. p.\r\n193.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_132_132\" id=\"Footnote_132_132\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_132_132\"\u003e\u003cspan class=\"label\"\u003e[132]\u003c/span\u003e\u003c/a\u003e Compare Paulsen, \u003ci\u003el. c.\u003c/i\u003e, pp. 607, 688.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_133_133\" id=\"Footnote_133_133\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_133_133\"\u003e\u003cspan class=\"label\"\u003e[133]\u003c/span\u003e\u003c/a\u003e It is to be hoped that the Americans will jealously guard their schools\r\nand universities against the influence of the State.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_134_134\" id=\"Footnote_134_134\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_134_134\"\u003e\u003cspan class=\"label\"\u003e[134]\u003c/span\u003e\u003c/a\u003e This article, which appeared in the Proceedings of the German Mathematical\r\nSociety of Prague for the year 1892, is printed as a supplement to the\r\narticle on \"The Causes of Harmony,\" at page 32.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_135_135\" id=\"Footnote_135_135\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_135_135\"\u003e\u003cspan class=\"label\"\u003e[135]\u003c/span\u003e\u003c/a\u003e The present exposition is taken from the volumes for 1700 (published in\r\n1703) and for 1701 (published in 1704), and partly also from the \u003ci\u003eHistoire de\r\nl\u0027Académie\u003c/i\u003e and partly from the \u003ci\u003eMémoires\u003c/i\u003e. Sauveur\u0027s later works enter less\r\ninto consideration here.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_136_136\" id=\"Footnote_136_136\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_136_136\"\u003e\u003cspan class=\"label\"\u003e[136]\u003c/span\u003e\u003c/a\u003e Euler, \u003ci\u003eTentamen novae theoriae musicae\u003c/i\u003e, Petropoli, 1739.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_137_137\" id=\"Footnote_137_137\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_137_137\"\u003e\u003cspan class=\"label\"\u003e[137]\u003c/span\u003e\u003c/a\u003e In attempting to perform his experiment of beats before the Academy,\r\nSauveur was not quite successful. \u003ci\u003eHistoire de l\u0027Académie\u003c/i\u003e, Année 1700, p. 136.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_138_138\" id=\"Footnote_138_138\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_138_138\"\u003e\u003cspan class=\"label\"\u003e[138]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eHistoire de l\u0027Académie\u003c/i\u003e, Année 1701, p. 134.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_139_139\" id=\"Footnote_139_139\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_139_139\"\u003e\u003cspan class=\"label\"\u003e[139]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eIbid.\u003c/i\u003e, p. 298.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_140_140\" id=\"Footnote_140_140\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_140_140\"\u003e\u003cspan class=\"label\"\u003e[140]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eHistoire de l\u0027Académie\u003c/i\u003e, Année 1702, p. 91.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_141_141\" id=\"Footnote_141_141\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_141_141\"\u003e\u003cspan class=\"label\"\u003e[141]\u003c/span\u003e\u003c/a\u003e From the \u003ci\u003eHistoire de l\u0027Académie\u003c/i\u003e, Année 1700, p. 139.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_142_142\" id=\"Footnote_142_142\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_142_142\"\u003e\u003cspan class=\"label\"\u003e[142]\u003c/span\u003e\u003c/a\u003e Because all octaves in use in music offer too great differences of rates\r\nof vibration.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_143_143\" id=\"Footnote_143_143\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_143_143\"\u003e\u003cspan class=\"label\"\u003e[143]\u003c/span\u003e\u003c/a\u003e \"Les battemens ne plaisent pas à l\u0027Oreille, à cause de l\u0027inégalité du son,\r\net l\u0027on peut croire avec beaucoup d\u0027apparence que ce qui rend les Octaves si\r\nagréables, c\u0027est qu\u0027on n\u0027y entend jamais de battemens.