diff options
| author | Roger Frank <rfrank@pglaf.org> | 2025-10-14 20:12:57 -0700 |
|---|---|---|
| committer | Roger Frank <rfrank@pglaf.org> | 2025-10-14 20:12:57 -0700 |
| commit | fd160cc57b7185c689d615b757c84cbf98ee9ce4 (patch) | |
| tree | e415054a3f519bc3ec93125ab81a8ea279c4a0ef /39508-h | |
Diffstat (limited to '39508-h')
| -rw-r--r-- | 39508-h/39508-h.htm | 16616 | ||||
| -rw-r--r-- | 39508-h/images/i_015.jpg | bin | 0 -> 5349 bytes | |||
| -rw-r--r-- | 39508-h/images/i_016.jpg | bin | 0 -> 5942 bytes | |||
| -rw-r--r-- | 39508-h/images/i_021-1.jpg | bin | 0 -> 7921 bytes | |||
| -rw-r--r-- | 39508-h/images/i_021.jpg | bin | 0 -> 3007 bytes | |||
| -rw-r--r-- | 39508-h/images/i_022.jpg | bin | 0 -> 7050 bytes | |||
| -rw-r--r-- | 39508-h/images/i_028.jpg | bin | 0 -> 3040 bytes | |||
| -rw-r--r-- | 39508-h/images/i_029.jpg | bin | 0 -> 7258 bytes | |||
| -rw-r--r-- | 39508-h/images/i_035.jpg | bin | 0 -> 9206 bytes | |||
| -rw-r--r-- | 39508-h/images/i_047-1.jpg | bin | 0 -> 8425 bytes | |||
| -rw-r--r-- | 39508-h/images/i_047.jpg | bin | 0 -> 4993 bytes | |||
| -rw-r--r-- | 39508-h/images/i_048.jpg | bin | 0 -> 5845 bytes | |||
| -rw-r--r-- | 39508-h/images/i_052.jpg | bin | 0 -> 24636 bytes | |||
| -rw-r--r-- | 39508-h/images/i_060.jpg | bin | 0 -> 1084 bytes | |||
| -rw-r--r-- | 39508-h/images/i_062.jpg | bin | 0 -> 10507 bytes | |||
| -rw-r--r-- | 39508-h/images/i_063.jpg | bin | 0 -> 940 bytes | |||
| -rw-r--r-- | 39508-h/images/i_065.jpg | bin | 0 -> 5213 bytes | |||
| -rw-r--r-- | 39508-h/images/i_069-1.jpg | bin | 0 -> 3634 bytes | |||
| -rw-r--r-- | 39508-h/images/i_069.jpg | bin | 0 -> 4202 bytes | |||
| -rw-r--r-- | 39508-h/images/i_070.jpg | bin | 0 -> 2702 bytes | |||
| -rw-r--r-- | 39508-h/images/i_078.jpg | bin | 0 -> 7262 bytes | |||
| -rw-r--r-- | 39508-h/images/i_081.jpg | bin | 0 -> 17085 bytes | |||
| -rw-r--r-- | 39508-h/images/i_090.jpg | bin | 0 -> 2447 bytes | |||
| -rw-r--r-- | 39508-h/images/i_093.jpg | bin | 0 -> 1126 bytes | |||
| -rw-r--r-- | 39508-h/images/i_094.jpg | bin | 0 -> 4018 bytes | |||
| -rw-r--r-- | 39508-h/images/i_102.jpg | bin | 0 -> 5402 bytes | |||
| -rw-r--r-- | 39508-h/images/i_112.jpg | bin | 0 -> 62172 bytes | |||
| -rw-r--r-- | 39508-h/images/i_119-1.jpg | bin | 0 -> 2214 bytes | |||
| -rw-r--r-- | 39508-h/images/i_119-2.jpg | bin | 0 -> 2124 bytes | |||
| -rw-r--r-- | 39508-h/images/i_124-1.jpg | bin | 0 -> 4988 bytes | |||
| -rw-r--r-- | 39508-h/images/i_124-2.jpg | bin | 0 -> 4357 bytes | |||
| -rw-r--r-- | 39508-h/images/i_125.jpg | bin | 0 -> 4568 bytes | |||
| -rw-r--r-- | 39508-h/images/i_126.jpg | bin | 0 -> 5484 bytes | |||
| -rw-r--r-- | 39508-h/images/i_127-1.jpg | bin | 0 -> 5249 bytes | |||
| -rw-r--r-- | 39508-h/images/i_127-s.jpg | bin | 0 -> 12627 bytes | |||
| -rw-r--r-- | 39508-h/images/i_129.jpg | bin | 0 -> 7883 bytes | |||
| -rw-r--r-- | 39508-h/images/i_134.jpg | bin | 0 -> 6891 bytes | |||
| -rw-r--r-- | 39508-h/images/i_135.jpg | bin | 0 -> 7409 bytes | |||
| -rw-r--r-- | 39508-h/images/i_139-1.jpg | bin | 0 -> 4246 bytes | |||
| -rw-r--r-- | 39508-h/images/i_139-2.jpg | bin | 0 -> 9913 bytes | |||
| -rw-r--r-- | 39508-h/images/i_143.jpg | bin | 0 -> 4433 bytes | |||
| -rw-r--r-- | 39508-h/images/i_150.jpg | bin | 0 -> 9041 bytes | |||
| -rw-r--r-- | 39508-h/images/i_151.jpg | bin | 0 -> 2092 bytes | |||
| -rw-r--r-- | 39508-h/images/i_155.jpg | bin | 0 -> 5791 bytes | |||
| -rw-r--r-- | 39508-h/images/i_157.jpg | bin | 0 -> 3669 bytes | |||
| -rw-r--r-- | 39508-h/images/i_296.jpg | bin | 0 -> 13560 bytes | |||
| -rw-r--r-- | 39508-h/images/i_298.jpg | bin | 0 -> 21845 bytes | |||
| -rw-r--r-- | 39508-h/images/i_302.jpg | bin | 0 -> 33118 bytes | |||
| -rw-r--r-- | 39508-h/images/i_304.jpg | bin | 0 -> 26551 bytes | |||
| -rw-r--r-- | 39508-h/images/i_324.jpg | bin | 0 -> 7900 bytes | |||
| -rw-r--r-- | 39508-h/images/i_325.jpg | bin | 0 -> 10267 bytes | |||
| -rw-r--r-- | 39508-h/images/i_331.jpg | bin | 0 -> 14656 bytes | |||
| -rw-r--r-- | 39508-h/images/i_333.jpg | bin | 0 -> 19737 bytes | |||
| -rw-r--r-- | 39508-h/images/i_334.jpg | bin | 0 -> 16312 bytes | |||
| -rw-r--r-- | 39508-h/images/i_336.jpg | bin | 0 -> 24044 bytes | |||
| -rw-r--r-- | 39508-h/images/i_338.jpg | bin | 0 -> 28974 bytes | |||
| -rw-r--r-- | 39508-h/images/i_341.jpg | bin | 0 -> 14556 bytes | |||
| -rw-r--r-- | 39508-h/images/i_342.jpg | bin | 0 -> 18539 bytes | |||
| -rw-r--r-- | 39508-h/images/i_399.jpg | bin | 0 -> 3093 bytes | |||
| -rw-r--r-- | 39508-h/images/i_400.jpg | bin | 0 -> 3602 bytes | |||
| -rw-r--r-- | 39508-h/music/112a.mid | bin | 0 -> 372 bytes | |||
| -rw-r--r-- | 39508-h/music/112b.mid | bin | 0 -> 372 bytes | |||
| -rw-r--r-- | 39508-h/music/112c.mid | bin | 0 -> 390 bytes | |||
| -rw-r--r-- | 39508-h/music/112d.mid | bin | 0 -> 406 bytes | |||
| -rw-r--r-- | 39508-h/music/112e.mid | bin | 0 -> 340 bytes | |||
| -rw-r--r-- | 39508-h/music/112f.mid | bin | 0 -> 430 bytes | |||
| -rw-r--r-- | 39508-h/music/112g.mid | bin | 0 -> 338 bytes | |||
| -rw-r--r-- | 39508-h/music/112h.mid | bin | 0 -> 462 bytes |
68 files changed, 16616 insertions, 0 deletions
diff --git a/39508-h/39508-h.htm b/39508-h/39508-h.htm new file mode 100644 index 0000000..6404463 --- /dev/null +++ b/39508-h/39508-h.htm @@ -0,0 +1,16616 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" + "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> + <head> + <meta http-equiv="Content-Type" content="text/html;charset=utf-8" /> + <meta http-equiv="Content-Style-Type" content="text/css" /> + <title> + The Project Gutenberg eBook of Popular Scientific Lectures, by Ernst Mach. + </title> + <style type="text/css"> + +body { + margin-left: 10%; + margin-right: 10%; +} + + h1,h2,h3,h4,h5,h6 { + text-align: center; /* all headings centered */ + clear: both; +} + +p { + margin-top: .51em; + text-align: justify; + margin-bottom: .49em; +} + +.p2 {margin-top: 2em;} +.p4 {margin-top: 4em;} +.p6 {margin-top: 6em;} + +.IX {list-style-type: none;} + +hr { + width: 33%; + margin-top: 2em; + margin-bottom: 2em; + margin-left: auto; + margin-right: auto; + clear: both; +} + +hr.tb {width: 45%;} +hr.chap {width: 65%} +hr.full {width: 95%;} + +hr.r5 {width: 5%; margin-top: 1em; margin-bottom: 1em;} +hr.r65 {width: 65%; margin-top: 3em; margin-bottom: 3em;} + +ul.index { list-style-type: none; } +li.ifrst { margin-top: 1em; } +li.indx { margin-top: .5em; } +li.isub1 {text-indent: 1em;} +li.isub2 {text-indent: 2em;} +li.isub3 {text-indent: 3em;} + +table { + margin-left: auto; + margin-right: auto; +} + + .tdl {text-align: left;} + .tdr {text-align: right;} + .tdc {text-align: center;} + +.pagenum { /* uncomment the next line for invisible page numbers */ + /* visibility: hidden; */ + position: absolute; + left: 92%; + font-size: smaller; + text-align: right; +} /* page numbers */ + +.linenum { + position: absolute; + top: auto; + left: 4%; +} /* poetry number */ + +.blockquot { + margin-left: 5%; + margin-right: 10%; +} + +.sidenote { + width: 20%; + padding-bottom: .5em; + padding-top: .5em; + padding-left: .5em; + padding-right: .5em; + margin-left: 1em; + float: right; + clear: right; + margin-top: 1em; + font-size: smaller; + color: black; + background: #eeeeee; + border: dashed 1px; +} + +.bb {border-bottom: solid 2px;} + +.bl {border-left: solid 2px;} + +.bt {border-top: solid 2px;} + +.br {border-right: solid 2px;} + +.bbox {border: solid 2px;} + +.center {text-align: center;} + +.right {text-align: right;} + +.smcap {font-variant: small-caps;} + +.small {font-size: 70%;} + +.big {font-size: 140%;} + +.bold {font-weight:bold;} + +.u {text-decoration: underline;} + +.caption {font-weight: bold;} + +/* Images */ +.figcenter { + margin: auto; + text-align: center; +} + +.figleft { + float: left; + clear: left; + margin-left: 0; + margin-bottom: 1em; + margin-top: 1em; + margin-right: 1em; + padding: 0; + text-align: center; +} + +.figright { + float: right; + clear: right; + margin-left: 1em; + margin-bottom: + 1em; + margin-top: 1em; + margin-right: 0; + padding: 0; + text-align: center; +} + +/* Footnotes */ +.footnotes {border: dashed 1px;} + +.footnote {margin-left: 10%; margin-right: 10%; font-size: 0.9em;} + +.footnote .label {position: absolute; right: 84%; text-align: right;} + +.fnanchor { + vertical-align: super; + font-size: .8em; + text-decoration: + none; +} + +/* Poetry */ +.poem { + margin-left:10%; + margin-right:10%; + text-align: left; +} + +.poem br {display: none;} + +.poem .stanza {margin: 1em 0em 1em 0em;} + +.poem span.i0 { + display: block; + margin-left: 0em; + padding-left: 3em; + text-indent: -3em; +} + +.poem span.i2 { + display: block; + margin-left: 2em; + padding-left: 3em; + text-indent: -3em; +} + +.poem span.i4 { + display: block; + margin-left: 4em; + padding-left: 3em; + text-indent: -3em; +} + +/* Transcriber's notes */ +.transnote {background-color: #E6E6FA; + color: black; + font-size:smaller; + padding:0.5em; + margin-bottom:5em; + font-family:sans-serif, serif; } + +/* Contents */ +.toc { + margin-left: 5%; + margin-right: 5%; + list-style-type: none; +} + +.label { + text-align: right; + position: absolute; + right: 5%; +} + +.tocsub {list-style-type:upper-roman;} + + </style> + </head> +<body> + + +<pre> + +The Project Gutenberg EBook of Popular scientific lectures, by Ernst Mach + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Popular scientific lectures + +Author: Ernst Mach + +Translator: Thomas Joseph McCormack + +Release Date: April 22, 2012 [EBook #39508] + +Language: English + +Character set encoding: UTF-8 + +*** START OF THIS PROJECT GUTENBERG EBOOK POPULAR SCIENTIFIC LECTURES *** + + + + +Produced by Anna Hall, Albert László and the Online +Distributed Proofreading Team at http://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive) + + + + + + +</pre> + +<p><span class="pagenum"><a name="Page_i" id="Page_i">[Pg i]</a></span></p> + +<p><span class="pagenum"><a name="Page_ii" id="Page_ii">[Pg ii]</a></span></p> +<h1>POPULAR SCIENTIFIC LECTURES.</h1> + + +<hr/> + +<h2><a name="BY_THE_SAME_AUTHOR" id="BY_THE_SAME_AUTHOR">BY THE SAME AUTHOR.</a></h2> + + +<blockquote><p><span class="smcap">The Science of Mechanics.</span> Translated from the +Second German Edition by T. J. McCormack. +250 Cuts and Illustrations. 534 Pages. Half +Morocco, Gilt Top. Price, $2.50.</p> + +<p><span class="smcap">Contributions to the Analysis of the Sensations.</span> +Translated by C. M. Williams. With Notes and +New Additions by the Author. 200 Pages. 36 +Cuts. Price, $1.00.</p> + +<p><span class="smcap">Popular Scientific Lectures.</span> Translated by T. +J. McCormack. Third Revised and Enlarged +Edition. 411 Pages. 59 Cuts. Cloth, $1.50; +Paper, 50 cents.</p></blockquote> + +<p class="center">THE OPEN COURT PUBLISHING CO.,<br /> +<span class="small">324 DEARBORN ST., CHICAGO.</span> +</p><p><span class="pagenum"><a name="Page_iii" id="Page_iii">[Pg iii]</a></span></p> + +<hr/> + + +<p class="center big bold">POPULAR<br /> +SCIENTIFIC LECTURES</p> + +<p class="center"><span class="small">BY</span><br/> +ERNST MACH</p> + +<p class="center small">FORMERLY PROFESSOR OF PHYSICS IN THE UNIVERSITY OF PRAGUE, NOW +PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE +SCIENCE IN THE UNIVERSITY OF VIENNA</p> + +<p class="center"><span class="small">TRANSLATED<br/> +BY<br/></span> +THOMAS J. McCORMACK</p> + +<p class="center">THIRD EDITION, REVISED AND ENLARGED</p> +<hr/> +<p class="center small">WITH FIFTY-NINE CUTS AND DIAGRAMS</p> +<hr/> +<p class="center big">CHICAGO<br/> +THE OPEN COURT PUBLISHING COMPANY</p> + +<p class="center small">FOR SALE BY<br/> +<span class="smcap">Kegan Paul, Trench, Truebner & Co.</span>, LONDON<br/> +1898 +</p><p><span class="pagenum"><a name="Page_iv" id="Page_iv">[Pg iv]</a></span></p> + + +<hr/> + +<p class="center">COPYRIGHT</p> + +<p class="center"><span class="smcap">By The Open Court Publishing Co.</span></p> + +<div class="center"> +<table border="0" cellpadding="0" cellspacing="0" summary="copyright dates"> +<tr><td align="left">Pages 1-258 </td><td align="left"> in 1894.</td></tr> +<tr><td align="left">Pages 338-374 </td><td align="left"> in 1894.</td></tr> +<tr><td align="left">Pages 259-281 </td><td align="left"> in 1896.</td></tr> +<tr><td align="left">Pages 282-308 </td><td align="left"> in 1897.</td></tr> +<tr><td align="left">Pages 309-337 </td><td align="left"> in 1898.</td></tr> +</table></div> + +<hr class="chap" /> +<p><span class="pagenum"><a name="Page_v" id="Page_v">[Pg v]</a></span></p> + + + + +<h2><a name="AUTHORS_PREFACE_TO_THE_FIRST" id="AUTHORS_PREFACE_TO_THE_FIRST">AUTHOR'S PREFACE TO THE FIRST +EDITION.</a></h2> + + +<p>Popular lectures, owing to the knowledge they presuppose, +and the time they occupy, can afford only a <i>modicum</i> +of instruction. They must select for this purpose easy subjects, +and restrict themselves to the exposition of the simplest and the +most essential points. Nevertheless, by an appropriate choice of +the matter, the <i>charm</i> and the <i>poetry</i> of research can be conveyed +by them. It is only necessary to set forth the attractive and the +alluring features of a problem, and to show what broad domains +of fact can be illuminated by the light radiating from the solution +of a single and ofttimes unobtrusive point.</p> + +<p>Furthermore, such lectures can exercise a favorable influence +by showing the substantial sameness of scientific and every-day +thought. The public, in this way, loses its shyness towards scientific +questions, and acquires an interest in scientific work which is +a great help to the inquirer. The latter, in his turn, is brought to +understand that his work is a small part only of the universal process +of life, and that the results of his labors must redound to the +benefit not only of himself and a few of his associates, but to that +of the collective whole.</p> + +<p>I sincerely hope that these lectures, in the present excellent +translation, will be productive of good in the direction indicated.</p> + +<p class="right"> +<span class="smcap">E. Mach.</span><br /> +</p> + +<p><span class="smcap">Prague</span>, December, 1894.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_vii" id="Page_vii">[Pg vii]</a><br /><a name="Page_vi" id="Page_vi">[Pg vi]</a></span></p> + + + + +<h2><a name="TRANSLATORS_NOTE_TO_THE" id="TRANSLATORS_NOTE_TO_THE">TRANSLATOR'S NOTE TO THE +THIRD EDITION.</a></h2> + + +<p>The present third edition of this work has been enlarged by +the addition of a new lecture, "On Some Phenomena Attending +the Flight of Projectiles." The additions to the second +consisted of the following four lectures and articles: Professor +Mach's Vienna Inaugural Lecture, "The Part Played by Accident +in Invention and Discovery," the lecture on "Sensations of Orientation," +recently delivered and summing up the results of an important +psychological investigation, and two historical articles (see +Appendix) on Acoustics and Sight.</p> + +<p>The lectures extend over a long period, from 1864 to 1898, +and differ greatly in style, contents, and purpose. They were first +published in collected form in English; afterwards two German +editions were called for.</p> + +<p>As the dates of the first five lectures are not given in the footnotes +they are here appended. The first lecture, "On the Forms +of Liquids," was delivered in 1868 and published with that "On +Symmetry" in 1872 (Prague). The second and third lectures, on +acoustics, were first published in 1865 (Graz); the fourth and fifth, +on optics, in 1867 (Graz). They belong to the earliest period of +Professor Mach's scientific activity, and with the lectures on electrostatics +and education will more than realise the hope expressed in +the author's Preface.</p> + +<p>The eighth, ninth, tenth, eleventh, and twelfth lectures are of<span class="pagenum"><a name="Page_viii" id="Page_viii">[Pg viii]</a></span> +a more philosophical character and deal principally with the methods +and nature of scientific inquiry. In the ideas summarised in +them will be found one of the most important contributions to the +theory of knowledge made in the last quarter of a century. Significant +hints in psychological method, and exemplary specimen-researches +in psychology and physics, are also presented; while in +physics many ideas find their first discussion that afterwards, under +other names and other authorship, became rallying-cries in this +department of inquiry.</p> + +<p>All the proofs of this translation have been read by Professor +Mach himself.</p> + +<p class="right"> +<span class="smcap">T. J. McCormack.</span><br /> +</p> + +<p><span class="smcap">La Salle, Ill.</span>, May, 1898.</p> +<hr class="chap" /> +<p><span class="pagenum"><a name="Page_ix" id="Page_ix">[Pg ix]</a></span></p> + + + + +<h2><a name="TABLE_OF_CONTENTS" id="TABLE_OF_CONTENTS">TABLE OF CONTENTS.</a></h2> + + +<ul class="toc"> +<li> <span class="label smcap">page</span></li> +<li><a href="#THE_FORMS_OF_LIQUIDS">The Forms of Liquids</a> <span class="label">1</span></li> +<li><a href="#THE_FIBRES_OF_CORTI">The Fibres of Corti</a> <span class="label">17</span></li> +<li><a href="#ON_THE_CAUSES_OF_HARMONY">On the Causes of Harmony</a> <span class="label">32</span></li> +<li><a href="#THE_VELOCITY_OF_LIGHT">The Velocity of Light</a> <span class="label">48</span></li> +<li><a href="#WHY_HAS_MAN_TWO_EYES">Why Has Man Two Eyes?</a> <span class="label">66</span></li> +<li><a href="#ON_SYMMETRY">On Symmetry</a> <span class="label">89</span></li> +<li><a href="#ON_THE_FUNDAMENTAL_CONCEPTS">On the Fundamental Concepts of Electrostatics</a> <span class="label">107</span></li> +<li><a href="#ON_THE_PRINCIPLE_OF_THE_CONSERVATION">On the Principle of the Conservation of Energy</a> <span class="label">137</span></li> +<li><a href="#THE_ECONOMICAL_NATURE_OF">On the Economical Nature of Physical Inquiry</a> <span class="label">186</span></li> +<li><a href="#ON_TRANSFORMATION_AND_ADAPTATION">On Transformation and Adaptation in Scientific Thought</a> <span class="label">214</span></li> +<li><a href="#ON_THE_PRINCIPLE_OF_COMPARISON">On the Principle of Comparison in Physics</a> <span class="label">236</span></li> +<li><a href="#THE_PART_PLAYED_BY_ACCIDENT_IN">On the Part Played by Accident in Invention and Discovery</a> <span class="label">259</span></li> +<li><a href="#ON_SENSATIONS_OF_ORIENTATION93">On Sensations of Orientation</a> <span class="label">282</span></li> +<li><a href="#ON_SOME_PHENOMENA_ATTENDING">On Some Phenomena Attending the Flight of Projectiles</a> <span class="label">309</span></li> +<li><a href="#ON_INSTRUCTION_IN_THE_CLASSICS">On Instruction in the Classics and the Mathematico-Physical Sciences</a> <span class="label">338</span></li> +<li><a href="#APPENDIX">Appendixes.</a> +<ul class="tocsub"><li><a href="#A_CONTRIBUTION_TO_THE_HISTORY_OF_ACOUSTICS">A Contribution to the History of Acoustics</a> <span class="label">375</span></li> +<li><a href="#REMARKS_ON_THE_THEORY_OF_SPATIAL_VISION">Remarks on the Theory of Spatial Vision</a> <span class="label">386</span></li></ul></li> +<li><a href="#INDEX">Index</a> <span class="label">393</span></li> +</ul> +<p><span class="pagenum"><a name="Page_x" id="Page_x">[Pg x]</a><br /><a name="Page_1" id="Page_1">[Pg 1]</a></span></p> + + +<hr class="chap" /> + +<h2><a name="THE_FORMS_OF_LIQUIDS" id="THE_FORMS_OF_LIQUIDS">THE FORMS OF LIQUIDS.</a></h2> + + +<p>What thinkest thou, dear Euthyphron, that the +holy is, and the just, and the good? Is the holy +holy because the gods love it, or are the gods holy because +they love the holy? By such easy questions did +the wise Socrates make the market-place of Athens unsafe +and relieve presumptuous young statesmen of the +burden of imaginary knowledge, by showing them how +confused, unclear, and self-contradictory their ideas +were.</p> + +<p>You know the fate of the importunate questioner. +So called good society avoided him on the promenade. +Only the ignorant accompanied him. And finally he +drank the cup of hemlock—a lot which we ofttimes +wish would fall to modern critics of his stamp.</p> + +<p>What we have learned from Socrates, however,—our +inheritance from him,—is scientific criticism. +Every one who busies himself with science recognises +how unsettled and indefinite the notions are which he +has brought with him from common life, and how, on +a minute examination of things, old differences are<span class="pagenum"><a name="Page_2" id="Page_2">[Pg 2]</a></span> +effaced and new ones introduced. The history of science +is full of examples of this constant change, development, +and clarification of ideas.</p> + +<p>But we will not linger by this general consideration +of the fluctuating character of ideas, which becomes a +source of real uncomfortableness, when we reflect that +it applies to almost every notion of life. Rather shall +we observe by the study of a physical example how +much a thing changes when it is closely examined, and +how it assumes, when thus considered, increasing definiteness +of form.</p> + +<p>The majority of you think, perhaps, you know +quite well the distinction between a liquid and a solid. +And precisely persons who have never busied themselves +with physics will consider this question one of +the easiest that can be put. But the physicist knows +that it is one of the most difficult. I shall mention +here only the experiments of Tresca, which show that +solids subjected to high pressures behave exactly as +liquids do; for example, may be made to flow out in +the form of jets from orifices in the bottoms of vessels. +The supposed difference of kind between liquids and +solids is thus shown to be a mere difference of degree.</p> + +<p>The common inference that because the earth is +oblate in form, it was originally fluid, is an error, in +the light of these facts. True, a rotating sphere, a few +inches in diameter will assume an oblate form only +if it is very soft, for example, is composed of freshly +kneaded clay or some viscous stuff. But the earth,<span class="pagenum"><a name="Page_3" id="Page_3">[Pg 3]</a></span> +even if it consisted of the rigidest stone, could not +help being crushed by its tremendous weight, and must +perforce behave as a fluid. Even our mountains could +not extend beyond a certain height without crumbling. +The earth <i>may</i> once have been fluid, but this by no +means follows from its oblateness.</p> + +<p>The particles of a liquid are displaced on the application +of the slightest pressure; a liquid conforms +exactly to the shapes of the vessels in which it is contained; +it possesses no form of its own, as you have +all learned in the schools. Accommodating itself in +the most trifling respects to the conditions of the vessel +in which it is placed, and showing, even on its surface, +where one would suppose it had the freest play, nothing +but a polished, smiling, expressionless countenance, +it is the courtier <i>par excellence</i> of the natural bodies.</p> + +<p>Liquids have no form of their own! No, not for the +superficial observer. But persons who have observed +that a raindrop is round and never angular, will not be +disposed to accept this dogma so unconditionally.</p> + +<p>It is fair to suppose that every man, even the weakest, +would possess a character, if it were not too difficult +in this world to keep it. So, too, we must suppose +that liquids would possess forms of their own, if +the pressure of the circumstances permitted it,—if +they were not crushed by their own weights.</p> + +<p>An astronomer once calculated that human beings +could not exist on the sun, apart from its great heat, +because they would be crushed to pieces there by their<span class="pagenum"><a name="Page_4" id="Page_4">[Pg 4]</a></span> +own weight. The greater mass of this body would +also make the weight of the human body there much +greater. But on the moon, because here we should +be much lighter, we could jump as high as the church-steeples +without any difficulty, with the same muscular +power which we now possess. Statues and "plaster" +casts of syrup are undoubtedly things of fancy, even +on the moon, but maple-syrup would flow so slowly +there that we could easily build a maple-syrup man on +the moon, for the fun of the thing, just as our children +here build snow-men.</p> + +<p>Accordingly, if liquids have no form of their own +with us on earth, they have, perhaps, a form of their +own on the moon, or on some smaller and lighter heavenly +body. The problem, then, simply is to get rid of +the effects of gravity; and, this done, we shall be able +to find out what the peculiar forms of liquids are.</p> + +<p>The problem was solved by Plateau of Ghent, whose +method was to immerse the liquid in another of the +same specific gravity.<a name="FNanchor_1_1" id="FNanchor_1_1"></a><a href="#Footnote_1_1" class="fnanchor">[1]</a> He employed for his experiments +oil and a mixture of alcohol and water. By +Archimedes's well-known principle, the oil in this mixture +loses its entire weight. It no longer sinks beneath +its weight; its formative forces, be they ever so +weak, are now in full play.</p> + +<p>As a fact, we now see, to our surprise, that the oil, +instead of spreading out into a layer, or lying in a<span class="pagenum"><a name="Page_5" id="Page_5">[Pg 5]</a></span> +formless mass, assumes the shape of a beautiful and +perfect sphere, freely suspended in the mixture, as +the moon is in space. We can construct in this way a +sphere of oil several inches in diameter.</p> + +<p>If, now, we affix a thin plate to a +wire and insert the plate in the oil +sphere, we can, by twisting the wire +between our fingers, set the whole ball +in rotation. Doing this, the ball assumes +an oblate shape, and we can, if +we are skilful enough, separate by such +rotation a ring from the ball, like that +which surrounds Saturn. This ring is +finally rent asunder, and, breaking up +into a number of smaller balls, exhibits +to us a kind of model of the origin of +the planetary system according to the +hypothesis of Kant and Laplace.</p> + +<div class="figright" style="width: 150px;"> +<img src="images/i_015.jpg" width="150" height="491" alt="" /> +<span class="caption">Fig. 1.</span> +</div> + +<p>Still more curious are the phenomena +exhibited when the formative +forces of the liquid are partly disturbed +by putting in contact with the liquid's +surface some rigid body. If we immerse, +for example, the wire framework of a cube in our +mass of oil, the oil will everywhere stick to the wire +framework. If the quantity of oil is exactly sufficient +we shall obtain an oil cube with perfectly smooth walls. +If there is too much or too little oil, the walls of the +cube will bulge out or cave in. In this manner we<span class="pagenum"><a name="Page_6" id="Page_6">[Pg 6]</a></span> +can produce all kinds of geometrical figures of oil, for +example, a three-sided pyramid, a cylinder (by bringing +the oil between two wire rings), and so on. Interesting +is the change of form that occurs when we +gradually suck out the oil by means of a glass tube +from the cube or pyramid. The wire holds the oil +fast. The figure grows smaller and smaller, until it is +at last quite thin. Ultimately it consists simply of a +number of thin, smooth plates of oil, which extend +from the edges of the cube to the centre, where they +meet in a small drop. The same is true of the pyramid.</p> + +<div class="figcenter" style="width: 300px;"> +<img src="images/i_016.jpg" width="300" height="204" alt="" /> +<span class="caption">Fig. 2.</span> +</div> + +<p>The idea now suggests itself that liquid figures as +thin as this, and possessing, therefore, so slight a +weight, cannot be crushed or deformed by their weight; +just as a small, soft ball of clay is not affected in this +respect by its weight. This being the case, we no +longer need our mixture of alcohol and water for the +production of figures, but can construct them in the<span class="pagenum"><a name="Page_7" id="Page_7">[Pg 7]</a></span> +open air. And Plateau, in fact, found that these thin +figures, or at least very similar ones, could be produced +in the air, by dipping the wire nets described +in a solution of soap and water and quickly drawing +them out again. The experiment is not difficult. The +figure is formed of itself. The preceding drawing +represents to the eye the forms obtained with cubical +and pyramidal nets. In the cube, thin, smooth films +of soap-suds proceed from the edges to a small, quadratic +film in the centre. In the pyramid, a film proceeds +from each edge to the centre.</p> + +<p>These figures are so beautiful that they hardly admit +of appropriate description. Their great regularity +and geometrical exactness evokes surprise from all who +see them for the first time. Unfortunately, they are of +only short duration. They burst, on the drying of the +solution in the air, but only after exhibiting to us the +most brilliant play of colors, such as is often seen in +soap-bubbles. Partly their beauty of form and partly +our desire to examine them more minutely induces us +to conceive of methods of endowing them with permanent +form. This is very simply done.<a name="FNanchor_2_2" id="FNanchor_2_2"></a><a href="#Footnote_2_2" class="fnanchor">[2]</a> Instead of +dipping the wire nets in solutions of soap, we dip them +in pure melted colophonium (resin). When drawn +out the figure at once forms and solidifies by contact +with the air.</p> + +<p>It is to be remarked that also solid fluid-figures can<span class="pagenum"><a name="Page_8" id="Page_8">[Pg 8]</a></span> +be constructed in the open air, if their weight be light +enough, or the wire nets of very small dimensions. If +we make, for example, of very fine wire a cubical net +whose sides measure about one-eighth of an inch in +length, we need simply to dip this net in water to obtain +a small solid cube of water. With a piece of blotting +paper the superfluous water may be easily removed +and the sides of the cube made smooth.</p> + +<p>Yet another simple method may be devised for observing +these figures. A drop of water on a greased +glass plate will not run if it is small enough, but will +be flattened by its weight, which presses it against +its support. The smaller the drop the less the flattening. +The smaller the drop the nearer it approaches +the form of a sphere. On the other hand, a drop suspended +from a stick is elongated by its weight. The +undermost parts of a drop of water on a support are +pressed against the support, and the upper parts are +pressed against the lower parts because the latter cannot +yield. But when a drop falls freely downward +all its parts move equally fast; no part is impeded by +another; no part presses against another. A freely +falling drop, accordingly, is not affected by its weight; +it acts as if it were weightless; it assumes a spherical +form.</p> + +<p>A moment's glance at the soap-film figures produced +by our various wire models, reveals to us a great +multiplicity of form. But great as this multiplicity is,<span class="pagenum"><a name="Page_9" id="Page_9">[Pg 9]</a></span> +the common features of the figures also are easily discernible.</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"All forms of Nature are allied, though none is the same as the other;<br /></span> +<span class="i0">Thus, their common chorus points to a hidden law."<br /></span> +</div></div> + +<p>This hidden law Plateau discovered. It may be +expressed, somewhat prosily, as follows:</p> + +<p>1) If several plane liquid films meet in a figure +they are always three in number, and, taken in pairs, +form, each with another, nearly equal angles.</p> + +<p>2) If several liquid edges meet in a figure they are +always four in number, and, taken in pairs, form, each +with another, nearly equal angles.</p> + +<p>This is a strange law, and its reason is not evident. +But we might apply this criticism to almost all laws. +It is not always that the motives of a law-maker are +discernible in the form of the law he constructs. But +our law admits of analysis into very simple elements +or reasons. If we closely examine the paragraphs +which state it, we shall find that their meaning is simply +this, that the surface of the liquid assumes the shape +of smallest area that is possible under the circumstances.</p> + +<p>If, therefore, some extraordinarily intelligent tailor, +possessing a knowledge of all the artifices of the higher +mathematics, should set himself the task of so covering +the wire frame of a cube with cloth that every piece +of cloth should be connected with the wire and joined +with the remaining cloth, and should seek to accomplish +this feat with the greatest saving of material, he<span class="pagenum"><a name="Page_10" id="Page_10">[Pg 10]</a></span> +would construct no other figure than that which is here +formed on the wire frame in our solution of soap and +water. Nature acts in the construction of liquid figures +on the principle of a covetous tailor, and gives no +thought in her work to the fashions. But, strange to +say, in this work, the most beautiful fashions are +of themselves produced.</p> + +<p>The two paragraphs which state our law apply primarily +only to soap-film figures, and are not applicable, +of course, to solid oil-figures. But the principle that +the superficial area of the liquid shall be the least +possible under the circumstances, is applicable to all +fluid figures. He who understands not only the letter +but also the reason of the law will not be at a loss +when confronted with cases to which the letter does +not accurately apply. And this is the case with the +principle of least superficial area. It is a sure guide +for us even in cases in which the above-stated paragraphs +are not applicable.</p> + +<p>Our first task will now be, to show by a palpable +illustration the mode of formation of liquid figures by +the principle of least superficial area. The oil on the +wire pyramid in our mixture of alcohol and water, being +unable to leave the wire edges, clings to them, and +the given mass of oil strives so to shape itself that its +surface shall have the least possible area. Suppose +we attempt to imitate this phenomenon. We take a +wire pyramid, draw over it a stout film of rubber, and +in place of the wire handle insert a small tube leading<span class="pagenum"><a name="Page_11" id="Page_11">[Pg 11]</a></span> +into the interior of the space enclosed by the rubber +(Fig. 3). Through this tube we can blow in or suck +out air. The quantity of air in the enclosure represents +the quantity of oil. The stretched rubber film, +which, clinging to the wire edges, +does its utmost to contract, represents +the surface of the oil endeavoring +to decrease its area. By +blowing in, and drawing out the air, +now, we actually obtain all the oil +pyramidal figures, from those bulged +out to those hollowed in. Finally, when +all the air is pumped or sucked out, the +soap-film figure is exhibited. The rubber +films strike together, assume the form of planes, +and meet at four sharp edges in the centre of the +pyramid.</p> + +<div class="figleft" style="width: 150px;"> +<img src="images/i_021.jpg" width="150" height="256" alt="" /> +<span class="caption">Fig. 3.</span> +</div> + +<div class="figright" style="width: 300px;"> +<img src="images/i_021-1.jpg" width="300" height="173" alt="" /> +<span class="caption">Fig. 4.</span> +</div> + +<p>The tendency of soap-films to assume smaller forms +may be directly demonstrated by a method of Van der +Mensbrugghe. If we dip a square wire frame to which<span class="pagenum"><a name="Page_12" id="Page_12">[Pg 12]</a></span> +a handle is attached into a solution of soap and water, +we shall obtain on the frame a beautiful, plane film of +soap-suds. (Fig. 4.) On this we lay a thread having its +two ends tied together. If, now, we puncture the part +enclosed by the thread, we shall obtain a soap-film +having a circular hole in it, whose circumference is +the thread. The remainder of the film decreasing in +area as much as it can, the hole assumes the largest +area that it can. But the figure of largest area, with +a given periphery, is the circle.</p> + +<div class="figcenter" style="width: 400px;"> +<img src="images/i_022.jpg" width="400" height="182" alt="" /> +<span class="caption">Fig. 5.</span> +</div> + +<p>Similarly, by the principle of least superficial area, +a freely suspended mass of oil assumes the shape of a +sphere. The sphere is the form of least surface for a +given content. This is evident. The more we put +into a travelling-bag, the nearer its shape approaches +the spherical form.</p> + +<p>The connexion of the two above-mentioned paragraphs +with the principle of least superficial area may +be shown by a yet simpler example. Picture to yourselves +four fixed pulleys, <i>a</i>, <i>b</i>, <i>c</i>, <i>d</i>, and two movable<span class="pagenum"><a name="Page_13" id="Page_13">[Pg 13]</a></span> +rings <i>f</i>, <i>g</i> (Fig. 5); about the pulleys and through the +rings imagine a smooth cord passed, fastened at one +extremity to a nail <i>e</i>, and loaded at the other with a +weight <i>h</i>. Now this weight always tends to sink, or, +what is the same thing, always tends to make the portion +of the string <i>e h</i> as long as possible, and consequently +the remainder of the string, wound round the +pulleys, as short as possible. The strings must remain +connected with the pulleys, and on account of the rings +also with each other. The conditions of the case, accordingly, +are similar to those of the liquid figures discussed. +The result also is a similar one. When, as +in the right hand figure of the cut, four pairs of strings +meet, a different configuration must be established. +The consequence of the endeavor of the string to +shorten itself is that the rings separate from each other, +and that now at all points only three pairs of strings +meet, every two at equal angles of one hundred and +twenty degrees. As a fact, by this arrangement the +greatest possible shortening of the string is attained; +as can be easily proved by geometry.</p> + +<p>This will help us to some extent to understand the +creation of beautiful and complicated figures by the +simple tendency of liquids to assume surfaces of least +superficial area. But the question arises, <i>Why</i> do +liquids seek surfaces of least superficial area?</p> + +<p>The particles of a liquid cling together. Drops +brought into contact coalesce. We can say, liquid +particles attract each other. If so, they seek to come<span class="pagenum"><a name="Page_14" id="Page_14">[Pg 14]</a></span> +as close as they can to each other. The particles at +the surface will endeavor to penetrate as far as they +can into the interior. This process will not stop, cannot +stop, until the surface has become as small as under +the circumstances it possibly can become, until as +few particles as possible remain at the surface, until +as many particles as possible have penetrated into the +interior, until the forces of attraction have no more +work to perform.<a name="FNanchor_3_3" id="FNanchor_3_3"></a><a href="#Footnote_3_3" class="fnanchor">[3]</a></p> + +<p>The root of the principle of least surface is to be +sought, accordingly, in another and much simpler +principle, which may be illustrated by some such analogy +as this. We can <i>conceive</i> of the natural forces of +attraction and repulsion as purposes or intentions of +nature. As a matter of fact, that interior pressure +which we feel before an act and which we call an intention +or purpose, is not, in a final analysis, so essentially +different from the pressure of a stone on its support, +or the pressure of a magnet on another, that it is +necessarily unallowable to use for both the same term—at +least for well-defined purposes.<a name="FNanchor_4_4" id="FNanchor_4_4"></a><a href="#Footnote_4_4" class="fnanchor">[4]</a> It is the purpose +of nature, accordingly, to bring the iron nearer +the magnet, the stone nearer the centre of the earth, +and so forth. If such a purpose can be realised, it is +carried out. But where she cannot realise her purposes, +nature does nothing. In this respect she acts +exactly as a good man of business does.</p> +<p><span class="pagenum"><a name="Page_15" id="Page_15">[Pg 15]</a></span></p> +<p>It is a constant purpose of nature to bring weights +lower. We can raise a weight by causing another, +larger weight to sink; that is, by satisfying another, +more powerful, purpose of nature. If we fancy we +are making nature serve our purposes in this, it will +be found, upon closer examination, that the contrary +is true, and that nature has employed us to attain her +purposes.</p> + +<p>Equilibrium, rest, exists only, but then always, when +nature is brought to a halt in her purposes, when the +forces of nature are as fully satisfied as, under the +circumstances, they can be. Thus, for example, heavy +bodies are in equilibrium, when their so-called centre +of gravity lies as low as it possibly can, or when as +much weight as the circumstances admit of has sunk +as low as it can.</p> + +<p>The idea forcibly suggests itself that perhaps this +principle also holds good in other realms. Equilibrium +exists also in the state when the purposes of the parties +are as fully satisfied as for the time being they can +be, or, as we may say, jestingly, in the language of +physics, when the social potential is a maximum.<a name="FNanchor_5_5" id="FNanchor_5_5"></a><a href="#Footnote_5_5" class="fnanchor">[5]</a></p> + +<p>You see, our miserly mercantile principle is replete +with consequences.<a name="FNanchor_6_6" id="FNanchor_6_6"></a><a href="#Footnote_6_6" class="fnanchor">[6]</a> The result of sober research, it +has become as fruitful for physics as the dry questions +of Socrates for science generally. If the principle +seems to lack in ideality, the more ideal are the fruits +which it bears.</p> +<p><span class="pagenum"><a name="Page_16" id="Page_16">[Pg 16]</a></span></p> +<p>But why, tell me, should science be ashamed of +such a principle? Is science<a name="FNanchor_7_7" id="FNanchor_7_7"></a><a href="#Footnote_7_7" class="fnanchor">[7]</a> itself anything more +than—a business? Is not its task to acquire with the +least possible work, in the least possible time, with the +least possible thought, the greatest possible part of +eternal truth?</p> +<p><span class="pagenum"><a name="Page_17" id="Page_17">[Pg 17]</a></span></p> + + + +<h2><a name="THE_FIBRES_OF_CORTI" id="THE_FIBRES_OF_CORTI">THE FIBRES OF CORTI.</a></h2> + + +<p>Whoever has roamed through a beautiful country +knows that the tourist's delights increase +with his progress. How pretty that wooded dell must +look from yonder hill! Whither does that clear brook +flow, that hides itself in yonder sedge? If I only +knew how the landscape looked behind that mountain! +Thus even the child thinks in his first rambles. It is +also true of the natural philosopher.</p> + +<p>The first questions are forced upon the attention of +the inquirer by practical considerations; the subsequent +ones are not. An irresistible attraction draws +him to these; a nobler interest which far transcends the +mere needs of life. Let us look at a special case.</p> + +<p>For a long time the structure of the organ of hearing +has actively engaged the attention of anatomists. +A considerable number of brilliant discoveries has been +brought to light by their labors, and a splendid array +of facts and truths established. But with these facts +a host of new enigmas has been presented.</p> + +<p>Whilst in the theory of the organisation and functions<span class="pagenum"><a name="Page_18" id="Page_18">[Pg 18]</a></span> +of the eye comparative clearness has been attained; +whilst, hand in hand with this, ophthalmology +has reached a degree of perfection which the preceding +century could hardly have dreamed of, and by the +help of the ophthalmoscope the observing physician +penetrates into the profoundest recesses of the eye, +the theory of the ear is still much shrouded in mysterious +darkness, full of attraction for the investigator.</p> + +<p>Look at this model of the ear. Even at that familiar +part by whose extent we measure the quantity of +people's intelligence, even at the external ear, the +problems begin. You see here a succession of helixes +or spiral windings, at times very pretty, whose significance +we cannot accurately state, yet for which there +must certainly be some reason.</p> + +<div class="figright" style="width: 300px;"> +<img src="images/i_028.jpg" width="300" height="205" alt="" /> +<span class="caption">Fig. 6.</span> +</div> + +<p>The shell or concha of the ear, <i>a</i> in the annexed +diagram, conducts the sound into the curved auditory +passage <i>b</i>, which is terminated by a thin membrane, +the so-called tympanic membrane, <i>e</i>. This membrane +is set in motion by the sound, and in its turn sets in +motion a series of little bones of very peculiar formation, +<i>c</i>. At the end of all is the labyrinth +<i>d</i>. The labyrinth consists of a group of +cavities filled with a liquid, in which the +innumerable fibres of the nerve of hearing +are imbedded. By the vibration of the chain of +bones <i>c</i>, the liquid of the labyrinth is shaken, and the +auditory nerve excited. Here the process of hearing<span class="pagenum"><a name="Page_19" id="Page_19">[Pg 19]</a></span> +begins. So much is certain. But the details of the +process are one and all unanswered questions.</p> + +<p>To these old puzzles, the Marchese Corti, as late +as 1851, added a new enigma. And, strange to say, +it is this last enigma, which, perhaps, has first received +its correct solution. This will be the subject of our +remarks to-day.</p> + +<p>Corti found in the cochlea, or snail-shell of the +labyrinth, a large number of microscopic fibres placed +side by side in geometrically graduated order. According +to Kölliker their number is three thousand. They +were also the subject of investigation at the hands of +Max Schultze and Deiters.</p> + +<p>A description of the details of this organ would +only weary you, besides not rendering the matter much +clearer. I prefer, therefore, to state briefly what in +the opinion of prominent investigators like Helmholtz +and Fechner is the peculiar function of Corti's fibres. +The cochlea, it seems, contains a large number of +elastic fibres of graduated lengths (Fig. 7), to which +the branches of the auditory nerve are +attached. These fibres, called the fibres, +pillars, or rods of Corti, being of unequal +length, must also be of unequal elasticity, +and, consequently, pitched to different +notes. The cochlea, therefore, is a species of pianoforte.</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_029.jpg" width="300" height="290" alt="" /> +<span class="caption">Fig. 7.</span> +</div> + +<p>What, now, may be the office of this structure, +which is found in no other organ of sense? May it<span class="pagenum"><a name="Page_20" id="Page_20">[Pg 20]</a></span> +not be connected with some special property of the +ear? It is quite probable; for the ear possesses a very +similar power. You know that it is possible to follow +the individual voices of a symphony. Indeed, the +feat is possible even in a fugue of Bach, where it is certainly +no inconsiderable achievement. The ear can +pick out the single constituent tonal parts, not only of a +harmony, but of the wildest clash of music imaginable. +The musical ear analyses every agglomeration of tones.</p> + +<p>The eye does not possess this ability. Who, for +example, could tell from the mere sight of white, without +a previous experimental knowledge of the fact, +that white is composed of a mixture of other colors? +Could it be, now, that these two facts, the property of +the ear just mentioned, and the structure discovered +by Corti, are really connected? It is very probable. +The enigma is solved if we assume that every note of +definite pitch has its special string in this pianoforte +of Corti, and, therefore, its special branch of the auditory +nerve attached to that string. But before I can +make this point perfectly plain to you, I must ask +you to follow me a few steps into the dry domain of +physics.</p> + +<p>Look at this pendulum. Forced from its position +of equilibrium by an impulse, it begins to swing with a +definite time of oscillation, dependent upon its length. +Longer pendulums swing more slowly, shorter ones +more quickly. We will suppose our pendulum to execute +one to-and-fro movement in a second.</p><p><span class="pagenum"><a name="Page_21" id="Page_21">[Pg 21]</a></span></p> + +<p>This pendulum, now, can be thrown into violent +vibration in two ways; either by a <i>single</i> heavy impulse, +or by a <i>number</i> of properly communicated slight +impulses. For example, we impart to the pendulum, +while at rest in its position of equilibrium, a very slight +impulse. It will execute a very small vibration. As +it passes a third time its position of equilibrium, a +second having elapsed, we impart to it again a slight +shock, in the same direction with the first. Again after +the lapse of a second, on its fifth passage through the +position of equilibrium, we strike it again in the same +manner; and so continue. You see, by this process +the shocks imparted augment continually the motion +of the pendulum. After each slight impulse, the pendulum +reaches out a little further in its swing, and +finally acquires a considerable motion.<a name="FNanchor_8_8" id="FNanchor_8_8"></a><a href="#Footnote_8_8" class="fnanchor">[8]</a></p> + +<p>But this is not the case under all circumstances. +It is possible only when the impulses imparted synchronise +with the swings of the pendulum. If we +should communicate the second impulse at the end of +half a second and in the same direction with the first +impulse, its effects would counteract the motion of the +pendulum. It is easily seen that our little impulses +help the motion of the pendulum more and more, according +as their time accords with the time of the +pendulum. If we strike the pendulum in any other +time than in that of its vibration, in some instances, it +is true, we shall augment its vibration, but in others<span class="pagenum"><a name="Page_22" id="Page_22">[Pg 22]</a></span> +again, we shall obstruct it. Our impulses will be less +effective the more the motion of our own hand departs +from the motion of the pendulum.</p> + +<p>What is true of the pendulum holds true of every +vibrating body. A tuning-fork when it sounds, also +vibrates. It vibrates more rapidly when its sound is +higher; more slowly when it is deeper. The standard +<i>A</i> of our musical scale is produced by about four hundred +and fifty vibrations in a second.</p> + +<p>I place by the side of each other on this table two +tuning-forks, exactly alike, resting on resonant cases. +I strike the first one a sharp blow, so that it emits a +loud note, and immediately grasp it again with my +hand to quench its note. Nevertheless, you still hear +the note distinctly sounded, and by feeling it you may +convince yourselves that the other fork which was not +struck now vibrates.</p> + +<p>I now attach a small bit of wax to one of the forks. +It is thrown thus out of tune; its note is made a little +deeper. I now repeat the same experiment with the +two forks, now of unequal pitch, by striking one of +them and again grasping it with my hand; but in the +present case the note ceases the very instant I touch +the fork.</p> + +<p>What has happened here in these two experiments? +Simply this. The vibrating fork imparts to the air and +to the table four hundred and fifty shocks a second, +which are carried over to the other fork. If the other +fork is pitched to the same note, that is to say, if it<span class="pagenum"><a name="Page_23" id="Page_23">[Pg 23]</a></span> +vibrates when struck in the same time with the first, +then the shocks first emitted, no matter how slight they +may be, are sufficient to throw the second fork into rapid +sympathetic vibration. But when the time of vibration +of the two forks is slightly different, this does not +take place. We may strike as many forks as we will, the +fork tuned to <i>A</i> is perfectly indifferent to their notes; +is deaf, in fact, to all except its own; and if you strike +three, or four, or five, or any number whatsoever, of +forks all at the same time, so as to make the shocks +which come from them ever so great, the <i>A</i> fork will +not join in with their vibrations unless another fork <i>A</i> +is found in the collection struck. It picks out, in other +words, from all the notes sounded, that which accords +with it.</p> + +<p>The same is true of all bodies which can yield +notes. Tumblers resound when a piano is played, on +the striking of certain notes, and so do window panes. +Nor is the phenomenon without analogy in other provinces. +Take a dog that answers to the name "Nero." +He lies under your table. You speak of Domitian, +Vespasian, and Marcus Aurelius Antoninus, you call +upon all the names of the Roman Emperors that occur +to you, but the dog does not stir, although a slight +tremor of his ear tells you of a faint response of his +consciousness. But the moment you call "Nero" he +jumps joyfully towards you. The tuning-fork is like +your dog. It answers to the name <i>A</i>.</p> + +<p>You smile, ladies. You shake your heads. The<span class="pagenum"><a name="Page_24" id="Page_24">[Pg 24]</a></span> +simile does not catch your fancy. But I have another, +which is very near to you: and for punishment you shall +hear it. You, too, are like tuning-forks. Many are the +hearts that throb with ardor for you, of which you take +no notice, but are cold. Yet what does it profit you! +Soon the heart will come that beats in just the proper +rhythm, and then your knell, too, has struck. Then +your heart, too, will beat in unison, whether you will +or no.</p> + +<p>The law of sympathetic vibration, here propounded +for sounding bodies, suffers some modification for +bodies incompetent to yield notes. Bodies of this +kind vibrate to almost every note. A high silk hat, +we know, will not sound; but if you will hold your +hat in your hand when attending your next concert you +will not only hear the pieces played, but also feel them +with your fingers. It is exactly so with men. People +who are themselves able to give tone to their surroundings, +bother little about the prattle of others. But the +person without character tarries everywhere: in the +temperance hall, and at the bar of the public-house—everywhere +where a committee is formed. The high +silk hat is among bells what the weakling is among +men of conviction.</p> + +<p>A sonorous body, therefore, always sounds when +its special note, either alone or in company with others, +is struck. We may now go a step further. What will +be the behaviour of a group of sonorous bodies which +in the pitch of their notes form a scale? Let us picture<span class="pagenum"><a name="Page_25" id="Page_25">[Pg 25]</a></span> +to ourselves, for example (Fig. 8), a series of rods +or strings pitched to the notes <i>c d e f g</i>.... On a +musical instrument the accord <i>c e g</i> is struck. Every +one of the rods of Fig. 8 will see if its special note is +contained in the accord, and if it finds +it, it will respond. The rod <i>c</i> will give +at once the note <i>c</i>, the rod <i>e</i> the note <i>e</i>, +the rod <i>g</i> the note <i>g</i>. All the other +rods will remain at rest, will not sound.</p> + +<div class="figright" style="width: 300px;"> +<img src="images/i_035.jpg" width="300" height="337" alt="" /> +<span class="caption">Fig. 8.</span> +</div> + +<p>We need not look about us long +for such an instrument. Every piano +is an instrument of this kind, with which the experiment +mentioned may be executed with splendid success. +Two pianos stand here by the side of each other, +both tuned alike. We will employ the first for exciting +the notes, while we will allow the second to respond; +after having first pressed upon the loud pedal, +so as to render all the strings capable of motion.</p> + +<p>Every harmony struck with vigor on the first piano +is distinctly repeated on the second. To prove that +it is the same strings that are sounded in both pianos, +we repeat the experiment in a slightly changed form. +We let go the loud pedal of the second piano and +pressing on the keys <i>c e g</i> of that instrument vigorously +strike the harmony <i>c e g</i> on the first piano. The harmony +<i>c e g</i> is now also sounded on the second piano. +But if we press only on one key <i>g</i> of one piano, while +we strike <i>c e g</i> on the other, only <i>g</i> will be sounded on<span class="pagenum"><a name="Page_26" id="Page_26">[Pg 26]</a></span> +the second. It is thus always the like strings of the +two pianos that excite each other.</p> + +<p>The piano can reproduce any sound that is composed +of its musical notes. It will reproduce, for example, +very distinctly, a vowel sound that is sung into +it. And in truth physics has proved that the vowels +may be regarded as composed of simple musical +notes.</p> + +<p>You see that by the exciting of definite tones in the +air quite definite motions are set up with mechanical +necessity in the piano. The idea might be made use +of for the performance of some pretty pieces of wizardry. +Imagine a box in which is a stretched string +of definite pitch. This is thrown into motion as often +as its note is sung or whistled. Now it would not be +a very difficult task for a skilful mechanic to so construct +the box that the vibrating cord would close a +galvanic circuit and open the lock. And it would not +be a much more difficult task to construct a box which +would open at the whistling of a certain melody. Sesame! +and the bolts fall. Truly, we should have here +a veritable puzzle-lock. Still another fragment rescued +from that old kingdom of fables, of which our day +has realised so much, that world of fairy-stories to +which the latest contributions are Casselli's telegraph, +by which one can write at a distance in one's own hand, +and Prof. Elisha Gray's telautograph. What would +the good old Herodotus have said to these things who +even in Egypt shook his head at much that he saw?<span class="pagenum"><a name="Page_27" id="Page_27">[Pg 27]</a></span> +ἐμοἱ μἑνe ού πιστα, just as simple-heartedly as then, +when he heard of the circumnavigation of Africa.</p> + +<p>A new puzzle-lock! But why invent one? Are +not we human beings ourselves puzzle-locks? Think +of the stupendous groups of thoughts, feelings, and +emotions that can be aroused in us by a word! Are +there not moments in all our lives when a mere name +drives the blood to our hearts? Who that has attended +a large mass-meeting has not experienced what +tremendous quantities of energy and motion can be +evolved by the innocent words, "Liberty, Equality, +Fraternity."</p> + +<p>But let us return to the subject proper of our discourse. +Let us look again at our piano, or what will +do just as well, at some other contrivance of the same +character. What does this instrument do? Plainly, +it decomposes, it analyses every agglomeration of +sounds set up in the air into its individual component +parts, each tone being taken up by a different string; +it performs a real spectral analysis of sound. A person +completely deaf, with the help of a piano, simply by +touching the strings or examining their vibrations with +a microscope, might investigate the sonorous motion of +the air, and pick out the separate tones excited in it.</p> + +<p>The ear has the same capacity as this piano. The +ear performs for the mind what the piano performs for +a person who is deaf. The mind without the ear is +deaf. But a deaf person, with the piano, does hear +after a fashion, though much less vividly, and more<span class="pagenum"><a name="Page_28" id="Page_28">[Pg 28]</a></span> +clumsily, than with the ear. The ear, thus, also decomposes +sound into its component tonal parts. I shall +now not be deceived, I think, if I assume that you +already have a presentiment of what the function of +Corti's fibres is. We can make the matter very plain to +ourselves. We will use the one piano for exciting the +sounds, and we shall imagine the second one in the +ear of the observer in the place of Corti's fibres, which +is a model of such an instrument. To every string of +the piano in the ear we will suppose a special fibre of +the auditory nerve attached, so that this fibre and this +alone, is irritated when the string is thrown into vibration. +If we strike now an accord on the external +piano, for every tone of that accord a definite string of +the internal piano will sound and as many different +nervous fibres will be irritated as there are notes in +the accord. The simultaneous sense-impressions due +to different notes can thus be preserved unmingled and +be separated by the attention. It is the same as with +the five fingers of the hand. With each finger I can +touch something different. Now the ear has three thousand +such fingers, and each one is designed for the +touching of a different tone.<a name="FNanchor_9_9" id="FNanchor_9_9"></a><a href="#Footnote_9_9" class="fnanchor">[9]</a> Our ear is a puzzle-lock +of the kind mentioned. It opens at the magic melody +of a sound. But it is a stupendously ingenious lock. +Not only one tone, but every tone makes it open; but +each one differently. To each tone it replies with a +different sensation.</p> +<p><span class="pagenum"><a name="Page_29" id="Page_29">[Pg 29]</a></span></p> +<p>More than once it has happened in the history of +science that a phenomenon predicted by theory, has +not been brought within the range of actual observation +until long afterwards. Leverrier predicted the +existence and the place of the planet Neptune, but it +was not until sometime later that Galle actually found +the planet at the predicted spot. Hamilton unfolded +theoretically the phenomenon of the so-called conical +refraction of light, but it was reserved for Lloyd some +time subsequently to observe the fact. The fortunes +of Helmholtz's theory of Corti's fibres have been somewhat +similar. This theory, too, received its substantial +confirmation from the subsequent observations of +V. Hensen. On the free surface of the bodies of Crustacea, +connected with the auditory nerves, rows of little +hairy filaments of varying lengths and thicknesses +are found, which to some extent are the analogues of +Corti's fibres. Hensen saw these hairs vibrate when +sounds were excited, and when different notes were +struck different hairs were set in vibration.</p> + +<p>I have compared the work of the physical inquirer +to the journey of the tourist. When the tourist ascends +a new hill he obtains of the whole district a +different view. When the inquirer has found the solution +of one enigma, the solution of a host of others +falls into his hands.</p> + +<p>Surely you have often felt the strange impression experienced<span class="pagenum"><a name="Page_30" id="Page_30">[Pg 30]</a></span> +when in singing through the scale the octave +is reached, and nearly the same sensation is produced +as by the fundamental tone. The phenomenon finds its +explanation in the view here laid down of the ear. And +not only this phenomenon but all the laws of the theory +of harmony may be grasped and verified from this +point of view with a clearness before undreamt of. +Unfortunately, I must content myself to-day with the +simple indication of these beautiful prospects. Their +consideration would lead us too far aside into the fields +of other sciences.</p> + +<p>The searcher of nature, too, must restrain himself +in his path. He also is drawn along from one beauty +to another as the tourist from dale to dale, and as circumstances +generally draw men from one condition of +life into others. It is not he so much that makes the +quests, as that the quests are made of him. Yet let +him profit by his time, and let not his glance rove aimlessly +hither and thither. For soon the evening sun +will shine, and ere he has caught a full glimpse of the +wonders close by, a mighty hand will seize him and +lead him away into a different world of puzzles.</p> + +<p>Respected hearers, science once stood in an entirely +different relation to poetry. The old Hindu +mathematicians wrote their theorems in verses, and +lotus-flowers, roses, and lilies, beautiful sceneries, +lakes, and mountains figured in their problems.</p> + +<p>"Thou goest forth on this lake in a boat. A lily +juts forth, one palm above the water. A breeze bends<span class="pagenum"><a name="Page_31" id="Page_31">[Pg 31]</a></span> +it downwards, and it vanishes two palms from its previous +spot beneath the surface. Quick, mathematician, +tell me how deep is the lake!"</p> + +<p>Thus spoke an ancient Hindu scholar. This poetry, +and rightly, has disappeared from science, but from +its dry leaves another poetry is wafted aloft which cannot +be described to him who has never felt it. Whoever +will fully enjoy this poetry must put his hand to +the plough, must himself investigate. Therefore, +enough of this! I shall reckon myself fortunate if you +do not repent of this brief excursion into the flowered +dale of physiology, and if you take with yourselves the +belief that we can say of science what we say of poetry,</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"Who the song would understand,<br /></span> +<span class="i0">Needs must seek the song's own land;<br /></span> +<span class="i0">Who the minstrel understand<br /></span> +<span class="i0">Needs must seek the minstrel's land."<br /></span> +<span class="pagenum"><a name="Page_32" id="Page_32">[Pg 32]</a></span></div></div> + + + + +<h2><a name="ON_THE_CAUSES_OF_HARMONY" id="ON_THE_CAUSES_OF_HARMONY">ON THE CAUSES OF HARMONY.</a></h2> + + +<p>We are to speak to-day of a theme which is perhaps +of somewhat more general interest—<i>the causes of +the harmony of musical sounds</i>. The first and simplest +experiences relative to harmony are very ancient. Not +so the explanation of its laws. These were first supplied +by the investigators of a recent epoch. Allow me +an historical retrospect.</p> + +<p>Pythagoras (586 B. C.) knew that the note yielded +by a string of steady tension was converted into its +octave when the length of the string was reduced one-half, +and into its fifth when reduced two-thirds; and +that then the first fundamental tone was consonant +with the two others. He knew generally that the same +string under fixed tension gives consonant tones when +successively divided into lengths that are in the proportions +of the simplest natural numbers; that is, in +the proportions of 1:2, 2:3, 3:4, 4:5.</p> + +<p>Pythagoras failed to reveal the causes of these laws. +What have consonant tones to do with the simple natural +numbers? That is the question we should ask<span class="pagenum"><a name="Page_33" id="Page_33">[Pg 33]</a></span> +to-day. But this circumstance must have appeared +less strange than inexplicable to Pythagoras. This +philosopher sought for the causes of harmony in the +occult, miraculous powers of numbers. His procedure +was largely the cause of the upgrowth of a numerical +mysticism, of which the traces may still be detected in +our oneirocritical books and among some scientists, to +whom marvels are more attractive than lucidity.</p> + +<p>Euclid (300 B. C.) gives a definition of consonance +and dissonance that could hardly be improved upon, +in point of verbal accuracy. The consonance (συμφωνία) +of two tones, he says, is the mixture, the +blending (κρᾶσις) of those two tones; dissonance +(διαφωνία), on the other hand, is the incapacity of +the tones to blend (ἀμιξία), whereby they are made +harsh for the ear. The person who knows the correct +explanation of the phenomenon hears it, so to speak, +reverberated in these words of Euclid. Still, Euclid +did not know the true cause of harmony. He had unwittingly +come very near to the truth, but without +really grasping it.</p> + +<p>Leibnitz (1646-1716 A. D.) resumed the question +which his predecessors had left unsolved. He, of +course, knew that musical notes were produced by vibrations, +that twice as many vibrations corresponded +to the octave as to the fundamental tone, etc. A passionate +lover of mathematics, he sought for the cause +of harmony in the secret computation and comparison +of the simple numbers of vibrations and in the secret<span class="pagenum"><a name="Page_34" id="Page_34">[Pg 34]</a></span> +satisfaction of the soul at this occupation. But how, +we ask, if one does not know that musical notes are +vibrations? The computation and the satisfaction at +the computation must indeed be pretty secret if it is +unknown. What queer ideas philosophers have! Could +anything more wearisome be imagined than computation +as a principle of æsthetics? Yes, you are not +utterly wrong in your conjecture, yet you may be sure +that Leibnitz's theory is not wholly nonsense, although +it is difficult to make out precisely what he meant by +his secret computation.</p> + +<p>The great Euler (1707-1783) sought the cause of +harmony, almost as Leibnitz did, in the pleasure which +the soul derives from the contemplation of order in the +numbers of the vibrations.<a name="FNanchor_10_10" id="FNanchor_10_10"></a><a href="#Footnote_10_10" class="fnanchor">[10]</a></p> + +<p>Rameau and D'Alembert (1717-1783) approached +nearer to the truth. They knew that in every sound +available in music besides the fundamental note also +the twelfth and the next higher third could be heard; +and further that the resemblance between a fundamental +tone and its octave was always strongly marked. +Accordingly, the combination of the octave, fifth, third, +etc., with the fundamental tone appeared to them "natural." +They possessed, we must admit, the correct +point of view; but with the simple naturalness of a +phenomenon no inquirer can rest content; for it is precisely +this naturalness for which he seeks his explanations.</p> +<p><span class="pagenum"><a name="Page_35" id="Page_35">[Pg 35]</a></span></p> +<p>Rameau's remark dragged along through the whole +modern period, but without leading to the full discovery +of the truth. Marx places it at the head of his +theory of composition, but makes no further application +of it. Also Goethe and Zelter in their correspondence +were, so to speak, on the brink of the truth. +Zelter knew of Rameau's view. Finally, you will be +appalled at the difficulty of the problem, when I tell +you that till very recent times even professors of physics +were dumb when asked what were the causes of +harmony.</p> + +<p>Not till quite recently did Helmholtz find the solution +of the question. But to make this solution clear +to you I must first speak of some experimental principles +of physics and psychology.</p> + +<p>1) In every process of perception, in every observation, +the attention plays a highly important part. +We need not look about us long for proofs of this. +You receive, for example, a letter written in a very +poor hand. Do your best, you cannot make it out. +You put together now these, now those lines, yet you +cannot construct from them a single intelligible character. +Not until you direct your attention to groups +of lines which really belong together, is the reading of +the letter possible. Manuscripts, the letters of which +are formed of minute figures and scrolls, can only be +read at a considerable distance, where the attention is<span class="pagenum"><a name="Page_36" id="Page_36">[Pg 36]</a></span> +no longer diverted from the significant outlines to the +details. A beautiful example of this class is furnished +by the famous iconographs of Giuseppe Arcimboldo in +the basement of the Belvedere gallery at Vienna. These +are symbolic representations of water, fire, etc.: human +heads composed of aquatic animals and of combustibles. +At a short distance one sees only the details, +at a greater distance only the whole figure. Yet +a point can be easily found at which, by a simple voluntary +movement of the attention, there is no difficulty +in seeing now the whole figure and now the smaller +forms of which it is composed. A picture is often seen +representing the tomb of Napoleon. The tomb is surrounded +by dark trees between which the bright heavens +are visible as background. One can look a long time +at this picture without noticing anything except the +trees, but suddenly, on the attention being accidentally +directed to the bright background, one sees +the figure of Napoleon between the trees. This case +shows us very distinctly the important part which attention +plays. The same sensuous object can, solely +by the interposition of attention, give rise to wholly +different perceptions.</p> + +<p>If I strike a harmony, or chord, on this piano, by +a mere effort of attention you can fix every tone of +that harmony. You then hear most distinctly the +fixed tone, and all the rest appear as a mere addition, +altering only the quality, or acoustic color, of the primary +tone. The effect of the same harmony is essentially<span class="pagenum"><a name="Page_37" id="Page_37">[Pg 37]</a></span> +modified if we direct our attention to different +tones.</p> + +<p>Strike in succession two harmonies, for example, +the two represented in the annexed diagram, and first +fix by the attention the upper note <i>e</i>, afterwards the +base <i>e</i>-<i>a</i>; in the two cases you will hear the same +sequence of harmonies differently. +In the first case, you have the impression +as if the fixed tone remained +unchanged and simply altered +its <i>timbre</i>; in the second case, +the whole acoustic agglomeration +seems to fall sensibly in depth. +There is an art of composition to guide the attention +of the hearer. But there is also an art of hearing, +which is not the gift of every person.</p> + +<div class="figright" style="width: 200px;"> +<img src="images/i_047.jpg" width="200" height="178" alt="" /> +<span class="caption">Fig. 9.</span> +</div> + +<p>The piano-player knows the remarkable effects obtained +when one of the keys of a chord that is struck +is let loose. Bar 1 played on the piano sounds almost +like bar 2. The note which lies next to the key let +loose resounds after its release as if it were freshly +struck. The attention no longer occupied with the +upper note is by that very fact insensibly led to the +upper note.</p> + +<div class="figcenter" style="width: 500px;"> +<img src="images/i_047-1.jpg" width="500" height="175" alt="" /> +<span class="caption">Fig. 10.</span> +</div> +<p><span class="pagenum"><a name="Page_38" id="Page_38">[Pg 38]</a></span></p> + +<p>Any tolerably cultivated musical ear can perform +the resolution of a harmony into its component parts. +By much practice we can go even further. Then, +every musical sound heretofore regarded as simple +can be resolved into a subordinate succession +of musical tones. For example, +if I strike on the piano the note 1, (annexed +diagram,) we shall hear, if we +make the requisite effort of attention, +besides the loud fundamental note the +feebler, higher overtones, or harmonics, +2 ... 7, that is, the octave, the twelfth, the double +octave, and the third, the fifth, and the seventh of +the double octave.</p> + +<div class="figright" style="width: 200px;"> +<img src="images/i_048.jpg" width="200" height="237" alt="" /> +<span class="caption">Fig. 11.</span> +</div> + +<p>The same is true of every musically available +sound. Each yields, with varying degrees of intensity, +besides its fundamental note, also the octave, the +twelfth, the double octave, etc. The phenomenon is +observable with special facility on the open and closed +flue-pipes of organs. According, now, as certain overtones +are more or less distinctly emphasised in a +sound, the <i>timbre</i> of the sound changes—that peculiar +quality of the sound by which we distinguish the music +of the piano from that of the violin, the clarinet, etc.</p> + +<p>On the piano these overtones can be very easily +rendered audible. If I strike, for example, sharply +note 1 of the foregoing series, whilst I simply press +down upon, one after another, the keys 2, 3, ... 7, +the notes 2, 3, ... 7 will continue to sound after the<span class="pagenum"><a name="Page_39" id="Page_39">[Pg 39]</a></span> +striking of 1, because the strings corresponding to +these notes, now freed from their dampers, are thrown +into sympathetic vibration.</p> + +<p>As you know, this sympathetic vibration of the like-pitched +strings with the overtones is really not to be +conceived as sympathy, but rather as lifeless mechanical +necessity. We must not think of this sympathetic +vibration as an ingenious journalist pictured it, who +tells a gruesome story of Beethoven's F minor sonata, +Op. 2, that I cannot withhold from you. "At the +last London Industrial Exhibition nineteen virtuosos +played the F minor sonata on the same piano. When +the twentieth stepped up to the instrument to play by +way of variation the same production, to the terror of +all present the piano began to render the sonata of its +own accord. The Archbishop of Canterbury, who +happened to be present, was set to work and forthwith +expelled the F minor devil."</p> + +<p>Although, now, the overtones or harmonics which +we have discussed are heard only upon a special effort +of the attention, nevertheless they play a highly important +part in the formation of musical <i>timbre</i>, as also +in the production of the consonance and dissonance of +sounds. This may strike you as singular. How can +a thing which is heard only under exceptional circumstances +be of importance generally for audition?</p> + +<p>But consider some familiar incidents of your every-day +life. Think of how many things you see which +you do not notice, which never strike your attention<span class="pagenum"><a name="Page_40" id="Page_40">[Pg 40]</a></span> +until they are missing. A friend calls upon you; you +cannot understand why he looks so changed. Not +until you make a close examination do you discover +that his hair has been cut. It is not difficult to tell +the publisher of a work from its letter-press, and yet +no one can state precisely the points by which this +style of type is so strikingly different from that style. +I have often recognised a book which I was in search +of from a simple piece of unprinted white paper that +peeped out from underneath the heap of books covering +it, and yet I had never carefully examined the +paper, nor could I have stated its difference from other +papers.</p> + +<p>What we must remember, therefore, is that every +sound that is musically available yields, besides its +fundamental note, its octave, its twelfth, its double +octave, etc., as overtones or harmonics, and that these +are important for the agreeable combination of several +musical sounds.</p> + +<p>2) One other fact still remains to be dealt with. +Look at this tuning-fork. It yields, when struck, a perfectly +smooth tone. But if you strike in company with +it a second fork which is of slightly different pitch, and +which alone also gives a perfectly smooth tone, you +will hear, if you set both forks on the table, or hold +both before your ear, a uniform tone no longer, but a +number of shocks of tones. The rapidity of the shocks +increases with the difference of the pitch of the forks. +These shocks, which become very disagreeable for the<span class="pagenum"><a name="Page_41" id="Page_41">[Pg 41]</a></span> +ear when they amount to thirty-three in a second, are +called "beats."</p> + +<p>Always, when one of two like musical sounds is +thrown out of unison with the other, beats arise. Their +number increases with the divergence from unison, and +simultaneously they grow more unpleasant. Their +roughness reaches its maximum at about thirty-three +beats in a second. On a still further departure from +unison, and a consequent increase of the number of +beats, the unpleasant effect is diminished, so that tones +which are widely apart in pitch no longer produce +offensive beats.</p> + +<p>To give yourselves a clear idea of the production +of beats, take two metronomes and set them almost +alike. You can, for that matter, set the two exactly +alike. You need not fear that they will strike alike. +The metronomes usually for sale in the shops are poor +enough to yield, when set alike, appreciably unequal +strokes. Set, now, these two metronomes, which strike +at unequal intervals, in motion; you will readily see +that their strokes alternately coincide and conflict with +each other. The alternation is quicker the greater the +difference of time of the two metronomes.</p> + +<p>If metronomes are not to be had, the experiment +may be performed with two watches.</p> + +<p>Beats arise in the same way. The rhythmical +shocks of two sounding bodies, of unequal pitch, sometimes +coincide, sometimes interfere, whereby they alternately<span class="pagenum"><a name="Page_42" id="Page_42">[Pg 42]</a></span> +augment and enfeeble each other's effects. +Hence the shock-like, unpleasant swelling of the tone.</p> + +<p>Now that we have made ourselves acquainted with +overtones and beats, we may proceed to the answer of +our main question, Why do certain relations of pitch +produce pleasant sounds, consonances, others unpleasant +sounds, dissonances? It will be readily seen that +all the unpleasant effects of simultaneous sound-combinations +are the result of beats produced by those +combinations. Beats are the only sin, the sole evil of +music. Consonance is the coalescence of sounds without +appreciable beats.</p> + +<div class="figright" style="width: 182px;"> +<img src="images/i_052.jpg" width="182" height="800" alt="" /> +<span class="caption">Fig. 12.</span> +</div> + +<p>To make this perfectly clear to you I have constructed +the model which you see in Fig. 12. It represents +a claviatur. At its top a movable strip of wood +<i>aa</i> with the marks 1, 2 ... 6 is placed. By setting +this strip in any position, for example, in that where the +mark 1 is over the note <i>c</i> of the claviatur, the marks +2, 3 ... 6, as you see, stand over the overtones of <i>c</i>. +The same happens when the strip is placed in any +other position. A second, exactly similar strip, <i>bb</i>, +possesses the same properties. Thus, together, the +two strips, in any two positions, point out by their<span class="pagenum"><a name="Page_43" id="Page_43">[Pg 43]</a></span> +marks all the tones brought into play upon the simultaneous +sounding of the notes indicated by the marks 1.</p> + +<p>The two strips, placed over the same fundamental +note, show that also all the overtones of those notes +coincide. The first note is simply intensified by the +other. The single overtones of a sound lie too far apart +to permit appreciable beats. The second sound supplies +nothing new, consequently, also, no new beats. +Unison is the most perfect consonance.</p> + +<p>Moving one of the two strips along the other is +equivalent to a departure from unison. All the overtones +of the one sound now fall alongside those of the +other; beats are at once produced; the combination +of the tones becomes unpleasant: we obtain a dissonance. +If we move the strip further and further along, +we shall find that as a general rule the overtones always +fall alongside each other, that is, always produce +beats and dissonances. Only in a few quite definite +positions do the overtones partially coincide. Such +positions, therefore, signify higher degrees of euphony—they +point out <i>the consonant intervals</i>.</p> + +<p>These consonant intervals can be readily found experimentally +by cutting Fig. 12 out of paper and moving +<i>bb</i> lengthwise along <i>aa</i>. The most perfect consonances +are the octave and the twelfth, since in these two cases +the overtones of the one sound coincide absolutely +with those of the other. In the octave, for example, +1<i>b</i> falls on 2<i>a</i>, 2<i>b</i> on 4<i>a</i>, 3<i>b</i> on 6<i>a</i>. Consonances, +therefore, are simultaneous sound-combinations not<span class="pagenum"><a name="Page_44" id="Page_44">[Pg 44]</a></span> +accompanied by disagreeable beats. This, by the way, +is, expressed in English, what Euclid said in Greek.</p> + +<p>Only such sounds are consonant as possess in common +some portion of their partial tones. Plainly we +must recognise between such sounds, also when struck +one after another, a certain affinity. For the second +sound, by virtue of the common overtones, will produce +partly the same sensation as the first. The octave is +the most striking exemplification of this. When we +reach the octave in the ascent of the scale we actually +fancy we hear the fundamental tone repeated. The +foundations of harmony, therefore, are the foundations +of melody.</p> + +<p>Consonance is the coalescence of sounds without +appreciable beats! This principle is competent to introduce +wonderful order and logic into the doctrines +of the fundamental bass. The compendiums of the +theory of harmony which (Heaven be witness!) have +stood hitherto little behind the cook-books in subtlety +of logic, are rendered extraordinarily clear and simple. +And what is more, all that the great masters, such as +Palestrina, Mozart, Beethoven, unconsciously got +right, and of which heretofore no text-book could render +just account, receives from the preceding principle +its perfect verification.</p> + +<p>But the beauty of the theory is, that it bears upon +its face the stamp of truth. It is no phantom of the +brain. Every musician can hear for himself the beats +which the overtones of his musical sounds produce.<span class="pagenum"><a name="Page_45" id="Page_45">[Pg 45]</a></span> +Every musician can satisfy himself that for any given +case the number and the harshness of the beats can +be calculated beforehand, and that they occur in exactly +the measure that theory determines.</p> + +<p>This is the answer which Helmholtz gave to the +question of Pythagoras, so far as it can be explained +with the means now at my command. A long period +of time lies between the raising and the solving of this +question. More than once were eminent inquirers +nearer to the answer than they dreamed of.</p> + +<p>The inquirer seeks the truth. I do not know if the +truth seeks the inquirer. But were that so, then the +history of science would vividly remind us of that +classical rendezvous, so often immortalised by painters +and poets. A high garden wall. At the right a +youth, at the left a maiden. The youth sighs, the +maiden sighs! Both wait. Neither dreams how near +the other is.</p> + +<p>I like this simile. Truth suffers herself to be +courted, but she has evidently no desire to be won. +She flirts at times disgracefully. Above all, she is determined +to be merited, and has naught but contempt +for the man who will win her too quickly. And if, +forsooth, one breaks his head in his efforts of conquest, +what matter is it, another will come, and truth is always +young. At times, indeed, it really seems as if +she were well disposed towards her admirer, but that +admitted—never! Only when Truth is in exceptionally +good spirits does she bestow upon her wooer a glance<span class="pagenum"><a name="Page_46" id="Page_46">[Pg 46]</a></span> +of encouragement. For, thinks Truth, if I do not do +something, in the end the fellow will not seek me at all.</p> + +<p>This one fragment of truth, then, we have, and it +shall never escape us. But when I reflect what it has +cost in labor and in the lives of thinking men, how it +painfully groped its way through centuries, a half-matured +thought, before it became complete; when I +reflect that it is the toil of more than two thousand +years that speaks out of this unobtrusive model of +mine, then, without dissimulation, I almost repent me +of the jest I have made.</p> + +<p>And think of how much we still lack! When, several +thousand years hence, boots, top-hats, hoops, pianos, +and bass-viols are dug out of the earth, out of the +newest alluvium as fossils of the nineteenth century; +when the scientists of that time shall pursue their +studies both upon these wonderful structures and upon +our modern Broadways, as we to-day make studies of +the implements of the stone age and of the prehistoric +lake-dwellings—then, too, perhaps, people will be unable +to comprehend how we could come so near to +many great truths without grasping them. And thus +it is for all time the unsolved dissonance, for all time +the troublesome seventh, that everywhere resounds in +our ears; we feel, perhaps, that it will find its solution, +but we shall never live to see the day of the pure +triple accord, nor shall our remotest descendants.</p> + +<p>Ladies, if it is the sweet purpose of your life to +sow confusion, it is the purpose of mine to be clear;<span class="pagenum"><a name="Page_47" id="Page_47">[Pg 47]</a></span> +and so I must confess to you a slight transgression +that I have been guilty of. On one point I have told +you an untruth. But you will pardon me this falsehood, +if in full repentance I make it good. The model +represented in Fig. 12 does not tell the whole truth, for +it is based upon the so-called "even temperament" +system of tuning. The overtones, however, of musical +sounds are not tempered, but purely tuned. By means +of this slight inexactness the model is made considerably +simpler. In this form it is fully adequate for +ordinary purposes, and no one who makes use of it in +his studies need be in fear of appreciable error.</p> + +<p>If you should demand of me, however, the full +truth, I could give you that only by the help of a mathematical +formula. I should have to take the chalk into +my hands and—think of it!—reckon in your presence. +This you might take amiss. Nor shall it happen. +I have resolved to do no more reckoning for to-day. +I shall reckon now only upon your forbearance, and +this you will surely not gainsay me when you reflect +that I have made only a limited use of my privilege to +weary you. I could have taken up much more of +your time, and may, therefore, justly close with Lessing's +epigram:</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"If thou hast found in all these pages naught that's worth the thanks,<br /></span> +<span class="i0">At least have gratitude for what I've spared thee."<br /></span> +<span class="pagenum"><a name="Page_48" id="Page_48">[Pg 48]</a></span></div></div> + + + + +<h2><a name="THE_VELOCITY_OF_LIGHT" id="THE_VELOCITY_OF_LIGHT">THE VELOCITY OF LIGHT.</a></h2> + + +<p>When a criminal judge has a right crafty knave +before him, one well versed in the arts of prevarication, +his main object is to wring a confession from +the culprit by a few skilful questions. In almost a similar +position the natural philosopher seems to be placed +with respect to nature. True, his functions here are +more those of the spy than the judge; but his object +remains pretty much the same. Her hidden motives +and laws of action is what nature must be made to +confess. Whether a confession will be extracted depends +upon the shrewdness of the inquirer. Not without +reason, therefore, did Lord Bacon call the experimental +method a questioning of nature. The +art consists in so putting our questions that they +may not remain unanswered without a breach of etiquette.</p> + +<p>Look, too, at the countless tools, engines, and instruments +of torture with which man conducts his +inquisitions of nature, and which mock the poet's +words:</p><p><span class="pagenum"><a name="Page_49" id="Page_49">[Pg 49]</a></span></p> + +<div class="poem"><div class="stanza"> +<span class="i0">"Mysterious even in open day,<br /></span> +<span class="i0">Nature retains her veil, despite our clamors;<br /></span> +<span class="i0">That which she doth not willingly display<br /></span> +<span class="i0">Cannot be wrenched from her with levers, screws, and hammers."<br /></span> +</div></div> + +<p>Look at these instruments and you will see that the +comparison with torture also is admissible.<a name="FNanchor_11_11" id="FNanchor_11_11"></a><a href="#Footnote_11_11" class="fnanchor">[11]</a></p> + +<p>This view of nature, as of something designedly +concealed from man, that can be unveiled only by +force or dishonesty, chimed in better with the conceptions +of the ancients than with modern notions. A +Grecian philosopher once said, in offering his opinion +of the natural science of his time, that it could only be +displeasing to the gods to see men endeavoring to spy +out what the gods were not minded to reveal to them.<a name="FNanchor_12_12" id="FNanchor_12_12"></a><a href="#Footnote_12_12" class="fnanchor">[12]</a> +Of course all the contemporaries of the speaker were +not of his opinion.</p> + +<p>Traces of this view may still be found to-day, but +upon the whole we are now not so narrow-minded. +We believe no longer that nature designedly hides +herself. We know now from the history of science +that our questions are sometimes meaningless, and +that, therefore, no answer can be forthcoming. Soon +we shall see how man, with all his thoughts and quests, +is only a fragment of nature's life.</p> + +<p><span class="pagenum"><a name="Page_50" id="Page_50">[Pg 50]</a></span></p><p>Picture, then, as your fancy dictates, the tools of +the physicist as instruments of torture or as engines of +endearment, at all events a chapter from the history of +those implements will be of interest to you, and it will +not be unpleasant to learn what were the peculiar difficulties +that led to the invention of such strange apparatus.</p> + +<p>Galileo (born at Pisa in 1564, died at Arcetri in +1642) was the first who asked what was the velocity +of light, that is, what time it would take for a light +struck at one place to become visible at another, a +certain distance away.<a name="FNanchor_13_13" id="FNanchor_13_13"></a><a href="#Footnote_13_13" class="fnanchor">[13]</a></p> + +<p>The method which Galileo devised was as simple +as it was natural. Two practised observers, with +muffled lanterns, were to take up positions in a dark +night at a considerable distance +from each other, one at +<i>A</i> and one at <i>B</i>. At a moment +previously fixed upon, <i>A</i> was +instructed to unmask his lantern; while as soon as <i>B</i> +saw the light of <i>A</i>'s lantern he was to unmask his. +Now it is clear that the time which <i>A</i> counted from +the uncovering of his lantern until he caught sight of +the light of <i>B</i>'s would be the time which it would take +light to travel from <i>A</i> to <i>B</i> and from <i>B</i> back to <i>A</i>.</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_060.jpg" width="300" height="93" alt="" /> +<span class="caption">Fig. 13.</span> +</div> + +<p>The experiment was not executed, nor could it, in +the nature of the case, have been a success. As we<span class="pagenum"><a name="Page_51" id="Page_51">[Pg 51]</a></span> +now know, light travels too rapidly to be thus noted. +The time elapsing between the arrival of the light at +<i>B</i> and its perception by the observer, with that between +the decision to uncover and the uncovering of +the lantern, is, as we now know, incomparably greater +than the time which it takes light to travel the greatest +earthly distances. The great velocity of light will be +made apparent, if we reflect that a flash of lightning +in the night illuminates instantaneously a very extensive +region, whilst the single reflected claps of thunder +arrive at the observer's ear very gradually and in appreciable +succession.</p> + +<p>During his life, then, the efforts of Galileo to determine +the velocity of light remained uncrowned with +success. But the subsequent history of the measurement +of the velocity of light is intimately associated +with his name, for with the telescope which he constructed +he discovered the four satellites of Jupiter, +and these furnished the next occasion for the determination +of the velocity of light.</p> + +<p>The terrestrial spaces were too small for Galileo's +experiment. The measurement was first executed +when the spaces of the planetary system were employed. +Olaf Römer, (born at Aarhuus in 1644, died +at Copenhagen in 1710) accomplished the feat (1675-1676), +while watching with Cassini at the observatory +of Paris the revolutions of Jupiter's moons.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/i_062.jpg" width="600" height="373" alt="" /> +<span class="caption">Fig. 14.</span> +</div> + +<p>Let <i>AB</i> (Fig. 14) be Jupiter's orbit. Let <i>S</i> stand +for the sun, <i>E</i> for the earth, <i>J</i> for Jupiter, and <i>T</i> for<span class="pagenum"><a name="Page_52" id="Page_52">[Pg 52]</a></span> +Jupiter's first satellite. When the earth is at <i>E</i><sub>1</sub> we +see the satellite enter regularly into Jupiter's shadow, +and by watching the time between two successive +eclipses, can calculate its time of revolution. The +time which Römer noted was forty-two hours, twenty-eight +minutes, and thirty-five seconds. Now, as the +earth passes along in its orbit towards E<sub>2</sub>, the revolutions +of the satellite grow apparently longer and longer: +the eclipses take place later and later. The greatest +retardation of the eclipse, which occurs when the earth +is at <i>E</i><sub>2</sub>, amounts to sixteen minutes and twenty-six +seconds. As the earth passes back again to <i>E</i><sub>1</sub>, the +revolutions grow apparently shorter, and they occur +in exactly the time that they first did when the earth +arrives at <i>E</i><sub>1</sub>. It is to be remarked that Jupiter changes +only very slightly its position during one revolution of +the earth. Römer guessed at once that these periodical +changes of the time of revolution of Jupiter's satellite<span class="pagenum"><a name="Page_53" id="Page_53">[Pg 53]</a></span> +were not actual, but apparent changes, which were +in some way connected with the velocity of light.</p> + +<p>Let us make this matter clear to ourselves by a simile. +We receive regularly by the post, news of the +political status at our capital. However far away we +may be from the capital, we hear the news of every +event, later it is true, but of all equally late. The +events reach us in the same succession of time as that +in which they took place. But if we are travelling +away from the capital, every successive post will have +a greater distance to pass over, and the events will +reach us more slowly than they took place. The reverse +will be the case if we are approaching the capital.</p> + +<p>At rest, we hear a piece of music played in the +same <i>tempo</i> at all distances. But the <i>tempo</i> will be +seemingly accelerated if we are carried +rapidly towards the band, or retarded if +we are carried rapidly away from it.<a name="FNanchor_14_14" id="FNanchor_14_14"></a><a href="#Footnote_14_14" class="fnanchor">[14]</a></p> + +<div class="figleft" style="width: 150px;"> +<img src="images/i_063.jpg" width="150" height="143" alt="" /> +<span class="caption">Fig. 15.</span> +</div> + +<p>Picture to yourself a cross, say the +sails of a wind-mill (Fig. 15), in uniform +rotation about its centre. Clearly, the rotation of the +cross will appear to you more slowly executed if you +are carried very rapidly away from it. For the post +which in this case conveys to you the light and brings +to you the news of the successive positions of the cross +will have to travel in each successive instant over a +longer path.</p> +<p><span class="pagenum"><a name="Page_54" id="Page_54">[Pg 54]</a></span></p> +<p>Now this must also be the case with the rotation +(the revolution) of the satellite of Jupiter. The greatest +retardation of the eclipse (16-1/2 minutes), due to +the passage of the earth from <i>E</i><sub>1</sub> to <i>E</i><sub>2</sub>, or to its removal +from Jupiter by a distance equal to the diameter +of the orbit of the earth, plainly corresponds to the +time which it takes light to traverse a distance equal to +the diameter of the earth's orbit. The velocity of light, +that is, the distance described by light in a second, as +determined by this calculation, is 311,000 kilometres,<a name="FNanchor_15_15" id="FNanchor_15_15"></a><a href="#Footnote_15_15" class="fnanchor">[15]</a> +or 193,000 miles. A subsequent correction of the diameter +of the earth's orbit, gives, by the same method, +the velocity of light as approximately 186,000 miles a +second.</p> + +<p>The method is exactly that of Galileo; only better +conditions are selected. Instead of a short terrestrial +distance we have the diameter of the earth's orbit, +three hundred and seven million kilometres; in place +of the uncovered and covered lanterns we have the +satellite of Jupiter, which alternately appears and disappears. +Galileo, therefore, although he could not +carry out himself the proposed measurement, found +the lantern by which it was ultimately executed.</p> + +<p>Physicists did not long remain satisfied with this +beautiful discovery. They sought after easier methods +of measuring the velocity of light, such as might +be performed on the earth. This was possible after the +difficulties of the problem were clearly exposed. A +measurement of the kind referred to was executed in +1849 by Fizeau (born at Paris in 1819).</p> +<p><span class="pagenum"><a name="Page_55" id="Page_55">[Pg 55]</a></span></p> +<p>I shall endeavor to make the principle of Fizeau's +apparatus clear to you. Let <i>s</i> (Fig. 16) be a disk free +to rotate about its centre, and perforated at its rim +with a series of holes. Let <i>l</i> be a luminous point +casting its light on an unsilvered glass, <i>a</i>, inclined at +an angle of forty-five degrees to the axis of the disk. +The ray of light, reflected at this point, passes through +one of the holes of the disk and falls at right angles +upon a mirror <i>b</i>, erected at a point about five miles +distant. From the mirror <i>b</i> the light is again reflected, +passes once more through the hole in <i>s</i>, and, penetrating +the glass plate, finally strikes the eye, <i>o</i>, of the observer. +The eye, <i>o</i>, thus, sees the image of the luminous +point <i>l</i> through the glass plate and the hole of +the disk in the mirror <i>b</i>.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/i_065.jpg" width="600" height="226" alt="" /> +<span class="caption">Fig. 16.</span> +</div> + +<p>If, now, the disk be set in rotation, the unpierced +spaces between the apertures will alternately take the +place of the apertures, and the eye o will now see the +image of the luminous point in <i>b</i> only at interrupted +intervals. On increasing the rapidity of the rotation,<span class="pagenum"><a name="Page_56" id="Page_56">[Pg 56]</a></span> +however, the interruptions for the eye become again +unnoticeable, and the eye sees the mirror <i>b</i> uniformly +illuminated.</p> + +<p>But all this holds true only for relatively small velocities +of the disk, when the light sent through an +aperture in <i>s</i> to <i>b</i> on its return strikes the aperture at +almost the same place and passes through it a second +time. Conceive, now, the speed of the disk to be so increased +that the light on its return finds before it an +unpierced space instead of an aperture, it will then no +longer be able to reach the eye. We then see the +mirror <i>b</i> only when no light is emitted from it, but +only when light is sent to it; it is covered when light +comes from it. In this case, accordingly, the mirror +will always appear dark.</p> + +<p>If the velocity of rotation at this point were still +further increased, the light sent through one aperture +could not, of course, on its return pass through the +same aperture but might strike the next and reach +the eye by that. Hence, by constantly increasing the +velocity of the rotation, the mirror <i>b</i> may be made to +appear alternately bright and dark. Plainly, now, if +we know the number of apertures of the disk, the number +of rotations per second, and the distance <i>sb</i>, we +can calculate the velocity of light. The result agrees +with that obtained by Römer.</p> + +<p>The experiment is not quite as simple as my exposition +might lead you to believe. Care must be +taken that the light shall travel back and forth over<span class="pagenum"><a name="Page_57" id="Page_57">[Pg 57]</a></span> +the miles of distance <i>sb</i> and <i>bs</i> undispersed. This +difficulty is obviated by means of telescopes.</p> + +<p>If we examine Fizeau's apparatus closely, we shall +recognise in it an old acquaintance: the arrangement +of Galileo's experiment. The luminous point <i>l</i> is the +lantern <i>A</i>, while the rotation of the perforated disk performs +mechanically the uncovering and covering of the +lantern. Instead of the unskilful observer <i>B</i> we have +the mirror <i>b</i>, which is unfailingly illuminated the instant +the light arrives from <i>s</i>. The disk <i>s</i>, by alternately +transmitting and intercepting the reflected light, assists +the observer <i>o</i>. Galileo's experiment is here executed, +so to speak, countless times in a second, yet the total +result admits of actual observation. If I might be +pardoned the use of a phrase of Darwin's in this field, +I should say that Fizeau's apparatus was the descendant +of Galileo's lantern.</p> + +<p>A still more refined and delicate method for the +measurement of the velocity of light was employed by +Foucault, but a description of it here would lead us +too far from our subject.</p> + +<p>The measurement of the velocity of sound is easily +executed by the method of Galileo. It was unnecessary, +therefore, for physicists to rack their brains further +about the matter; but the idea which with light +grew out of necessity was applied also in this field. +Koenig of Paris constructs an apparatus for the measurement +of the velocity of sound which is closely allied +to the method of Fizeau.</p><p><span class="pagenum"><a name="Page_58" id="Page_58">[Pg 58]</a></span></p> + +<p>The apparatus is very simple. It consists of two +electrical clock-works which strike simultaneously, +with perfect precision, tenths of seconds. If we place +the two clock-works directly side by side, we hear +their strokes simultaneously, wherever we stand. But +if we take our stand by the side of one of the works +and place the other at some distance from us, in general +a coincidence of the strokes will now not be heard. +The companion strokes of the remote clock-work arrive, +as sound, later. The first stroke of the remote +work is heard, for example, immediately after the first +of the adjacent work, and so on. But by increasing +the distance we may produce again a coincidence of the +strokes. For example, the first stroke of the remote +work coincides with the second of the near work, the +second of the remote work with the third of the near +work, and so on. If, now, the works strike tenths of +seconds and the distance between them is increased +until the first coincidence is noted, plainly that distance +is travelled over by the sound in a tenth of a +second.</p> + +<p>We meet frequently the phenomenon here presented, +that a thought which centuries of slow and +painful endeavor are necessary to produce, when once +developed, fairly thrives. It spreads and runs everywhere, +even entering minds in which it could never +have arisen. It simply cannot be eradicated.</p> + +<p>The determination of the velocity of light is not the +only case in which the direct perception of the senses<span class="pagenum"><a name="Page_59" id="Page_59">[Pg 59]</a></span> +is too slow and clumsy for use. The usual method +of studying events too fleet for direct observation consists +in putting into reciprocal action with them other +events already known, the velocities of all of which +are capable of comparison. The result is +usually unmistakable, and susceptible of +direct inference respecting the character of +the event which is unknown. The velocity +of electricity cannot be determined by direct +observation. But it was ascertained +by Wheatstone, simply by the expedient of +watching an electric spark in a mirror rotating with +tremendous known velocity.</p> + +<div class="figleft" style="width: 150px;"> +<img src="images/i_069.jpg" width="150" height="238" alt="" /> +<span class="caption">Fig. 17.</span> +</div> + +<div class="figright" style="width: 200px;"> +<img src="images/i_069-1.jpg" width="200" height="189" alt="" /> +<span class="caption">Fig. 18.</span> +</div> + +<p>If we wave a staff irregularly hither and thither, +simple observation cannot determine how quickly it +moves at each point of its course. But let us look at +the staff through holes in the rim of a +rapidly rotating disk (Fig. 17). We +shall then see the moving staff only +in certain positions, namely, when a +hole passes in front of the eye. The +single pictures of the staff remain for a +time impressed upon the eye; we think we see several +staffs, having some such disposition as that represented +in Fig. 18. If, now, the holes of the disk are equally +far apart, and the disk is rotated with uniform velocity, +we see clearly that the staff has moved slowly +from <i>a</i> to <i>b</i>, more quickly from <i>b</i> to <i>c</i>, still more quickly +from <i>c</i> to <i>d</i>, and with its greatest velocity from <i>d</i> to <i>e</i>.</p><p><span class="pagenum"><a name="Page_60" id="Page_60">[Pg 60]</a></span></p> + +<p>A jet of water flowing from an orifice in the bottom +of a vessel has the appearance of perfect quiet and +uniformity, but if we illuminate it for a second, in a +dark room, by means of an electric flash we shall see +that the jet is composed of separate drops. By their +quick descent the images of the drops are +obliterated and the jet appears uniform. +Let us look at the jet through the rotating +disk. The disk is supposed to be rotated so +rapidly that while the second aperture +passes into the place of the first, drop 1 +falls into the place of 2, 2 into the place of 3, and so on. +We see drops then always in the same places. The +jet appears to be at rest. If we turn the disk a trifle +more slowly, then while the second aperture passes +into the place of the first, drop 1 will have fallen somewhat +lower than 2, 2 somewhat lower than 3, etc. +Through every successive aperture we shall see drops +in successively lower positions. The jet will appear to +be flowing slowly downwards.</p> + +<div class="figright" style="width: 150px;"> +<img src="images/i_070.jpg" width="150" height="184" alt="" /> +<span class="caption">Fig. 19.</span> +</div> + +<p>Now let us turn the disk more rapidly. Then while +the second aperture is passing into the place of the +first, drop 1 will not quite have reached the place of 2, +but will be found slightly above 2, 2 slightly above 3, +etc. Through the successive apertures we shall see +the drops at successively higher places. It will now +look as if the jet were flowing upwards, as if the drops +were rising from the lower vessel into the higher.</p> + +<p>You see, physics grows gradually more and more<span class="pagenum"><a name="Page_61" id="Page_61">[Pg 61]</a></span> +terrible. The physicist will soon have it in his power +to play the part of the famous lobster chained to the +bottom of the Lake of Mohrin, whose direful mission, +if ever liberated, the poet Kopisch humorously describes +as that of a reversal of all the events of the +world; the rafters of houses become trees again, cows +calves, honey flowers, chickens eggs, and the poet's +own poem flows back into his inkstand.</p> +<p><span class="pagenum"><a name="Page_62" id="Page_62">[Pg 62]</a></span></p><p><span class="pagenum"><a name="Page_63" id="Page_63">[Pg 63]</a></span></p><p><span class="pagenum"><a name="Page_64" id="Page_64">[Pg 64]</a></span></p> +<hr class="tb" /> + +<p>You will now allow me the privilege of a few general +remarks. You have seen that the same principle +often lies at the basis of large classes of apparatus +designed for different purposes. Frequently it is some +very unobtrusive idea which is productive of so much +fruit and of such extensive transformations in physical +technics. It is not otherwise here than in practical +life.</p> + +<p>The wheel of a waggon appears to us a very simple +and insignificant creation. But its inventor was certainly +a man of genius. The round trunk of a tree +perhaps first accidentally led to the observation of the +ease with which a load can be moved on a roller. +Now, the step from a simple supporting roller to a +fixed roller, or wheel, appears a very easy one. At +least it appears very easy to us who are accustomed +from childhood up to the action of the wheel. But if +we put ourselves vividly into the position of a man +who never saw a wheel, but had to invent one, we shall +begin to have some idea of its difficulties. Indeed, it +is even doubtful whether a single man could have accomplished +this feat, whether perhaps centuries were +not necessary to form the first wheel from the primitive +roller.<a name="FNanchor_16_16" id="FNanchor_16_16"></a><a href="#Footnote_16_16" class="fnanchor">[16]</a></p> + +<p>History does not name the progressive minds who +constructed the first wheel; their time lies far back of +the historic period. No scientific academy crowned +their efforts, no society of engineers elected them +honorary members. They still live only in the stupendous +results which they called forth. Take from +us the wheel, and little will remain of the arts and industries +of modern life. All disappears. From the +spinning-wheel to the spinning-mill, from the turning-lathe +to the rolling-mill, from the wheelbarrow to the +railway train, all vanishes.</p> + +<p>In science the wheel is equally important. Whirling +machines, as the simplest means of obtaining quick +motions with inconsiderable changes of place, play a +part in all branches of physics. You know Wheatstone's +rotating mirror, Fizeau's wheel, Plateau's perforated +rotating disks, etc. Almost the same principle +lies at the basis of all these apparatus. They differ +from one another no more than the pen-knife differs, +in the purposes it serves, from the knife of the anatomist +or the knife of the vine-dresser. Almost the same +might be said of the screw.</p> + +<p>It will now perhaps be clear to you that new +thoughts do not spring up suddenly. Thoughts need +their time to ripen, grow, and develop in, like every +natural product; for man, with his thoughts, is also a +part of nature.</p> + +<p>Slowly, gradually, and laboriously one thought is +transformed into a different thought, as in all likelihood +one animal species is gradually transformed into new +species. Many ideas arise simultaneously. They fight +the battle for existence not otherwise than do the +Ichthyosaurus, the Brahman, and the horse.</p> + +<p>A few remain to spread rapidly over all fields of +knowledge, to be redeveloped, to be again split up, to +begin again the struggle from the start. As many +animal species long since conquered, the relicts of +ages past, still live in remote regions where their enemies +cannot reach them, so also we find conquered +ideas still living on in the minds of many men. Whoever +will look carefully into his own soul will acknowledge +that thoughts battle as obstinately for existence +as animals. Who will gainsay that many vanquished +modes of thought still haunt obscure crannies of his +brain, too faint-hearted to step out into the clear light +of reason? What inquirer does not know that the +hardest battle, in the transformation of his ideas, is +fought with himself.</p> + +<p>Similar phenomena meet the natural inquirer in all +paths and in the most trifling matters. The true inquirer +seeks the truth everywhere, in his country-walks +and on the streets of the great city. If he is +not too learned, he will observe that certain things, +like ladies' hats, are constantly subject to change. I +have not pursued special studies on this subject, but +as long as I can remember, one form has always +gradually changed into another. First, they wore hats +with long projecting rims, within which, scarcely accessible +with a telescope, lay concealed the face of the +beautiful wearer. The rim grew smaller and smaller; +the bonnet shrank to the irony of a hat. Now a tremendous +superstructure is beginning to grow up in its +place, and the gods only know what its limits will be. +It is not otherwise with ladies' hats than with butterflies, +whose multiplicity of form often simply comes +from a slight excrescence on the wing of one species +developing in a cognate species to a tremendous fold. +Nature, too, has its fashions, but they last thousands +of years. I could elucidate this idea by many additional +examples; for instance, by the history of the +evolution of the coat, if I were not fearful that my +gossip might prove irksome to you.</p> +<p><span class="pagenum"><a name="Page_65" id="Page_65">[Pg 65]</a></span></p><p><span class="pagenum"><a name="Page_66" id="Page_66">[Pg 66]</a></span></p> +<hr class="tb" /> + +<p>We have now wandered through an odd corner of +the history of science. What have we learned? The +solution of a small, I might almost say insignificant, +problem—the measurement of the velocity of light. +And more than two centuries have worked at its solution! +Three of the most eminent natural philosophers, +Galileo, an Italian, Römer, a Dane, and Fizeau, a +Frenchman, have fairly shared its labors. And so it +is with countless other questions. When we contemplate +thus the many blossoms of thought that must +wither and fall before one shall bloom, then shall we +first truly appreciate Christ's weighty but little consolatory +words: "Many be called but few are chosen."</p> + +<p>Such is the testimony of every page of history. +But is history right? Are really only those chosen +whom she names? Have those lived and battled in +vain, who have won no prize?</p> + +<p>I doubt it. And so will every one who has felt the +pangs of sleepless nights spent in thought, at first fruitless, +but in the end successful. No thought in such +struggles was thought in vain; each one, even the most +insignificant, nay, even the erroneous thought, that +which apparently was the least productive, served to +prepare the way for those that afterwards bore fruit. +And as in the thought of the individual naught is in +vain, so, also, it is in that of humanity.</p> + +<p>Galileo wished to measure the velocity of light. +He had to close his eyes before his wish was realised. +But he at least found the lantern by which his successor +could accomplish the task.</p> + +<p>And so I may maintain that we all, so far as inclination +goes, are working at the civilisation of the future. +If only we all strive for the right, then are we <i>all</i> +called and <i>all</i> chosen!</p> + + + + +<h2><a name="WHY_HAS_MAN_TWO_EYES" id="WHY_HAS_MAN_TWO_EYES">WHY HAS MAN TWO EYES?</a></h2> + + +<p>Why has man two eyes? That the pretty symmetry +of his face may not be disturbed, the +artist answers. That his second eye may furnish a +substitute for his first if that be lost, says the far-sighted +economist. That we may weep with two eyes +at the sins of the world, replies the religious enthusiast.</p> + +<p>Odd opinions! Yet if you should approach a modern +scientist with this question you might consider +yourself fortunate if you escaped with less than a rebuff. +"Pardon me, madam, or my dear sir," he would +say, with stern expression, "man fulfils no purpose in +the possession of his eyes; nature is not a person, and +consequently not so vulgar as to pursue purposes of +any kind."</p> + +<p>Still an unsatisfactory answer! I once knew a professor +who would shut with horror the mouths of his +pupils if they put to him such an unscientific question.</p> + +<p>But ask a more tolerant person, ask me. I, I candidly +confess, do not know exactly why man has two<span class="pagenum"><a name="Page_67" id="Page_67">[Pg 67]</a></span> +eyes, but the reason partly is, I think, that I may see +you here before me to-night and talk with you upon +this delightful subject.</p> + +<p>Again you smile incredulously. Now this is one of +those questions that a hundred wise men together +could not answer. You have heard, so far, only five of +these wise men. You will certainly want to be spared +the opinions of the other ninety-five. To the first you +will reply that we should look just as pretty if we were +born with only one eye, like the Cyclops; to the second +we should be much better off, according to his +principle, if we had four or eight eyes, and that in this +respect we are vastly inferior to spiders; to the third, +that you are not just in the mood to weep; to the +fourth, that the unqualified interdiction of the question +excites rather than satisfies your curiosity; while of +me you will dispose by saying that my pleasure is not +as intense as I think, and certainly not great enough +to justify the existence of a double eye in man since +the fall of Adam.</p> + +<p>But since you are not satisfied with my brief and +obvious answer, you have only yourselves to blame +for the consequences. You must now listen to a longer +and more learned explanation, such as it is in my +power to give.</p> + +<p>As the church of science, however, debars the question +"Why?" let us put the matter in a purely orthodox +way: Man has two eyes, what <i>more</i> can he see with +two than with one?</p><p><span class="pagenum"><a name="Page_68" id="Page_68">[Pg 68]</a></span></p> + +<p>I will invite you to take a walk with me? We see +before us a wood. What is it that makes this real +wood contrast so favorably with a painted wood, no +matter how perfect the painting may be? What makes +the one so much more lovely than the other? Is it the +vividness of the coloring, the distribution of the lights +and the shadows? I think +not. On the contrary, it +seems to me that in this +respect painting can accomplish +very much.</p> + +<p>The cunning hand of +the painter can conjure up +with a few strokes of his +brush forms of wonderful +plasticity. By the help of +other means even more +can be attained. Photographs +of reliefs are so +plastic that we often imagine +we can actually lay +hold of the elevations and +depressions.</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_078.jpg" width="300" height="496" alt="" /> +<span class="caption">Fig. 20.</span> +</div> + +<p>But one thing the painter never can give with the +vividness that nature does—the difference of near and +far. In the real woods you see plainly that you can +lay hold of some trees, but that others are inaccessibly +far. The picture of the painter is rigid. The picture +of the real woods changes on the slightest movement.<span class="pagenum"><a name="Page_69" id="Page_69">[Pg 69]</a></span> +Now this branch is hidden behind that; now that behind +this. The trees are alternately visible and invisible.</p> + +<p>Let us look at this matter a little more closely. +For convenience sake we shall remain upon the highway, +I, II. (Fig. 20.) To the right and the left lies the +forest. Standing at I, we see, let us say, three trees +(1, 2, 3) in a line, so that the two remote ones are +covered by the nearest. Moving further along, this +changes. At II we shall not have to look round so far +to see the remotest tree 3 as to see the nearer tree 2, +nor so far to see this as to see 1. <i>Hence, as we move +onward, objects that are near to us seem to lag behind as +compared with objects that are remote from us, the lagging +increasing with the proximity of the objects.</i> Very remote +objects, towards which we must always look in the +same direction as we proceed, appear to travel along +with us.</p> + +<p>If we should see, therefore, jutting above the brow +of yonder hill the tops of two trees whose distance +from us we were in doubt about, we should have in +our hands a very easy means of deciding the question. +We should take a few steps forward, say to the right, +and the tree-top which receded most to the left would +be the one nearer to us. In truth, from the amount +of the recession a geometer could actually determine +the distance of the trees from us without ever going +near them. It is simply the scientific development of<span class="pagenum"><a name="Page_70" id="Page_70">[Pg 70]</a></span> +this perception that enables us to measure the distances +of the stars.</p> + +<p><i>Hence, from change of view in forward motion the +distances of objects in our field of vision can be measured.</i></p> + +<p>Rigorously, however, even forward motion is not +necessary. For every observer is composed really of +<i>two</i> observers. Man has <i>two</i> eyes. The right eye is +a short step ahead of the left eye in the right-hand direction. +Hence, the two eyes receive <i>different</i> pictures +of the same woods. The right eye will see the +near trees displaced to the left, and the left eye will +see them displaced to the right, the displacement being +greater, the greater the proximity. This difference is +sufficient for forming ideas of distance.</p> + +<p>We may now readily convince ourselves of the following +facts:</p> + +<p>1. With one eye, the other being shut, you have a +very uncertain judgment of distances. You will find +it, for example, no easy task, with one eye shut, to +thrust a stick through a ring hung up before you; you +will miss the ring in almost every instance.</p> + +<p>2. You see the same object differently with the +right eye from what you do with the left.</p> + +<p>Place a lamp-shade on the table in front of you +with its broad opening turned downwards, and look +at it from above. (Fig. 21.) You will see with your +right eye the image 2, with your left eye the image 1. +Again, place the shade with its wide opening turned +upwards; you will receive with your right eye the image<span class="pagenum"><a name="Page_71" id="Page_71">[Pg 71]</a></span> +4, with your left eye the image 3. Euclid mentions +phenomena of this character.</p> + +<p>3. Finally, you know that it is easy to judge of +distances with both eyes. Accordingly your judgment +must spring in some way from a co-operation of the +two eyes. In the preceding example the openings in +the different images received by the two eyes seem +displaced with respect to one another, and this displacement +is sufficient for the inference that the one +opening is nearer than the other.</p> + +<div class="figcenter" style="width: 450px;"> +<img src="images/i_081.jpg" width="450" height="446" alt="" /> +<span class="caption">Fig. 21.</span> +</div> + +<p>I have no doubt that you, ladies, have frequently +received delicate compliments upon your eyes, but I<span class="pagenum"><a name="Page_72" id="Page_72">[Pg 72]</a></span> +feel sure that no one has ever told you, and I know not +whether it will flatter you, that you have in your eyes, +be they blue or black, little geometricians. You say +you know nothing of them? Well, for that matter, +neither do I. But the facts are as I tell you.</p> + +<p>You understand little of geometry? I shall accept +that confession. Yet with the help of your two eyes +you judge of distances? Surely that is a geometrical +problem. And what is more, you know the solution +of this problem: for you estimate distances correctly. +If, then, <i>you</i> do not solve the problem, the little geometricians +in your eyes must do it clandestinely and whisper +the solution to you. I doubt not they are fleet little +fellows.</p> + +<p>What amazes me most here is, that you know nothing +about these little geometricians. But perhaps they +also know nothing about you. Perhaps they are models +of punctuality, routine clerks who bother about +nothing but their fixed work. In that case we may +be able to deceive the gentlemen.</p> + +<p>If we present to our right eye an image which looks +exactly like the lamp-shade for the right eye, and to +our left eye an image which looks exactly like a lamp-shade +for the left eye, we shall imagine that we see +the whole lamp-shade bodily before us.</p> + +<p>You know the experiment. If you are practised in +squinting, you can perform it directly with the figure, +looking with your right eye at the right image, and +with your left eye at the left image. In this way the<span class="pagenum"><a name="Page_73" id="Page_73">[Pg 73]</a></span> +experiment was first performed by Elliott. Improved +and perfected, its form is Wheatstone's stereoscope, +made so popular and useful by Brewster.</p> + +<p>By taking two photographs of the same object from +two different points, corresponding to the two eyes, a +very clear three-dimensional picture of distant places +or buildings can be produced by the stereoscope.</p> + +<p>But the stereoscope accomplishes still more than +this. It can visualise things for us which we never see +with equal clearness in real objects. You know that +if you move much while your photograph is being +taken, your picture will come out like that of a Hindu +deity, with several heads or several arms, which, at +the spaces where they overlap, show forth with equal +distinctness, so that we seem to see the one picture +<i>through</i> the other. If a person moves quickly away +from the camera before the impression is completed, +the objects behind him will also be imprinted upon +the photograph; the person will look transparent. +Photographic ghosts are made in this way.</p> + +<p>Some very useful applications may be made of this +discovery. For example, if we photograph a machine +stereoscopically, successively removing during the +operation the single parts (where of course the impression +suffers interruptions), we obtain a transparent +view, endowed with all the marks of spatial solidity, +in which is distinctly visualised the interaction of parts +normally concealed. I have employed this method for<span class="pagenum"><a name="Page_74" id="Page_74">[Pg 74]</a></span> +obtaining transparent stereoscopic views of anatomical +structures.</p> + +<p>You see, photography is making stupendous advances, +and there is great danger that in time some +malicious artist will photograph his innocent patrons +with solid views of their most secret thoughts and +emotions. How tranquil politics will then be! What +rich harvests our detective force will reap!</p> +<p><span class="pagenum"><a name="Page_75" id="Page_75">[Pg 75]</a></span><span class="pagenum"><a name="Page_76" id="Page_76">[Pg 76]</a></span><span class="pagenum"><a name="Page_77" id="Page_77">[Pg 77]</a></span><span class="pagenum"><a name="Page_78" id="Page_78">[Pg 78]</a></span><span class="pagenum"><a name="Page_79" id="Page_79">[Pg 79]</a></span><span class="pagenum"><a name="Page_80" id="Page_80">[Pg 80]</a></span><span class="pagenum"><a name="Page_81" id="Page_81">[Pg 81]</a></span><span class="pagenum"><a name="Page_82" id="Page_82">[Pg 82]</a></span><span class="pagenum"><a name="Page_83" id="Page_83">[Pg 83]</a></span><span class="pagenum"><a name="Page_84" id="Page_84">[Pg 84]</a></span><span class="pagenum"><a name="Page_85" id="Page_85">[Pg 85]</a></span><span class="pagenum"><a name="Page_86" id="Page_86">[Pg 86]</a></span></p> +<hr class="tb" /> + +<p>By the joint action of the two eyes, therefore, we +arrive at our judgments of distances, as also of the +forms of bodies.</p> + +<p>Permit me to mention here a few additional facts +connected with this subject, which will assist us in the +comprehension of certain phenomena in the history of +civilisation.</p> + +<p>You have often heard, and know from personal experience, +that remote objects appear perspectively +dwarfed. In fact, it is easy to satisfy yourself that +you can cover the image of a man a few feet away +from you simply by holding up your finger a short distance +in front of your eye. Still, as a general rule, +you do not notice this shrinkage of objects. On the +contrary, you imagine you see a man at the end of a +large hall, as large as you see him near by you. For +your eye, in its measurement of the distances, makes +remote objects correspondingly larger. The eye, so to +speak, is aware of this perspective contraction and is +not deceived by it, although its possessor is unconscious +of the fact. All persons who have attempted to draw +from nature have vividly felt the difficulty which this +superior dexterity of the eye causes the perspective +conception. Not until one's judgment of distances is +made uncertain, by their size, or from lack of points +of reference, or from being too quickly changed, is the +perspective rendered very prominent.</p> + +<p>On sweeping round a curve on a rapidly moving +railway train, where a wide prospect is suddenly +opened up, the men upon distant hills appear like +dolls.<a name="FNanchor_17_17" id="FNanchor_17_17"></a><a href="#Footnote_17_17" class="fnanchor">[17]</a> You have at the moment, here, no known +references for the measurement of distances. The +stones at the entrance of a tunnel grow visibly larger +as we ride towards it; they shrink visibly in size as we +ride from it.</p> + +<p>Usually both eyes work together. As certain views +are frequently repeated, and lead always to substantially +the same judgments of distances, the eyes in +time must acquire a special skill in geometrical constructions. +In the end, undoubtedly, this skill is so +increased that a single eye alone is often tempted to +exercise that office.</p> + +<p>Permit me to elucidate this point by an example. +Is any sight more familiar to you than that of a vista +down a long street? Who has not looked with hopeful +eyes time and again into a street and measured its +depth. I will take you now into an art-gallery where +I will suppose you to see a picture representing a vista +into a street. The artist has not spared his rulers to +get his perspective perfect. The geometrician in your +left eye thinks, "Ah ha! I have computed that case a +hundred times or more. I know it by heart. It is a +vista into a street," he continues; "where the houses +are lower is the remote end." The geometrician in +the right eye, too much at his ease to question his +possibly peevish comrade in the matter, answers the +same. But the sense of duty of these punctual little +fellows is at once rearoused. They set to work at their +calculations and immediately find that all the points +of the picture are equally distant from them, that is, +lie all upon a plane surface.</p> + +<p>What opinion will you now accept, the first or the +second? If you accept the first you will see distinctly +the vista. If you accept the second you will see nothing +but a painted sheet of distorted images.</p> + +<p>It seems to you a trifling matter to look at a picture +and understand its perspective. Yet centuries +elapsed before humanity came fully to appreciate this +trifle, and even the majority of you first learned it from +education.</p> + +<p>I can remember very distinctly that at three years +of age all perspective drawings appeared to me as +gross caricatures of objects. I could not understand +why artists made tables so broad at one end and so +narrow at the other. Real tables seemed to me just +as broad at one end as at the other, because my eye +made and interpreted its calculations without my intervention. +But that the picture of the table on the +plane surface was not to be conceived as a plane painted +surface but stood for a table and so was to be imaged +with all the attributes of extension was a joke that I +did not understand. But I have the consolation that +whole nations have not understood it.</p> + +<p>Ingenuous people there are who take the mock +murders of the stage for real murders, the dissembled +actions of the players for real actions, and who can +scarcely restrain themselves, when the characters of the +play are sorely pressed, from running in deep indignation +to their assistance. Others, again, can never forget +that the beautiful landscapes of the stage are +painted, that Richard III. is only the actor, Mr. Booth, +whom they have met time and again at the clubs.</p> + +<p>Both points of view are equally mistaken. To look +at a drama or a picture properly one must understand +that both are <i>shows</i>, simply <i>denoting</i> something real. +A certain preponderance of the intellectual life over +the sensuous life is requisite for such an achievement, +where the intellectual elements are safe from destruction +by the direct sensuous impressions. A certain +liberty in choosing one's point of view is necessary, a +sort of humor, I might say, which is strongly wanting +in children and in childlike peoples.</p> + +<p>Let us look at a few historical facts. I shall not +take you as far back as the stone age, although we +possess sketches from this epoch which show very original +ideas of perspective. But let us begin our sight-seeing +in the tombs and ruined temples of ancient +Egypt, where the numberless reliefs and gorgeous colorings +have defied the ravages of thousands of years.</p> + +<p>A rich and motley life is here opened to us. We +find the Egyptians represented in all conditions of life. +What at once strikes our attention in these pictures +is the delicacy of their technical execution. The contours +are extremely exact and distinct. But on the +other hand only a few bright colors are found, unblended +and without trace of transition. Shadows are +totally wanting. The paint is laid on the surfaces in +equal thicknesses.</p> + +<p>Shocking for the modern eye is the perspective. +All the figures are equally large, with the exception of +the king, whose form is unduly exaggerated. Near and +far appear equally large. Perspective contraction is +nowhere employed. A pond with water-fowl is represented +flat, as if its surface were vertical.</p> + +<p>Human figures are portrayed as they are never +seen, the legs from the side, the face in profile. The +breast lies in its full breadth across the plane of representation. +The heads of cattle appear in profile, +while the horns lie in the plane of the drawing. The +principle which the Egyptians followed might be best +expressed by saying that their figures are pressed in +the plane of the drawing as plants are pressed in a +herbarium.</p> + +<p>The matter is simply explained. If the Egyptians +were accustomed to looking at things ingenuously +with both eyes at once, the construction of perspective +pictures in space could not be familiar to them. +They saw all arms, all legs on real men in their natural +lengths. The figures pressed into the planes resembled +more closely, of course, in their eyes the +originals than perspective pictures could.</p> + +<p>This will be better understood if we reflect that +painting was developed from relief. The minor dissimilarities +between the pressed figures and the originals +must gradually have compelled men to the adoption +of perspective drawing. But physiologically the +painting of the Egyptians is just as much justified as +the drawings of our children are.</p> + +<p>A slight advance beyond the Egyptians is shown +by the Assyrians. The reliefs rescued from the ruined +mounds of Nimrod at Mossul are, upon the whole, +similar to the Egyptian reliefs. They were made known +to us principally by Layard.</p> + +<p>Painting enters on a new phase among the Chinese. +This people have a marked feeling for perspective +and correct shading, yet without being very logical +in the application of their principles. Here, too, +it seems, they took the first step but did not go far. +In harmony with this immobility is their constitution, +in which the muzzle and the bamboo-rod play significant +functions. In accord with it, too, is their +language, which like the language of children has not +yet developed into a grammar, or, rather, according +to the modern conception, has not yet degenerated +into a grammar. It is the same also with their music +which is satisfied with the five-toned scale.</p> + +<p>The mural paintings at Herculaneum and Pompeii +are distinguished by grace of representation, as also +by a pronounced sense for perspective and correct illumination, +yet they are not at all scrupulous in construction. +Here still we find abbreviations avoided. +But to offset this defect, the members of the body are +brought into unnatural positions, in which they appear +in their full lengths. Abridgements are more frequently +observed in clothed than in unclothed figures.</p> + +<p>A satisfactory explanation of these phenomena first +occurred to me on the making of a few simple experiments +which show how differently one may see the +same object, after some mastery of one's senses has +been attained, simply by the arbitrary +movement of the attention.</p> + +<div class="figcenter" style="width: 150px;"> +<img src="images/i_090.jpg" width="150" height="191" alt="" /> +<span class="caption">Fig. 22.</span> +</div> + +<p>Look at the annexed drawing (Fig. 22). +It represents a folded sheet of paper with +either its depressed or its elevated side +turned towards you, as you wish. You can +conceive the drawing in either sense, and +in either case it will appear to you differently.</p> + +<p>If, now, you have a real folded sheet of paper on +the table before you, with its sharp edges turned towards +you, you can, on looking at it with one eye, see +the sheet alternately elevated, as it really is, or depressed. +Here, however, a remarkable phenomenon +is presented. When you see the sheet properly, neither +illumination nor form presents anything conspicuous. +When you see it bent back you see it perspectively +distorted. Light and shadow appear much brighter +or darker, or as if overlaid thickly with bright colors. +Light and shadow now appear devoid of all cause. +They no longer harmonise with the body's form, and +are thus rendered much more prominent.</p> + +<p>In common life we employ the perspective and +illumination of objects to determine their forms and +position. Hence we do not notice the lights, the +shadows, and the distortions. They first powerfully +enter consciousness when we employ a different construction +from the usual spatial one. In looking at +the planar image of a camera obscura we are amazed +at the plenitude of the light and the profundity of the +shadows, both of which we do not notice in real objects.</p> + +<p>In my earliest youth the shadows and lights on pictures +appeared to me as spots void of meaning. When +I began to draw I regarded shading as a mere custom +of artists. I once drew the portrait of our pastor, a +friend of the family, and shaded, from no necessity, +but simply from having seen something similar in +other pictures, the whole half of his face black. I was +subjected for this to a severe criticism on the part of +my mother, and my deeply offended artist's pride is +probably the reason that these facts remained so +strongly impressed upon my memory.</p> + +<p>You see, then, that many strange things, not only +in the life of individuals, but also in that of humanity, +and in the history of general civilisation, may be explained +from the simple fact that man has two eyes.</p> + +<p>Change man's eye and you change his conception +of the world. We have observed the truth of this fact +among our nearest kin, the Egyptians, the Chinese, +and the lake-dwellers; how must it be among some of +our remoter relatives,—with monkeys and other animals? +Nature must appear totally different to animals +equipped with substantially different eyes from those +of men, as, for example, to insects. But for the present +science must forego the pleasure of portraying this +appearance, as we know very little as yet of the mode +of operation of these organs.</p> + +<p>It is an enigma even how nature appears to animals +closely related to man; as to birds, who see +scarcely anything with two eyes at once, but since +their eyes are placed on opposite sides of their heads, +have a separate field of vision for each.<a name="FNanchor_18_18" id="FNanchor_18_18"></a><a href="#Footnote_18_18" class="fnanchor">[18]</a></p> + +<p>The soul of man is pent up in the prison-house of +his head; it looks at nature through its two windows, +the eyes. It would also fain know how nature looks +through other windows. A desire apparently never to +be fulfilled. But our love for nature is inventive, and +here, too, much has been accomplished.</p> + +<p>Placing before me an angular mirror, consisting of +two plane mirrors slightly inclined to each other, I see +my face twice reflected. In the right-hand mirror I +obtain a view of the right side, and in the left-hand +mirror a view of the left +side, of my face. Also +I shall see the face of a +person standing in front +of me, more to the right with my right eye, more to +the left with my left. But in order to obtain such +widely different views of a face as those shown in the +angular mirror, my two eyes would have to be set much +further apart from each other than they actually are.</p> + +<div class="figright" style="width: 220px;"> +<img src="images/i_093.jpg" width="220" height="54" alt="" /> +<span class="caption">Fig. 23.</span> +</div> + +<p>Squinting with my right eye at the image in the +right-hand mirror, with my left eye at the image in +the left-hand mirror, my vision will be the vision of a +giant having an enormous head with his two eyes set +far apart. This, also, is the impression which my own +face makes upon me. I see it now, single and solid. +Fixing my gaze, the relief from second to second is +magnified, the eyebrows start forth prominently from +above the eyes, the nose seems to grow a foot in +length, my mustache shoots forth like a fountain from +my lip, the teeth seem to retreat immeasurably. But +by far the most horrible aspect of the phenomenon is +the nose.</p> + +<p>Interesting in this connexion is the telestereoscope +of Helmholtz. In the telestereoscope we view a landscape +by looking with our right eye (Fig. 24) through +the mirror <i>a</i> into the mirror <i>A</i>, and with our left eye +through the mirror <i>b</i> into the mirror <i>B</i>. The mirrors +<i>A</i> and <i>B</i> stand far apart. +Again we see with the +widely separated eyes +of a giant. Everything +appears dwarfed and +near us. The distant +mountains look like +moss-covered stones at our feet. Between, you see the +reduced model of a city, a veritable Liliput. You +are tempted almost to stroke with your hand the soft +forest and city, did you not fear that you might prick +your fingers on the sharp, needle-shaped steeples, or +that they might crackle and break off.</p> + +<div class="figleft" style="width: 350px;"> +<img src="images/i_094.jpg" width="350" height="201" alt="" /> +<span class="caption">Fig. 24.</span> +</div> + +<p>Liliput is no fable. We need only Swift's eyes, +the telestereoscope, to see it.</p> + +<p>Picture to yourself the reverse case. Let us suppose +ourselves so small that we could take long walks +in a forest of moss, and that our eyes were correspondingly +near each other. The moss-fibres would appear +like trees. On them we should see strange, unshapely +monsters creeping about. Branches of the oak-tree, +at whose base our moss-forest lay, would seem to us +dark, immovable, myriad-branched clouds, painted +high on the vault of heaven; just as the inhabitants +of Saturn, forsooth, might see their enormous ring. +On the tree-trunks of our mossy woodland we should +find colossal globes several feet in diameter, brilliantly +transparent, swayed by the winds with slow, peculiar +motions. We should approach inquisitively and should +find that these globes, in which here and there animals +were gaily sporting, were liquid globes, in fact +that they were water. A short, incautious step, the +slightest contact, and woe betide us, our arm is irresistibly +drawn by an invisible power into the interior of +the sphere and held there unrelentingly fast! A drop +of dew has engulfed in its capillary maw a manikin, +in revenge for the thousands of drops that its big human +counterparts have quaffed at breakfast. Thou +shouldst have known, thou pygmy natural scientist, +that with thy present puny bulk thou shouldst not joke +with capillarity!</p> + +<p>My terror at the accident brings me back to my +senses. I see I have turned idyllic. You must pardon +me. A patch of greensward, a moss or heather forest +with its tiny inhabitants have incomparably more +charms for me than many a bit of literature with its +apotheosis of human character. If I had the gift of +writing novels I should certainly not make John and +Mary my characters. Nor should I transfer my loving +pair to the Nile, nor to the age of the old Egyptian +Pharaohs, although perhaps I should choose that time +in preference to the present. For I must candidly +confess that I hate the rubbish of history, interesting +though it may be as a mere phenomenon, because we +cannot simply observe it but must also <i>feel</i> it, because +it comes to us mostly with supercilious arrogance, +mostly unvanquished. The hero of my novel would be +a cockchafer, venturing forth in his fifth year for the +first time with his newly grown wings into the light, +free air. Truly it could do no harm if man would thus +throw off his inherited and acquired narrowness of +mind by making himself acquainted with the world-view +of allied creatures. He could not help gaining +incomparably more in this way than the inhabitant of +a small town would in circumnavigating the globe and +getting acquainted with the views of strange peoples.</p> +<p><span class="pagenum"><a name="Page_87" id="Page_87">[Pg 87]</a></span></p><p><span class="pagenum"><a name="Page_88" id="Page_88">[Pg 88]</a></span></p><p><span class="pagenum"><a name="Page_89" id="Page_89">[Pg 89]</a></span></p> +<hr class="tb" /> + +<p>I have now conducted you, by many paths and by-ways, +rapidly over hedge and ditch, to show you what +wide vistas we may reach in every field by the rigorous +pursuit of a single scientific fact. A close examination +of the two eyes of man has conducted us not +only into the dim recesses of humanity's childhood, +but has also carried us far beyond the bourne of human +life.</p> + +<p>It has surely often struck you as strange that the +sciences are divided into two great groups; that the +so-called humanistic sciences, belonging to the so-called +"higher education," are placed in almost a hostile +attitude to the natural sciences.</p> + +<p>I must confess I do not overmuch believe in this +partition of the sciences. I believe that this view will +appear as childlike and ingenuous to a matured age +as the want of perspective in the old paintings of Egypt +does to us. Can it really be that "higher culture" is to +be gotten only from a few old pots and palimpsests, +which are at best mere scraps of nature, or that more +is to be learned from them alone than from all the rest +of nature? I believe that both these sciences are simply +parts of the same science, which have begun at +different ends. If these two ends still act towards +each other as the Montagues and Capulets, if their retainers +still indulge in lively tilts, I believe that after +all they are not in earnest. On the one side there is +surely a Romeo, and on the other a Juliet, who, some +day, it is hoped, will unite the two houses with a less +tragic sequel than that of the play.</p> + +<p>Philology began with the unqualified reverence and +apotheosis of the Greeks. Now it has begun to draw +other languages, other peoples and their histories, into +its sphere; it has, through the mediation of comparative +linguistics, already struck up, though as yet somewhat +cautiously, a friendship with physiology.</p> + +<p>Physical science began in the witch's kitchen. It +now embraces the organic and inorganic worlds, and +with the physiology of articulation and the theory of +the senses, has even pushed its researches, at times +impertinently, into the province of mental phenomena.</p> + +<p>In short, we come to the understanding of much +within us solely by directing our glance without, and +<i>vice versa</i>. Every object belongs to both sciences. +You, ladies, are very interesting and difficult problems +for the psychologist, but you are also extremely pretty +phenomena of nature. Church and State are objects +of the historian's research, but not less phenomena of +nature, and in part, indeed, very curious phenomena. +If the historical sciences have inaugurated wide extensions +of view by presenting to us the thoughts of +new and strange peoples, the physical sciences in a +certain sense do this in a still greater degree. In +making man disappear in the All, in annihilating him, +so to speak, they force him to take an unprejudiced +position without himself, and to form his judgments by +a different standard from that of the petty human.</p> + +<p>But if you should ask me now why man has two +eyes, I should answer:</p> + +<p>That he may look at nature justly and accurately; +that he may come to understand that he himself, with +all his views, correct and incorrect, with all his <i>haute +politique</i>, is simply an evanescent shred of nature; +that, to speak with Mephistopheles, he is a part of the +part, and that it is absolutely unjustified,</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"For man, the microcosmic fool, to see<br /></span> +<span class="i0">Himself a whole so frequently."<br /></span> +</div></div> + + + + +<h2><a name="ON_SYMMETRY" id="ON_SYMMETRY">ON SYMMETRY.</a></h2><p><a name="FNanchor_19_19" id="FNanchor_19_19"></a><a href="#Footnote_19_19" class="fnanchor">[19]</a></p> + + +<p>An ancient philosopher once remarked that people +who cudgelled their brains about the nature of +the moon reminded him of men who discussed the +laws and institutions of a distant city of which they +had heard no more than the name. The true philosopher, +he said, should turn his glance within, should +study himself and his notions of right and wrong; only +thence could he derive real profit.</p> + +<p>This ancient formula for happiness might be restated +in the familiar words of the Psalm:</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"Dwell in the land, and verily thou shalt be fed."<br /></span> +</div></div> + +<p>To-day, if he could rise from the dead and walk +about among us, this philosopher would marvel much +at the different turn which matters have taken.</p> +<p><span class="pagenum"><a name="Page_90" id="Page_90">[Pg 90]</a></span></p> +<p>The motions of the moon and the other heavenly +bodies are accurately known. Our knowledge of the +motions of our own body is by far not so complete. +The mountains and natural divisions of the moon have +been accurately outlined on maps, but physiologists +are just beginning to find their way in the geography +of the brain. The chemical constitution of many fixed +stars has already been investigated. The chemical +processes of the animal body are questions of much +greater difficulty and complexity. We have our <i>Mécanique +céleste</i>. But a <i>Mécanique sociale</i> or a <i>Mécanique +morale</i> of equal trustworthiness remains to be written.</p> + +<p>Our philosopher would indeed admit that we have +made great progress. But we have not followed his +advice. The patient has recovered, but he took for his +recovery exactly the opposite of what the doctor prescribed.</p> + +<p>Humanity is now returned, much wiser, from its +journey in celestial space, against which it was so +solemnly warned. Men, after having become acquainted +with the great and simple facts of the world without, +are now beginning to examine critically the world +within. It sounds absurd, but it is true, that only after +we have thought about the moon are we able to take +up ourselves. It was necessary that we should acquire +simple and clear ideas in a less complicated domain, +before we entered the more intricate one of psychology, +and with these ideas astronomy principally furnished +us.</p><p><span class="pagenum"><a name="Page_91" id="Page_91">[Pg 91]</a></span></p> + +<p>To attempt any description of that stupendous +movement, which, originally springing out of the physical +sciences, went beyond the domain of physics and is +now occupied with the problems of psychology, would +be presumptuous in this place. I shall only attempt +here, to illustrate to you by a few simple examples the +methods by which the province of psychology can be +reached from the facts of the physical world—especially +the adjacent province of sense-perception. And I wish +it to be remembered that my brief attempt is not to be +taken as a measure of the present state of such scientific +questions.</p> +<p><span class="pagenum"><a name="Page_92" id="Page_92">[Pg 92]</a></span></p><p><span class="pagenum"><a name="Page_93" id="Page_93">[Pg 93]</a></span></p><p><span class="pagenum"><a name="Page_94" id="Page_94">[Pg 94]</a></span></p><p><span class="pagenum"><a name="Page_95" id="Page_95">[Pg 95]</a></span></p><p><span class="pagenum"><a name="Page_96" id="Page_96">[Pg 96]</a></span></p><p><span class="pagenum"><a name="Page_97" id="Page_97">[Pg 97]</a></span></p><p><span class="pagenum"><a name="Page_98" id="Page_98">[Pg 98]</a></span></p><p><span class="pagenum"><a name="Page_99" id="Page_99">[Pg 99]</a></span></p><p><span class="pagenum"><a name="Page_100" id="Page_100">[Pg 100]</a></span></p><p><span class="pagenum"><a name="Page_101" id="Page_101">[Pg 101]</a></span></p><p><span class="pagenum"><a name="Page_102" id="Page_102">[Pg 102]</a></span></p><p><span class="pagenum"><a name="Page_103" id="Page_103">[Pg 103]</a></span></p><p><span class="pagenum"><a name="Page_104" id="Page_104">[Pg 104]</a></span></p> +<hr class="tb" /> + +<p>It is a well-known fact that some objects please us, +while others do not. Generally speaking, anything +that is constructed according to fixed and logically +followed rules, is a product of tolerable beauty. We see +thus nature herself, who always acts according to fixed +rules, constantly producing such pretty things. Every +day the physicist is confronted in his workshop with +the most beautiful vibration-figures, tone-figures, phenomena +of polarisation, and forms of diffraction.</p> + +<p>A rule always presupposes a repetition. Repetitions, +therefore, will probably be found to play some +important part in the production of agreeable effects. +Of course, the nature of agreeable effects is not exhausted +by this. Furthermore, the repetition of a +physical event becomes the source of agreeable effects +only when it is connected with a repetition of sensations.</p> + +<p>An excellent example that repetition of sensations +is a source of agreeable effects is furnished by the +copy-book of every schoolboy, which is usually a treasure-house +of such things, and only in need of an Abbé +Domenech to become celebrated. Any figure, no matter +how crude or poor, if several times repeated, with +the repetitions placed in line, will produce a tolerable +frieze.</p> + +<div class="figright" style="width: 300px;"> +<img src="images/i_102.jpg" width="300" height="185" alt="" /> +<span class="caption">Fig. 25.</span> +</div> + +<p>Also the pleasant effect of symmetry is due to the +repetition of sensations. Let us abandon ourselves a +moment to this thought, yet not imagine when we have +developed it, that we have fully exhausted the nature +of the agreeable, much less of the beautiful.</p> + +<p>First, let us get a clear conception of what symmetry +is. And in preference to a definition let us take +a living picture. You know that the reflexion of an +object in a mirror has a great likeness to the object itself. +All its proportions and outlines are the same. +Yet there is a difference between the object and its reflexion +in the mirror, which you will readily observe.</p> + +<p>Hold your right hand before a mirror, and you will +see in the mirror a left hand. Your right glove will +produce its mate in the glass. For you could never +use the reflexion of your right glove, if it were present +to you as a real thing, for covering your right hand, +but only for covering your left. Similarly, your right +ear will give as its reflexion a left ear; and you will at +once perceive that the left half of your body could very +easily be substituted for the reflexion of your right half. +Now just as in the place of a missing right ear a left ear +cannot be put, unless the lobule of the ear be turned upwards, +or the opening into the concha backwards, so, +despite all similarity of form, the reflexion of an object +can never take the place of the object itself.<a name="FNanchor_20_20" id="FNanchor_20_20"></a><a href="#Footnote_20_20" class="fnanchor">[20]</a></p> + +<p>The reason of this difference between the object +and its reflexion is simple. The reflexion appears as +far behind the mirror as the object is in front of it. The +parts of the object, accordingly, which are nearest the +mirror will also be nearest the mirror in the reflexion. +Consequently, the succession of the parts in the reflexion +will be reversed, as may best be seen in the reflexion +of the face of a watch or of a manuscript.</p> + +<p>It will also be readily seen, that if a point of the object +be joined with its reflexion in the image, the line +of junction will cut the mirror at right angles and be +bisected by it. This holds true of all corresponding +points of object and image.</p> + +<p>If, now, we can divide an object by a plane into +two halves so that each half, as seen in the reflecting +plane of division, is a reproduction of the other half, +such an object is termed symmetrical, and the plane +of division is called the plane of symmetry.</p> + +<p>If the plane of symmetry is vertical, we can say +that the body is vertically symmetrical. An example +of vertical symmetry is a Gothic cathedral.</p> + +<p>If the plane of symmetry is horizontal, we can say +that the object is horizontally symmetrical. A landscape +on the shores of a lake with its reflexion in the +water, is a system of horizontal symmetry.</p> + +<p>Exactly here is a noticeable difference. The vertical +symmetry of a Gothic cathedral strikes us at once, +whereas we can travel up and down the whole length +of the Rhine or the Hudson without becoming aware +of the symmetry between objects and their reflexions +in the water. Vertical symmetry pleases us, whilst +horizontal symmetry is indifferent, and is noticed only +by the experienced eye.</p> + +<p>Whence arises this difference? I say from the fact +that vertical symmetry produces a repetition of the +same sensation, while horizontal symmetry does not. +I shall now show that this is so.</p> + +<p>Let us look at the following letters:</p> + +<p class="center">d b +q p +</p> + +<p>It is a fact known to all mothers and teachers, that +children in their first attempts to read and write, constantly +confound d and b, and q and p, but never d +and q, or b and p. Now d and b and q and p are the +two halves of a <i>vertically</i> symmetrical figure, while d +and q, and b and p are two halves of a <i>horizontally</i> symmetrical +figure. The first two are confounded; but +confusion is only possible of things that excite in us +the same or similar sensations.</p> + +<p>Figures of two flower-girls are frequently seen on +the decorations of gardens and of drawing-rooms, one +of whom carries a flower-basket in her right hand and +the other a flower-basket in her left. All know how +apt we are, unless we are very careful, to confound these +figures with one another.</p> + +<p>While turning a thing round from right to left is +scarcely noticed, the eye is not at all indifferent to the +turning of a thing upside down. A human face which +has been turned upside down is scarcely recognisable +as a face, and makes an impression which is altogether +strange. The reason of this is not to be sought in the +unwontedness of the sight, for it is just as difficult to +recognise an arabesque that has been inverted, where +there can be no question of a habit. This curious fact +is the foundation of the familiar jokes played with the +portraits of unpopular personages, which are so drawn +that in the upright position of the page an exact picture +of the person is presented, but on being inverted +some popular animal is shown.</p> + +<p>It is a fact, then, that the two halves of a vertically +symmetrical figure are easily confounded and that they +therefore probably produce very nearly the same sensations. +The question, accordingly, arises, <i>why</i> do the +two halves of a vertically symmetrical figure produce +the same or similar sensations? The answer is: Because +our apparatus of vision, which consists of our +eyes and of the accompanying muscular apparatus is +itself vertically symmetrical.<a name="FNanchor_21_21" id="FNanchor_21_21"></a><a href="#Footnote_21_21" class="fnanchor">[21]</a></p> + +<p>Whatever external resemblances one eye may have +with another they are still not alike. The right eye of +a man cannot take the place of a left eye any more +than a left ear or left hand can take the place of a +right one. By artificial means, we can change the part +which each of our eyes plays. (Wheatstone's pseudoscope.) +But we then find ourselves in an entirely new +and strange world. What is convex appears concave; +what is concave, convex. What is distant appears +near, and what is near appears far.</p> + +<p>The left eye is the reflexion of the right. And the +light-feeling retina of the left eye is a reflexion of the +light-feeling retina of the right, in all its functions.</p> + +<p>The lense of the eye, like a magic lantern, casts +images of objects on the retina. And you may picture +to yourself the light-feeling retina of the eye, with its +countless nerves, as a hand with innumerable fingers, +adapted to feeling light. The ends of the visual nerves, +like our fingers, are endowed with varying degrees of +sensitiveness. The two retinæ act like a right and a +left hand; the sensation of touch and the sensation of +light in the two instances are similar.</p> + +<p>Examine the right-hand portion of this letter T: +namely, T. Instead of the two retinæ on which this +image falls, imagine feeling the object, my two hands. +The ┌, grasped with the right hand, gives a different +sensation from that which it gives when grasped with +the left. But if we turn our character about from right +to left, thus: ┐, it will give the same sensation in the +left hand that it gave before in the right. The sensation +is repeated.</p> + +<p>If we take a whole T, the right half will produce in +the right hand the same sensation that the left half +produces in the left, and <i>vice versa</i>.</p> + +<p>The symmetrical figure gives the same sensation +twice.</p> + +<p>If we turn the T over thus: ├, or invert the half +T thus: L, so long as we do not change the position +of our hands we can make no use of the foregoing reasoning.</p> + +<p>The retinæ, in fact, are exactly like our two hands. +They, too, have their thumbs and index fingers, though +they are thousands in number; and we may say the +thumbs are on the side of the eye near the nose, +and the remaining fingers on the side away from the +nose.</p> + +<p>With this I hope to have made perfectly clear that +the pleasing effect of symmetry is chiefly due to the +repetition of sensations, and that the effect in question +takes place in symmetrical figures, only where +there is a repetition of sensation. The pleasing effect +of regular figures, the preference which straight lines, +especially vertical and horizontal straight lines, enjoy, +is founded on a similar reason. A straight line, +both in a horizontal and in a vertical position, can cast +on the two retinæ the same image, which falls moreover +on symmetrically corresponding spots. This also, +it would appear, is the reason of our psychological +preference of straight to curved lines, and not their +property of being the shortest distance between two +points. The straight line is felt, to put the matter +briefly, as symmetrical to itself, which is the case also +with the plane. Curved lines are felt as deviations +from straight lines, that is, as deviations from symmetry.<a name="FNanchor_22_22" id="FNanchor_22_22"></a><a href="#Footnote_22_22" class="fnanchor">[22]</a> +The presence of a sense for symmetry in people +possessing only one eye from birth, is indeed a riddle. +Of course, the sense of symmetry, although primarily +acquired by means of the eyes, cannot be wholly limited +to the visual organs. It must also be deeply +rooted in other parts of the organism by ages of practice +and can thus not be eliminated forthwith by the +loss of one eye. Also, when an eye is lost, the symmetrical +muscular apparatus is left, as is also the +symmetrical apparatus of innervation.</p> + +<p>It appears, however, unquestionable that the phenomena +mentioned have, in the main, their origin in +the peculiar structure of our eyes. It will therefore +be seen at once that our notions of what is beautiful +and ugly would undergo a change if our eyes were different. +Also, if this view is correct, the theory of the +so-called eternally beautiful is somewhat mistaken. It +can scarcely be doubted that our culture, or form of +civilisation, which stamps upon the human body its +unmistakable traces, should not also modify our conceptions +of the beautiful. Was not formerly the development +of all musical beauty restricted to the narrow +limits of a five-toned scale?</p> + +<p>The fact that a repetition of sensations is productive +of pleasant effects is not restricted to the realm of +the visible. To-day, both the musician and the physicist +know that the harmonic or the melodic addition +of one tone to another affects us agreeably only when +the added tone reproduces a part of the sensation +which the first one excited. When I add an octave +to a fundamental tone, I hear in the octave a part of +what was heard in the fundamental tone. (Helmholtz.) +But it is not my purpose to develop this idea +fully here.<a name="FNanchor_23_23" id="FNanchor_23_23"></a><a href="#Footnote_23_23" class="fnanchor">[23]</a> We shall only ask to-day, whether there +is anything similar to the symmetry of figures in the +province of sounds.</p> + +<p>Look at the reflexion of your piano in the mirror.</p> + +<p>You will at once remark that you have never seen +such a piano in the actual world, for it has its high +keys to the left and its low ones to the right. Such +pianos are not manufactured.</p> + +<p>If you could sit down at such a piano and play in +your usual manner, plainly every step which you +imagined you were performing in the upward scale +would be executed as a corresponding step in the +downward scale. The effect would be not a little surprising.</p> + +<p>For the practised musician who is always accustomed +to hearing certain sounds produced when certain +keys are struck, it is quite an anomalous spectacle +to watch a player in the glass and to observe that he +always does the opposite of what we hear.</p> + +<p>But still more remarkable would be the effect of +attempting to strike a harmony on such a piano. For +a melody it is not indifferent whether we execute a +step in an upward or a downward scale. But for a +harmony, so great a difference is not produced by reversal. +I always retain the same consonance whether +I add to a fundamental note an upper or a lower third. +Only the order of the intervals of the harmony is reversed. +In point of fact, when we execute a movement +in a major key on our reflected piano, we hear a +sound in a minor key, and <i>vice versa</i>.</p> + +<p>It now remains to execute the experiments indicated. +Instead of playing upon the piano in the mirror, +which is impossible, or of having a piano of this +kind built, which would be somewhat expensive, we +may perform our experiments in a simpler manner, as +follows:</p> + +<p>1) We play on our own piano in our usual manner, +look into the mirror, and then repeat on our real piano +what we see in the mirror. In this way we transform +all steps upwards into corresponding steps downwards. +We play a movement, and then another movement, +which, with respect to the key-board, is symmetrical +to the first.</p> + +<p>2) We place a mirror beneath the music in which +the notes are reflected as in a body of water, and play +according to the notes in the mirror. In this way also, +all steps upwards are changed into corresponding, +equal steps downwards.</p> + +<p>3) We turn the music upside down and read the +notes from right to left and from below upwards. In +doing this, we must regard all sharps as flats and all +flats as sharps, because they correspond to half lines +and spaces. Besides, in this use of the music we can +only employ the bass clef, as only in this clef are the +notes not changed by symmetrical reversal.</p> + +<p>You can judge of the effect of these experiments +from the examples which appear in the annexed musical +cut. (Page 102.) The movement which appears in +the upper lines is symmetrically reversed in the lower.</p> + +<p>The effect of the experiments may be briefly formulated. +The melody is rendered unrecognisable. The +harmony suffers a transposition from a major into a +minor key and <i>vice versa</i>. The study of these pretty +effects, which have long been familiar to physicists +and musicians, was revived some years ago by Von +Oettingen.<a name="FNanchor_24_24" id="FNanchor_24_24"></a><a href="#Footnote_24_24" class="fnanchor">[24]</a></p> + +<div class="figcenter" style="width: 525px;"> +<img src="images/i_112.jpg" width="525" height="800" alt="" /> +<span class="caption">Fig. 26.</span><br /> +<a href="music/112a.mid">Listen to 1.</a><br /> +<a href="music/112b.mid">Listen to 2.</a><br /> +<a href="music/112c.mid">Listen to 3.</a><br /> +<a href="music/112d.mid">Listen to 4.</a><br /> +<a href="music/112e.mid">Listen to 5.</a><br /> +<a href="music/112f.mid">Listen to 6.</a><br /> +<a href="music/112g.mid">Listen to 7.</a><br /> +<a href="music/112h.mid">Listen to 8.</a><br /> +</div> + +<p>(See pages 101 and 103.)]</p> + +<p>Now, although in all the preceding examples I have +transposed steps upward into equal and similar steps +downward, that is, as we may justly say, have played +for every movement the movement which is symmetrical +to it, yet the ear notices either little or nothing of +symmetry. The transposition from a major to a minor +key is the sole indication of symmetry remaining. The +symmetry is there for the mind, but is wanting for +sensation. No symmetry exists for the ear, because a +reversal of musical sounds conditions no repetition of +sensations. If we had an ear for height and an ear +for depth, just as we have an eye for the right and an +eye for the left, we should also find that symmetrical +sound-structures existed for our auditory organs. The +contrast of major and minor for the ear corresponds to +inversion for the eye, which is also only symmetry for +the mind, but not for sensation.</p> + +<p>By way of supplement to what I have said, I will +add a brief remark for my mathematical readers.</p> + +<p>Our musical notation is essentially a graphical representation +of a piece of music in the form of curves, +where the time is the abscissæ, and the logarithms of +the number of vibrations the ordinates. The deviations +of musical notation from this principle are only +such as facilitate interpretation, or are due to historical +accidents.</p> + +<p>If, now, it be further observed that the sensation +of pitch also is proportional to the logarithm of the +number of vibrations, and that the intervals between +the notes correspond to the differences of the logarithms +of the numbers of vibrations, the justification +will be found in these facts of calling the harmonies +and melodies which appear in the mirror, symmetrical +to the original ones.</p> +<p><span class="pagenum"><a name="Page_105" id="Page_105">[Pg 105]</a></span></p><p><span class="pagenum"><a name="Page_106" id="Page_106">[Pg 106]</a></span></p><p><span class="pagenum"><a name="Page_107" id="Page_107">[Pg 107]</a></span></p> +<hr class="tb" /> + +<p>I simply wish to bring home to your minds by these +fragmentary remarks that the progress of the physical +sciences has been of great help to those branches of +psychology that have not scorned to consider the results +of physical research. On the other hand, psychology +is beginning to return, as it were, in a spirit +of thankfulness, the powerful stimulus which it received +from physics.</p> + +<p>The theories of physics which reduce all phenomena +to the motion and equilibrium of smallest particles, +the so-called molecular theories, have been +gravely threatened by the progress of the theory of the +senses and of space, and we may say that their days +are numbered.</p> + +<p>I have shown elsewhere<a name="FNanchor_25_25" id="FNanchor_25_25"></a><a href="#Footnote_25_25" class="fnanchor">[25]</a> that the musical scale is +simply a species of space—a space, however, of only +one dimension, and that, a one-sided one. If, now, a +person who could only hear, should attempt to develop +a conception of the world in this, his linear space, he +would become involved in many difficulties, as his space +would be incompetent to comprehend the many sides +of the relations of reality. But is it any more justifiable +for us, to attempt to force the whole world into the +space of our eye, in aspects in which it is not accessible +to the eye? Yet this is the dilemma of all molecular +theories.</p> + +<p>We possess, however, a sense, which, with respect +to the scope of the relations which it can comprehend, +is richer than any other. It is our reason. This stands +above the senses. It alone is competent to found a +permanent and sufficient view of the world. The +mechanical conception of the world has performed +wonders since Galileo's time. But it must now yield +to a broader view of things. A further development of +this idea is beyond the limits of my present purpose.</p> + +<p>One more point and I have done. The advice of +our philosopher to restrict ourselves to what is near +at hand and useful in our researches, which finds a +kind of exemplification in the present cry of inquirers +for limitation and division of labor, must not be too +slavishly followed. In the seclusion of our closets, we +often rack our brains in vain to fulfil a work, the +means of accomplishing which lies before our very +doors. If the inquirer must be perforce a shoemaker, +tapping constantly at his last, it may perhaps be permitted +him to be a shoemaker of the type of Hans +Sachs, who did not deem it beneath him to take a +look now and then at his neighbor's work and to +comment on the latter's doings.</p> + +<p>Let this be my apology, therefore, if I have forsaken +for a moment to-day the last of my specialty.</p> + + + + +<h2><a name="ON_THE_FUNDAMENTAL_CONCEPTS" id="ON_THE_FUNDAMENTAL_CONCEPTS">ON THE FUNDAMENTAL CONCEPTS +OF ELECTROSTATICS.</a><a name="FNanchor_26_26" id="FNanchor_26_26"></a><a href="#Footnote_26_26" class="fnanchor">[26]</a></h2> + + +<p>The task has been assigned me to develop before +you in a popular manner the fundamental quantitative +concepts of electrostatics—"quantity of electricity," +"potential," "capacity," and so forth. It +would not be difficult, even within the brief limits of +an hour, to delight the eye with hosts of beautiful experiments +and to fill the imagination with numerous +and varied conceptions. But we should, in such a +case, be still far from a lucid and easy grasp of the +phenomena. The means would still fail us for reproducing +the facts accurately in thought—a procedure +which for the theoretical and practical man is of equal +importance. These means are the <i>metrical concepts</i> of +electricity.</p> + +<p>As long as the pursuit of the facts of a given province +of phenomena is in the hands of a few isolated +investigators, as long as every experiment can be easily +repeated, the fixing of the collected facts by provisional<span class="pagenum"><a name="Page_108" id="Page_108">[Pg 108]</a></span> +description is ordinarily sufficient. But the case is +different when the whole world must make use of the +results reached by many, as happens when the science +acquires broader foundations and scope, and +particularly so when it begins to supply intellectual +nourishment to an important branch of the practical +arts, and to draw from that province in return stupendous +empirical results. Then the facts must be so +described that individuals in all places and at all times +can, from a few easily obtained elements, put the facts +accurately together in thought, and reproduce them +from the description. This is done with the help of +the metrical concepts and the international measures.</p> + +<p>The work which was begun in this direction in the +period of the purely scientific development of the science, +especially by Coulomb (1784), Gauss (1833), and +Weber (1846), was powerfully stimulated by the requirements +of the great technical undertakings manifested +since the laying of the first transatlantic cable, +and brought to a brilliant conclusion by the labors of +the British Association, 1861, and of the Paris Congress, +1881, chiefly through the exertions of Sir William +Thomson.</p> + +<p>It is plain, that in the time allotted to me I cannot +conduct you over all the long and tortuous paths which +the science has actually pursued, that it will not be +possible at every step to remind you of all the little +precautions for the avoidance of error which the early +steps have taught us. On the contrary, I must make<span class="pagenum"><a name="Page_109" id="Page_109">[Pg 109]</a></span> +shift with the simplest and rudest tools. I shall conduct +you by the shortest paths from the facts to the +ideas, in doing which, of course, it will not be possible +to anticipate all the stray and chance ideas which may +and must arise from prospects into the by-paths which +we leave untrodden.</p> +<p><span class="pagenum"><a name="Page_110" id="Page_110">[Pg 110]</a></span></p><p><span class="pagenum"><a name="Page_111" id="Page_111">[Pg 111]</a></span></p><p><span class="pagenum"><a name="Page_112" id="Page_112">[Pg 112]</a></span></p><p><span class="pagenum"><a name="Page_113" id="Page_113">[Pg 113]</a></span></p><p><span class="pagenum"><a name="Page_114" id="Page_114">[Pg 114]</a></span></p><p><span class="pagenum"><a name="Page_115" id="Page_115">[Pg 115]</a></span></p><p><span class="pagenum"><a name="Page_116" id="Page_116">[Pg 116]</a></span></p><p><span class="pagenum"><a name="Page_117" id="Page_117">[Pg 117]</a></span></p><p><span class="pagenum"><a name="Page_118" id="Page_118">[Pg 118]</a></span></p><p><span class="pagenum"><a name="Page_119" id="Page_119">[Pg 119]</a></span></p><p><span class="pagenum"><a name="Page_120" id="Page_120">[Pg 120]</a></span></p><p><span class="pagenum"><a name="Page_121" id="Page_121">[Pg 121]</a></span></p><p><span class="pagenum"><a name="Page_122" id="Page_122">[Pg 122]</a></span></p><p><span class="pagenum"><a name="Page_123" id="Page_123">[Pg 123]</a></span></p><p><span class="pagenum"><a name="Page_124" id="Page_124">[Pg 124]</a></span></p><p><span class="pagenum"><a name="Page_125" id="Page_125">[Pg 125]</a></span></p><p><span class="pagenum"><a name="Page_126" id="Page_126">[Pg 126]</a></span></p><p><span class="pagenum"><a name="Page_127" id="Page_127">[Pg 127]</a></span></p> +<hr class="tb" /> + +<p>Here are two small, light bodies (Fig. 27) of equal +size, freely suspended, which we "electrify" either +by friction with a third body or by contact with a body +already electrified. At once a repulsive force is set +up which drives the two bodies away from each other +in opposition to the action of gravity. This force could +accomplish anew the same mechanical work which +was expended to produce it.<a name="FNanchor_27_27" id="FNanchor_27_27"></a><a href="#Footnote_27_27" class="fnanchor">[27]</a></p> + +<div class="figleft" style="width: 150px;"> +<img src="images/i_119-1.jpg" width="150" height="253" alt="" /> +<span class="caption">Fig. 27.</span> +</div> + +<div class="figright" style="width: 250px;"> +<img src="images/i_119-2.jpg" width="250" height="170" alt="" /> +<span class="caption">Fig. 28.</span> +</div> + +<p>Coulomb, now, by means of delicate experiments +with the torsion-balance, satisfied himself that if the +bodies in question, say at a distance of two centimetres, +repelled each other with the same force with +which a milligramme-weight strives to fall to the +ground, at half that distance, or at one centimetre, +they would repel each other with the force of four +milligrammes, and at double that distance, or at four +centimetres, they would repel each other with the force +of only one-fourth of a milligramme. He found that +the electrical force acts inversely as the square of the +distance.</p> + +<p>Let us imagine, now, that we possessed some +means of measuring electrical repulsion by weights, +a means which would be supplied, for example, by our +electrical pendulums; then we could make the following +observation.</p> + +<p>The body <i>A</i> (Fig. 28) is repelled by the body <i>K</i> at +a distance of two centimetres with a force of one milligramme. +If we touch <i>A</i>, now, with an equal body <i>B</i>, +the half of this force of repulsion will pass to the body +<i>B</i>; both <i>A</i> and <i>B</i>, now, at a distance of two centimetres +from <i>K</i>, are repelled only with the force of one-half +a milligramme. But both together are repelled +still with the force of one milligramme. Hence, <i>the +divisibility of electrical force</i> among bodies in contact <i>is +a fact</i>. It is a useful, but by no means a necessary +supplement to this fact, to imagine an electrical fluid +present in the body <i>A</i>, with the quantity of which the +electrical force varies, and half of which flows over to +<i>B</i>. For, in the place of the new physical picture, +thus, an old, familiar one is substituted, which moves +spontaneously in its wonted courses.</p> + +<p>Adhering to this idea, we define the <i>unit</i> of electrical +quantity, according to the now almost universally +adopted centimetre-gramme-second (C. G. S.) system, +as that quantity which at a distance of one centimetre +repels an equal quantity with unit of force, that +is, with a force which in one second would impart to +a mass of one gramme a velocity-increment of a centimetre. +As a gramme mass acquires through the action +of gravity a velocity-increment of about 981 centimetres +in a second, accordingly, a gramme is attracted +to the earth with 981, or, in round numbers, 1000 units +of force of the centimetre-gramme-second system, +while a milligramme-weight would strive to fall to the +earth with approximately the unit force of this system.