\r\n\u003c/p\u003e\r\n\u003cp\u003e\r\n\"En suivant cette idée, on trouve que les accords dont on ne peut entendre\r\nles battemens, sont justement ceux que les Musiciens traitent de Consonances,\r\net que ceux dont les battemens se font sentir, sont les Dissonances, et que\r\nquand un accord est Dissonance dans une certaine octave et Consonance\r\ndans une autre, c\u0027est qu\u0027il bat dans l\u0027une, et qu\u0027il ne bat pas dans l\u0027autre.\r\nAussi est il traité de Consonance imparfaite. Il est fort aisé par les principes\r\nde Mr. Sauveur qu\u0027on a établis ici, de voir quels accords battent, et dans\r\nquelles Octaves au-dessus on au-dessous du son fixe. Si cette hypothèse est\r\nvraye, elle découvrira la véritable source des Règles de la composition, inconnue\r\njusqu\u0027à présent à la Philosophie, qui s\u0027en remettait presque entièrement\r\nau jugement de l\u0027Oreille. Ces sortes de jugemens naturels, quelque\r\nbisarres qu\u0027ils paroissent quelquefois, ne le sont point, ils ont des causes\r\ntrès réelles, dont la connaissance appartient à la Philosophie, pourvue qu\u0027elle\r\ns\u0027en puisse mettre en possession.\"\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_144_144\" id=\"Footnote_144_144\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_144_144\"\u003e\u003cspan class=\"label\"\u003e[144]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eHarmonics or the Philosophy of Musical Sounds\u003c/i\u003e, Cambridge, 1749. I saw\r\nthis book only hastily in 1864 and drew attention to it in a work published in\r\n1866. I did not come into its actual possession until three years ago and then\r\nonly did I learn its exact contents.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_145_145\" id=\"Footnote_145_145\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_145_145\"\u003e\u003cspan class=\"label\"\u003e[145]\u003c/span\u003e\u003c/a\u003e \u003ci\u003eHarmonics\u003c/i\u003e, pp. 118 and 243.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_146_146\" id=\"Footnote_146_146\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_146_146\"\u003e\u003cspan class=\"label\"\u003e[146]\u003c/span\u003e\u003c/a\u003e \"Short cycle\" is the period in which the same phases of the two co-operant\r\ntones are repeated.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_147_147\" id=\"Footnote_147_147\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_147_147\"\u003e\u003cspan class=\"label\"\u003e[147]\u003c/span\u003e\u003c/a\u003e This article, designed to illustrate historically that on Symmetry, at\r\npage 89, first appeared in Fichte\u0027s \u003ci\u003eZeitschrift für Philosophie\u003c/i\u003e, for 1865.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_148_148\" id=\"Footnote_148_148\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_148_148\"\u003e\u003cspan class=\"label\"\u003e[148]\u003c/span\u003e\u003c/a\u003e Comp. Cornelius, \u003ci\u003eUeber das Sehen\u003c/i\u003e; Wundt, \u003ci\u003eTheorie der Sinneswahrnehmung\u003c/i\u003e.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_149_149\" id=\"Footnote_149_149\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_149_149\"\u003e\u003cspan class=\"label\"\u003e[149]\u003c/span\u003e\u003c/a\u003e Comp. Mach, \u003ci\u003eUeber das Sehen von Lagen and Winkeln\u003c/i\u003e. \u003ci\u003eSitzungsb. der\r\nWiener Akademie\u003c/i\u003e, 1861.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\u003cdiv class=\"footnote\"\u003e\u003cp\u003e\u003ca name=\"Footnote_150_150\" id=\"Footnote_150_150\"\u003e\u003c/a\u003e\u003ca href=\"#FNanchor_150_150\"\u003e\u003cspan class=\"label\"\u003e[150]\u003c/span\u003e\u003c/a\u003e Comp. Mach, \u003ci\u003eZur Theorie des Gehörorgans\u003c/i\u003e. \u003ci\u003eSitsungsber, der Wiener\r\nAkad.\u003c/i\u003e, 1863.\u0026mdash;\u003ci\u003eUeber einige Erscheinungen der physiolog. Akustik.\u003c/i\u003e \u003ci\u003eIbid.\u003c/i\u003e, 1864.\u003c/p\u003e\u003c/div\u003e\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\u003cpre\u003e\r\n\r\n\r\n\r\n\r\n\r\nEnd of Project Gutenberg\u0027s Popular scientific lectures, by Ernst Mach\r\n\u003c/article\u003e"}],"SectionSequence":["Back Link","Work Title","Deck","Author","Period","Era","Composition","Date Note","Region","Terra Avita","Terra Avita Region","Modern Country","Original Title","Language","Primary Discipline","Secondary Discipline","Tradition","Full Versions","Core Thesis","Classification","Arguments","Influence","Significance","Evidence Note","Full Text"],"Counts":{"ContextCards":3,"GeoCards":4,"DisciplineCards":2,"Links":11,"Sections":25,"Styles":3,"Scripts":1}}