</p> + +<p>We may easily obtain by this means a clear idea of +what the unit quantity of electricity is. Two small +bodies, <i>K</i>, weighing each a gramme, are hung up by +vertical threads, five metres in length and almost +weightless, so as to touch each other. If the two bodies +be equally electrified and move apart upon electrification +to a distance of one centimetre, their charge is approximately +equivalent to the electrostatic unit of electric +quantity, for the repulsion then holds in equilibrium +a gravitational force-component of approximately +one milligramme, which strives to bring the bodies together.</p> + +<p>Vertically beneath a small sphere suspended from +the equilibrated beam of a balance a second sphere is +placed at a distance of a centimetre. If both be equally +electrified the sphere suspended from the balance will +be rendered apparently lighter by the repulsion. If by +adding a weight of one milligramme equilibrium is +restored, each of the spheres contains in round numbers +the electrostatic unit of electrical quantity.</p> + +<p>In view of the fact that the same electrical bodies +exert at different distances different forces upon one +another, exception might be taken to the measure of +quantity here developed. What kind of a quantity is +that which now weighs more, and now weighs less, so +to speak? But this apparent deviation from the +method of determination commonly used in practical +life, that by weight, is, closely considered, an agreement. +On a high mountain a heavy mass also is less +powerfully attracted to the earth than at the level of +the sea, and if it is permitted us in our determinations +to neglect the consideration of level, it is only because +the comparison of a body with fixed conventional +weights is invariably effected at the same level. In +fact, if we were to make one of the two weights equilibrated +on our balance approach sensibly to the centre +of the earth, by suspending it from a very long thread, +as Prof. von Jolly of Munich suggested, we should +make the gravity of that weight, its heaviness, proportionately +greater.</p> + +<p>Let us picture to ourselves, now, two different +electrical fluids, a positive and a negative fluid, of such +nature that the particles of the one attract the particles +of the other according to the law of the inverse squares, +but the particles of the same fluid repel each other by +the same law; in non-electrical bodies let us imagine +the two fluids uniformly distributed in equal quantities, +in electric bodies one of the two in excess; in +conductors, further, let us imagine the fluids mobile, +in non-conductors immobile; having formed such pictures, +we possess the conception which Coulomb developed +and to which he gave mathematical precision. +We have only to give this conception free play in our +minds and we shall see as in a clear picture the fluid +particles, say of a positively charged conductor, receding +from one another as far as they can, all making +for the surface of the conductor and there seeking out +the prominent parts and points until the greatest possible +amount of work has been performed. On increasing +the size of the surface, we see a dispersion, +on decreasing its size we see a condensation of the particles. +In a second, non-electrified conductor brought +into the vicinity of the first, we see the two fluids immediately +separate, the positive collecting itself on the +remote and the negative on the adjacent side of its +surface. In the fact that this conception reproduces, +lucidly and spontaneously, all the data which arduous +research only slowly and gradually discovered, is contained +its advantage and scientific value. With this, +too, its value is exhausted. We must not seek in nature +for the two hypothetical fluids which we have +added as simple mental adjuncts, if we would not go +astray. Coulomb's view may be replaced by a totally +different one, for example, by that of Faraday, and the +most proper course is always, after the general survey +is obtained, to go back to the actual facts, to the electrical +forces.</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_124-1.jpg" width="300" height="310" alt="" /> +<span class="caption">Fig. 29.</span> +</div> + +<div class="figright" style="width: 300px;"> +<img src="images/i_124-2.jpg" width="300" height="276" alt="" /> +<span class="caption">Fig. 30.</span> +</div> + +<p>We will now make ourselves familiar with the concept +of electrical quantity, and with the method of +measuring or estimating it. Imagine a common Leyden +jar (Fig. 29), the inner and outer coatings of which +are connected together by means of two common metallic +knobs placed about a centimetre apart. If the +inside coating be charged with the quantity of electricity ++<i>q</i>, on the outer coating a distribution of the +electricities will take place. A positive quantity almost +equal<a name="FNanchor_28_28" id="FNanchor_28_28"></a><a href="#Footnote_28_28" class="fnanchor">[28]</a> to the quantity +<i>q</i> flows off to the earth, while +a corresponding quantity-<i>q</i> is still left on the outer +coating. The knobs of the jar receive their portion of +these quantities and when the quantity <i>q</i> is sufficiently +great a rupture of the insulating air between the knobs, +accompanied by the self-discharge of the jar, takes +place. For any given distance and size of the knobs, +a charge of a definite electric quantity <i>q</i> is always necessary +for the spontaneous discharge of the jar.</p> + +<p>Let us insulate, now, the outer coating of a Lane's +unit jar <i>L</i>, the jar just described, and put in connexion +with it the inner coating of a jar <i>F</i> exteriorly connected +with the earth (Fig. 30). Every time that <i>L</i> is +charged with +<i>q</i>, a like quantity +<i>q</i> is collected on +the inner coating of <i>F</i>, and the spontaneous discharge +of the jar <i>L</i>, which is now +again empty, takes place. The +number of the discharges of +the jar <i>L</i> furnishes us, thus, +with a measure of the quantity +collected in the jar <i>F</i>, and +if after 1, 2, 3, ... spontaneous +discharges of <i>L</i> the jar <i>F</i> is +discharged, it is evident that the charge of <i>F</i> has been +proportionately augmented.</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_125.jpg" width="300" height="255" alt="" /> +<span class="caption">Fig. 31.</span> +</div> + +<p>Let us supply now, to effect the spontaneous discharge, +the jar <i>F</i> with knobs of the same size and +at the same distance apart as those of the jar <i>L</i> (Fig. +31). If we find, then, that five discharges of the unit +jar take place before one spontaneous discharge of the +jar <i>F</i> occurs, plainly the jar <i>F</i>, for equal distances between +the knobs of the two jars, equal striking distances, +is able to hold five times the quantity of electricity +that <i>L</i> can, that is, has five times the <i>capacity</i> +of <i>L</i>.<a name="FNanchor_29_29" id="FNanchor_29_29"></a><a href="#Footnote_29_29" class="fnanchor">[29]</a></p> + +<div class="figright" style="width: 400px;"> +<img src="images/i_126.jpg" width="400" height="345" alt="" /> +<span class="caption">Fig. 32.</span> +</div> + +<p>We will now replace the unit jar <i>L</i>, with which we +measure electricity, so to speak, <i>into</i> the jar <i>F</i>, by a +Franklin's pane, consisting of two parallel flat metal +plates (Fig. 32), separated only by air. If here, for +example, thirty spontaneous discharges of the pane are +sufficient to fill the jar, ten discharges will be found +sufficient if the air-space between the two plates be +filled with a cake of sulphur. Hence, the capacity +of a Franklin's pane of sulphur is about three times +greater than that of one of the same shape and size +made of air, or, as it is the custom to say, the specific +inductive capacity of sulphur (that of air being taken +as the unit) is about 3.<a name="FNanchor_30_30" id="FNanchor_30_30"></a><a href="#Footnote_30_30" class="fnanchor">[30]</a> We are here arrived at a +very simple fact, which clearly shows us the significance +of the number called <i>dielectric constant</i>, or <i>specific +inductive capacity</i>, the knowledge of which is so important +for the theory of submarine cables.</p> + +<p>Let us consider a jar <i>A</i>, which is charged with a +certain quantity of electricity. We can discharge the +jar directly. But we can also discharge the jar <i>A</i> +(Fig. 33) partly into a jar <i>B</i>, by connecting the two +outer coatings with each other. In this operation a +portion of the quantity of electricity passes, accompanied +by sparks, into the jar <i>B</i>, and we now find both +jars charged.</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_127-1.jpg" width="300" height="283" alt="" /> +<span class="caption">Fig. 33.</span> +</div> + +<div class="figright" style="width: 300px;"> +<img src="images/i_127-s.jpg" width="300" height="214" alt="" /> +<span class="caption">Fig. 34.</span> +</div> + +<p>It may be shown as follows that the conception of +a constant quantity of electricity can be regarded as +the expression of a pure fact. Picture to yourself any +sort of electrical conductor (Fig. 34); cut it up into a +large number of small pieces, and place these pieces by +means of an insulated rod at a distance of one centimetre +from an electrical body which acts with unit of +force on an equal and like-constituted body at the +same distance. Take the sum of the forces which +this last body exerts on the single pieces of the conductor. +The sum of these forces will be the quantity +of electricity on the whole conductor. It remains the +same, whether we change the form and the size of the +conductor, or whether we bring it near or move it +away from a second electrical conductor, so long as we +keep it insulated, that is, do not discharge it.</p> + +<p>A basis of reality for the notion of electric quantity +seems also to present itself from another quarter. +If a current, that is, in the usual view, a definite +quantity of electricity per second, is sent through a +column of acidulated water; in the direction of the +positive stream, hydrogen, but in the opposite direction, +oxygen is liberated at the extremities of the column. +For a given quantity of electricity a given quantity +of oxygen appears. You may picture the column +of water as a column of hydrogen and a column of +oxygen, fitted into each other, and may say the electric +current is a chemical current and <i>vice versa</i>. Although +this notion is more difficult to adhere to in the field of +statical electricity and with non-decomposable conductors, +its further development is by no means hopeless.</p> + +<p>The concept quantity of electricity, thus, is not so +aerial as might appear, but is able to conduct us with +certainty through a multitude of varied phenomena, +and is suggested to us by the facts in almost palpable +form. We can collect electrical force in a body, measure +it out with one body +into another, carry it +over from one body into +another, just as we can +collect a liquid in a vessel, +measure it out with +one vessel into another, +or pour it from one into +another.</p> + +<p>For the analysis of +mechanical phenomena, +a metrical notion, derived +from experience, +and bearing the designation <i>work</i>, has proved itself +useful. A machine can be set in motion only when +the forces acting on it can perform work.</p> + +<div class="figleft" style="width: 350px;"> +<img src="images/i_129.jpg" width="350" height="431" alt="" /> +<span class="caption">Fig. 35.</span> +</div> + +<p>Let us consider, for example, a wheel and axle +(Fig. 35) having the radii 1 and 2 metres, loaded respectively +with the weights 2 and 1 kilogrammes. On +turning the wheel and axle, the 1 kilogramme-weight, +let us say, sinks two metres, while the 2 kilogramme-weight +rises one metre. On both sides the product</p> + +<p class="center">KGR. M. KGR. M.</p> + +<p class="center"> 1 × 2 = 2 × 1. +</p> + +<p>is equal. So long as this is so, the wheel and axle will +not move of itself. But if we take such loads, or so +change the radii of the wheels, that this product (kgr. +× metre) on displacement is in excess on one side, +that side will sink. As we see, this product is characteristic +for mechanical events, and for this reason has +been invested with a special name, <i>work</i>.</p> + +<p>In all mechanical processes, and as all physical +processes present a mechanical side, in all physical +processes, work plays a determinative part. Electrical +forces, also, produce only changes in which work is performed. +To the extent that forces come into play in +electrical phenomena, electrical phenomena, be they +what they may, extend into the domain of mechanics +and are subject to the laws which hold in this domain. +The universally adopted measure of work, +now, is the product of the force into the distance +through which it acts, and in the C. G. S. system, the +unit of work is the action through one centimetre of +a force which would impart in one second to a +gramme-mass a velocity-increment of one centimetre, +that is, in round numbers, the action through a centimetre +of a pressure equal to the weight of a milligramme. +From a positively charged body, electricity, +yielding to the force of repulsion and performing work, +flows off to the earth, providing conducting connexions +exist. To a negatively charged body, on the other +hand, the earth under the same circumstances gives +off positive electricity. The electrical work possible +in the interaction of a body with the earth, characterises +the electrical condition of that body. We will call +the work which must be expended on the unit quantity +of positive electricity to raise it from the earth to the +body <i>K</i> the <i>potential</i> of the body <i>K</i>.<a name="FNanchor_31_31" id="FNanchor_31_31"></a><a href="#Footnote_31_31" class="fnanchor">[31]</a></p> + +<p>We ascribe to the body <i>K</i> in the C. G. S. system +the potential +1, if we must expend the unit of work +to raise the positive electrostatic unit of electric quantity +from the earth to that body; the potential -1, if +we gain in this procedure the unit of work; the potential +0, if no work at all is performed in the operation.</p> + +<p>The different parts of one and the same electrical +conductor in electrical equilibrium have the same potential, +for otherwise the electricity would perform +work and move about upon the conductor, and equilibrium +would not have existed. Different conductors of +equal potential, put in connexion with one another, do +not exchange electricity any more than bodies of equal +temperature in contact exchange heat, or in connected +vessels, in which the same pressures exist, liquids +flow from one vessel to the other. Exchange of electricity +takes place only between conductors of different +potentials, but in conductors of given form and position +a definite difference of potential is necessary for +a spark, which pierces the insulating air, to pass +between them.</p> + +<p>On being connected, every two conductors assume +at once the same potential. With this the means +is given of determining the potential of a conductor +through the agency of a second conductor expressly +adapted to the purpose called an electrometer, just as +we determine the temperature of a body with a thermometer. +The values of the potentials of bodies obtained +in this way simplify vastly our analysis of their +electrical behavior, as will be evident from what has +been said.</p> + +<p>Think of a positively charged conductor. Double +all the electrical forces exerted by this conductor on a +point charged with unit quantity, that is, double the +quantity at each point, or what is the same thing, +double the total charge. Plainly, equilibrium still subsists. +But carry, now, the positive electrostatic unit +towards the conductor. Everywhere we shall have to +overcome double the force of repulsion we did before, +everywhere we shall have to expend double the work. +By doubling the charge of the conductor a double potential +has been produced. Charge and potential go +hand in hand, are proportional. Consequently, calling +the total quantity of electricity of a conductor <i>Q</i> +and its potential <i>V</i>, we can write: <i>Q</i> = <i>CV</i>, where <i>C</i> +stands for a constant, the import of which will be understood +simply from noting that <i>C</i> = <i>Q</i>/<i>V</i>.<a name="FNanchor_32_32" id="FNanchor_32_32"></a><a href="#Footnote_32_32" class="fnanchor">[32]</a> But the +division of a number representing the units of quantity +of a conductor by the number representing its +units of potential tells us the quantity which falls to +the share of the unit of potential. Now the number +<i>C</i> here we call the capacity of a conductor, and have +substituted, thus, in the place of the old relative determination +of capacity, an absolute determination.<a name="FNanchor_33_33" id="FNanchor_33_33"></a><a href="#Footnote_33_33" class="fnanchor">[33]</a></p> + +<p>In simple cases the connexion between charge, potential, +and capacity is easily ascertained. Our conductor, +let us say, is a sphere of radius <i>r</i>, suspended +free in a large body of air. There being no other conductors +in the vicinity, the charge <i>q</i> will then distribute +itself uniformly upon the surface of the sphere, and +simple geometrical considerations yield for its potential +the expression <i>V</i> = <i>q</i>/<i>r</i>. Hence, <i>q</i>/<i>V</i> = <i>r</i>; that is, +the capacity of a sphere is measured by its radius, and +in the C. G. S. system in centimetres.<a name="FNanchor_34_34" id="FNanchor_34_34"></a><a href="#Footnote_34_34" class="fnanchor">[34]</a> It is clear +also, since a potential is a quantity divided by a length, +that a quantity divided by a potential must be a length.</p> + +<p>Imagine (Fig. 36) a jar composed of two concentric +conductive spherical shells of the radii <i>r</i> and <i>r</i><sub>1</sub>, +having only air between them. Connecting the outside +sphere with the earth, and charging the inside +sphere by means of a thin, insulated wire passing +through the first, with the quantity <i>Q</i>, we shall have +<i>V</i> = (<i>r</i><sub>1</sub>-<i>r</i>)/(<i>r</i><sub>1</sub><i>r</i>)<i>Q</i>, and for the capacity in this case +(<i>r</i><sub>1</sub><i>r</i>)/(<i>r</i><sub>1</sub>-<i>r</i>), or, to take +a specific example, if <i>r</i> = 16 +and <i>r</i><sub>1</sub> = 19, a capacity of +about 100 centimetres.</p> + +<div class="figright" style="width: 350px;"> +<img src="images/i_134.jpg" width="350" height="352" alt="" /> +<span class="caption">Fig. 36.</span> +</div> + +<p>We shall now use these +simple cases for illustrating +the principle by which +capacity and potential are +determined. First, it is +clear that we can use the +jar composed of concentric spheres with its known capacity +as our unit jar and by means of this ascertain, +in the manner above laid down, the capacity of any +given jar <i>F</i>. We find, for example, that 37 discharges +of this unit jar of the capacity 100, just charges the +jar investigated at the same striking distance, that is, +at the same potential. Hence, the capacity of the jar +investigated is 3700 centimetres. The large battery +of the Prague physical laboratory, which consists of +sixteen such jars, all of nearly equal size, has a capacity, +therefore, of something like 50,000 centimetres, +or the capacity of a sphere, a kilometre in diameter, +freely suspended in atmospheric space. This remark +distinctly shows us the great superiority which Leyden +jars possess for the storage of electricity as compared +with common conductors. In fact, as Faraday pointed +out, jars differ from simple conductors mainly by their +great capacity.</p> + +<div class="figcenter" style="width: 450px;"> +<img src="images/i_135.jpg" width="450" height="356" alt="" /> +<span class="caption">Fig. 37.</span> +</div> + +<p>For determining potential, imagine the inner coating +of a jar <i>F</i>, the outer coating of which communicates +with the ground, connected by a long, thin wire +with a conductive sphere <i>K</i> placed free in a large atmospheric +space, compared with whose dimensions +the radius of the sphere vanishes. (Fig. 37.) The +jar and the sphere assume at once the same potential. +But on the surface of the sphere, if that be sufficiently +far removed from all other conductors, a uniform layer +of electricity will be found. If the sphere, having the +radius <i>r</i>, contains the charge <i>q</i>, its potential is <i>V</i> = <i>q</i>/<i>r</i>. +If the upper half of the sphere be severed from the +lower half and equilibrated on a balance with one of +whose beams it is connected by silk threads, the upper +half will be repelled from the lower half with the force +<i>P</i> = <i>q</i><sup>2</sup>/8<i>r</i><sup>2</sup> = 1/8<i>V</i><sup>2</sup>. This repulsion <i>P</i> may be counter-balanced +by additional weights placed on the beam-end, +and so ascertained. The potential is then <i>V</i> = +√(8<i>P</i>).<a name="FNanchor_35_35" id="FNanchor_35_35"></a><a href="#Footnote_35_35" class="fnanchor">[35]</a></p> + +<p>That the potential is proportional to the square +root of the force is not difficult to see. A doubling or +trebling of the potential means that the charge of all +the parts is doubled or trebled; hence their combined +power of repulsion quadrupled or nonupled.</p> + +<p>Let us consider a special case. I wish to produce +the potential 40 on the sphere. What additional weight +must I give to the half sphere in grammes that the +force of repulsion shall maintain the balance in exact +equilibrium? As a gramme weight is approximately +equivalent to 1000 units of force, we have only the +following simple example to work out: 40×40 = 8× +1000.<i>x</i>, where <i>x</i> stands for the number of grammes. +In round numbers we get <i>x</i> = 0.2 gramme. I charge +the jar. The balance is deflected; I have reached, +or rather passed, the potential 40, and you see when I +discharge the jar the associated spark.<a name="FNanchor_36_36" id="FNanchor_36_36"></a><a href="#Footnote_36_36" class="fnanchor">[36]</a></p> + +<p>The striking distance between the knobs of a machine +increases with the difference of the potential, +although not proportionately to that difference. The +striking distance increases faster than the potential +difference. For a distance between the knobs of one +centimetre on this machine the difference of potential +is 110. It can easily be increased tenfold. Of the +tremendous differences of potential which occur in +nature some idea may be obtained from the fact that +the striking distances of lightning in thunder-storms +is counted by miles. The differences of potential in +galvanic batteries are considerably smaller than those +of our machine, for it takes fully one hundred elements +to give a spark of microscopic striking distance.</p> +<p><span class="pagenum"><a name="Page_128" id="Page_128">[Pg 128]</a></span></p><p><span class="pagenum"><a name="Page_129" id="Page_129">[Pg 129]</a></span></p><p><span class="pagenum"><a name="Page_130" id="Page_130">[Pg 130]</a></span></p><p><span class="pagenum"><a name="Page_131" id="Page_131">[Pg 131]</a></span></p><p><span class="pagenum"><a name="Page_132" id="Page_132">[Pg 132]</a></span></p><p><span class="pagenum"><a name="Page_133" id="Page_133">[Pg 133]</a></span></p><p><span class="pagenum"><a name="Page_134" id="Page_134">[Pg 134]</a></span></p> +<hr class="tb" /> + +<p>We shall now employ the ideas reached to shed +some light upon another important relation between +electrical and mechanical phenomena. We shall investigate +what is the potential <i>energy</i>, or the <i>store of +work</i>, contained in a charged conductor, for example, +in a jar.</p> + +<p>If we bring a quantity of electricity up to a conductor, +or, to speak less pictorially, if we generate by +work electrical force in a conductor, this force is able +to produce anew the work by which it was generated. +How great, now, is the energy or capacity for work of +a conductor of known charge <i>Q</i> and known potential +<i>V</i>?</p> + +<p>Imagine the given charge <i>Q</i> divided into very small +parts <i>q</i>, <i>q</i><sub>1</sub>, <i>q</i><sub>2</sub> ..., and these little parts successively +carried up to the conductor. The first very small +quantity <i>q</i> is brought up without any appreciable work +and produces by its presence a small potential <i>V</i><sub>'</sub>. To +bring up the second quantity, accordingly, we must do +the work <i>q</i><sub>'</sub><i>V</i><sub>'</sub>, and similarly for the quantities which +follow the work <i>q</i><sub>''</sub><i>V</i><sub>''</sub>, <i>q</i><sub>'''</sub><i>V</i><sub>'''</sub>, and so forth. Now, +as the potential rises proportionately to the quantities +added until the value <i>V</i> is reached, we have, agreeably +to the graphical representation of Fig. 38, for the +total work performed,</p> + +<p class="center"><i>W</i> = 1/2<i>QV</i>, +</p> + +<p>which corresponds to the total energy of the charged +conductor. Using the equation <i>Q</i> = <i>CV</i>, where <i>C</i> +stands for capacity, we also have,</p> + +<p class="center"><i>W</i> = 1/2<i>CV</i><sup>2</sup>, or <i>W</i> = <i>Q</i><sup>2</sup>/2<i>C</i>. +</p> + +<p>It will be helpful, perhaps, to elucidate this idea +by an analogy from the province of mechanics. If we +pump a quantity of liquid, <i>Q</i>, gradually into a cylindrical +vessel (Fig. 39), the level of the liquid in the +vessel will gradually rise. The more we have pumped +in, the greater the pressure we must overcome, or the +higher the level to which we must lift the liquid. The +stored-up work is rendered again available when the +heavy liquid <i>Q</i>, which reaches up to the level <i>h</i>, flows +out. This work <i>W</i> corresponds to the fall of the whole +liquid weight <i>Q</i>, through the distance <i>h</i>/2 or through +the altitude of its centre of gravity. We have</p> + +<p class="center"><i>W</i> = 1/2<i>Qh</i>. +</p> + +<p>Further, since <i>Q</i> = <i>Kh</i>, or since the weight of the +liquid and the height <i>h</i> are proportional, we get also</p> + +<p class="center"><i>W</i> = 1/2<i>Kh</i><sup>2</sup> and <i>W</i> = <i>Q</i><sup>2</sup>/2<i>K</i>. +</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_139-1.jpg" width="300" height="208" alt="" /> +<span class="caption">Fig. 38.</span> +</div> + +<div class="figright" style="width: 300px;"> +<img src="images/i_139-2.jpg" width="300" height="283" alt="" /> +<span class="caption">Fig. 39.</span> +</div> + +<p>As a special case let us consider our jar. Its capacity +is <i>C</i> = 3700, its potential <i>V</i> = 110; accordingly, +its quantity <i>Q</i> = <i>CV</i> = 407,000 electrostatic units and +its energy <i>W</i> = 1/2<i>QV</i> = 22,385,000 C. G. S. units of +work.</p> + +<p>The unit of work of the C. G. S. system is not readily +appreciable by the senses, nor does it well admit of +representation, as we are accustomed to work with +weights. Let us adopt, therefore, as our unit of work +the gramme-centimetre, or the gravitational pressure +of a gramme-weight through the distance of a centimetre, +which in round numbers is 1000 times greater +than the unit assumed above; in this case, our numerical +result will be approximately 1000 times smaller. +Again, if we pass, as more familiar in practice, to the +kilogramme-metre as our unit of work, our unit, the +distance being increased a hundred fold, and the weight +a thousand fold, will be 100,000 times larger. The +numerical result expressing the work done is in this +case 100,000 times less, being in round numbers 0.22 +kilogramme-metre. We can obtain a clear idea of the +work done here by letting a kilogramme-weight fall 22 +centimetres.</p> + +<p>This amount of work, accordingly, is performed on +the charging of the jar, and on its discharge appears +again, according to the circumstances, partly as sound, +partly as a mechanical disruption of insulators, partly +as light and heat, and so forth.</p> + +<p>The large battery of the Prague physical laboratory, +with its sixteen jars charged to equal potentials, +furnishes, although the effect of the discharge is imposing, +a total amount of work of only three kilogramme-metres.</p> + +<p>In the development of the ideas above laid down +we are not restricted to the method there pursued; in +fact, that method was selected only as one especially +fitted to familiarise us with the phenomena. On the +contrary, the connexion of the physical processes is so +multifarious that we can come at the same event from +very different directions. Particularly are electrical +phenomena connected with all other physical events; +and so intimate is this connexion that we might justly +call the study of electricity the theory of the general +connexion of physical processes.</p> + +<p>With respect to the principle of the conservation +of energy which unites electrical with mechanical phenomena, +I should like to point out briefly two ways of +following up the study of this connexion.</p> + +<p>A few years ago Professor Rosetti, taking an influence-machine, +which he set in motion by means of +weights alternately in the electrical and non-electrical +condition with the same velocities, determined the +mechanical work expended in the two cases and was +thus enabled, after deducting the work of friction, to +ascertain the mechanical work consumed in the development +of the electricity.</p> + +<p>I myself have made this experiment in a modified, +and, as I think, more advantageous form. Instead +of determining the work of friction by special trial, I +arranged my apparatus so that it was eliminated of itself +in the measurement and could consequently be +neglected. The so-called fixed disk of the machine, the +axis of which is placed vertically, is suspended somewhat +like a chandelier by three vertical threads of +equal lengths <i>l</i> at a distance <i>r</i> from the axis. Only +when the machine is excited does this fixed disk, which +represents a Prony's brake, receive, through its reciprocal +action with the rotating disk, a deflexion <i>α</i> and a +moment of torsion which is expressed by <i>D</i> = <i>(Pr<sup>2</sup>/l)α</i>, +where <i>P</i> is the weight of the disk.<a name="FNanchor_37_37" id="FNanchor_37_37"></a><a href="#Footnote_37_37" class="fnanchor">[37]</a> The angle <i>α</i> is +determined by a mirror set in the disk. The work expended +in <i>n</i> rotations is given by <i>2nπD</i>.</p> + +<p>If we close the machine, as Rosetti did, we obtain +a continuous current which has all the properties of a +very weak galvanic current; for example, it produces a +deflexion in a multiplier which we interpose, and so +forth. We can directly ascertain, now, the mechanical +work expended in the maintenance of this current.</p> + +<p>If we charge a jar by means of a machine, the energy +of the jar employed in the production of sparks, +in the disruption of the insulators, etc., corresponds +to a part only of the mechanical work expended, a +second part of it being consumed in the arc which +forms the circuit.<a name="FNanchor_38_38" id="FNanchor_38_38"></a><a href="#Footnote_38_38" class="fnanchor">[38]</a> This machine, with the interposed +jar, affords in miniature a picture of the transference +of force, or more properly of work. And in fact nearly +the same laws hold here for the economical coefficient +as obtain for large dynamo-machines.</p> + +<p>Another means of investigating electrical energy is +by its transformation into heat. A long time ago +(1838), before the mechanical theory of heat had attained +its present popularity, Riess performed experiments +in this field with the help of his electrical +air-thermometer or thermo-electrometer.</p> + +<div class="figleft" style="width: 200px;"> +<img src="images/i_143.jpg" width="200" height="320" alt="" /> +<span class="caption">Fig. 40.</span> +</div> + +<p>If the discharge be conducted +through a fine wire +passing through the globe of +the air-thermometer, a development +of heat is observed +proportional to the expression +above-discussed <i>W</i> = 1/2<i>QV</i>. +Although the total energy has +not yet been transformed +into measurable heat by this +means, in as much as a portion +is left behind in the spark in the air outside the thermometer, +still everything tends to show that the total +heat developed in all parts of the conductor and along +all the paths of discharge is the equivalent of the work +1/2<i>QV</i>.</p> + +<p>It is not important here whether the electrical energy +is transformed all at once or partly, by degrees. +For example, if of two equal jars one is charged with +the quantity <i>Q</i> at the potential <i>V</i> the energy present +is 1/2<i>QV</i>. If the first jar be discharged into the second, +<i>V</i>, since the capacity is now doubled, falls to <i>V</i>/2. +Accordingly, the energy 1/4<i>QV</i> remains, while 1/4<i>QV</i> is +transformed in the spark of discharge into heat. The +remainder, however, is equally distributed between +the two jars so that each on discharge is still able to +transform 1/8<i>QV</i> into heat.</p> +<p><span class="pagenum"><a name="Page_135" id="Page_135">[Pg 135]</a></span></p><p><span class="pagenum"><a name="Page_136" id="Page_136">[Pg 136]</a></span></p><p><span class="pagenum"><a name="Page_137" id="Page_137">[Pg 137]</a></span></p> +<hr class="tb" /> + +<p>We have here discussed electricity in the limited +phenomenal form in which it was known to the inquirers +before Volta, and which has been called, perhaps +not very felicitously, "statical electricity." It is +evident, however, that the nature of electricity is everywhere +one and the same; that a substantial difference +between statical and galvanic electricity does not exist. +Only the quantitative circumstances in the two provinces +are so widely different that totally new aspects +of phenomena may appear in the second, for example, +magnetic effects, which in the first remained unnoticed, +whilst, <i>vice versa</i>, in the second field statical attractions +and repulsions are scarcely appreciable. As a fact, +we can easily show the magnetic effect of the current +of discharge of an influence-machine on the galvanoscope +although we could hardly have made the original +discovery of the magnetic effects with this current. +The statical distant action of the wire poles of +a galvanic element also would hardly have been noticed +had not the phenomenon been known from a +different quarter in a striking form.</p> + +<p>If we wished to characterise the two fields in their +chief and most general features, we should say that in +the first, high potentials and small quantities come +into play, in the second small potentials and large +quantities. A jar which is discharging and a galvanic +element deport themselves somewhat like an air-gun +and the bellows of an organ. The first gives forth +suddenly under a very high pressure a small quantity +of air; the latter liberates gradually under a very slight +pressure a large quantity of air.</p> + +<p>In point of principle, too, nothing prevents our retaining +the electrostatical units in the domain of galvanic +electricity and in measuring, for example, the +strength of a current by the number of electrostatic +units which flow per second through its cross-section. +But this would be in a double aspect impractical. In +the first place, we should totally neglect the magnetic +facilities for measurement so conveniently offered by +the current, and substitute for this easy means a method +which can be applied only with difficulty and is not +capable of great exactness. In the second place our +units would be much too small, and we should find +ourselves in the predicament of the astronomer who +attempted to measure celestial distances in metres instead +of in radii of the earth and the earth's orbit; for +the current which by the magnetic C. G. S. standard +represents the unit, would require a flow of some +30,000,000,000 electrostatic units per second through +its cross-section. Accordingly, different units must +be adopted here. The development of this point, however, +lies beyond my present task.</p> + + + + +<h2><a name="ON_THE_PRINCIPLE_OF_THE_CONSERVATION" id="ON_THE_PRINCIPLE_OF_THE_CONSERVATION">ON THE PRINCIPLE OF THE CONSERVATION +OF ENERGY.</a><a name="FNanchor_39_39" id="FNanchor_39_39"></a><a href="#Footnote_39_39" class="fnanchor">[39]</a></h2> + + +<p>In a popular lecture, distinguished for its charming +simplicity and clearness, which Joule delivered in +the year 1847,<a name="FNanchor_40_40" id="FNanchor_40_40"></a><a href="#Footnote_40_40" class="fnanchor">[40]</a> that famous physicist declares that the +living force which a heavy body has acquired by its +descent through a certain height and which it carries +with it in the form of the velocity with which it is impressed, +is the <i>equivalent</i> of the attraction of gravity +through the space fallen through, and that it would be +"absurd" to assume that this living force could be destroyed +without some restitution of that equivalent. +He then adds: "You will therefore be surprised to +hear that until very <i>recently</i> the universal opinion has +been that living force could be absolutely and irrevocably +destroyed at any one's option." Let us add +that to-day, after forty-seven years, the <i>law of the conservation +of energy</i>, wherever civilisation exists, is accepted +as a fully established truth and receives the +widest applications in all domains of natural science.</p> + +<p><span class="pagenum"><a name="Page_138" id="Page_138">[Pg 138]</a></span></p><p>The fate of all momentous discoveries is similar. +On their first appearance they are regarded by the +majority of men as errors. J. R. Mayer's work on the +principle of energy (1842) was rejected by the first +physical journal of Germany; Helmholtz's treatise +(1847) met with no better success; and even Joule, to +judge from an intimation of Playfair, seems to have +encountered difficulties with his first publication (1843). +Gradually, however, people are led to see that the new +view was long prepared for and ready for enunciation, +only that a few favored minds had perceived it much +earlier than the rest, and in this way the opposition of +the majority is overcome. With proofs of the fruitfulness +of the new view, with its success, confidence +in it increases. The majority of the men who employ +it cannot enter into a deep-going analysis of it; for +them, its success is its proof. It can thus happen that +a view which has led to the greatest discoveries, like +Black's theory of caloric, in a subsequent period in a +province where it does not apply may actually become +an obstacle to progress by its blinding our eyes to facts +which do not fit in with our favorite conceptions. If +a theory is to be protected from this dubious rôle, the +grounds and motives of its evolution and existence +must be examined from time to time with the utmost +care.</p> + +<p>The most multifarious physical changes, thermal,<span class="pagenum"><a name="Page_139" id="Page_139">[Pg 139]</a></span> +electrical, chemical, and so forth, can be brought +about by mechanical work. When such alterations +are reversed they yield anew the mechanical work in +exactly the quantity which was required for the production +of the part reversed. This is the <i>principle of +the conservation of energy</i>; "energy" being the term +which has gradually come into use for that "indestructible +something" of which the measure is mechanical +<i>work</i>.</p> + +<p>How did we acquire this idea? What are the +sources from which we have drawn it? This question +is not only of interest in itself, but also for the important +reason above touched upon. The opinions which +are held concerning the foundations of the law of energy +still diverge very widely from one another. Many +trace the principle to the impossibility of a perpetual +motion, which they regard either as sufficiently proved +by experience, or as self-evident. In the province of +pure mechanics the impossibility of a perpetual motion, +or the continuous production of <i>work</i> without +some <i>permanent</i> alteration, is easily demonstrated. Accordingly, +if we start from the theory that all physical +processes are purely <i>mechanical</i> processes, motions of +molecules and atoms, we embrace also, by this <i>mechanical</i> +conception of physics, the impossibility of a +perpetual motion in the <i>whole</i> physical domain. At +present this view probably counts the most adherents. +Other inquirers, however, are for accepting only a +purely <i>experimental</i> establishment of the law of energy.</p><p><span class="pagenum"><a name="Page_140" id="Page_140">[Pg 140]</a></span></p> + +<p>It will appear, from the discussion to follow, that +<i>all</i> the factors mentioned have co-operated in the development +of the view in question; but that in addition +to them a logical and purely formal factor, hitherto +little considered, has also played a very important part.</p> + + +<h3>I. THE PRINCIPLE OF THE EXCLUDED PERPETUAL +MOTION.</h3> + +<p>The law of energy in its modern form is not identical +with the principle of the excluded perpetual motion, +but it is very closely +related to it. The latter +principle, however, is by +no means new, for in the +province of mechanics it +has controlled for centuries +the thoughts and investigations +of the greatest thinkers. Let us convince +ourselves of this by the study of a few historical +examples.</p> + +<div class="figright" style="width: 300px;"> +<img src="images/i_150.jpg" width="300" height="272" alt="" /> +<span class="caption">Fig. 41.</span> +</div> + +<p>S. Stevinus, in his famous work <i>Hypomnemata mathematica</i>, +Tom. IV, <i>De statica</i>, (Leyden, 1605, p. 34), +treats of the equilibrium of bodies on inclined planes.</p> + +<p>Over a triangular prism <i>ABC</i>, one side of which, +<i>AC</i>, is horizontal, an endless cord or chain is slung, +to which at equal distances apart fourteen balls of +equal weight are attached, as represented in cross-section +in Figure 41. Since we can imagine the lower<span class="pagenum"><a name="Page_141" id="Page_141">[Pg 141]</a></span> +symmetrical part of the cord <i>ABC</i> taken away, Stevinus +concludes that the four balls on <i>AB</i> hold in equilibrium +the two balls on <i>BC</i>. For if the equilibrium were +for a moment disturbed, it could never subsist: the +cord would keep moving round forever in the same direction,—we +should have a perpetual motion. He says:</p> + +<blockquote><p>"But if this took place, our row or ring of balls would come +once more into their original position, and from the same cause the +eight globes to the left would again be heavier than the six to the +right, and therefore those eight would sink a second time and these +six rise, and all the globes would keep up, of themselves, <i>a continuous +and unending motion, which is false</i>."<a name="FNanchor_41_41" id="FNanchor_41_41"></a><a href="#Footnote_41_41" class="fnanchor">[41]</a></p></blockquote> + +<p>Stevinus, now, easily derives from this principle +the laws of equilibrium on the inclined plane and numerous +other fruitful consequences.</p> + +<p>In the chapter "Hydrostatics" of +the same work, page 114, Stevinus sets +up the following principle: "Aquam +datam, datum sibi intra aquam locum +servare,"—a given mass of water preserves +within water its given place.</p> + +<div class="figright" style="width: 150px;"> +<img src="images/i_151.jpg" width="150" height="172" alt="" /> +<span class="caption">Fig. 42.</span> +</div> + +<p>This principle is demonstrated as follows (see Fig. +42):</p> + +<blockquote><p>"For, assuming it to be possible by natural means, let us suppose +that A does not preserve the place assigned to it, but sinks +down to D. This being posited, the water which succeeds A will, +for the same reason, also flow down to <i>D</i>; <i>A</i> will be forced out of +its place in <i>D</i>; and thus this body of water, for the conditions in it +are everywhere the same, <i>will set up a perpetual motion, which is +absurd</i>."<a name="FNanchor_42_42" id="FNanchor_42_42"></a><a href="#Footnote_42_42" class="fnanchor">[42]</a></p></blockquote><p><span class="pagenum"><a name="Page_142" id="Page_142">[Pg 142]</a></span></p> + +<p>From this all the principles of hydrostatics are deduced. +On this occasion Stevinus also first develops +the thought so fruitful for modern analytical mechanics +that the equilibrium of a system is not destroyed by +the addition of rigid connexions. As we know, the +principle of the conservation of the centre of gravity +is now sometimes deduced from D'Alembert's principle +with the help of that remark. If we were to reproduce +Stevinus's demonstration to-day, we should have +to change it slightly. We find no difficulty in imagining +the cord on the prism possessed of unending uniform +motion if all hindrances are thought away, but +we should protest against the assumption of an accelerated +motion or even against that of a uniform motion, +if the resistances were not removed. Moreover, +for greater precision of proof, the string of balls might +be replaced by a heavy homogeneous cord of infinite +flexibility. But all this does not affect in the least the +historical value of Stevinus's thoughts. It is a fact, +Stevinus deduces apparently much simpler truths from +the principle of an impossible perpetual motion.</p> +<p><span class="pagenum"><a name="Page_143" id="Page_143">[Pg 143]</a></span></p> +<p>In the process of thought which conducted Galileo +to his discoveries at the end of the sixteenth century, +the following principle plays an important part, that +a body in virtue of the velocity acquired in its descent +can rise exactly as high as it fell. This principle, +which appears frequently and with much clearness in +Galileo's thought, is simply another form of the principle +of excluded perpetual motion, as we shall see it +is also in Huygens.</p> + +<p>Galileo, as we know, arrived at the law of uniformly +accelerated motion by <i>a priori</i> considerations, as that +law which was the "simplest and most natural," after +having first assumed a different law which he was compelled +to reject. To verify his law he executed experiments +with falling bodies on inclined planes, measuring +the times of descent by the weights of the water +which flowed out of a small orifice in a large vessel. +In this experiment he assumes as a fundamental principle, +that the velocity acquired in descent down an +inclined plane always corresponds to the vertical height +descended through, a conclusion which for him is the +immediate outcome of the fact that a body which has +fallen down one inclined plane can, with the velocity it +has acquired, rise on another plane of any inclination +only to the same vertical height. This principle of +the height of ascent also led him, as it seems, to the +law of inertia. Let us hear his own masterful words +in the <i>Dialogo terzo</i> (<i>Opere</i>, Padova, 1744, Tom. III). +On page 96 we read:</p><p><span class="pagenum"><a name="Page_144" id="Page_144">[Pg 144]</a></span></p> + +<blockquote><p>"I take it for granted that the velocities acquired by a body +in descent down planes of different inclinations are equal if the +heights of those planes are equal."<a name="FNanchor_43_43" id="FNanchor_43_43"></a><a href="#Footnote_43_43" class="fnanchor">[43]</a></p></blockquote> + +<p>Then he makes Salviati say in the dialogue:<a name="FNanchor_44_44" id="FNanchor_44_44"></a><a href="#Footnote_44_44" class="fnanchor">[44]</a></p> + +<blockquote><p>"What you say seems very probable, but I wish to go further +and by an experiment so to increase the probability of it that it shall +amount almost to absolute demonstration. Suppose this sheet of +paper to be a vertical wall, and from a nail driven in it a ball of lead +weighing two or three ounces to hang by a very fine thread <i>AB</i> four +or five feet long. (Fig. 43.) On the wall mark a horizontal line <i>DC</i> +perpendicular to the vertical <i>AB</i>, which latter ought to hang about +two inches from the wall. If now the thread <i>AB</i> with the ball +attached take the position <i>AC</i> and the ball be let go, you will see +the ball first descend through the arc <i>CB</i> and passing beyond +<i>B</i> rise through the arc +<i>BD</i> almost to the level +of the line <i>CD</i>, being +prevented from reaching +it exactly by the resistance +of the air and +of the thread. From +this we may truly conclude +that its impetus at +the point <i>B</i>, acquired by +its descent through the +arc <i>CB</i>, is sufficient to +urge it through a similar arc <i>BD</i> to the same height. Having +performed this experiment and repeated it several times, let us +drive in the wall, in the projection of the vertical <i>AB</i>, as at <i>E</i> or +at <i>F</i>, a nail five or six inches long, so that the thread <i>AC</i>, carrying +as before the ball through the arc <i>CB</i>, at the moment it reaches +the position <i>AB</i>, shall strike the nail <i>E</i>, and the ball be thus compelled +to move up the arc <i>BG</i> described about <i>E</i> as centre. +Then we shall see what the same impetus will here accomplish, +acquired now as before at the same point <i>B</i>, which then drove the +same moving body through the arc <i>BD</i> to the height of the horizontal +<i>CD</i>. Now gentlemen, you will be pleased to see the ball +rise to the horizontal line at the point <i>G</i>, and the same thing also +happen if the nail be placed lower as at <i>F</i>, in which case the ball +would describe the arc <i>BJ</i>, always terminating its ascent precisely +at the line <i>CD</i>. If the nail be placed so low that the length of +thread below it does not reach to the height of <i>CD</i> (which would +happen if <i>F</i> were nearer <i>B</i> than to the intersection of <i>AB</i> with the +horizontal <i>CD</i>), then the thread will wind itself about the nail. +This experiment leaves no room for doubt as to the truth of the +supposition. For as the two arcs <i>CB</i>, <i>DB</i> are equal and similarly +situated, the momentum acquired in the descent of the arc <i>CB</i> is +the same as that acquired in the descent of the arc <i>DB</i>; but the +momentum acquired at <i>B</i> by the descent through the arc <i>CB</i> is capable +of driving up the same moving body through the arc <i>BD</i>; +hence also the momentum acquired in the descent <i>DB</i> is equal to +that which drives the same moving body through the same arc +from <i>B</i> to <i>D</i>, so that in general every momentum acquired in the +descent of an arc is equal to that which causes the same moving +body to ascend through the same arc; but all the momenta which +cause the ascent of all the arcs <i>BD</i>, <i>BG</i>, <i>BJ</i>, are equal since they +are made by the same momentum acquired in the descent <i>CB</i>, as +the experiment shows: therefore all the momenta acquired in the +descent of the arcs <i>DB</i>, <i>GB</i>, <i>JB</i> are equal."</p></blockquote> + +<p><span class="pagenum"><a name="Page_145" id="Page_145">[Pg 145]</a></span></p> +<div class="figcenter" style="width: 300px;"> +<img src="images/i_155.jpg" width="300" height="246" alt="" /> +<span class="caption">Fig. 43.</span> +</div> +<p><span class="pagenum"><a name="Page_146" id="Page_146">[Pg 146]</a></span></p> + +<p>The remark relative to the pendulum may be applied +to the inclined plane and leads to the law of inertia. +We read on page 124:<a name="FNanchor_45_45" id="FNanchor_45_45"></a><a href="#Footnote_45_45" class="fnanchor">[45]</a></p> +<p><span class="pagenum"><a name="Page_147" id="Page_147">[Pg 147]</a></span></p> +<blockquote><p>"It is plain now that a movable body, starting from rest at <i>A</i> +and descending down the inclined plane <i>AB</i>, acquires a velocity +proportional to the increment of its time: the velocity possessed +at <i>B</i> is the greatest of the velocities acquired, and by its nature +immutably impressed, provided all causes of new acceleration or +retardation are taken away: I say acceleration, having in view its +possible further progress along the plane extended; retardation, in +view of the possibility of its being reversed and made to mount the +ascending plane <i>BC</i>. But in the horizontal plane <i>GH</i> its equable +motion, according to its velocity as acquired in the descent from <i>A</i> +to <i>B</i>, will be continued <i>ad infinitum</i>." (Fig. 44.)</p></blockquote> + +<div class="figcenter" style="width: 400px;"> +<img src="images/i_157.jpg" width="400" height="156" alt="" /> +<span class="caption">Fig. 44.</span> +</div> + +<p>Huygens, upon whose shoulders the mantel of Galileo +fell, forms a sharper conception of the law of inertia +and generalises the principle respecting the heights of +ascent which was so fruitful in Galileo's hands. He +employs the latter principle in the solution of the problem +of the centre of oscillation and is perfectly clear in +the statement that the principle respecting the heights +of ascent is identical with the principle of the excluded +perpetual motion.</p> + +<p>The following important passages then occur (Hugenii, +<i>Horologium oscillatorium, pars secunda</i>). <i>Hypotheses</i>:</p> + +<p><span class="pagenum"><a name="Page_148" id="Page_148">[Pg 148]</a></span></p><blockquote><p>"If gravity did not exist, nor the atmosphere obstruct the motions +of bodies, a body would keep up forever the motion once impressed +upon it, with equable velocity, in a straight line."<a name="FNanchor_46_46" id="FNanchor_46_46"></a><a href="#Footnote_46_46" class="fnanchor">[46]</a></p></blockquote> + +<p>In part four of the <i>Horologium de centro oscillationis</i> +we read:</p> + +<blockquote><p>"If any number of weights be set in motion by the force of +gravity, the common centre of gravity of the weights as a whole +cannot possibly rise higher than the place which it occupied when +the motion began.</p> + +<p>"That this hypothesis of ours may arouse no scruples, we +will state that it simply imports, what no one has ever denied, that +heavy bodies do not move <i>upwards</i>.—And truly if the devisers of +the new machines who make such futile attempts to construct a +perpetual motion would acquaint themselves with this principle, +they could easily be brought to see their errors and to understand +that the thing is utterly impossible by mechanical means."<a name="FNanchor_47_47" id="FNanchor_47_47"></a><a href="#Footnote_47_47" class="fnanchor">[47]</a></p></blockquote> + +<p>There is possibly a Jesuitical mental reservation +contained in the words "mechanical means." One +might be led to believe from them that Huygens held +a non-mechanical perpetual motion for possible.</p> + +<p>The generalisation of Galileo's principle is still +more clearly put in Prop. IV of the same chapter:</p> + +<blockquote><p>"If a pendulum, composed of several weights, set in motion +from rest, complete any part of its full oscillation, and from that +point onwards, the individual weights, with their common connexions +dissolved, change their acquired velocities upwards and ascend +as far as they can, the common centre of gravity of all will be carried +up to the same altitude with that which it occupied before the +beginning of the oscillation."<a name="FNanchor_48_48" id="FNanchor_48_48"></a><a href="#Footnote_48_48" class="fnanchor">[48]</a></p></blockquote> + +<p><span class="pagenum"><a name="Page_149" id="Page_149">[Pg 149]</a></span></p><p>On this last principle now, which is a generalisation, +applied to a system of masses, of one of Galileo's +ideas respecting a single mass and which from Huygens's +explanation we recognise as the principle of excluded +perpetual motion, Huygens grounds his theory +of the centre of oscillation. Lagrange characterises +this principle as precarious and is rejoiced at James +Bernoulli's successful attempt, in 1681, to reduce the +theory of the centre of oscillation to the laws of the +lever, which appeared to him clearer. All the great +inquirers of the seventeenth and eighteenth centuries +broke a lance on this problem, and it led ultimately, +in conjunction with the principle of virtual velocities, +to the principle enunciated by D'Alembert in 1743 in +his <i>Traité de dynamique</i>, though previously employed +in a somewhat different form by Euler and Hermann.</p> + +<p>Furthermore, the Huygenian principle respecting +the heights of ascent became the foundation of the +"law of the conservation of living force," as that was +enunciated by John and Daniel Bernoulli and employed<span class="pagenum"><a name="Page_150" id="Page_150">[Pg 150]</a></span> +with such signal success by the latter in his +<i>Hydrodynamics</i>. The theorems of the Bernoullis differ +in form only from Lagrange's expression in the <i>Analytical +Mechanics</i>.</p> + +<p>The manner in which Torricelli reached his famous +law of efflux for liquids leads again to our principle. +Torricelli assumed that the liquid which flows out of +the basal orifice of a vessel cannot by its velocity of +efflux ascend to a greater height than its level in the +vessel.</p> + +<p>Let us next consider a point which belongs to pure +mechanics, the history of the principle of <i>virtual motions</i> +or <i>virtual velocities</i>. This principle was not first +enunciated, as is usually stated, and as Lagrange also +asserts, by Galileo, but earlier, by Stevinus. In his +<i>Trochleostatica</i> of the above-cited work, page 72, he +says:</p> + +<blockquote><p>"Observe that this axiom of statics holds good here:</p> + +<p>"As the space of the body acting is to the space of the body +acted upon, so is the power of the body acted upon to the power of +the body acting."<a name="FNanchor_49_49" id="FNanchor_49_49"></a><a href="#Footnote_49_49" class="fnanchor">[49]</a></p></blockquote> + +<p>Galileo, as we know, recognised the truth of the +principle in the consideration of the simple machines, +and also deduced the laws of the equilibrium of liquids +from it.</p> + +<p>Torricelli carries the principle back to the properties +of the centre of gravity. The condition controlling<span class="pagenum"><a name="Page_151" id="Page_151">[Pg 151]</a></span> +equilibrium in a simple machine, in which power +and load are represented by weights, is that the common +centre of gravity of the weights shall not sink. +Conversely, if the centre of gravity cannot sink equilibrium +obtains, because heavy bodies of themselves +do not move upwards. In this form the principle of +virtual velocities is identical with Huygens's principle +of the impossibility of a perpetual motion.</p> + +<p>John Bernoulli, in 1717, first perceived the universal +import of the principle of virtual movements for all +systems; a discovery stated in a letter to Varignon. +Finally, Lagrange gives a general demonstration of +the principle and founds upon it his whole <i>Analytical +Mechanics</i>. But this general demonstration is based +after all upon Huygens and Torricelli's remarks. Lagrange, +as is known, conceives simple pulleys arranged +in the directions of the forces of the system, passes a +cord through these pulleys, and appends to its free +extremity a weight which is a common measure of all +the forces of the system. With no difficulty, now, the +number of elements of each pulley may be so chosen +that the forces in question shall be replaced by them. +It is then clear that if the weight at the extremity cannot +sink, equilibrium subsists, because heavy bodies +cannot of themselves move upwards. If we do not go +so far, but wish to abide by Torricelli's idea, we may +conceive every individual force of the system replaced +by a special weight suspended from a cord passing +over a pulley in the direction of the force and attached<span class="pagenum"><a name="Page_152" id="Page_152">[Pg 152]</a></span> +at its point of application. Equilibrium subsists then +when the common centre of gravity of all the weights +together cannot sink. The fundamental supposition +of this demonstration is plainly the impossibility of a +perpetual motion.</p> + +<p>Lagrange tried in every way to supply a proof free +from extraneous elements and fully satisfactory, but +without complete success. Nor were his successors +more fortunate.</p> + +<p>The whole of mechanics, thus, is based upon an +idea, which, though unequivocal, is yet unwonted and +not coequal with the other principles and axioms of +mechanics. Every student of mechanics, at some stage +of his progress, feels the uncomfortableness of this +state of affairs; every one wishes it removed; but seldom +is the difficulty stated in words. Accordingly, the +zealous pupil of the science is highly rejoiced when he +reads in a master like Poinsot (<i>Théorie générale de +l'équilibre et du mouvement des systèmes</i>) the following +passage, in which that author is giving his opinion of +the <i>Analytical Mechanics</i>:</p> + +<blockquote><p>"In the meantime, because our attention in that work was first +wholly engrossed with the consideration of its beautiful development +of mechanics, which seemed to spring complete from a single +formula, we naturally believed that the science was completed or +that it only remained to seek the demonstration of the principle of +virtual velocities. But that quest brought back all the difficulties +that we had overcome by the principle itself. That law so general, +wherein are mingled the vague and unfamiliar ideas of infinitely +small movements and of perturbations of equilibrium, only grew<span class="pagenum"><a name="Page_153" id="Page_153">[Pg 153]</a></span> +obscure upon examination; and the work of Lagrange supplying +nothing clearer than the march of analysis, we saw plainly that the +clouds had only appeared lifted from the course of mechanics because +they had, so to speak, been gathered at the very origin of that +science.</p> + +<p>"At bottom, a general demonstration of the principle of virtual +velocities would be equivalent to the establishment of the whole +of mechanics upon a different basis: for the demonstration of a +law which embraces a whole science is neither more nor less than +the reduction of that science to another law just as general, but +evident, or at least more simple than the first, and which, consequently, +would render that useless."<a name="FNanchor_50_50" id="FNanchor_50_50"></a><a href="#Footnote_50_50" class="fnanchor">[50]</a></p></blockquote> + +<p>According to Poinsot, therefore, a proof of the +principle of virtual movements is tantamount to a total +rehabilitation of mechanics.</p> + +<p>Another circumstance of discomfort to the mathematician +is, that in the historical form in which mechanics +at present exists, dynamics is founded on +statics, whereas it is desirable that in a science which +pretends to deductive completeness the more special +statical theorems should be deducible from the more +general dynamical principles.</p> +<p><span class="pagenum"><a name="Page_154" id="Page_154">[Pg 154]</a></span></p> +<p>In fact, a great master, Gauss, gave expression to +this desire in his presentment of the principle of least +constraint (Crelle's <i>Journal für reine und angewandte +Mathematik</i>, Vol. IV, p. 233) in the following words: +"Proper as it is that in the gradual development of a +science, and in the instruction of individuals, the easy +should precede the difficult, the simple the complex, +the special the general, yet the mind, when once it has +reached a higher point of view, demands the contrary +course, in which all statics shall appear simply as a +special case of mechanics." Gauss's own principle, +now, possesses all the requisites of universality, but +its difficulty is that it is not immediately intelligible +and that Gauss deduced it with the help of D'Alembert's +principle, a procedure which left matters where +they were before.</p> + +<p>Whence, now, is derived this strange part which +the principle of virtual motion plays in mechanics? +For the present I shall only make this reply. It would +be difficult for me to tell the difference of impression +which Lagrange's proof of the principle made on me +when I first took it up as a student and when I subsequently +resumed it after having made historical researches. +It first appeared to me insipid, chiefly on +account of the pulleys and the cords which did not fit +in with the mathematical view, and whose action I +would much rather have discovered from the principle<span class="pagenum"><a name="Page_155" id="Page_155">[Pg 155]</a></span> +itself than have taken for granted. But now that I +have studied the history of the science I cannot imagine +a more beautiful demonstration.</p> + +<p>In fact, through all mechanics it is this self-same +principle of excluded perpetual motion which accomplishes +almost all, which displeased Lagrange, but +which he still had to employ, at least tacitly, in his own +demonstration. If we give this principle its proper +place and setting, the paradox is explained.</p> + +<p>The principle of excluded perpetual motion is thus +no new discovery; it has been the guiding idea, for +three hundred years, of all the great inquirers. But +the principle cannot properly be <i>based</i> upon mechanical +perceptions. For long before the development of +mechanics the conviction of its truth existed and even +contributed to that development. Its power of conviction, +therefore, must have more universal and +deeper roots. We shall revert to this point.</p> + + +<h3>II. MECHANICAL PHYSICS.</h3> + +<p>It cannot be denied that an unmistakable tendency +has prevailed, from Democritus to the present day, to +explain <i>all</i> physical events <i>mechanically</i>. Not to mention +earlier obscure expressions of that tendency we +read in Huygens the following:<a name="FNanchor_51_51" id="FNanchor_51_51"></a><a href="#Footnote_51_51" class="fnanchor">[51]</a></p> + +<blockquote><p>"There can be no doubt that light consists of the <i>motion</i> of a +certain substance. For if we examine its production, we find that +here on earth it is principally fire and flame which engender it, both +of which contain beyond doubt bodies which are in rapid movement, +since they dissolve and destroy many other bodies more solid +than they: while if we regard its effects, we see that when light is +accumulated, say by concave mirrors, it has the property of combustion +just as fire has, that is to say, it disunites the parts of +bodies, which is assuredly a proof of <i>motion</i>, at least in the <i>true +philosophy</i>, in which the causes of all natural effects are conceived +as <i>mechanical</i> causes. Which in my judgment must be accomplished +or all hope of ever understanding physics renounced."<a name="FNanchor_52_52" id="FNanchor_52_52"></a><a href="#Footnote_52_52" class="fnanchor">[52]</a></p></blockquote><p><span class="pagenum"><a name="Page_156" id="Page_156">[Pg 156]</a></span></p> + +<p>S. Carnot,<a name="FNanchor_53_53" id="FNanchor_53_53"></a><a href="#Footnote_53_53" class="fnanchor">[53]</a> in introducing the principle of excluded +perpetual motion into the theory of heat, makes the +following apology:</p> + +<blockquote><p>"It will be objected here, perhaps, that a perpetual motion +proved impossible for <i>purely mechanical actions</i>, is perhaps not so +when the influence of <i>heat</i> or of electricity is employed. But can +phenomena of heat or electricity be thought of as due to anything +else than to <i>certain motions of bodies</i>, and as such must they not be +subject to the general laws of mechanics?"<a name="FNanchor_54_54" id="FNanchor_54_54"></a><a href="#Footnote_54_54" class="fnanchor">[54]</a></p></blockquote> + +<p><span class="pagenum"><a name="Page_157" id="Page_157">[Pg 157]</a></span></p><p>These examples, which might be multiplied by +quotations from recent literature indefinitely, show +that a tendency to explain all things mechanically +actually exists. This tendency is also intelligible. +Mechanical events as simple motions in space and +time best admit of observation and pursuit by the help +of our highly organised senses. We reproduce mechanical +processes almost without effort in our imagination. +Pressure as a circumstance that produces motion +is very familiar to us from daily experience. All +changes which the individual personally produces in +his environment, or humanity brings about by means +of the arts in the world, are effected through the instrumentality +of <i>motions</i>. Almost of necessity, therefore, +motion appears to us as the most important +physical factor. Moreover, mechanical properties may +be discovered in all physical events. The sounding +bell trembles, the heated body expands, the electrified +body attracts other bodies. Why, therefore, should +we not attempt to grasp all events under their mechanical +aspect, since that is so easily apprehended and +most accessible to observation and measurement? In +fact, no objection <i>is</i> to be made to the attempt to elucidate +the properties of physical events by mechanical +<i>analogies</i>.</p> + +<p>But modern physics has proceeded <i>very far</i> in this +direction. The point of view which Wundt represents +in his excellent treatise <i>On the Physical Axioms</i> is probably<span class="pagenum"><a name="Page_158" id="Page_158">[Pg 158]</a></span> +shared by the majority of physicists. The axioms +of physics which Wundt sets up are as follows:</p> + +<p>1. All natural causes are motional causes.</p> + +<p>2. Every motional cause lies outside the object +moved.</p> + +<p>3. All motional causes act in the direction of the +straight line of junction, and so forth.</p> + +<p>4. The effect of every cause persists.</p> + +<p>5. Every effect involves an equal countereffect.</p> + +<p>6. Every effect is equivalent to its cause.</p> + +<p>These principles might be studied properly enough +as fundamental principles of mechanics. But when +they are set up as axioms of physics, their enunciation +is simply tantamount to a negation of all events except +motion.</p> + +<p>According to Wundt, all changes of nature are +mere changes of place. All causes are motional causes +(page 26). Any discussion of the philosophical grounds +on which Wundt supports his theory would lead us +deep into the speculations of the Eleatics and the +Herbartians. Change of place, Wundt holds, is the +<i>only</i> change of a thing in which a thing remains identical +with itself. If a thing changed <i>qualitatively</i>, we +should be obliged to imagine that something was annihilated +and something else created in its place, which +is not to be reconciled with our idea of the identity of +the object observed and of the indestructibility of +matter. But we have only to remember that the Eleatics +encountered difficulties of exactly the same sort<span class="pagenum"><a name="Page_159" id="Page_159">[Pg 159]</a></span> +in motion. Can we not also imagine that a thing is +destroyed in <i>one</i> place and in <i>another</i> an exactly similar +thing created? After all, do we really know <i>more</i> +why a body leaves one place and appears in another, +than why a <i>cold</i> body grows <i>warm</i>? Granted that we +had a perfect knowledge of the mechanical processes +of nature, could we and should we, for that reason, +<i>put out of the world</i> all other processes that we do not +understand? On this principle it would really be the +simplest course to deny the existence of the whole +world. This is the point at which the Eleatics ultimately +arrived, and the school of Herbart stopped +little short of the same goal.</p> + +<p>Physics treated in this sense supplies us simply +with a diagram of the world, in which we do not know +reality again. It happens, in fact, to men who give +themselves up to this view for many years, that the +world of sense from which they start as a province of +the greatest familiarity, suddenly becomes, in their +eyes, the supreme "world-riddle."</p> + +<p>Intelligible as it is, therefore, that the efforts of +thinkers have always been bent upon the "reduction +of all physical processes to the motions of atoms," it +must yet be affirmed that this is a chimerical ideal. +This ideal has often played an effective part in popular +lectures, but in the workshop of the serious inquirer +it has discharged scarcely the least function. +What has really been achieved in mechanical physics +is either the <i>elucidation</i> of physical processes by more<span class="pagenum"><a name="Page_160" id="Page_160">[Pg 160]</a></span> +familiar <i>mechanical analogies</i>, (for example, the theories +of light and of electricity,) or the exact <i>quantitative</i> +ascertainment of the connexion of mechanical processes +with other physical processes, for example, the +results of thermodynamics.</p> + + +<h3>III. THE PRINCIPLE OF ENERGY IN PHYSICS.</h3> + +<p>We can know only from <i>experience</i> that mechanical +processes produce other physical transformations, or +<i>vice versa</i>. The attention was first directed to the connexion +of mechanical processes, especially the performance +of work, with changes of thermal conditions +by the invention of the steam-engine, and by its great +technical importance. Technical interests and the +need of scientific lucidity meeting in the mind of S. +Carnot led to the remarkable development from which +thermodynamics flowed. It is simply <i>an accident of +history</i> that the development in question was not connected +with the practical applications of <i>electricity</i>.</p> + +<p>In the determination of the maximum quantity of +<i>work</i> that, generally, a heat-machine, or, to take a +special case, a steam-engine, can perform with the +expenditure of a <i>given</i> amount of heat of combustion, +Carnot is guided by mechanical analogies. A body can +do work on being heated, by expanding under pressure. +But to do this the body must receive heat from a <i>hotter</i> +body. Heat, therefore, to do work, must pass from a +hotter body to a colder body, just as water must fall +from a higher level to a lower level to put a mill-wheel<span class="pagenum"><a name="Page_161" id="Page_161">[Pg 161]</a></span> +in motion. Differences of temperature, accordingly, +represent forces able to do work exactly as do differences +of height in heavy bodies. Carnot pictures to +himself an ideal process in which no heat flows away +unused, that is, without doing work. With a given expenditure +of heat, accordingly, this process furnishes +the maximum of work. An analogue of the process +would be a mill-wheel which scooping its water out of +a higher level would slowly carry it to a lower level +without the loss of a drop. A peculiar property of the +process is, that with the expenditure of the same work +the water can be raised again exactly to its original +level. This property of <i>reversibility</i> is also shared by +the process of Carnot. His process also can be reversed +by the expenditure of the same amount of work, +and the heat again brought back to its original temperature +level.</p> + +<p>Suppose, now, we had <i>two</i> different reversible processes +<i>A</i>, <i>B</i>, such that in <i>A</i> a quantity of heat, <i>Q</i>, +flowing off from the temperature <i>t</i><sub>1</sub> to the lower temperature +<i>t</i><sub>2</sub> should perform the work <i>W</i>, but in <i>B</i> under +the same circumstances it should perform a greater +quantity of work <i>W</i> + <i>W'</i>; then, we could join <i>B</i> in +the sense assigned and <i>A</i> in the reverse sense into a +<i>single</i> process. Here <i>A</i> would reverse the transformation +of heat produced by <i>B</i> and would leave a surplus +of work <i>W'</i>, produced, so to speak, from nothing. +The combination would present a perpetual motion.</p> + +<p>With the feeling, now, that it makes little difference<span class="pagenum"><a name="Page_162" id="Page_162">[Pg 162]</a></span> +whether the mechanical laws are broken directly +or indirectly (by processes of heat), and convinced of +the existence of a <i>universal</i> law-ruled connexion of nature, +Carnot here excludes for the first time from the +province of <i>general</i> physics the possibility of a perpetual +motion. <i>But it follows, then, that the quantity +of work W, produced by the passage of a quantity of heat +Q from a temperature t<sub>1</sub> to a temperature t<sub>2</sub>, is independent +of the nature of the substances as also of the character +of the process, so far as that is unaccompanied by +loss, but is wholly dependent upon the temperature t<sub>1</sub>, t<sub>2</sub>.</i></p> + +<p>This important principle has been fully confirmed +by the special researches of Carnot himself (1824), of +Clapeyron (1834), and of Sir William Thomson (1849), +now Lord Kelvin. The principle was reached <i>without +any assumption whatever</i> concerning the nature of heat, +simply by the exclusion of a perpetual motion. Carnot, +it is true, was an adherent of the theory of Black, according +to which the sum-total of the quantity of heat +in the world is constant, but so far as his investigations +have been hitherto considered the decision on +this point is of no consequence. Carnot's principle +led to the most remarkable results. W. Thomson +(1848) founded upon it the ingenious idea of an "absolute" +scale of temperature. James Thomson (1849) +conceived a Carnot process to take place with water +freezing under pressure and, therefore, performing +work. He discovered, thus, that the freezing point is +lowered 0·0075° Celsius by every additional atmosphere<span class="pagenum"><a name="Page_163" id="Page_163">[Pg 163]</a></span> +of pressure. This is mentioned merely as an +example.</p> + +<p>About twenty years after the publication of Carnot's +book a further advance was made by J. R. Mayer +and J. P. Joule. Mayer, while engaged as a physician +in the service of the Dutch, observed, during a +process of bleeding in Java, an unusual redness of the +venous blood. In agreement with Liebig's theory of +animal heat he connected this fact with the diminished +loss of heat in warmer climates, and with the diminished +expenditure of organic combustibles. The total +expenditure of heat of a man at rest must be equal to +the total heat of combustion. But since <i>all</i> organic actions, +even the mechanical actions, must be set down +to the credit of the heat of combustion, some connexion +must exist between mechanical work and expenditure +of heat.</p> + +<p>Joule started from quite similar convictions concerning +the galvanic battery. A heat of association +equivalent to the consumption of the zinc can be made +to appear in the galvanic cell. If a current is set up, +a part of this heat appears in the conductor of the +current. The interposition of an apparatus for the +decomposition of water causes a part of this heat to +disappear, which on the burning of the explosive gas +formed, is reproduced. If the current runs an electromotor, +a portion of the heat again disappears, which, +on the consumption of the work by friction, again +makes its appearance. Accordingly, both the heat<span class="pagenum"><a name="Page_164" id="Page_164">[Pg 164]</a></span> +produced and the work produced, appeared to Joule +also as connected with the consumption of material. +The thought was therefore present, both to Mayer and +to Joule, of regarding heat and work as equivalent +quantities, so connected with each other that what is +lost in one form universally appears in another. The +result of this was a <i>substantial</i> conception of heat and +of work, and <i>ultimately a substantial conception of energy</i>. +Here every physical change of condition is regarded +as energy, the destruction of which generates +work or equivalent heat. An electric charge, for example, +is energy.</p> + +<p>In 1842 Mayer had calculated from the physical +constants then universally accepted that by the disappearance +of one kilogramme-calorie 365 kilogramme-metres +of work could be performed, and <i>vice versa</i>. +Joule, on the other hand, by a long series of delicate +and varied experiments beginning in 1843 ultimately +determined the mechanical equivalent of the kilogramme-calorie, +more exactly, as 425 kilogramme-metres.</p> + +<p>If we estimate every change of physical condition +by the <i>mechanical work</i> which can be performed upon +the <i>disappearance</i> of that condition, and call this measure +<i>energy</i>, then we can measure all physical changes +of condition, no matter how different they may be, +with the same common measure, and say: <i>the sum-total +of all energy remains constant</i>. This is the form that +the principle of excluded perpetual motion received at<span class="pagenum"><a name="Page_165" id="Page_165">[Pg 165]</a></span> +the hands of Mayer, Joule, Helmholtz, and W. Thomson +in its extension to the whole domain of physics.</p> + +<p>After it had been proved that heat must <i>disappear</i> +if mechanical work was to be done at its expense, +Carnot's principle could no longer be regarded as a +complete expression of the facts. Its improved form +was first given, in 1850, by Clausius, whom Thomson +followed in 1851. It runs thus: "If a quantity of heat +<i>Q'</i> is transformed into work in a reversible process, +<i>another</i> quantity of heat <i>Q</i> of the absolute<a name="FNanchor_55_55" id="FNanchor_55_55"></a><a href="#Footnote_55_55" class="fnanchor">[55]</a> temperature +<i>T<sub>1</sub></i> is lowered to the absolute temperature <i>T<sub>2</sub></i>." +Here <i>Q'</i> is dependent only on <i>Q</i>, <i>T<sub>1</sub></i>, <i>T<sub>2</sub></i>, but is independent +of the substances used and of the character of +the process, so far as that is unaccompanied by loss. +Owing to this last fact, it is sufficient to find the relation +which obtains for some one well-known physical +substance, say a gas, and some definite simple process. +The relation found will be the one that holds +generally. We get, thus,</p> + +<p class="center"><i>Q'/(Q' + Q)</i> = <i>(T<sub>1</sub>-T<sub>2</sub>)/T<sub>1</sub></i> (1) +</p> + +<p>that is, the quotient of the available heat <i>Q'</i> transformed +into work divided by the sum of the transformed +and transferred heats (the total sum used), the +so-called <i>economical coefficient</i> of the process, is,</p> + +<p><i>(T<sub>1</sub>-T<sub>2</sub>)/T<sub>1</sub></i>.</p> +<p><span class="pagenum"><a name="Page_166" id="Page_166">[Pg 166]</a></span></p> + +<h3>IV. THE CONCEPTIONS OF HEAT.</h3> + +<p>When a cold body is put in contact with a warm +body it is observed that the first body is warmed and +that the second body is cooled. We may say that the +first body is warmed <i>at the expense of</i> the second body. +This suggests the notion of a thing, or heat-substance, +which passes from the one body to the other. If two +masses of water <i>m</i>, <i>m'</i>, of unequal temperatures, be +put together, it will be found, upon the rapid equalisation +of the temperatures, that the respective changes +of temperatures <i>u</i> and <i>u'</i> are inversely proportional to +the masses and of opposite signs, so that the algebraical +sum of the products is,</p> + +<p class="center"><i>mu</i> + <i>m'u'</i> = 0. +</p> + +<p>Black called the products <i>mu</i>, <i>m'u'</i>, which are decisive +for our knowledge of the process, <i>quantities of heat</i>. +We may form a very clear <i>picture</i> of these products +by conceiving them with Black as measures of the +quantities of some substance. But the essential thing +is not this picture but the <i>constancy</i> of the sum of these +products in simple processes of conduction. If a quantity +of heat disappears at one point, an equally large +quantity will make its appearance at some other point. +The retention of this idea leads to the discovery of +specific heat. Black, finally, perceives that also something +else may appear for a vanished quantity of heat, +namely: the fusion or vaporisation of a definite quantity<span class="pagenum"><a name="Page_167" id="Page_167">[Pg 167]</a></span> +of matter. He adheres here still to this favorite +view, though with some freedom, and considers the +vanished quantity of heat as still present, but as <i>latent</i>.</p> + +<p>The generally accepted notion of a caloric, or heat-stuff, +was strongly shaken by the work of Mayer and +Joule. If the quantity of heat can be increased and +diminished, people said, heat cannot be a substance, +but must be a <i>motion</i>. The subordinate part of this +statement has become much more popular than all the +rest of the doctrine of energy. But we may convince +ourselves that the motional conception of heat is now +as unessential as was formerly its conception as a substance. +Both ideas were favored or impeded solely +by accidental historical circumstances. It does not +follow that heat is not a substance from the fact that +a mechanical equivalent exists for quantity of heat. +We will make this clear by the following question +which bright students have sometimes put to me. Is +there a mechanical equivalent of electricity as there is +a mechanical equivalent of heat? Yes, and no. There +is no mechanical equivalent of <i>quantity</i> of electricity +as there is an equivalent of <i>quantity</i> of heat, because +the same quantity of electricity has a very different +capacity for work, according to the circumstances in +which it is placed; but there <i>is</i> a mechanical equivalent +of electrical energy.</p> + +<p>Let us ask another question. Is there a mechanical +equivalent of water? No, there is no mechanical +equivalent of quantity of water, but there is a mechanical<span class="pagenum"><a name="Page_168" id="Page_168">[Pg 168]</a></span> +equivalent of weight of water multiplied by +its distance of descent.</p> + +<p>When a Leyden jar is discharged and work thereby +performed, we do not picture to ourselves that the +quantity of electricity disappears as work is done, but +we simply assume that the electricities come into different +positions, equal quantities of positive and negative +electricity being united with one another.</p> + +<p>What, now, is the reason of this difference of view +in our treatment of heat and of electricity? The reason +is purely historical, wholly conventional, and, what +is still more important, is wholly indifferent. I may +be allowed to establish this assertion.</p> + +<p>In 1785 Coulomb constructed his torsion balance, +by which he was enabled to measure the repulsion of +electrified bodies. Suppose we have two small balls, +<i>A</i>, <i>B</i>, which over their whole extent are similarly +electrified. These two balls will exert on one another, +at a certain distance <i>r</i> of their centres, a certain repulsion +<i>p</i>. We bring into contact with <i>B</i> now a ball +<i>C</i>, suffer both to be equally electrified, and then measure +the repulsion of <i>B</i> from <i>A</i> and of <i>C</i> from <i>A</i> at the +same distance <i>r</i>. The sum of these repulsions is again +<i>p</i>. Accordingly something has remained constant. +If we ascribe this effect to a substance, then we infer +naturally its constancy. But the essential point of the +exposition is the divisibility of the electric force <i>p</i> and +not the simile of substance.</p> + +<p>In 1838 Riess constructed his electrical air-thermometer<span class="pagenum"><a name="Page_169" id="Page_169">[Pg 169]</a></span> +(the thermoelectrometer). This gives a measure +of the quantity of heat produced by the discharge of +jars. This quantity of heat is not proportional to the +quantity of electricity contained in the jar by Coulomb's +measure, but if <i>Q</i> be this quantity and <i>C</i> be the +capacity, is proportional to <i>Q</i><sup>2</sup>/2<i>C</i>, or, more simply +still, to the energy of the charged jar. If, now, we +discharge the jar completely through the thermometer, +we obtain a certain quantity of heat, <i>W</i>. But if +we make the discharge through the thermometer into +a second jar, we obtain a quantity less than <i>W</i>. But we +may obtain the remainder by completely discharging +both jars through the air-thermometer, when it will +again be proportional to the energy of the two jars. On +the first, incomplete discharge, accordingly, a part of +the electricity's capacity for work was lost.</p> + +<p>When the charge of a jar produces heat its energy +is changed and its value by Riess's thermometer is decreased. +But by Coulomb's measure the quantity remains +unaltered.</p> + +<p>Now let us imagine that Riess's thermometer had +been invented before Coulomb's torsion balance, which +is not a difficult feat, since both inventions are independent +of each other; what would be more natural than +that the "quantity" of electricity contained in a jar +should be measured by the heat produced in the thermometer? +But then, this so-called quantity of electricity +would decrease on the production of heat or on +the performance of work, whereas it now remains unchanged;<span class="pagenum"><a name="Page_170" id="Page_170">[Pg 170]</a></span> +in that case, therefore, electricity would not +be a <i>substance</i> but a <i>motion</i>, whereas now it is still a +substance. The reason, therefore, why we have other +notions of electricity than we have of heat, is purely +historical, accidental, and conventional.</p> + +<p>This is also the case with other physical things. +Water does not disappear when work is done. Why? +Because we measure quantity of water with scales, just +as we do electricity. But suppose the capacity of +water for work were called quantity, and had to be +measured, therefore, by a mill instead of by scales; +then this quantity also would disappear as it performed +the work. It may, now, be easily conceived +that many substances are not so easily got at as water. +In that case we should be unable to carry out the one +kind of measurement with the scales whilst many other +modes of measurement would still be left us.</p> + +<p>In the case of heat, now, the historically established +measure of "quantity" is accidentally the work-value +of the heat. Accordingly, its quantity disappears when +work is done. But that heat is not a substance follows +from this as little as does the opposite conclusion that +it is a substance. In Black's case the quantity of heat +remains constant because the heat passes into no <i>other</i> +form of energy.</p> + +<p>If any one to-day should still wish to think of heat +as a substance, we might allow that person this liberty +with little ado. He would only have to assume that +that which we call quantity of heat was the energy of<span class="pagenum"><a name="Page_171" id="Page_171">[Pg 171]</a></span> +a substance whose quantity remained unaltered, but +whose energy changed. In point of fact we might +much better say, in analogy with the other terms of +physics, energy of heat, instead of quantity of heat.</p> + +<p>When we wonder, therefore, at the discovery that +heat is motion, we wonder at something that was never +discovered. It is perfectly indifferent and possesses +not the slightest scientific value, whether we think of +heat as a substance or not. The fact is, heat behaves +in some connexions like a substance, in others not. +Heat is latent in steam as oxygen is latent in water.</p> + + +<h3>V. THE CONFORMITY IN THE DEPORTMENT OF THE +ENERGIES.</h3> + +<p>The foregoing reflexions will gain in lucidity from +a consideration of the conformity which obtains in the +behavior of all energies, a point to which I called attention +long ago.<a name="FNanchor_56_56" id="FNanchor_56_56"></a><a href="#Footnote_56_56" class="fnanchor">[56]</a></p> + +<p>A weight <i>P</i> at a height <i>H</i><sub>1</sub> represents an energy +<i>W</i><sub>1</sub> = <i>PH</i><sub>1</sub>. If we suffer the weight to sink to a lower +height <i>H</i><sub>2</sub>, during which work is done, and the work +done is employed in the production of living force, +heat, or an electric charge, in short, is transformed, +then the energy <i>W</i><sub>2</sub> = <i>PH</i><sub>2</sub> is still <i>left</i>. The equation +subsists</p> + +<p><span class="pagenum"><a name="Page_172" id="Page_172">[Pg 172]</a></span></p><p><i>W</i><sub>1</sub>/<i>H</i><sub>1</sub> = <i>W</i><sub>2</sub>/<i>H</i><sub>2</sub>, (2) +or, denoting the <i>transformed</i> energy by <i>W</i>' = <i>W</i><sub>1</sub>-<i>W</i><sub>2</sub> +and the <i>transferred</i> energy, that transported to the +lower level, by <i>W</i> = <i>W</i><sub>2</sub>,</p> + +<p class="center"><i>W</i>'/(<i>W</i>' + <i>W</i>) = (<i>H</i><sub>1</sub>-<i>H</i><sub>2</sub>)/<i>H</i><sub>1</sub>, (3) +</p> + +<p>an equation in all respects analogous to equation (1) +at page 165. The property in question, therefore, is +by no means peculiar to heat. Equation (2) gives the +relation between the energy taken from the higher +level and that deposited on the lower level (the energy +left behind); it says that these <i>energies</i> are proportional +to the <i>heights of the levels</i>. An equation analogous +to equation (2) may be set up for <i>every</i> form of +energy; hence the equation which corresponds to +equation (3), and so to equation (1), may be regarded +as valid for every form. For electricity, for example, +<i>H</i><sub>1</sub>, <i>H</i><sub>2</sub> signify the potentials.</p> + +<p>When we observe for the first time the agreement +here indicated in the transformative law of the energies, +it appears surprising and unexpected, for we do +not perceive at once its reason. But to him who pursues +the comparative historical method that reason +will not long remain a secret.</p> + +<p>Since Galileo, mechanical work, though long under +a different name, has been a <i>fundamental concept</i> of +mechanics, as also a very important notion in the applied +sciences. The transformation of work into living<span class="pagenum"><a name="Page_173" id="Page_173">[Pg 173]</a></span> +force, and of living force into work, suggests directly +the notion of energy—the idea having been first +fruitfully employed by Huygens, although Thomas +Young first called it by the <i>name</i> of "energy." Let +us add to this the constancy of weight (really the constancy +of mass) and we shall see that with respect to +mechanical energy it is involved in the very definition +of the term that the capacity for work or the potential +energy of a weight is proportional to the height of the +level at which it is, in the geometrical sense, and that +it decreases on the lowering of the weight, on transformation, +proportionally to the height of the level. +The zero level here is wholly arbitrary. With this, +equation (2) is given, from which all the other forms +follow.</p> + +<p>When we reflect on the tremendous start which +mechanics had over the other branches of physics, it +is not to be wondered at that the attempt was always +made to apply the notions of that science wherever +this was possible. Thus the notion of mass, for example, +was imitated by Coulomb in the notion of +quantity of electricity. In the further development +of the theory of electricity, the notion of work was +likewise immediately introduced in the theory of potential, +and heights of electrical level were measured +by the work of unit of quantity raised to that level. +But with this the preceding equation with all its consequences +is given for electrical energy. The case with +the other energies was similar.</p><p><span class="pagenum"><a name="Page_174" id="Page_174">[Pg 174]</a></span></p> + +<p><i>Thermal</i> energy, however, appears as a special +case. Only by the peculiar experiments mentioned +could it be discovered that heat is an energy. But the +measure of this energy by Black's quantity of heat is +the outcome of fortuitous circumstances. In the first +place, the accidental slight variability of the capacity +for heat <i>c</i> with the temperature, and the accidental +slight deviation of the usual thermometrical scales +from the scale derived from <i>the tensions of gases</i>, brings +it about that the notion "quantity of heat" can be set +up and that the quantity of heat <i>ct</i> corresponding to a +difference of temperature <i>t</i> is nearly proportional to +the energy of the heat. It is a quite accidental historical +circumstance that Amontons hit upon the idea +of measuring temperature by the tension of a gas. It +is certain in this that he did not think of the work of +the heat.<a name="FNanchor_57_57" id="FNanchor_57_57"></a><a href="#Footnote_57_57" class="fnanchor">[57]</a> But the numbers standing for temperature, +thus, are made proportional to the tensions of +gases, that is, to the work done by gases, with otherwise +equal changes of volume. It thus happens that +<i>temperature heights</i> and <i>level heights of work</i> are proportional +to one another.</p> + +<p>If properties of the thermal condition varying +greatly from the tensions of gases had been chosen, +this relation would have assumed very complicated +forms, and the agreement between heat and the other +energies above considered would not subsist. It is<span class="pagenum"><a name="Page_175" id="Page_175">[Pg 175]</a></span> +very instructive to reflect upon this point. A <i>natural +law</i>, therefore, is not implied in the conformity of the +behavior of the energies, but this conformity is rather +conditioned by the uniformity of our modes of conception +and is also partly a matter of good fortune.</p> + + +<h3>VI. THE DIFFERENCES OF THE ENERGIES AND THE +LIMITS OF THE PRINCIPLE OF ENERGY.</h3> + +<p>Of every quantity of heat <i>Q</i> which does work in a +reversible process (one unaccompanied by loss) between +the absolute temperatures <i>T</i><sub>1</sub>, <i>T</i><sub>2</sub>, only the portion</p> + +<p>(<i>T</i><sub>1</sub>-<i>T</i><sub>2</sub>)/<i>T</i><sub>1</sub></p> + +<p>is transformed into work, while the remainder is transferred +to the lower temperature-level <i>T</i><sub>2</sub>. This transferred +portion can, upon the reversal of the process, +with the same expenditure of work, again be brought +back to the level <i>T</i><sub>1</sub>. But if the process is not reversible, +then more heat than in the foregoing case flows +to the lower level, and the surplus can no longer be +brought back to the higher level <i>T</i><sub>2</sub> without some <i>special</i> +expenditure. W. Thomson (1852), accordingly, +drew attention to the fact, that in all non-reversible, +that is, in all real thermal processes, quantities of heat +are lost for mechanical work, and that accordingly a +dissipation or waste of mechanical energy is taking +place. In all cases, heat is only partially transformed +into work, but frequently work is wholly transformed<span class="pagenum"><a name="Page_176" id="Page_176">[Pg 176]</a></span> +into heat. Hence, a tendency exists towards a diminution +of the <i>mechanical</i> energy and towards an increase +of the <i>thermal</i> energy of the world.</p> + +<p>For a simple, closed cyclical process, accompanied +by no loss, in which the quantity of heat <i>Q_</i>{1} is taken +from the level <i>T_</i>{1}, and the quantity <i>Q_</i>{2} is deposited +upon the level <i>T_</i>{2}, the following relation, agreeably to +equation (2), exists,</p> + +<p class="center">-(<i>Q</i><sub>1</sub>/<i>T</i><sub>1</sub>) + (<i>Q</i><sub>2</sub>/<i>T</i><sub>2</sub>) = 0. +</p> + +<p>Similarly, for any number of compound reversible +cycles Clausius finds the algebraical sum</p> + +<p class="center">Σ<i>Q</i>/<i>T</i> = 0, +</p> + +<p>and supposing the temperature to change continuously,</p> + +<p class="center">∫<i>dQ</i>/<i>T</i> = 0 (4) +</p> + +<p>Here the elements of the quantities of heat deducted +from a given level are reckoned negative, and the elements +imparted to it, positive. If the process is not +reversible, then expression (4), which Clausius calls +<i>entropy</i>, increases. In actual practice this is always +the case, and Clausius finds himself led to the statement:</p> + +<p>1. That the energy of the world remains constant.</p> + +<p>2. That the entropy of the world tends toward a +maximum.</p> + +<p>Once we have noted the above-indicated conformity +in the behavior of different energies, the <i>peculiarity</i><span class="pagenum"><a name="Page_177" id="Page_177">[Pg 177]</a></span> +of thermal energy here mentioned must strike us. +Whence is this peculiarity derived, for, generally every +energy passes only partly into another form, which is +also true of thermal energy? The explanation will be +found in the following.</p> + +<p>Every transformation of a special kind of energy <i>A</i> +is accompanied with a fall of potential of that particular +kind of energy, including heat. But whilst for the +other kinds of energy a transformation and therefore a +loss of energy on the part of the kind sinking in potential +is connected with the fall of the potential, with +heat the case is different. Heat can suffer a fall of +potential without sustaining a loss of energy, at least +according to the customary mode of estimation. If a +weight sinks, it must create perforce kinetic energy, +or heat, or some other form of energy. Also, an electrical +charge cannot suffer a fall of potential without +loss of energy, i. e., without transformation. But heat +can pass with a fall of temperature to a body of greater +capacity and the same thermal energy still be preserved, +so long as we regard <i>every quantity</i> of heat as +energy. This it is that gives to heat, besides its +property of energy, in many cases the character of a +material <i>substance</i>, or quantity.</p> + +<p>If we look at the matter in an unprejudiced light, +we must ask if there is any scientific sense or purpose +in still considering as energy a quantity of heat that +can no longer be transformed into mechanical work, +(for example, the heat of a closed equably warmed<span class="pagenum"><a name="Page_178" id="Page_178">[Pg 178]</a></span> +material system). The principle of energy certainly +plays in this case a wholly superfluous rôle, which is +assigned to it only from habit.<a name="FNanchor_58_58" id="FNanchor_58_58"></a><a href="#Footnote_58_58" class="fnanchor">[58]</a> To maintain the principle +of energy in the face of a knowledge of the dissipation +or waste of mechanical energy, in the face of +the increase of entropy is equivalent almost to the +liberty which Black took when he regarded the heat +of liquefaction as still present but latent.<a name="FNanchor_59_59" id="FNanchor_59_59"></a><a href="#Footnote_59_59" class="fnanchor">[59]</a> It is to be +remarked further, that the expressions "energy of the +world" and "entropy of the world" are slightly permeated +with scholasticism. Energy and entropy are +<i>metrical</i> notions. What meaning can there be in applying +these notions to a case in which they are not +applicable, in which their values are not determinable?</p> + +<p>If we could really determine the entropy of the +world it would represent a true, absolute measure of +time. In this way is best seen the utter tautology of +a statement that the entropy of the world increases +with the time. Time, and the fact that certain changes +take place only in a definite sense, are one and the +same thing.</p> + +<p><span class="pagenum"><a name="Page_179" id="Page_179">[Pg 179]</a></span></p> +<h3>VII. THE SOURCES OF THE PRINCIPLE OF ENERGY.</h3> + +<p>We are now prepared to answer the question, What +are the sources of the principle of energy? All knowledge +of nature is derived in the last instance from experience. +In this sense they are right who look upon +the principle of energy as a result of experience.</p> + +<p>Experience teaches that the sense-elements αβγδ... +into which the world may be decomposed, are subject +to change. It tells us further, that certain of these +elements are <i>connected</i> with other elements, so that they +appear and disappear together; or, that the appearance +of the elements of one class is connected with the +disappearance of the elements of the other class. We +will avoid here the notions of cause and effect because +of their obscurity and equivocalness. The result +of experience may be expressed as follows: <i>The +sensuous elements of the world (αβγδ...) show themselves +to be interdependent.</i> This interdependence is +best represented by some such conception as is in +geometry that of the mutual dependence of the sides +and angles of a triangle, only much more varied and +complex.</p> + +<p>As an example, we may take a mass of gas enclosed +in a cylinder and possessed of a definite volume (α), +which we change by a pressure (β) on the piston, at +the same time feeling the cylinder with our hand and<span class="pagenum"><a name="Page_180" id="Page_180">[Pg 180]</a></span> +receiving a sensation of heat (γ). Increase of pressure +diminishes the volume and increases the sensation +of heat.</p> + +<p>The various facts of experience are not in all respects +alike. Their common sensuous elements are +placed in relief by a process of abstraction and thus +impressed upon the memory. In this way the expression +is obtained of the features of <i>agreement</i> of extensive +groups of facts. The simplest sentence which we can +utter is, by the very nature of language, an abstraction +of this kind. But account must also be taken of the +<i>differences</i> of related facts. Facts may be so nearly related +as to contain the same kind of a αβγ..., but the +relation be such that the αβγ... of the one differ +from the αβγ... of the other only by the number of +equal parts into which they can be divided. Such +being the case, if rules can be given for deducing <i>from +one another</i> the numbers which are the measures of +these αβγ..., then we possess in such rules the <i>most +general</i> expression of a group of facts, as also that expression +which corresponds to all its differences. This +is the goal of quantitative investigation.</p> + +<p>If this goal be reached what we have found is that +between the αβγ... of a group of facts, or better, between +the numbers which are their measures, a number +of equations exists. The simple fact of change +brings it about that the number of these equations +must be smaller than the number of the αβγ.... If +the former be smaller by one than the latter, then one<span class="pagenum"><a name="Page_181" id="Page_181">[Pg 181]</a></span> +portion of the αβγ... is <i>uniquely</i> determined by the +other portion.</p> + +<p>The quest of relations of this last kind is the most +important function of special experimental research, +because we are enabled by it to complete in thought +facts that are only partly given. It is self-evident that +only experience can ascertain that between the αβγ... +relations exist and of what kind they are. Further, +only experience can tell that the relations that exist +between the αβγ... are such that changes of them +can be reversed. If this were not the fact all occasion +for the enunciation of the principle of energy, as is +easily seen, would be wanting. In experience, therefore, +is buried the ultimate well-spring of all knowledge +of nature, and consequently, in this sense, also +the ultimate source of the principle of energy.</p> + +<p>But this does not exclude the fact that the principle +of energy has also a logical root, as will now be +shown. Let us assume on the basis of experience that +one group of sensuous elements αβγ... determines +<i>uniquely</i> another group λμν.... Experience further +teaches that changes of αβγ... can be <i>reversed</i>. It +is then a logical consequence of this observation, that +every time that αβγ... assume the same values this +is also the case with λμν.... Or, that purely <i>periodical</i> +changes of αβγ... can produce no <i>permanent</i> +changes of λμν.... If the group λμν... is a mechanical +group, then a perpetual motion is excluded.</p><p><span class="pagenum"><a name="Page_182" id="Page_182">[Pg 182]</a></span></p> + +<p>It will be said that this is a vicious circle, which +we will grant. But psychologically, the situation is +essentially different, whether I think simply of the +unique determination and reversibility of events, or +whether I exclude a perpetual motion. The attention +takes in the two cases different directions and diffuses +light over different sides of the question, which logically +of course are necessarily connected.</p> + +<p>Surely that firm, logical setting of the thoughts noticeable +in the great inquirers, Stevinus, Galileo, and +the rest, which, consciously or instinctively, was supported +by a fine feeling for the slightest contradictions, +has no other purpose than to limit the bounds of +thought and so exempt it from the possibility of error. +In this, therefore, the logical root of the principle of +excluded perpetual motion is given, namely, in that +universal conviction which existed even before the development +of mechanics and co-operated in that development.</p> + +<p>It is perfectly natural that the principle of excluded +perpetual motion should have been first developed in +the simple domain of pure mechanics. Towards the +transference of that principle into the domain of general +physics the idea contributed much that all physical +phenomena are mechanical phenomena. But the +foregoing discussion shows how little essential this +notion is. The issue really involved is the recognition +of a general interconnexion of nature. This once established, +we see with Carnot that it is indifferent<span class="pagenum"><a name="Page_183" id="Page_183">[Pg 183]</a></span> +whether the mechanical laws are broken directly or +circuitously.</p> + +<p>The principle of the excluded perpetual motion is +very closely related to the modern principle of energy, +but it is not identical with it, for the latter is to be +deduced from the former only by means of a definite +<i>formal conception</i>. As may be seen from the preceding +exposition, the perpetual motion can be excluded without +our employing or possessing the notion of <i>work</i>. +The modern principle of energy results primarily from +a <i>substantial</i> conception of work and of every change +of physical condition which by being reversed produces +work. The strong need of such a conception, +which is by no means necessary, but in a formal sense +is very convenient and lucid, is exhibited in the case +of J. R. Mayer and Joule. It was before remarked +that this conception was suggested to both inquirers +by the observation that both the production of heat +and the production of mechanical work were connected +with an expenditure of substance. Mayer says: "Ex +nihilo nil fit," and in another place, "The creation or +destruction of a force (work) lies without the province +of human activity." In Joule we find this passage: +"It is manifestly <i>absurd</i> to suppose that the powers +with which God has endowed matter can be destroyed."</p> + +<p>Some writers have observed in such statements the +attempt at a <i>metaphysical</i> establishment of the doctrine +of energy. But we see in them simply the formal need +of a simple, clear, and living grasp of the facts, which<span class="pagenum"><a name="Page_184" id="Page_184">[Pg 184]</a></span> +receives its development in practical and technical life, +and which we carry over, as best we can, into the +province of science. As a fact, Mayer writes to Griesinger: +"If, finally, you ask me how I became involved +in the whole affair, my answer is simply this: Engaged +during a sea voyage almost exclusively with the study +of physiology, I discovered the new theory for the +sufficient reason that I <i>vividly felt the need of it</i>."</p> + +<p>The substantial conception of work (energy) is by +no means a necessary one. And it is far from true that +the problem is solved with the recognition of the need +of such a conception. Rather let us see how Mayer +gradually endeavored to satisfy that need. He first +regards quantity of motion, or momentum, <i>mv</i>, as the +equivalent of work, and did not light, until later, on +the notion of living force (<i>mv<sup>2</sup>/2</i>). In the province +of electricity he was unable to assign the expression +which is the equivalent of work. This was done later +by Helmholtz. The formal need, therefore, is <i>first</i> +present, and our conception of nature is subsequently +gradually <i>adapted</i> to it.</p> + +<p>The laying bare of the experimental, logical, and +formal root of the present principle of energy will perhaps +contribute much to the removal of the mysticism +which still clings to this principle. With respect to +our formal need of a very simple, palpable, substantial +conception of the processes in our environment, it +remains an open question how far nature corresponds +to that need, or how far we can satisfy it. In one<span class="pagenum"><a name="Page_185" id="Page_185">[Pg 185]</a></span> +phase of the preceding discussions it would seem as +if the substantial notion of the principle of energy, like +Black's material conception of heat, has its natural +limits in facts, beyond which it can only be artificially +adhered to.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_186" id="Page_186">[Pg 186]</a></span></p> + + + + +<h2><a name="THE_ECONOMICAL_NATURE_OF" id="THE_ECONOMICAL_NATURE_OF">THE ECONOMICAL NATURE OF +PHYSICAL INQUIRY.</a><a name="FNanchor_60_60" id="FNanchor_60_60"></a><a href="#Footnote_60_60" class="fnanchor">[60]</a></h2> + + +<p>When the human mind, with its limited powers, +attempts to mirror in itself the rich life of the +world, of which it is itself only a small part, and which +it can never hope to exhaust, it has every reason for +proceeding economically. Hence that tendency, expressed +in the philosophy of all times, to compass by +a few organic thoughts the fundamental features of +reality. "Life understands not death, nor death life." +So spake an old Chinese philosopher. Yet in his unceasing +desire to diminish the boundaries of the incomprehensible, +man has always been engaged in attempts +to understand death by life and life by death.</p> + +<p>Among the ancient civilised peoples, nature was +filled with demons and spirits having the feelings and +desires of men. In all essential features, this animistic +view of nature, as Tylor<a name="FNanchor_61_61" id="FNanchor_61_61"></a><a href="#Footnote_61_61" class="fnanchor">[61]</a> has aptly termed it, is shared +in common by the fetish-worshipper of modern Africa +and the most advanced nations of antiquity. As a +theory of the world it has never completely disappeared. +The monotheism of the Christians never fully +overcame it, no more than did that of the Jews. In +the belief in witchcraft and in the superstitions of the +sixteenth and seventeenth centuries, the centuries of +the rise of natural science, it assumed frightful pathological +dimensions. Whilst Stevinus, Kepler, and +Galileo were slowly rearing the fabric of modern physical +science, a cruel and relentless war was waged +with firebrand and rack against the devils that glowered +from every corner. To-day even, apart from all survivals +of that period, apart from the traces of fetishism +which still inhere in our physical concepts,<a name="FNanchor_62_62" id="FNanchor_62_62"></a><a href="#Footnote_62_62" class="fnanchor">[62]</a> those +very ideas still covertly lurk in the practices of modern +spiritualism.</p> +<p><span class="pagenum"><a name="Page_187" id="Page_187">[Pg 187]</a></span></p> + +<p>By the side of this animistic conception of the +world, we meet from time to time, in different forms, +from Democritus to the present day, another view, +which likewise claims exclusive competency to comprehend +the universe. This view may be characterised +as the <i>physico-mechanical</i> view of the world. To-day, +that view holds, indisputably, the first place in the +thoughts of men, and determines the ideals and the +character of our times. The coming of the mind of +man into the full consciousness of its powers, in the +eighteenth century, was a period of genuine disillusionment. +It produced the splendid precedent of a life<span class="pagenum"><a name="Page_188" id="Page_188">[Pg 188]</a></span> +really worthy of man, competent to overcome the old +barbarism in the practical fields of life; it created the +<i>Critique of Pure Reason</i>, which banished into the realm +of shadows the sham-ideas of the old metaphysics; it +pressed into the hands of the mechanical philosophy +the reins which it now holds.</p> + +<p>The oft-quoted words of the great Laplace,<a name="FNanchor_63_63" id="FNanchor_63_63"></a><a href="#Footnote_63_63" class="fnanchor">[63]</a> which +I will now give, have the ring of a jubilant toast to +the scientific achievements of the eighteenth century: +"A mind to which were given for a single instant all +the forces of nature and the mutual positions of all its +masses, if it were otherwise powerful enough to subject +these problems to analysis, could grasp, with a +single formula, the motions of the largest masses as +well as of the smallest atoms; nothing would be uncertain +for it; the future and the past would lie revealed +before its eyes." In writing these words, Laplace, +as we know, had also in mind the atoms of the +brain. That idea has been expressed more forcibly +still by some of his followers, and it is not too much +to say that Laplace's ideal is substantially that of the +great majority of modern scientists.</p> + +<p>Gladly do we accord to the creator of the <i>Mécanique +céleste</i> the sense of lofty pleasure awakened in +him by the great success of the Enlightenment, to +which we too owe our intellectual freedom. But to-day, +with minds undisturbed and before <i>new</i> tasks, it<span class="pagenum"><a name="Page_189" id="Page_189">[Pg 189]</a></span> +becomes physical science to secure itself against self-deception +by a careful study of its character, so that +it can pursue with greater sureness its true objects. +If I step, therefore, beyond the narrow precincts of my +specialty in this discussion, to trespass on friendly +neighboring domains, I may plead in my excuse that +the subject-matter of knowledge is common to all domains +of research, and that fixed, sharp lines of demarcation +cannot be drawn.</p> + +<p>The belief in occult magic powers of nature has +gradually died away, but in its place a new belief has +arisen, the belief in the magical power of science. +Science throws her treasures, not like a capricious +fairy into the laps of a favored few, but into the laps +of all humanity, with a lavish extravagance that no +legend ever dreamt of! Not without apparent justice, +therefore, do her distant admirers impute to her the +power of opening up unfathomable abysses of nature, +to which the senses cannot penetrate. Yet she who +came to bring light into the world, can well dispense +with the darkness of mystery, and with pompous show, +which she needs neither for the justification of her +aims nor for the adornment of her plain achievements.</p> + +<p>The homely beginnings of science will best reveal +to us its simple, unchangeable character. Man acquires +his first knowledge of nature half-consciously +and automatically, from an instinctive habit of mimicking +and forecasting facts in thought, of supplementing +sluggish experience with the swift wings of thought,<span class="pagenum"><a name="Page_190" id="Page_190">[Pg 190]</a></span> +at first only for his material welfare. When he hears +a noise in the underbrush he constructs there, just as +the animal does, the enemy which he fears; when he +sees a certain rind he forms mentally the image of the +fruit which he is in search of; just as we mentally associate +a certain kind of matter with a certain line in +the spectrum or an electric spark with the friction of a +piece of glass. A knowledge of causality in this form +certainly reaches far below the level of Schopenhauer's +pet dog, to whom it was ascribed. It probably exists +in the whole animal world, and confirms that great +thinker's statement regarding the will which created +the intellect for its purposes. These primitive psychical +functions are rooted in the economy of our organism +not less firmly than are motion and digestion. +Who would deny that we feel in them, too, the elemental +power of a long practised logical and physiological +activity, bequeathed to us as an heirloom from +our forefathers?</p> + +<p>Such primitive acts of knowledge constitute to-day +the solidest foundation of scientific thought. Our instinctive +knowledge, as we shall briefly call it, by virtue +of the conviction that we have consciously and +intentionally contributed nothing to its formation, confronts +us with an authority and logical power which +consciously acquired knowledge even from familiar +sources and of easily tested fallibility can never possess. +All so-called axioms are such instinctive knowledge. +Not consciously gained knowledge alone, but powerful<span class="pagenum"><a name="Page_191" id="Page_191">[Pg 191]</a></span> +intellectual instinct, joined with vast conceptive powers, +constitute the great inquirer. The greatest advances +of science have always consisted in some successful +formulation, in clear, abstract, and communicable terms, +of what was instinctively known long before, and of +thus making it the permanent property of humanity. +By Newton's principle of the equality of pressure and +counterpressure, whose truth all before him had felt, but +which no predecessor had abstractly formulated, mechanics +was placed by a single stroke on a higher level. +Our statement might also be historically justified by +examples from the scientific labors of Stevinus, S. +Carnot, Faraday, J. R. Mayer, and others.</p> + +<p>All this, however, is merely the soil from which +science starts. The first real beginnings of science +appear in society, particularly in the manual arts, +where the necessity for the communication of experience +arises. Here, where some new discovery is to +be described and related, the compulsion is first felt of +clearly defining in consciousness the important and +essential features of that discovery, as many writers +can testify. The aim of instruction is simply the saving +of experience; the labor of one man is made to +take the place of that of another.</p> + +<p>The most wonderful economy of communication is +found in language. Words are comparable to type, +which spare the repetition of written signs and thus +serve a multitude of purposes; or to the few sounds +of which our numberless different words are composed.<span class="pagenum"><a name="Page_192" id="Page_192">[Pg 192]</a></span> +Language, with its helpmate, conceptual thought, by +fixing the essential and rejecting the unessential, constructs +its rigid pictures of the fluid world on the plan +of a mosaic, at a sacrifice of exactness and fidelity but +with a saving of tools and labor. Like a piano-player +with previously prepared sounds, a speaker excites in +his listener thoughts previously prepared, but fitting +many cases, which respond to the speaker's summons +with alacrity and little effort.</p> + +<p>The principles which a prominent political economist, +E. Hermann,<a name="FNanchor_64_64" id="FNanchor_64_64"></a><a href="#Footnote_64_64" class="fnanchor">[64]</a> has formulated for the economy of +the industrial arts, are also applicable to the ideas of +common life and of science. The economy of language +is augmented, of course, in the terminology of science. +With respect to the economy of written intercourse +there is scarcely a doubt that science itself will realise +that grand old dream of the philosophers of a Universal +Real Character. That time is not far distant. +Our numeral characters, the symbols of mathematical +analysis, chemical symbols, and musical notes, which +might easily be supplemented by a system of color-signs, +together with some phonetic alphabets now in +use, are all beginnings in this direction. The logical +extension of what we have, joined with a use of the +ideas which the Chinese ideography furnishes us, will +render the special invention and promulgation of a +Universal Character wholly superfluous.</p> + +<p>The communication of scientific knowledge always<span class="pagenum"><a name="Page_193" id="Page_193">[Pg 193]</a></span> +involves description, that is, a mimetic reproduction +of facts in thought, the object of which is to replace +and save the trouble of new experience. Again, to +save the labor of instruction and of acquisition, concise, +abridged description is sought. This is really all +that natural laws are. Knowing the value of the acceleration +of gravity, and Galileo's laws of descent, we +possess simple and compendious directions for reproducing +in thought all possible motions of falling bodies. +A formula of this kind is a complete substitute +for a full table of motions of descent, because by means +of the formula the data of such a table can be easily +constructed at a moment's notice without the least +burdening of the memory.</p> + +<p>No human mind could comprehend all the individual +cases of refraction. But knowing the index of refraction +for the two media presented, and the familiar +law of the sines, we can easily reproduce or fill out in +thought every conceivable case of refraction. The advantage +here consists in the disburdening of the memory; +an end immensely furthered by the written preservation +of the natural constants. More than this comprehensive +and condensed report about facts is not +contained in a natural law of this sort. In reality, the +law always contains less than the fact itself, because it +does not reproduce the fact as a whole but only in +that aspect of it which is important for us, the rest being +either intentionally or from necessity omitted. +Natural laws may be likened to intellectual type of a<span class="pagenum"><a name="Page_194" id="Page_194">[Pg 194]</a></span> +higher order, partly movable, partly stereotyped, which +last on new editions of experience may become downright +impediments.</p> + +<p>When we look over a province of facts for the first +time, it appears to us diversified, irregular, confused, +full of contradictions. We first succeed in grasping +only single facts, unrelated with the others. The +province, as we are wont to say, is not <i>clear</i>. By and +by we discover the simple, permanent elements of the +mosaic, out of which we can mentally construct the +whole province. When we have reached a point where +we can discover everywhere the same facts, we no +longer feel lost in this province; we comprehend it +without effort; it is <i>explained</i> for us.</p> + +<p>Let me illustrate this by an example. As soon as +we have grasped the fact of the rectilinear propagation +of light, the regular course of our thoughts stumbles +at the phenomena of refraction and diffraction. As soon +as we have cleared matters up by our index of refraction +we discover that a special index is necessary for +each color. Soon after we have accustomed ourselves +to the fact that light added to light increases its intensity, +we suddenly come across a case of total darkness +produced by this cause. Ultimately, however, +we see everywhere in the overwhelming multifariousness +of optical phenomena the fact of the spatial and +temporal periodicity of light, with its velocity of propagation +dependent on the medium and the period. This +tendency of obtaining a survey of a given province<span class="pagenum"><a name="Page_195" id="Page_195">[Pg 195]</a></span> +with the least expenditure of thought, and of representing +all its facts by some one single mental process, +may be justly termed an economical one.</p> + +<p>The greatest perfection of mental economy is attained +in that science which has reached the highest +formal development, and which is widely employed in +physical inquiry, namely, in mathematics. Strange as +it may sound, the power of mathematics rests upon +its evasion of all unnecessary thought and on its wonderful +saving of mental operations. Even those arrangement-signs +which we call numbers are a system +of marvellous simplicity and economy. When we employ +the multiplication-table in multiplying numbers +of several places, and so use the results of old operations +of counting instead of performing the whole of +each operation anew; when we consult our table of +logarithms, replacing and saving thus new calculations +by old ones already performed; when we employ +determinants instead of always beginning afresh the +solution of a system of equations; when we resolve +new integral expressions into familiar old integrals; +we see in this simply a feeble reflexion of the intellectual +activity of a Lagrange or a Cauchy, who, with +the keen discernment of a great military commander, +substituted for new operations whole hosts of old ones. +No one will dispute me when I say that the most elementary +as well as the highest mathematics are economically-ordered +experiences of counting, put in forms +ready for use.</p><p><span class="pagenum"><a name="Page_196" id="Page_196">[Pg 196]</a></span></p> + +<p>In algebra we perform, as far as possible, all numerical +operations which are identical in form once +for all, so that only a remnant of work is left for the +individual case. The use of the signs of algebra and +analysis, which are merely symbols of operations to +be performed, is due to the observation that we can +materially disburden the mind in this way and spare +its powers for more important and more difficult duties, +by imposing all mechanical operations upon the +hand. One result of this method, which attests its +economical character, is the construction of calculating +machines. The mathematician Babbage, the inventor +of the difference-engine, was probably the first who +clearly perceived this fact, and he touched upon it, +although only cursorily, in his work, <i>The Economy of +Manufactures and Machinery</i>.</p> + +<p>The student of mathematics often finds it hard to +throw off the uncomfortable feeling that his science, in +the person of his pencil, surpasses him in intelligence,—an +impression which the great Euler confessed he +often could not get rid of. This feeling finds a sort of +justification when we reflect that the majority of the +ideas we deal with were conceived by others, often +centuries ago. In great measure it is really the intelligence +of other people that confronts us in science. +The moment we look at matters in this light, the uncanniness +and magical character of our impressions +cease, especially when we remember that we can think +over again at will any one of those alien thoughts.</p><p><span class="pagenum"><a name="Page_197" id="Page_197">[Pg 197]</a></span></p> + +<p>Physics is experience, arranged in economical order. +By this order not only is a broad and comprehensive +view of what we have rendered possible, but also +the defects and the needful alterations are made manifest, +exactly as in a well-kept household. Physics +shares with mathematics the advantages of succinct +description and of brief, compendious definition, which +precludes confusion, even in ideas where, with no apparent +burdening of the brain, hosts of others are contained. +Of these ideas the rich contents can be produced +at any moment and displayed in their full perceptual +light. Think of the swarm of well-ordered notions +pent up in the idea of the potential. Is it wonderful +that ideas containing so much finished labor should +be easy to work with?</p> + +<p>Our first knowledge, thus, is a product of the +economy of self-preservation. By communication, the +experience of <i>many</i> persons, individually acquired at +first, is collected in <i>one</i>. The communication of +knowledge and the necessity which every one feels of +managing his stock of experience with the least expenditure +of thought, compel us to put our knowledge in +economical forms. But here we have a clue which +strips science of all its mystery, and shows us what its +power really is. With respect to specific results it +yields us nothing that we could not reach in a sufficiently +long time without methods. There is no problem +in all mathematics that cannot be solved by direct +counting. But with the present implements of mathematics<span class="pagenum"><a name="Page_198" id="Page_198">[Pg 198]</a></span> +many operations of counting can be performed +in a few minutes which without mathematical methods +would take a lifetime. Just as a single human being, +restricted wholly to the fruits of his own labor, could +never amass a fortune, but on the contrary the accumulation +of the labor of many men in the hands of one is +the foundation of wealth and power, so, also, no knowledge +worthy of the name can be gathered up in a +single human mind limited to the span of a human life +and gifted only with finite powers, except by the most +exquisite economy of thought and by the careful +amassment of the economically ordered experience of +thousands of co-workers. What strikes us here as the +fruits of sorcery are simply the rewards of excellent +housekeeping, as are the like results in civil life. But +the business of science has this advantage over every +other enterprise, that from <i>its</i> amassment of wealth no +one suffers the least loss. This, too, is its blessing, +its freeing and saving power.</p> + +<p>The recognition of the economical character of +science will now help us, perhaps, to understand better +certain physical notions.</p> + +<p>Those elements of an event which we call "cause +and effect" are certain salient features of it, which are +important for its mental reproduction. Their importance +wanes and the attention is transferred to fresh +characters the moment the event or experience in +question becomes familiar. If the connexion of such +features strikes us as a necessary one, it is simply because<span class="pagenum"><a name="Page_199" id="Page_199">[Pg 199]</a></span> +the interpolation of certain intermediate links +with which we are very familiar, and which possess, +therefore, higher authority for us, is often attended +with success in our explanations. That <i>ready</i> experience +fixed in the mosaic of the mind with which we meet +new events, Kant calls an innate concept of the understanding +(<i>Verstandesbegriff</i>).</p> + +<p>The grandest principles of physics, resolved into +their elements, differ in no wise from the descriptive +principles of the natural historian. The question, +"Why?" which is always appropriate where the explanation +of a contradiction is concerned, like all proper +habitudes of thought, can overreach itself and be asked +where nothing remains to be understood. Suppose we +were to attribute to nature the property of producing +like effects in like circumstances; just these like circumstances +we should not know how to find. Nature +exists once only. Our schematic mental imitation alone +produces like events. Only in the mind, therefore, does +the mutual dependence of certain features exist.</p> + +<p>All our efforts to mirror the world in thought would +be futile if we found nothing permanent in the varied +changes of things. It is this that impels us to form the +notion of substance, the source of which is not different +from that of the modern ideas relative to the conservation +of energy. The history of physics furnishes +numerous examples of this impulse in almost all fields, +and pretty examples of it may be traced back to the +nursery. "Where does the light go to when it is put<span class="pagenum"><a name="Page_200" id="Page_200">[Pg 200]</a></span> +out?" asks the child. The sudden shrivelling up of a +hydrogen balloon is inexplicable to a child; it looks +everywhere for the large body which was just there +but is now gone.</p> + +<p>Where does heat come from? Where does heat +go to? Such childish questions in the mouths of mature +men shape the character of a century.</p> + +<p>In mentally separating a body from the changeable +environment in which it moves, what we really do +is to extricate a group of sensations on which our +thoughts are fastened and which is of relatively greater +stability than the others, from the stream of all our +sensations. Absolutely unalterable this group is not. +Now this, now that member of it appears and disappears, +or is altered. In its full identity it never recurs. +Yet the sum of its constant elements as compared +with the sum of its changeable ones, especially if we +consider the continuous character of the transition, is +always so great that for the purpose in hand the former +usually appear sufficient to determine the body's identity. +But because we can separate from the group +every single member without the body's ceasing to be +for us the same, we are easily led to believe that after +abstracting all the members something additional +would remain. It thus comes to pass that we form +the notion of a substance distinct from its attributes, +of a thing-in-itself, whilst our sensations are regarded +merely as symbols or indications of the properties of +this thing-in-itself. But it would be much better to<span class="pagenum"><a name="Page_201" id="Page_201">[Pg 201]</a></span> +say that bodies or things are compendious mental symbols +for groups of sensations—symbols that do not exist +outside of thought. Thus, the merchant regards +the labels of his boxes merely as indexes of their contents, +and not the contrary. He invests their contents, +not their labels, with real value. The same +economy which induces us to analyse a group and to +establish special signs for its component parts, parts +which also go to make up other groups, may likewise +induce us to mark out by some single symbol a whole +group.</p> + +<p>On the old Egyptian monuments we see objects +represented which do not reproduce a single visual +impression, but are composed of various impressions. +The heads and the legs of the figures appear in profile, +the head-dress and the breast are seen from the +front, and so on. We have here, so to speak, a mean +view of the objects, in forming which the sculptor has +retained what he deemed essential, and neglected what +he thought indifferent. We have living exemplifications +of the processes put into stone on the walls of +these old temples, in the drawings of our children, and +we also observe a faithful analogue of them in the formation +of ideas in our own minds. Only in virtue of +some such facility of view as that indicated, are we +allowed to speak of a body. When we speak of a cube +with trimmed corners—a figure which is not a cube—we +do so from a natural instinct of economy, which +prefers to add to an old familiar conception a correction<span class="pagenum"><a name="Page_202" id="Page_202">[Pg 202]</a></span> +instead of forming an entirely new one. This is +the process of all judgment.</p> + +<p>The crude notion of "body" can no more stand +the test of analysis than can the art of the Egyptians +or that of our little children. The physicist who sees +a body flexed, stretched, melted, and vaporised, cuts +up this body into smaller permanent parts; the chemist +splits it up into elements. Yet even an element is +not unalterable. Take sodium. When warmed, the +white, silvery mass becomes a liquid, which, when the +heat is increased and the air shut out, is transformed +into a violet vapor, and on the heat being still more +increased glows with a yellow light. If the name sodium +is still retained, it is because of the continuous +character of the transitions and from a necessary instinct +of economy. By condensing the vapor, the +white metal may be made to reappear. Indeed, even +after the metal is thrown into water and has passed +into sodium hydroxide, the vanished properties may +by skilful treatment still be made to appear; just as a +moving body which has passed behind a column and +is lost to view for a moment may make its appearance +after a time. It is unquestionably very convenient +always to have ready the name and thought for a +group of properties wherever that group by any possibility +can appear. But more than a compendious economical +symbol for these phenomena, that name and +thought is not. It would be a mere empty word for +one in whom it did not awaken a large group of well-ordered<span class="pagenum"><a name="Page_203" id="Page_203">[Pg 203]</a></span> +sense-impressions. And the same is true of +the molecules and atoms into which the chemical element +is still further analysed.</p> + +<p>True, it is customary to regard the conservation of +weight, or, more precisely, the conservation of mass, +as a direct proof of the constancy of matter. But this +proof is dissolved, when we go to the bottom of it, +into such a multitude of instrumental and intellectual +operations, that in a sense it will be found to constitute +simply an equation which our ideas in imitating +facts have to satisfy. That obscure, mysterious lump +which we involuntarily add in thought, we seek for in +vain outside the mind.</p> + +<p>It is always, thus, the crude notion of substance +that is slipping unnoticed into science, proving itself +constantly insufficient, and ever under the necessity of +being reduced to smaller and smaller world-particles. +Here, as elsewhere, the lower stage is not rendered +indispensable by the higher which is built upon it, no +more than the simplest mode of locomotion, walking, +is rendered superfluous by the most elaborate means of +transportation. Body, as a compound of light and +touch sensations, knit together by sensations of space, +must be as familiar to the physicist who seeks it, as to +the animal who hunts its prey. But the student of the +theory of knowledge, like the geologist and the astronomer, +must be permitted to reason back from the forms +which are created before his eyes to others which he +finds ready made for him.</p><p><span class="pagenum"><a name="Page_204" id="Page_204">[Pg 204]</a></span></p> + +<p>All physical ideas and principles are succinct directions, +frequently involving subordinate directions, +for the employment of economically classified experiences, +ready for use. Their conciseness, as also the +fact that their contents are rarely exhibited in full, +often invests them with the semblance of independent +existence. Poetical myths regarding such ideas,—for +example, that of Time, the producer and devourer of +all things,—do not concern us here. We need only +remind the reader that even Newton speaks of an <i>absolute</i> +time independent of all phenomena, and of an +absolute space—views which even Kant did not shake +off, and which are often seriously entertained to-day. +For the natural inquirer, determinations of time are +merely abbreviated statements of the dependence of +one event upon another, and nothing more. When +we say the acceleration of a freely falling body is 9·810 +metres per second, we mean the velocity of the body +with respect to the centre of the earth is 9·810 metres +greater when the earth has performed an additional +86400th part of its rotation—a fact which itself can be +determined only by the earth's relation to other heavenly +bodies. Again, in velocity is contained simply a +relation of the position of a body to the position of +the earth.<a name="FNanchor_65_65" id="FNanchor_65_65"></a><a href="#Footnote_65_65" class="fnanchor">[65]</a> Instead of referring events to the earth +we may refer them to a clock, or even to our internal +sensation of time. Now, because all are connected, +and each may be made the measure of the rest, the illusion +easily arises that time has significance independently +of all.<a name="FNanchor_66_66" id="FNanchor_66_66"></a><a href="#Footnote_66_66" class="fnanchor">[66]</a></p> + +<p><span class="pagenum"><a name="Page_205" id="Page_205">[Pg 205]</a></span></p><p>The aim of research is the discovery of the equations +which subsist between the elements of phenomena. +The equation of an ellipse expresses the universal +<i>conceivable</i> relation between its co-ordinates, of which +only the real values have <i>geometrical</i> significance. +Similarly, the equations between the elements of <i>phenomena</i> +express a universal, mathematically conceivable +relation. Here, however, for many values only +certain directions of change are <i>physically</i> admissible. +As in the ellipse only certain <i>values</i> satisfying the +equation are realised, so in the physical world only +certain <i>changes</i> of value occur. Bodies are always accelerated +towards the earth. Differences of temperature, +left to themselves, always grow less; and so on. +Similarly, with respect to space, mathematical and +physiological researches have shown that the space of +experience is simply an <i>actual</i> case of many conceivable +cases, about whose peculiar properties experience +alone can instruct us. The elucidation which this idea +diffuses cannot be questioned, despite the absurd uses +to which it has been put.</p> + +<p>Let us endeavor now to summarise the results of<span class="pagenum"><a name="Page_206" id="Page_206">[Pg 206]</a></span> +our survey. In the economical schematism of science +lie both its strength and its weakness. Facts are always +represented at a sacrifice of completeness and +never with greater precision than fits the needs of the +moment. The incongruence between thought and experience, +therefore, will continue to subsist as long as +the two pursue their course side by side; but it will +be continually diminished.</p> + +<p>In reality, the point involved is always the completion +of some partial experience; the derivation of +one portion of a phenomenon from some other. In +this act our ideas must be based directly upon sensations. +We call this measuring.<a name="FNanchor_67_67" id="FNanchor_67_67"></a><a href="#Footnote_67_67" class="fnanchor">[67]</a> The condition of +science, both in its origin and in its application, is a +<i>great relative stability</i> of our environment. What it +teaches us is interdependence. Absolute forecasts, +consequently, have no significance in science. With +great changes in celestial space we should lose our +co-ordinate systems of space and time.</p> + +<p>When a geometer wishes to understand the form of +a curve, he first resolves it into small rectilinear elements. +In doing this, however, he is fully aware that +these elements are only provisional and arbitrary devices +for comprehending in parts what he cannot comprehend +as a whole. When the law of the curve is +found he no longer thinks of the elements. Similarly, +it would not become physical science to see in its self-created,<span class="pagenum"><a name="Page_207" id="Page_207">[Pg 207]</a></span> +changeable, economical tools, molecules and +atoms, realities behind phenomena, forgetful of the +lately acquired sapience of her older sister, philosophy, +in substituting a mechanical mythology for the old +animistic or metaphysical scheme, and thus creating +no end of suppositious problems. The atom must remain +a tool for representing phenomena, like the +functions of mathematics. Gradually, however, as +the intellect, by contact with its subject-matter, grows +in discipline, physical science will give up its mosaic +play with stones and will seek out the boundaries and +forms of the bed in which the living stream of phenomena +flows. The goal which it has set itself is the +<i>simplest</i> and <i>most economical</i> abstract expression of facts.</p> +<p><span class="pagenum"><a name="Page_208" id="Page_208">[Pg 208]</a></span></p><p><span class="pagenum"><a name="Page_209" id="Page_209">[Pg 209]</a></span></p><p><span class="pagenum"><a name="Page_210" id="Page_210">[Pg 210]</a></span></p><p><span class="pagenum"><a name="Page_211" id="Page_211">[Pg 211]</a></span></p><p><span class="pagenum"><a name="Page_212" id="Page_212">[Pg 212]</a></span></p><p><span class="pagenum"><a name="Page_213" id="Page_213">[Pg 213]</a></span></p><p><span class="pagenum"><a name="Page_214" id="Page_214">[Pg 214]</a></span></p> +<hr class="tb" /> + +<p>The question now remains, whether the same +method of research which till now we have tacitly restricted +to physics, is also applicable in the psychical +domain. This question will appear superfluous to the +physical inquirer. Our physical and psychical views +spring in exactly the same manner from instinctive +knowledge. We read the thoughts of men in their +acts and facial expressions without knowing how. +Just as we predict the behavior of a magnetic needle +placed near a current by imagining Ampère's swimmer +in the current, similarly we predict in thought the +acts and behavior of men by assuming sensations, feelings, +and wills similar to our own connected with their +bodies. What we here instinctively perform would +appear to us as one of the subtlest achievements of +science, far outstripping in significance and ingenuity +Ampère's rule of the swimmer, were it not that every +child unconsciously accomplished it. The question +simply is, therefore, to grasp scientifically, that is, by +conceptional thought, what we are already familiar +with from other sources. And here much is to be +accomplished. A long sequence of facts is to be disclosed +between the physics of expression and movement +and feeling and thought.</p> + +<p>We hear the question, "But how is it possible to +explain feeling by the motions of the atoms of the +brain?" Certainly this will never be done, no more +than light or heat will ever be deduced from the law +of refraction. We need not deplore, therefore, the +lack of ingenious solutions of this question. The problem +is not a problem. A child looking over the walls +of a city or of a fort into the moat below sees with +astonishment living people in it, and not knowing of +the portal which connects the wall with the moat, cannot +understand how they could have got down from +the high ramparts. So it is with the notions of physics. +We cannot climb up into the province of psychology +by the ladder of our abstractions, but we can climb +down into it.</p> + +<p>Let us look at the matter without bias. The world +consists of colors, sounds, temperatures, pressures, +spaces, times, and so forth, which now we shall not +call sensations, nor phenomena, because in either term +an arbitrary, one-sided theory is embodied, but simply +<i>elements</i>. The fixing of the flux of these elements, +whether mediately or immediately, is the real object of +physical research. As long as, neglecting our own +body, we employ ourselves with the interdependence +of those groups of elements which, including men and +animals, make up <i>foreign</i> bodies, we are physicists. +For example, we investigate the change of the red +color of a body as produced by a change of illumination. +But the moment we consider the special influence +on the red of the elements constituting our +body, outlined by the well-known perspective with +head invisible, we are at work in the domain of physiological +psychology. We close our eyes, and the red +together with the whole visible world disappears. +There exists, thus, in the perspective field of every sense +a portion which exercises on all the rest a different +and more powerful influence than the rest upon one +another. With this, however, all is said. In the light +of this remark, we call <i>all</i> elements, in so far as we regard +them as dependent on this special part (our body), +<i>sensations</i>. That the world is our sensation, in this +sense, cannot be questioned. But to make a system +of conduct out of this provisional conception, and to +abide its slaves, is as unnecessary for us as would be +a similar course for a mathematician who, in varying a +series of variables of a function which were previously +assumed to be constant, or in interchanging the independent +variables, finds his method to be the source +of some very surprising ideas for him.<a name="FNanchor_68_68" id="FNanchor_68_68"></a><a href="#Footnote_68_68" class="fnanchor">[68]</a></p> + +<p>If we look at the matter in this unbiassed light it +will appear indubitable that the method of physiological +psychology is none other than that of physics; +what is more, that this science is a part of physics. +Its subject-matter is not different from that of physics. +It will unquestionably determine the relations +the sensations bear to the physics of our body. We +have already learned from a member of this academy +(Hering) that in all probability a sixfold manifoldness +of the chemical processes of the visual substance corresponds +to the sixfold manifoldness of color-sensation, +and a threefold manifoldness of the physiological processes +to the threefold manifoldness of space-sensations. +The paths of reflex actions and of the will are +followed up and disclosed; it is ascertained what region +of the brain subserves the function of speech, +what region the function of locomotion, etc. That +which still clings to our body, namely, our thoughts, +will, when those investigations are finished, present no +difficulties new in principle. When experience has +once clearly exhibited these facts and science has +marshalled them in economic and perspicuous order, +there is no doubt that we shall <i>understand</i> them. For +other "understanding" than a mental mastery of facts +never existed. Science does not create facts from facts, +but simply <i>orders</i> known facts.</p> + +<p>Let us look, now, a little more closely into the modes +of research of physiological psychology. We have a +very clear idea of how a body moves in the space encompassing +it. With our optical field of sight we are +very familiar. But we are unable to state, as a rule, +how we have come by an idea, from what corner of +our intellectual field of sight it has entered, or by what +region the impulse to a motion is sent forth. Moreover, +we shall never get acquainted with this mental +field of view from self-observation alone. Self-observation, +in conjunction with physiological research, +which seeks out physical connexions, can put this field +of vision in a clear light before us, and will thus first +really reveal to us our inner man.</p> + +<p>Primarily, natural science, or physics, in its widest +sense, makes us acquainted with only the firmest connexions +of groups of elements. Provisorily, we may +not bestow too much attention on the single constituents +of those groups, if we are desirous of retaining a +comprehensible whole. Instead of equations between +the primitive variables, physics gives us, as much the +easiest course, equations between <i>functions</i> of those +variables. Physiological psychology teaches us how +to separate the visible, the tangible, and the audible +from bodies—a labor which is subsequently richly requited, +as the division of the subjects of physics well +shows. Physiology further analyses the visible into +light and space sensations; the first into colors, the +last also into their component parts; it resolves noises +into sounds, these into tones, and so on. Unquestionably +this analysis can be carried much further than it +has been. It will be possible in the end to exhibit the +common elements at the basis of very abstract but +definite logical acts of like form,—elements which the +acute jurist and mathematician, as it were, <i>feels</i> out, +with absolute certainty, where the uninitiated hears +only empty words. Physiology, in a word, will reveal +to us the true real elements of the world. Physiological +psychology bears to physics in its widest sense a relation +similar to that which chemistry bears to physics +in its narrowest sense. But far greater than the mutual +support of physics and chemistry will be that +which natural science and psychology will render each +other. And the results that shall spring from this +union will, in all likelihood, far outstrip those of the +modern mechanical physics.</p> + +<p>What those ideas are with which we shall comprehend +the world when the closed circuit of physical and +psychological facts shall lie complete before us, (that +circuit of which we now see only two disjoined parts,) +cannot be foreseen at the outset of the work. The +men will be found who will see what is right and +will have the courage, instead of wandering in the +intricate paths of logical and historical accident, to +enter on the straight ways to the heights from which +the mighty stream of facts can be surveyed. Whether +the notion which we now call matter will continue to +have a scientific significance beyond the crude purposes +of common life, we do not know. But we certainly +shall wonder how colors and tones which were +such innermost parts of us could suddenly get lost in +our physical world of atoms; how we could be suddenly +surprised that something which outside us simply +clicked and beat, in our heads should make light +and music; and how we could ask whether matter can +feel, that is to say, whether a mental symbol for a +group of sensations can feel?</p> + +<p>We cannot mark out in hard and fast lines the +science of the future, but we can foresee that the rigid +walls which now divide man from the world will gradually +disappear; that human beings will not only confront +each other, but also the entire organic and so-called +lifeless world, with less selfishness and with livelier +sympathy. Just such a presentiment as this perhaps +possessed the great Chinese philosopher Licius +some two thousand years ago when, pointing to a heap +of mouldering human bones, he said to his scholars in +the rigid, lapidary style of his tongue: "These and I +alone have the knowledge that we neither live nor are +dead."</p> + + + + +<h2><a name="ON_TRANSFORMATION_AND_ADAPTATION" id="ON_TRANSFORMATION_AND_ADAPTATION">ON TRANSFORMATION AND ADAPTATION +IN SCIENTIFIC THOUGHT.</a><a name="FNanchor_69_69" id="FNanchor_69_69"></a><a href="#Footnote_69_69" class="fnanchor">[69]</a></h2> + + +<p>It was towards the close of the sixteenth century +that Galileo with a superb indifference to the dialectic +arts and sophistic subtleties of the Schoolmen of +his time, turned the attention of his brilliant mind +to nature. By nature his ideas were transformed and +released from the fetters of inherited prejudice. At +once the mighty revolution was felt, that was therewith +effected in the realm of human thought—felt indeed in +circles far remote and wholly unrelated to the sphere +of science, felt in strata of society that hitherto had +only indirectly recognised the influence of scientific +thought.</p> +<p><span class="pagenum"><a name="Page_215" id="Page_215">[Pg 215]</a></span></p> +<p>And how great and how far-reaching that revolution +was! From the beginning of the seventeenth century +till its close we see arising, at least in embryo, +almost all that plays a part in the natural and technical +science of to-day, almost all that in the two centuries +following so wonderfully transformed the facial +appearance of the earth, and all that is moving onward +in process of such mighty evolution to-day. And all +this, the direct result of Galilean ideas, the direct outcome +of that freshly awakened sense for the investigation +of natural phenomena which taught the Tuscan +philosopher to form the concept and the law of falling +bodies from the <i>observation</i> of a falling stone! Galileo +began his investigations without an implement worthy +of the name; he measured time in the most primitive +way, by the efflux of water. Yet soon afterwards the +telescope, the microscope, the barometer, the thermometer, +the air-pump, the steam engine, the pendulum, +and the electrical machine were invented in rapid +succession. The fundamental theorems of dynamical +science, of optics, of heat, and of electricity were all +disclosed in the century that followed Galileo.</p> + +<p>Of scarcely less importance, it seems, was that +movement which was prepared for by the illustrious +biologists of the hundred years just past, and formally +begun by the late Mr. Darwin. Galileo quickened the +sense for the simpler phenomena of <i>inorganic</i> nature. +And with the same simplicity and frankness that +marked the efforts of Galileo, and without the aid of<span class="pagenum"><a name="Page_216" id="Page_216">[Pg 216]</a></span> +technical or scientific instruments, without physical or +chemical experiment, but solely by the power of +thought and observation, Darwin grasps a new property +of <i>organic</i> nature—which we may briefly call its +<i>plasticity</i>.<a name="FNanchor_70_70" id="FNanchor_70_70"></a><a href="#Footnote_70_70" class="fnanchor">[70]</a> With the same directness of purpose, Darwin, +too, pursues his way. With the same candor +and love of truth, he points out the strength and the +weakness of his demonstrations. With masterly equanimity +he holds aloof from the discussion of irrelevant +subjects and wins alike the admiration of his adherents +and of his adversaries.</p> + +<p>Scarcely thirty years have elapsed<a name="FNanchor_71_71" id="FNanchor_71_71"></a><a href="#Footnote_71_71" class="fnanchor">[71]</a> since Darwin first +propounded the principles of his theory of evolution.<span class="pagenum"><a name="Page_217" id="Page_217">[Pg 217]</a></span> +Yet, already we see his ideas firmly rooted in every +branch of human thought, however remote. Everywhere, +in history, in philosophy, even in the physical +sciences, we hear the watchwords: heredity, adaptation, +selection. We speak of the struggle for existence +among the heavenly bodies and of the struggle for existence +in the world of molecules.<a name="FNanchor_72_72" id="FNanchor_72_72"></a><a href="#Footnote_72_72" class="fnanchor">[72]</a></p> + +<p>The impetus given by Galileo to scientific thought +was marked in every direction; thus, his pupil, Borelli, +founded the school of exact medicine, from +whence proceeded even distinguished mathematicians. +And now Darwinian ideas, in the same way, are animating +all provinces of research. It is true, nature is +not made up of two distinct parts, the inorganic and +the organic; nor must these two divisions be treated +perforce by totally distinct methods. Many <i>sides</i>, however, +nature has. Nature is like a thread in an intricate +tangle, which must be followed and traced, now from +this point, now from that. But we must never imagine,—and +this physicists have learned from Faraday and +J. R. Mayer,—that progress along paths once entered +upon is the <i>only</i> means of reaching the truth.</p> + +<p>It will devolve upon the specialists of the future to +determine the relative tenability and fruitfulness of the +Darwinian ideas in the different provinces. Here I +wish simply to consider the growth of natural <i>knowledge</i> +in the light of the theory of evolution. For knowledge, +too, is a product of organic nature. And although<span class="pagenum"><a name="Page_218" id="Page_218">[Pg 218]</a></span> +ideas, as such, do not comport themselves in all respects +like independent organic individuals, and although +violent comparisons should be avoided, still, if Darwin +reasoned rightly, the general imprint of evolution and +transformation must be noticeable in ideas also.</p> + +<p>I shall waive here the consideration of the fruitful +topic of the transmission of ideas or rather of the +transmission of the aptitude for certain ideas.<a name="FNanchor_73_73" id="FNanchor_73_73"></a><a href="#Footnote_73_73" class="fnanchor">[73]</a> Nor +would it come within my province to discuss psychical +evolution in any form, as Spencer<a name="FNanchor_74_74" id="FNanchor_74_74"></a><a href="#Footnote_74_74" class="fnanchor">[74]</a> and many other +modern psychologists have done, with varying success. +Neither shall I enter upon a discussion of the +struggle for existence and of natural selection among +scientific theories.<a name="FNanchor_75_75" id="FNanchor_75_75"></a><a href="#Footnote_75_75" class="fnanchor">[75]</a> We shall consider here only such +processes of transformation as every student can easily +observe in his own mind.</p> +<p><span class="pagenum"><a name="Page_219" id="Page_219">[Pg 219]</a></span></p><p><span class="pagenum"><a name="Page_220" id="Page_220">[Pg 220]</a></span></p><p><span class="pagenum"><a name="Page_221" id="Page_221">[Pg 221]</a></span></p><p><span class="pagenum"><a name="Page_222" id="Page_222">[Pg 222]</a></span></p><p><span class="pagenum"><a name="Page_223" id="Page_223">[Pg 223]</a></span></p><p><span class="pagenum"><a name="Page_224" id="Page_224">[Pg 224]</a></span></p><p><span class="pagenum"><a name="Page_225" id="Page_225">[Pg 225]</a></span></p><p><span class="pagenum"><a name="Page_226" id="Page_226">[Pg 226]</a></span></p><p><span class="pagenum"><a name="Page_227" id="Page_227">[Pg 227]</a></span></p><p><span class="pagenum"><a name="Page_228" id="Page_228">[Pg 228]</a></span></p><p><span class="pagenum"><a name="Page_229" id="Page_229">[Pg 229]</a></span></p><p><span class="pagenum"><a name="Page_230" id="Page_230">[Pg 230]</a></span></p><p><span class="pagenum"><a name="Page_231" id="Page_231">[Pg 231]</a></span></p><p><span class="pagenum"><a name="Page_232" id="Page_232">[Pg 232]</a></span></p><p><span class="pagenum"><a name="Page_233" id="Page_233">[Pg 233]</a></span></p> +<hr class="tb" /> + +<p>The child of the forest picks out and pursues with +marvellous acuteness the trails of animals. He outwits +and overreaches his foes with surpassing cunning. +He is perfectly at home in the sphere of his peculiar +experience. But confront him with an unwonted phenomenon; +place him face to face with a technical product +of modern civilisation, and he will lapse into impotency +and helplessness. Here are facts which he +does not comprehend. If he endeavors to grasp their +meaning, he misinterprets them. He fancies the moon, +when eclipsed, to be tormented by an evil spirit. To +his mind a puffing locomotive is a living monster. The +letter accompanying a commission with which he is +entrusted, having once revealed his thievishness, is in +his imagination a conscious being, which he must hide +beneath a stone, before venturing to commit a fresh +trespass. Arithmetic to him is like the art of the +geomancers in the Arabian Nights,—an art which is +able to accomplish every imaginable impossibility. +And, like Voltaire's <i>ingénu</i>, when placed in our social +world, he plays, as we think, the maddest pranks.</p> + +<p>With the man who has made the achievements of +modern science and civilisation his own, the case is +quite different. He sees the moon pass temporarily +into the shadow of the earth. He feels in his thoughts +the water growing hot in the boiler of the locomotive; +he feels also the increase of the tension which pushes +the piston forward. Where he is not able to trace the +direct relation of things he has recourse to his yard-stick +and table of logarithms, which aid and facilitate +his thought without predominating over it. Such opinions +as he cannot concur in, are at least known to him, +and he knows how to meet them in argument.</p> + +<p>Now, wherein does the difference between these +two men consist? The train of thought habitually +employed by the first one does not correspond to the +facts that he sees. He is surprised and nonplussed +at every step. But the thoughts of the second man +follow and anticipate events, his thoughts have become +adapted or accommodated to the larger field of +observation and activity in which he is located; he conceives +things as they are. The Indian's sphere of experience, +however, is quite different; his bodily organs +of sense are in constant activity; he is ever intensely +alert and on the watch for his foes; or, his entire attention +and energy are engaged in procuring sustenance. +Now, how can such a creature project his mind +into futurity, foresee or prophesy? This is not possible +until our fellow-beings have, in a measure, relieved +us of our concern for existence. It is then that we +acquire freedom for observation, and not infrequently +too that narrowness of thought which society helps and +teaches us to disregard.</p> + +<p>If we move for a time within a fixed circle of phenomena +which recur with unvarying uniformity, our +thoughts gradually adapt themselves to our environment; +our ideas reflect unconsciously our surroundings. +The stone we hold in our hand, when dropped, +not only falls to the ground in reality; it also falls in +our thoughts. Iron-filings dart towards a magnet in +imagination as well as in fact, and, when thrown into +a fire, they grew hot in conception as well.</p> + +<p>The impulse to complete mentally a phenomenon +that has been only partially observed, has not its origin +in the phenomenon itself; of this fact, we are fully +sensible. And we well know that it does not lie within +the sphere of our volition. It seems to confront us +rather as a power and a law imposed from without +and controlling both thought and facts.</p> + +<p>The fact that we are able by the help of this law to +prophesy and forecast, merely proves a sameness or +uniformity of environment sufficient to effect a mental +adaptation of this kind. A necessity of fulfilment, +however, is not contained in this compulsory principle +which controls our thoughts; nor is it in any way determined +by the possibility of prediction. We are always +obliged, in fact, to await the completion of what +has been predicted. Errors and departures are constantly +discernible, and are slight only in provinces of +great rigid constancy, as in astronomy.</p> + +<p>In cases where our thoughts follow the connexion +of events with ease, and in instances where we positively +forefeel the course of a phenomenon, it is natural +to fancy that the latter is determined by and must +conform to our thoughts. But the belief in that mysterious +agency called <i>causality</i>, which holds thought and +event in unison, is violently shaken when a person first +enters a province of inquiry in which he has previously +had no experience. Take for instance the strange +interaction of electric currents and magnets, or the +reciprocal action of currents, which seem to defy all +the resources of mechanical science. Let him be confronted +with such phenomena and he will immediately +feel himself forsaken by his power of prediction; he +will bring nothing with him into this strange field of +events but the hope of soon being able to adapt his +ideas to the new conditions there presented.</p> + +<p>A person constructs from a bone the remaining +anatomy of an animal; or from the visible part of a +half-concealed wing of a butterfly he infers and reconstructs +the part concealed. He does so with a feeling +of highest confidence in the accuracy of his results; +and in these processes we find nothing preternatural +or transcendent. But when physicists adapt their +thoughts to conform to the dynamical course of events +in time, we invariably surround their investigations +with a metaphysical halo; yet these latter adaptations +bear quite the same character as the former, and our +only reason for investing them with a metaphysical +garb, perhaps, is their high practical value.<a name="FNanchor_76_76" id="FNanchor_76_76"></a><a href="#Footnote_76_76" class="fnanchor">[76]</a></p> + +<p>Let us consider for a moment what takes place +when the field of observation to which our ideas have +been adapted and now conform, becomes enlarged. +We had, let us say, always seen heavy bodies sink +when their support was taken away; we had also seen, +perhaps, that the sinking of heavier bodies forced +lighter bodies upwards. But now we see a lever in +action, and we are suddenly struck with the fact that +a lighter body is lifting another of much greater weight. +Our customary train of thought demands its rights; +the new and unwonted event likewise demands its +rights. From this conflict between thought and fact +the <i>problem</i> arises; out of this partial contrariety springs +the question, "Why?" With the new adaptation to the +enlarged field of observation, the problem disappears, +or, in other words, is solved. In the instance cited, +we must adopt the habit of always considering the +mechanical work performed.</p> + +<p>The child just awakening into consciousness of the +world, knows no problem. The bright flower, the +ringing bell, are all new to it; yet it is surprised at +nothing. The out and out Philistine, whose only +thoughts lie in the beaten path of his every-day pursuits, +likewise has no problems. Everything goes its +wonted course, and if perchance a thing go wrong at +times, it is at most a mere object of curiosity and +not worth serious consideration. In fact, the question +"Why?" loses all warrant in relations where we are +familiar with every aspect of events. But the capable +and talented young man has his head full of problems; +he has acquired, to a greater or less degree, certain +habitudes of thought, and at the same time he is constantly +observing what is new and unwonted, and in +his case there is no end to the questions, "Why?"</p> + +<p>Thus, the factor which most promotes scientific +thought is the gradual widening of the field of experience. +We scarcely notice events we are accustomed +to; the latter do not really develop their intellectual +significance until placed in contrast with something to +which we are unaccustomed. Things that at home +are passed by unnoticed, delight us when abroad, +though they may appear in only slightly different forms. +The sun shines with heightened radiance, the flowers +bloom in brighter colors, our fellow-men accost us +with lighter and happier looks. And, returning home, +we find even the old familiar scenes more inspiring +and suggestive than before.</p> + +<p>Every motive that prompts and stimulates us to +modify and transform our thoughts, proceeds from +what is new, uncommon, and not understood. Novelty +excites wonder in persons whose fixed habits of thought +are shaken and disarranged by what they see. But the +element of wonder never lies in the phenomenon or +event observed; its place is in the person observing. +People of more vigorous mental type aim at once at an +<i>adaptation of thought</i> that will conform to what they +have observed. Thus does science eventually become +the natural foe of the wonderful. The sources of the +marvellous are unveiled, and surprise gives way to +calm interpretation.</p> + +<p>Let us consider such a mental transformative process +in detail. The circumstance that heavy bodies +fall to the earth appears perfectly natural and regular. +But when a person observes that wood floats upon +water, and that flames and smoke rise in the air, then +the contrary of the first phenomenon is presented. +An olden theory endeavors to explain these facts by imputing +to substances the power of volition, as that attribute +which is most familiar to man. It asserted +that every substance seeks its proper place, heavy +bodies tending downwards and light ones upwards. +It soon turned out, however, that even smoke had +weight, that it, too, sought its place below, and that +it was forced upwards only because of the downward +tendency of the air, as wood is forced to the surface of +water because the water exerts the greater downward +pressure.</p> + +<p>Again, we see a body thrown into the air. It ascends. +How is it that it does not seek its proper place? Why +does the velocity of its "violent" motion decrease as +it rises, while that of its "natural" fall increases as it +descends. If we mark closely the relation between +these two facts, the problem will solve itself. We shall +see, as Galileo did, that the decrease of velocity in +rising and the increase of velocity in falling are one +and the same phenomenon, viz., an increase of velocity +towards the earth. Accordingly, it is not a place +that is assigned to the body, but an increase of velocity +towards the earth.</p> + +<p>By this idea the movements of heavy bodies are +rendered perfectly familiar. Newton, now, firmly +grasping this new way of thinking, sees the moon and +the planets moving in their paths upon principles similar +to those which determine the motion of a projectile +thrown into the air. Yet the movements of the +planets were marked by peculiarities which compelled +him once more to modify slightly his customary mode +of thought. The heavenly bodies, or rather the parts +composing them, do not move with constant accelerations +towards each other, but "attract each other," +directly as the mass and inversely as the square of the +distance.</p> + +<p>This latter notion, which includes the one applying +to terrestrial bodies as a special case, is, as we see, +quite different from the conception from which we +started. How limited in scope was the original idea +and to what a multitude of phenomena is not the present +one applicable! Yet there is a trace, after all, +of the "search for place" in the expression "attraction." +And it would be folly, indeed, for us to avoid, +with punctilious dread, this conception of "attraction" +as bearing marks of its pedigree. It is the historical +base of the Newtonian conception and it still continues +to direct our thoughts in the paths so long familiar to +us. Thus, the happiest ideas do not fall from heaven, +but spring from notions already existing.</p> + +<p>Similarly, a ray of light was first regarded as a continuous +and homogeneous straight line. It then became +the path of projection for minute missiles; then +an aggregate of the paths of countless different kinds +of missiles. It became periodic; it acquired various +sides; and ultimately it even lost its motion in a +straight line.</p> + +<p>The electric current was conceived originally as +the flow of a hypothetical fluid. To this conception +was soon added the notion of a chemical current, the +notion of an electric, magnetic, and anisotropic optical +field, intimately connected with the path of the current. +And the richer a conception becomes in following +and keeping pace with facts, the better adapted it +is to anticipate them.</p> + +<p>Adaptive processes of this kind have no assignable +beginning, inasmuch as every problem that incites +to new adaptation, presupposes a fixed habitude of +thought. Moreover, they have no visible end; in so +far as experience never ceases. Science, accordingly, +stands midway in the evolutionary process; and science +may advantageously direct and promote this process, +but it can never take its place. That science is inconceivable +the principles of which would enable a person +with no experience to construct the world of experience, +without a knowledge of it. One might just as +well expect to become a great musician, solely by the +aid of theory, and without musical experience; or to +become a painter by following the directions of a text-book.</p> + +<p>In glancing over the history of an idea with which +we have become perfectly familiar, we are no longer +able to appreciate the full significance of its growth. +The deep and vital changes that have been effected in +the course of its evolution, are recognisable only from +the astounding narrowness of view with which great +contemporary scientists have occasionally opposed +each other. Huygens's wave-theory of light was incomprehensible +to Newton, and Newton's idea of universal +gravity was unintelligible to Huygens. But a +century afterwards both notions were reconcilable, +even in ordinary minds.</p> + +<p>On the other hand, the original creations of pioneer +intellects, unconsciously formed, do not assume +a foreign garb; their form is their own. In them, +childlike simplicity is joined to the maturity of manhood, +and they are not to be compared with processes +of thought in the average mind. The latter are carried +on as are the acts of persons in the state of mesmerism, +where actions involuntarily follow the images which +the words of other persons suggest to their minds.</p> + +<p>The ideas that have become most familiar through +long experience, are the very ones that intrude themselves +into the conception of every new fact observed. +In every instance, thus, they become involved in a +struggle for self-preservation, and it is just they that +are seized by the inevitable process of transformation.</p> + +<p>Upon this process rests substantially the method +of explaining by hypothesis new and uncomprehended +phenomena. Thus, instead of forming entirely new +notions to explain the movements of the heavenly +bodies and the phenomena of the tides, we imagine the +material particles composing the bodies of the universe +to possess weight or gravity with respect to one another. +Similarly, we imagine electrified bodies to be +freighted with fluids that attract and repel, or we conceive +the space between them to be in a state of elastic +tension. In so doing, we substitute for new ideas +distinct and more familiar notions of old experience—notions +which to a great extent run unimpeded in their +courses, although they too must suffer partial transformation.</p> + +<p>The animal cannot construct new members to perform +every new function that circumstances and fate +demand of it. On the contrary it is obliged to make +use of those it already possesses. When a vertebrate +animal chances into an environment where it must +learn to fly or swim, an additional pair of extremities is +not grown for the purpose. On the contrary, the animal +must adapt and transform a pair that it already +has.</p> + +<p>The construction of hypotheses, therefore, is not +the product of artificial scientific methods. This process +is unconsciously carried on in the very infancy of +science. Even later, hypotheses do not become detrimental +and dangerous to progress except when more +reliance is placed on them than on the facts themselves; +when the contents of the former are more +highly valued than the latter, and when, rigidly adhering +to hypothetical notions, we overestimate the +ideas we possess as compared with those we have to +acquire.</p> + +<p>The extension of our sphere of experience always +involves a transformation of our ideas. It matters not +whether the face of nature becomes actually altered, +presenting new and strange phenomena, or whether +these phenomena are brought to light by an intentional +or accidental turn of observation. In fact, all the varied +methods of scientific inquiry and of purposive +mental adaptation enumerated by John Stuart Mill, +those of observation as well as those of experiment, +are ultimately recognisable as forms of one fundamental +method, the method of change, or variation. It is +through change of circumstances that the natural philosopher +learns. This process, however, is by no means +confined to the investigator of nature. The historian, +the philosopher, the jurist, the mathematician, the +artist, the æsthetician,<a name="FNanchor_77_77" id="FNanchor_77_77"></a><a href="#Footnote_77_77" class="fnanchor">[77]</a> all illuminate and unfold their +ideas by producing from the rich treasures of memory +similar, but different, cases; thus, they observe and +experiment in their thoughts. Even if all sense-experience +should suddenly cease, the events of the days +past would meet in different attitudes in the mind +and the process of adaptation would still continue—a +process which, in contradistinction to the adaptation +of thoughts to facts in practical spheres, would be +strictly theoretical, being an adaptation of thoughts to +thoughts.</p> + +<p>The method of change or variation brings before us +like cases of phenomena, having partly the same and +partly different elements. It is only by comparing +different cases of refracted light at changing angles of +incidence that the common factor, the constancy of +the refractive index, is disclosed. And only by comparing +the refractions of light of different colors, does +the difference, the inequality of the indices of refraction, +arrest the attention. Comparison based upon +change leads the mind simultaneously to the highest +abstractions and to the finest distinctions.</p> + +<p>Undoubtedly, the animal also is able to distinguish +between the similar and dissimilar of two cases. Its +consciousness is aroused by a noise or a rustling, and +its motor centre is put in readiness. The sight of the +creature causing the disturbance, will, according to its +size, provoke flight or prompt pursuit; and in the latter +case, the more exact distinctions will determine the +mode of attack. But man alone attains to the faculty +of voluntary and conscious comparison. Man alone +can, by his power of abstraction, rise, in one moment, +to the comprehension of principles like the conservation +of mass or the conservation of energy, and in the +next observe and mark the arrangement of the iron +lines in the spectrum. In thus dealing with the objects +of his conceptual life, his ideas unfold and expand, +like his nervous system, into a widely ramified +and organically articulated tree, on which he may follow +every limb to its farthermost branches, and, when +occasion demands, return to the trunk from which he +started.</p> + +<p>The English philosopher Whewell has remarked +that two things are requisite to the formation of science: +facts and ideas. Ideas alone lead to empty +speculation; mere facts can yield no organic knowledge. +We see that all depends upon the capacity of +adapting existing notions to fresh facts.</p> + +<p>Over-readiness to yield to every new fact prevents +fixed habits of thought from arising. Excessively rigid +habits of thought impede freedom of observation. In +the struggle, in the compromise between judgment +and prejudgment (prejudice), if we may use the term, +our understanding of things broadens.</p> + +<p>Habitual judgment, applied to a new case without +antecedent tests, we call prejudgment or prejudice. +Who does not know its terrible power! But we think +less often of the importance and utility of prejudice. +Physically, no one could exist, if he had to guide and +regulate the circulation, respiration, and digestion of +his body by conscious and purposive acts. So, too, +no one could exist intellectually if he had to form judgments +on every passing experience, instead of allowing +himself to be controlled by the judgments he has +already formed. Prejudice is a sort of reflex motion +in the province of intelligence.</p> + +<p>On prejudices, that is, on habitual judgments not +tested in every case to which they are applied, reposes +a goodly portion of the thought and work of the natural +scientist. On prejudices reposes most of the conduct +of society. With the sudden disappearance of +prejudice society would hopelessly dissolve. That +prince displayed a deep insight into the power of intellectual +habit, who quelled the loud menaces and +demands of his body-guard for arrears of pay and compelled +them to turn about and march, by simply pronouncing +the regular word of command; he well knew +that they would be unable to resist that.</p> + +<p>Not until the discrepancy between habitual judgments +and facts becomes great is the investigator implicated +in appreciable illusion. Then tragic complications +and catastrophes occur in the practical life of +individuals and nations—crises where man, placing +custom above life, instead of pressing it into the service +of life, becomes the victim of his error. The very +power which in intellectual life advances, fosters, and +sustains us, may in other circumstances delude and +destroy us.</p> +<p><span class="pagenum"><a name="Page_234" id="Page_234">[Pg 234]</a></span></p><p><span class="pagenum"><a name="Page_235" id="Page_235">[Pg 235]</a></span></p><p><span class="pagenum"><a name="Page_236" id="Page_236">[Pg 236]</a></span></p> +<hr class="tb" /> + +<p>Ideas are not all of life. They are only momentary +efflorescences of light, designed to illuminate the paths +of the will. But as delicate reagents on our organic +evolution our ideas are of paramount importance. No +theory can gainsay the vital transformation which we +feel taking place within us through their agency. Nor +is it necessary that we should have a proof of this process. +We are immediately assured of it.</p> + +<p>The transformation of ideas thus appears as a part +of the general evolution of life, as a part of its adaptation +to a constantly widening sphere of action. A +granite boulder on a mountain-side tends towards the +earth below. It must abide in its resting-place for +thousands of years before its support gives way. The +shrub that grows at its base is farther advanced; it +accommodates itself to summer and winter. The fox +which, overcoming the force of gravity, creeps to the +summit where he has scented his prey, is freer in his +movements than either. The arm of man reaches +further still; and scarcely anything of note happens +in Africa or Asia that does not leave an imprint upon +his life. What an immense portion of the life of +other men is reflected in ourselves; their joys, their +affections, their happiness and misery! And this too, +when we survey only our immediate surroundings, +and confine our attention to modern literature. How +much more do we experience when we travel through +ancient Egypt with Herodotus, when we stroll through +the streets of Pompeii, when we carry ourselves back +to the gloomy period of the crusades or to the golden +age of Italian art, now making the acquaintance of a +physician of Molière, and now that of a Diderot or of +a D'Alembert. What a great part of the life of others, +of their character and their purpose, do we not absorb +through poetry and music! And although they only +gently touch the chords of our emotions, like the memory +of youth softly breathing upon the spirit of an +aged man, we have nevertheless lived them over again +in part. How great and comprehensive does self become +in this conception; and how insignificant the +person! Egoistical systems both of optimism and pessimism +perish with their narrow standard of the import +of intellectual life. We feel that the real pearls +of life lie in the ever changing contents of consciousness, +and that the person is merely an indifferent symbolical +thread on which they are strung.<a name="FNanchor_78_78" id="FNanchor_78_78"></a><a href="#Footnote_78_78" class="fnanchor">[78]</a></p> + +<p>We are prepared, thus, to regard ourselves and +every one of our ideas as a product and a subject of +universal evolution; and in this way we shall advance +sturdily and unimpeded along the paths which the +future will throw open to us.<a name="FNanchor_79_79" id="FNanchor_79_79"></a><a href="#Footnote_79_79" class="fnanchor">[79]</a></p> + + + + +<h2><a name="ON_THE_PRINCIPLE_OF_COMPARISON" id="ON_THE_PRINCIPLE_OF_COMPARISON">ON THE PRINCIPLE OF COMPARISON +IN PHYSICS.</a><a name="FNanchor_80_80" id="FNanchor_80_80"></a><a href="#Footnote_80_80" class="fnanchor">[80]</a></h2> + + +<p>Twenty years ago when Kirchhoff defined the object +of mechanics as the "description, in complete +and very simple terms, of the motions occurring in nature," +he produced by the statement a peculiar impression. +Fourteen years subsequently, Boltzmann, in the +life-like picture which he drew of the great inquirer, +could still speak of the universal astonishment at this +novel method of treating mechanics, and we meet with +epistemological treatises to-day, which plainly show +how difficult is the acceptance of this point of view. A +modest and small band of inquirers there were, however, +to whom Kirchhoff's few words were tidings of a +welcome and powerful ally in the epistemological field.</p> + +<p>Now, how does it happen that we yield our assent +so reluctantly to the philosophical opinion of an inquirer +for whose scientific achievements we have only +words of praise? One reason probably is that few inquirers +can find time and leisure, amid the exacting<span class="pagenum"><a name="Page_237" id="Page_237">[Pg 237]</a></span> +employments demanded for the acquisition of new +knowledge, to inquire closely into that tremendous +psychical process by which science is formed. Further, +it is inevitable that much should be put into Kirchhoff's +rigid words that they were not originally intended to +convey, and that much should be found wanting in +them that had always been regarded as an essential +element of scientific knowledge. What can mere description +accomplish? What has become of explanation, +of our insight into the causal connexion of things?</p> +<p><span class="pagenum"><a name="Page_238" id="Page_238">[Pg 238]</a></span></p><p><span class="pagenum"><a name="Page_239" id="Page_239">[Pg 239]</a></span></p> +<hr class="tb" /> + +<p>Permit me, for a moment, to contemplate not the +results of science, but the mode of its <i>growth</i>, in a +frank and unbiassed manner. We know of only <i>one</i> +source of <i>immediate revelation</i> of scientific facts—<i>our +senses</i>. Restricted to this source alone, thrown wholly +upon his own resources, obliged to start always anew, +what could the isolated individual accomplish? Of a +stock of knowledge so acquired the science of a distant +negro hamlet in darkest Africa could hardly give +us a sufficiently humiliating conception. For there +that veritable miracle of thought-transference has already +begun its work, compared with which the miracles +of the spiritualists are rank monstrosities—<i>communication +by language</i>. Reflect, too, that by means +of the magical characters which our libraries contain +we can raise the spirits of the "the sovereign dead of +old" from Faraday to Galileo and Archimedes, through +ages of time—spirits who do not dismiss us with ambiguous +and derisive oracles, but tell us the best they +know; then shall we feel what a stupendous and indispensable +factor in the formation of science <i>communication</i> +is. Not the dim, half-conscious <i>surmises</i> +of the acute observer of nature or critic of humanity +belong to science, but only that which they possess +clearly enough to <i>communicate</i> to others.</p> + +<p>But how, now, do we go about this communication +of a newly acquired experience, of a newly observed +fact? As the different calls and battle-cries of gregarious +animals are unconsciously formed signs for +a common observation or action, irrespective of the +causes which produce such action—a fact that already +involves the germ of the concept; so also the words +of human language, which is only more highly specialised, +are names or signs for universally known +facts, which all can observe or have observed. If the +mental representation, accordingly, follows the new +fact at once and <i>passively</i>, then that new fact must, of +itself, immediately be constituted and represented in +thought by facts already universally known and commonly +observed. Memory is always ready to put forward +for <i>comparison</i> known facts which resemble the +new event, or agree with it in certain features, and +so renders possible that elementary internal judgment +which the mature and definitively formulated judgment +soon follows.</p> + +<p>Comparison, as the fundamental condition of communication, +is the most powerful inner vital element +of science. The zoölogist sees in the bones of the +wing-membranes of bats, fingers; he compares the +bones of the cranium with the vertebræ, the embryos +of different organisms with one another, and the different +stages of development of the same organism +with one another. The geographer sees in Lake Garda +a fjord, in the Sea of Aral a lake in process of drying +up. The philologist compares different languages with +one another, and the formations of the same language +as well. If it is not customary to speak of comparative +physics in the same sense that we speak of comparative +anatomy, the reason is that in a science of +such great experimental activity the attention is turned +away too much from the <i>contemplative</i> element. But +like all other sciences, physics lives and grows by +comparison.</p> +<p><span class="pagenum"><a name="Page_240" id="Page_240">[Pg 240]</a></span></p><p><span class="pagenum"><a name="Page_241" id="Page_241">[Pg 241]</a></span></p> +<hr class="tb" /> + +<p>The manner in which the result of the comparison +finds expression in the communication, varies of course +very much. When we say that the colors of the spectrum +are red, yellow, green, blue, and violet, the designations +employed may possibly have been derived +from the technology of tattooing, or they may subsequently +have acquired the significance of standing for +the colors of the rose, the lemon, the leaf, the corn-flower, +and the violet. From the frequent repetition +of such comparisons, however, made under the most +manifold circumstances, the inconstant features, as +compared with the permanent congruent features, get +so obliterated that the latter acquire a fixed significance +independent of every object and connexion, or take on +as we say an <i>abstract</i> or <i>conceptual</i> import. No one +thinks at the word "red" of any other agreement with +the rose than that of color, or at the word "straight" +of any other property of a stretched cord than the +sameness of direction. Just so, too, numbers, originally +the names of the fingers of the hands and feet, +from being used as arrangement-signs for all kinds of +objects, were lifted to the plane of abstract concepts. +A verbal report (communication) of a fact that uses +only these purely abstract implements, we call a <i>direct +description</i>.</p> + +<p>The direct description of a fact of any great extent +is an irksome task, even where the requisite notions +are already completely developed. What a simplification +it involves if we can say, the fact <i>A</i> now +considered comports itself, not in <i>one</i>, but in <i>many</i> or +in <i>all</i> its features, like an old and well-known fact <i>B</i>. +The moon comports itself as a heavy body does with +respect to the earth; light like a wave-motion or an +electric vibration; a magnet, as if it were laden with +gravitating fluids, and so on. We call such a description, +in which we appeal, as it were, to a description +already and elsewhere formulated, or perhaps still to +be precisely formulated, an <i>indirect description</i>. We +are at liberty to supplement this description, gradually, +by direct description, to correct it, or to replace it altogether. +We see, thus, without difficulty, that what is +called a <i>theory</i> or a <i>theoretical idea</i>, falls under the +category of what is here termed indirect description.</p> +<p><span class="pagenum"><a name="Page_242" id="Page_242">[Pg 242]</a></span></p><p><span class="pagenum"><a name="Page_243" id="Page_243">[Pg 243]</a></span></p><p><span class="pagenum"><a name="Page_244" id="Page_244">[Pg 244]</a></span></p><p><span class="pagenum"><a name="Page_245" id="Page_245">[Pg 245]</a></span></p><p><span class="pagenum"><a name="Page_246" id="Page_246">[Pg 246]</a></span></p><p><span class="pagenum"><a name="Page_247" id="Page_247">[Pg 247]</a></span></p><p><span class="pagenum"><a name="Page_248" id="Page_248">[Pg 248]</a></span></p><p><span class="pagenum"><a name="Page_249" id="Page_249">[Pg 249]</a></span></p><p><span class="pagenum"><a name="Page_250" id="Page_250">[Pg 250]</a></span></p><p><span class="pagenum"><a name="Page_251" id="Page_251">[Pg 251]</a></span></p><p><span class="pagenum"><a name="Page_252" id="Page_252">[Pg 252]</a></span></p> +<hr class="tb" /> + +<p>What, now, is a theoretical idea? Whence do we +get it? What does it accomplish for us? Why does it +occupy a higher place in our judgment than the mere +holding fast to a fact or an observation? Here, too, +memory and comparison alone are in play. But instead +of <i>a single</i> feature of resemblance culled from +memory, in this case <i>a great system</i> of resemblances +confronts us, a well-known physiognomy, by means of +which the new fact is immediately transformed into an +old acquaintance. Besides, it is in the power of the +idea to offer us more than we actually see in the new +fact, at the first moment; it can extend the fact, and +enrich it with features which we are first induced to +<i>seek</i> from such suggestions, and which are often actually +found. It is this <i>rapidity</i> in extending knowledge +that gives to theory a preference over simple observation. +But that preference is wholly <i>quantitative</i>. +Qualitatively, and in real essential points, theory differs +from observation neither in the mode of its origin +nor in its last results.</p> + +<p>The adoption of a theory, however, always involves +a danger. For a theory puts in the place of a fact <i>A</i> +in thought, always a <i>different</i>, but simpler and more +familiar fact <i>B</i>, which in <i>some</i> relations can mentally +represent <i>A</i>, but for the very reason that it is different, +in other relations cannot represent it. If now, as +may readily happen, sufficient care is not exercised, +the most fruitful theory may, in special circumstances, +become a downright obstacle to inquiry. Thus, the +emission-theory of light, in accustoming the physicist +to think of the projectile path of the "light-particles" +as an undifferentiated straight-line, demonstrably impeded +the discovery of the periodicity of light. By +putting in the place of light the more familiar phenomena +of sound, Huygens renders light in many of +its features a familiar event, but with respect to polarisation, +which lacks the longitudinal waves with which +alone he was acquainted, it had for him a doubly +strange aspect. He is unable thus to grasp in abstract +thought the fact of polarisation, which is before his +eyes, whilst Newton, merely by adapting to the observation +his thoughts, and putting this question, "<i>Annon +radiorum luminis diversa sunt latera?</i>" abstractly +grasped polarisation, that is, directly described it, a +century before Malus. On the other hand, if the +agreement of the fact with the idea theoretically representing +it, extends further than its inventor originally +anticipated, then we may be led by it to unexpected +discoveries, of which conical refraction, circular polarisation +by total reflexion, Hertz's waves offer ready +examples, in contrast to the illustrations given above.</p> + +<p>Our insight into the conditions indicated will be +improved, perhaps, by contemplating the development +of some theory or other more in detail. Let us consider +a magnetised bar of steel by the side of a second +unmagnetised bar, in all other respects the same. The +second bar gives no indication of the presence of iron-filings; +the first attracts them. Also, when the iron-filings +are absent, we must think of the magnetised +bar as in a different condition from that of the unmagnetised. +For, that the mere presence of the iron-filings +does not induce the phenomenon of attraction is proved +by the second unmagnetised bar. The ingenuous man, +who finds in his will, as his most familiar source of +power, the best facilities for comparison, conceives a +species of <i>spirit</i> in the magnet. The behavior of a +warm body or of an <i>electrified</i> body suggests similar +ideas. This is the point of view of the oldest theory, +<i>fetishism</i>, which the inquirers of the early Middle +Ages had not yet overcome, and which in its last vestiges, +in the conception of forces, still flourishes in +modern physics. We see, thus, the <i>dramatic</i> element +need no more be absent in a scientific description, than +in a thrilling novel.</p> + +<p>If, on subsequent examination, it be observed that +a cold body, in contact with a hot body, warms itself, +so to speak, <i>at the expense</i> of the hot body; further, +that when the substances are the same, the cold body, +which, let us say, has twice the mass of the other, +gains only half the number of degrees of temperature +that the other loses, a wholly new impression arises. +The demoniac character of the event vanishes, for the +supposed spirit acts not by caprice, but according to +fixed laws. In its place, however, <i>instinctively</i> the +notion of a <i>substance</i> is substituted, part of which flows +over from the one body to the other, but the total +amount of which, representable by the sum of the products +of the masses into the respective changes of +temperature, remains constant. Black was the first to +be <i>powerfully</i> struck with this resemblance of thermal +processes to the motion of a substance, and under its +guidance discovered the specific heat, the heat of fusion, +and the heat of vaporisation of bodies. Gaining +strength and fixity, however, from these successes, +this notion of substance subsequently stood in the way +of scientific advancement. It blinded the eyes of the +successors of Black, and prevented them from seeing +the manifest fact, which every savage knows, that heat +is <i>produced</i> by friction. Fruitful as that notion was +for Black, helpful as it still is to the learner to-day in +Black's special field, permanent and universal validity +as a <i>theory</i> it could never maintain. But what is essential, +conceptually, in it, viz., the constancy of the product-sum +above mentioned, retains its value and may +be regarded as a <i>direct description</i> of Black's facts.</p> + +<p>It stands to reason that those theories which push +themselves forward unsought, instinctively, and wholly +of their own accord, should have the greatest power, +should carry our thoughts most with them, and exhibit +the staunchest powers of self-preservation. On the +other hand, it may also be observed that when critically +scrutinised such theories are extremely apt to +lose their cogency. We are constantly busied with +"substance," its modes of action have stamped themselves +indelibly upon our thoughts, our vividest and +clearest reminiscences are associated with it. It should +cause us no surprise, therefore, that Robert Mayer and +Joule, who gave the final blow to Black's substantial +conception of heat, should have re-introduced the +same notion of substance in a more abstract and modified +form, only applying to a much more extensive +field.</p> + +<p>Here, too, the psychological circumstances which +impart to the new conception its power, lie clearly before +us. By the unusual redness of the venous blood +in tropical climates Mayer's attention is directed to +the lessened expenditure of internal heat and to the +proportionately lessened <i>consumption of material</i> by the +human body in those climates. But as every effort of +the human organism, including its mechanical work, +is connected with the consumption of material, and as +work by friction can engender heat, therefore heat and +work appear in kind equivalent, and between them a +proportional relation must subsist. Not <i>every</i> quantity, +but the appropriately calculated <i>sum</i> of the two, as +connected with a proportionate consumption of material, +appears <i>substantial</i>.</p> + +<p>By exactly similar considerations, relative to the +economy of the galvanic element, Joule arrived at his +view; he found experimentally that the sum of the +heat evolved in the circuit, of the heat consumed in the +combustion of the gas developed, of the electro-magnetic +work of the current, properly calculated,—in +short, the sum of all the effects of the battery,—is connected +with a proportionate consumption of zinc. Accordingly, +this sum itself has a substantial character.</p> + +<p>Mayer was so absorbed with the view attained, +that the indestructibility of <i>force</i>, in our phraseology +<i>work</i>, appeared to him <i>a priori</i> evident. "The creation +or annihilation of a force," he says, "lies without +the province of human thought and power." Joule +expressed himself to a similar effect: "It is manifestly +absurd to suppose that the powers with which God +has endowed matter can be destroyed." Strange to +say, on the basis of such utterances, not Joule, but +Mayer, was stamped as a metaphysician. We may +be sure, however, that both men were merely giving +expression, and that half-unconsciously, to a powerful +<i>formal</i> need of the new simple view, and that both +would have been extremely surprised if it had been +proposed to them that their principle should be submitted +to a philosophical congress or ecclesiastical +synod for a decision upon its validity. But with all +agreements, the attitude of these two men, in other +respects, was totally different. Whilst Mayer represented +this <i>formal</i> need with all the stupendous instinctive +force of genius, we might say almost with the +ardor of fanaticism, yet was withal not wanting in the +conceptive ability to compute, prior to all other inquirers, +the mechanical equivalent of heat from old +physical constants long known and at the disposal of +all, and so to set up for the new doctrine a programme +embracing all physics and physiology; Joule, on the +other hand, applied himself to the exact verification of +the doctrine by beautifully conceived and masterfully +executed experiments, extending over all departments +of physics. Soon Helmholtz too attacked the problem, +in a totally independent and characteristic manner. +After the professional virtuosity with which this physicist +grasped and disposed of all the points unsettled +by Mayer's programme and more besides, what especially +strikes us is the consummate critical lucidity of +this young man of twenty-six years. In his exposition +is wanting that vehemence and impetuosity which +marked Mayer's. The principle of the conservation +of energy is no self-evident or <i>a priori</i> proposition for +him. What follows, on the assumption that that proposition +obtains? In this hypothetical form, he subjugates +his matter.</p> + +<p>I must confess, I have always marvelled at the +æsthetic and ethical taste of many of our contemporaries +who have managed to fabricate out of this relation +of things, odious national and personal questions, +instead of praising the good fortune that made <i>several</i> +such men work together and of rejoicing at the instructive +diversity and idiosyncrasies of great minds +fraught with such rich consequences for us.</p> + +<p>We know that still another theoretical conception +played a part in the development of the principle of +energy, which Mayer held aloof from, namely, the conception +that heat, as also the other physical processes, +are due to motion. But once the principle of energy +has been reached, these auxiliary and transitional theories +discharge no essential function, and we may regard +the principle, like that which Black gave, as a +contribution to the <i>direct description</i> of a widely extended +domain of facts.</p> + +<p>It would appear from such considerations not only +advisable, but even necessary, with all due recognition +of the helpfulness of theoretic ideas in research, +yet gradually, as the new facts grow familiar, to substitute +for indirect description <i>direct</i> description, which +contains nothing that is unessential and restricts itself +absolutely to the abstract apprehension of facts. We +might almost say, that the descriptive sciences, so +called with a tincture of condescension, have, in respect +of scientific character, outstripped the physical +expositions lately in vogue. Of course, a virtue has +been made of necessity here.</p> + +<p>We must admit, that it is not in our power to describe +directly every fact, on the moment. Indeed, +we should succumb in utter despair if the whole wealth +of facts which we come step by step to know, were +presented to us all at once. Happily, only detached +and unusual features first strike us, and such we bring +nearer to ourselves by <i>comparison</i> with every-day +events. Here the notions of the common speech are +first developed. The comparisons then grow more +manifold and numerous, the fields of facts compared +more extensive, the concepts that make direct description +possible, proportionately more general and more +abstract.</p> + +<p>First we become familiar with the motion of freely +falling bodies. The concepts of force, mass, and work +are then carried over, with appropriate modifications, +to the phenomena of electricity and magnetism. A +stream of water is said to have suggested to Fourier +the first distinct picture of currents of heat. A special +case of vibrations of strings investigated by Taylor, +cleared up for him a special case of the conduction of +heat. Much in the same way that Daniel Bernoulli +and Euler constructed the most diverse forms of vibrations +of strings from Taylor's cases, so Fourier constructs +out of simple cases of conduction the most +multifarious motions of heat; and that method has +extended itself over the whole of physics. Ohm forms +his conception of the electric current in imitation of +Fourier's. The latter, also, adopts Fick's theory of +diffusion. In an analogous manner a conception of +the magnetic current is developed. All sorts of stationary +currents are thus made to exhibit common +features, and even the condition of complete equilibrium +in an extended medium shares these features +with the dynamical condition of equilibrium of a stationary +current. Things as remote as the magnetic +lines of force of an electric current and the stream-lines +of a frictionless liquid vortex enter in this way +into a peculiar relationship of similarity. The concept +of potential, originally enunciated for a restricted +province, acquires a wide-reaching applicability. +Things as dissimilar as pressure, temperature, +and electromotive force, now show points of agreement +in relation to ideas derived by definite methods +from that concept: viz., fall of pressure, fall of temperature, +fall of potential, as also with the further notions +of liquid, thermal, and electric strength of current. +That relationship between systems of ideas in +which the dissimilarity of every two homologous concepts +as well as the agreement in logical relations +of every two homologous pairs of concepts, is clearly +brought to light, is called an <i>analogy</i>. It is an effective +means of mastering heterogeneous fields of facts in +unitary comprehension. The path is plainly shown in +which <i>a universal physical phenomenology</i> embracing all +domains, will be developed.</p> + +<p>In the process described we attain for the first time +to what is indispensable in the direct description of +broad fields of fact—the wide-reaching <i>abstract concept</i>. +And now I must put a question smacking of the school-master, +but unavoidable: What is a concept? Is it a +hazy representation, admitting withal of mental visualisation? +No. Mental visualisation accompanies it +only in the simplest cases, and then merely as an adjunct. +Think, for example, of the "coefficient of self-induction," +and seek for its visualised mental image. +Or is, perhaps, the concept a mere word? The adoption +of this forlorn idea, which has been actually proposed +of late by a reputed mathematician would only +throw us back a thousand years into the deepest scholasticism. +We must, therefore, reject it.</p> + +<p>The solution is not far to seek. We must not think +that sensation, or representation, is a purely passive +process. The lowest organisms respond to it with a +simple reflex motion, by engulfing the prey which approaches +them. In higher organisms the centripetal +stimulus encounters in the nervous system obstacles +and aids which modify the centrifugal process. In still +higher organisms, where prey is pursued and examined, +the process in question may go through extensive +paths of circular motions before it comes to relative +rest. Our own life, too, is enacted in such +processes; all that we call science may be regarded +as parts, or middle terms, of such activities.</p> + +<p>It will not surprise us now if I say: the definition +of a concept, and, when it is very familiar, even its +name, is an <i>impulse</i> to some accurately determined, +often complicated, critical, comparative, or constructive +<i>activity</i>, the usually sense-perceptive result of +which is a term or member of the concept's scope. It +matters not whether the concept draws the attention +only to one certain sense (as sight) or to a phase of a +sense (as color, form), or is the starting-point of a +complicated action; nor whether the activity in question +(chemical, anatomical, and mathematical operations) +is muscular or technical, or performed wholly +in the imagination, or only intimated. The concept is +to the physicist what a musical note is to a piano-player. +A trained physicist or mathematician reads a +memoir like a musician reads a score. But just as the +piano-player must first learn to move his fingers singly +and collectively, before he can follow his notes without +effort, so the physicist or mathematician must go +through a long apprenticeship before he gains control, +so to speak, of the manifold delicate innervations +of his muscles and imagination. Think of how frequently +the beginner in physics or mathematics performs +more, or less, than is required, or of how frequently +he conceives things differently from what they +are! But if, after having had sufficient discipline, he +lights upon the phrase "coefficient of self-induction," +he knows immediately what that term requires of him. +Long and thoroughly practised <i>actions</i>, which have +their origin in the necessity of comparing and representing +facts by other facts, are thus the very kernel +of concepts. In fact, positive and philosophical philology +both claim to have established that all roots +represent concepts and stood originally for muscular +activities alone. The slow assent of physicists to +Kirchhoff's dictum now becomes intelligible. They +best could feel the vast amount of individual labor, +theory, and skill required before the ideal of direct +description could be realised.</p> +<p><span class="pagenum"><a name="Page_253" id="Page_253">[Pg 253]</a></span></p><p><span class="pagenum"><a name="Page_254" id="Page_254">[Pg 254]</a></span></p><p><span class="pagenum"><a name="Page_255" id="Page_255">[Pg 255]</a></span></p><p><span class="pagenum"><a name="Page_256" id="Page_256">[Pg 256]</a></span></p><p><span class="pagenum"><a name="Page_257" id="Page_257">[Pg 257]</a></span></p><p><span class="pagenum"><a name="Page_258" id="Page_258">[Pg 258]</a></span></p><p><span class="pagenum"><a name="Page_259" id="Page_259">[Pg 259]</a></span></p> +<hr class="tb" /> + +<p>Suppose, now, the ideal of a given province of +facts is reached. Does description accomplish all that +the inquirer can ask? In my opinion, it does. Description +is a building up of facts in thought, and this +building up is, in the experimental sciences, often the +condition of actual execution. For the physicist, to +take a special case, the metrical units are the building-stones, +the concepts the directions for building, and +the facts the result of the building. Our mental +imagery is almost a complete substitute for the fact, +and by means of it we can ascertain all the fact's properties. +We do not know that worst which we ourselves +have made.</p> + +<p>People require of science that it should <i>prophesy</i>, +and Hertz uses that expression in his posthumous +<i>Mechanics</i>. But, natural as it is, the expression is too +narrow. The geologist and the palæontologist, at times +the astronomer, and always the historian and the philologist, +prophesy, so to speak, <i>backwards</i>. The descriptive +sciences, like geometry and mathematics, prophesy +neither forward or backwards, but seek from given +conditions the conditioned. Let us say rather: <i>Science +completes in thought facts that are only partly given</i>. +This is rendered possible by description, for description +presupposes the interdependence of the descriptive +elements: otherwise nothing would be described.</p> + +<p>It is said, description leaves the sense of causality +unsatisfied. In fact, many imagine they understand +motions better when they picture to themselves the +pulling forces; and yet the <i>accelerations</i>, the facts, +accomplish more, without superfluous additions. I +hope that the science of the future will discard the +idea of cause and effect, as being formally obscure; +and in my feeling that these ideas contain a strong +tincture of fetishism, I am certainly not alone. The +more proper course is, <i>to regard the abstract determinative +elements of a fact as interdependent</i>, in a purely logical +way, as the mathematician or geometer does. +True, by comparison with the will, forces are brought +nearer to our feeling; but it may be that ultimately the +will itself will be made clearer by comparison with the +accelerations of masses.</p> + +<p>If we are asked, candidly, when is a fact <i>clear</i> to +us, we must say "when we can reproduce it by very +<i>simple</i> and very familiar intellectual operations, such +as the construction of accelerations, or the geometrical +summation of accelerations, and so forth." The +requirement of <i>simplicity</i> is of course to the expert +a different matter from what it is to the novice. For +the first, description by a system of differential equations +is sufficient; for the second, a gradual construction +out of elementary laws is required. The first +discerns at once the connexion of the two expositions. +Of course, it is not disputed that the <i>artistic</i> value of +materially equivalent descriptions may not be different.</p> + +<p>Most difficult is it to persuade strangers that the +grand universal laws of physics, such as apply indiscriminately +to material, electrical, magnetic, and other +systems, are not essentially different from descriptions. +As compared with many sciences, physics occupies in +this respect a position of vantage that is easily explained. +Take, for example, anatomy. As the anatomist +in his quest for agreements and differences in +animals ascends to ever higher and higher <i>classifications</i>, +the individual facts that represent the ultimate +terms of the system, are still so different that they +must be <i>singly</i> noted. Think, for example, of the common +marks of the Vertebrates, of the class-characters +of Mammals and Birds on the one hand and of Fishes +on the other, of the double circulation of the blood on +the one hand and of the single on the other. In the +end, always <i>isolated</i> facts remain, which show only a +<i>slight</i> likeness to one another.</p> + +<p>A science still more closely allied to physics, chemistry, +is often in the same strait. The abrupt change +of the qualitative properties, in all likelihood conditioned +by the slight stability of the intermediate states, +the remote resemblance of the co-ordinated facts of +chemistry render the treatment of its data difficult. +Pairs of bodies of different qualitative properties unite +in different mass-ratios; but no connexion between +the first and the last is to be noted, at first.</p> + +<p>Physics, on the other hand, reveals to us wide domains +of <i>qualitatively homogeneous</i> facts, differing from +one another only in the number of equal parts into +which their characteristic marks are divisible, that is, +differing only <i>quantitatively</i>. Even where we have to +deal with qualities (colors and sounds), quantitative +characters of those qualities are at our disposal. Here +the classification is so simple a task that it rarely impresses +us as such, whilst in infinitely fine gradations, +in a <i>continuum of facts</i>, our number-system is ready beforehand +to follow as far as we wish. The co-ordinated +facts are here extremely similar and very closely affined, +as are also their descriptions which consist in +the determination of the numerical measures of one +given set of characters from those of a different set by +means of familiar mathematical operations—methods +of derivation. Thus, the common characteristics of +all descriptions can be found here; and with them a +succinct, comprehensive description, or a rule for the +construction of all single descriptions, is assigned,—and +this we call <i>law</i>. Well-known examples are the +formulæ for freely falling bodies, for projectiles, for +central motion, and so forth. If physics apparently +accomplishes more by its methods than other sciences, +we must remember that in a sense it has presented to +it much simpler problems.</p> + +<p>The remaining sciences, whose facts also present a +physical side, need not be envious of physics for this +superiority; for all its acquisitions ultimately redound +to their benefit as well. But also in other ways this +mutual help shall and must change. Chemistry has advanced +very far in making the methods of physics her +own. Apart from older attempts, the periodical series +of Lothar Meyer and Mendelejeff are a brilliant and +adequate means of producing an easily surveyed system +of facts, which by gradually becoming complete, +will take the place almost of a continuum of facts. +Further, by the study of solutions, of dissociation, in +fact generally of phenomena which present a continuum +of cases, the methods of thermodynamics have +found entrance into chemistry. Similarly we may hope +that, at some future day, a mathematician, letting the +fact-continuum of embryology play before his mind, +which the palæontologists of the future will supposedly +have enriched with more intermediate and derivative +forms between Saurian and Bird than the isolated +Pterodactyl, Archæopteryx, Ichthyornis, and so forth, +which we now have—that such a mathematician shall +transform, by the variation of a few parameters, as in +a dissolving view, one form into another, just as we +transform one conic section into another.</p> + +<p>Reverting now to Kirchhoff's words, we can come +to some agreement regarding their import. Nothing +can be built without building-stones, mortar, scaffolding, +and a builder's skill. Yet assuredly the wish is +well founded, that will show to posterity the complete +structure in its finished form, bereft of unsightly scaffolding. +It is the pure logical and æsthetic sense of the +mathematician that speaks out of Kirchhoff's words. +Modern expositions of physics aspire after his ideal; +that, too, is intelligible. But it would be a poor didactic +shift, for one whose business it was to train +architects, to say: "Here is a splendid edifice; if thou +wouldst really build, go thou and do likewise".</p> + +<p>The barriers between the special sciences, which +make division of work and concentration possible, but +which appear to us after all as cold and conventional +restrictions, will gradually disappear. Bridge upon +bridge is thrown over the gaps. Contents and methods, +even of the remotest branches, are compared. +When the Congress of Natural Scientists shall meet a +hundred years hence, we may expect that they will +represent a unity in a higher sense than is possible to-day, +not in sentiment and aim alone, but in method +also. In the meantime, this great change will be +helped by our keeping constantly before our minds the +fact of the intrinsic relationship of all research, which +Kirchhoff characterised with such classical simplicity.</p> + + + + +<h2><a name="THE_PART_PLAYED_BY_ACCIDENT_IN" id="THE_PART_PLAYED_BY_ACCIDENT_IN">THE PART PLAYED BY ACCIDENT IN +INVENTION AND DISCOVERY.</a><a name="FNanchor_81_81" id="FNanchor_81_81"></a><a href="#Footnote_81_81" class="fnanchor">[81]</a></h2> + + +<p>It is characteristic of the naïve and sanguine +beginnings of thought in youthful men and +nations, that all problems are held to be soluble and +fundamentally intelligible on the first appearance of +success. The sage of Miletus, on seeing plants take +their rise from moisture, believed he had comprehended +the whole of nature, and he of Samos, on discovering +that definite numbers corresponded to the +lengths of harmonic strings, imagined he could exhaust +the nature of the world by means of numbers. +Philosophy and science in such periods are blended. +Wider experience, however, speedily discloses the +error of such a course, gives rise to criticism, and +leads to the division and ramification of the sciences.</p> + +<p>At the same time, the necessity of a broad and +general view of the world remains; and to meet this +need philosophy parts company with special inquiry.<span class="pagenum"><a name="Page_260" id="Page_260">[Pg 260]</a></span> +It is true, the two are often found united in gigantic +personalities. But as a rule their ways diverge more +and more widely from each other. And if the estrangement +of philosophy from science can reach a point +where data unworthy of the nursery are not deemed too +scanty as foundations of the world, on the other hand +the thorough-paced specialist may go to the extreme +of rejecting point-blank the possibility of a broader +view, or at least of deeming it superfluous, forgetful +of Voltaire's apophthegm, nowhere more applicable +than here, <i>Le superflu—chose très nécessaire</i>.</p> + +<p>It is true, the history of philosophy, owing to the +insufficiency of its constructive data, is and must be +largely a history of error. But it would be the height +of ingratitude on our part to forget that the seeds of +thoughts which still fructify the soil of special research, +such as the theory of irrationals, the conceptions +of conservation, the doctrine of evolution, the +idea of specific energies, and so forth, may be traced +back in distant ages to philosophical sources. Furthermore, +to have deferred or abandoned the attempt +at a broad philosophical view of the world from a full +knowledge of the insufficiency of our materials, is +quite a different thing from never having undertaken +it at all. The revenge of its neglect, moreover, is +constantly visited upon the specialist by his committal +of the very errors which philosophy long ago exposed. +As a fact, in physics and physiology, particularly +during the first half of this century, are to be<span class="pagenum"><a name="Page_261" id="Page_261">[Pg 261]</a></span> +met intellectual productions which for naïve simplicity +are not a jot inferior to those of the Ionian school, or +to the Platonic ideas, or to that much reviled ontological +proof.</p> + +<p>Latterly, there has been evidence of a gradual +change in the situation. Recent philosophy has set +itself more modest and more attainable ends; it is +no longer inimical to special inquiry; in fact, it is +zealously taking part in that inquiry. On the other +hand, the special sciences, mathematics and physics, +no less than philology, have become eminently philosophical. +The material presented is no longer accepted +uncritically. The glance of the inquirer is +bent upon neighboring fields, whence that material +has been derived. The different special departments +are striving for closer union, and gradually the conviction +is gaining ground that philosophy can consist +only of mutual, complemental criticism, interpenetration, +and union of the special sciences into a consolidated +whole. As the blood in nourishing the body +separates into countless capillaries, only to be collected +again and to meet in the heart, so in the science +of the future all the rills of knowledge will gather +more and more into a common and undivided stream.</p> + +<p>It is this view—not an unfamiliar one to the present +generation—that I purpose to advocate. Entertain +no hope, or rather fear, that I shall construct +systems for you. I shall remain a natural inquirer. +Nor expect that it is my intention to skirt all the<span class="pagenum"><a name="Page_262" id="Page_262">[Pg 262]</a></span> +fields of natural inquiry. I can attempt to be your +guide only in that branch which is familiar to me, and +even there I can assist in the furtherment of only a +small portion of the allotted task. If I shall succeed +in rendering plain to you the relations of physics, +psychology, and the theory of knowledge, so that you +may draw from each profit and light, redounding to +the advantage of each, I shall regard my work as not +having been in vain. Therefore, to illustrate by an +example how, consonantly with my powers and views, +I conceive such inquiries should be conducted, I shall +treat to-day, in the form of a brief sketch, of the following +special and limited subject—of <i>the part which +accidental circumstances play in the development of inventions +and discoveries</i>.</p> +<p><span class="pagenum"><a name="Page_263" id="Page_263">[Pg 263]</a></span></p><p><span class="pagenum"><a name="Page_264" id="Page_264">[Pg 264]</a></span></p><p><span class="pagenum"><a name="Page_265" id="Page_265">[Pg 265]</a></span></p><p><span class="pagenum"><a name="Page_266" id="Page_266">[Pg 266]</a></span></p><p><span class="pagenum"><a name="Page_267" id="Page_267">[Pg 267]</a></span></p><p><span class="pagenum"><a name="Page_268" id="Page_268">[Pg 268]</a></span></p><p><span class="pagenum"><a name="Page_269" id="Page_269">[Pg 269]</a></span></p><p><span class="pagenum"><a name="Page_270" id="Page_270">[Pg 270]</a></span></p><p><span class="pagenum"><a name="Page_271" id="Page_271">[Pg 271]</a></span></p><p><span class="pagenum"><a name="Page_272" id="Page_272">[Pg 272]</a></span></p><p><span class="pagenum"><a name="Page_273" id="Page_273">[Pg 273]</a></span></p><p><span class="pagenum"><a name="Page_274" id="Page_274">[Pg 274]</a></span></p><p><span class="pagenum"><a name="Page_275" id="Page_275">[Pg 275]</a></span></p><p><span class="pagenum"><a name="Page_276" id="Page_276">[Pg 276]</a></span></p><p><span class="pagenum"><a name="Page_277" id="Page_277">[Pg 277]</a></span></p><p><span class="pagenum"><a name="Page_278" id="Page_278">[Pg 278]</a></span></p><p><span class="pagenum"><a name="Page_279" id="Page_279">[Pg 279]</a></span></p><p><span class="pagenum"><a name="Page_280" id="Page_280">[Pg 280]</a></span></p><p><span class="pagenum"><a name="Page_281" id="Page_281">[Pg 281]</a></span></p><p><span class="pagenum"><a name="Page_282" id="Page_282">[Pg 282]</a></span></p> +<hr class="tb" /> + +<p>When we Germans say of a man that he was not +the inventor of gunpowder,<a name="FNanchor_82_82" id="FNanchor_82_82"></a><a href="#Footnote_82_82" class="fnanchor">[82]</a> we impliedly cast a grave +suspicion on his abilities. But the expression is not +a felicitous one, as there is probably no invention in +which deliberate thought had a smaller, and pure luck +a larger, share than in this. It is well to ask, Are we +justified in placing a low estimate on the achievement +of an inventor because accident has assisted him in +his work? Huygens, whose discoveries and inventions +are justly sufficient to entitle him to an opinion +in such matters, lays great emphasis on this factor. +He asserts that a man capable of inventing the telescope +without the concurrence of accident must have +been gifted with superhuman genius.<a name="FNanchor_83_83" id="FNanchor_83_83"></a><a href="#Footnote_83_83" class="fnanchor">[83]</a></p> + +<p>A man living in the midst of civilisation finds himself +surrounded by a host of marvellous inventions, +considering none other than the means of satisfying +the needs of daily life. Picture such a man transported +to the epoch preceding the invention of these +ingenious appliances, and imagine him undertaking +in a serious manner to comprehend their origin. At +first the intellectual power of the men capable of producing +such marvels will strike him as incredible, or, +if we adopt the ancient view, as divine. But his astonishment +is considerably allayed by the disenchanting +yet elucidative revelations of the history of primitive +culture, which to a large extent prove that these +inventions took their rise very slowly and by imperceptible +degrees.</p> + +<p>A small hole in the ground with fire kindled in it +constituted the primitive stove. The flesh of the +quarry, wrapped with water in its skin, was boiled by +contact with heated stones. Cooking by stones was +also done in wooden vessels. Hollow gourds were +protected from the fire by coats of clay. Thus, from +the burned clay accidentally originated the enveloping +pot, which rendered the gourd superfluous, although +for a long time thereafter the clay was still spread +over the gourd, or pressed into woven wicker-work +before the potter's art assumed its final independence. +Even then the wicker-work ornament was retained, as +a sort of attest of its origin.</p> + +<p>We see, thus, it is by accidental circumstances, or +by such as lie without our purpose, foresight, and +power, that man is gradually led to the acquaintance +of improved means of satisfying his wants. Let the +reader picture to himself the genius of a man who +could have foreseen without the help of accident that +clay handled in the ordinary manner would produce a +useful cooking utensil! The majority of the inventions +made in the early stages of civilisation, including +language, writing, money, and the rest, could not +have been the product of deliberate methodical reflexion +for the simple reason that no idea of their +value and significance could have been had except +from practical use. The invention of the bridge may +have been suggested by the trunk of a tree which had +fallen athwart a mountain-torrent; that of the tool by +the use of a stone accidentally taken into the hand to +crack nuts. The use of fire probably started in and +was disseminated from regions where volcanic eruptions, +hot springs, and burning jets of natural gas +afforded opportunity for quietly observing and turning +to practical account the properties of fire. Only +after that had been done could the significance of the +fire-drill be appreciated, an instrument which was +probably discovered from boring a hole through a +piece of wood. The suggestion of a distinguished inquirer +that the invention of the fire-drill originated on +the occasion of a religious ceremony is both fantastic +and incredible. And as to the use of fire, we should +no more attempt to derive that from the invention of +the fire-drill than we should from the invention of sulphur +matches. Unquestionably the opposite course +was the real one.<a name="FNanchor_84_84" id="FNanchor_84_84"></a><a href="#Footnote_84_84" class="fnanchor">[84]</a></p> + +<p>Similar phenomena, though still largely veiled in +obscurity, mark the initial transition of nations from +a hunting to a nomadic life and to agriculture.<a name="FNanchor_85_85" id="FNanchor_85_85"></a><a href="#Footnote_85_85" class="fnanchor">[85]</a> We +shall not multiply examples, but content ourselves +with the remark that the same phenomena recur in +historical times, in the ages of great technical inventions, +and, further, that regarding them the most +whimsical notions have been circulated—notions which +ascribe to accident an unduly exaggerated part, and +one which in a psychological respect is absolutely impossible. +The observation of steam escaping from a +tea-kettle and of the clattering of the lid is supposed +to have led to the invention of the steam-engine. Just +think of the gap between this spectacle and the conception +of the performance of great mechanical work +by steam, for a man totally ignorant of the steam-engine! +Let us suppose, however, that an engineer, +versed in the practical construction of pumps, should +accidentally dip into water an inverted bottle that had +been filled with steam for drying and still retained its +steam. He would see the water rush violently into +the bottle, and the idea would very naturally suggest +itself of founding on this experience a convenient and +useful atmospheric steam-pump, which by imperceptible +degrees, both psychologically possible and immediate, +would then undergo a natural and gradual transformation +into Watt's steam-engine.</p> + +<p>But granting that the most important inventions +are brought to man's notice accidentally and in ways +that are beyond his foresight, yet it does not follow +that accident alone is sufficient to produce an invention. +The part which man plays is by no means a +passive one. Even the first potter in the primeval +forest must have felt some stirrings of genius within +him. In all such cases, the inventor is obliged <i>to take +note</i> of the new fact, he must discover and grasp its +advantageous feature, and must have the power to +turn that feature to account in the realisation of his +purpose. He must <i>isolate</i> the new feature, impress it +upon his memory, unite and interweave it with the +rest of his thought; in short, he must possess the capacity +<i>to profit by experience</i>.</p> + +<p>The capacity to profit by experience might well be +set up as a test of intelligence. This power varies +considerably in men of the same race, and increases +enormously as we advance from the lower animals to +man. The former are limited in this regard almost +entirely to the reflex actions which they have inherited +with their organism, they are almost totally incapable +of individual experience, and considering their simple +wants are scarcely in need of it. The ivory-snail +(<i>Eburna spirata</i>) never learns to avoid the carnivorous +Actinia, no matter how often it may wince under the +latter's shower of needles, apparently having no memory +for pain whatever.<a name="FNanchor_86_86" id="FNanchor_86_86"></a><a href="#Footnote_86_86" class="fnanchor">[86]</a> A spider can be lured forth +repeatedly from its hole by touching its web with a +tuning-fork. The moth plunges again and again into +the flame which has burnt it. The humming-bird +hawk-moth<a name="FNanchor_87_87" id="FNanchor_87_87"></a><a href="#Footnote_87_87" class="fnanchor">[87]</a> dashes repeatedly against the painted +roses of the wall-paper, like the unhappy and desperate +thinker who never wearies of attacking the same +insoluble chimerical problem. As aimlessly almost as +Maxwell's gaseous molecules and in the same unreasoning +manner common flies in their search for light +and air stream against the glass pane of a half-opened +window and remain there from sheer inability to find +their way around the narrow frame. But a pike separated +from the minnows of his aquarium by a glass +partition, learns after the lapse of a few months, +though only after having butted himself half to death, +that he cannot attack these fishes with impunity. +What is more, he leaves them in peace even after the +removal of the partition, though he will bolt a strange +fish at once. Considerable memory must be attributed +to birds of passage, a memory which, probably +owing to the absence of disturbing thoughts, acts with +the precision of that of some idiots. Finally, the +susceptibility to training evinced by the higher vertebrates +is indisputable proof of the ability of these animals +to profit by experience.</p> + +<p>A powerfully developed <i>mechanical</i> memory, which +recalls vividly and faithfully old situations, is sufficient +for avoiding definite particular dangers, or for taking +advantage of definite particular opportunities. But +more is required for the development of <i>inventions</i>. +More extensive chains of images are necessary here, +the excitation by mutual contact of widely different +trains of ideas, a more powerful, more manifold, and +richer connexion of the contents of memory, a more +powerful and impressionable psychical life, heightened +by use. A man stands on the bank of a mountain-torrent, +which is a serious obstacle to him. He remembers +that he has crossed just such a torrent before +on the trunk of a fallen tree. Hard by trees are +growing. He has often moved the trunks of fallen +trees. He has also felled trees before, and then moved +them. To fell trees he has used sharp stones. He +goes in search of such a stone, and as the old situations +that crowd into his memory and are held there in living +reality by the definite powerful interest which he +has in crossing just this torrent,—as these impressions +are made to pass before his mind in the <i>inverse order</i> in +which they were here evoked, he invents the bridge.</p> + +<p>There can be no doubt but the higher vertebrates +adapt their actions in some moderate degree to circumstances. +The fact that they give no appreciable +evidence of advance by the accumulation of inventions, +is satisfactorily explained by a difference of degree +or intensity of intelligence as compared with +man; the assumption of a difference of kind is not +necessary. A person who saves a little every day, be +it ever so little, has an incalculable advantage over +him who daily squanders that amount, or is unable to +keep what he has accumulated. A slight quantitative +difference in such things explains enormous differences +of advancement.</p> + +<p>The rules which hold good in prehistoric times +also hold good in historical times, and the remarks +made on invention may be applied almost without +modification to discovery; for the two are distinguished +solely by the use to which the new knowledge +is put. In both cases the investigator is concerned +with some <i>newly observed</i> relation of new or old properties, +abstract or concrete. It is observed, for example, +that a substance which gives a chemical reaction +<i>A</i> is also the cause of a chemical reaction <i>B</i>. If this +observation fulfils no purpose but that of furthering +the scientist's insight, or of removing a source of intellectual +discomfort, we have a discovery; but an invention, +if in using the substance giving the reaction +<i>A</i> to produce the desired reaction <i>B</i>, we have a practical +end in view, and seek to remove a source of material +discomfort. The phrase, <i>disclosure of the connexion +of reactions</i>, is broad enough to cover discoveries +and inventions in all departments. It embraces the +Pythagorean proposition, which is a combination of a +geometrical and an arithmetical reaction, Newton's +discovery of the connexion of Kepler's motions with +the law of the inverse squares, as perfectly as it does +the detection of some minute but appropriate alteration +in the construction of a tool, or of some appropriate +change in the methods of a dyeing establishment.</p> + +<p>The disclosure of new provinces of facts before +unknown can only be brought about by accidental circumstances, +under which are <i>remarked</i> facts that commonly +go unnoticed. The achievement of the discoverer +here consists in his <i>sharpened attention</i>, which +detects the uncommon features of an occurrence and +their determining conditions from their most evanescent +marks,<a name="FNanchor_88_88" id="FNanchor_88_88"></a><a href="#Footnote_88_88" class="fnanchor">[88]</a> and discovers means of submitting them +to exact and full observation. Under this head belong +the first disclosures of electrical and magnetic +phenomena, Grimaldi's observation of interference, +Arago's discovery of the increased check suffered by a +magnetic needle vibrating in a copper envelope as +compared with that observed in a bandbox, Foucault's +observation of the stability of the plane of vibration +of a rod accidentally struck while rotating in a turning-lathe, +Mayer's observation of the increased redness +of venous blood in the tropics, Kirchhoff's observation +of the augmentation of the <i>D</i>-line in the solar +spectrum by the interposition of a sodium lamp, +Schönbein's discovery of ozone from the phosphoric +smell emitted on the disruption of air by electric +sparks, and a host of others. All these facts, of which +unquestionably many were <i>seen</i> numbers of times before +they were <i>noticed</i>, are examples of the inauguration +of momentous discoveries by accidental circumstances, +and place the importance of strained attention +in a brilliant light.</p> + +<p>But not only is a significant part played in the beginning +of an inquiry by co-operative circumstances +beyond the foresight of the investigator; their influence +is also active in its prosecution. Dufay, thus, whilst +following up the behavior of <i>one</i> electrical state which +he had assumed, discovers the existence of <i>two</i>. Fresnel +learns by accident that the interference-bands received +on ground glass are seen to better advantage +in the open air. The diffraction-phenomenon of two +slits proved to be considerably different from what +Fraunhofer had anticipated, and in following up this +circumstance he was led to the important discovery of +grating-spectra. Faraday's induction-phenomenon departed +widely from the initial conception which occasioned +his experiments, and it is precisely this deviation +that constitutes his real discovery.</p> + +<p>Every man has pondered on some subject. Every +one of us can multiply the examples cited, by less illustrious +ones from his own experience. I shall cite +but one. On rounding a railway curve once, I accidentally +remarked a striking apparent inclination of +the houses and trees. I inferred that the direction of +the total resultant <i>physical</i> acceleration of the body +reacts <i>physiologically</i> as the vertical. Afterwards, in +attempting to inquire more carefully into this phenomenon, +and this only, in a large whirling machine, +the collateral phenomena conducted me to the sensation +of angular acceleration, vertigo, Flouren's experiments +on the section of the semi-circular canals +etc., from which gradually resulted views relating to +sensations of direction which are also held by Breuer +and Brown, which were at first contested on all hands, +but are now regarded on many sides as correct, and +which have been recently enriched by the interesting +inquiries of Breuer concerning the <i>macula acustica</i>, and +Kreidel's experiments with magnetically orientable +crustacea.<a name="FNanchor_89_89" id="FNanchor_89_89"></a><a href="#Footnote_89_89" class="fnanchor">[89]</a> Not disregard of accident but a direct and +purposeful employment of it advances research.</p> + +<p>The more powerful the psychical connexion of the +memory pictures is,—and it varies with the individual +and the mood,—the more apt is the same accidental +observation to be productive of results. Galileo knows +that the air has weight; he also knows of the "resistance +to a vacuum," expressed both in weight and +in the height of a column of water. But the two ideas +dwelt asunder in his mind. It remained for Torricelli +to vary the specific gravity of the liquid measuring the +pressure, and not till then was the air included in the +list of pressure-exerting fluids. The reversal of the +lines of the spectrum was seen repeatedly before +Kirchhoff, and had been mechanically explained. But +it was left for his penetrating vision to discern the +evidence of the connexion of this phenomenon with +questions of heat, and to him alone through persistent +labor was revealed the sweeping significance of the +fact for the mobile equilibrium of heat. Supposing, +then, that such a rich organic connexion of the elements +of memory exists, and is the prime distinguishing +mark of the inquirer, next in importance certainly +is that <i>intense interest</i> in a definite object, in a definite +idea, which fashions advantageous combinations of +thought from elements before disconnected, and obtrudes +that idea into every observation made, and into +every thought formed, making it enter into relationship +with all things. Thus Bradley, deeply engrossed +with the subject of aberration, is led to its solution +by an exceedingly unobtrusive experience in crossing +the Thames. It is permissible, therefore, to ask +whether accident leads the discoverer, or the discoverer +accident, to a successful outcome in scientific +quests.</p> + +<p>No man should dream of solving a great problem +unless he is so thoroughly saturated with his subject +that everything else sinks into comparative insignificance. +During a hurried meeting with Mayer in Heidelberg +once, Jolly remarked, with a rather dubious +implication, that if Mayer's theory were correct water +could be warmed by shaking. Mayer went away without +a word of reply. Several weeks later, and now +unrecognised by Jolly, he rushed into the latter's presence +exclaiming: "Es ischt aso!" (It is so, it is +so!) It was only after considerable explanation that +Jolly found out what Mayer wanted to say. The incident +needs no comment.<a name="FNanchor_90_90" id="FNanchor_90_90"></a><a href="#Footnote_90_90" class="fnanchor">[90]</a></p> + +<p>A person deadened to sensory impressions and +given up solely to the pursuit of his own thoughts, +may also light on an idea that will divert his mental +activity into totally new channels. In such cases it is +a psychical accident, an intellectual experience, as +distinguished from a physical accident, to which the +person owes his discovery—a discovery which is here +made "deductively" by means of mental copies of the +world, instead of experimentally. <i>Purely</i> experimental +inquiry, moreover, does not exist, for, as Gauss says, +virtually we always experiment with our thoughts. +And it is precisely that constant, corrective interchange +or intimate union of experiment and deduction, +as it was cultivated by Galileo in his <i>Dialogues</i> +and by Newton in his <i>Optics</i>, that is the foundation of +the benign fruitfulness of modern scientific inquiry as +contrasted with that of antiquity, where observation +and reflexion ofttimes pursued their respective courses +like two strangers.</p> + +<p>We have to wait for the appearance of a favorable +physical accident. The movement of our thoughts +obeys the law of association. In the case of meagre +experience the result of this law is simply the mechanical +reproduction of definite sensory experiences. On +the other hand, if the psychical life is subjected to the +incessant influences of a powerful and rich experience, +then every representative element in the mind is connected +with so many others that the actual and natural +course of the thoughts is easily influenced and determined +by insignificant circumstances, which accidentally +are decisive. Hereupon, the process termed imagination +produces its protean and infinitely diversified +forms. Now what can we do to guide this process, +seeing that the combinatory law of the images is without +our reach? Rather let us ask, what influence can +a powerful and constantly recurring idea exert on the +movement of our thoughts? According to what has +preceded, the answer is involved in the question itself. +The <i>idea</i> dominates the thought of the inquirer, not +the latter the former.</p> + +<p>Let us see, now, if we can acquire a profounder +insight into the process of discovery. The condition +of the discoverer is, as James has aptly remarked, not +unlike the situation of a person who is trying to remember +something that he has forgotten. Both are +sensible of a gap, and have only a remote presentiment +of what is missing. Suppose I meet in a company +a well-known and affable gentleman whose name +I have forgotten, and who to my horror asks to be introduced +to some one. I set to work according to +Lichtenberg's rule, and run down the alphabet in +search of the initial letter of his name. A vague sympathy +holds me at the letter <i>G</i>. Tentatively I add the +second letter and am arrested at <i>e</i>, and long before I +have tried the third letter <i>r</i>, the name "Gerson" sounds +sonorously upon my ear, and my anguish is gone. +While taking a walk I meet a gentleman from whom +I receive a communication. On returning home, and +in attending to weightier affairs, the matter slips my +mind. Moodily, but in vain, I ransack my memory. +Finally I observe that I am going over my walk again +in thought. On the street corner in question the self-same +gentleman stands before me and repeats his +communication. In this process are successively recalled +to consciousness all the percepts which were +connected with the percept that was lost, and with +them, finally, that, too, is brought to light. In the +first case—where the experience had already been +made and is permanently impressed on our thought—a +<i>systematic</i> procedure is both possible and easy, for +we know that a name must be composed of a limited +number of sounds. But at the same time it should be +observed that the labor involved in such a combinatorial +task would be enormous if the name were long +and the responsiveness of the mind weaker.</p> + +<p>It is often said, and not wholly without justification, +that the scientist has solved a <i>riddle</i>. Every problem +in geometry may be clothed in the garb of a <i>riddle</i>. +Thus: "What thing is that <i>M</i> which has the properties +<i>A</i>, <i>B</i>, <i>C</i>?" "What circle is that which touches +the straight lines <i>A</i>, <i>B</i>, but touches <i>B</i> in the point <i>C</i>?" +The first two conditions marshal before the imagination +the group of circles whose centres lie in the line +of symmetry of <i>A</i>, <i>B</i>. The third condition reminds +us of all the circles having centres in the straight line +that stands at right angles to <i>B</i> in <i>C</i>. The <i>common</i> +term, or common terms, of the two groups of images +solves the riddle—satisfies the problem. Puzzles dealing +with things or words induce similar processes, but +the memory in such cases is exerted in many directions +and more varied and less clearly ordered provinces +of ideas are surveyed. The difference between +the situation of a geometer who has a construction to +make, and that of an engineer, or a scientist, confronted +with a problem, is simply this, that the first +moves in a field with which he is thoroughly acquainted, +whereas the two latter are obliged to familiarise +themselves with this field subsequently, and in +a measure far transcending what is commonly required. +In this process the mechanical engineer has +at least always a definite goal before him and definite +means to accomplish his aim, whilst in the case of the +scientist that aim is in many instances presented only +in vague and general outlines. Often the very formulation +of the riddle devolves on him. Frequently it +is not until the aim has been reached that the broader +outlook requisite for systematic procedure is obtained. +By far the larger portion of his success, therefore, is +contingent on luck and instinct. It is immaterial, so +far as its character is concerned, whether the process +in question is brought rapidly to a conclusion in the +brain of one man, or whether it is spun out for centuries +in the minds of a long succession of thinkers. +The same relation that a word solving a riddle bears +to that riddle is borne by the modern conception of +light to the facts discovered by Grimaldi, Römer, +Huygens, Newton, Young, Malus, and Fresnel, and +only by the help of this slowly developed conception +is our mental vision enabled to embrace the broad +domain of facts in question.</p> + +<p>A welcome complement to the discoveries which +the history of civilisation and comparative psychology +have furnished, is to be found in the confessions of +great scientists and artists. Scientists <i>and</i> artists, we +might say, for Liebig boldly declared there was no +essential difference between the two. Are we to regard +Leonardo da Vinci as a scientist or as an artist? +If the artist builds up his work from a few motives, +the scientist discovers the motives which permeate +reality. If scientists like Lagrange or Fourier are in +a certain measure artists in the presentation of their +results, on the other hand, artists like Shakespeare or +Ruysdael are scientists in the insight which must +have preceded their creations.</p> + +<p>Newton, when questioned about his methods of +work, could give no other answer but that he was +wont to ponder again and again on a subject; and +similar utterances are accredited to D'Alembert and +Helmholtz. Scientists and artists both recommend +persistent labor. After the repeated survey of a field +has afforded opportunity for the interposition of advantageous +accidents, has rendered all the traits that +suit with the mood or the dominant thought more +vivid, and has gradually relegated to the background +all things that are inappropriate, making their future +appearance impossible; then from the teeming, swelling +host of fancies which a free and high-flown imagination +calls forth, suddenly that particular form +arises to the light which harmonises perfectly with +the ruling idea, mood, or design. Then it is that that +which has resulted slowly as the result of a gradual +selection, appears as if it were the outcome of a deliberate +act of creation. Thus are to be explained the +statements of Newton, Mozart, Richard Wagner, and +others, when they say that thoughts, melodies, and +harmonies had poured in upon them, and that they +had simply retained the right ones. Undoubtedly, +the man of genius, too, consciously or instinctively, +pursues systematic methods wherever it is possible; +but in his delicate presentiment he will omit many a +task or abandon it after a hasty trial on which a less +endowed man would squander his energies in vain. +Thus, the genius accomplishes<a name="FNanchor_91_91" id="FNanchor_91_91"></a><a href="#Footnote_91_91" class="fnanchor">[91]</a> in a brief space of +time undertakings for which the life of an ordinary +man would far from suffice. We shall hardly go astray +if we regard genius as only a slight deviation from +the average mental endowment—as possessing simply +a greater sensitiveness of cerebral reaction and a +greater swiftness of reaction. The men who, obeying +their inner impulses, make sacrifices for an idea instead +of advancing their material welfare, may appear +to the full-blooded Philistine as fools; yet we shall +scarcely adopt Lombroso's view, that genius is to be +regarded as a disease, although it is unfortunately +true that the sensitive brains and fragile constitutions +succumb most readily to sickness.</p> + +<p>The remark of C. G. J. Jacobi that mathematics +is slow of growth and only reaches the truth by long +and devious paths, that the way to its discovery must +be prepared for long beforehand, and that then the +truth will make its long-deferred appearance as if impelled +by some divine necessity<a name="FNanchor_92_92" id="FNanchor_92_92"></a><a href="#Footnote_92_92" class="fnanchor">[92]</a>—all this holds true +of every science. We are astounded often to note +that it required the combined labors of many eminent +thinkers for a full century to reach a truth which it +takes us only a few hours to master and which once +acquired seems extremely easy to reach under the +right sort of circumstances. To our humiliation we +learn that even the greatest men are born more for +life than for science. The extent to which even they +are indebted to accident—to that singular conflux of +the physical and the psychical life in which the continuous +but yet imperfect and never-ending adaptation +of the latter to the former finds its distinct expression—that +has been the subject of our remarks to-day. +Jacobi's poetical thought of a divine necessity acting +in science will lose none of its loftiness for us if we +discover in this necessity the same power that destroys +the unfit and fosters the fit. For loftier, nobler, +and more romantic than poetry is the truth and the +reality.</p> + + + + +<h2><a name="ON_SENSATIONS_OF_ORIENTATION93" id="ON_SENSATIONS_OF_ORIENTATION93">ON SENSATIONS OF ORIENTATION.</a><a name="FNanchor_93_93" id="FNanchor_93_93"></a><a href="#Footnote_93_93" class="fnanchor">[93]</a></h2> + + +<p>Through the co-operation of a succession of inquirers, +among whom are particularly to be mentioned +Goltz of Strassburg and Breuer of Vienna, +considerable advances have been made during the +last twenty-five years in our knowledge of the means +by which we ascertain our position in space and the +direction of our motion, or orient ourselves, as the +phrase goes. I presume that you are already acquainted +with the physiological part of the processes +with which our sensations of movement, or, more generally +speaking, our sensations of orientation, are connected. +Here I shall consider more particularly the +physical side of the matter. In fact, I was originally +led to the consideration of these questions by the +observation of extremely simple and perfectly well-known +physical facts, before I had any great acquaintance +with physiology and while pursuing unbiasedly +my natural thoughts; and I am of the conviction that<span class="pagenum"><a name="Page_283" id="Page_283">[Pg 283]</a></span> +the way which I have pursued, and which is entirely +free from hypotheses, will, if you will follow my exposition, +be that of easiest acquisition for the most of +you.</p> + +<p>No man of sound common sense could ever have +doubted that a pressure or force is requisite to set a +body in motion in a given direction and that a contrary +pressure is required to stop suddenly a body in +motion. Though the law of inertia was first formulated +with anything like exactness by Galileo, the +facts at the basis of it were known long previously to +men of the stamp of Leonardo da Vinci, Rabelais, +and others, and were illustrated by them with appropriate +experiments. Leonardo knew that by a swift +stroke with a ruler one can knock out from a vertical +column of checkers a single checker without over-throwing +the column. The experiment with a coin +resting on a piece of pasteboard covering a goblet, +which falls into the goblet when the pasteboard is +jerked away, like all experiments of the kind, is certainly +very old.</p> + +<p>With Galileo the experience in question assumes +greater clearness and force. In the famous dialogue +on the Copernican system which cost him his freedom, +he explains the tides in an unfelicitous, though +in principle correct manner, by the analogue of a +platter of water swung to and fro. In opposition to +the Aristotelians of his time, who believed the descent<span class="pagenum"><a name="Page_284" id="Page_284">[Pg 284]</a></span> +of a heavy body could be accelerated by the +superposition of another heavy body, he asserted that +a body could never be accelerated by one lying upon +it unless the first in some way impeded the superposed +body in its descent. To seek to press a falling +body by means of another placed upon it, is as senseless +as trying to prod a man with a lance when the man +is speeding away from one with the same velocity as +the lance. Even this little excursion into physics can +explain much to us. You know the peculiar sensation +which one has in falling, as when one jumps from a +high springboard into the water, and which is also +experienced in some measure at the beginning of the +descent of elevators and swings. The reciprocal gravitational +pressure of the different parts of our body, +which is certainly felt in some manner, vanishes in +free descent, or, in the case of the elevator, is diminished +on the beginning of the descent. A similar sensation +would be experienced if we were suddenly +transported to the moon where the acceleration of +gravity is much less than upon the earth. I was led +to these considerations in 1866 by a suggestion in +physics, and having also taken into account the alterations +of the blood-pressure in the cases in question, +I found I coincided without knowing it with Wollaston +and Purkinje. The first as early as 1810 in his Croonian +lecture had touched on the subject of sea-sickness +and explained it by alterations of the blood-pressure,<span class="pagenum"><a name="Page_285" id="Page_285">[Pg 285]</a></span> +and later had laid similar considerations at the +basis of his explanation of vertigo (1820-1826).<a name="FNanchor_94_94" id="FNanchor_94_94"></a><a href="#Footnote_94_94" class="fnanchor">[94]</a></p> + +<p>Newton was the first to enunciate with perfect +generality that a body can change the velocity and +direction of its motion only by the action of a force, +or the action of a second body. A corollary of this +law which was first expressly deduced by Euler is +that a body can never be set <i>rotating</i> or made to cease +rotating of itself but only by forces and other bodies. +For example, turn an open watch which has run down +freely backwards and forwards in your hand. The +balance-wheel will not fully catch the rapid rotations, +it does not even respond fully to the elastic force of +the spring which proves too weak to carry the wheel +entirely with it.</p> + +<p>Let us consider now that whether we move ourselves +by means of our legs, or whether we are +moved by a vehicle or a boat, at first only a part +of our body is directly moved and the rest of it is +afterwards set in motion by the first part. We see +that pressures, pulls, and tensions are always produced +between the parts of the body in this action, +which pressures, pulls, and tensions give rise to sensations +by which the forward or rotary movements in +which we are engaged are made perceptible.<a name="FNanchor_95_95" id="FNanchor_95_95"></a><a href="#Footnote_95_95" class="fnanchor">[95]</a> But it +is quite natural that sensations so familiar should be +little noticed and that attention should be drawn to +them only under special circumstances when they occur +unexpectedly or with unusual strength.</p> + +<p><span class="pagenum"><a name="Page_286" id="Page_286">[Pg 286]</a></span></p> +<div class="figcenter" style="width: 450px;"> +<img src="images/i_296.jpg" width="450" height="330" alt="" /> +<span class="caption">Fig. 45.</span> +</div> + +<p>Thus my attention was drawn to this point by the +sensation of falling and subsequently by another singular +occurrence. I was rounding a sharp railway +curve once when I suddenly saw all the trees, houses, +and factory chimneys along the track swerve from the +vertical and assume a strikingly inclined position. +What had hitherto appeared to me perfectly natural, +namely, the fact that we distinguish the vertical so +perfectly and sharply from every other direction, now<span class="pagenum"><a name="Page_287" id="Page_287">[Pg 287]</a></span> +struck me as enigmatical. Why is it that the same +direction can now appear vertical to me and now cannot? +By what is the vertical distinguished for us? +(Compare Figure 45.)</p> + +<p>The rails are raised on the convex or outward side +of the track in order to insure the stability of the carriage +as against the action of the centrifugal force, the +whole being so arranged that the combination of the +force of gravity with the centrifugal force of the train +shall give rise to a force perpendicular to the plane +of the rails.</p> + +<p>Let us assume, now, that under all circumstances +we somehow sense the direction of the total resultant +mass-acceleration whencesoever it may arise as the +vertical. Then both the ordinary and the extraordinary +phenomena will be alike rendered intelligible.<a name="FNanchor_96_96" id="FNanchor_96_96"></a><a href="#Footnote_96_96" class="fnanchor">[96]</a></p> + +<p>I was now desirous of putting the view I had +reached to a more convenient and exact test than was +possible on a railway journey where one has no control +over the determining circumstances and cannot +alter them at will. I accordingly had the simple apparatus +constructed which is represented in Figure 46.</p> + +<p>In a large frame <i>BB</i>, which is fastened to the walls, +rotates about a vertical axis <i>AA</i> a second frame <i>RR</i>, +and within the latter a third one <i>rr</i>, which can be set<span class="pagenum"><a name="Page_288" id="Page_288">[Pg 288]</a></span> +at any distance and position from the axis, made stationary +or movable, and is provided with a chair for +the observer.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/i_298.jpg" width="600" height="385" alt="" /> +<span class="caption">Fig. 46.</span> +</div> + +<p>From Mach's <i>Bewegungsempfindungen</i>, Leipsic, Engelmann, 1875.]</p> + +<p>The observer takes his seat in the chair and to +prevent disturbances of judgment is enclosed in a paper +box. If the observer together with the frame <i>rr</i> +be then set in uniform rotation, he will feel and see +the beginning of the rotation both as to direction and +amount very distinctly although every outward visible +or tangible point of reference is wanting. If the motion +be uniformly continued the sensation of rotation +will gradually cease entirely and the observer will imagine +himself at rest. But if <i>rr</i> be placed outside the +axis of rotation, at once on the rotation beginning, a +strikingly apparent, palpable, actually visible inclination +of the entire paper box is produced, slight when<span class="pagenum"><a name="Page_289" id="Page_289">[Pg 289]</a></span> +the rotation is slow, strong when the rotation is rapid, +and continuing as long as the rotation lasts. It is absolutely +impossible for the observer to escape perceiving +the inclination, although here also all outward +points of reference are wanting. If the observer, for +example, is seated so as to look towards the axis, he +will feel the box strongly tipped backwards, as it necessarily +must be if the direction of the total resultant +force is perceived as the vertical. For other positions +of the observer the situation is similar.<a name="FNanchor_97_97" id="FNanchor_97_97"></a><a href="#Footnote_97_97" class="fnanchor">[97]</a></p> + +<p>Once, while performing one of these experiments, +and after rotating so long that I was no longer conscious +of the movement, I suddenly caused the apparatus +to be stopped, whereupon I immediately felt +and saw myself with the whole box rapidly flung round +in rotation in the opposite direction, although I knew +that the whole apparatus was at rest and every outward +point of reference for the perception of motion +was wanting. Every one who disbelieves in sensations +of movement should be made acquainted with +these phenomena. Had Newton known them and had +he ever observed how we may actually imagine ourselves +turned and displaced in space without the assistance +of stationary bodies as points of reference, he +would certainly have been confirmed more than ever<span class="pagenum"><a name="Page_290" id="Page_290">[Pg 290]</a></span> +in his unfortunate speculations regarding absolute +space.</p> + +<p>The sensation of rotation in the opposite direction +after the apparatus has been stopped, slowly and gradually +ceases. But on accidentally inclining my head +once during this occurrence, the axis of apparent rotation +was also observed to incline in exactly the same +manner both as to direction and as to amount. It is +accordingly clear that the acceleration or retardation +of rotation is felt. The acceleration operates as a +stimulus. The sensation, however, like almost all +sensations, though it gradually decreases, lasts perceptibly +longer than the stimulus. Hence the long +continued apparent rotation after the stopping of the +apparatus. The organ, however, which causes the +persistence of this sensation must have its seat in the +<i>head</i>, since otherwise the axis of apparent rotation +could not assume the same motion as the head.</p> + +<p>If I were to say, now, that a light had flashed +upon me in making these last observations, the expression +would be a feeble one. I ought to say I experienced +a perfect illumination. My juvenile experiences +of vertigo occurred to me. I remembered +Flourens's experiments relative to the section of the +semi-circular canals of the labyrinths of doves and +rabbits, where this inquirer had observed phenomena +similar to vertigo, but which he preferred to interpret, +from his bias to the acoustic theory of the labyrinth, +as the expression of painful auditive disturbances. I<span class="pagenum"><a name="Page_291" id="Page_291">[Pg 291]</a></span> +saw that Goltz had nearly but not quite hit the bull's +eye with his theory of the semi-circular canals. This +inquirer, who, from his happy habit of following his +own natural thoughts without regard for tradition, +has cleared up so much in science, spoke, as early as +1870, on the ground of experiments, as follows: "It +is uncertain whether the semi-circular canals are auditive +organs or not. In any event they form an apparatus +which serves for the preservation of equilibrium. +They are, so to speak, the sense-organs of equilibrium +of the head and indirectly of the whole body." I +remembered the galvanic dizziness which had been +observed by Ritter and Purkinje on the passage of a +current through the head, when the persons experimented +upon imagined they were falling towards the +cathode. The experiment was immediately repeated, +and sometime later (1874) I was enabled to demonstrate +the same objectively with fishes, all of which +placed themselves sidewise and in the same direction +in the field of the current as if at command.<a name="FNanchor_98_98" id="FNanchor_98_98"></a><a href="#Footnote_98_98" class="fnanchor">[98]</a> Müller's +doctrine of specific energies now appeared to me +to bring all these new and old observations into a simple, +connected unity.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/i_302.jpg" width="600" height="406" alt="" /> +<span class="caption">Fig. 47.</span> +</div> + +<p>The labyrinth of a dove (stereoscopically reproduced), from R. Ewald, +<i>Nervus Octavus</i>, Wiesbaden, Bergmann, 1892.]</p> + +<p>Let us picture to ourselves the labyrinth of the +ear with its three semi-circular canals lying in three +mutually perpendicular planes (Comp. Fig. 47), the<span class="pagenum"><a name="Page_292" id="Page_292">[Pg 292]</a></span> +mysterious position of which inquirers have endeavored +to explain in every possible and impossible way. +Let us conceive the nerves of the ampullæ, or the dilated +extensions of the semi-circular canals, equipped +with a capacity for responding to every imaginable +stimulus with a sensation of rotation just as the nerves +of the retina of the eye when excited by pressures, +by electrical or chemical stimuli always respond with +the sensation of light; let us picture to ourselves, +further, that the usual excitation of the ampullæ +nerves is produced by the inertia of the contents of +the semi-circular canals, which contents on suitable +rotations in the plane of the semi-circular canal are +left behind in the motion, or at least have a tendency<span class="pagenum"><a name="Page_293" id="Page_293">[Pg 293]</a></span> +to remain behind and consequently exert a pressure. +It will be seen that on this supposition all the single +facts which without the theory appear as so many +different individual phenomena, become from this single +point of view clear and intelligible.</p> + +<p>I had the satisfaction, immediately after the communication +in which I set forth this idea,<a name="FNanchor_99_99" id="FNanchor_99_99"></a><a href="#Footnote_99_99" class="fnanchor">[99]</a> of seeing a +paper by Breuer appear<a name="FNanchor_100_100" id="FNanchor_100_100"></a><a href="#Footnote_100_100" class="fnanchor">[100]</a> in which this author had +arrived by entirely different methods at results that +agreed in all essential points with my own. A few +weeks later appeared the researches of Crum Brown +of Edinburgh, whose methods were even still nearer +mine. Breuer's paper was far richer in physiological +respects than mine, and he had particularly gone +into greater detail in his investigation of the collateral +effects of the reflex motions and orientation of +the eyes in the phenomena under consideration.<a name="FNanchor_101_101" id="FNanchor_101_101"></a><a href="#Footnote_101_101" class="fnanchor">[101]</a> In +addition certain experiments which I had suggested in +my paper as a test of the correctness of the view +in question had already been performed by Breuer. +Breuer has also rendered services of the highest order +in the further elaboration of this field. But in a +physical regard, my paper was, of course, more complete.</p> + +<p>In order to portray to the eye the behavior of the +semi-circular canals, I have constructed here a little<span class="pagenum"><a name="Page_294" id="Page_294">[Pg 294]</a></span> +apparatus. (See Fig. 48.) The large rotatable disc +represents the osseous semi-circular canal, which is +continuous with the bones of the head; the small disc, +which is free to rotate on the axis of the first, represents +the mobile and partly liquid contents of the semi-circular +canal. On rotating the large disc, the small +disc as you see remains +behind. I +have to turn some +time before the +small disc is carried +along with the large +one by friction. But +if I now stop the +large disc the small +disc as you see continues +to rotate.</p> + +<div class="figcenter" style="width: 350px;"> +<img src="images/i_304.jpg" width="350" height="497" alt="" /> +<span class="caption">Fig. 48.</span> +</div> + +<p>Model representing the action of the semi-circular +canals.]</p> + +<p>Simply assume +now that the rotation +of the small +disc, say in the direction +of the hands +of a watch, would +give rise to a sensation of rotation in the opposite +direction, and conversely, and you already understand +a good portion of the facts above set forth. +The explanation still holds, even if the small disc +does not perform appreciable rotations but is checked +by a contrivance similar to an elastic spring, the tension<span class="pagenum"><a name="Page_295" id="Page_295">[Pg 295]</a></span> +of which disengages a sensation. Conceive, now, +three such contrivances with their mutually perpendicular +planes of rotation joined together so as to +form a single apparatus; then to this apparatus as a +whole, no rotation can be imparted without its being +indicated by the small mobile discs or by the springs +which are attached to them. Conceive both the right +and the left ear equipped with such an apparatus, and +you will find that it answers all the purposes of the +semi-circular canals, which you see represented stereoscopically +in Fig. 47 for the ear of a dove.</p> + +<p>Of the many experiments which I have made on +my own person, and the results of which could be +predicted by the new view according to the behavior +of the model and consequently according to the rules +of mechanics, I shall cite but one. I fasten a horizontal +board in the frame <i>RR</i> of my rotatory apparatus, +lie down upon the same with my right ear upon the +board, and cause the apparatus to be uniformly rotated. +As soon as I no longer perceive the rotation, +I turn around upon my left ear and immediately the +sensation of rotation again starts up with marked vividness. +The experiment can be repeated as often as +one wishes. A slight turn of the head even is sufficient +for reviving the sensation of rotation which in +the perfectly quiescent state at once disappears altogether.</p> + +<p>We will imitate the experiment on the model. I +turn the large disc until finally the small disc is carried<span class="pagenum"><a name="Page_296" id="Page_296">[Pg 296]</a></span> +along with it. If, now, while the rotation continues +uniform, I burn off a little thread which you +see here, the small disc will be flipped round by a +spring into its own plane 180°, so as now to present +its opposite side to you, when the rotation at once begins +in the opposite direction.</p> + +<p>We have consequently a very simple means for determining +whether one is actually the subject or not +of uniform and imperceptible rotations. If the earth +rotated much more rapidly than it really does, or if +our semi-circular canals were much more sensitive, a +Nansen sleeping at the North Pole would be waked +by a sensation of rotation every time he turned over. +Foucault's pendulum experiment as a demonstration +of the earth's rotation would be superfluous under +such circumstances. The only reason we cannot prove +the rotation of the earth with the help of our model, +lies in the small angular velocity of the earth and in +the consequent liability to great experimental errors.<a name="FNanchor_102_102" id="FNanchor_102_102"></a><a href="#Footnote_102_102" class="fnanchor">[102]</a></p> + +<p>Aristotle has said that "The sweetest of all +things is knowledge." And he is right. But if you +were to suppose that the <i>publication</i> of a new view +were productive of unbounded sweetness, you would +be mightily mistaken. No one disturbs his fellow-men +with a new view unpunished. Nor should the fact be +made a subject of reproach to these fellow-men. To<span class="pagenum"><a name="Page_297" id="Page_297">[Pg 297]</a></span> +presume to revolutionise the current way of thinking +with regard to any question, is no pleasant task, and +above all not an easy one. They who have advanced +new views know best what serious difficulties stand in +their way. With honest and praiseworthy zeal, men +set to work in search of everything that does not +suit with them. They seek to discover whether they +cannot explain the facts better or as well, or approximately +as well, by the traditional views. And that, +too, is justified. But at times some extremely artless +animadversions are heard that almost nonplus us. +"If a sixth sense existed it could not fail to have +been discovered thousands of years ago." Indeed; +there was a time, then, when only seven planets could +have existed! But I do not believe that any one will +lay any weight on the philological question whether +the set of phenomena which we have been considering +should be called a sense. The phenomena will not +disappear when the name disappears. It was further +said to me that animals exist which have no labyrinth, +but which can yet orientate themselves, and that consequently +the labyrinth has nothing to do with orientation. +We do not walk forsooth with our legs, because +snakes propel themselves without them!</p> + +<p>But if the promulgator of a new idea cannot hope +for any great pleasure from its publication, yet the +critical process which his views undergo is extremely +helpful to the subject-matter of them. All the defects +which necessarily adhere to the new view are gradually<span class="pagenum"><a name="Page_298" id="Page_298">[Pg 298]</a></span> +discovered and eliminated. Over-rating and exaggeration +give way to more sober estimates. And +so it came about that it was found unpermissible to +attribute all functions of orientation exclusively to the +labyrinth. In these critical labors Delage, Aubert, +Breuer, Ewald, and others have rendered distinguished +services. It can also not fail to happen that +fresh facts become known in this process which could +have been predicted by the new view, which actually +were predicted in part, and which consequently furnish +a support for the new view. Breuer and Ewald +succeeded in electrically and mechanically exciting +the labyrinth, and even single parts of the labyrinth, +and thus in producing the movements that belong to +such stimuli. It was shown that when the semi-circular +canals were absent vertigo could not be produced, +when the entire labyrinth was removed the orientation +of the head was no longer possible, that without +the labyrinth galvanic vertigo could not be induced. I +myself constructed as early as 1875 an apparatus for +observing animals in rotation, which was subsequently +reinvented in various forms and has since received the +name of "cyclostat."<a name="FNanchor_103_103" id="FNanchor_103_103"></a><a href="#Footnote_103_103" class="fnanchor">[103]</a> In experiments with the most +varied kinds of animals it was shown that, for example, +the larvæ of frogs are not subject to vertigo until +their semi-circular canals which at the start are wanting +are developed (K. Schäfer). A large percentage +of the deaf and dumb are afflicted with grave affections<span class="pagenum"><a name="Page_299" id="Page_299">[Pg 299]</a></span> +of the labyrinth. The American psychologist, +William James, has made whirling experiments with +many deaf and dumb subjects, and in a large number +of them found that susceptibility to giddiness is wanting. +He also found that many deaf and dumb people +on being ducked under water, whereby they lose their +weight and consequently have no longer the full assistance +of their muscular sense, utterly lose their +sense of position in space, do not know which is up +and which is down, and are thrown into the greatest +consternation,—results which do not occur in normal +men. Such facts are convincing proof that we do not +orientate ourselves entirely by means of the labyrinth, +important as it is for us. Dr. Kreidl has made experiments +similar to those of James and found that +not only is vertigo absent in deaf and dumb people +when whirled about, but that also the reflex movements +of the eyes which are normally induced by the +labyrinth are wanting. Finally, Dr. Pollak has found +that galvanic vertigo does not exist in a large percentage +of the deaf and dumb. Neither the jerking +movements nor the uniform movements of the eyes +were observed which normal human beings exhibit in +the Ritter and Purkinje experiment.</p> + +<p>After the physicist has arrived at the idea that the +semi-circular canals are the organ of sensation of rotation +or of angular acceleration, he is next constrained +to ask for the organs that mediate the sensation +of acceleration noticed in forward movements.<span class="pagenum"><a name="Page_300" id="Page_300">[Pg 300]</a></span> +In searching for an organ for this function, he of +course is not apt to select one that stands in no anatomical +and spatial relation with the semi-circular +canals. And in addition there are physiological considerations +to be weighed. The preconceived opinion +once having been abandoned that the <i>entire</i> labyrinth +is auditory in its function, there remains after the +cochlea is reserved for sensations of tone and the +semi-circular canals for the sensation of angular acceleration, +the vestibule for the discharge of additional +functions. The vestibule, particularly the part of it +known as the sacculus, appeared to me, by reason of +the so-called otoliths which it contains, eminently +adapted for being the organ of sensation of forward +acceleration or of the position of the head. In this +conjecture I again closely coincided with Breuer.</p> + +<p>That a sensation of position, of direction and +amount of mass-acceleration exists, our experience in +elevators as well as of movement in curved paths is +sufficient proof. I have also attempted to produce and +destroy suddenly great velocities of forward movement +by means of various contrivances of which I +shall mention only one here. If, while enclosed in +the paper box of my large whirling apparatus at some +distance from the axis, my body is in uniform rotation +which I no longer feel, and I then loosen the connexions +of the frame <i>rr</i> with <i>R</i> thus making the former +moveable and I then suddenly stop the larger frame, +my forward motion is abruptly impeded while the<span class="pagenum"><a name="Page_301" id="Page_301">[Pg 301]</a></span> +frame <i>rr</i> continues to rotate. I imagine now that I +am speeding on in a straight line in a direction opposite +to that of the checked motion. Unfortunately, for +many reasons it cannot be proved convincingly that +the organ in question has its seat in the head. According +to the opinion of Delage, the labyrinth has +nothing to do with this particular sensation of movement. +Breuer, on the other hand, is of the opinion +that the organ of forward movement in man is stunted +and the persistence of the sensation in question is too +brief to permit our instituting experiments as obvious +as in the case of rotation. In fact, Crum Brown once +observed while in an irritated condition peculiar vertical +phenomena in his own person, which were all +satisfactorily explained by an abnormally long persistence +of the sensation of rotation, and I myself in an +analogous case on the stopping of a railway train felt +the apparent backward motion in striking intensity +and for an unusual length of time.</p> + +<p>There is no doubt whatever that we feel changes +of vertical acceleration, and it will appear from the +following extremely probable that the otoliths of the +vestibule are the sense-organ for the <i>direction</i> of the +mass-acceleration. It will then be incompatible with +a really logical view to regard the latter as incapable +of sensing horizontal accelerations.</p> + +<p>In the lower animals the analogue of the labyrinth +is shrunk to a little vesicle filled with a liquid and +containing tiny crystals, auditive stones, or otoliths, of<span class="pagenum"><a name="Page_302" id="Page_302">[Pg 302]</a></span> +greater specific gravity, suspended on minute hairs. +These crystals appear physically well adapted for indicating +both the direction of gravity and the direction +of incipient movements. That they discharge the former +function, Delage was the first to convince himself +by experiments with lower animals which on the removal +of the otoliths utterly lost their bearings and +could no longer regain their normal position. Loeb +also found that fishes without labyrinths swim now on +their bellies and now on their backs. But the most +remarkable, most beautiful, and most convincing experiment +is that which Dr. Kreidl instituted with +crustaceans. According to Hensen, certain Crustacea +on sloughing spontaneously introduce fine grains of +sand as auditive stones into their otolith vesicle. At +the ingenious suggestion of S. Exner, Dr. Kreidl constrained +some of these animals to put up with iron +filings (<i>ferrum limatum</i>). If the pole of an electro-magnet +be brought near the animal, it will at once +turn its back away from the pole accompanying the +movement with appropriate reflex motions of the eye +the moment the current is closed, exactly as if gravity +had been brought to bear upon the animal in the +same direction as the magnetic force.<a name="FNanchor_104_104" id="FNanchor_104_104"></a><a href="#Footnote_104_104" class="fnanchor">[104]</a> This, in fact, +is what should be expected from the function ascribed +to the otoliths. If the eyes be covered with asphalt<span class="pagenum"><a name="Page_303" id="Page_303">[Pg 303]</a></span> +varnish, and the auditive sacs removed, the crustaceans +lose their sense of direction utterly, tumble +head over heels, lie on their side or their back indifferently. +This does not happen when the eyes only +are covered. For vertebrates, Breuer has demonstrated +by searching investigations that the otoliths, +or better, statoliths, slide in three planes parallel to +the planes of the semi-circular canals, and are consequently +perfectly adapted for indicating changes +both in the amount and the direction of the mass-acceleration.<a name="FNanchor_105_105" id="FNanchor_105_105"></a><a href="#Footnote_105_105" class="fnanchor">[105]</a></p> + +<p>I have already remarked that not every function +of orientation can be ascribed exclusively to the labyrinth. +The deaf and dumb who have to be immersed +in water, and the crustaceans who must have their +eyes closed if they are to be perfectly disorientated, are +proof of this fact. I saw a blind cat at Hering's laboratory +which to one who was not a very attentive observer +behaved exactly like a seeing cat. It played +nimbly with objects rolling on the floor, stuck its head +inquisitively into open drawers, sprang dexterously +upon chairs, ran with perfect accuracy through open<span class="pagenum"><a name="Page_304" id="Page_304">[Pg 304]</a></span> +doors, and never bumped against closed ones. The +visual sense had here been rapidly replaced by the +tactual and auditive senses. And it appears from +Ewald's investigations that even after the labyrinths +have been removed, animals gradually learn to move +about again quite in the normal fashion, presumably +because the eliminated function of the labyrinth is +now performed by some part of the brain. A certain +peculiar weakness of the muscles alone is perceptible +which Ewald ascribes to the absence of the stimulus +which is otherwise constantly emitted by the labyrinth +(the labyrinth-tonus). But if the part of the +brain which discharges the deputed function be removed, +the animals are again completely disorientated +and absolutely helpless.</p> + +<p>It may be said that the views enunciated by Breuer, +Crum Brown and myself in 1873 and 1874, and which +are substantially a fuller and richer development of +Goltz's idea, have upon the whole been substantiated. +At least they have exercised a helpful and stimulative +influence. New problems have of course arisen in the +course of the investigation which still await solution, +and much work remains to be done. At the same +time we see how fruitful the renewed co-operation of +the various special departments of science may become +after a period of isolation and invigorating labor +apart.</p> + +<p>I may be permitted, therefore, to consider the relation +between hearing and orientation from another<span class="pagenum"><a name="Page_305" id="Page_305">[Pg 305]</a></span> +and more general point of view. What we call the +auditive organ is in the lower animals simply a sac +containing auditive stones. As we ascend the scale, +1, 2, 3 semi-circular canals gradually develop from +them, whilst the structure of the otolith organ itself +becomes more complicated. Finally, in the higher +vertebrates, and particularly in the mammals, a part +of the latter organ (the lagena) becomes the cochlea, +which Helmholtz explained as the organ for sensations +of tone. In the belief that the entire labyrinth +was an auditive organ, Helmholtz, contrary to the results +of his own masterly analysis, originally sought +to interpret another part of the labyrinth as the organ +of noises. I showed a long time ago (1873) that every +tonal stimulus by shortening the duration of the excitation +to a few vibrations, gradually loses its character +of pitch and takes on that of a sharp, dry report or +noise.<a name="FNanchor_106_106" id="FNanchor_106_106"></a><a href="#Footnote_106_106" class="fnanchor">[106]</a> All the intervening stages between tones and +noises can be exhibited. Such being the case, it will +hardly be assumed that one organ is suddenly and at +some given point replaced in function by another. On +the basis of different experiments and reasonings S. +Exner also regards the assumption of a special organ +for the sensing of noises as unnecessary.</p> + +<p>If we will but reflect how small a portion of the +labyrinth of higher animals is apparently in the service +of the sense of hearing, and how large, on the other<span class="pagenum"><a name="Page_306" id="Page_306">[Pg 306]</a></span> +hand, the portion is which very likely serves the purposes +of orientation, how much the first anatomical +beginnings of the auditive sac of lower animals resemble +that part of the fully developed labyrinth which +does not hear, the view is irresistibly suggested which +Breuer and I (1874, 1875) expressed, that the auditive +organ took its development from an organ for sensing +movements by adaptation to weak periodic motional +stimuli, and that many apparatuses in the lower animals +which are held to be organs of hearing are not +auditive organs at all.<a name="FNanchor_107_107" id="FNanchor_107_107"></a><a href="#Footnote_107_107" class="fnanchor">[107]</a></p> + +<p>This view appears to be perceptibly gaining +ground. Dr. Kreidl by skilfully-planned experiments +has arrived at the conclusion that even fishes do not +hear, whereas E. H. Weber, in his day, regarded the +ossicles which unite the air-bladder of fishes with the +labyrinth as organs expressly designed for conducting +sound from the former to the latter.<a name="FNanchor_108_108" id="FNanchor_108_108"></a><a href="#Footnote_108_108" class="fnanchor">[108]</a> Störensen has +investigated the excitation of sounds by the air-bladder +of fishes, as also the conduction of shocks through +Weber's ossicles. He regards the air-bladder as particularly +adapted for receiving the noises made by +other fishes and conducting them to the labyrinth. +He has heard the loud grunting tones of the fishes +in South American rivers, and is of the opinion that +they allure and find each other in this manner. According +to these views certain fishes are neither deaf +nor dumb.<a name="FNanchor_109_109" id="FNanchor_109_109"></a><a href="#Footnote_109_109" class="fnanchor">[109]</a> The question here involved might be +solved perhaps by sharply distinguishing between the +sensation of hearing proper, and the perception of +shocks. The first-mentioned sensation may, even in +the case of many vertebrates, be extremely restricted, +or perhaps even absolutely wanting. But besides the +auditive function, Weber's ossicles may perfectly well +discharge some other function. Although, as Moreau +has shown, the air-bladder itself is not an organ of +equilibrium in the simple physical sense of Borelli, +yet doubtless some function of this character is still +reserved for it. The union with the labyrinth favors +this conception, and so a host of new problems rises +here before us.</p> +<p><span class="pagenum"><a name="Page_307" id="Page_307">[Pg 307]</a></span></p> +<p>I should like to close with a reminiscence from the +year 1863. Helmholtz's <i>Sensations of Tone</i> had just +been published and the function of the cochlea now +appeared clear to the whole world. In a private conversation +which I had with a physician, the latter declared +it to be an almost hopeless undertaking to seek +to fathom the function of the other parts of the labyrinth, +whereas I in youthful boldness maintained that +the question could hardly fail to be solved, and that +very soon, although of course I had then no glimmering +of how it was to be done. Ten years later the +question was substantially solved.</p> + +<p>To-day, after having tried my powers frequently +and in vain on many questions, I no longer believe<span class="pagenum"><a name="Page_308" id="Page_308">[Pg 308]</a></span> +that we can make short work of the problems of science. +Nevertheless, I should not consider an "ignorabimus" +as an expression of modesty, but rather as +the opposite. That expression is a suitable one only +with regard to problems which are wrongly formulated +and which are therefore not problems at all. +Every real problem can and will be solved in due +course of time without supernatural divination, entirely +by accurate observation and close, searching +thought.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_309" id="Page_309">[Pg 309]</a></span></p> + + + + +<h2><a name="ON_SOME_PHENOMENA_ATTENDING" id="ON_SOME_PHENOMENA_ATTENDING">ON SOME PHENOMENA ATTENDING +THE FLIGHT OF PROJECTILES.</a><a name="FNanchor_110_110" id="FNanchor_110_110"></a><a href="#Footnote_110_110" class="fnanchor">[110]</a></h2> + + +<blockquote><p>"I have led my ragamuffins where they were +peppered."—<i>Falstaff.</i></p> + +<p>"He goes but to see a noise that he heard."—<i>Midsummer +Night's Dream.</i></p></blockquote> + +<p>To shoot, in the shortest time possible, as many +holes as possible in one another's bodies, and +not always for exactly pardonable objects and ideals, +seems to have risen to the dignity of a duty with modern +men, who, by a singular inconsistency, and in +subservience to a diametrically contrary ideal, are +bound by the equally holy obligation of making these +holes as small as possible, and, when made, of stopping +them up and of healing them as speedily as +possible. Since, then, shooting and all that appertains +thereto, is a very important, if not the most important, +affair of modern life, you will doubtless not be averse +to giving your attention for an hour to some experiments +which have been undertaken, not for advancing +the ends of war, but for promoting the ends of science,<span class="pagenum"><a name="Page_310" id="Page_310">[Pg 310]</a></span> +and which throw some light on the phenomena +attending the flight of projectiles.</p> + +<p>Modern science strives to construct its picture of +the world not from speculations but so far as possible +from facts. It verifies its constructs by recourse to +observation. Every newly observed fact completes +its world-picture, and every divergence of a construct +from observation points to some imperfection, to some +lacuna in it. What is seen is put to the test of, and +supplemented by, what is thought, which is again +naught but the result of things previously seen. It +is always peculiarly fascinating, therefore, to subject +to direct verification by observation, that is, to render +palpable to the senses, something which we have only +theoretically excogitated or theoretically surmised.</p> + +<p>In 1881, on hearing in Paris the lecture of the Belgian +artillerist Melsens, who hazarded the conjecture +that projectiles travelling at a high rate of speed carry +masses of compressed air before them which are instrumental +in producing in bodies struck by the projectiles +certain well-known facts of the nature of explosions, +the desire arose in me of experimentally testing +his conjecture and of rendering the phenomenon, +if it really existed, perceptible. The desire was the +stronger as I could say that all the means for realising +it existed, and that I had in part already used and +tested them for other purposes.</p> + +<p>And first let us get clear regarding the difficulties +which have to be surmounted. Our task is that of<span class="pagenum"><a name="Page_311" id="Page_311">[Pg 311]</a></span> +observing a bullet or other projectile which is rushing +through space at a velocity of many hundred yards a +second, together with the disturbances which the bullet +causes in the surrounding atmosphere. Even the +opaque solid body itself, the projectile, is only exceptionally +visible under such circumstances—only when +it is of considerable size and when we see its line of +flight in strong perspective abridgement so that the +velocity is apparently diminished. We see a large +projectile quite clearly when we stand behind the cannon +and look steadily along its line of flight or in the +less pleasant case when the projectile is speeding towards +us. There is, however, a very simple and effective +method of observing swiftly moving bodies with as +little trouble as if they were held at rest at some point +in their path. The method is that of illumination by +a brilliant electric spark of extremely short duration +in a dark room. But since, for the full intellectual +comprehension of a picture presented to the eye, a +certain, not inconsiderable interval of time is necessary, +the method of instantaneous photography will +naturally also be employed. The pictures, which are +of extremely minute duration, are thus permanently +recorded and can be examined and analysed at one's +convenience and leisure.</p> + +<p>With the difficulty just mentioned is associated +still another and greater difficulty which is due to the +air. The atmosphere in its usual condition is generally +not visible even when at rest. But the task presented<span class="pagenum"><a name="Page_312" id="Page_312">[Pg 312]</a></span> +to us is to render visible masses of air which +in addition are moving with a high velocity.</p> + +<p>To be visible, a body must either emit light itself, +must shine, or must affect in some way the light which +falls upon it, must take up that light entirely or partly, +absorb it, or must have a deflective effect upon it, that +is, reflect or refract it. We cannot see the air as we +can a flame, for it shines only exceptionally, as in a +Geissler's tube. The atmosphere is extremely transparent +and colorless; it cannot be seen, therefore, as +a dark or colored body can, or as chlorine gas can, +or vapor of bromine or iodine. Air, finally, has so +small an index of refraction and so small a deflective +influence upon light, that the refractive effect is commonly +imperceptible altogether.</p> + +<p>A glass rod is visible in air or in water, but it is +almost invisible in a mixture of benzol and bisulphuret +of carbon, which has the same mean index of refraction +as the glass. Powdered glass in the same mixture +has a vivid coloring, because owing to the decomposition +of the colors the indices are the same +for only one color which traverses the mixture unimpeded, +whilst the other colors undergo repeated reflexions.<a name="FNanchor_111_111" id="FNanchor_111_111"></a><a href="#Footnote_111_111" class="fnanchor">[111]</a></p> + +<p>Water is invisible in water, alcohol in alcohol. But +if alcohol be mixed with water the flocculent streaks +of the alcohol in the water will be seen at once and<span class="pagenum"><a name="Page_313" id="Page_313">[Pg 313]</a></span> +<i>vice versa</i>. And in like manner the air, too, under +favorable circumstances, may be seen. Over a roof +heated by the burning sun, a tremulous wavering of +objects is noticeable, as there is also over red-hot +stoves, radiators, and registers. In all these cases +tiny flocculent masses of hot and cold air, of slightly +differing refrangibility, are mingled together.</p> + +<p>In like manner the more highly refracting parts of +non-homogeneous masses of glass, the so-called striæ +or imperfections of the glass, are readily detectible +among the less refracting parts which constitute the +bulk of the same. Such glasses are unserviceable for +optical purposes, and special attention has been devoted +to the investigation of the methods for eliminating +or avoiding these defects. The result has been +the development of an extremely delicate method for +detecting optical faults—the so-called method of Foucault +and Toepler—which is suitable also for our +present purpose.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/i_324.jpg" width="600" height="169" alt="" /> +<span class="caption">Fig. 49.</span> +</div> + +<p>Even Huygens when trying to detect the presence +of striæ in polished glasses viewed them under oblique +illumination, usually at a considerable distance, so as +to give full scope to the aberrations, and had recourse +for greater exactitude to a telescope. But the method +was carried to its highest pitch of perfection in 1867 +by Toepler who employed the following procedure: +A small luminous source <i>a</i> (Fig. 49) illuminates a lens +<i>L</i> which throws an image <i>b</i> of the luminous source. +If the eye be so placed that the image falls on the<span class="pagenum"><a name="Page_314" id="Page_314">[Pg 314]</a></span> +pupil, the entire lens, if perfect, will appear equally +illuminated, for the reason that all points of it send +out rays to the eye. Coarse imperfections of form or +of homogeneity are rendered visible only in case the +aberrations are so large that the light from many spots +passes by the pupil of the eye. But if the image <i>b</i> be +partly intercepted by the edge of a small slide, then +those spots in the lens as thus partly darkened will +appear brighter whose light by its greater aberrations +still reaches the eye in spite of the intercepting slide, +while those spots will appear darker which in consequence +of aberration in the other direction throw their +light entirely upon the slide. This artifice of the intercepting +slide which had previously been employed +by Foucault for the investigation of the optical imperfections +of mirrors enhances enormously the delicacy +of the method, which is still further augmented by +Toepler's employment of a telescope behind the slide. +Toepler's method, accordingly, enjoys all the advantages +of the Huygens and the Foucault procedure +combined. It is so delicate that the minutest irregularities +in the air surrounding the lens can be rendered +distinctly visible, as I shall show by an example. I<span class="pagenum"><a name="Page_315" id="Page_315">[Pg 315]</a></span> +place a candle before the lens <i>L</i> (Fig. 50) and so arrange +a second lens <i>M</i> that the flame of the candle is +imaged upon the screen <i>S</i>. As soon as the intercepting +slide is pushed into the focus, <i>b</i>, of the light issuing +from <i>a</i>, you see the images of the changes of +density and the images of the movements induced in +the air by the flame quite distinctly upon the screen. +The distinctness of the phenomenon as a whole depends +upon the position of the intercepting slide <i>b</i>. +The removal of <i>b</i> increases the illumination but decreases +the distinctness. If the luminous source <i>a</i> be +removed, we see the image of the candle flame only +upon the screen <i>S</i>. If we remove the flame and allow +<i>a</i> to continue shining, the screen <i>S</i> will appear uniformly +illuminated.</p> + +<div class="figcenter" style="width: 700px;"> +<img src="images/i_325.jpg" width="700" height="265" alt="" /> +<span class="caption">Fig. 50.</span> +</div> + +<p>After Toepler had sought long and in vain to render +the irregularities produced in air by sound-waves +visible by this principle, he was at last conducted to +his goal by the favorable circumstances attending the +production of electric sparks. The waves generated +in the air by electric sparks and accompanying the +explosive snapping of the same, are of sufficiently<span class="pagenum"><a name="Page_316" id="Page_316">[Pg 316]</a></span> +short period and sufficiently powerful to be rendered +visible by these methods. Thus we see how by a +careful regard for the merest and most shadowy indications +of a phenomenon and by slight progressive +and appropriate alterations of the circumstances and +the methods, ultimately the most astounding results +can be attained. Consider, for example, two such +phenomena as the rubbing of amber and the electric +lighting of modern streets. A person ignorant of the +myriad minute links that join these two things together, +will be absolutely nonplussed at their connexion, +and will comprehend it no more than the ordinary +observer who is unacquainted with embryology, anatomy, +and paleontology will understand the connexion +between a saurian and a bird. The high value and +significance of the co-operation of inquirers through +centuries, where each has but to take up the thread of +work of his predecessors and spin it onwards, is rendered +forcibly evident by such examples. And such +knowledge destroys, too, in the clearest manner imaginable +that impression of the marvellous which the +spectator may receive from science, and at the same +time is a most salutary admonishment to the worker +in science against superciliousness. I have also to +add the sobering remark that all our art would be in +vain did not nature herself afford at least some slight +guiding threads leading from a hidden phenomenon +into the domain of the observable. And so it need +not surprise us that once under particularly favorable<span class="pagenum"><a name="Page_317" id="Page_317">[Pg 317]</a></span> +circumstances an extremely powerful sound-wave +which had been caused by the explosion of several +hundred pounds of dynamite threw a directly visible +shadow in the sunlight, as Boys has recently told us. +If the sound-waves were absolutely without influence +upon the light, this could not have occurred, and all +our artifices would then, too, be in vain. And so, +similarly, the phenomenon accompanying projectiles +which I am about to show you was once in a very imperfect +manner incidentally seen by a French artillerist, +Journée, while that observer was simply following +the line of flight of a projectile with a telescope, just +as also the undulations produced by candle flames are +in a weak degree directly visible and in the bright sunlight +are imaged in shadowy waves upon a uniform +white background.</p> + +<p><i>Instantaneous illumination</i> by the electric spark, +the method of rendering visible small optical differences +or striæ, which may hence be called the <i>striate</i>, +or <i>differential</i>, method,<a name="FNanchor_112_112" id="FNanchor_112_112"></a><a href="#Footnote_112_112" class="fnanchor">[112]</a> invented by Foucault and +Toepler, and finally the <i>recording</i> of the image by a <i>photographic</i> +plate,—these therefore are the chief means +which are to lead us to our goal.</p> +<p><span class="pagenum"><a name="Page_318" id="Page_318">[Pg 318]</a></span></p> +<p>I instituted my first experiments in the summer of +1884 with a target-pistol, shooting the bullet through +a striate field as described above, and taking care that +the projectile whilst in the field should disengage an +illuminating electric spark from a Leyden jar or Franklin's +pane, which spark produced a photographic impression +of the projectile upon a plate, especially arranged +for the purpose. I obtained the image of the +projectile at once and without difficulty. I also readily +obtained, with the still rather defective dry plate which +I was using, exceedingly delicate images of the sound-waves +(spark-waves). But no atmospheric condensation +produced by the projectile was visible. I now +determined the velocity of my projectile and found it +to be only 240 metres per second, or considerably less +than the velocity of sound (which is 340 metres per +second). I saw immediately that under such circumstances +no noticeable compression of the air could be +produced, for any atmospheric compression must of +necessity travel forward at the same speed with sound +(340 metres per second) and consequently would be +always ahead of and speeding away from the projectile.</p> + +<p>I was so thoroughly convinced, however, of the +existence of the supposed phenomenon at a velocity +exceeding 340 metres per second, that I requested<span class="pagenum"><a name="Page_319" id="Page_319">[Pg 319]</a></span> +Professor Salcher, of Fiume, an Austrian port on the +Gulf of Quarnero, to undertake the experiment with +projectiles travelling at a high rate of speed. In the +summer of 1886 Salcher in conjunction with Professor +Riegler conducted in a spacious and suitable apartment +placed at their disposal by the Directors of the +Royal Imperial Naval Academy, experiments of the +kind indicated and conforming in method exactly to +those which I had instituted, with the precise results +expected. The phenomenon, in fact, accorded perfectly +with the <i>a priori</i> sketch of it which I had drafted +previously to the experiment. As the experimenting +was continued, new and unforeseen features made their +appearance.</p> + +<p>It would be unfair, of course, to expect from the +very first experiments faultless and highly distinct photographs. +It was sufficient that success was secured +and that I had convinced myself that further labor +and expenditure would not be vain. And on this +score I am greatly indebted to the two gentlemen +above mentioned.</p> + +<p>The Austrian Naval Department subsequently +placed a cannon at Salcher's disposal in Pola, an +Adriatic seaport, and I myself, together with my son, +then a student of medicine, having received and accepted +a courteous invitation from Krupp, repaired to +Meppen, a town in Hanover, where we conducted +with only the necessary apparatus several experiments +on the open artillery range. All these experiments<span class="pagenum"><a name="Page_320" id="Page_320">[Pg 320]</a></span> +furnished tolerably good and complete pictures. Some +little progress, too, was made. The outcome of our +experience on both artillery ranges, however, was the +settled conviction that really good results could be +obtained only by the most careful conduct of the experiments +in a laboratory especially adapted to the +purpose. The expensiveness of the experiments on +a large scale was not the determining consideration +here, for the size of the projectile is indifferent. Given +the same velocity and the results are quite similar, +whether the projectiles are large or small. On the +other hand, in a laboratory the experimenter has perfect +control over the initial velocity, which, provided +the proper equipment is at hand, can be altered at +will simply by altering the charge and the weight of +the projectile. The requisite experiments were accordingly +conducted by me in my laboratory at Prague, +partly in conjunction with my son and partly afterwards +by him alone. The latter are the most perfect +and I shall accordingly speak in detail here of +these only.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/i_331.jpg" width="600" height="341" alt="" /> +<span class="caption">Fig. 51.</span> +</div> + +<p>Picture to yourself an apparatus for detecting optical +striæ set up in a dark room. In order not to +make the description too complicated, I shall give the +essential features only of the apparatus, leaving out +of account altogether the minuter details which are +rather of consequence for the technical performance +of the experiment than for its understanding. We +suppose the projectile speeding on its path, accordingly,<span class="pagenum"><a name="Page_321" id="Page_321">[Pg 321]</a></span> +through the field of our differential optical apparatus. +On reaching the centre of the field (Fig. 51) +the projectile disengages an illuminating electric spark +<i>a</i>, and the image of the projectile, so produced, is photographically +impressed upon the plate of the camera +behind the intercepting slide <i>b</i>. In the last and +best experiments the lens <i>L</i> was replaced by a spherical +silvered-glass mirror made by K. Fritsch (formerly +Prokesch) of Vienna, whereby the apparatus was +naturally more complicated than it appears in our diagram. +The projectile having been carefully aimed +passes in crossing the differential field between two +vertical isolated wires which are connected with the +two coatings of a Leyden jar, and completely filling +the space between the wires discharges the jar. In +the axis of the differential apparatus the circuit has a +second gap <i>a</i> which furnishes the illuminating spark, +the image of which falls on the intercepting slide <i>b</i>. +The wires in the differential field having occasioned<span class="pagenum"><a name="Page_322" id="Page_322">[Pg 322]</a></span> +manifold disturbances were subsequently done away +with. In the new arrangement the projectile passes +through a ring (see dotted line, Fig. 51), to the air in +which it imparts a sharp impulse which travels forward +in the tube <i>r</i> as a sound-wave having the approximate +velocity of 340 metres per second, topples +over through the aperture of an electric screen the +flame of a candle situated at the other opening of the +tube, and so discharges the jar. The length of the +tube <i>r</i> is so adjusted that the discharge occurs the +moment the projectile enters the centre of the now +fully clear and free field of vision. We will also leave +out of account the fact that to secure fully the success +of the experiment, a large jar is first discharged +by the flame, and that by the agency of this first discharge +the discharge of a second small jar having a +spark of very short period which furnishes the spark +really illuminating the projectile is effected. Sparks +from large jars have an appreciable duration, and +owing to the great velocity of the projectiles furnish +blurred photographs only. By carefully husbanding +the light of the differential apparatus, and owing to +the fact that much more light reaches the photographic +plate in this way than would otherwise reach +it, we can obtain beautiful, strong, and sharp photographs +with incredibly small sparks. The contours of +the pictures appear as very delicate and very sharp, +closely adjacent double lines. From their distance +from one another, and from the velocity of the projectile,<span class="pagenum"><a name="Page_323" id="Page_323">[Pg 323]</a></span> +the duration of the illumination, or of the spark, +is found to be 1/800000 of a second. It is evident, +therefore, that experiments with mechanical snap +slides can furnish no results worthy of the name.</p> + +<div class="figcenter" style="width: 400px;"> +<img src="images/i_333.jpg" width="400" height="517" alt="" /> +<span class="caption">Fig. 52.</span> +</div> + +<p>Let us consider now first the picture of a projectile +in the rough, as represented in Figure 52, and +then let us examine it in its photographic form as seen +in Figure 53. The latter picture is of a shot from an +Austrian Mannlicher rifle. If I were not to tell you +what the picture represented you would very likely +imagine it to be a bird's eye view of a boat <i>b</i> moving +swiftly through the water. In front you see the bow-wave +and behind the body a phenomenon <i>k</i> which +closely resembles the eddies formed in the wake of a<span class="pagenum"><a name="Page_324" id="Page_324">[Pg 324]</a></span> +ship. And as a matter of fact the dark hyperboloid +arc which streams from the tip of the projectile really +is a compressed wave of air exactly analogous to the +bow-wave produced by a ship moving through the +water, with the exception that the wave of air is not +a surface-wave. The air-wave is produced in atmospheric +space and encompasses the projectile in the +form of a shell on all sides. The wave is visible for +the same reason that the heated shell of air surrounding +the candle flame of our former experiments is visible. +And the cylinder of friction-heated air which the +projectile throws off in the form of vortex rings really +does answer to the water in the wake of a vessel.</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_334.jpg" width="300" height="363" alt="" /> +<span class="caption">Fig. 53. Photograph of a blunted projectile.]</span> +</div> + +<p><span class="pagenum"><a name="Page_325" id="Page_325">[Pg 325]</a></span></p> + +<p>Now just as a slowly moving boat produces no +bow-wave, but the bow-wave is seen only when the +boat moves with a speed which is greater than the +velocity of propagation of surface-waves in water, so, +in like manner, no wave of compression is visible in +front of a projectile so long as the speed of the projectile +is less than the velocity of sound. But if the +speed of the projectile reaches and exceeds the velocity +of sound, then the head-wave, as we shall call it, +augments noticeably in power, and is more and more +extended, that is, the angle made by the contours of +the wave with the direction of flight is more and more +diminished, just as when the speed of a boat is increased +a similar phenomenon is noticed in connexion +with the bow-wave. In fact, we can from an instantaneous +photograph so taken approximately estimate +the speed with which the projectile is travelling.</p> + +<p>The explanation of the bow-wave of a ship and +that of the head-wave of a body travelling in atmospheric +space both repose upon the same principle, +long ago employed by Huygens. Conceive a number +of pebbles to be cast into a pond of water at regular +intervals in such wise that all the spots struck are situate +in the same straight line, and that every spot +subsequently struck lies a short space farther to the +right. The spots first struck will furnish then the +wave-circles which are widest, and all of them together +will, at the points where they are thickest, +form a sort of cornucopia closely resembling the bow-wave.<span class="pagenum"><a name="Page_326" id="Page_326">[Pg 326]</a></span> +(Fig. 54.) The resemblance is greater the +smaller the pebbles are, and the more quickly they +succeed each other. If a rod be dipped into the water +and quickly carried along its surface, the falling of +the pebbles will then take place, so to speak, uninterruptedly, +and we shall have a real bow-wave. If we +put the compressed air-wave in the place of the surface-waves +of the water, we shall have the head-wave +of the projectile.</p> + +<div class="figcenter" style="width: 600px;"> +<img src="images/i_336.jpg" width="600" height="265" alt="" /> +<span class="caption">Fig. 54.</span> +</div> + +<p>You may be disposed to say now, it is all very +pretty and interesting to observe a projectile in its +flight, but of what practical use is it?</p> + +<p>It is true, I reply, one cannot <i>wage war</i> with photographed +projectiles. And I have likewise often had +to say to medical students attending my lectures on +physics, when they inquired for the practical value of +some physical observation, "You cannot, gentlemen, +cure diseases with it." I had also once to give my +opinion regarding how much physics should be taught +at a school for millers, supposing the instruction +there to be confined <i>exactly</i> to what was necessary for<span class="pagenum"><a name="Page_327" id="Page_327">[Pg 327]</a></span> +a miller. I was obliged to reply: "A miller always +<i>needs</i> exactly as much physics as he <i>knows</i>." Knowledge +which one does not possess one cannot use.</p> + +<p>Let us forego entirely the consideration that as a +general thing every scientific advance, every new +problem elucidated, every extension or enrichment of +our knowledge of facts, affords a better foundation for +practical pursuits. Let us rather put the special +question, Is it not possible to derive some really practical +knowledge from our theoretical acquaintance +with the phenomena which take place in the space +surrounding a projectile?</p> + +<p>No physicist who has ever studied waves of sound +or photographed them will have the least doubt regarding +the sound-wave character of the atmospheric +condensation encompassing the head of a flying projectile. +We have therefore, without ado, called this +condensation the head-wave.</p> + +<p>Knowing this, it follows that the view of Melsens +according to which the projectile carries along with +it masses of air which it forces into the bodies struck, +is untenable. A forward-moving sound-wave is not a +forward-moving mass of matter but a forward-moving +form of motion, just as a water-wave or the waves of +a field of wheat are only forward-moving forms of motion +and not movements of masses of water or masses +of wheat.</p> + +<p>By interference-experiments, on which I cannot +touch here but which will be found roughly represented<span class="pagenum"><a name="Page_328" id="Page_328">[Pg 328]</a></span> +in Figure 55, it was found that the bell-shaped +head-wave in question is an extremely thin shell and +that the condensations of the same are quite moderate, +scarcely exceeding two-tenths of an atmosphere. +There can be no question, therefore, of explosive effects +in the body struck by the projectile through so +slight a degree of atmospheric compression. The +phenomena attending wounds from rifle balls, for example, +are not to be explained as Melsens and Busch +explain them, but are due, as Kocher and Reger maintain, +to the effects of the impact of the projectile itself.</p> + +<div class="figright" style="width: 400px;"> +<img src="images/i_338.jpg" width="400" height="394" alt="" /> +<span class="caption">Fig. 55.</span> +</div> + +<p>A simple experiment will show how insignificant is +the part played by the friction of the air, or the supposed +conveyance of the air along with the moving +projectile. If the photograph of the projectile be<span class="pagenum"><a name="Page_329" id="Page_329">[Pg 329]</a></span> +taken while passing through a flame, i. e., a visible +gas, the flame will be seen to be, not torn and deformed, +but smoothly and cleanly perforated, like any +solid body. Within and around the flame the contours +of the head-wave will be seen. The flickering, +the extinction of the flame, etc., take place only after +the projectile has travelled on a considerable distance +in its path, and is then affected by the powder gases +which hurry after the bullet or by the air preceding +the powder-gases.</p> + +<p>The physicist who examines the head-wave and +recognises its sound-wave character also sees that the +wave in question is of the same kind with the short +sharp waves produced by electric sparks, that it is a +<i>noise</i>-wave. Hence, whenever any portion of the head-wave +strikes the ear it will be heard as a report. Appearances +point to the conclusion that the projectile +carries this report along with it. In addition to this +report, which advances with the velocity of the projectile +and so usually travels at a speed greater than the +velocity of sound, there is also to be heard the report +of the exploding powder which travels forward with +the ordinary velocity of sound. Hence two explosions +will be heard, each distinct in time. The circumstance +that this fact was long misconstrued by +practical observers but when actually noticed frequently +received grotesque explanations and that ultimately +my view was accepted as the correct one, appears +to me in itself a sufficient justification that<span class="pagenum"><a name="Page_330" id="Page_330">[Pg 330]</a></span> +researches such as we are here speaking of are not utterly +superfluous even in practical directions. That +the flashes and sounds of discharging artillery are +used for estimating the distances of batteries is well +known, and it stands to reason that any unclear theoretical +conception of the facts here involved will seriously +affect the correctness of practical calculations.</p> + +<p>It may appear astonishing to a person hearing it +for the first time, that a single shot has a double report +due to two different velocities of propagation. +But the reflexion that projectiles whose velocity is less +than the velocity of sound produce no head-waves (because +every impulse imparted to the air travels forward, +that is, ahead, with exactly the velocity of +sound), throws full light when logically developed +upon the peculiar circumstance above mentioned. If +the projectile moves faster than sound, the air ahead +of it cannot recede from it quickly enough. The air +is condensed and warmed, and thereupon, as all know, +the velocity of sound is augmented until the head-wave +travels forward as rapidly as the projectile itself, so +that there is no need whatever of any additional augmentation +of the velocity of propagation. If such a +wave were left entirely to itself, it would increase in +length and soon pass into an ordinary sound-wave, +travelling with less velocity. But the projectile is always +behind it and so maintains it at its proper density +and velocity. Even if the projectile penetrates a +piece of cardboard or a board of wood, which catches<span class="pagenum"><a name="Page_331" id="Page_331">[Pg 331]</a></span> +and obstructs the head-wave, there will, as Figure 56 +shows, immediately appear at the emerging apex a +newly formed, not to say newly born, head-wave. We +may observe on the cardboard the reflexion and diffraction +of the head-wave, and by means of a flame +its refraction, so that no doubt as to its nature can remain.</p> + +<div class="figright" style="width: 350px;"> +<img src="images/i_341.jpg" width="350" height="411" alt="" /> +<span class="caption">Fig. 56.</span> +</div> + +<p>Permit me, now, to illustrate the most essential of +the points that I have just adduced, by means of a few +rough drawings taken from older and less perfect photographs.</p> + +<p>In the sketch of Figure 57 you see the projectile, +which has just left the barrel of the rifle, touch a wire +and disengage the illuminating spark. At the apex of<span class="pagenum"><a name="Page_332" id="Page_332">[Pg 332]</a></span> +the projectile you already see the beginnings of a +powerful head-wave, and in front of the wave a transparent +fungiform cluster. This latter is the air which +has been forced out of the barrel by the projectile. +Circular sound-waves, noise-waves, which are soon +overtaken by the projectile, also issue from the barrel. +But behind the projectile opaque puffs of powder-gas +rush forth. It is scarcely necessary to add that many +other questions in ballistics may be studied by this +method, as, for example, the movement of the gun-carriage.</p> + +<div class="figleft" style="width: 450px;"> +<img src="images/i_342.jpg" width="450" height="354" alt="" /> +<span class="caption">Fig. 57.</span> +</div> + +<p>A distinguished French artillerist, M. Gossot, has +applied the views of the head-wave here given in quite +a different manner. The practice in measuring the +velocity of projectiles is to cause the projectile to pass +through wire screens placed at different points in its +path, and by the tearing of these screens to give rise<span class="pagenum"><a name="Page_333" id="Page_333">[Pg 333]</a></span> +to electro-magnetic time-signals on falling slabs or +rotating drums. Gossot caused these signals to be +made directly by the impact of the head-wave, did +away thus with the wire screens, and carried the +method so far as to be able to measure the velocities +of projectiles travelling in high altitudes, where the +use of wire screens was quite out of the question.</p> + +<p>The laws of the resistance of fluids and of air to +bodies travelling in them form an extremely complicated +problem, which can be reasoned out very simply +and prettily as a matter of pure philosophy but +practice offers not a few difficulties. The same +body having the velocity 2, 3, 4 ... displaces in the +same interval 2, 3, 4 ... times the same mass of air, +or the same mass of fluid, and imparts to it <i>in addition</i> +2, 3, 4 ... times the same velocity. But for this, +plainly, 4, 9, 16 ... times the original force is required. +Hence, the resistance, it is said, increases +with the square of the velocity. This is all very pretty +and simple and obvious. But practice and theory are +at daggers' points here. Practice tells us that when +we increase the velocity, the law of the resistance +changes. For every portion of the velocity the law is +different.</p> + +<p>The studies of the talented English naval architect, +Froude, have thrown light upon this question. +Froude has shown that the resistance is conditioned +by a combination of the most multifarious phenomena. +A ship in motion is subjected to the friction of<span class="pagenum"><a name="Page_334" id="Page_334">[Pg 334]</a></span> +the water. It causes eddies and it generates in addition +waves which radiate outward from it. Every one +of these phenomena are dependent upon the velocity +in some different manner, and it is consequently not +astonishing that the law of the resistance should be a +complicated one.</p> + +<p>The preceding observations suggest quite analogous +reflexions for projectiles. Here also we have friction, +the formation of eddies, and the generation of +waves. Here, also, therefore, we should not be surprised +at finding the law of the resistance of the air a +complicated one, nor puzzled at learning that in actuality +the law of resistance changes as soon as the +speed of the projectile exceeds the velocity of sound, +for this is the precise point at which one important +element of the resistance, namely, the formation of +waves, first comes into play.</p> + +<p>No one doubts that a pointed bullet pierces the +air with less resistance than a blunt bullet. The +photographs themselves show that the head-wave is +weaker for a pointed projectile. It is not impossible, +similarly, that forms of bullets will be invented which +generate fewer eddies, etc., and that we shall study +these phenomena also by photography. I am of opinion +from the few experiments which I have made in +this direction that not much more can be done by +changing the form of the projectile when the velocity +is very great, but I have not gone into the question +thoroughly. Researches of the kind we are considering<span class="pagenum"><a name="Page_335" id="Page_335">[Pg 335]</a></span> +can certainly not be detrimental to practical artillery, +and it is no less certain that experiments by artillerists +on a large scale will be of undoubted benefit +to physics.</p> + +<p>No one who has had the opportunity of studying +modern guns and projectiles in their marvellous perfection, +their power and precision, can help confessing +that a high technical and scientific achievement has +found its incarnation in these objects. We may surrender +ourselves so completely to this impression as +to forget for a moment the terrible purposes they +serve.</p> + +<p>Permit me, therefore, before we separate, to say a +few words on this glaring contrast. The greatest man +of war and of silence which the present age has produced +once asserted that perpetual peace is a dream, +and not a beautiful dream at that. We may accord +to this profound student of mankind a judgment in +these matters and can also appreciate the soldier's +horror of stagnation from all too lengthy peace. But +it requires a strong belief in the insuperableness of +mediæval barbarism to hope for and to expect no +great improvement in international relations. Think +of our forefathers and of the times when club law +ruled supreme, when within the same country and the +same state brutal assaults and equally brutal self-defence +were universal and self-evident. This state +of affairs grew so oppressive that finally a thousand +and one circumstances compelled people to put an<span class="pagenum"><a name="Page_336" id="Page_336">[Pg 336]</a></span> +end to it, and the cannon had most to say in accomplishing +the work. Yet the rule of club law was not +abolished so quickly after all. It had simply passed +to other clubs. We must not abandon ourselves to +dreams of the Rousseau type. Questions of law will +in a sense forever remain questions of might. Even +in the United States where every one is as a matter +of principle entitled to the same privileges, the ballot +according to Stallo's pertinent remark is but a milder +substitute for the club. Nor need I tell you that +many of our own fellow-citizens are still enamored of +the old original methods. Very, very gradually, however, +as civilisation progresses, the intercourse of men +takes on gentler forms, and no one who really knows +the good old times will ever honestly wish them back +again, however beautifully they may be painted and +rhymed about.</p> + +<p>In the intercourse of the nations, however, the old +club law still reigns supreme. But since its rule is +taxing the intellectual, the moral, and the material resources +of the nations to the utmost and constitutes +scarcely less a burden in peace than in war, scarcely +less a yoke for the victor than for the vanquished, it +must necessarily grow more and more unendurable. +Reason, fortunately, is no longer the exclusive possession +of those who modestly call themselves the +upper ten thousand. Here, as everywhere, the evil +itself will awaken the intellectual and ethical forces +which are destined to mitigate it. Let the hate of<span class="pagenum"><a name="Page_337" id="Page_337">[Pg 337]</a></span> +races and of nationalities run riot as it may, the intercourse +of nations will still increase and grow more intimate. +By the side of the problems which separate +nations, the great and common ideals which claim the +exclusive powers of the men of the future appear one +after another in greater distinctness and in greater +might.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_338" id="Page_338">[Pg 338]</a></span></p> + + + + +<h2><a name="ON_INSTRUCTION_IN_THE_CLASSICS" id="ON_INSTRUCTION_IN_THE_CLASSICS">ON INSTRUCTION IN THE CLASSICS +AND THE SCIENCES.</a><a name="FNanchor_113_113" id="FNanchor_113_113"></a><a href="#Footnote_113_113" class="fnanchor">[113]</a></h2> + + +<p>Perhaps the most fantastic proposition that Maupertuis,<a name="FNanchor_114_114" id="FNanchor_114_114"></a><a href="#Footnote_114_114" class="fnanchor">[114]</a> +the renowned president of the Berlin +Academy, ever put forward for the approval of his +contemporaries was that of founding a city in which, +to instruct and discipline young students, only Latin +should be spoken. Maupertuis's Latin city remained +an idle wish. But for centuries Latin and Greek <i>institutions</i> +exist in which our children spend a goodly +portion of their days, and whose atmosphere constantly +surrounds them, even when without their walls.</p> +<p><span class="pagenum"><a name="Page_339" id="Page_339">[Pg 339]</a></span></p> +<p>For centuries instruction in the ancient languages +has been zealously cultivated. For centuries its necessity +has been alternately championed and contested. +More strongly than ever are authoritative voices now +raised against the preponderance of instruction in the +classics and in favor of an education more suited to +the needs of the time, especially for a more generous +treatment of mathematics and the natural sciences.</p> + +<p>In accepting your invitation to speak here on the +relative educational value of the classical and the +mathematico-physical sciences in colleges and high +schools, I find my justification in the duty and the +necessity laid upon every teacher of forming from his +own experiences an opinion upon this important question, +as partly also in the special circumstance that in +my youth I was personally under the influence of +school-life for only a short time, just previous to my +entering the university, and had, therefore, ample opportunity +to observe the effects of widely different +methods upon my own person.</p> + +<p>Passing now, to a review of the arguments which +the advocates of instruction in the classics advance,<span class="pagenum"><a name="Page_340" id="Page_340">[Pg 340]</a></span> +and of what the adherents of instruction in the physical +sciences in their turn adduce, we find ourselves in +rather a perplexing position with respect to the arguments +of the first named. For these have been different +at different times, and they are even now of a very +multifarious character, as must be where men advance, +in favor of an institution that exists and which they are +determined to retain at any cost, everything they can +possibly think of. We shall find here much that has +evidently been brought forward only to impress the +minds of the ignorant; much, too, that was advanced +in good faith and which is not wholly without foundation. +We shall get a fair idea of the reasoning employed +by considering, first, the arguments that have grown +out of the historical circumstances connected with the +original introduction of the classics, and, lastly, those +which were subsequently adduced as accidental afterthoughts.</p> +<p><span class="pagenum"><a name="Page_341" id="Page_341">[Pg 341]</a></span></p><p><span class="pagenum"><a name="Page_342" id="Page_342">[Pg 342]</a></span></p><p><span class="pagenum"><a name="Page_343" id="Page_343">[Pg 343]</a></span></p><p><span class="pagenum"><a name="Page_344" id="Page_344">[Pg 344]</a></span></p><p><span class="pagenum"><a name="Page_345" id="Page_345">[Pg 345]</a></span></p><p><span class="pagenum"><a name="Page_346" id="Page_346">[Pg 346]</a></span></p><p><span class="pagenum"><a name="Page_347" id="Page_347">[Pg 347]</a></span></p> +<hr class="tb" /> + +<p>Instruction in Latin, as Paulsen<a name="FNanchor_115_115" id="FNanchor_115_115"></a><a href="#Footnote_115_115" class="fnanchor">[115]</a> has minutely +shown, was introduced by the Roman Church along +with Christianity. With the Latin language were also +transmitted the scant and meagre remnants of ancient +science. Whoever wished to acquire this ancient education, +then the only one worthy of the name, for him +the Latin language was the only and indispensable +means; such a person had to learn Latin to rank +among educated people.</p> + +<p>The wide-spread influence of the Roman Church +wrought many and various results. Among those for +which all are glad, we may safely count the establishment +of a sort of <i>uniformity</i> among the nations and of a +regular international intercourse by means of the Latin +language, which did much to unite the nations in the +common work of civilisation, carried on from the fifteenth +to the eighteenth century. The Latin language +was thus long the language of scholars, and instruction +in Latin the road to a liberal education—a shibboleth +still employed, though long inappropriate.</p> + +<p>For scholars as a class, it is to be regretted, perhaps, +that Latin has ceased to be the medium of international +communication. But the attributing of the +loss of this function by the Latin language to its incapacity +to accommodate itself to the numerous new +ideas and conceptions which have arisen in the course +of the development of science is, in my opinion, wholly +erroneous. It would be difficult to find a modern +scientist who had enriched science with as many new +ideas as Newton has, yet Newton knew how to express +those ideas very correctly and precisely in the +Latin language. If this view were correct, it would +also hold true of every living language. Originally +every language has to adapt itself to new ideas.</p> + +<p>It is far more likely that Latin was displaced as +the literary vehicle of science by the influence of the +nobility. By their desire to enjoy the fruits of literature +and science, through a less irksome medium than +Latin, the nobility performed for the people at large +an undeniable service. For the days were now past +when acquaintance with the language and literature of +science was restricted to a caste, and in this step, perhaps, +was made the most important advance of modern +times. To-day, when international intercourse is firmly +established in spite of the many languages employed, +no one would think of reintroducing Latin.<a name="FNanchor_116_116" id="FNanchor_116_116"></a><a href="#Footnote_116_116" class="fnanchor">[116]</a></p> + +<p>The facility with which the ancient languages lend +themselves to the expression of new ideas is evidenced +by the fact that the great majority of our scientific +ideas, as survivals of this period of Latin intercourse, +bear Latin and Greek designations, while in great +measure scientific ideas are even now invested with +names from these sources. But to deduce from the +existence and use of such terms the necessity of still +learning Latin and Greek on the part of all who employ +them is carrying the conclusion too far. All terms, +appropriate and inappropriate,—and there are a large +number of inappropriate and monstrous combinations +in science,—rest on convention. The essential thing +is, that people should associate with the sign the precise +idea that is designated by it. It matters little +whether a person can correctly derive the words <i>telegraph</i>, +<i>tangent</i>, <i>ellipse</i>, <i>evolute</i>, etc., if the correct idea +is present in his mind when he uses them. On the +other hand, no matter how well he may know their etymology, +his knowledge will be of little use to him if +the correct idea is absent. Ask the average and fairly +educated classical scholar to translate a few lines for +you from Newton's <i>Principia</i>, or from Huygens's <i>Horologium</i>, +and you will discover at once what an extremely +subordinate rôle the mere knowledge of language +plays in such things. Without its associated +thought a word remains a mere sound. The fashion of +employing Greek and Latin designations—for it can +be termed nothing else—has a natural root in history; +it is impossible for the practice to disappear suddenly, +but it has fallen of late considerably into disuse. The +terms <i>gas</i>, <i>ohm</i>, <i>Ampère</i>, <i>volt</i>, etc., are in international +use, but they are not Latin nor Greek. Only the person +who rates the unessential and accidental husk +higher than its contents, can speak of the necessity of +learning Latin or Greek for such reasons, to say nothing +of spending eight or ten years on the task. Will +not a dictionary supply in a few seconds all the information +we wish on such subjects?<a name="FNanchor_117_117" id="FNanchor_117_117"></a><a href="#Footnote_117_117" class="fnanchor">[117]</a></p> + +<p>It is indisputable that our modern civilisation took +up the threads of the ancient civilisation, that at +many points it begins where the latter left off, and +that centuries ago the remains of the ancient culture +were the only culture existing in Europe. Then, of +course, a classical education really was the liberal education, +the higher education, the ideal education, for +it was the <i>sole</i> education. But when the same claim +is now raised in behalf of a classical education, it must +be uncompromisingly contested as bereft of all foundation. +For our civilisation has gradually attained +its independence; it has lifted itself far above the ancient +civilisation, and has entered generally new directions +of progress. Its note, its characteristic feature, +is the enlightenment that has come from the great +mathematical and physical researches of the last centuries, +and which has permeated not only the practical +arts and industries but is also gradually finding +its way into all fields of thought, including philosophy +and history, sociology and linguistics. Those traces +of ancient views that are still discoverable in philosophy, +law, art, and science, operate more as hindrances +than helps, and will not long stand before the development +of independent and more natural views.</p> + +<p>It ill becomes classical scholars, therefore, to regard +themselves, at this day, as the educated class +<i>par excellence</i>, to condemn as uneducated all persons +who do not understand Latin and Greek, to complain +that with such people profitable conversations are not +to be carried on, etc. The most delectable stories +have got into circulation, illustrative of the defective +education of scientists and engineers. A renowned +inquirer, for example, is said to have once announced +his intention of holding a free course of university lectures, +with the word "frustra"; an engineer who spent +his leisure hours in collecting insects is said to have +declared that he was studying "etymology." It is +true, incidents of this character make us shudder or +smile, according to our mood or temperament. But +we must admit, the next moment, that in giving way +to such feelings we have merely succumbed to a childish +prejudice. A lack of tact but certainly no lack of +education is displayed in the use of such half-understood +expressions. Every candid person will confess +that there are many branches of knowledge about which +he had better be silent. We shall not be so uncharitable +as to turn the tables and discuss the impression +that classical scholars might make on a scientist or +engineer, in speaking of science. Possibly many ludicrous +stories might be told of them, and of far more +serious import, which should fully compensate for the +blunders of the other party.</p> + +<p>The mutual severity of judgment which we have +here come upon, may also forcibly bring home to us +how really scarce a true liberal culture is. We may +detect in this mutual attitude, too, something of that +narrow, mediæval arrogance of caste, where a man +began, according to the special point of view of the +speaker, with the scholar, the soldier, or the nobleman. +Little sense or appreciation is to be found in it for the +<i>common</i> task of humanity, little feeling for the need of +mutual assistance in the great work of civilisation, +little breadth of mind, little truly liberal culture.</p> + +<p>A knowledge of Latin, and partly, also, a knowledge +of Greek, is still a necessity for the members of +a few professions by nature more or less directly concerned +with the civilisations of antiquity, as for lawyers, +theologians, philologists, historians, and generally +for a small number of persons, among whom +from time to time I count myself, who are compelled +to seek for information in the Latin literature of the +centuries just past.<a name="FNanchor_118_118" id="FNanchor_118_118"></a><a href="#Footnote_118_118" class="fnanchor">[118]</a> But that all young persons in +search of a higher education should pursue for this +reason Latin and Greek to such excess; that persons +intending to become physicians and scientists should +come to the universities defectively educated, or even +miseducated; and that they should be compelled to +come only from schools that do <i>not</i> supply them with +the proper preparatory knowledge is going a little bit +too far.</p> +<p><span class="pagenum"><a name="Page_348" id="Page_348">[Pg 348]</a></span></p><p><span class="pagenum"><a name="Page_349" id="Page_349">[Pg 349]</a></span></p><p><span class="pagenum"><a name="Page_350" id="Page_350">[Pg 350]</a></span></p><p><span class="pagenum"><a name="Page_351" id="Page_351">[Pg 351]</a></span></p><p><span class="pagenum"><a name="Page_352" id="Page_352">[Pg 352]</a></span></p> +<hr class="tb" /> + +<p>After the conditions which had given to the study +of Latin and Greek their high import had ceased to +exist, the traditional curriculum, naturally, was retained. +Then, the different effects of this method of +education, good and bad, which no one had thought of +at its introduction, were realised and noted. As natural, +too, was it that those who had strong interests +in the preservation of these studies, from knowing no +others or from living by them, or for still other reasons, +should emphasise the <i>good</i> results of such instruction. +They pointed to the good effects as if they +had been consciously aimed at by the method and could +be attained only through its agency.</p> + +<p>One real benefit that students might derive from +a rightly conducted course in the classics would be +the opening up of the rich literary treasures of antiquity, +and intimacy with the conceptions and views +of the world held by two advanced nations. A person +who has read and understood the Greek and Roman +authors has felt and experienced more than one who is +restricted to the impressions of the present. He sees +how men placed in different circumstances judge quite +differently of the same things from what we do to-day. +His own judgments will be rendered thus more independent. +Again, the Greek and Latin authors are indisputably +a rich fountain of recreation, of enlightenment, +and of intellectual pleasure after the day's toil, and +the individual, not less than civilised humanity generally, +will remain grateful to them for all time. Who +does not recall with pleasure the wanderings of Ulysses, +who does not listen joyfully to the simple narratives +of Herodotus, who would ever repent of having +made the acquaintance of Plato's Dialogues, or of +having tasted Lucian's divine humor? Who would +give up the glances he has obtained into the private +life of antiquity from Cicero's letters, from Plautus or +Terence? To whom are not the portraits of Suetonius +undying reminiscences? Who, in fact, would throw +away <i>any</i> knowledge he had once gained?</p> + +<p>Yet people who draw from these sources only, who +know only this culture, have surely no right to dogmatise +about the value of some other culture. As objects +of research for individuals, this literature is extremely +valuable, but it is a different question whether +it is equally valuable as the almost exclusive means of +education of our youth.</p> + +<p>Do not other nations and other literatures exist +from which we ought to learn? Is not nature herself +our first school-mistress? Are our highest models always +to be the Greeks, with their narrow provinciality +of mind, that divided the world into "Greeks and barbarians," +with their superstitions, with their eternal +questioning of oracles? Aristotle with his incapacity +to learn from facts, with his word-science; Plato with +his heavy, interminable dialogues, with his barren, at +times childish, dialectics—are they unsurpassable?<a name="FNanchor_119_119" id="FNanchor_119_119"></a><a href="#Footnote_119_119" class="fnanchor">[119]</a> +The Romans with their apathy, their pompous externality, +set off by fulsome and bombastic phrases, with +their narrow-minded, philistine philosophy, with their +frenzied sensuality, with their cruel and bestial indulgence +in animal and man baiting, with their outrageous +maltreatment and plundering of their subjects—are +they patterns worthy of imitation? Or shall, perhaps, +our science edify itself with the works of Pliny who +cites midwives as authorities and himself stands on +their point of view?</p> + +<p>Besides, if an acquaintance with the ancient world +really were attained, we might come to some settlement +with the advocates of classical education. But it +is words and forms, and forms and words only, that +are supplied to our youth; and even collateral subjects +are forced into the strait-jacket of the same +rigid method and made a science of words, sheer feats +of mechanical memory. Really, we feel ourselves set +back a thousand years into the dull cloister-cells of the +Middle Ages.</p> + +<p>This must be changed. It is possible to get acquainted +with the views of the Greeks and Romans by +a shorter road than the intellect deadening process +of eight or ten years of declining, conjugating, analysing, +and extemporisation. There are to-day plenty of +educated persons who have acquired through good +translations vivider, clearer, and more just views of +classical antiquity than the graduates of our gymnasiums +and colleges.<a name="FNanchor_120_120" id="FNanchor_120_120"></a><a href="#Footnote_120_120" class="fnanchor">[120]</a></p> + +<p>For us moderns, the Greeks and the Romans are +simply two objects of archæological and historical research +like all others. If we put them before our +youth in fresh and living pictures, and not merely in +words and syllables, the effect will be assured. We +derive a totally different enjoyment from the Greeks +when we approach them after a study of the results +of modern research in the history of civilisation. We +read many a chapter of Herodotus differently when we +attack his works equipped with a knowledge of natural +science, and with information about the stone age and +the lake-dwellers. What our classical institutions <i>pretend</i> +to give can and actually will be given to our youth +with much more fruitful results by competent <i>historical</i> +instruction, which must supply, not names and numbers +alone, nor the mere history of dynasties and wars, +but be in every sense of the word a true history of +civilisation.</p> + +<p>The view still widely prevails that although all +"higher, ideal culture," all extension of our view of +the world, is acquired by philological and in a lesser +degree by historical studies, still the mathematics and +natural sciences should not be neglected on account +of their usefulness. This is an opinion to which I must +refuse my assent. It were strange if man could learn +more, could draw more intellectual nourishment, from +the shards of a few old broken jugs, from inscribed +stones, or yellow parchments, than from all the rest +of nature. True, man is man's first concern, but he +is not his sole concern.</p> + +<p>In ceasing to regard man as the centre of the world; +in discovering that the earth is a top whirled about +the sun, which speeds off with it into infinite space; +in finding that in the fixed stars the same elements +exist as on earth; in meeting everywhere the same +processes of which the life of man is merely a vanishingly +small part—in such things, too, is a widening of +our view of the world, and edification, and poetry. +There are here perhaps grander and more significant +facts than the bellowing of the wounded Ares, or the +charming island of Calypso, or the ocean-stream engirdling +the earth. He only should speak of the relative +value of these two domains of thought, of their +poetry, who knows both.</p> + +<p>The "utility" of physical science is, in a measure, +only a <i>collateral</i> product of that flight of the intellect +which produced science. No one, however, should +underrate the utility of science who has shared in the +realisation by modern industrial art of the Oriental +world of fables, much less one upon whom those treasures +have been poured, as it were, from the fourth dimension, +without his aid or understanding.</p> + +<p>Nor may we believe that science is useful only to +the practical man. Its influence permeates all our affairs, +our whole life; everywhere its ideas are decisive. +How differently does the jurist, the legislator, or the +political economist think, who knows, for example, +that a square mile of the most fertile soil can support +with the solar heat annually consumed only a definite +number of human beings, which no art or science can +increase. Many economical theories, which open new +air-paths of progress, air-paths in the literal sense of +the word, would be made impossible by such knowledge.</p> +<p><span class="pagenum"><a name="Page_353" id="Page_353">[Pg 353]</a></span></p><p><span class="pagenum"><a name="Page_354" id="Page_354">[Pg 354]</a></span></p> +<hr class="tb" /> + +<p>The eulogists of classical education love to emphasise +the cultivation of taste which comes from employment +with the ancient models. I candidly confess +that there is something absolutely revolting in this to +me. To form the taste, then, our youths must sacrifice +ten years of their life! Luxury takes precedence over +necessity. Have the future generations, in the face +of the difficult problems, the great social questions, +which they must meet, and that with strengthened +mind and heart, no more important duties to fulfil than +these?</p> + +<p>But let us assume that this end were desirable. +Can taste be formed by rules and precepts? Do not +ideals of beauty change? Is it not a stupendous absurdity +to force one's self artificially to admire things +which, with all their historical interest, with all their +beauty in individual points, are for the most part +foreign to the rest of our thoughts and feelings, provided +we have such of <i>our own</i>. A nation that is +truly such, has its own taste and will not go to others +for it. And every individual perfect man has his own +taste.<a name="FNanchor_121_121" id="FNanchor_121_121"></a><a href="#Footnote_121_121" class="fnanchor">[121]</a></p> + +<p>And what, after all, does this cultivation of taste +consist in? In the acquisition of the personal literary +style of a few select authors! What should we think +of a people that would force its youth a thousand +years from now, by years of practice, to master the +tortuous or bombastic style of some successful lawyer +or politician of to-day? Should we not justly accuse +them of a woful lack of taste?</p> + +<p>The evil effects of this imagined cultivation of the +taste find expression often enough. The young <i>savant</i> +who regards the composition of a scientific essay as a +rhetorical exercise instead of a simple and unadorned +presentation of the facts and the truth, still sits unconsciously +on the school-bench, and still unwittingly represents +the point of view of the Romans, by whom the +elaboration of speeches was regarded as a serious scientific (!) +employment.</p> +<p><span class="pagenum"><a name="Page_355" id="Page_355">[Pg 355]</a></span></p><p><span class="pagenum"><a name="Page_356" id="Page_356">[Pg 356]</a></span></p><p><span class="pagenum"><a name="Page_357" id="Page_357">[Pg 357]</a></span></p> +<hr class="tb" /> + +<p>Far be it from me to underrate the value of the development +of the instinct of speech and of the increased +comprehension of our own language which comes from +philological studies. By the study of a foreign language, +especially of one which differs widely from ours, +the signs and forms of words are first clearly distinguished +from the thoughts which they express. Words +of the closest possible correspondence in different languages +never coincide absolutely with the ideas they +stand for, but place in relief slightly different aspects +of the same thing, and by the study of language the +attention is directed to these shades of difference. But +it would be far from admissible to contend that the +study of Latin and Greek is the most fruitful and natural, +let alone the <i>only</i>, means of attaining this end. +Any one who will give himself the pleasure of a few +hours' companionship with a Chinese grammar; who +will seek to make clear to himself the mode of speech +and thought of a people who never advanced as far as +the analysis of articulate sounds, but stopped at the +analysis of syllables, to whom our alphabetical characters, +therefore, are an inexplicable puzzle, and who +express all their rich and profound thoughts by means +of a few syllables with variable emphasis and position,—such +a person, perhaps, will acquire new, and extremely +elucidative ideas upon the relation of language +and thought. But should our children, therefore, +study Chinese? Certainly not. No more, then, +should they be burdened with Latin, at least in the +measure they are.</p> + +<p>It is a beautiful achievement to reproduce a Latin +thought in a modern language with the maximum fidelity +of meaning and expression—for the <i>translator</i>. +Moreover, we shall be very grateful to the translator +for his performance. But to demand this feat of every +educated man, without consideration of the sacrifice of +time and labor which it entails, is unreasonable. And +for this very reason, as classical teachers admit, that +ideal is never perfectly attained, except in rare cases +with scholars possessed of special talents and great +industry. Without slurring, therefore, the high importance +of the study of the ancient languages as a +profession, we may yet feel sure that the instinct for +speech which is part of every liberal education can, +and must, be acquired in a different way. Should we, +indeed, be forever lost if the Greeks had not lived before +us?</p> + +<p>The fact is, we must carry our demands further +than the representatives of classical philology. We +must ask of every educated man a fair scientific conception +of the nature and value of language, of the +formation of language, of the alteration of the meaning +of roots, of the degeneration of fixed forms of +speech to grammatical forms, in brief, of all the main +results of modern comparative philology. We should +judge that this were attainable by a careful study of +our mother tongue and of the languages next allied to +it, and subsequently of the more ancient tongues from +which the former are derived. If any one object that +this is too difficult and entails too much labor, I should +advise such a person to place side by side an English, +a Dutch, a Danish, a Swedish, and a German Bible, and +to compare a few lines of them; he will be amazed at +the multitude of suggestions that offer themselves.<a name="FNanchor_122_122" id="FNanchor_122_122"></a><a href="#Footnote_122_122" class="fnanchor">[122]</a> +In fact, I believe that a really progressive, fruitful, rational, +and instructive study of languages can be conducted +only on this plan. Many of my audience will +remember, perhaps, the bright and encouraging effect, +like that of a ray of sunlight on a gloomy day, which +the meagre and furtive remarks on comparative philology +in Curtius's Greek grammar wrought in that +barren and lifeless desert of verbal quibbles.</p> +<p><span class="pagenum"><a name="Page_358" id="Page_358">[Pg 358]</a></span></p><p><span class="pagenum"><a name="Page_359" id="Page_359">[Pg 359]</a></span></p> +<hr class="tb" /> + +<p>The principal result obtained by the present method +of studying the ancient languages is that which comes +from the student's employment with their complicated +grammars. It consists in the sharpening of the attention +and in the exercise of the judgment by the practice +of subsuming special cases under general rules, +and of distinguishing between different cases. Obviously, +the same result can be reached by many other +methods; for example, by difficult games of cards. +Every science, the mathematics and the physical sciences +included, accomplish as much, if not more, in +this disciplining of the judgment. In addition, the +matter treated by those sciences has a much higher intrinsic +interest for young people, and so engages spontaneously +their attention; while on the other hand they +are elucidative and useful in other directions in which +grammar can accomplish nothing.</p> + +<p>Who cares, so far as the matter of it is concerned, +whether we say <i>hominum</i> or <i>hominorum</i> in the genitive +plural, interesting as the fact may be for the philologist? +And who would dispute that the intellectual +need of causal insight is awakened not by grammar +but by the natural sciences?</p> + +<p>It is not our intention, therefore, to gainsay in the +least the good influence which the study of Latin and +Greek grammar <i>also</i> exercises on the sharpening of the +judgment. In so far as the study of words as such +must greatly promote lucidity and accuracy of expression, +in so far as Latin and Greek are not yet +wholly indispensable to many branches of knowledge, +we willingly concede to them a place in our schools, +but would demand that the disproportionate amount of +time allotted to them, wrongly withdrawn from other +useful studies, should be considerably curtailed. That +in the end Latin and Greek will not be employed as +the universal means of education, we are fully convinced. +They will be relegated to the closet of the +scholar or professional philologist, and gradually make +way for the modern languages and the modern science +of language.</p> + +<p>Long ago Locke reduced to their proper limits the +exaggerated notions which obtained of the close connexion +of thought and speech, of logic and grammar, +and recent investigators have established on still surer +foundations his views. How little a complicated grammar +is necessary for expressing delicate shades of +thought is demonstrated by the Italians and French, +who, although they have almost totally discarded the +grammatical redundancies of the Romans, are yet not +surpassed by the latter in accuracy of thought, and +whose poetical, but especially whose scientific literature, +as no one will dispute, can bear favorable comparison +with the Roman.</p> + +<p>Reviewing again the arguments advanced in favor +of the study of the ancient languages, we are obliged +to say that in the main and as applied to the present, +they are wholly devoid of force. In so far as the +aims which this study theoretically pursues are still +worthy of attainment, they appear to us as altogether +too narrow, and are surpassed in this only by the +means employed. As almost the sole, indisputable result +of this study we must count the increase of the +student's skill and precision in expression. One inclined +to be uncharitable might say that our gymnasiums +and classical academies turn out men who can +speak and write, but, unfortunately, have little to write +or speak about. Of that broad, liberal view, of that +famed universal culture, which the classical curriculum +is supposed to yield, serious words need not be lost. +This culture might, perhaps, more properly be termed +the contracted or lopsided culture.</p> +<p><span class="pagenum"><a name="Page_360" id="Page_360">[Pg 360]</a></span></p><p><span class="pagenum"><a name="Page_361" id="Page_361">[Pg 361]</a></span></p><p><span class="pagenum"><a name="Page_362" id="Page_362">[Pg 362]</a></span><span class="pagenum"><a name="Page_363" id="Page_363">[Pg 363]</a></span></p><p><span class="pagenum"><a name="Page_364" id="Page_364">[Pg 364]</a></span></p><p><span class="pagenum"><a name="Page_365" id="Page_365">[Pg 365]</a></span></p><p><span class="pagenum"><a name="Page_366" id="Page_366">[Pg 366]</a></span></p><p><span class="pagenum"><a name="Page_367" id="Page_367">[Pg 367]</a></span></p><p><span class="pagenum"><a name="Page_368" id="Page_368">[Pg 368]</a></span></p><p><span class="pagenum"><a name="Page_369" id="Page_369">[Pg 369]</a></span></p><p><span class="pagenum"><a name="Page_370" id="Page_370">[Pg 370]</a></span><span class="pagenum"><a name="Page_371" id="Page_371">[Pg 371]</a></span></p> +<hr class="tb" /> + +<p>While considering the study of languages we threw +a few side glances at mathematics and the natural sciences. +Let us now inquire whether these, as branches +of study, cannot accomplish much that is to be attained +in no other way. I shall meet with no contradiction +when I say that without at least an elementary mathematical +and scientific education a man remains a total +stranger in the world in which he lives, a stranger in +the civilisation of the time that bears him. Whatever +he meets in nature, or in the industrial world, either +does not appeal to him at all, from his having neither +eye nor ear for it, or it speaks to him in a totally unintelligible +language.</p> + +<p>A real understanding of the world and its civilisation, +however, is not the only result of the study of +mathematics and the physical sciences. Much more +essential for the preparatory school is the <i>formal</i> cultivation +which comes from these studies, the strengthening +of the reason and the judgment, the exercise +of the imagination. Mathematics, physics, chemistry, +and the so-called descriptive sciences are so much +alike in this respect, that, apart from a few points, we +need not separate them in our discussion.</p> + +<p>Logical sequence and continuity of ideas, so necessary +for fruitful thought, are <i>par excellence</i> the results of +mathematics; the ability to follow facts with thoughts, +that is, to observe or collect experiences, is chiefly developed +by the natural sciences. Whether we notice +that the sides and the angles of a triangle are connected +in a definite way, that an equilateral triangle possesses +certain definite properties of symmetry, or whether we +notice the deflexion of a magnetic needle by an electric +current, the dissolution of zinc in diluted sulphuric +acid, whether we remark that the wings of a butterfly +are slightly colored on the under, and the fore-wings +of the moth on the upper, surface: indiscriminately +here we proceed from <i>observations</i>, from individual +acts of immediate intuitive knowledge. The field of +observation is more restricted and lies closer at hand +in mathematics; it is more varied and broader but +more difficult to compass in the natural sciences. The +essential thing, however, is for the student to learn to +make observations in all these fields. The philosophical +question whether our acts of knowledge in mathematics +are of a special kind is here of no importance +for us. It is true, of course, that the observation can +be practised by languages also. But no one, surely, +will deny, that the concrete, living pictures presented +in the fields just mentioned possess different +and more powerful attractions for the mind of the +youth than the abstract and hazy figures which language +offers, and on which the attention is certainly not +so spontaneously bestowed, nor with such good results.<a name="FNanchor_123_123" id="FNanchor_123_123"></a><a href="#Footnote_123_123" class="fnanchor">[123]</a></p> + +<p>Observation having revealed the different properties +of a given geometrical or physical object, it is discovered +that in many cases these properties <i>depend</i> in +some way upon one another. This interdependence +of properties (say that of equal sides and equal angles +at the base of a triangle, the relation of pressure to +motion,) is nowhere so distinctly marked, nowhere is +the necessity and permanency of the interdependence +so plainly noticeable, as in the fields mentioned. +Hence the continuity and logical consequence of the +ideas which we acquire in those fields. The relative +simplicity and perspicuity of geometrical and physical +relations supply here the conditions of natural and +easy progress. Relations of equal simplicity are not +met with in the fields which the study of language +opens up. Many of you, doubtless, have often wondered +at the little respect for the notions of cause and +effect and their connexion that is sometimes found +among professed representatives of the classical studies. +The explanation is probably to be sought in the +fact that the analogous relation of motive and action +familiar to them from their studies, presents nothing +like the clear simplicity and determinateness that the +relation of cause and effect does.</p> + +<p>That perfect mental grasp of all possible cases, +that economical order and organic union of the thoughts +which comes from it, which has grown for every one +who has ever tasted it a permanent need which he +seeks to satisfy in every new province, can be developed +only by employment with the relative simplicity of +mathematical and scientific investigations.</p> + +<p>When a set of facts comes into apparent conflict +with another set of facts, and a problem is presented, +its solution consists ordinarily in a more refined distinction +or in a more extended view of the facts, as +may be aptly illustrated by Newton's solution of the +problem of dispersion. When a new mathematical or +scientific fact is <i>demonstrated</i>, or <i>explained</i>, such demonstration +also rests simply upon showing the connexion +of the new fact with the facts already known; for +example, that the radius of a circle can be laid off as +chord exactly six times in the circle is explained or +proved by dividing the regular hexagon inscribed in +the circle into equilateral triangles. That the quantity +of heat developed in a second in a wire conveying an +electric current is quadrupled on the doubling of the +strength of the current, we explain from the doubling of +the fall of the potential due to the doubling of the +current's intensity, as also from the doubling of the +quantity flowing through, in a word, from the quadrupling +of the work done. In point of principle, explanation +and direct proof do not differ much.</p> + +<p>He who solves scientifically a geometrical, physical, +or technical problem, easily remarks that his +procedure is a <i>methodical</i> mental quest, rendered possible +by the economical order of the province—a simplified +purposeful quest as contrasted with unmethodical, +unscientific guess-work. The geometer, for example, +who has to construct a circle touching two given +straight lines, casts his eye over the relations of symmetry +of the desired construction, and seeks the centre +of his circle solely in the line of symmetry of the two +straight lines. The person who wants a triangle of +which two angles and the sum of the sides are given, +grasps in his mind the determinateness of the form of +this triangle and restricts his search for it to a certain +group of triangles of the <i>same form</i>. Under very different +circumstances, therefore, the simplicity, the intellectual +perviousness, of the subject-matter of mathematics +and natural science is felt, and promotes both +the discipline and the self-confidence of the reason.</p> + +<p>Unquestionably, much more will be attained by instruction +in the mathematics and the natural sciences +than now is, when more natural methods are adopted. +One point of importance here is that young students +should not be spoiled by premature abstraction, but +should be made acquainted with their material from +living pictures of it before they are made to work with +it by purely ratiocinative methods. A good stock of +geometrical experience could be obtained, for example, +from geometrical drawing and from the practical +construction of models. In the place of the unfruitful +method of Euclid, which is only fit for special, restricted +uses, a broader and more conscious method +must be adopted, as Hankel has pointed out.<a name="FNanchor_124_124" id="FNanchor_124_124"></a><a href="#Footnote_124_124" class="fnanchor">[124]</a> Then, +if, on reviewing geometry, and after it presents no +substantial difficulties, the more general points of view, +the principles of scientific method are placed in relief +and brought to consciousness, as Von Nagel,<a name="FNanchor_125_125" id="FNanchor_125_125"></a><a href="#Footnote_125_125" class="fnanchor">[125]</a> J. K. +Becker,<a name="FNanchor_126_126" id="FNanchor_126_126"></a><a href="#Footnote_126_126" class="fnanchor">[126]</a> Mann,<a name="FNanchor_127_127" id="FNanchor_127_127"></a><a href="#Footnote_127_127" class="fnanchor">[127]</a> and others have well done, fruitful +results will be surely attained. In the same way, +the subject-matter of the natural sciences should be +made familiar by pictures and experiment before a +profounder and reasoned grasp of these subjects is +attempted. Here the emphasis of the more general +points of view is to be postponed.</p> + +<p>Before my present audience it would be superfluous +for me to contend further that mathematics and natural +science are justified constituents of a sound education,—a +claim that even philologists, after some +resistance, have conceded. Here I may count upon +assent when I say that mathematics and the natural +sciences pursued alone as means of instruction yield a +richer education in matter and form, a more general +education, an education better adapted to the needs +and spirit of the time,—than the philological branches +pursued alone would yield.</p> + +<p>But how shall this idea be realised in the curricula +of our intermediate educational institutions? It is unquestionable +in my mind that the German <i>Realschulen</i> +and <i>Realgymnasien</i>, where the exclusive classical course +is for the most part replaced by mathematics, science, +and modern languages, give the <i>average</i> man a more +timely education than the gymnasium proper, although +they are not yet regarded as fit preparatory schools for +future theologians and professional philologists. The +German gymnasiums are too one-sided. With these +the first changes are to be made; of these alone we +shall speak here. Possibly a <i>single</i> preparatory school, +suitably planned, might serve all purposes.</p> + +<p>Shall we, then, in our gymnasiums fill out the hours +of study which stand at our disposal, or are still to be +wrested from the classicists, with as great and as varied +a quantity of mathematical and scientific matter +as possible? Expect no such proposition from me. +No one will suggest such a course who has himself +been actively engaged in scientific thought. Thoughts +can be awakened and fructified as a field is fructified +by sunshine and rain. But thoughts cannot be juggled +out and worried out by heaping up materials and +the hours of instruction, nor by any sort of precepts: +they must grow naturally of their own free accord. +Furthermore, thoughts cannot be accumulated beyond +a certain limit in a single head, any more than the produce +of a field can be increased beyond certain limits.</p> + +<p>I believe that the amount of matter necessary for a +useful education, such as should be offered to <i>all</i> the +pupils of a preparatory school, is very small. If I had +the requisite influence, I should, in all composure, and +fully convinced that I was doing what was best, first +greatly curtail in the lower classes the amount of matter +in both the classical and the scientific courses; I +should cut down considerably the number of the school +hours and the work done outside the school. I am +not with many teachers of opinion that ten hours work +a day for a child is not too much. I am convinced +that the mature men who offer this advice so lightly +are themselves unable to give their attention successfully +for as long a time to any subject that is new to +them, (for example, to elementary mathematics or +physics,) and I would ask every one who thinks the +contrary to make the experiment upon himself. Learning +and teaching are not routine office-work that can +be kept up mechanically for long periods. But even +such work tires in the end. If our young men are +not to enter the universities with blunted and impoverished +minds, if they are not to leave in the preparatory +schools their vital energy, which they should +there gather, great changes must be made. Waiving +the injurious effects of overwork upon the body, the +consequences of it for the mind seem to me positively +dreadful.</p> + +<p>I know of nothing more terrible than the poor creatures +who have learned too much. Instead of that +sound powerful judgment which would probably have +grown up if they had learned nothing, their thoughts +creep timidly and hypnotically after words, principles, +and formulæ, constantly by the same paths. What +they have acquired is a spider's web of thoughts too +weak to furnish sure supports, but complicated enough +to produce confusion.</p> + +<p>But how shall better methods of mathematical and +scientific education be combined with the decrease of +the subject-matter of instruction? I think, by abandoning +systematic instruction altogether, at least in so +far as that is required of <i>all</i> young pupils. I see no +necessity whatever that the graduates of our high +schools and preparatory schools should be little philologists, +and at the same time little mathematicians, +physicists, and botanists; in fact, I do not see the possibility +of such a result. I see in the endeavor to attain +this result, in which every instructor seeks for his +own branch a place apart from the others, the main +mistake of our whole system. I should be satisfied if +every young student could come into living contact +with and pursue to their ultimate logical consequences +merely a <i>few</i> mathematical or scientific discoveries. +Such instruction would be mainly and naturally associated +with selections from the great scientific classics. +A few powerful and lucid ideas could thus be made +to take root in the mind and receive thorough elaboration. +This accomplished, our youth would make a +different showing from what they do to-day.<a name="FNanchor_128_128" id="FNanchor_128_128"></a><a href="#Footnote_128_128" class="fnanchor">[128]</a></p> + +<p>What need is there, for example, of burdening the +head of a young student with all the details of botany? +The student who has botanised under the guidance of +a teacher finds on all hands, not indifferent things, but +known or unknown things, by which he is stimulated, +and his gain made permanent. I express here, not my +own, but the opinion of a friend, a practical teacher. +Again, it is not at all necessary that all the matter that +is offered in the schools should be learned. The best +that we have learned, that which has remained with +us for life, outlived the test of examination. How can +the mind thrive when matter is heaped on matter, and +new materials piled constantly on old, undigested materials? +The question here is not so much that of the +accumulation of positive knowledge as of intellectual +discipline. It seems also unnecessary that <i>all</i> branches +should be treated at school, and that exactly the same +studies should be pursued in all schools. A single +philological, a single historical, a single mathematical, +a single scientific branch, pursued as common subjects +of instruction for all pupils, are sufficient to accomplish +all that is necessary for the intellectual development. +On the other hand, a wholesome mutual stimulus +would be produced by this greater variety in the +positive culture of men. Uniforms are excellent for +soldiers, but they will not fit heads. Charles V. learned +this, and it should never be forgotten. On the contrary, +teachers and pupils both need considerable latitude, if +they are to yield good results.</p> + +<p>With John Karl Becker I am of the opinion that +the utility and amount for individuals of every study +should be precisely determined. All that exceeds this +amount should be unconditionally banished from the +lower classes. With respect to mathematics, Becker,<a name="FNanchor_129_129" id="FNanchor_129_129"></a><a href="#Footnote_129_129" class="fnanchor">[129]</a> +in my judgment, has admirably solved this question.</p> + +<p>With respect to the upper classes the demand assumes +a different form. Here also the amount of matter +obligatory on all pupils ought not to exceed a certain +limit. But in the great mass of knowledge that a +young man must acquire to-day for his profession it is +no longer just that ten years of his youth should be +wasted with mere preludes. The upper classes should +supply a truly useful preparation for the professions, +and should not be modelled upon the wants merely of +future lawyers, ministers, and philologists. Again, it +would be both foolish and impossible to attempt to +prepare the same person properly for all the different +professions. In such case the function of the schools +would be, as Lichtenberg feared, simply to select the +persons best fitted for being drilled, whilst precisely the +finest special talents, which do not submit to indiscriminate +discipline, would be excluded from the contest. +Hence, a certain amount of liberty in the choice +of studies must be introduced in the upper classes, by +means of which it will be free for every one who is clear +about the choice of his profession to devote his chief +attention either to the study of the philologico-historical +or to that of the mathematico-scientific branches. +Then the matter now treated could be retained, and in +some branches, perhaps, judiciously extended,<a name="FNanchor_130_130" id="FNanchor_130_130"></a><a href="#Footnote_130_130" class="fnanchor">[130]</a> without +burdening the scholar with many branches or increasing +the number of the hours of study. With more +homogeneous work the student's capacity for work increases, +one part of his labor supporting the other +instead of obstructing it. If, however, a young man +should subsequently choose a different profession, then +it is <i>his</i> business to make up what he has lost. No +harm certainly will come to society from this change, +nor could it be regarded as a misfortune if philologists +and lawyers with mathematical educations or physical +scientists with classical educations should now and +then appear.</p> +<p><span class="pagenum"><a name="Page_372" id="Page_372">[Pg 372]</a></span></p><p><span class="pagenum"><a name="Page_373" id="Page_373">[Pg 373]</a></span><span class="pagenum"><a name="Page_374" id="Page_374">[Pg 374]</a></span></p><p><span class="pagenum"><a name="Page_375" id="Page_375">[Pg 375]</a></span></p> +<hr class="tb" /> + +<p>The view is now wide-spread that a Latin and +Greek education no longer meets the general wants of +the times, that a more opportune, a more "liberal" +education exists. The phrase, "a liberal education," +has been greatly misused. A truly liberal education is +unquestionably very rare. The <i>schools</i> can hardly offer +such; at best they can only bring home to the student +the necessity of it. It is, then, his business to acquire, +as best he can, a more or less liberal education. It +would be very difficult, too, at any one time to give a +definition of a "liberal" education which would satisfy +every one, still more difficult to give one which would +hold good for a hundred years. The educational +ideal, in fact, varies much. To one, a knowledge of +classical antiquity appears not too dearly bought "with +early death." We have no objection to this person, +or to those who think like him, pursuing their ideal +after their own fashion. But we may certainly protest +strongly against the realisation of such ideals on our +own children. Another,—Plato, for example,—puts +men ignorant of geometry on a level with animals.<a name="FNanchor_131_131" id="FNanchor_131_131"></a><a href="#Footnote_131_131" class="fnanchor">[131]</a> +If such narrow views had the magical powers of the +sorceress Circe, many a man who perhaps justly +thought himself well educated would become conscious +of a not very flattering transformation of himself. +Let us seek, therefore, in our educational system +to meet the wants of the present, and not establish +prejudices for the future.</p> + +<p>But how does it come, we must ask, that institutions +so antiquated as the German gymnasiums could +subsist so long in opposition to public opinion? The +answer is simple. The schools were first organised by +the Church; since the Reformation they have been in +the hands of the State. On so large a scale, the plan +presents many advantages. Means can be placed at +the disposal of education such as no private source, at +least in Europe, could furnish. Work can be conducted +upon the same plan in many schools, and so +experiments made of extensive scope which would be +otherwise impossible. A single man with influence +and ideas can under such circumstances do great +things for the promotion of education.</p> + +<p>But the matter has also its reverse aspect. The +party in power works for its own interests, uses the +schools for its special purposes. Educational competition +is excluded, for all successful attempts at improvement +are impossible unless undertaken or permitted +by the State. By the uniformity of the people's +education, a prejudice once in vogue is permanently +established. The highest intelligences, the strongest +wills cannot overthrow it suddenly. In fact, as everything +is adapted to the view in question, a sudden +change would be physically impossible. The two +classes which virtually hold the reins of power in the +State, the jurists and theologians, know only the one-sided, +predominantly classical culture which they have +acquired in the State schools, and would have this culture +alone valued. Others accept this opinion from +credulity; others, underestimating their true worth for +society, bow before the power of the prevalent opinion; +others, again, affect the opinion of the ruling +classes even against their better judgment, so as to +abide on the same plane of respect with the latter. I +will make no charges, but I must confess that the deportment +of medical men with respect to the question +of the qualification of graduates of your <i>Realschulen</i> +has frequently made that impression upon me. Let +us remember, finally, that an influential statesman, +even within the boundaries which the law and public +opinion set him, can do serious harm to the cause +of education by considering his own one-sided views +infallible, and in enforcing them recklessly and inconsiderately—which +not only <i>can</i> happen, but has, repeatedly, +happened.<a name="FNanchor_132_132" id="FNanchor_132_132"></a><a href="#Footnote_132_132" class="fnanchor">[132]</a> The monopoly of education by +the State<a name="FNanchor_133_133" id="FNanchor_133_133"></a><a href="#Footnote_133_133" class="fnanchor">[133]</a> thus assumes in our eyes a somewhat different +aspect. And to revert to the question above asked, +there is not the slightest doubt that the German gymnasiums +in their present form would have ceased to +exist long ago if the State had not supported them.</p> + +<p>All this must be changed. But the change will +not be made of itself, nor without our energetic interference, +and it will be made slowly. But the path is +marked out for us, the will of the people must acquire +and exert upon our school legislation a greater and +more powerful influence. Furthermore, the questions +at issue must be publicly and candidly discussed that +the views of the people may be clarified. All who feel +the insufficiency of the existing <i>régime</i> must combine +into a powerful organisation that their views may +acquire impressiveness and the opinions of the individual +not die away unheard.</p> + +<p>I recently read, gentlemen, in an excellent book of +travels, that the Chinese speak with unwillingness of +politics. Conversations of this sort are usually cut +short with the remark that they may bother about such +things whose business it is and who are paid for it. +Now it seems to me that it is not only the business of +the State, but a very serious concern of all of us, how +our children shall be educated in the public schools +at <i>our</i> cost.</p> + + + + +<h2><a name="APPENDIX" id="APPENDIX">APPENDIX.</a></h2> + +<p class="center">I.</p> + +<h3><a id="A_CONTRIBUTION_TO_THE_HISTORY_OF_ACOUSTICS"></a>A CONTRIBUTION TO THE HISTORY OF ACOUSTICS.<a name="FNanchor_134_134" id="FNanchor_134_134"></a><a href="#Footnote_134_134" class="fnanchor">[134]</a></h3> + + +<p>While searching for papers by Amontons, several +volumes of the Memoirs of the Paris Academy +for the first years of the eighteenth century, fell +into my hands. It is difficult to portray the delight +which one experiences in running over the leaves of +these volumes. One sees as an actual spectator almost +the rise of the most important discoveries and witnesses +the progress of many fields of knowledge from +almost total ignorance to relatively perfect clearness.</p> + +<p>I propose to discuss here the fundamental researches +of Sauveur in Acoustics. It is astonishing +how extraordinarily near Sauveur was to the view +which Helmholtz was the first to adopt in its full extent +a hundred and fifty years later.</p> + +<p>The <i>Histoire de l'Académie</i> for 1700, p. 131, tells +us that Sauveur had succeeded in making music an<span class="pagenum"><a name="Page_376" id="Page_376">[Pg 376]</a></span> +object of scientific research, and that he had invested +the new science with the name of "acoustics." On +five successive pages a number of discoveries are recorded +which are more fully discussed in the volume +for the year following.</p> + +<p>Sauveur regards the <i>simplicity</i> of the ratios obtaining +between the rates of vibration of consonances as +something universally known.<a name="FNanchor_135_135" id="FNanchor_135_135"></a><a href="#Footnote_135_135" class="fnanchor">[135]</a> He is in hope, by +further research, of determining the chief rules of musical +composition and of fathoming the "metaphysics +of the agreeable," the main law of which he asserts +to be the union of "simplicity with multiplicity." +Precisely as Euler<a name="FNanchor_136_136" id="FNanchor_136_136"></a><a href="#Footnote_136_136" class="fnanchor">[136]</a> did a number of years later, he +regards a consonance as more perfect according as +the ratio of its vibrational rates is expressed in smaller +whole numbers, because the smaller these whole numbers +are the oftener the vibrations of the two tones +coincide, and hence the more readily they are apprehended. +As the limit of consonance, he takes the +ratio 5:6, although he does not conceal the fact that +practice, sharpened attention, habit, taste, and even +prejudice play collateral rôles in the matter, and that +consequently the question is not a purely scientific +one.</p> + +<p>Sauveur's ideas took their development from his<span class="pagenum"><a name="Page_377" id="Page_377">[Pg 377]</a></span> +having instituted at all points more exact quantitative +investigations than his predecessors. He is first desirous +of determining as the foundation of musical +tuning a fixed note of one hundred vibrations which +can be reproduced at any time; the fixing of the notes +of musical instruments by the common tuning pipes +then in use with rates of vibration unknown, appearing +to him inadequate. According to Mersenne (<i>Harmonie +Universelle</i>, 1636), a given cord seventeen feet +long and weighted with eight pounds executes eight +visible vibrations in a second. By diminishing its +length then in a given proportion we obtain a proportionately +augmented rate of vibration. But this procedure +appears too uncertain to Sauveur, and he employs +for his purpose the beats (<i>battemens</i>), which were +known to the organ-makers of his day, and which he +correctly explains as due to the alternate coincidence +and non-coincidence of the same vibrational phases of +differently pitched notes.<a name="FNanchor_137_137" id="FNanchor_137_137"></a><a href="#Footnote_137_137" class="fnanchor">[137]</a> At every coincidence there +is a swelling of the sound, and hence the number of +beats per second will be equal to the difference of the +rates of vibration. If we tune two of three organ-pipes +to the remaining one in the ratio of the minor and major +third, the mutual ratio of the rates of vibration of +the first two will be as 24: 25, that is to say, for every +24 vibrations to the lower note there will be 25 to the +higher, and one beat. If the two pipes give together<span class="pagenum"><a name="Page_378" id="Page_378">[Pg 378]</a></span> +four beats in a second, then the higher has the fixed +tone of 100 vibrations. The open pipe in question +will consequently be five feet in length. We also determine +by this procedure the absolute rates of vibration +of all the other notes.</p> + +<p>It follows at once that a pipe eight times as long +or 40 feet in length will yield a vibrational rate of +12-1/2, which Sauveur ascribes to the lowest audible +tone, and further also that a pipe 64 times as small +will execute 6,400 vibrations, which Sauveur took for +the highest audible limit. The author's delight at his +successful enumeration of the "imperceptible vibrations" +is unmistakably asserted here, and it is justified +when we reflect that to-day even Sauveur's principle, +slightly modified, constitutes the simplest and most +delicate means we have for exactly determining rates +of vibration. Far more important still, however, is a +second observation which Sauveur made while studying +beats, and to which we shall revert later.</p> + +<p>Strings whose lengths can be altered by movable +bridges are much easier to handle than pipes in such +investigations, and it was natural that Sauveur should +soon resort to their use.</p> + +<p>One of his bridges accidentally not having been +brought into full and hard contact with the string, +and consequently only imperfectly impeding the vibrations, +Sauveur discovered the harmonic overtones of +the string, at first by the unaided ear, and concluded +from this fact that the string was divided into aliquot<span class="pagenum"><a name="Page_379" id="Page_379">[Pg 379]</a></span> +parts. The string when plucked, and when the bridge +stood at the third division for example, yielded the +twelfth of its fundamental note. At the suggestion +of some academician<a name="FNanchor_138_138" id="FNanchor_138_138"></a><a href="#Footnote_138_138" class="fnanchor">[138]</a> probably, variously colored +paper riders were placed at the nodes (<i>noeuds</i>) and +ventral segments (<i>ventres</i>), and the division of the +string due to the excitation of the overtones (<i>sons +harmoniques</i>) belonging to its fundamental note (<i>son +fondamental</i>) thus rendered visible. For the clumsy +bridge the more convenient feather or brush was soon +substituted. +. +While engaged in these investigations Sauveur also +observed the sympathetic vibration of a string induced +by the excitation of a second one in unison with it. +He also discovered that the overtone of a string can +respond to another string tuned to its note. He even +went further and discovered that on exciting one string +the overtone which it has in common with another, +differently pitched string can be produced on that +other; for example, on strings having for their vibrational +ratio 3:4, the fourth of the lower and the third +of the higher may be made to respond. It follows indisputably +from this that the excited string yields +overtones simultaneously with its fundamental tone. +Previously to this Sauveur's attention had been drawn +by other observers to the fact that the overtones of +musical instruments can be picked out by attentive +listening, particularly in the night.<a name="FNanchor_139_139" id="FNanchor_139_139"></a><a href="#Footnote_139_139" class="fnanchor">[139]</a> He himself mentions<span class="pagenum"><a name="Page_380" id="Page_380">[Pg 380]</a></span> +the simultaneous sounding of the overtones and +the fundamental tone.<a name="FNanchor_140_140" id="FNanchor_140_140"></a><a href="#Footnote_140_140" class="fnanchor">[140]</a> That he did not give the +proper consideration to this circumstance was, as will +afterwards be seen, fatal to his theory.</p> + +<p>While studying beats Sauveur makes the remark +that they are <i>displeasing</i> to the ear. He held the beats +were distinctly audible only when less than six occurred +in a second. Larger numbers were not distinctly +perceptible and gave rise accordingly to no +disturbance. He then attempts to reduce the difference +between consonance and dissonance to a question +of beats. Let us hear his own words.<a name="FNanchor_141_141" id="FNanchor_141_141"></a><a href="#Footnote_141_141" class="fnanchor">[141]</a></p> + +<blockquote><p>"Beats are unpleasing to the ear because of the unevenness +of the sound, and it may be held with much plausibility that the +reason why octaves are so pleasing is that we never hear their +beats.<a name="FNanchor_142_142" id="FNanchor_142_142"></a><a href="#Footnote_142_142" class="fnanchor">[142]</a></p> + +<p>"In following out this idea, we find that the chords whose +beats we cannot hear are precisely those which the musicians call +consonances and that those whose beats are heard are the dissonances, +and that when a chord is a dissonance in one octave and a +consonance in another, it beats in the one and does not beat in the +other. Consequently it is called an imperfect consonance. It is +very easy by the principles of M. Sauveur, here established, to ascertain +what chords beat and in what octaves, above or below the +fixed note. If this hypothesis be correct, it will disclose the true +source of the rules of composition, hitherto unknown to science, +and given over almost entirely to judgment by the ear. These +sorts of natural judgment, marvellous though they may sometimes +appear, are not so but have very real causes, the knowledge of +which belongs to science, provided it can gain possession thereof."<a name="FNanchor_143_143" id="FNanchor_143_143"></a><a href="#Footnote_143_143" class="fnanchor">[143]</a></p></blockquote> + +<p><span class="pagenum"><a name="Page_381" id="Page_381">[Pg 381]</a></span></p><p>Sauveur thus correctly discerns in beats the cause +of the disturbance of consonance, to which all disharmony +is "probably" to be referred. It will be seen, +however, that according to his view all distant intervals +must necessarily be consonances and all near intervals +dissonances. He also overlooks the absolute +difference in point of principle between his old view, +mentioned at the outset, and his new view, rather attempting +to obliterate it.</p> + +<p>R. Smith<a name="FNanchor_144_144" id="FNanchor_144_144"></a><a href="#Footnote_144_144" class="fnanchor">[144]</a> takes note of the theory of Sauveur and +calls attention to the first of the above-mentioned defects. +Being himself essentially involved in the old +view of Sauveur, which is usually attributed to Euler, +he yet approaches in his criticism a brief step nearer<span class="pagenum"><a name="Page_382" id="Page_382">[Pg 382]</a></span> +to the modern theory, as appears from the following +passage.<a name="FNanchor_145_145" id="FNanchor_145_145"></a><a href="#Footnote_145_145" class="fnanchor">[145]</a></p> + +<blockquote><p>"The truth is, this gentleman confounds the distinction between +perfect and imperfect consonances, by comparing imperfect +consonances which beat because the succession of their short cycles<a name="FNanchor_146_146" id="FNanchor_146_146"></a><a href="#Footnote_146_146" class="fnanchor">[146]</a> +is periodically confused and interrupted, with perfect ones +which cannot beat, because the succession of their short cycles is +never confused nor interrupted.</p> + +<p>"The <i>fluttering roughness</i> above mentioned is perceivable +in all other perfect consonances, in a smaller degree in proportion +as their cycles are shorter and simpler, and their pitch is higher; +and is of a <i>different kind</i> from the <i>smoother beats</i> and undulations +of <i>tempered consonances</i>; because we can alter the rate of +the latter by altering the temperament, but not of the former, the +consonance being perfect at a given pitch: And because a judicious +ear can often hear, at the same time, both the flutterings and the +beats of a tempered consonance; sufficiently distinct from each +other.</p> + +<p>"For nothing gives greater offence to the hearer, though ignorant +of the cause of it, than those rapid, piercing beats of high +and loud sounds, which make imperfect consonances with one another. +And yet a few slow beats, like the slow undulations of a +close shake now and then introduced, are far from being disagreeable."</p></blockquote> + +<p>Smith is accordingly clear that other "roughnesses" +exist besides the beats which Sauveur considered, +and if the investigations had been continued +on the basis of Sauveur's idea, these additional roughnesses +would have turned out to be the beats of the<span class="pagenum"><a name="Page_383" id="Page_383">[Pg 383]</a></span> +overtones, and the theory thus have attained the +point of view of Helmholtz.</p> + +<p>Reviewing the differences between Sauveur's and +Helmholtz's theories, we find the following:</p> + +<p>1. The theory according to which consonance depends +on the frequent and regular coincidence of vibrations +and their ease of enumeration, appears from +the new point of view inadmissible. The simplicity +of the ratios obtaining between the rates of vibration +is indeed a <i>mathematical</i> characteristic of consonance +as well as a <i>physical</i> condition thereof, for the reason +that the coincidence of the overtones as also their +further physical and physiological consequences is +connected with this fact. But no <i>physiological</i> or <i>psychological</i> +explanation of consonance is given by this +fact, for the simple reason that in the acoustic nerve-process +nothing corresponding to the periodicity of +the sonant stimulus is discoverable.</p> + +<p>2. In the recognition of beats as a disturbance of +consonance, both theories agree. Sauveur's theory, +however, does not take into account the fact that +clangs, or musical sounds generally, are composite +and that the disturbance in the consonances of distant +intervals principally arise from the beats of the overtones. +Furthermore, Sauveur was wrong in asserting +that the number of beats must be less than six in a +second in order to produce disturbances. Even Smith +knows that very slow beats are not a cause of disturbance, +and Helmholtz found a much higher number<span class="pagenum"><a name="Page_384" id="Page_384">[Pg 384]</a></span> +(33) for the maximum of disturbance. Finally, Sauveur +did not consider that although the number of +beats increases with the recession from unison, yet +their <i>strength</i> is diminished. On the basis of the +principle of specific energies and of the laws of sympathetic +vibration the new theory finds that two atmospheric +motions of like amplitude but different periods, +<i>a</i> sin(<i>rt</i>) and <i>a</i> sin[(<i>r</i> + ρ)(<i>t</i> + τ)], cannot be +communicated with the same amplitude to the same +nervous end-organ. On the contrary, an end-organ +that reacts best to the period <i>r</i> responds more weakly +to the period <i>r</i> + ρ, the two amplitudes bearing to each +other the proportion <i>a</i>: φ<i>a</i>. Here φ decreases when +ρ increases, and when ρ = 0 it becomes equal to 1, so +that only the portion of the stimulus φ<i>a</i> is subject to +beats, and the portion (1-φ)<i>a</i> continues smoothly +onward without disturbance.</p> + +<p>If there is any moral to be drawn from the history +of this theory, it is that considering how near Sauveur's +errors were to the truth, it behooves us to exercise +some caution also with regard to the new theory. +And in reality there seems to be reason for +doing so.</p> + +<p>The fact that a musician will never confound a +more perfectly consonant chord on a poorly tuned +piano with a less perfectly consonant chord on a well +tuned piano, although the roughness in the two cases +may be the same, is sufficient indication that the degree +of roughness is not the only characteristic of a<span class="pagenum"><a name="Page_385" id="Page_385">[Pg 385]</a></span> +harmony. As the musician knows, even the harmonic +beauties of a Beethoven sonata are not easily effaced +on a poorly tuned piano; they scarcely suffer more +than a Raphael drawing executed in rough unfinished +strokes. The <i>positive physiologico-psychological</i> characteristic +which distinguishes one harmony from another +is not given by the beats. Nor is this characteristic +to be found in the fact that, for example, in sounding +a major third the fifth partial tone of the lower note +coincides with the fourth of the higher note. This +characteristic comes into consideration only for the +investigating and abstracting reason. If we should +regard it also as characteristic of the sensation, we +should lapse into a fundamental error which would +be quite analogous to that cited in (1).</p> + +<p>The <i>positive physiological</i> characteristics of the intervals +would doubtless be speedily revealed if it were +possible to conduct aperiodic, for example galvanic, +stimuli to the single sound-sensing organs, in which +case the beats would be totally eliminated. Unfortunately +such an experiment can hardly be regarded as +practicable. The employment of acoustic stimuli of +short duration and consequently also free from beats, +involves the additional difficulty of a pitch not precisely +determinable.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_386" id="Page_386">[Pg 386]</a></span></p> + + + + +<p class="center">II.</p> + +<h3><a id="REMARKS_ON_THE_THEORY_OF_SPATIAL_VISION"></a>REMARKS ON THE THEORY OF SPATIAL VISION.<a name="FNanchor_147_147" id="FNanchor_147_147"></a><a href="#Footnote_147_147" class="fnanchor">[147]</a></h3> + + +<p>According to Herbart, spatial vision rests on reproduction-series. +In such an event, of course, and +if the supposition is correct, the magnitudes of the +residua with which the percepts or representations +are coalesced (the helps to coalescence) are of cardinal +influence. Furthermore, since the coalescences +must first be fully perfected before they make their +appearance, and since upon their appearance the inhibitory +ratios are brought into play, ultimately, then, +if we leave out of account the accidental order of time +in which the percepts are given, everything in spatial +vision depends on the oppositions and affinities, or, +in brief, on the qualities of the percepts, which enter +into series.</p> + +<p>Let us see how the theory stands with respect to +the special facts involved.</p> + +<p>1. If intersecting series only, running anteriorly +and posteriorly, are requisite for the production of +spatial sensation, why are not analogues of them found +in all the senses?</p> + +<p>2. Why do we measure differently colored objects<span class="pagenum"><a name="Page_387" id="Page_387">[Pg 387]</a></span> +and variegated objects with one and the same spatial +measure? How do we recognise differently colored +objects as the same in size? Where do we get our +measure of space from and what is it?</p> + +<p>3. Why is it that differently colored figures of the +same form reproduce one another and are recognised +as the same?</p> + +<p>Here are difficulties enough. Herbart is unable to +solve them by his theory. The unprejudiced student +sees at once that his "inhibition by reason of form" +and "preference by reason of form" are absolutely +impossible. Think of Herbart's example of the red +and black letters.</p> + +<p>The "help to coalescence" is a passport, so to +speak, made out to the name and person of the percept. +A percept which is coalesced with another cannot +reproduce all others qualitatively different from it +for the simple reason that the latter are in like manner +coalesced with one another. Two qualitatively different +series certainly do not reproduce themselves because +they present the same order of degree of coalescence.</p> + +<p>If it is certain that only things simultaneous and +things which are alike are reproduced, a basic principle +of Herbart's psychology which even the most +absolute empiricists will not deny, nothing remains +but to modify the theory of spatial perception or to +invent in its place a new principle in the manner indicated, +a step which hardly any one would seriously<span class="pagenum"><a name="Page_388" id="Page_388">[Pg 388]</a></span> +undertake. The new principle could not fail to throw +all psychology into the most dreadful confusion.</p> + +<p>As to the modification which is needed there can +be hardly any doubt as to how in the face of the facts +and conformably to Herbart's own principles it is to +be carried out. If two differently colored figures of +equal size reproduce each other and are recognised as +equal, the result can be due to nothing but to the existence +in both series of presentations of a presentation +or percept which is qualitatively <i>the same</i>. The +colors are different. Consequently, like or equal percepts +must be connected with the colors which are +yet independent of the colors. We have not to look +long for them, for they are the like effects of the muscular +feelings of the eye when confronted by the two +figures. We might say we reach the vision of space +by the registering of light-sensations in a schedule of +graduated muscle-sensations.<a name="FNanchor_148_148" id="FNanchor_148_148"></a><a href="#Footnote_148_148" class="fnanchor">[148]</a></p> + +<p>A few considerations will show the likelihood of +the rôle of the muscle-sensations. The muscular apparatus +of <i>one</i> eye is unsymmetrical. The two eyes +together form a system which is vertical in symmetry. +This already explains much.</p> + +<p>1. The <i>position</i> of a figure influences its view. According +to the position in which objects are viewed +different muscle-sensations come into play and the +impression is altered. To recognise inverted letters<span class="pagenum"><a name="Page_389" id="Page_389">[Pg 389]</a></span> +as such long experience is required. The best proof +of this are the letters d, b, p, q, which are represented +by the same figure in different positions and yet are +always distinguished as different.<a name="FNanchor_149_149" id="FNanchor_149_149"></a><a href="#Footnote_149_149" class="fnanchor">[149]</a></p> + +<p>2. It will not escape the attentive observer that for +the same reasons and even with the same figure and +in the same position the fixation point is also decisive. +The figure seems to change <i>during</i> the act of vision. +For example, an eight-pointed star constructed by +successively joining in a regular octagon the first corner +with the fourth, the fourth with the seventh, etc., +skipping in every case two corners, assumes alternately, +according to where we suffer the centre of vision +to rest, a predominantly architectonic or a freer +and more open character. Vertical and horizontal +lines are always differently apprehended from what +oblique lines are.</p> + +<div class="figleft" style="width: 300px;"> +<img src="images/i_399.jpg" width="300" height="130" alt="" /> +<span class="caption">Fig. 58.</span> +</div> + +<p>3. The reason why we prefer vertical symmetry +and regard it as something special in its kind, whereas +we do not recognise +horizontal symmetry +at all immediately, is +due to the vertical +symmetry of the muscular +apparatus of the eye. The left-hand side <i>a</i> of +the accompanying vertically-symmetrical figure induces +in the left eye the same muscular feelings as the<span class="pagenum"><a name="Page_390" id="Page_390">[Pg 390]</a></span> +right-hand side <i>b</i> does in the right eye. The pleasing +effect of symmetry has its cause primarily in the repetition +of muscular feelings. That a repetition actually +occurs here, sometimes sufficiently marked in character +as to lead to the confounding of objects, is +proved apart from the theory by the fact which is +familiar to every one <i>quem dii oderunt</i> that children +frequently reverse figures from the right to the left, +but never from above downwards; for example, write +ε instead of 3 until they finally come to notice the +slight difference. Figure 50 shows how pleasing the +repetition of muscular +feelings may be. As +will be readily understood, +vertical and horizontal lines exhibit relations +similar to symmetrical figures which are immediately +disturbed when oblique positions are chosen for the +lines. Compare what Helmholtz says regarding the +repetition and coincidence of partial tones.</p> + +<div class="figright" style="width: 400px;"> +<img src="images/i_400.jpg" width="400" height="88" alt="" /> +<span class="caption">Fig. 59.</span> +</div> + +<p>I may be permitted to add a general remark. It +is a quite universal phenomenon in psychology that +certain qualitatively quite different series of percepts +mutually awaken and reproduce one another and in a +certain aspect produce the appearance of sameness or +similarity. We say of such series that they are of +like or of similar form, naming their abstracted likeness +<i>form</i>.</p> + +<blockquote><p>1. Of spatial figures we have already spoken.</p> + +<p>2. We call two melodies like melodies when they<span class="pagenum"><a name="Page_391" id="Page_391">[Pg 391]</a></span> +present the same succession of pitch-ratios; +the absolute pitch (or key) may be as different +as can be. We can so select the melodies that +not even two partial tones of the notes in each +are common. Yet we recognise the melodies +as alike. And, what is more, we notice the +form of the melody more readily and recognise +it again more easily than the key (the absolute +pitch) in which it was played.</p> + +<p>3. We recognise in two different melodies the +same rhythm no matter how different the melodies +may be otherwise. We know and recognise +the rhythm more easily even than the absolute +duration (the tempo).</p></blockquote> + +<p>These examples will suffice. In all these and in +all similar cases the recognition and likeness cannot +depend upon the qualities of the percepts, for these +are different. On the other hand recognition, conformably +to the principles of psychology, is possible +only with percepts which are the same in quality. +Consequently there is no other escape than to imagine +the qualitatively unlike percepts of the two series as +necessarily connected with other percepts which are +qualitatively alike.</p> + +<p>Since in differently colored figures of like form, like +muscular feelings are necessarily induced if the figures +are recognised as alike, so there must necessarily lie +at the basis of all forms also, and we might even say +at the basis of all abstractions, percepts of a peculiar<span class="pagenum"><a name="Page_392" id="Page_392">[Pg 392]</a></span> +quality. And this holds true for space and form as +well as for time, rhythm, pitch, the form of melodies, +intensity, etc. But whence is psychology to derive all +these qualities? Have no fear, they will all be found, +as were the sensations of muscles for the theory of +space. The organism is at present still rich enough +to meet all the requirements of psychology in this direction, +and it is even time to give serious ear to the +question of "corporeal resonance" which psychology +so loves to dwell on.</p> + +<p>Different psychical qualities appear to bear a very +intimate mutual relation to one another. Special research +on the subject, as well also as the demonstration +that this remark may be generally employed in +physics, will follow later.<a name="FNanchor_150_150" id="FNanchor_150_150"></a><a href="#Footnote_150_150" class="fnanchor">[150]</a></p> +<p><span class="pagenum"><a name="Page_393" id="Page_393">[Pg 393]</a></span></p> + + + +<h2><a name="INDEX" id="INDEX">INDEX.</a></h2> + + +<ul class="IX"><li>Absolute, temperature, <a href="#Page_162">162</a>;</li> +<li><span style="margin-left: 1em;">time, <a href="#Page_204">204</a>;</span></li> +<li><span style="margin-left: 1em;">forecasts, have no signification in science, <a href="#Page_206">206</a>.</span></li> + +<li>Abstract, meaning of the term, <a href="#Page_240">240</a>.</li> + +<li>Abstraction, <a href="#Page_180">180</a>, <a href="#Page_200">200</a>, <a href="#Page_208">208</a>, <a href="#Page_231">231</a>.</li> + +<li>Acceleration, organ for forward, <a href="#Page_299">299</a> et seq.</li> + +<li>Accelerations, <a href="#Page_204">204</a>, <a href="#Page_216">216</a>, footnote, <a href="#Page_225">225</a>-<a href="#Page_226">226</a>, <a href="#Page_253">253</a>.</li> + +<li>Accident, logical and historical, in science, <a href="#Page_160">160</a>, <a href="#Page_168">168</a>, <a href="#Page_170">170</a>, <a href="#Page_213">213</a>;</li> +<li><span style="margin-left: 1em;">in inventions and discoveries, <a href="#Page_262">262</a> et seq.</span></li> + +<li>Accord, the pure triple, <a href="#Page_46">46</a>.</li> + +<li>Accumulators, electrical, <a href="#Page_125">125</a> et seq.;</li> +<li><span style="margin-left: 1em;"><a href="#Page_132">132</a>, footnote.</span></li> + +<li>Acoustic color, <a href="#Page_36">36</a>.</li> + +<li>Acoustics, Sauveur on, <a href="#Page_375">375</a> et seq.</li> + +<li>Action and reaction, importance of the principle of, <a href="#Page_191">191</a>.</li> + +<li>Adaptation, in organic and inorganic matter, <a href="#Page_216">216</a>, <a href="#Page_229">229</a>;</li> +<li><span style="margin-left: 1em;">in scientific thought, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>.</span></li> + +<li>Æsthetics, computation as a principle of, <a href="#Page_34">34</a>;</li> +<li><span style="margin-left: 1em;">researches in, <a href="#Page_89">89</a>, footnote;</span></li> +<li><span style="margin-left: 1em;">repetition, a principle of, <a href="#Page_91">91</a>.</span></li> + +<li>Africa, <a href="#Page_186">186</a>, <a href="#Page_234">234</a>, <a href="#Page_237">237</a>.</li> + +<li>Agreeable effects, due to repetition of sensations, <a href="#Page_92">92</a>, <a href="#Page_97">97</a> et seq.</li> + +<li>Agriculture, transition to, <a href="#Page_265">265</a>.</li> + +<li>Air-gun, <a href="#Page_135">135</a>.</li> + +<li>Alcohol and water, mixture of oil and, in Plateau's experiments, <a href="#Page_4">4</a>.</li> + +<li>Algebra, economy of, <a href="#Page_196">196</a>.</li> + +<li>Alien thoughts in science, <a href="#Page_196">196</a>.</li> + +<li>All, the, <a href="#Page_88">88</a>.</li> + +<li>Amontons, <a href="#Page_174">174</a>, <a href="#Page_346">346</a>.</li> + +<li>Ampère, the word, <a href="#Page_314">314</a>.</li> + +<li>Ampère's swimmer, <a href="#Page_207">207</a>.</li> + +<li>Analogies, mechanical, <a href="#Page_157">157</a>, <a href="#Page_160">160</a>;</li> +<li><span style="margin-left: 1em;">generally, <a href="#Page_236">236</a>-<a href="#Page_258">258</a>.</span></li> + +<li>Analogy, defined, <a href="#Page_250">250</a>.</li> + +<li>Analysis, <a href="#Page_188">188</a>.</li> + +<li>Analytical geometry, not necessary to physicians, <a href="#Page_370">370</a>, footnote.</li> + +<li>Anatomic structures, transparent stereoscopic views of, <a href="#Page_74">74</a>.</li> + +<li>Anatomy, character of research in, <a href="#Page_255">255</a>.</li> + +<li>Andrieu, Jules, <a href="#Page_49">49</a>, footnote.</li> + +<li>Animals, the psychical activity of, <a href="#Page_190">190</a>, <a href="#Page_231">231</a>;</li> +<li><span style="margin-left: 1em;">the language of, <a href="#Page_238">238</a>;</span></li> +<li><span style="margin-left: 1em;">their capacity for experience, <a href="#Page_266">266</a> et seq.</span></li> + +<li>Animism, <a href="#Page_186">186</a>, <a href="#Page_187">187</a>, <a href="#Page_243">243</a>, <a href="#Page_254">254</a>.</li> + +<li>Anisotropic optical fields, <a href="#Page_227">227</a>.</li> + +<li>Apparatus for producing movements of rotation, <a href="#Page_287">287</a> et seq.</li> + +<li>Arabesque, an inverted, <a href="#Page_95">95</a>.</li> + +<li>Arabian Nights, <a href="#Page_219">219</a>.</li> + +<li>Arago, <a href="#Page_270">270</a>.</li> + +<li>Aral, the Sea of, <a href="#Page_239">239</a>.</li> + +<li>Archæopteryx, <a href="#Page_257">257</a>.</li> + +<li>Archimedes, <a href="#Page_4">4</a>, <a href="#Page_237">237</a>.</li> + +<li>Arcimboldo, Giuseppe, <a href="#Page_36">36</a>.</li> + +<li>Area, principle of least superficial, <a href="#Page_10">10</a> et seq.</li> + +<li>Ares, the bellowing of the wounded, <a href="#Page_272">272</a>.</li> + +<li>Aristotelians, <a href="#Page_283">283</a>.</li> + +<li>Aristotle, <a href="#Page_348">348</a>, <a href="#Page_296">296</a>.</li> + +<li>Art, development of, <a href="#Page_28">28</a> et seq.</li> + +<li>Artillery, practical, <a href="#Page_334">334</a>-<a href="#Page_335">335</a>.</li> + +<li>Artistic value of scientific descriptions, <a href="#Page_254">254</a>.</li> + +<li>Arts, practical, <a href="#Page_108">108</a>.</li> + +<li>Ascent, heights of, <a href="#Page_143">143</a>-<a href="#Page_151">151</a>.</li> + +<li><span class="pagenum"><a name="Page_394" id="Page_394">[Pg 394]</a></span>Asia, 234.</li> + +<li>Assyrians, the art of, <a href="#Page_79">79</a>.</li> + +<li>Astronomer, measures celestial by terrestrial distances, <a href="#Page_136">136</a>.</li> + +<li>Astronomy, antecedent to psychology, <a href="#Page_90">90</a>;</li> +<li><span style="margin-left: 1em;">rigidity of its truths, <a href="#Page_221">221</a>.</span></li> + +<li>Atomic theories, <a href="#Page_104">104</a>.</li> + +<li>Atoms, <a href="#Page_207">207</a>.</li> + +<li>Attention, the rôle of, in sensuous perception, <a href="#Page_35">35</a> et seq.</li> + +<li>Attraction, generally, <a href="#Page_226">226</a>;</li> +<li><span style="margin-left: 1em;">of liquid particles, <a href="#Page_13">13</a>-<a href="#Page_14">14</a>;</span></li> +<li><span style="margin-left: 1em;">in electricity, <a href="#Page_109">109</a> et seq.</span></li> + +<li>Aubert, <a href="#Page_298">298</a>.</li> + +<li>Audition. See <i>Ear</i>.</li> + +<li>Austrian gymnasiums, <a href="#Page_370">370</a>, footnote.</li> + +<li>Axioms, instinctive knowledge, <a href="#Page_190">190</a>.</li> + +</ul> + +<ul class="IX"><li>Babbage, on the economy of machinery, <a href="#Page_196">196</a>.</li> + +<li>Bach, <a href="#Page_20">20</a>.</li> + +<li>Backwards, prophesying, <a href="#Page_253">253</a>.</li> + +<li>Bacon, Lord, <a href="#Page_48">48</a>, <a href="#Page_280">280</a>.</li> + +<li>Baer, C. E. von, <a href="#Page_235">235</a>.</li> + +<li>Balance, electrical, <a href="#Page_127">127</a>, footnote;</li> +<li><span style="margin-left: 1em;">torsion, <a href="#Page_109">109</a>, <a href="#Page_168">168</a>.</span></li> + +<li>Balloon, a hydrogen, <a href="#Page_199">199</a>.</li> + +<li>Barbarism and civilisation, <a href="#Page_335">335</a> et seq.</li> + +<li>Bass-clef, <a href="#Page_101">101</a>.</li> + +<li>Bass, fundamental, <a href="#Page_44">44</a>.</li> + +<li>Beats, <a href="#Page_40">40</a>-<a href="#Page_45">45</a>, <a href="#Page_377">377</a> et seq.</li> + +<li>Beautiful, our notions of, variable, <a href="#Page_99">99</a>.</li> + +<li>Beauty, objects of, in nature, <a href="#Page_91">91</a>.</li> + +<li>Becker, J. K., <a href="#Page_364">364</a>, <a href="#Page_369">369</a>.</li> + +<li>Beethoven, <a href="#Page_39">39</a>, <a href="#Page_44">44</a>.</li> + +<li>Beginnings of science, <a href="#Page_189">189</a>, <a href="#Page_191">191</a>.</li> + +<li>Belvedere Gallery at Vienna, <a href="#Page_36">36</a>.</li> + +<li>Bernoulli, Daniel, on the conservation of living force, <a href="#Page_149">149</a>;</li> +<li><span style="margin-left: 1em;">on the vibrations of strings, <a href="#Page_249">249</a>.</span></li> + +<li>Bernoulli, James, on the centre of oscillation, <a href="#Page_149">149</a>.</li> + +<li>Bernoulli, John, on the conservation of living force, <a href="#Page_149">149</a>;</li> +<li><span style="margin-left: 1em;">on the principle of virtual velocities, <a href="#Page_151">151</a>.</span></li> + +<li>Bible, parallel passages from, for language study, <a href="#Page_356">356</a>.</li> + +<li>Binocular vision, <a href="#Page_66">66</a> et seq.</li> + +<li>Black, his theory of caloric, <a href="#Page_138">138</a>, <a href="#Page_162">162</a>;</li> +<li><span style="margin-left: 1em;">on quantity of heat, <a href="#Page_166">166</a>, <a href="#Page_174">174</a>;</span></li> +<li><span style="margin-left: 1em;">on latent heat, <a href="#Page_167">167</a>, <a href="#Page_178">178</a>;</span></li> +<li><span style="margin-left: 1em;">researches in heat generally, <a href="#Page_244">244</a>.</span></li> + +<li>Blind cat, <a href="#Page_303">303</a>.</li> + +<li>Bodies, heavy, seek their places, <a href="#Page_224">224</a> et seq.;</li> +<li><span style="margin-left: 1em;">rotating, <a href="#Page_285">285</a>.</span></li> + +<li>Body, a mental symbol for groups of sensations, <a href="#Page_200">200</a>-<a href="#Page_203">203</a>;</li> +<li><span style="margin-left: 1em;">the human, our knowledge of, <a href="#Page_90">90</a>.</span></li> + +<li>Boltzmann, <a href="#Page_236">236</a>.</li> + +<li>Booth, Mr., <a href="#Page_77">77</a>.</li> + +<li>Borelli, <a href="#Page_217">217</a>.</li> + +<li>Boulder, a granite, <a href="#Page_233">233</a>.</li> + +<li>Bow-wave of ships and moving projectiles, <a href="#Page_323">323</a> et seq.</li> + +<li>Boys, <a href="#Page_317">317</a>.</li> + +<li>Bradley, <a href="#Page_273">273</a>.</li> + +<li>Brahman, the, <a href="#Page_63">63</a>.</li> + +<li>Brain, localisation of functions in, <a href="#Page_210">210</a>.</li> + +<li>Breuer, <a href="#Page_272">272</a>, <a href="#Page_282">282</a> et seq., <a href="#Page_293">293</a>, <a href="#Page_298">298</a>, <a href="#Page_300">300</a>, <a href="#Page_301">301</a>, <a href="#Page_303">303</a>, <a href="#Page_306">306</a>.</li> + +<li>Brewster, his stereoscope, <a href="#Page_73">73</a>.</li> + +<li>Bridge, invention of the, <a href="#Page_264">264</a>, <a href="#Page_268">268</a>.</li> + +<li>British Association, <a href="#Page_108">108</a>.</li> + +<li>Brooklyn Bridge, <a href="#Page_75">75</a>, footnote.</li> + +<li>Brown, Crum, <a href="#Page_293">293</a>, <a href="#Page_301">301</a>.</li> + +<li>Building, our concepts directions for, <a href="#Page_253">253</a>;</li> +<li><span style="margin-left: 1em;">facts the result of, <a href="#Page_253">253</a>;</span></li> +<li><span style="margin-left: 1em;">science compared to, <a href="#Page_257">257</a>.</span></li> + +<li>Building-stones, metrical units are, <a href="#Page_253">253</a>.</li> + +<li>Busch, <a href="#Page_328">328</a>.</li> + +<li>Business of a merchant, science compared to the, <a href="#Page_16">16</a>.</li> + +<li>Butterfly, a, <a href="#Page_22">22</a>.</li> +</ul> + +<ul class="IX"><li>Calculating machines, their economical character, <a href="#Page_196">196</a>.</li> + +<li>Caloric, theory of, stood in the way of scientific advancement, <a href="#Page_138">138</a>, <a href="#Page_167">167</a>.</li> + +<li>Calypso, the island of, <a href="#Page_351">351</a>.</li> + +<li>Canterbury, Archbishop of, <a href="#Page_39">39</a>.</li> + +<li>Cantor, M., <a href="#Page_361">361</a>, footnote.</li> + +<li>Capacity, electrical, <a href="#Page_116">116</a> et seq., <a href="#Page_123">123</a>;</li> +<li><span style="margin-left: 1em;">thermal, <a href="#Page_123">123</a>;</span></li> +<li><span style="margin-left: 1em;">specific inductive, <a href="#Page_117">117</a>.</span></li> + +<li>Capulets and Montagues, <a href="#Page_87">87</a>.</li> + +<li>Cards, difficult games of, <a href="#Page_357">357</a>.</li> + +<li>Carnot, S., excludes perpetual motion in heat, <a href="#Page_156">156</a>, <a href="#Page_162">162</a>;</li> +<li><span style="margin-left: 1em;">his mechanical view of physics, <a href="#Page_156">156</a>;</span></li> +<li><span class="pagenum"><a name="Page_395" id="Page_395">[Pg 395]</a></span><span style="margin-left: 1em;">on thermodynamics, <a href="#Page_160">160</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">his principle, <a href="#Page_162">162</a>;</span></li> +<li><span style="margin-left: 1em;">also, <a href="#Page_191">191</a>.</span></li> + +<li>Carus, Dr. Paul, <a href="#Page_265">265</a>, footnote.</li> + +<li>Casselli's telegraph, <a href="#Page_26">26</a>.</li> + +<li>Cassini, <a href="#Page_51">51</a>.</li> + +<li>Cauchy, character of the intellectual activity of a, <a href="#Page_195">195</a>.</li> + +<li>Causal insight, awakened by science, <a href="#Page_357">357</a>.</li> + +<li>Causality, <a href="#Page_157">157</a>-<a href="#Page_159">159</a>, <a href="#Page_190">190</a>, <a href="#Page_198">198</a> et seq., <a href="#Page_221">221</a> et seq., <a href="#Page_237">237</a>, <a href="#Page_253">253</a>, <a href="#Page_254">254</a>.</li> + +<li>Cause and effect, <a href="#Page_198">198</a> et seq. See also <i>Causality</i>.</li> + +<li>Centimetre-gramme-second system, <a href="#Page_111">111</a>.</li> + +<li>Centre of gravity, must lie as low as possible for equilibrium to subsist, <a href="#Page_15">15</a>;</li> +<li><span style="margin-left: 1em;">Torricelli's principle of, <a href="#Page_150">150</a> et seq.</span></li> + +<li>Centre of oscillation, <a href="#Page_149">149</a>.</li> + +<li>Change, method of, in science, <a href="#Page_230">230</a>.</li> + +<li>Changeable character of bodies, <a href="#Page_202">202</a>.</li> + +<li>Changes, physical, how they occur, <a href="#Page_205">205</a>.</li> + +<li>Character, a Universal Real, <a href="#Page_192">192</a>.</li> + +<li>Character, like the forms of liquids, <a href="#Page_3">3</a>;</li> +<li><span style="margin-left: 1em;">persons of, <a href="#Page_24">24</a>.</span></li> + +<li>Charles the Fifth, <a href="#Page_369">369</a>.</li> + +<li>Chemical, elements, <a href="#Page_202">202</a>;</li> +<li><span style="margin-left: 1em;">symbols, <a href="#Page_192">192</a>;</span></li> +<li><span style="margin-left: 1em;">current, <a href="#Page_118">118</a>.</span></li> + +<li>Chemistry, character of research in, <a href="#Page_255">255</a>;</li> +<li><span style="margin-left: 1em;">the method of thermodynamics in, <a href="#Page_257">257</a>.</span></li> + +<li>Child, a, modes of thought of, <a href="#Page_223">223</a>;</li> +<li><span style="margin-left: 1em;">looking into a moat, <a href="#Page_208">208</a>.</span></li> + +<li>Child of the forest, his interpretation of new events, <a href="#Page_218">218</a>-<a href="#Page_219">219</a>.</li> + +<li>Childish questions, <a href="#Page_199">199</a>-<a href="#Page_200">200</a>.</li> + +<li>Children, the drawings of, <a href="#Page_201">201</a>-<a href="#Page_202">202</a>.</li> + +<li>Chinese language, economy of, <a href="#Page_192">192</a>;</li> +<li><span style="margin-left: 1em;">study of, <a href="#Page_354">354</a>.</span></li> + +<li>Chinese philosopher, an old, <a href="#Page_186">186</a>.</li> + +<li>Chinese, speak with unwillingness of politics, <a href="#Page_374">374</a>;</li> +<li><span style="margin-left: 1em;">the art of, <a href="#Page_79">79</a>-<a href="#Page_80">80</a>.</span></li> + +<li>Chosen, many are called but few are, <a href="#Page_65">65</a>.</li> + +<li>Christ, saying of, <a href="#Page_65">65</a>.</li> + +<li>Christianity, Latin introduced with, <a href="#Page_311">311</a>.</li> + +<li>Christians and Jews, monotheism of the, <a href="#Page_187">187</a>.</li> + +<li>Church and State, <a href="#Page_88">88</a>.</li> + +<li>Cicero, <a href="#Page_318">318</a>.</li> + +<li>Circe, <a href="#Page_372">372</a>.</li> + +<li>Circle, the figure of least area with given periphery, <a href="#Page_12">12</a>.</li> + +<li>Circular polarisation, <a href="#Page_242">242</a>.</li> + +<li>Civilisation and barbarism, <a href="#Page_335">335</a> et seq.</li> + +<li>Civilisation, some phenomena of, explained by binocular vision, <a href="#Page_74">74</a>.</li> + +<li>Civilised man, his modes of conception and interpretation, <a href="#Page_219">219</a>.</li> + +<li>Clapeyron, <a href="#Page_162">162</a>.</li> + +<li>Class-characters of animals, <a href="#Page_255">255</a>.</li> + +<li>Classical, culture, the good and bad effects of, <a href="#Page_347">347</a>;</li> +<li><span style="margin-left: 1em;">scholars, not the only educated people, <a href="#Page_345">345</a>.</span></li> + +<li>Classics, on instruction in, <a href="#Page_338">338</a>-<a href="#Page_374">374</a>;</li> +<li><span style="margin-left: 1em;">the scientific, <a href="#Page_368">368</a>.</span></li> + +<li>Classification in science, <a href="#Page_255">255</a>.</li> + +<li>Clausius, on thermodynamics, <a href="#Page_165">165</a>;</li> +<li><span style="margin-left: 1em;">on reversible cycles, <a href="#Page_176">176</a>.</span></li> + +<li>Claviatur, Mach's, <a href="#Page_42">42</a>-<a href="#Page_43">43</a>.</li> + +<li>Club-law, <a href="#Page_335">335</a>.</li> + +<li>Cochlea, the, a species of piano-forte, <a href="#Page_19">19</a>.</li> + +<li>Cockchafer, <a href="#Page_86">86</a>.</li> + +<li>Coefficient of self-induction, <a href="#Page_250">250</a>, <a href="#Page_252">252</a>.</li> + +<li>Colophonium, solution of, <a href="#Page_7">7</a>.</li> + +<li>Color, acoustic, <a href="#Page_36">36</a>.</li> + +<li>Color-sensation, <a href="#Page_210">210</a>.</li> + +<li>Color-signs, their economy, <a href="#Page_192">192</a>.</li> + +<li>Colors, origin of the names of, <a href="#Page_239">239</a>.</li> + +<li>Column, body moving behind a, <a href="#Page_202">202</a>.</li> + +<li>Communication, its functions, import and fruits, <a href="#Page_197">197</a>, <a href="#Page_238">238</a> et seq.;</li> +<li><span style="margin-left: 1em;">by language, <a href="#Page_237">237</a>;</span></li> +<li><span style="margin-left: 1em;">high importance of, <a href="#Page_191">191</a> et seq.</span></li> + +<li>Comparative physics, <a href="#Page_239">239</a>.</li> + +<li>Comparison in science, <a href="#Page_231">231</a>, <a href="#Page_238">238</a> et seq.</li> + +<li>Computation, a principle of æsthetics, <a href="#Page_34">34</a>.</li> + +<li>Concepts, abstract, defined, <a href="#Page_250">250</a>-<a href="#Page_252">252</a>;</li> +<li><span style="margin-left: 1em;">metrical, in electricity, <a href="#Page_107">107</a> et seq.</span></li> + +<li>Conceptual, meaning of the term, <a href="#Page_240">240</a>.</li> + +<li>Conceptual thought, <a href="#Page_192">192</a>.</li> + +<li>Concha, <a href="#Page_18">18</a>.</li> + +<li>Condensers, electrical, <a href="#Page_125">125</a> et seq. <a href="#Page_132">132</a>, footnote.</li> + +<li><span class="pagenum"><a name="Page_396" id="Page_396">[Pg 396]</a></span>Conductors and non-conductors. See <i>Electrical</i>, etc.</li> + +<li>Conformity in the deportment of the energies, <a href="#Page_171">171</a>-<a href="#Page_175">175</a>.</li> + +<li>Confusion of objects, cause of, <a href="#Page_95">95</a>.</li> + +<li>Conic sections, <a href="#Page_257">257</a>.</li> + +<li>Conical refraction, <a href="#Page_29">29</a>, <a href="#Page_242">242</a>.</li> + +<li>Conservation of energy, <a href="#Page_137">137</a> et seq. See <i>Energy</i>.</li> + +<li>Conservation of weight or mass, <a href="#Page_203">203</a>.</li> + +<li>Consonance, connexion of the simple natural numbers with, <a href="#Page_33">33</a>;</li> +<li><span style="margin-left: 1em;">Euclid's definition of, <a href="#Page_33">33</a>;</span></li> +<li><span style="margin-left: 1em;">explanation of, <a href="#Page_42">42</a>;</span></li> +<li><span style="margin-left: 1em;">scientific definition of, <a href="#Page_44">44</a>;</span></li> +<li><span style="margin-left: 1em;">and dissonance reduced to beats, <a href="#Page_376">376</a>, <a href="#Page_370">370</a>, <a href="#Page_383">383</a>.</span></li> + +<li>Consonant intervals, <a href="#Page_43">43</a>.</li> + +<li>Constancy of matter, <a href="#Page_203">203</a>.</li> + +<li>Constant, the dielectric, <a href="#Page_117">117</a>.</li> + +<li>Constants, the natural, <a href="#Page_193">193</a>.</li> + +<li>Continuum of facts, <a href="#Page_256">256</a> et seq.</li> + +<li>Cornelius, <a href="#Page_388">388</a>, footnote.</li> + +<li>Corti, the Marchese, his discovery of minute rods in the labyrinth of the ear, <a href="#Page_19">19</a>.</li> + +<li>Coulomb, his electrical researches, <a href="#Page_108">108</a>, <a href="#Page_109">109</a>, <a href="#Page_113">113</a>;</li> +<li><span style="margin-left: 1em;">his notion of quantity of electricity, <a href="#Page_173">173</a>;</span></li> +<li><span style="margin-left: 1em;">his torsion-balance, <a href="#Page_168">168</a>.</span></li> + +<li>Crew, Prof. Henry, <a href="#Page_317">317</a>, footnote.</li> + +<li>Criticism, Socrates the father of scientific, <a href="#Page_1">1</a>, <a href="#Page_16">16</a>.</li> + +<li><i>Critique of Pure Reason</i>, Kant's, <a href="#Page_188">188</a>.</li> + +<li>Crucible, derivation of the word, <a href="#Page_49">49</a>, footnote.</li> + +<li>Crustacea, auditory filaments of, <a href="#Page_29">29</a>, <a href="#Page_272">272</a>, <a href="#Page_302">302</a>.</li> + +<li>Cube of oil, <a href="#Page_5">5</a>.</li> + +<li>Culture, ancient and modern, <a href="#Page_344">344</a>.</li> + +<li>Currents, chemical, <a href="#Page_118">118</a>;</li> +<li><span style="margin-left: 1em;">electrical, <a href="#Page_118">118</a>;</span></li> +<li><span style="margin-left: 1em;">galvanic, <a href="#Page_132">132</a>;</span></li> +<li><span style="margin-left: 1em;">measurement of electrical, <a href="#Page_135">135</a>-<a href="#Page_136">136</a>;</span></li> +<li><span style="margin-left: 1em;">of heat, <a href="#Page_244">244</a>, <a href="#Page_249">249</a>-<a href="#Page_250">250</a>;</span></li> +<li><span style="margin-left: 1em;">strength of, <a href="#Page_250">250</a>.</span></li> + +<li>Curtius, <a href="#Page_356">356</a>.</li> + +<li>Curved lines, their asymmetry, <a href="#Page_98">98</a>.</li> + +<li>Curves, how their laws are investigated, <a href="#Page_206">206</a>.</li> + +<li>Cycles, reversible, Clausius on, <a href="#Page_176">176</a>.</li> + +<li>Cyclical processes, closed, <a href="#Page_175">175</a>.</li> + +<li>Cyclops, <a href="#Page_67">67</a>.</li> + +<li>Cyclostat, <a href="#Page_298">298</a>.</li> + +<li>Cylinder, of oil, <a href="#Page_6">6</a>;</li> +<li><span style="margin-left: 1em;">mass of gas enclosed in a, <a href="#Page_179">179</a>.</span></li> + +</ul> + +<ul class="IX"><li>D'Alembert, on the causes of harmony, <a href="#Page_34">34</a>;</li> +<li><span style="margin-left: 1em;">his principle, <a href="#Page_142">142</a>, <a href="#Page_149">149</a>, <a href="#Page_154">154</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_234">234</a>, <a href="#Page_279">279</a>.</span></li> + +<li>Danish schools, <a href="#Page_338">338</a>, footnote.</li> + +<li>Darwin, his study of organic nature, <a href="#Page_215">215</a> et seq.;</li> +<li><span style="margin-left: 1em;">his methods of research, <a href="#Page_216">216</a>.</span></li> + +<li>Deaf and dumb, not subject to giddiness, <a href="#Page_299">299</a>.</li> + +<li>Deaf person, with a piano, analyses sounds, <a href="#Page_27">27</a>.</li> + +<li>Death and life, <a href="#Page_186">186</a>.</li> + +<li>Definition, compendious, <a href="#Page_197">197</a>.</li> + +<li>Deiters, <a href="#Page_19">19</a>.</li> + +<li>Delage, <a href="#Page_298">298</a>, <a href="#Page_301">301</a>, <a href="#Page_302">302</a>.</li> + +<li>Democritus, his mechanical conception of the world, <a href="#Page_155">155</a>, <a href="#Page_187">187</a>.</li> + +<li>Demonstration, character of, <a href="#Page_362">362</a>.</li> + +<li>Deportment of the energies, conformity in the, <a href="#Page_171">171</a>-<a href="#Page_175">175</a>.</li> + +<li>Derivation, laws only methods of, <a href="#Page_256">256</a>.</li> + +<li>Descent, Galileo's laws of, <a href="#Page_193">193</a>;</li> +<li><span style="margin-left: 1em;">generally, <a href="#Page_143">143</a> et seq., <a href="#Page_204">204</a>, <a href="#Page_215">215</a>.</span></li> + +<li>Description, <a href="#Page_108">108</a>, <a href="#Page_191">191</a>, <a href="#Page_236">236</a>, <a href="#Page_237">237</a>;</li> +<li><span style="margin-left: 1em;">a condition of scientific knowledge, <a href="#Page_193">193</a>;</span></li> +<li><span style="margin-left: 1em;">direct and indirect, <a href="#Page_240">240</a>;</span></li> +<li><span style="margin-left: 1em;">in physics, <a href="#Page_197">197</a>, <a href="#Page_199">199</a>.</span></li> + +<li>Descriptive sciences, their resemblance to the abstract, <a href="#Page_248">248</a>.</li> + +<li>Determinants, <a href="#Page_195">195</a>.</li> + +<li>Diderot, <a href="#Page_234">234</a>.</li> + +<li>Dielectric constant, the, <a href="#Page_117">117</a>.</li> + +<li>Difference-engine, the, <a href="#Page_196">196</a>.</li> + +<li>Differential coefficients, their relation to symmetry, <a href="#Page_98">98</a>.</li> + +<li>Differential laws, <a href="#Page_204">204</a>.</li> + +<li>Differential method, for detecting optical imperfections, <a href="#Page_317">317</a>.</li> + +<li>Diffraction, <a href="#Page_91">91</a>, <a href="#Page_194">194</a>.</li> + +<li>Diffusion, Fick's theory of, <a href="#Page_249">249</a>.</li> + +<li>Discharge of Leyden jars, <a href="#Page_114">114</a> et seq.</li> + +<li>Discoveries, the gist of, <a href="#Page_270">270</a>, <a href="#Page_375">375</a>.</li> + +<li>Discovery and invention, distinction between, <a href="#Page_269">269</a>.</li> + +<li>Dissonance, explanation of, <a href="#Page_42">42</a>;</li> +<li><span style="margin-left: 1em;">definition of, <a href="#Page_33">33</a>, <a href="#Page_44">44</a>. See <i>Consonance</i>.</span></li> + +<li>Distances, estimation of, by the eye, <a href="#Page_68">68</a> et seq.</li> + +<li>Dogs, like tuning-forks, <a href="#Page_23">23</a>;</li> +<li><span class="pagenum"><a name="Page_397" id="Page_397">[Pg 397]</a></span><span style="margin-left: 1em;">their mentality, <a href="#Page_190">190</a>.</span></li> + +<li>Domenech, Abbé, <a href="#Page_92">92</a>.</li> + +<li>Dramatic element in science, <a href="#Page_243">243</a>.</li> + +<li>Drop of water, on a greased plate, <a href="#Page_8">8</a>;</li> +<li><span style="margin-left: 1em;">on the end of a stick, <a href="#Page_8">8</a>;</span></li> +<li><span style="margin-left: 1em;">in free descent, <a href="#Page_8">8</a>.</span></li> + +<li>Dubois, <a href="#Page_218">218</a>.</li> + +<li>Dubois-Reymond, <a href="#Page_370">370</a>, footnote.</li> + +<li>Dufay, <a href="#Page_271">271</a>.</li> + +<li>Dynamics, foundations of, <a href="#Page_153">153</a> et seq.</li> + +</ul> + +<ul class="IX"><li>Ear, researches in the theory of, <a href="#Page_17">17</a> et seq.;</li> +<li><span style="margin-left: 1em;">diagram of, <a href="#Page_18">18</a>;</span></li> +<li><span style="margin-left: 1em;">its analysis of sounds, <a href="#Page_20">20</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">a puzzle-lock, <a href="#Page_28">28</a>;</span></li> +<li><span style="margin-left: 1em;">reflected in a mirror, <a href="#Page_93">93</a>;</span></li> +<li><span style="margin-left: 1em;">no symmetry in its sensation, <a href="#Page_103">103</a>.</span></li> + +<li>Earth, its oblateness not due to its original fluid condition, <a href="#Page_2">2</a>;</li> +<li><span style="margin-left: 1em;">rotation of, <a href="#Page_204">204</a>;</span></li> +<li><span style="margin-left: 1em;">internal disturbances of, <a href="#Page_285">285</a>.</span></li> + +<li>Economical, nature of physical inquiry, <a href="#Page_186">186</a>;</li> +<li><span style="margin-left: 1em;">procedure of the human mind, <a href="#Page_186">186</a>;</span></li> +<li><span style="margin-left: 1em;">order of physics, <a href="#Page_197">197</a>;</span></li> +<li><span style="margin-left: 1em;">schematism of science, <a href="#Page_206">206</a>;</span></li> +<li><span style="margin-left: 1em;">tools of science, <a href="#Page_207">207</a>;</span></li> +<li><span style="margin-left: 1em;">coefficient of dynamos, <a href="#Page_133">133</a>.</span></li> + +<li>Economy, of the actions of nature, <a href="#Page_15">15</a>;</li> +<li><span style="margin-left: 1em;">the purpose of science, <a href="#Page_16">16</a>;</span></li> +<li><span style="margin-left: 1em;">of language, <a href="#Page_191">191</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">of the industrial arts, <a href="#Page_192">192</a>;</span></li> +<li><span style="margin-left: 1em;">of mathematics, <a href="#Page_195">195</a>-<a href="#Page_196">196</a>;</span></li> +<li><span style="margin-left: 1em;">of machinery, <a href="#Page_196">196</a>;</span></li> +<li><span style="margin-left: 1em;">of self-preservation, our first knowledge derived from, <a href="#Page_197">197</a>;</span></li> +<li><span style="margin-left: 1em;">generally, <a href="#Page_186">186</a> et seq., <a href="#Page_269">269</a>.</span></li> + +<li>Education, higher, <a href="#Page_86">86</a>;</li> +<li><span style="margin-left: 1em;">liberal, <a href="#Page_341">341</a> et seq., <a href="#Page_371">371</a>.</span></li> + +<li>Efflux, liquid, <a href="#Page_150">150</a>.</li> + +<li>Ego, its nature, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li> + +<li>Egypt, <a href="#Page_234">234</a>.</li> + +<li>Egyptians, art of, <a href="#Page_78">78</a> et seq., <a href="#Page_201">201</a>.</li> + +<li>Eighteenth century, the scientific achievements of, <a href="#Page_187">187</a>, <a href="#Page_188">188</a>.</li> + +<li>Eleatics, on motion, <a href="#Page_158">158</a>.</li> + +<li>Electrical, attraction and repulsion, <a href="#Page_109">109</a> et seq., <a href="#Page_168">168</a>;</li> +<li><span style="margin-left: 1em;">capacity, <a href="#Page_116">116</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">force, <a href="#Page_110">110</a>, <a href="#Page_119">119</a>, <a href="#Page_168">168</a>;</span></li> +<li><span style="margin-left: 1em;">spark, <a href="#Page_117">117</a>, <a href="#Page_127">127</a>, <a href="#Page_132">132</a>, <a href="#Page_133">133</a>, <a href="#Page_190">190</a>;</span></li> +<li><span style="margin-left: 1em;">energy, measurement of, <a href="#Page_128">128</a> et seq., <a href="#Page_169">169</a>;</span></li> +<li><span style="margin-left: 1em;">currents, conceptions of, <a href="#Page_118">118</a>, <a href="#Page_132">132</a>, <a href="#Page_135">135</a>-<a href="#Page_136">136</a>, <a href="#Page_226">226</a>-<a href="#Page_227">227</a>, <a href="#Page_249">249</a>, <a href="#Page_250">250</a>;</span></li> +<li><span style="margin-left: 1em;">fluids, <a href="#Page_112">112</a> et seq., <a href="#Page_228">228</a>;</span></li> +<li><span style="margin-left: 1em;">pendulums, <a href="#Page_110">110</a>;</span></li> +<li><span style="margin-left: 1em;">levels, <a href="#Page_173">173</a>;</span></li> +<li><span style="margin-left: 1em;">potential, <a href="#Page_121">121</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">quantity, <a href="#Page_111">111</a>, <a href="#Page_118">118</a>, <a href="#Page_119">119</a>.</span></li> + +<li>Electricity, as a substance and as a motion, <a href="#Page_170">170</a>;</li> +<li><span style="margin-left: 1em;">difference between the conceptions of heat and, <a href="#Page_168">168</a> et seq.,</span></li> +<li><span style="margin-left: 1em;">rôle of work in, <a href="#Page_120">120</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">galvanic, <a href="#Page_134">134</a>.</span></li> +<li><span style="margin-left: 1em;">See <i>Electrical</i>.</span></li> + +<li>Electrometer, W. Thomson's absolute, <a href="#Page_127">127</a>, footnote.</li> + +<li>Electrometers, <a href="#Page_122">122</a>, <a href="#Page_127">127</a>.</li> + +<li>Electrostatic unit, <a href="#Page_111">111</a>.</li> + +<li>Electrostatics, concepts of, <a href="#Page_107">107</a> et seq.</li> + +<li>Elements, interdependence of the sensuous, <a href="#Page_179">179</a>;</li> +<li><span style="margin-left: 1em;">of bodies, <a href="#Page_202">202</a>;</span></li> +<li><span style="margin-left: 1em;">of phenomena, equations between, <a href="#Page_205">205</a>;</span></li> +<li><span style="margin-left: 1em;">of sensations, <a href="#Page_200">200</a>;</span></li> +<li><span style="margin-left: 1em;">used instead of sensations, <a href="#Page_208">208</a>-<a href="#Page_209">209</a>.</span></li> + +<li>Ellipse, equation of, <a href="#Page_205">205</a>;</li> +<li><span style="margin-left: 1em;">the word, <a href="#Page_342">342</a>.</span></li> + +<li>Embryology, possible future state of, <a href="#Page_257">257</a>.</li> + +<li>Energies, conformity in the deportment of, <a href="#Page_171">171</a>-<a href="#Page_175">175</a>;</li> +<li><span style="margin-left: 1em;">differences of, <a href="#Page_175">175</a>.</span></li> + +<li>Energy, a metrical notion, <a href="#Page_178">178</a>;</li> +<li><span style="margin-left: 1em;">conservation of, <a href="#Page_137">137</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">defined, <a href="#Page_139">139</a>;</span></li> +<li><span style="margin-left: 1em;">metaphysical establishment of the doctrine of, <a href="#Page_183">183</a>;</span></li> +<li><span style="margin-left: 1em;">kinetic, <a href="#Page_177">177</a>;</span></li> +<li><span style="margin-left: 1em;">potential, <a href="#Page_128">128</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">substantial conception of, <a href="#Page_164">164</a>, <a href="#Page_185">185</a>, <a href="#Page_244">244</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">conservation of, in electrical phenomena, <a href="#Page_131">131</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">limits of principle of, <a href="#Page_175">175</a>;</span></li> +<li><span style="margin-left: 1em;">principle of, in physics, <a href="#Page_160">160</a>-<a href="#Page_166">166</a>;</span></li> +<li><span style="margin-left: 1em;">sources of principle of, <a href="#Page_179">179</a>, <a href="#Page_181">181</a>;</span></li> +<li><span style="margin-left: 1em;">thermal, <a href="#Page_177">177</a>;</span></li> +<li><span style="margin-left: 1em;">Thomas Young on, <a href="#Page_173">173</a>.</span></li> + +<li>Energy-value of heat, <a href="#Page_178">178</a>, footnote.</li> + +<li>Enlightenment, the, <a href="#Page_188">188</a>.</li> + +<li>Entropy, a metrical notion, <a href="#Page_178">178</a>.</li> + +<li>Environment, stability of our, <a href="#Page_206">206</a>.</li> + +<li>Equations for obtaining facts, <a href="#Page_180">180</a>;</li> +<li><span style="margin-left: 1em;">between the elements of phenomena, <a href="#Page_205">205</a>.</span></li> + +<li>Equilibrium, conditions of, in simple machines, <a href="#Page_151">151</a>;</li> +<li><span style="margin-left: 1em;">figures of liquid, <a href="#Page_4">4</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">general condition of, <a href="#Page_15">15</a>;</span></li> +<li><span style="margin-left: 1em;">in the State, <a href="#Page_15">15</a>.</span></li> + +<li>Etymology, the word, misused for entomology, <a href="#Page_316">316</a>.</li> + +<li>Euclid, on consonance and dissonance, <a href="#Page_33">33</a>;</li> +<li><span style="margin-left: 1em;">his geometry, <a href="#Page_364">364</a>.</span></li> + +<li><span class="pagenum"><a name="Page_398" id="Page_398">[Pg 398]</a></span>Euler, on the causes of harmony, <a href="#Page_34">34</a>;</li> +<li><span style="margin-left: 1em;">impression of the mathematical processes on, <a href="#Page_196">196</a>;</span></li> +<li><span style="margin-left: 1em;">on the vibrations of strings, <a href="#Page_249">249</a>, <a href="#Page_285">285</a>, <a href="#Page_376">376</a>.</span></li> + +<li>Euler and Hermann's principle, <a href="#Page_149">149</a>.</li> + +<li>Euthyphron, questioned by Socrates, <a href="#Page_1">1</a>.</li> + +<li>Evolute, the word, <a href="#Page_342">342</a>.</li> + +<li>Evolution, theory of, as applied to ideas, <a href="#Page_216">216</a> et seq.</li> + +<li>Ewald, <a href="#Page_298">298</a>, <a href="#Page_304">304</a>.</li> + +<li>Excluded perpetual motion, logical root of the principle of, <a href="#Page_182">182</a>.</li> + +<li>Exner, S., <a href="#Page_302">302</a>, <a href="#Page_305">305</a>.</li> + +<li>Experience, communication of, <a href="#Page_191">191</a>;</li> +<li><span style="margin-left: 1em;">our ready, <a href="#Page_199">199</a>;</span></li> +<li><span style="margin-left: 1em;">the principle of energy derived from, <a href="#Page_179">179</a>;</span></li> +<li><span style="margin-left: 1em;">the wellspring of all knowledge of nature, <a href="#Page_181">181</a>;</span></li> +<li><span style="margin-left: 1em;">incongruence between thought and, <a href="#Page_206">206</a>.</span></li> + +<li>Experimental research, function of, <a href="#Page_181">181</a>.</li> + +<li>Explanation, nature of, <a href="#Page_194">194</a>, <a href="#Page_237">237</a>, <a href="#Page_362">362</a>.</li> + +<li>Eye, cannot analyse colors, <a href="#Page_20">20</a>;</li> +<li><span style="margin-left: 1em;">researches in the theory of the, <a href="#Page_18">18</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">loss of, as affecting vision, <a href="#Page_98">98</a>.</span></li> + +<li>Eyes, purpose of, <a href="#Page_66">66</a> et seq.;</li> +<li><span style="margin-left: 1em;">their structure symmetrical not identical, <a href="#Page_96">96</a>.</span></li> + +</ul> + +<ul class="IX"><li>Face, human, inverted, <a href="#Page_95">95</a>.</li> + +<li>Facts and ideas, necessary to science, <a href="#Page_231">231</a>.</li> + +<li>Facts, description of, <a href="#Page_108">108</a>;</li> +<li><span style="margin-left: 1em;">agreement of, <a href="#Page_180">180</a>;</span></li> +<li><span style="margin-left: 1em;">relations of, <a href="#Page_180">180</a>;</span></li> +<li><span style="margin-left: 1em;">how represented, <a href="#Page_206">206</a>;</span></li> +<li><span style="margin-left: 1em;">reflected in imagination, <a href="#Page_220">220</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">the result of constructions, <a href="#Page_253">253</a>;</span></li> +<li><span style="margin-left: 1em;">a continuum of, <a href="#Page_256">256</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">equations for obtaining, <a href="#Page_180">180</a>.</span></li> + +<li>Falling bodies, <a href="#Page_204">204</a>, <a href="#Page_215">215</a>;</li> +<li><span style="margin-left: 1em;">Galileo on the law of, <a href="#Page_143">143</a> et seq., <a href="#Page_284">284</a>.</span></li> + +<li>Falling, cats, <a href="#Page_303">303</a>, footnote.</li> + +<li>Falstaff, <a href="#Page_309">309</a>.</li> + +<li>Familiar intermediate links of thought, <a href="#Page_198">198</a>.</li> + +<li>Faraday, <a href="#Page_191">191</a>, <a href="#Page_217">217</a>, <a href="#Page_237">237</a>;</li> +<li><span style="margin-left: 1em;">his conception of electricity, <a href="#Page_114">114</a>, <a href="#Page_271">271</a>.</span></li> + +<li>Fechner, theory of Corti's fibres, <a href="#Page_19">19</a> et seq.</li> + +<li>Feeling, cannot be explained by motions of atoms, <a href="#Page_208">208</a> et seq.</li> + +<li>Fetishism, <a href="#Page_186">186</a>, <a href="#Page_243">243</a>, <a href="#Page_254">254</a>;</li> +<li><span style="margin-left: 1em;">in our physical concepts, <a href="#Page_187">187</a>.</span></li> + +<li>Fibres of Corti, <a href="#Page_17">17</a> et seq.</li> + +<li>Fick, his theory of diffusion, <a href="#Page_249">249</a>.</li> + +<li>Figures, symmetry of, <a href="#Page_92">92</a> et seq.</li> + +<li>Figures of liquid equilibrium, <a href="#Page_4">4</a> et seq.</li> + +<li>Fire, use of, <a href="#Page_264">264</a>.</li> + +<li>Fishes, <a href="#Page_306">306</a>.</li> + +<li>Fixed note, determining of a, <a href="#Page_377">377</a>.</li> + +<li>Fizeau, his determination of the velocity of light, <a href="#Page_55">55</a> et seq.</li> + +<li>Flats, reversed into sharps, <a href="#Page_101">101</a>.</li> + +<li>Flouren's experiments, <a href="#Page_272">272</a>, <a href="#Page_290">290</a>.</li> + +<li>Flower-girl, the baskets of a, <a href="#Page_95">95</a>.</li> + +<li>Fluids, electrical, <a href="#Page_112">112</a> et seq.</li> + +<li>Force, electric, <a href="#Page_110">110</a>, <a href="#Page_119">119</a>, <a href="#Page_168">168</a>;</li> +<li><span style="margin-left: 1em;">unit of <a href="#Page_111">111</a>;</span></li> +<li><span style="margin-left: 1em;">living, <a href="#Page_137">137</a>, <a href="#Page_149">149</a>, <a href="#Page_184">184</a>;</span></li> +<li><span style="margin-left: 1em;">generally <a href="#Page_253">253</a>.</span></li> +<li><span style="margin-left: 1em;">See the related headings.</span></li> + +<li>Forces, will compared to, <a href="#Page_254">254</a>.</li> + +<li>Foreseeing events, <a href="#Page_220">220</a> et seq.</li> + +<li>Formal conceptions, rôle of, <a href="#Page_183">183</a>.</li> + +<li>Formal need of a clear view of facts, <a href="#Page_183">183</a>, <a href="#Page_246">246</a>;</li> +<li><span style="margin-left: 1em;">how far it corresponds to nature, <a href="#Page_184">184</a>.</span></li> + +<li>Formative forces of liquids, <a href="#Page_4">4</a>.</li> + +<li>Forms of liquids, <a href="#Page_3">3</a> et seq.</li> + +<li>Forward movement, sensation of, <a href="#Page_300">300</a>.</li> + +<li>Forwards, prophesying, <a href="#Page_253">253</a>.</li> + +<li>Foucault, <a href="#Page_57">57</a>, <a href="#Page_70">70</a>, <a href="#Page_296">296</a>.</li> + +<li>Foucault and Toepler, method of, for detecting optical faults, <a href="#Page_313">313</a> et seq., <a href="#Page_320">320</a>.</li> + +<li>Foundation of scientific thought, primitive acts of knowledge, the, <a href="#Page_190">190</a>.</li> + +<li>Fourier, on processes of heat, <a href="#Page_249">249</a>, <a href="#Page_278">278</a>.</li> + +<li>Fox, a, <a href="#Page_234">234</a>.</li> + +<li>Franklin's pane, <a href="#Page_116">116</a>.</li> + +<li>Frary, <a href="#Page_338">338</a>, footnote.</li> + +<li>Fraunhofer, <a href="#Page_271">271</a>.</li> + +<li>Freezing-point, lowered by pressure, <a href="#Page_162">162</a>.</li> + +<li>Fresnel, <a href="#Page_271">271</a>.</li> + +<li>Fritsch, <a href="#Page_321">321</a>.</li> + +<li>Frogs, larvæ of, not subject to vertigo, <a href="#Page_298">298</a>.</li> + +<li>Froude, <a href="#Page_333">333</a>.</li> + +<li>Frustra, misuse of the word, <a href="#Page_345">345</a>.</li> + +<li>Future, science of the, <a href="#Page_213">213</a>.</li> + +</ul> + +<ul class="IX"><li>Galileo, on the motion of pendulums, <a href="#Page_21">21</a>;</li> +<li><span style="margin-left: 1em;">his attempted measurement of the velocity of light, <a href="#Page_50">50</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">his exclusion of a perpetual motion, <a href="#Page_143">143</a>;</span></li> +<li><span style="margin-left: 1em;">on velocities acquired in free descent, <a href="#Page_143">143</a>-<a href="#Page_147">147</a>;</span></li> +<li><span style="margin-left: 1em;">on the law of inertia, <a href="#Page_146">146</a>-<a href="#Page_147">147</a>;</span></li> +<li><span style="margin-left: 1em;">on virtual velocities, <a href="#Page_150">150</a>;</span></li> +<li><span style="margin-left: 1em;">on work, <a href="#Page_172">172</a>;</span></li> +<li><span style="margin-left: 1em;">his laws of descent, <a href="#Page_193">193</a>;</span></li> +<li><span style="margin-left: 1em;">on falling bodies, <a href="#Page_225">225</a>;</span></li> +<li><span style="margin-left: 1em;">great results of his study of nature, <a href="#Page_214">214</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">his rude scientific implements, <a href="#Page_215">215</a>;</span></li> +<li><span style="margin-left: 1em;">selections from his works for use in instruction, <a href="#Page_368">368</a>;</span></li> +<li><span class="pagenum"><a name="Page_399" id="Page_399">[Pg 399]</a></span><span style="margin-left: 1em;">also <a href="#Page_105">105</a>, <a href="#Page_182">182</a>, <a href="#Page_187">187</a>, <a href="#Page_237">237</a>, <a href="#Page_272">272</a>, <a href="#Page_274">274</a>, <a href="#Page_283">283</a>.</span></li> + +<li>Galle, observes the planet Neptune, <a href="#Page_29">29</a>.</li> + +<li>Galvanic, electricity, <a href="#Page_134">134</a>;</li> +<li><span style="margin-left: 1em;">current, <a href="#Page_132">132</a>;</span></li> +<li><span style="margin-left: 1em;">dizziness, <a href="#Page_291">291</a>;</span></li> +<li><span style="margin-left: 1em;">vertigo, <a href="#Page_298">298</a>.</span></li> + +<li>Galvanoscope, <a href="#Page_135">135</a>.</li> + +<li>Galvanotropism, <a href="#Page_291">291</a>.</li> + +<li>Garda, Lake, <a href="#Page_239">239</a>.</li> + +<li>Gas, the word, <a href="#Page_264">264</a>;</li> +<li><span style="margin-left: 1em;">mass of, enclosed in a cylinder, <a href="#Page_179">179</a>.</span></li> + +<li>Gases, tensions of, for scales of temperature, <a href="#Page_174">174</a>.</li> + +<li>Gauss, on the foundations of dynamics, <a href="#Page_154">154</a>;</li> +<li><span style="margin-left: 1em;">his principle, <a href="#Page_154">154</a>;</span></li> +<li><span style="margin-left: 1em;">also, <a href="#Page_108">108</a>, <a href="#Page_274">274</a>.</span></li> + +<li>Genius, <a href="#Page_279">279</a>, <a href="#Page_280">280</a>.</li> + +<li>Geography, comparison in, <a href="#Page_239">239</a>.</li> + +<li>Geometers, in our eyes, <a href="#Page_72">72</a>.</li> + +<li>Geotropism, <a href="#Page_289">289</a>.</li> + +<li>German schools and gymnasiums, <a href="#Page_372">372</a>, <a href="#Page_373">373</a>, <a href="#Page_338">338</a>, footnote.</li> + +<li>Ghosts, photographic, <a href="#Page_73">73</a>.</li> + +<li>Glass, invisible in a mixture of the same refrangibility, <a href="#Page_312">312</a>;</li> +<li><span style="margin-left: 1em;">powdered, visible in a mixture of the same refrangibility, <a href="#Page_312">312</a>.</span></li> + +<li>Glove, in a mirror, <a href="#Page_93">93</a>.</li> + +<li>Goethe, quotations from, <a href="#Page_9">9</a>, <a href="#Page_31">31</a>, <a href="#Page_49">49</a>, <a href="#Page_88">88</a>;</li> +<li><span style="margin-left: 1em;">on the cause of harmony, <a href="#Page_35">35</a>.</span></li> + +<li>Goltz, <a href="#Page_282">282</a>, <a href="#Page_291">291</a>.</li> + +<li>Gossot, <a href="#Page_332">332</a>.</li> + +<li>Gothic cathedral, <a href="#Page_94">94</a>.</li> + +<li>Gravitation, discovery of, <a href="#Page_225">225</a> et seq.</li> + +<li>Gravity, how to get rid of the effects of, in liquids, <a href="#Page_4">4</a>;</li> +<li><span style="margin-left: 1em;">also <a href="#Page_228">228</a>.</span></li> + +<li>Gray, Elisha, his telautograph, <a href="#Page_26">26</a>.</li> + +<li>Greased plate, drop of water on a, <a href="#Page_8">8</a>.</li> + +<li>Great minds, idiosyncrasies of, <a href="#Page_247">247</a>.</li> + +<li>Greek language, scientific terms derivedfrom, <a href="#Page_342">342</a>-<a href="#Page_343">343</a>;</li> +<li><span style="margin-left: 1em;">common words derived from, <a href="#Page_343">343</a>, footnote;</span></li> +<li><span style="margin-left: 1em;">still necessary for some professions, <a href="#Page_346">346</a>;</span></li> +<li><span style="margin-left: 1em;">its literary wealth, <a href="#Page_347">347</a>-<a href="#Page_348">348</a>;</span></li> +<li><span style="margin-left: 1em;">narrowness and one-sidedness of its literature, <a href="#Page_348">348</a>-<a href="#Page_349">349</a>;</span></li> +<li><span style="margin-left: 1em;">its excessive study useless, <a href="#Page_349">349</a>-<a href="#Page_350">350</a>;</span></li> +<li><span style="margin-left: 1em;">its study sharpens the judgment, <a href="#Page_357">357</a>-<a href="#Page_358">358</a>;</span></li> +<li><span style="margin-left: 1em;">a knowledge of it not necessary to a liberal education, <a href="#Page_371">371</a>.</span></li> + +<li>Greeks, their provinciality and narrow-mindedness, <a href="#Page_349">349</a>;</li> +<li><span style="margin-left: 1em;">now only objects of historical research, <a href="#Page_350">350</a>.</span></li> + +<li>Griesinger, <a href="#Page_184">184</a>.</li> + +<li>Grimaldi, <a href="#Page_270">270</a>.</li> + +<li>Grimm, <a href="#Page_344">344</a>, footnote.</li> + +<li>Grunting fishes, <a href="#Page_306">306</a>.</li> + +</ul> + +<ul class="IX"><li>Habitudes of thought, <a href="#Page_199">199</a>, <a href="#Page_224">224</a>, <a href="#Page_227">227</a>, <a href="#Page_232">232</a>.</li> + +<li>Haeckel, <a href="#Page_222">222</a>, <a href="#Page_235">235</a>.</li> + +<li>Hamilton, deduction of the conical refraction of light, <a href="#Page_29">29</a>.</li> + +<li>Hankel, <a href="#Page_364">364</a>.</li> + +<li>Harmonics, <a href="#Page_38">38</a>, <a href="#Page_40">40</a>.</li> + +<li>Harmony, on the causes of, <a href="#Page_32">32</a> et seq.;</li> +<li><span style="margin-left: 1em;">laws of the theory of, explained, <a href="#Page_30">30</a>;</span></li> +<li><span style="margin-left: 1em;">the investigation of the ancients concerning, <a href="#Page_32">32</a>;</span></li> +<li><span style="margin-left: 1em;">generally, <a href="#Page_103">103</a>.</span></li> +<li><span style="margin-left: 1em;">See <i>Consonance</i>.</span></li> + +<li>Harris, electrical balance of, <a href="#Page_127">127</a>, footnote.</li> + +<li>Hartwich, Judge, <a href="#Page_343">343</a>, <a href="#Page_353">353</a>, footnote.</li> + +<li>Hat, a high silk, <a href="#Page_24">24</a>.</li> + +<li>Hats, ladies', development of, <a href="#Page_64">64</a>.</li> + +<li>Head-wave of a projectile, <a href="#Page_323">323</a> et seq.</li> + +<li>Hearing and orientation, relation between, <a href="#Page_304">304</a> et seq.</li> + +<li>Heat, a material substance, <a href="#Page_177">177</a>;</li> +<li><span style="margin-left: 1em;">difference between the conceptions of electricity and, <a href="#Page_168">168</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">substantial conception of, <a href="#Page_243">243</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">Carnot on, <a href="#Page_156">156</a>, <a href="#Page_160">160</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">Fourier on the conduction of, <a href="#Page_249">249</a>;</span></li> +<li><span style="margin-left: 1em;">not necessarily a motion, <a href="#Page_167">167</a>, <a href="#Page_170">170</a>, <a href="#Page_171">171</a>;</span></li> +<li><span style="margin-left: 1em;">mechanical equivalent of, <a href="#Page_164">164</a>, <a href="#Page_167">167</a>;</span></li> +<li><span style="margin-left: 1em;">of liquefaction, <a href="#Page_178">178</a>;</span></li> +<li><span style="margin-left: 1em;">quantity of, <a href="#Page_166">166</a>;</span></li> +<li><span style="margin-left: 1em;">latent, <a href="#Page_167">167</a>, <a href="#Page_178">178</a>, <a href="#Page_244">244</a>;</span></li> +<li><span style="margin-left: 1em;">specific, <a href="#Page_166">166</a>, <a href="#Page_244">244</a>;</span></li> +<li><span style="margin-left: 1em;">the conceptions of, <a href="#Page_160">160</a>-<a href="#Page_171">171</a>;</span></li> +<li><span style="margin-left: 1em;">machine, <a href="#Page_160">160</a>;</span></li> +<li><span style="margin-left: 1em;">a measure of electrical energy, <a href="#Page_133">133</a> et seq.;</span></li> +<li><span class="pagenum"><a name="Page_400" id="Page_400">[Pg 400]</a></span><span style="margin-left: 1em;">mechanical theory of, <a href="#Page_133">133</a>;</span></li> +<li><span style="margin-left: 1em;">where does it come from? <a href="#Page_200">200</a>.</span></li> + +<li>Heavy bodies, sinking of, <a href="#Page_222">222</a>.</li> + +<li>Heights of ascent, <a href="#Page_143">143</a>-<a href="#Page_151">151</a>.</li> + +<li>Helm, <a href="#Page_172">172</a>.</li> + +<li>Helmholtz, applies the principle of energy to electricity, <a href="#Page_184">184</a>;</li> +<li><span style="margin-left: 1em;">his telestereoscope, <a href="#Page_84">84</a>;</span></li> +<li><span style="margin-left: 1em;">his theory of Corti's fibres, <a href="#Page_19">19</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">on harmony, <a href="#Page_35">35</a>, <a href="#Page_99">99</a>;</span></li> +<li><span style="margin-left: 1em;">on the conservation of energy, <a href="#Page_165">165</a>, <a href="#Page_247">247</a>;</span></li> +<li><span style="margin-left: 1em;">his method of thought, <a href="#Page_247">247</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_138">138</a>, <a href="#Page_305">305</a>, <a href="#Page_307">307</a>, <a href="#Page_375">375</a>, <a href="#Page_383">383</a>.</span></li> + +<li>Hensen, V., on the auditory function of the filaments of Crustacea, <a href="#Page_29">29</a>, <a href="#Page_302">302</a>.</li> + +<li>Herbart, <a href="#Page_386">386</a> et seq.</li> + +<li>Herbartians, on motion, <a href="#Page_158">158</a>.</li> + +<li>Herculaneum, art in, <a href="#Page_80">80</a>.</li> + +<li>Heredity, in organic and inorganic matter, <a href="#Page_216">216</a>, footnote.</li> + +<li>Hering, on development, <a href="#Page_222">222</a>;</li> +<li><span style="margin-left: 1em;">on vision, <a href="#Page_210">210</a>.</span></li> + +<li>Hermann, E., on the economy of the industrial arts, <a href="#Page_192">192</a>.</li> + +<li>Hermann, L., <a href="#Page_291">291</a>.</li> + +<li>Herodotus, <a href="#Page_26">26</a>, <a href="#Page_234">234</a>, <a href="#Page_347">347</a>, <a href="#Page_350">350</a>.</li> + +<li>Hertz, his waves, <a href="#Page_242">242</a>;</li> +<li><span style="margin-left: 1em;">his use of the phrase "prophesy," <a href="#Page_253">253</a>.</span></li> + +<li>Herzen, <a href="#Page_361">361</a>, footnote.</li> + +<li>Hindu mathematicians, their beautiful problems, <a href="#Page_30">30</a>.</li> + +<li>Holtz's electric machine, <a href="#Page_132">132</a>.</li> + +<li>Horse, <a href="#Page_63">63</a>.</li> + +<li>Household, physics compared to a well-kept, <a href="#Page_197">197</a>.</li> + +<li>Housekeeping in science and civil life, <a href="#Page_198">198</a>.</li> + +<li>Hudson, the, <a href="#Page_94">94</a>.</li> + +<li>Human beings, puzzle-locks, <a href="#Page_27">27</a>.</li> + +<li>Human body, our knowledge of, <a href="#Page_90">90</a>.</li> + +<li>Human mind, must proceed economically, <a href="#Page_186">186</a>.</li> + +<li>Humanity, likened to a polyp-plant, <a href="#Page_235">235</a>.</li> + +<li>Huygens, his mechanical view of physics, <a href="#Page_155">155</a>;</li> +<li><span style="margin-left: 1em;">on the nature of light and heat, <a href="#Page_155">155</a>-<a href="#Page_156">156</a>;</span></li> +<li><span style="margin-left: 1em;">his principle of the heights of ascent, <a href="#Page_149">149</a>;</span></li> +<li><span style="margin-left: 1em;">on the law of inertia and the motion of a compound pendulum, <a href="#Page_147">147</a>-<a href="#Page_149">149</a>;</span></li> +<li><span style="margin-left: 1em;">on the impossible perpetual motion, <a href="#Page_147">147</a>-<a href="#Page_148">148</a>;</span></li> +<li><span style="margin-left: 1em;">on work, <a href="#Page_173">173</a>;</span></li> +<li><span style="margin-left: 1em;">selections from his works for use in instruction, <a href="#Page_368">368</a>;</span></li> +<li><span style="margin-left: 1em;">his view of light, <a href="#Page_227">227</a>-<a href="#Page_228">228</a>, <a href="#Page_262">262</a>.</span></li> + +<li>Huygens, optical method for detecting imperfections in optical glasses <a href="#Page_313">313</a>.</li> + +<li>Hydrogen balloon, <a href="#Page_199">199</a>.</li> + +<li>Hydrostatics, Stevinus's principle of, <a href="#Page_141">141</a>.</li> + +<li>Hypotheses, their rôle in explanation, <a href="#Page_228">228</a> et seq.</li> + +</ul> + +<ul class="IX"><li>Ichthyornis, <a href="#Page_257">257</a>.</li> + +<li>Ichthyosaurus, <a href="#Page_63">63</a>.</li> + +<li>Idea? what is a theoretical, <a href="#Page_241">241</a>.</li> + +<li>Idealism, <a href="#Page_209">209</a>.</li> + +<li>Ideas, a product of organic nature, <a href="#Page_217">217</a> et seq.;</li> +<li><span style="margin-left: 1em;">and facts, necessary to science, <a href="#Page_231">231</a>;</span></li> +<li><span style="margin-left: 1em;">not all of life, <a href="#Page_233">233</a>;</span></li> +<li><span style="margin-left: 1em;">their growth and importance, <a href="#Page_233">233</a>;</span></li> +<li><span style="margin-left: 1em;">a product of universal evolution, <a href="#Page_235">235</a>;</span></li> +<li><span style="margin-left: 1em;">the history of, <a href="#Page_227">227</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">in great minds, <a href="#Page_228">228</a>;</span></li> +<li><span style="margin-left: 1em;">the rich contents of, <a href="#Page_197">197</a>;</span></li> +<li><span style="margin-left: 1em;">their unsettled character in common life, their clarification in science, <a href="#Page_1">1</a>-<a href="#Page_2">2</a>.</span></li> + +<li>Ideography, the Chinese, <a href="#Page_192">192</a>.</li> + +<li>Imagery, mental, <a href="#Page_253">253</a>.</li> + +<li>Imagination, facts reflected in, <a href="#Page_220">220</a> et seq.</li> + +<li>Inclined plane, law of, <a href="#Page_140">140</a>-<a href="#Page_141">141</a>.</li> + +<li>Incomprehensible, the, <a href="#Page_186">186</a>.</li> + +<li>Indian, his modes of conception and interpretation, <a href="#Page_218">218</a> et seq.</li> + +<li>Individual, a thread on which pearls are strung, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li> + +<li>Industrial arts, economy of the, E. Hermann on, <a href="#Page_192">192</a>.</li> + +<li>Inertia, law of, <a href="#Page_143">143</a> et seq., <a href="#Page_146">146</a> et seq., <a href="#Page_216">216</a>, footnote, <a href="#Page_283">283</a> et seq.</li> + +<li>Innate concepts of the understanding, Kant on, <a href="#Page_199">199</a>.</li> + +<li>Innervation, visual, <a href="#Page_99">99</a>.</li> + +<li>Inquirer, his division of labor, <a href="#Page_105">105</a>;</li> +<li><span style="margin-left: 1em;">compared to a shoemaker, <a href="#Page_105">105</a>-<a href="#Page_106">106</a>;</span></li> +<li><span style="margin-left: 1em;">what constitutes the great, <a href="#Page_191">191</a>;</span></li> +<li><span style="margin-left: 1em;">the true, seeks the truth everywhere, <a href="#Page_63">63</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">the, compared to a wooer, <a href="#Page_45">45</a>.</span></li> + +<li>Instinctive knowledge, <a href="#Page_189">189</a>, <a href="#Page_190">190</a>.</li> + +<li><span class="pagenum"><a name="Page_401" id="Page_401">[Pg 401]</a></span>Instruction, aim of, the saving of experience, <a href="#Page_191">191</a>;</li> +<li><span style="margin-left: 1em;">in the classics, mathematics, and sciences, <a href="#Page_338">338</a>-<a href="#Page_374">374</a>;</span></li> +<li><span style="margin-left: 1em;">limitation of matter of, <a href="#Page_365">365</a> et seq.</span></li> + +<li>Insulators, <a href="#Page_130">130</a>.</li> + +<li>Integrals, <a href="#Page_195">195</a>.</li> + +<li>Intellectual development, conditions of, <a href="#Page_286">286</a> et seq.</li> + +<li>Intentions, acts of nature compared to, <a href="#Page_14">14</a>-<a href="#Page_15">15</a>.</li> + +<li>Interconnexion of nature, <a href="#Page_182">182</a>.</li> + +<li>Interdependence, of properties, <a href="#Page_361">361</a>;</li> +<li><span style="margin-left: 1em;">of the sensuous elements of the world, <a href="#Page_179">179</a>.</span></li> + +<li>Interference experiments with the head-wave of moving projectiles, <a href="#Page_327">327</a>-<a href="#Page_328">328</a>.</li> + +<li>International intercourse, established by Latin, <a href="#Page_341">341</a>.</li> + +<li>International measures, <a href="#Page_108">108</a>.</li> + +<li>Invention, discovery and, distinction between, <a href="#Page_269">269</a>.</li> + +<li>Inventions, requisites for the development of, <a href="#Page_266">266</a>, <a href="#Page_268">268</a> et seq.</li> + +<li>Iron-filings, <a href="#Page_220">220</a>, <a href="#Page_243">243</a>.</li> + +<li>Italian art, <a href="#Page_234">234</a>.</li> + +</ul> + +<ul class="IX"><li>Jacobi, C. G. J., on mathematics, <a href="#Page_280">280</a>.</li> + +<li>James, W., <a href="#Page_275">275</a>, <a href="#Page_299">299</a>.</li> + +<li>Java, <a href="#Page_163">163</a>.</li> + +<li>Jews and Christians, monotheism of the, <a href="#Page_187">187</a>.</li> + +<li>Jolly, Professor von, <a href="#Page_112">112</a>, <a href="#Page_274">274</a>.</li> + +<li>Joule, J. P., on the conservation of energy, <a href="#Page_163">163</a>-<a href="#Page_165">165</a>, <a href="#Page_167">167</a>, <a href="#Page_183">183</a>;</li> +<li><span style="margin-left: 1em;">his conception of energy, <a href="#Page_245">245</a>;</span></li> +<li><span style="margin-left: 1em;">his metaphysics, <a href="#Page_183">183</a>, <a href="#Page_246">246</a>;</span></li> +<li><span style="margin-left: 1em;">his method of thought, <a href="#Page_247">247</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_137">137</a>, <a href="#Page_138">138</a>.</span></li> + +<li>Journée, <a href="#Page_317">317</a>.</li> + +<li>Judge, criminal, the natural philosopher compared to a, <a href="#Page_48">48</a>.</li> + +<li>Judgment, essentially economy of thought, <a href="#Page_201">201</a>-<a href="#Page_202">202</a>;</li> +<li><span style="margin-left: 1em;">sharpened by languages and sciences, <a href="#Page_357">357</a>-<a href="#Page_358">358</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_232">232</a>-<a href="#Page_233">233</a>, <a href="#Page_238">238</a>.</span></li> + +<li>Juliet, Romeo and, <a href="#Page_87">87</a>.</li> + +<li>Jupiter, its satellites employed in the determination of the velocity of light, <a href="#Page_51">51</a> et seq.</li> + +<li>Jurisprudence, Latin and Greek unnecessary for the study of, <a href="#Page_346">346</a>, footnote.</li> + +</ul> + +<ul class="IX"><li>Kant, his hypothesis of the origin of the planetary system, <a href="#Page_5">5</a>;</li> +<li><span style="margin-left: 1em;">his <i>Critique of Pure Reason</i>, <a href="#Page_188">188</a>;</span></li> +<li><span style="margin-left: 1em;">on innate concepts of the understanding, <a href="#Page_199">199</a>;</span></li> +<li><span style="margin-left: 1em;">on time, <a href="#Page_204">204</a>;</span></li> +<li><span style="margin-left: 1em;">also footnote, <a href="#Page_93">93</a>.</span></li> + +<li>Kepler, <a href="#Page_187">187</a>, <a href="#Page_270">270</a>.</li> + +<li>Kinetic energy, <a href="#Page_177">177</a>.</li> + +<li>Kirchhoff, his epistemological ideas, <a href="#Page_257">257</a>-<a href="#Page_258">258</a>;</li> +<li><span style="margin-left: 1em;">his definition of mechanics, <a href="#Page_236">236</a>, <a href="#Page_258">258</a>, <a href="#Page_271">271</a>, <a href="#Page_273">273</a>.</span></li> + +<li>Knight, <a href="#Page_289">289</a>.</li> + +<li>Knowledge, a product of organic nature, <a href="#Page_217">217</a> et seq., <a href="#Page_235">235</a>;</li> +<li><span style="margin-left: 1em;">instinctive, <a href="#Page_190">190</a>;</span></li> +<li><span style="margin-left: 1em;">made possible by economy of thought, <a href="#Page_198">198</a>;</span></li> +<li><span style="margin-left: 1em;">our first, derived from the economy of self-preservation, <a href="#Page_197">197</a>;</span></li> +<li><span style="margin-left: 1em;">the theory of, <a href="#Page_203">203</a>;</span></li> +<li><span style="margin-left: 1em;">our primitive acts of the foundation of science, <a href="#Page_190">190</a>.</span></li> + +<li>Kocher, <a href="#Page_328">328</a>.</li> + +<li>Koenig, measurement of the velocity of sound, <a href="#Page_57">57</a> et seq.</li> + +<li>Kölliker, <a href="#Page_19">19</a>.</li> + +<li>Kopisch, <a href="#Page_61">61</a>.</li> + +<li>Kreidl, <a href="#Page_299">299</a>, <a href="#Page_302">302</a>, <a href="#Page_306">306</a>;</li> +<li><span style="margin-left: 1em;">his experiments, <a href="#Page_272">272</a>.</span></li> + +<li>Krupp, <a href="#Page_319">319</a>.</li> + +</ul> + +<ul class="IX"><li>Labels, the value of, <a href="#Page_201">201</a>.</li> + +<li>Labor, the accumulation of, the foundation of wealth and power, <a href="#Page_198">198</a>;</li> +<li><span style="margin-left: 1em;">inquirer's division of, <a href="#Page_105">105</a>, <a href="#Page_258">258</a>.</span></li> + +<li>Labyrinth, of the ear, <a href="#Page_18">18</a>, <a href="#Page_291">291</a>, <a href="#Page_305">305</a>.</li> + +<li>Lactantius, on the study of moral and physical science, <a href="#Page_89">89</a>.</li> + +<li>Ladder of our abstraction, the, <a href="#Page_208">208</a>.</li> + +<li>Ladies, their eyes, <a href="#Page_71">71</a>;</li> +<li><span style="margin-left: 1em;">like tuning-forks, <a href="#Page_23">23</a>-<a href="#Page_24">24</a>.</span></li> + +<li>Lagrange, on Huygens's principle, <a href="#Page_149">149</a>;</li> +<li><span style="margin-left: 1em;">on the principle of virtual velocities, <a href="#Page_150">150</a>-<a href="#Page_155">155</a>;</span></li> +<li><span style="margin-left: 1em;">character of the intellectual activity of a, <a href="#Page_195">195</a>, <a href="#Page_278">278</a>.</span></li> + +<li>Lake-dwellers, <a href="#Page_46">46</a>, <a href="#Page_271">271</a>.</li> + +<li>Lamp-shade, <a href="#Page_70">70</a>.</li> + +<li>Lane's unit jar, <a href="#Page_115">115</a>.</li> + +<li>Language, knowledge of the nature of, demanded by a liberal education, <a href="#Page_356">356</a>;</li> +<li><span style="margin-left: 1em;">relationship between, and thought, <a href="#Page_358">358</a>;</span></li> +<li><span style="margin-left: 1em;">communication by <a href="#Page_237">237</a>;</span></li> +<li><span style="margin-left: 1em;">economy of, <a href="#Page_191">191</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">human its character, <a href="#Page_238">238</a>;</span></li> +<li><span class="pagenum"><a name="Page_402" id="Page_402">[Pg 402]</a></span><span style="margin-left: 1em;">of animals, <a href="#Page_238">238</a>;</span></li> +<li><span style="margin-left: 1em;">instruction in, <a href="#Page_338">338</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">its methods, <a href="#Page_192">192</a>.</span></li> + +<li>Laplace, on the atoms of the brain, <a href="#Page_188">188</a>;</li> +<li><span style="margin-left: 1em;">on the scientific achievements of the eighteenth century, <a href="#Page_188">188</a>;</span></li> +<li><span style="margin-left: 1em;">his hypothesis of the origin of the planetary system, <a href="#Page_5">5</a>.</span></li> + +<li>Latent heat, <a href="#Page_167">167</a>, <a href="#Page_178">178</a>, <a href="#Page_244">244</a>.</li> + +<li>Latin city of Maupertuis, <a href="#Page_339">339</a>.</li> + +<li>Latin, instruction in, <a href="#Page_311">311</a> et seq.;</li> +<li><span style="margin-left: 1em;">introduced with the Christian Church, <a href="#Page_340">340</a>;</span></li> +<li><span style="margin-left: 1em;">the language of scholars, the medium of international intercourse, its power, utility, and final abandonment, <a href="#Page_341">341</a>-<a href="#Page_347">347</a>;</span></li> +<li><span style="margin-left: 1em;">the wealth of its literature, <a href="#Page_348">348</a>;</span></li> +<li><span style="margin-left: 1em;">the excessive study of, <a href="#Page_346">346</a>, <a href="#Page_349">349</a>, <a href="#Page_354">354</a>, <a href="#Page_355">355</a>;</span></li> +<li><span style="margin-left: 1em;">its power to sharpen the judgment, <a href="#Page_357">357</a>-<a href="#Page_358">358</a>.</span></li> + +<li>Lavish extravagance of science, <a href="#Page_189">189</a>.</li> + +<li>Law, a, defined, <a href="#Page_256">256</a>;</li> +<li><span style="margin-left: 1em;">a natural, not contained in the conformity of the energies, <a href="#Page_175">175</a>.</span></li> + +<li>Law-maker, motives of not always discernible, <a href="#Page_9">9</a>.</li> + +<li>Layard, <a href="#Page_79">79</a>.</li> + +<li>Learning, its nature, <a href="#Page_366">366</a> et seq.</li> + +<li>Least superficial area, principle of, accounted for by the mutual attractions of liquid particles, <a href="#Page_13">13</a>-<a href="#Page_14">14</a>;</li> +<li><span style="margin-left: 1em;">illustrated by a pulley arrangement, <a href="#Page_12">12</a>-<a href="#Page_13">13</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_9">9</a> et seq.</span></li> + +<li>Leibnitz, on harmony, <a href="#Page_33">33</a>;</li> +<li><span style="margin-left: 1em;">on international intercourse, <a href="#Page_342">342</a>, footnote.</span></li> + +<li>Lessing, quotation from, <a href="#Page_47">47</a>.</li> + +<li>Letters of the alphabet, their symmetry, <a href="#Page_94">94</a>, <a href="#Page_97">97</a>.</li> + +<li>Level heights of work, <a href="#Page_172">172</a>-<a href="#Page_174">174</a>.</li> + +<li>Lever, a, in action, <a href="#Page_222">222</a>.</li> + +<li>Leverrier, prediction of the planet Neptune, <a href="#Page_29">29</a>.</li> + +<li>Leyden jar, <a href="#Page_114">114</a>.</li> + +<li>Liberal education, a, <a href="#Page_341">341</a> et seq., <a href="#Page_359">359</a>, <a href="#Page_371">371</a>.</li> + +<li>Libraries, thoughts stored up in, <a href="#Page_237">237</a>.</li> + +<li>Lichtenberg, on instruction, <a href="#Page_276">276</a>, <a href="#Page_370">370</a>.</li> + +<li>Licius, a Chinese philosopher, <a href="#Page_213">213</a>.</li> + +<li>Liebig, <a href="#Page_163">163</a>, <a href="#Page_278">278</a>.</li> + +<li>Life and death, <a href="#Page_186">186</a>.</li> + +<li>Light, history of as elucidating how theories obstruct research, <a href="#Page_242">242</a>;</li> +<li><span style="margin-left: 1em;">Huygens's and Newton's views of, <a href="#Page_227">227</a>-<a href="#Page_228">228</a>;</span></li> +<li><span style="margin-left: 1em;">its different conceptions, <a href="#Page_226">226</a>;</span></li> +<li><span style="margin-left: 1em;">rectilinear propagation of, <a href="#Page_194">194</a>;</span></li> +<li><span style="margin-left: 1em;">rôle of, in vision, <a href="#Page_81">81</a>;</span></li> +<li><span style="margin-left: 1em;">spatial and temporal periodicity of, explains optical phenomena, <a href="#Page_194">194</a>;</span></li> +<li><span style="margin-left: 1em;">numerical velocity of, <a href="#Page_58">58</a>;</span></li> +<li><span style="margin-left: 1em;">where does it go to? <a href="#Page_199">199</a>;</span></li> +<li><span style="margin-left: 1em;">generally, <a href="#Page_48">48</a> et seq.</span></li> + +<li>Like effects in like circumstances, <a href="#Page_199">199</a>.</li> + +<li>Likeness, <a href="#Page_388">388</a>, <a href="#Page_391">391</a>.</li> + +<li>Lilliput, <a href="#Page_84">84</a>.</li> + +<li>Lines, straight, their symmetry, <a href="#Page_98">98</a>;</li> +<li><span style="margin-left: 1em;">curved, their asymmetry, <a href="#Page_98">98</a>;</span></li> +<li><span style="margin-left: 1em;">of force, <a href="#Page_249">249</a>.</span></li> + +<li>Links of thought, intermediate, <a href="#Page_198">198</a>.</li> + +<li>Liquefaction, latent heat of, <a href="#Page_178">178</a>.</li> + +<li>Liquid, efflux, law of, <a href="#Page_150">150</a>;</li> +<li><span style="margin-left: 1em;">equilibrium, figures of, <a href="#Page_4">4</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">the latter produced in open air, <a href="#Page_7">7</a>-<a href="#Page_8">8</a>;</span></li> +<li><span style="margin-left: 1em;">their beauty and multiplicity of form, <a href="#Page_7">7</a>, <a href="#Page_8">8</a>;</span></li> +<li><span style="margin-left: 1em;">made permanent by melted colophonium, <a href="#Page_7">7</a>.</span></li> + +<li>Liquids, forms of, <a href="#Page_1">1</a>-<a href="#Page_16">16</a>;</li> +<li><span style="margin-left: 1em;">difference between, and solids, <a href="#Page_2">2</a>;</span></li> +<li><span style="margin-left: 1em;">their mobility and adaptiveness of form, <a href="#Page_3">3</a>;</span></li> +<li><span style="margin-left: 1em;">the courtiers <i>par excellence</i> of the natural bodies, <a href="#Page_3">3</a>;</span></li> +<li><span style="margin-left: 1em;">possess under certain circumstances forms of their own, <a href="#Page_3">3</a>.</span></li> + +<li>Living force, <a href="#Page_137">137</a>, <a href="#Page_184">184</a>;</li> +<li><span style="margin-left: 1em;">law of the conservation of, <a href="#Page_149">149</a>.</span></li> + +<li>Lloyd, observation of the conical refraction of light, <a href="#Page_29">29</a>.</li> + +<li>Lobster, of Lake Mohrin, the, <a href="#Page_61">61</a>.</li> + +<li>Localisation, cerebral, <a href="#Page_210">210</a>.</li> + +<li>Locke, on language and thought, <a href="#Page_358">358</a>.</li> + +<li>Locomotive, steam in the boiler of, <a href="#Page_219">219</a>.</li> + +<li>Loeb, J., <a href="#Page_289">289</a>, <a href="#Page_291">291</a>, <a href="#Page_302">302</a>.</li> + +<li>Logarithms, <a href="#Page_195">195</a>, <a href="#Page_219">219</a>;</li> +<li><span style="margin-left: 1em;">in music, <a href="#Page_103">103</a>-<a href="#Page_104">104</a>.</span></li> + +<li>Logical root, of the principle of energy, <a href="#Page_181">181</a>;</li> +<li><span style="margin-left: 1em;">of the principle of excluded perpetual motion, <a href="#Page_182">182</a>.</span></li> + +<li>Lombroso, <a href="#Page_280">280</a>.</li> + +<li>Lucian, <a href="#Page_347">347</a>.</li> + +</ul> + +<ul class="IX"><li><i>Macula acustica</i>, <a href="#Page_272">272</a>.</li> + +<li>Magic lantern, <a href="#Page_96">96</a>.</li> + +<li>Magic powers of nature, <a href="#Page_189">189</a>.</li> + +<li><span class="pagenum"><a name="Page_403" id="Page_403">[Pg 403]</a></span>Magical power of science, belief in the, <a href="#Page_189">189</a>.</li> + +<li>Magnet, a, <a href="#Page_220">220</a>;</li> +<li><span style="margin-left: 1em;">will compared to the pressure of a, <a href="#Page_14">14</a>;</span></li> +<li><span style="margin-left: 1em;">coercive force of a, <a href="#Page_216">216</a>.</span></li> + +<li>Magnetic needle, near a current, <a href="#Page_207">207</a>.</li> + +<li>Magnetised bar of steel, <a href="#Page_242">242</a>-<a href="#Page_243">243</a>.</li> + +<li>Major and minor keys in music, <a href="#Page_100">100</a> et seq.</li> + +<li>Malus, <a href="#Page_242">242</a>.</li> + +<li>Man, a fragment of nature's life, <a href="#Page_49">49</a>;</li> +<li><span style="margin-left: 1em;">his life embraces others, <a href="#Page_234">234</a>.</span></li> + +<li>Mann, <a href="#Page_364">364</a>.</li> + +<li>Manuscript in a mirror, <a href="#Page_93">93</a>.</li> + +<li>Maple syrup, statues of, on Moon, <a href="#Page_4">4</a>.</li> + +<li>Marx, <a href="#Page_35">35</a>.</li> + +<li>Material, the relations of work with heat and the consumption of, <a href="#Page_245">245</a> et seq.</li> + +<li>Mathematical methods, their character, <a href="#Page_197">197</a>-<a href="#Page_198">198</a>.</li> + +<li>Mathematics, economy of, <a href="#Page_195">195</a>;</li> +<li><span style="margin-left: 1em;">on instruction in, <a href="#Page_338">338</a>-<a href="#Page_374">374</a>;</span></li> +<li><span style="margin-left: 1em;">C. G. J. Jacobi on, <a href="#Page_280">280</a>.</span></li> + +<li>Matter, constancy of, <a href="#Page_203">203</a>;</li> +<li><span style="margin-left: 1em;">its nature, <a href="#Page_203">203</a>;</span></li> +<li><span style="margin-left: 1em;">the notion of, <a href="#Page_213">213</a>.</span></li> + +<li>Maupertuis, his Latin city, <a href="#Page_338">338</a>.</li> + +<li>Maximal and minimal problems, their rôle in physics, <a href="#Page_14">14</a>, footnote.</li> + +<li>Mayer, J. R., his conception of energy, <a href="#Page_245">245</a>, <a href="#Page_246">246</a>;</li> +<li><span style="margin-left: 1em;">his methods of thought, <a href="#Page_247">247</a>;</span></li> +<li><span style="margin-left: 1em;">on the conservation of energy, <a href="#Page_163">163</a>, <a href="#Page_164">164</a>, <a href="#Page_165">165</a>, <a href="#Page_167">167</a>, <a href="#Page_183">183</a>, <a href="#Page_184">184</a>;</span></li> +<li><span style="margin-left: 1em;">his metaphysical utterances, <a href="#Page_183">183</a>, <a href="#Page_246">246</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_138">138</a>, <a href="#Page_184">184</a>, <a href="#Page_191">191</a>, <a href="#Page_217">217</a>, <a href="#Page_271">271</a>, <a href="#Page_274">274</a>.</span></li> + +<li>Measurement, definition of, <a href="#Page_206">206</a>.</li> + +<li>Measures, international, <a href="#Page_108">108</a>.</li> + +<li>Mécanique céleste, <a href="#Page_90">90</a>, <a href="#Page_188">188</a>;</li> +<li><span style="margin-left: 1em;">sociale, and morale, the, <a href="#Page_90">90</a>.</span></li> + +<li>Mechanical, conception of the world, <a href="#Page_105">105</a>, <a href="#Page_155">155</a> et seq., <a href="#Page_188">188</a>, <a href="#Page_207">207</a>;</li> +<li><span style="margin-left: 1em;">energy, W. Thomson on waste of, <a href="#Page_175">175</a>;</span></li> +<li><span style="margin-left: 1em;">analogies between —— and thermal energy, <a href="#Page_17">17</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">equivalent of heat, electricity, etc., <a href="#Page_164">164</a>, <a href="#Page_167">167</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">mythology, <a href="#Page_207">207</a>;</span></li> +<li><span style="margin-left: 1em;">phenomena, physical events as, <a href="#Page_182">182</a>;</span></li> +<li><span style="margin-left: 1em;">philosophy, <a href="#Page_188">188</a>;</span></li> +<li><span style="margin-left: 1em;">physics, <a href="#Page_155">155</a>-<a href="#Page_160">160</a>, <a href="#Page_212">212</a>;</span></li> +<li><span style="margin-left: 1em;">substitution-value of heat, <a href="#Page_178">178</a>, footnote.</span></li> + +<li>Mechanics, Kirchhoff's definition of, <a href="#Page_236">236</a>.</li> + +<li>Medicine, students of, <a href="#Page_326">326</a>.</li> + +<li>Melody, <a href="#Page_101">101</a>.</li> + +<li>Melsens, <a href="#Page_310">310</a>, <a href="#Page_327">327</a>.</li> + +<li>Memory, a treasure-house for comparison, <a href="#Page_230">230</a>;</li> +<li><span style="margin-left: 1em;">common elements impressed upon the, <a href="#Page_180">180</a>;</span></li> +<li><span style="margin-left: 1em;">its importance, <a href="#Page_238">238</a>;</span></li> +<li><span style="margin-left: 1em;">science disburdens the, <a href="#Page_193">193</a>.</span></li> + +<li>Mendelejeff, his periodical series, <a href="#Page_256">256</a>.</li> + +<li>Mental, adaptation, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>;</li> +<li><span style="margin-left: 1em;">completion of phenomena, <a href="#Page_220">220</a>;</span></li> +<li><span style="margin-left: 1em;">imagery, <a href="#Page_253">253</a>;</span></li> +<li><span style="margin-left: 1em;">imitation, our schematic, <a href="#Page_199">199</a>;</span></li> +<li><span style="margin-left: 1em;">processes, economical, <a href="#Page_195">195</a>;</span></li> +<li><span style="margin-left: 1em;">reproduction, <a href="#Page_198">198</a>;</span></li> +<li><span style="margin-left: 1em;">visualisation, <a href="#Page_250">250</a>.</span></li> + +<li>Mephistopheles, <a href="#Page_88">88</a>.</li> + +<li>Mercantile principle, a miserly, at the basis of science, <a href="#Page_15">15</a>.</li> + +<li>Mersenne, <a href="#Page_377">377</a>.</li> + +<li>Mesmerism, the mental state of ordinary minds, <a href="#Page_228">228</a>.</li> + +<li>Metaphysical establishment of doctrine of energy, <a href="#Page_183">183</a>.</li> + +<li>Metaphysical spooks, <a href="#Page_222">222</a>.</li> + +<li>Metrical, concepts of electricity, <a href="#Page_107">107</a> et seq.;</li> +<li><span style="margin-left: 1em;">notions, energy and entropy are, <a href="#Page_178">178</a>;</span></li> +<li><span style="margin-left: 1em;">units, the building-stones of the physicist, <a href="#Page_253">253</a>.</span></li> + +<li>Metronomes, <a href="#Page_41">41</a>.</li> + +<li>Meyer, Lothar, his periodical series, <a href="#Page_256">256</a>.</li> + +<li>Middle Ages, <a href="#Page_243">243</a>, <a href="#Page_349">349</a>.</li> + +<li>Midsummer Night's Dream, <a href="#Page_309">309</a>.</li> + +<li>Mill, John Stuart, <a href="#Page_230">230</a>.</li> + +<li>Millers, school for, <a href="#Page_326">326</a>.</li> + +<li>Mill-wheel, doing work, <a href="#Page_161">161</a>.</li> + +<li>Mimicking facts in thought, <a href="#Page_189">189</a>, <a href="#Page_193">193</a>.</li> + +<li>Minor and major keys in music, <a href="#Page_100">100</a> et seq.</li> + +<li>Mirror, symmetrical reversion of objects in, <a href="#Page_92">92</a> et seq.</li> + +<li>Miserly mercantile principle at the basis of science, <a href="#Page_15">15</a>.</li> + +<li>Moat, child looking into, <a href="#Page_208">208</a>.</li> + +<li>Modern scientists, adherents of the mechanical philosophy, <a href="#Page_188">188</a>.</li> + +<li>Molecular theories, <a href="#Page_104">104</a>.</li> + +<li>Molecules, <a href="#Page_203">203</a>, <a href="#Page_207">207</a>.</li> + +<li>Molière, <a href="#Page_234">234</a>.</li> + +<li>Momentum, <a href="#Page_184">184</a>.</li> + +<li>Monocular vision, <a href="#Page_98">98</a>.</li> + +<li><span class="pagenum"><a name="Page_404" id="Page_404">[Pg 404]</a></span>Monotheism of the Christians and Jews, <a href="#Page_187">187</a>.</li> + +<li>Montagues and Capulets, <a href="#Page_87">87</a>.</li> + +<li>Moon, eclipse of, <a href="#Page_219">219</a>;</li> +<li><span style="margin-left: 1em;">lightness of bodies on, <a href="#Page_4">4</a>;</span></li> +<li><span style="margin-left: 1em;">the study of the, <a href="#Page_90">90</a>, <a href="#Page_284">284</a>.</span></li> + +<li>Moreau, <a href="#Page_307">307</a>.</li> + +<li>Mosaic of thought, <a href="#Page_192">192</a>.</li> + +<li>Motion, a perpetual, <a href="#Page_181">181</a>;</li> +<li><span style="margin-left: 1em;">quantity of, <a href="#Page_184">184</a>;</span></li> +<li><span style="margin-left: 1em;">the Eleatics on, <a href="#Page_158">158</a>;</span></li> +<li><span style="margin-left: 1em;">Wundt on, <a href="#Page_158">158</a>;</span></li> +<li><span style="margin-left: 1em;">the Herbartians on, <a href="#Page_158">158</a>.</span></li> + +<li>Motions, natural and violent, <a href="#Page_226">226</a>;</li> +<li><span style="margin-left: 1em;">their familiar character, <a href="#Page_157">157</a>.</span></li> + +<li>Mountains of the earth, would crumble if very large, <a href="#Page_3">3</a>;</li> +<li><span style="margin-left: 1em;">weight of bodies on, <a href="#Page_112">112</a>.</span></li> + +<li>Mozart, <a href="#Page_44">44</a>, <a href="#Page_279">279</a>.</li> + +<li>Müller, Johann, <a href="#Page_291">291</a>.</li> + +<li>Multiplication-table, <a href="#Page_195">195</a>.</li> + +<li>Multiplier, <a href="#Page_132">132</a>.</li> + +<li>Music, band of, its <i>tempo</i> accelerated and retarded, <a href="#Page_53">53</a>;</li> +<li><span style="margin-left: 1em;">the principle of repetition in, <a href="#Page_99">99</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">its notation, mathematically illustrated, <a href="#Page_103">103</a>-<a href="#Page_104">104</a>.</span></li> + +<li>Musical notes, reversion of, <a href="#Page_101">101</a> et seq.;</li> +<li><span style="margin-left: 1em;">their economy, <a href="#Page_192">192</a>.</span></li> + +<li>Musical scale, a species of one-dimensional space, <a href="#Page_105">105</a>.</li> + +<li>Mystery, in physics, <a href="#Page_222">222</a>;</li> +<li><span style="margin-left: 1em;">science can dispense with, <a href="#Page_189">189</a>.</span></li> + +<li>Mysticism, numerical, <a href="#Page_33">33</a>;</li> +<li><span style="margin-left: 1em;">in the principle of energy, <a href="#Page_184">184</a>.</span></li> + +<li>Mythology, the mechanical, of philosophy, <a href="#Page_207">207</a>.</li> + +</ul> + +<ul class="IX"><li>Nagel, von, <a href="#Page_364">364</a>.</li> + +<li>Nansen, <a href="#Page_296">296</a>.</li> + +<li>Napoleon, picture representing the tomb of, <a href="#Page_36">36</a>.</li> + +<li>Nations, intercourse and ideas of, <a href="#Page_336">336</a>-<a href="#Page_337">337</a>.</li> + +<li>Natural constants, <a href="#Page_193">193</a>.</li> + +<li>Natural law, a, not contained in the conformity of the energies, <a href="#Page_175">175</a>.</li> + +<li>Natural laws, abridged descriptions, <a href="#Page_193">193</a>;</li> +<li><span style="margin-left: 1em;">likened to type, <a href="#Page_193">193</a>.</span></li> + +<li>Natural motions, <a href="#Page_225">225</a>.</li> + +<li>Natural selection in scientific theories, <a href="#Page_63">63</a>, <a href="#Page_218">218</a>.</li> + +<li>Nature, experience the well-spring of all knowledge of, <a href="#Page_181">181</a>;</li> +<li><span style="margin-left: 1em;">fashions of, <a href="#Page_64">64</a>;</span></li> +<li><span style="margin-left: 1em;">first knowledge of, instinctive, <a href="#Page_189">189</a>;</span></li> +<li><span style="margin-left: 1em;">general interconnexion of, <a href="#Page_182">182</a>;</span></li> +<li><span style="margin-left: 1em;">has many sides, <a href="#Page_217">217</a>;</span></li> +<li><span style="margin-left: 1em;">her forces compared to purposes, <a href="#Page_14">14</a>-<a href="#Page_15">15</a>;</span></li> +<li><span style="margin-left: 1em;">likened to a good man of business, <a href="#Page_15">15</a>;</span></li> +<li><span style="margin-left: 1em;">the economy of her actions, <a href="#Page_15">15</a>;</span></li> +<li><span style="margin-left: 1em;">how she appears to other animals, <a href="#Page_83">83</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">inquiry of, viewed as a torture, <a href="#Page_48">48</a>-<a href="#Page_49">49</a>;</span></li> +<li><span style="margin-left: 1em;">view of, as something designedly concealed from man, <a href="#Page_49">49</a>;</span></li> +<li><span style="margin-left: 1em;">like a covetous tailor, <a href="#Page_9">9</a>-<a href="#Page_10">10</a>;</span></li> +<li><span style="margin-left: 1em;">magic powers of, <a href="#Page_189">189</a>;</span></li> +<li><span style="margin-left: 1em;">our view of, modified by binocular vision, <a href="#Page_82">82</a>;</span></li> +<li><span style="margin-left: 1em;">the experimental method a questioning of, <a href="#Page_48">48</a>.</span></li> + +<li>Negro hamlet, the science of a, <a href="#Page_237">237</a>.</li> + +<li>Neptune, prediction and discovery of the planet, <a href="#Page_29">29</a>.</li> + +<li>New views, <a href="#Page_296">296</a> et seq.</li> + +<li>Newton, describes polarisation, <a href="#Page_242">242</a>;</li> +<li><span style="margin-left: 1em;">expresses his wealth of thought in Latin, <a href="#Page_341">341</a>;</span></li> +<li><span style="margin-left: 1em;">his discovery of gravitation, <a href="#Page_225">225</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">his solution of dispersion, <a href="#Page_362">362</a>;</span></li> +<li><span style="margin-left: 1em;">his principle of the equality of pressure and counterpressure, <a href="#Page_191">191</a>;</span></li> +<li><span style="margin-left: 1em;">his view of light, <a href="#Page_227">227</a>-<a href="#Page_228">228</a>;</span></li> +<li><span style="margin-left: 1em;">on absolute time, <a href="#Page_204">204</a>;</span></li> +<li><span style="margin-left: 1em;">selections from his works for use in instruction, <a href="#Page_368">368</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_270">270</a>, <a href="#Page_274">274</a>, <a href="#Page_279">279</a>, <a href="#Page_285">285</a>, <a href="#Page_289">289</a>.</span></li> + +<li>Nobility, they displace Latin, <a href="#Page_342">342</a>.</li> + +<li>Notation, musical, mathematically illustrated, <a href="#Page_103">103</a>-<a href="#Page_104">104</a>.</li> + +<li>Numbers, economy of, <a href="#Page_195">195</a>;</li> +<li><span style="margin-left: 1em;">their connexion with consonance, <a href="#Page_32">32</a>.</span></li> + +<li>Numerical mysticism, <a href="#Page_33">33</a>.</li> + +<li>Nursery, the questions of the, <a href="#Page_199">199</a>.</li> + +</ul> + +<ul class="IX"><li>Observation, <a href="#Page_310">310</a>.</li> + +<li>Observation, in science, <a href="#Page_261">261</a>.</li> + +<li>Ocean-stream, <a href="#Page_272">272</a>.</li> + +<li>Oettingen, Von, <a href="#Page_103">103</a>.</li> + +<li>Ohm, on electric currents, <a href="#Page_249">249</a>.</li> + +<li>Ohm, the word, <a href="#Page_343">343</a>.</li> + +<li>Oil, alcohol, water, and, employed in Plateau's experiments, <a href="#Page_4">4</a>;</li> +<li><span style="margin-left: 1em;">free mass of, assumes the shape of a sphere, <a href="#Page_12">12</a>;</span></li> +<li><span style="margin-left: 1em;">geometrical figures of, <a href="#Page_5">5</a> et seq.</span></li> + +<li>One-eyed people, vision of, <a href="#Page_98">98</a>.</li> + +<li>Ophthalmoscope, <a href="#Page_18">18</a>.</li> + +<li>Optic nerves, <a href="#Page_96">96</a>.</li> + +<li><span class="pagenum"><a name="Page_405" id="Page_405">[Pg 405]</a></span>Optimism and pessimism, <a href="#Page_234">234</a>.</li> + +<li>Order of physics, <a href="#Page_197">197</a>.</li> + +<li>Organ, bellows of an, <a href="#Page_135">135</a>.</li> + +<li>Organic nature, results of Darwin's studies of, <a href="#Page_215">215</a> et seq.</li> +<li><span style="margin-left: 1em;">See <i>Adaptation</i> and <i>Heredity</i>.</span></li> + +<li>Oriental world of fables, <a href="#Page_273">273</a>.</li> + +<li>Orientation, sensations of, <a href="#Page_282">282</a> et seq.</li> + +<li>Oscillation, centre of, <a href="#Page_147">147</a> et seq.</li> + +<li>Ostwald, <a href="#Page_172">172</a>.</li> + +<li>Otoliths, <a href="#Page_301">301</a> et seq.</li> + +<li>Overtones, <a href="#Page_28">28</a>, <a href="#Page_40">40</a>, <a href="#Page_349">349</a>.</li> + +<li>Ozone, Schöbein's discovery of, <a href="#Page_271">271</a>.</li> + +</ul> + +<ul class="IX"><li>Painted things, the difference between real and, <a href="#Page_68">68</a>.</li> + +<li>Palestrina, <a href="#Page_44">44</a>.</li> + +<li>Parameter, <a href="#Page_257">257</a>.</li> + +<li>Partial tones, <a href="#Page_390">390</a>.</li> + +<li>Particles, smallest, <a href="#Page_104">104</a>.</li> + +<li>Pascheles, Dr. W., <a href="#Page_285">285</a>.</li> + +<li>Paulsen, <a href="#Page_338">338</a>, <a href="#Page_340">340</a>, <a href="#Page_373">373</a>.</li> + +<li>Pearls of life, strung on the individual as on a thread, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li> + +<li>Pencil surpasses the mathematician in intelligence, <a href="#Page_196">196</a>.</li> + +<li>Pendulum, motion of a, <a href="#Page_144">144</a> et seq.,</li> +<li><span style="margin-left: 1em;">increased motion of, due to slight impulses, <a href="#Page_21">21</a>;</span></li> +<li><span style="margin-left: 1em;">electrical, <a href="#Page_110">110</a>.</span></li> + +<li>Percepts, of like form, <a href="#Page_390">390</a>.</li> + +<li>Periodical, changes, <a href="#Page_181">181</a>;</li> +<li><span style="margin-left: 1em;">series, <a href="#Page_256">256</a>.</span></li> + +<li>Permanent, changes, <a href="#Page_181">181</a>, <a href="#Page_199">199</a>;</li> +<li><span style="margin-left: 1em;">elements of the world, <a href="#Page_194">194</a>.</span></li> + +<li>Perpetual motion, a, <a href="#Page_181">181</a>;</li> +<li><span style="margin-left: 1em;">defined, <a href="#Page_139">139</a>;</span></li> +<li><span style="margin-left: 1em;">impossibility of, <a href="#Page_139">139</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">the principle of the, excluded, <a href="#Page_140">140</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">excluded from general physics, <a href="#Page_162">162</a>.</span></li> + +<li>Personality, its nature, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li> + +<li>Perspective, <a href="#Page_76">76</a> et seq.;</li> +<li><span style="margin-left: 1em;">contraction of, <a href="#Page_74">74</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">distortion of, <a href="#Page_77">77</a>.</span></li> + +<li>Pessimism and optimism, <a href="#Page_234">234</a>.</li> + +<li>Pharaohs, <a href="#Page_85">85</a>.</li> + +<li>Phenomenology, a universal physical, <a href="#Page_250">250</a>.</li> + +<li>Philistine, modes of thought of, <a href="#Page_223">223</a>.</li> + +<li>Philology, comparison in, <a href="#Page_239">239</a>.</li> + +<li>Philosopher, an ancient, on the moral and physical sciences, <a href="#Page_89">89</a>.</li> + +<li>Philosophy, its character at all times, <a href="#Page_186">186</a>;</li> +<li><span style="margin-left: 1em;">mechanical, <a href="#Page_155">155</a> et seq., <a href="#Page_188">188</a>, <a href="#Page_207">207</a>, <a href="#Page_259">259</a> et seq.</span></li> + +<li>Phonetic alphabets, their economy, <a href="#Page_192">192</a>.</li> + +<li>Photography, by the electric spark, <a href="#Page_318">318</a> et seq.</li> + +<li>Photography of projectiles, <a href="#Page_309">309</a>-<a href="#Page_337">337</a>.</li> + +<li>Photography, stupendous advances of, <a href="#Page_74">74</a>.</li> + +<li>Physical, concepts, fetishism in our, <a href="#Page_187">187</a>;</li> +<li><span style="margin-left: 1em;">ideas and principles, their nature, <a href="#Page_204">204</a>;</span></li> +<li><span style="margin-left: 1em;">inquiry, the economical nature of, <a href="#Page_186">186</a>;</span></li> +<li><span style="margin-left: 1em;">research, object of <a href="#Page_207">207</a>, <a href="#Page_209">209</a>.</span></li> + +<li>Physical phenomena, as mechanical phenomena, <a href="#Page_182">182</a>;</li> +<li><span style="margin-left: 1em;">relations between, <a href="#Page_205">205</a>.</span></li> + +<li>Physico-mechanical view of the world, <a href="#Page_155">155</a>, <a href="#Page_187">187</a>, <a href="#Page_188">188</a>, <a href="#Page_207">207</a> et seq.</li> + +<li>Physics, compared to a well-kept household, <a href="#Page_197">197</a>;</li> +<li><span style="margin-left: 1em;">economical experience, <a href="#Page_197">197</a>;</span></li> +<li><span style="margin-left: 1em;">the principles of, descriptive, <a href="#Page_199">199</a>;</span></li> +<li><span style="margin-left: 1em;">the methods of, <a href="#Page_209">209</a>;</span></li> +<li><span style="margin-left: 1em;">its method characterised, <a href="#Page_211">211</a>;</span></li> +<li><span style="margin-left: 1em;">comparison in, <a href="#Page_239">239</a>;</span></li> +<li><span style="margin-left: 1em;">the facts of, qualitatively homogeneous, <a href="#Page_255">255</a>;</span></li> +<li><span style="margin-left: 1em;">how it began, <a href="#Page_37">37</a>;</span></li> +<li><span style="margin-left: 1em;">helped by psychology, <a href="#Page_104">104</a>;</span></li> +<li><span style="margin-left: 1em;">study of its own character, <a href="#Page_189">189</a>;</span></li> +<li><span style="margin-left: 1em;">the goal of, <a href="#Page_207">207</a>, <a href="#Page_209">209</a>.</span></li> + +<li>Physiological psychology, its methods, <a href="#Page_211">211</a> et seq.</li> + +<li>Physiology, its scope, <a href="#Page_212">212</a>.</li> + +<li>Piano, its mirrored counterpart, <a href="#Page_100">100</a> et seq.;</li> +<li><span style="margin-left: 1em;">used to illustrate the facts of sympathetic vibration, <a href="#Page_25">25</a> et seq.</span></li> + +<li>Piano-player, a speaker compared to, <a href="#Page_192">192</a>.</li> + +<li>Picture, physical, a, <a href="#Page_110">110</a>.</li> + +<li>Pike, learns by experience, <a href="#Page_267">267</a>.</li> + +<li>Pillars of Corti, <a href="#Page_19">19</a>.</li> + +<li>Places, heavy bodies seek their, <a href="#Page_224">224</a> et seq.</li> + +<li>Planetary system, origin of, illustrated, <a href="#Page_5">5</a>.</li> + +<li>Plasticity of organic nature, <a href="#Page_216">216</a>.</li> + +<li>Plateau, his law of free liquid equilibrium, <a href="#Page_9">9</a>;</li> +<li><span style="margin-left: 1em;">his method of getting rid of the effects of gravity, <a href="#Page_4">4</a>.</span></li> + +<li>Plates of oil, thin, <a href="#Page_6">6</a>.</li> + +<li>Plato, <a href="#Page_347">347</a>, <a href="#Page_371">371</a>.</li> + +<li>Plautus, <a href="#Page_347">347</a>.</li> + +<li>Playfair, <a href="#Page_138">138</a>.</li> + +<li><span class="pagenum"><a name="Page_406" id="Page_406">[Pg 406]</a></span>Pleasant effects, cause of, <a href="#Page_94">94</a> et seq.</li> + +<li>Pliny, <a href="#Page_349">349</a>.</li> + +<li>Poetry and science, <a href="#Page_30">30</a>, <a href="#Page_31">31</a>, <a href="#Page_351">351</a>.</li> + +<li>Poinsot, on the foundations of mechanics, <a href="#Page_152">152</a> et seq.</li> + +<li>Polarisation, <a href="#Page_91">91</a>;</li> +<li><span style="margin-left: 1em;">abstractly described by Newton, <a href="#Page_242">242</a>.</span></li> + +<li>Politics, Chinese speak with unwillingness of, <a href="#Page_374">374</a>.</li> + +<li>Pollak, <a href="#Page_299">299</a>.</li> + +<li>Polyp plant, humanity likened to a, <a href="#Page_235">235</a>.</li> + +<li>Pompeii, <a href="#Page_234">234</a>;</li> +<li><span style="margin-left: 1em;">art in, <a href="#Page_80">80</a>.</span></li> + +<li>Popper J., <a href="#Page_172">172</a>, <a href="#Page_216">216</a>.</li> + +<li>Potential, social, <a href="#Page_15">15</a>;</li> +<li><span style="margin-left: 1em;">electrical, <a href="#Page_121">121</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">measurement of, <a href="#Page_126">126</a>;</span></li> +<li><span style="margin-left: 1em;">fall of, <a href="#Page_177">177</a>;</span></li> +<li><span style="margin-left: 1em;">swarm of notions in the idea of, <a href="#Page_197">197</a>;</span></li> +<li><span style="margin-left: 1em;">its wide scope, <a href="#Page_250">250</a>.</span></li> + +<li>Pottery, invention of, <a href="#Page_263">263</a>.</li> + +<li>Prediction, <a href="#Page_221">221</a> et seq.</li> + +<li>Prejudice, the function, power, and dangers of, <a href="#Page_232">232</a>-<a href="#Page_233">233</a>.</li> + +<li>Preparatory schools, the defects of the German, <a href="#Page_346">346</a>-<a href="#Page_347">347</a>;</li> +<li><span style="margin-left: 1em;">what they should teach, <a href="#Page_364">364</a> et seq.</span></li> + +<li>Pressure of a stone or of a magnet, will compared to, <a href="#Page_14">14</a>;</li> +<li><span style="margin-left: 1em;">also <a href="#Page_157">157</a>.</span></li> + +<li>Primitive acts of knowledge the foundation of scientific thought, <a href="#Page_190">190</a>.</li> + +<li>Problem, nature of a, <a href="#Page_223">223</a>.</li> + +<li>Problems which are wrongly formulated, <a href="#Page_308">308</a>.</li> + +<li>Process, Carnot's, <a href="#Page_161">161</a> et seq.</li> + +<li>Projectiles, the effects of the impact of, <a href="#Page_310">310</a>, <a href="#Page_327">327</a>-<a href="#Page_328">328</a>;</li> +<li><span style="margin-left: 1em;">seen with the naked eye, <a href="#Page_311">311</a>, <a href="#Page_317">317</a>;</span></li> +<li><span style="margin-left: 1em;">measuring the velocity of, <a href="#Page_332">332</a>;</span></li> +<li><span style="margin-left: 1em;">photography of, <a href="#Page_309">309</a>-<a href="#Page_337">337</a>.</span></li> + +<li>Prony's brake, <a href="#Page_132">132</a>.</li> + +<li>Proof, nature of, <a href="#Page_284">284</a>.</li> + +<li>Prophesying events, <a href="#Page_220">220</a> et seq.</li> + +<li>Psalms, quotation from the, <a href="#Page_89">89</a>.</li> + +<li>Pseudoscope, Wheatstone's, <a href="#Page_96">96</a>.</li> + +<li>Psychology, preceded by astronomy, <a href="#Page_90">90</a>;</li> +<li><span style="margin-left: 1em;">how reached, <a href="#Page_91">91</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">helps physical science, <a href="#Page_104">104</a>;</span></li> +<li><span style="margin-left: 1em;">its method the same as that of physics, <a href="#Page_207">207</a> et seq.</span></li> + +<li>Pully arrangement, illustrating principle of least superficial area, <a href="#Page_12">12</a>-<a href="#Page_13">13</a>.</li> + +<li>Purkinje, <a href="#Page_284">284</a>, <a href="#Page_285">285</a>, <a href="#Page_291">291</a>, <a href="#Page_299">299</a>.</li> + +<li>Purposes, the acts of nature compared to, <a href="#Page_14">14</a>-<a href="#Page_15">15</a>;</li> +<li><span style="margin-left: 1em;">nature pursues no, <a href="#Page_66">66</a>.</span></li> + +<li>Puzzle-lock, a, <a href="#Page_26">26</a>.</li> + +<li>Puzzles, <a href="#Page_277">277</a>.</li> + +<li>Pyramid of oil, <a href="#Page_6">6</a>.</li> + +<li>Pythagoras, his discovery of the laws of harmony, <a href="#Page_32">32</a>, <a href="#Page_259">259</a>.</li> + +</ul> + +<ul class="IX"><li>Quality of tones, <a href="#Page_36">36</a>.</li> + +<li>Quantitative investigation, the goal of, <a href="#Page_180">180</a>.</li> + +<li>Quantity of electricity, <a href="#Page_111">111</a>, <a href="#Page_118">118</a>, <a href="#Page_119">119</a>, <a href="#Page_167">167</a>-<a href="#Page_170">170</a>, <a href="#Page_173">173</a>;</li> +<li><span style="margin-left: 1em;">of heat, <a href="#Page_166">166</a>, <a href="#Page_167">167</a>-<a href="#Page_171">171</a>, <a href="#Page_174">174</a>, <a href="#Page_177">177</a>, <a href="#Page_244">244</a>;</span></li> +<li><span style="margin-left: 1em;">of motion, <a href="#Page_184">184</a>.</span></li> + +<li>Quests made of the inquirer, not by him, <a href="#Page_30">30</a>.</li> + +<li>Quételet, <a href="#Page_15">15</a>, footnote.</li> + +</ul> + +<ul class="IX"><li>Rabelais, <a href="#Page_283">283</a>.</li> + +<li>Raindrop, form of, <a href="#Page_3">3</a>.</li> + +<li>Rameau, <a href="#Page_34">34</a>.</li> + +<li>Reaction and action, principle of, <a href="#Page_191">191</a>.</li> + +<li>Reactions, disclosure of the connexion of, <a href="#Page_270">270</a> et seq.</li> + +<li>Realgymnasien, <a href="#Page_365">365</a>.</li> + +<li>Realschulen, <a href="#Page_365">365</a>, <a href="#Page_373">373</a>.</li> + +<li>Reason, stands above the senses, <a href="#Page_105">105</a>.</li> + +<li>Reflex action, <a href="#Page_210">210</a>.</li> + +<li>Reflexion, produces symmetrical reversion of objects, <a href="#Page_93">93</a> et seq.</li> + +<li>Refraction, <a href="#Page_29">29</a>, <a href="#Page_193">193</a>, <a href="#Page_194">194</a>, <a href="#Page_208">208</a>, <a href="#Page_230">230</a>, <a href="#Page_231">231</a>.</li> + +<li>Reger, <a href="#Page_328">328</a>.</li> + +<li>Reliefs, photographs of, <a href="#Page_68">68</a>.</li> + +<li>Repetition, its rôle in æsthetics, <a href="#Page_89">89</a>, footnote, <a href="#Page_91">91</a> et seq., <a href="#Page_97">97</a>, <a href="#Page_98">98</a> et seq., <a href="#Page_390">390</a>.</li> + +<li>Reproduction of facts in thought, <a href="#Page_189">189</a>, <a href="#Page_193">193</a>, <a href="#Page_198">198</a>, <a href="#Page_253">253</a>.</li> + +<li>Repulsion, electric, <a href="#Page_109">109</a> et seq., <a href="#Page_168">168</a>.</li> + +<li>Research, function of experimental <a href="#Page_181">181</a>;</li> +<li><span style="margin-left: 1em;">the aim of, <a href="#Page_205">205</a>.</span></li> + +<li>Resemblances between facts, <a href="#Page_255">255</a>.</li> + +<li>Resin, solution of, <a href="#Page_7">7</a>.</li> + +<li>Resistance, laws of, for bodies travelling in air and fluids, <a href="#Page_333">333</a> et seq.</li> + +<li>Resonance, corporeal, <a href="#Page_392">392</a>.</li> + +<li>Response of sonorous bodies, <a href="#Page_25">25</a>.</li> + +<li>Retina, the corresponding spots of <a href="#Page_98">98</a>;</li> +<li><span class="pagenum"><a name="Page_407" id="Page_407">[Pg 407]</a></span><span style="margin-left: 1em;">nerves of compared to fingers of a hand, <a href="#Page_96">96</a> et seq.</span></li> + +<li>Reversible processes, <a href="#Page_161">161</a> et seq., <a href="#Page_175">175</a>, <a href="#Page_176">176</a>, <a href="#Page_181">181</a>, <a href="#Page_182">182</a>.</li> + +<li>Rhine, the, <a href="#Page_94">94</a>.</li> + +<li>Richard the Third, <a href="#Page_77">77</a>.</li> + +<li>Riddles, <a href="#Page_277">277</a>.</li> + +<li>Riders, <a href="#Page_379">379</a>.</li> + +<li>Riegler, <a href="#Page_319">319</a>.</li> + +<li>Riess, experiment with the thermo-electrometer, <a href="#Page_133">133</a> et seq., <a href="#Page_169">169</a>.</li> + +<li>Rigid connexions, <a href="#Page_142">142</a>.</li> + +<li>Rind of a fruit, <a href="#Page_190">190</a>.</li> + +<li>Rings of oil, illustrating formation of rings of Saturn, <a href="#Page_5">5</a>.</li> + +<li>Ritter, <a href="#Page_291">291</a>, <a href="#Page_299">299</a>.</li> + +<li>Rods of Corti, <a href="#Page_19">19</a>.</li> + +<li>Rolph, W. H., <a href="#Page_216">216</a>.</li> + +<li>Roman Church, Latin introduced with the, <a href="#Page_340">340</a> et seq.</li> + +<li>Romans, their provinciality and narrow-mindedness, <a href="#Page_270">270</a>.</li> + +<li>Romeo and Juliet, <a href="#Page_87">87</a>.</li> + +<li>Römer, Olaf, <a href="#Page_51">51</a> et seq.</li> + +<li>Roots, the nature of, in language, <a href="#Page_252">252</a>.</li> + +<li>Rosetti, his experiment on the work required to develop electricity, <a href="#Page_131">131</a>.</li> + +<li>Rotating bodies, <a href="#Page_285">285</a>.</li> + +<li>Rotation, apparatus of, in physics, <a href="#Page_59">59</a> et seq.;</li> +<li><span style="margin-left: 1em;">sensations of, <a href="#Page_288">288</a> et seq.</span></li> + +<li>Rousseau, <a href="#Page_336">336</a>.</li> + +<li>Rubber pyramid, illustrating the principle of least superficial area, <a href="#Page_10">10</a>-<a href="#Page_11">11</a>.</li> + +<li>Ruysdael, <a href="#Page_279">279</a>.</li> +</ul> + +<ul class="IX"> +<li>Sachs, Hans, <a href="#Page_106">106</a>.</li> + +<li>Salcher, Prof. <a href="#Page_319">319</a>.</li> + +<li>Salviati, <a href="#Page_144">144</a>.</li> + +<li>Saturn, rings of, their formation illustrated, <a href="#Page_5">5</a>.</li> + +<li>Saurians, <a href="#Page_257">257</a>.</li> + +<li>Sauveur, on acoustics, <a href="#Page_34">34</a>, <a href="#Page_375">375</a> et seq.</li> + +<li>Savage, modes of conception and interpretation of a, <a href="#Page_218">218</a> et seq.</li> + +<li>Schäfer, K., <a href="#Page_298">298</a>.</li> + +<li><i>Schlierenmethode</i>, <a href="#Page_317">317</a>.</li> + +<li>Schönbein's discovery of ozone, <a href="#Page_271">271</a>.</li> + +<li>School-boy, copy-book of, <a href="#Page_92">92</a>.</li> + +<li>Schoolmen, <a href="#Page_214">214</a>.</li> + +<li>Schools, State-control of, <a href="#Page_372">372</a> et seq.</li> + +<li>Schopenhauer, <a href="#Page_190">190</a>.</li> + +<li>Schultze, Max, <a href="#Page_19">19</a>.</li> + +<li>Science, a miserly mercantile principle at its basis, <a href="#Page_15">15</a>;</li> +<li><span style="margin-left: 1em;">compared to a business, <a href="#Page_16">16</a>;</span></li> +<li><span style="margin-left: 1em;">viewed as a maximum or minimum problem, <a href="#Page_16">16</a>, footnote;</span></li> +<li><span style="margin-left: 1em;">its process not greatly different from the intellectual activity of ordinary life, <a href="#Page_16">16</a>, footnote;</span></li> +<li><span style="margin-left: 1em;">economy of its task, <a href="#Page_16">16</a>;</span></li> +<li><span style="margin-left: 1em;">relation of, to poetry, <a href="#Page_30">30</a>, <a href="#Page_31">31</a>, <a href="#Page_351">351</a>;</span></li> +<li><span style="margin-left: 1em;">the church of, <a href="#Page_67">67</a>;</span></li> +<li><span style="margin-left: 1em;">beginnings of, <a href="#Page_189">189</a>, <a href="#Page_191">191</a>;</span></li> +<li><span style="margin-left: 1em;">belief in the magical power of, <a href="#Page_189">189</a>;</span></li> +<li><span style="margin-left: 1em;">can dispense with mystery, <a href="#Page_189">189</a>;</span></li> +<li><span style="margin-left: 1em;">lavish extravagance of, <a href="#Page_189">189</a>;</span></li> +<li><span style="margin-left: 1em;">economy of the terminology of, <a href="#Page_192">192</a>;</span></li> +<li><span style="margin-left: 1em;">partly made up of the intelligence of others, <a href="#Page_196">196</a>;</span></li> +<li><span style="margin-left: 1em;">stripped of mystery, <a href="#Page_197">197</a>;</span></li> +<li><span style="margin-left: 1em;">its true power, <a href="#Page_197">197</a>;</span></li> +<li><span style="margin-left: 1em;">the economical schematism of, <a href="#Page_206">206</a>;</span></li> +<li><span style="margin-left: 1em;">the object of, <a href="#Page_206">206</a>;</span></li> +<li><span style="margin-left: 1em;">the tools of, <a href="#Page_207">207</a>;</span></li> +<li><span style="margin-left: 1em;">does not create facts, <a href="#Page_211">211</a>;</span></li> +<li><span style="margin-left: 1em;">of the future, <a href="#Page_213">213</a>;</span></li> +<li><span style="margin-left: 1em;">revolution in, dating from Galileo, <a href="#Page_214">214</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">the natural foe of the marvellous, <a href="#Page_224">224</a>;</span></li> +<li><span style="margin-left: 1em;">characterised, <a href="#Page_227">227</a>;</span></li> +<li><span style="margin-left: 1em;">growth of, <a href="#Page_237">237</a>;</span></li> +<li><span style="margin-left: 1em;">dramatic element in, <a href="#Page_243">243</a>;</span></li> +<li><span style="margin-left: 1em;">described, <a href="#Page_251">251</a>;</span></li> +<li><span style="margin-left: 1em;">its function, <a href="#Page_253">253</a>;</span></li> +<li><span style="margin-left: 1em;">classification in, <a href="#Page_255">255</a>, <a href="#Page_259">259</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">the way of discovery in, <a href="#Page_316">316</a>.</span></li> +<li><span style="margin-left: 1em;">See also <i>Physics</i>.</span></li> + +<li>Sciences, partition of the, <a href="#Page_86">86</a>;</li> +<li><span style="margin-left: 1em;">the barriers and relations between the <a href="#Page_257">257</a>-<a href="#Page_258">258</a>;</span></li> +<li><span style="margin-left: 1em;">on instruction in the, <a href="#Page_338">338</a>-<a href="#Page_374">374</a>.</span></li> + +<li>Scientific, criticism, Socrates the father of, <a href="#Page_1">1</a>, <a href="#Page_16">16</a>;</li> +<li><span style="margin-left: 1em;">discoveries, their fate, <a href="#Page_138">138</a>;</span></li> +<li><span style="margin-left: 1em;">knowledge, involves description, <a href="#Page_193">193</a>;</span></li> +<li><span style="margin-left: 1em;">thought, transformation and adaptation in, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>;</span></li> +<li><span style="margin-left: 1em;">thought, advanced by new experiences, <a href="#Page_223">223</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">thought, the difficulty of, <a href="#Page_366">366</a>;</span></li> +<li><span style="margin-left: 1em;">terms, <a href="#Page_342">342</a>-<a href="#Page_343">343</a>;</span></li> +<li><span style="margin-left: 1em;">founded on primitive acts of knowledge, <a href="#Page_190">190</a>.</span></li> + +<li>Scientists, stories about their ignorance, <a href="#Page_342">342</a>.</li> + +<li>Screw, the, <a href="#Page_62">62</a>.</li> + +<li>Sea-sickness, <a href="#Page_284">284</a>.</li> + +<li>Secret computation, Leibnitz's, <a href="#Page_33">33</a>.</li> + +<li>Seek their places, bodies, <a href="#Page_226">226</a>.</li> + +<li>Self-induction, coefficient of, <a href="#Page_250">250</a>, <a href="#Page_252">252</a>.</li> + +<li>Self-observation, <a href="#Page_211">211</a>.</li> + +<li><span class="pagenum"><a name="Page_408" id="Page_408">[Pg 408]</a></span>Self-preservation, our first knowledge derived from the economy of, <a href="#Page_197">197</a>;</li> +<li><span style="margin-left: 1em;">struggle for, among ideas, <a href="#Page_228">228</a>.</span></li> + +<li>Semi-circular canals, <a href="#Page_290">290</a> et seq.</li> + +<li>Sensation of rounding a railway curve, <a href="#Page_286">286</a>.</li> + +<li>Sensations, analysed, <a href="#Page_251">251</a>;</li> +<li><span style="margin-left: 1em;">when similar, produce agreeable effects, <a href="#Page_96">96</a>;</span></li> +<li><span style="margin-left: 1em;">their character, <a href="#Page_200">200</a>;</span></li> +<li><span style="margin-left: 1em;">defined, <a href="#Page_209">209</a>;</span></li> +<li><span style="margin-left: 1em;">of orientation, <a href="#Page_282">282</a> et seq.</span></li> + +<li>Sense-elements, <a href="#Page_179">179</a>.</li> + +<li>Senses, theory of, <a href="#Page_104">104</a>;</li> +<li><span style="margin-left: 1em;">the source of our knowledge of facts, <a href="#Page_237">237</a>.</span></li> + +<li>Seventh, the troublesome, <a href="#Page_46">46</a>.</li> + +<li>Shadow method, <a href="#Page_313">313</a> et seq., <a href="#Page_317">317</a> footnote.</li> + +<li>Shadows, rôle of, in vision, <a href="#Page_81">81</a>.</li> + +<li>Shakespeare, <a href="#Page_278">278</a>.</li> + +<li>Sharps, reversed into flats, <a href="#Page_101">101</a>.</li> + +<li>Shell, spherical, law of attraction for a, <a href="#Page_124">124</a>, footnote.</li> + +<li>Shoemaker, inquirer compared to, <a href="#Page_105">105</a>-<a href="#Page_106">106</a>.</li> + +<li>Shooting, <a href="#Page_309">309</a>.</li> + +<li>Shots, double report of, <a href="#Page_229">229</a> et seq.</li> + +<li>Similarity, <a href="#Page_249">249</a>.</li> + +<li>Simony, <a href="#Page_280">280</a>.</li> + +<li>Simplicity, a varying element in description, <a href="#Page_254">254</a>.</li> + +<li>Sines, law of the, <a href="#Page_193">193</a>.</li> + +<li>Sinking of heavy bodies, <a href="#Page_222">222</a>.</li> + +<li>Sixth sense, <a href="#Page_297">297</a>.</li> + +<li>Smith, R., on acoustics, <a href="#Page_34">34</a>, <a href="#Page_381">381</a>, <a href="#Page_383">383</a>.</li> + +<li>Soap-films, Van der Mensbrugghe's experiment with, <a href="#Page_11">11</a>-<a href="#Page_12">12</a>.</li> + +<li>Soapsuds, films and figures of, <a href="#Page_7">7</a>.</li> + +<li>Social potential, <a href="#Page_15">15</a>.</li> + +<li>Socrates, the father of scientific criticism, <a href="#Page_1">1</a>, <a href="#Page_16">16</a>.</li> + +<li>Sodium, <a href="#Page_202">202</a>.</li> + +<li>Sodium-light, vibrations of, as a measure of time, <a href="#Page_205">205</a>.</li> + +<li>Solidity, conception of, by the eye, <a href="#Page_71">71</a> et seq.;</li> +<li><span style="margin-left: 1em;">spatial, photographs of, <a href="#Page_73">73</a>.</span></li> + +<li>Solids, and liquids, their difference merely one of degree, <a href="#Page_2">2</a>.</li> + +<li>Sonorous bodies, <a href="#Page_24">24</a> et seq.</li> + +<li>Soret, J. P., <a href="#Page_89">89</a>.</li> + +<li>Sounds, symmetry of, <a href="#Page_99">99</a> et seq.;</li> +<li><span style="margin-left: 1em;">generally, <a href="#Page_22">22</a>-<a href="#Page_47">47</a>, <a href="#Page_212">212</a>.</span></li> + +<li>Sound-waves rendered visible, <a href="#Page_315">315</a> et seq.</li> + +<li>Sources of the principle of energy, <a href="#Page_179">179</a> et seq.</li> + +<li>Space, <a href="#Page_205">205</a>;</li> +<li><span style="margin-left: 1em;">sensation of, <a href="#Page_210">210</a>.</span></li> + +<li>Spark, electric, <a href="#Page_117">117</a>, <a href="#Page_127">127</a>, <a href="#Page_132">132</a>, <a href="#Page_133">133</a>, <a href="#Page_190">190</a>.</li> + +<li>Spatial vision, <a href="#Page_386">386</a>.</li> + +<li>Species, stability of, a theory, <a href="#Page_216">216</a>.</li> + +<li>Specific energies, <a href="#Page_291">291</a>.</li> + +<li>Specific heat, <a href="#Page_166">166</a>, <a href="#Page_244">244</a>.</li> + +<li>Specific inductive capacity, <a href="#Page_117">117</a>.</li> + +<li>Spectral analysis of sound, <a href="#Page_27">27</a>.</li> + +<li>Spectrum, mental associations of the, <a href="#Page_190">190</a>.</li> + +<li>Speech, the instinct of, cultivated by languages, <a href="#Page_354">354</a>.</li> + +<li>Spencer, <a href="#Page_218">218</a>, <a href="#Page_222">222</a>.</li> + +<li>Sphere, a soft rotating, <a href="#Page_2">2</a>;</li> +<li><span style="margin-left: 1em;">the figure of least surface, <a href="#Page_12">12</a>;</span></li> +<li><span style="margin-left: 1em;">electrical capacity of, <a href="#Page_123">123</a> et seq.</span></li> + +<li>Spherical shell, law of attraction for <a href="#Page_124">124</a>, footnote.</li> + +<li>Spiders, the eyes of, <a href="#Page_67">67</a>.</li> + +<li>Spirits, as explanation of the world <a href="#Page_186">186</a>, <a href="#Page_243">243</a>.</li> + +<li>Spiritualism, modern, <a href="#Page_187">187</a>.</li> + +<li>Spooks, metaphysical, <a href="#Page_222">222</a>.</li> + +<li>Squinting, <a href="#Page_72">72</a>.</li> + +<li>Stability of our environment, <a href="#Page_206">206</a>.</li> + +<li>Stallo, <a href="#Page_336">336</a>.</li> + +<li>Stars, the fixed, <a href="#Page_90">90</a>.</li> + +<li>State, benefits and evils of its control of the schools, <a href="#Page_372">372</a> et seq.;</li> +<li><span style="margin-left: 1em;">the Church and, <a href="#Page_88">88</a>.</span></li> + +<li>Statical electricity, <a href="#Page_134">134</a>.</li> + +<li>Stationary currents, <a href="#Page_249">249</a>.</li> + +<li>Statoliths, <a href="#Page_303">303</a>.</li> + +<li>Steam-engine, <a href="#Page_160">160</a>, <a href="#Page_265">265</a>.</li> + +<li>Steeple-jacks, <a href="#Page_75">75</a>.</li> + +<li>Stereoscope, Wheatstone and Brewster's, <a href="#Page_73">73</a>.</li> + +<li>Stevinus, on the inclined plane, <a href="#Page_140">140</a>;</li> +<li><span style="margin-left: 1em;">on hydrostatics, <a href="#Page_141">141</a>;</span></li> +<li><span style="margin-left: 1em;">on the equilibrium of systems, <a href="#Page_142">142</a>;</span></li> +<li><span style="margin-left: 1em;">discovers the principle of virtual velocities, <a href="#Page_150">150</a>;</span></li> +<li><span style="margin-left: 1em;">characterisation of his thought, <a href="#Page_142">142</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_182">182</a>, <a href="#Page_187">187</a>, <a href="#Page_191">191</a>.</span></li> + +<li>Stone Age, <a href="#Page_46">46</a>, <a href="#Page_321">321</a>.</li> + +<li>Störensen, <a href="#Page_306">306</a>.</li> + +<li>Stove, primitive, <a href="#Page_263">263</a>.</li> + +<li>Straight line, a, its symmetry, <a href="#Page_98">98</a>.</li> + +<li>Straight, meaning of the word, <a href="#Page_240">240</a>.</li> + +<li><span class="pagenum"><a name="Page_409" id="Page_409">[Pg 409]</a></span>Street, vista into a, <a href="#Page_75">75</a>.</li> + +<li>Striae, in glass, <a href="#Page_313">313</a>.</li> + +<li>Striate method, for detecting optical imperfections, <a href="#Page_317">317</a>.</li> + +<li>Striking distance, <a href="#Page_115">115</a>, <a href="#Page_127">127</a>.</li> + +<li>Strings, vibrations of, <a href="#Page_249">249</a>.</li> + +<li>Struggle for existence among ideas, <a href="#Page_217">217</a>.</li> + +<li>Substance, heat conceived as a, <a href="#Page_177">177</a>, <a href="#Page_243">243</a> et seq.;</li> +<li><span style="margin-left: 1em;">electricity as a, <a href="#Page_170">170</a>;</span></li> +<li><span style="margin-left: 1em;">the source of our notion of, <a href="#Page_199">199</a>;</span></li> +<li><span style="margin-left: 1em;">rôle of the notion of, <a href="#Page_203">203</a>, <a href="#Page_244">244</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">energy conceived as a, <a href="#Page_164">164</a>, <a href="#Page_185">185</a>, <a href="#Page_244">244</a> et seq.</span></li> + +<li>Substitution-value of heat, <a href="#Page_178">178</a>, footnote.</li> + +<li>Suetonius, <a href="#Page_348">348</a>.</li> + +<li>Sulphur, specific inductive capacity of, <a href="#Page_117">117</a>.</li> + +<li>Sun, human beings could not exist on, <a href="#Page_3">3</a>.</li> + +<li>Swift, <a href="#Page_84">84</a>, <a href="#Page_280">280</a>.</li> + +<li>Swimmer, Ampère's, <a href="#Page_207">207</a>.</li> + +<li>Symmetry, definition of, <a href="#Page_92">92</a>;</li> +<li><span style="margin-left: 1em;">figures of, <a href="#Page_92">92</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">plane of, <a href="#Page_94">94</a>;</span></li> +<li><span style="margin-left: 1em;">vertical and horizontal, <a href="#Page_94">94</a>;</span></li> +<li><span style="margin-left: 1em;">in music, <a href="#Page_99">99</a> et seq.</span></li> + +<li>Sympathetic vibration, <a href="#Page_22">22</a> et seq., <a href="#Page_379">379</a>.</li> + +</ul> + +<ul class="IX"><li>Tailor, nature like a covetous, <a href="#Page_9">9</a>-<a href="#Page_10">10</a>.</li> + +<li>Tangent, the word, <a href="#Page_263">263</a>.</li> + +<li>Taste, doubtful cultivation of, by the classics, <a href="#Page_352">352</a>-<a href="#Page_353">353</a>;</li> +<li><span style="margin-left: 1em;">of the ancients, <a href="#Page_353">353</a>.</span></li> + +<li>Taylor, on the vibration of strings, <a href="#Page_249">249</a>.</li> + +<li>Teaching, its nature, <a href="#Page_366">366</a> et seq.</li> + +<li>Telegraph, the word, <a href="#Page_263">263</a>.</li> + +<li>Telescope, <a href="#Page_262">262</a>.</li> + +<li>Telestereoscope, the, <a href="#Page_84">84</a>.</li> + +<li>Temperament, even, in tuning, <a href="#Page_47">47</a>.</li> + +<li>Temperature, absolute, <a href="#Page_162">162</a>;</li> +<li><span style="margin-left: 1em;">differences of, <a href="#Page_205">205</a>;</span></li> +<li><span style="margin-left: 1em;">differences of, viewed as level surfaces, <a href="#Page_161">161</a>;</span></li> +<li><span style="margin-left: 1em;">heights of, <a href="#Page_174">174</a>;</span></li> +<li><span style="margin-left: 1em;">scale of, derived from tensions of gases, <a href="#Page_174">174</a>.</span></li> + +<li>Terence, <a href="#Page_347">347</a>.</li> + +<li>Terms, scientific, <a href="#Page_342">342</a>-<a href="#Page_343">343</a>.</li> + +<li>Thales, <a href="#Page_259">259</a>.</li> + +<li>Theories, their scope, function, and power, <a href="#Page_241">241</a>-<a href="#Page_242">242</a>;</li> +<li><span style="margin-left: 1em;">must be replaced by direct description, <a href="#Page_248">248</a>.</span></li> + +<li>Thermal, energy, <a href="#Page_174">174</a>, <a href="#Page_177">177</a>;</li> +<li><span style="margin-left: 1em;">capacity, <a href="#Page_123">123</a>, footnote.</span></li> + +<li>Thermodynamics, <a href="#Page_160">160</a> et seq.</li> + +<li>Thermoelectrometer, Riess's, <a href="#Page_133">133</a>, <a href="#Page_169">169</a>.</li> + +<li>Thing-in-itself, the, <a href="#Page_200">200</a>.</li> + +<li>Things, mental symbols for groups of sensations, <a href="#Page_200">200</a>-<a href="#Page_201">201</a>.</li> + +<li>Thomson, James, on the lowering of the freezing-point of water by pressure, <a href="#Page_162">162</a>.</li> + +<li>Thomson, W., his absolute electrometer, <a href="#Page_127">127</a>, footnote;</li> +<li><span style="margin-left: 1em;">on thermodynamics, <a href="#Page_162">162</a>;</span></li> +<li><span style="margin-left: 1em;">on the conservation of energy, <a href="#Page_165">165</a>;</span></li> +<li><span style="margin-left: 1em;">on the mechanical measures of temperature, <a href="#Page_174">174</a>, footnote;</span></li> +<li><span style="margin-left: 1em;">on waste of mechanical energy, <a href="#Page_175">175</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_108">108</a>, <a href="#Page_173">173</a>, footnote.</span></li> + +<li>Thought, habitudes of, <a href="#Page_199">199</a>, <a href="#Page_224">224</a>, <a href="#Page_227">227</a>, <a href="#Page_232">232</a>;</li> +<li><span style="margin-left: 1em;">relationship between language and, <a href="#Page_329">329</a>;</span></li> +<li><span style="margin-left: 1em;">incongruence between experience and, <a href="#Page_206">206</a>;</span></li> +<li><span style="margin-left: 1em;">luxuriance of a fully developed, <a href="#Page_58">58</a>;</span></li> +<li><span style="margin-left: 1em;">transformation in scientific, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>.</span></li> + +<li>Thoughts, their development and the struggle for existence among them, <a href="#Page_63">63</a>;</li> +<li><span style="margin-left: 1em;">importance of erroneous, <a href="#Page_65">65</a>;</span></li> +<li><span style="margin-left: 1em;">as reproductions of facts, <a href="#Page_107">107</a>.</span></li> + +<li>Thread, the individual a, on which pearls are strung, <a href="#Page_234">234</a>-<a href="#Page_235">235</a>.</li> + +<li>Tides, <a href="#Page_283">283</a>.</li> + +<li>Timbre, <a href="#Page_37">37</a>, <a href="#Page_38">38</a>, <a href="#Page_39">39</a>.</li> + +<li>Time, <a href="#Page_178">178</a>, <a href="#Page_204">204</a>, <a href="#Page_205">205</a>, footnote.</li> + +<li>Toepler and Foucault, method of, for detecting optical faults, <a href="#Page_313">313</a> et seq., <a href="#Page_320">320</a>.</li> + +<li>Tone-figures, <a href="#Page_91">91</a>.</li> + +<li>Tones, <a href="#Page_22">22</a>-<a href="#Page_47">47</a>, <a href="#Page_99">99</a> et seq., <a href="#Page_212">212</a>.</li> + +<li>Torsion, moment of, <a href="#Page_132">132</a>.</li> + +<li>Torsion-balance, Coulomb's, <a href="#Page_109">109</a>, <a href="#Page_168">168</a>.</li> + +<li>Torricelli, on virtual velocities, <a href="#Page_150">150</a>;</li> +<li><span style="margin-left: 1em;">his law of liquid efflux, <a href="#Page_150">150</a>;</span></li> +<li><span style="margin-left: 1em;">on the atmosphere, <a href="#Page_273">273</a>.</span></li> + +<li>Tourist, journey of, work of the inquirer compared to, <a href="#Page_17">17</a>, <a href="#Page_29">29</a>, <a href="#Page_30">30</a>.</li> + +<li>Transatlantic cable, <a href="#Page_108">108</a>.</li> + +<li>Transformation and adaptation in scientific thought, <a href="#Page_214">214</a>-<a href="#Page_235">235</a>.</li> + +<li>Transformation of ideas, <a href="#Page_63">63</a>.</li> + +<li>Transformative law of the energies, <a href="#Page_172">172</a>.</li> + +<li><span class="pagenum"><a name="Page_410" id="Page_410">[Pg 410]</a></span>Translation, difficulties of, <a href="#Page_354">354</a>.</li> + +<li>Tree, conceptual life compared to a, <a href="#Page_231">231</a>.</li> + +<li>Triangle, mutual dependence of the sides and angles of a, <a href="#Page_179">179</a>.</li> + +<li>Triple accord, <a href="#Page_46">46</a>.</li> + +<li>Truth, wooed by the inquirer, <a href="#Page_45">45</a>;</li> +<li><span style="margin-left: 1em;">difficulty of its acquisition, <a href="#Page_46">46</a>.</span></li> + +<li>Tumblers, resounding, <a href="#Page_23">23</a>.</li> + +<li>Tuning-forks, explanation of their motion, <a href="#Page_22">22</a> et seq.</li> + +<li>Tylor, <a href="#Page_186">186</a>.</li> + +<li>Tympanum, <a href="#Page_18">18</a>.</li> + +<li>Type, natural laws likened to, <a href="#Page_193">193</a>;</li> +<li><span style="margin-left: 1em;">words compared to, <a href="#Page_191">191</a>.</span></li> + +</ul> + +<ul class="IX"><li>Ulysses, <a href="#Page_347">347</a>.</li> + +<li>Understanding, what it means, <a href="#Page_211">211</a>.</li> + +<li>Uniforms, do not fit heads, <a href="#Page_369">369</a>.</li> + +<li>Unique determination, <a href="#Page_181">181</a>-<a href="#Page_182">182</a>.</li> + +<li>Unison, <a href="#Page_43">43</a>.</li> + +<li>Unit, electrostatic, <a href="#Page_111">111</a>.</li> +<li><span style="margin-left: 1em;">See <i>Force</i> and <i>Work</i>.</span></li> + +<li>United States, <a href="#Page_336">336</a>.</li> + +<li>Universal Real Character, a, <a href="#Page_192">192</a>.</li> + +<li>Utility of physical science, <a href="#Page_351">351</a>.</li> + +</ul> + +<ul class="IX"><li>Variation, the method of, in science, <a href="#Page_230">230</a>;</li> +<li><span style="margin-left: 1em;">in biology, <a href="#Page_216">216</a>.</span></li> + +<li>Velocity, of light, <a href="#Page_48">48</a> et seq.;</li> +<li><span style="margin-left: 1em;">of the descent of bodies, <a href="#Page_143">143</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">meaning of, <a href="#Page_204">204</a>;</span></li> +<li><span style="margin-left: 1em;">virtual, <a href="#Page_149">149</a>-<a href="#Page_155">155</a>.</span></li> + +<li><i>Verstandesbegriffe</i>, <a href="#Page_199">199</a>.</li> + +<li>Vertical, perception of the, <a href="#Page_272">272</a>, <a href="#Page_286">286</a> et seq.;</li> +<li><span style="margin-left: 1em;">symmetry, <a href="#Page_389">389</a>.</span></li> + +<li>Vertigo, <a href="#Page_285">285</a>, <a href="#Page_290">290</a>.</li> + +<li>Vestibule of the ear, <a href="#Page_300">300</a>.</li> + +<li>Vibration, <a href="#Page_22">22</a> et seq.</li> + +<li>Vibration-figures, <a href="#Page_91">91</a>.</li> + +<li>Vinci, Leonardo da, <a href="#Page_278">278</a>, <a href="#Page_283">283</a>.</li> + +<li>Violent motions, <a href="#Page_225">225</a>.</li> + +<li>Virtual velocities, <a href="#Page_149">149</a>-<a href="#Page_155">155</a>.</li> + +<li>Visibility, general conditions of, <a href="#Page_312">312</a>.</li> + +<li>Vision, symmetry of our apparatus of, <a href="#Page_96">96</a>.</li> +<li><span style="margin-left: 1em;">See <i>Eye</i>.</span></li> + +<li>Visual nerves, <a href="#Page_96">96</a>.</li> + +<li>Visualisation, mental, <a href="#Page_250">250</a>.</li> + +<li>Volt, the word, <a href="#Page_343">343</a>.</li> + +<li>Volta, <a href="#Page_127">127</a>, footnote, <a href="#Page_134">134</a>.</li> + +<li>Voltaire, <a href="#Page_260">260</a>.</li> + +<li>Voltaire's ingènu, <a href="#Page_219">219</a>.</li> + +<li>Vowels, composed of simple musical notes, <a href="#Page_26">26</a>.</li> + +</ul> + +<ul class="IX"><li>Wagner, Richard, <a href="#Page_279">279</a>.</li> + +<li>Wald, F., <a href="#Page_178">178</a>, footnote.</li> + +<li>Wallace, <a href="#Page_216">216</a>.</li> + +<li>War, and peace, reflexions upon, <a href="#Page_309">309</a>, <a href="#Page_335">335</a> et seq.</li> + +<li>Waste of mechanical energy, W. Thomson on, <a href="#Page_175">175</a>.</li> + +<li>Watches, experiment with, <a href="#Page_41">41</a>;</li> +<li><span style="margin-left: 1em;">in a mirror, <a href="#Page_93">93</a>.</span></li> + +<li>Water, jet of, resolved into drops, <a href="#Page_60">60</a>;</li> +<li><span style="margin-left: 1em;">free, solid figures of, <a href="#Page_8">8</a>;</span></li> +<li><span style="margin-left: 1em;">objects reflected in, <a href="#Page_94">94</a>, <a href="#Page_191">191</a>;</span></li> +<li><span style="margin-left: 1em;">possible modes of measurement of, <a href="#Page_170">170</a>.</span></li> + +<li>Watt, <a href="#Page_266">266</a>.</li> + +<li>Wealth, the foundation of, <a href="#Page_198">198</a>.</li> + +<li>Weapons, modern, <a href="#Page_335">335</a>.</li> + +<li>Weber, <a href="#Page_108">108</a>, <a href="#Page_306">306</a>.</li> + +<li>Weight of bodies, varies with their distance from the centre of the earth, <a href="#Page_112">112</a>.</li> + +<li>Weismann, <a href="#Page_216">216</a>.</li> + +<li>Wheatstone, his stereoscope, <a href="#Page_73">73</a>;</li> +<li><span style="margin-left: 1em;">his pseudoscope, <a href="#Page_96">96</a>;</span></li> +<li><span style="margin-left: 1em;">also <a href="#Page_59">59</a>.</span></li> + +<li>Wheel, history and importance of, <a href="#Page_61">61</a> et seq.</li> + +<li>Whewell, on the formation of science, <a href="#Page_231">231</a>.</li> + +<li>Whole, the, <a href="#Page_204">204</a>, footnote.</li> + +<li>Why, the question, <a href="#Page_199">199</a>, <a href="#Page_223">223</a>.</li> + +<li>Will, Schopenhauer on the, <a href="#Page_190">190</a>;</li> +<li><span style="margin-left: 1em;">man's most familiar source of power, <a href="#Page_243">243</a>;</span></li> +<li><span style="margin-left: 1em;">used to explain the world, <a href="#Page_186">186</a>;</span></li> +<li><span style="margin-left: 1em;">forces compared to, <a href="#Page_254">254</a>;</span></li> +<li><span style="margin-left: 1em;">compared to pressure, <a href="#Page_14">14</a>.</span></li> + +<li>Windmill, a rotating, <a href="#Page_53">53</a>.</li> + +<li>Wire frames and nets, for constructing liquid figures of equilibrium, <a href="#Page_4">4</a> et seq.</li> + +<li>Witchcraft, <a href="#Page_187">187</a>.</li> + +<li>Wollaston, <a href="#Page_284">284</a>, <a href="#Page_285">285</a>.</li> + +<li>Wonderful, science the natural foe of the, <a href="#Page_224">224</a>.</li> + +<li>Woods, the relative distance of trees in, <a href="#Page_68">68</a>.</li> + +<li>Wooer, inquirer compared to a, <a href="#Page_45">45</a>.</li> + +<li>Words and sounds, <a href="#Page_343">343</a>.</li> + +<li>Words, compared to type, <a href="#Page_191">191</a>.</li> + +<li><span class="pagenum"><a name="Page_411" id="Page_411">[Pg 411]</a></span>Work, of liquid forces of attraction, <a href="#Page_14">14</a>;</li> +<li><span style="margin-left: 1em;">in electricity, <a href="#Page_173">173</a>;</span></li> +<li><span style="margin-left: 1em;">measure of, <a href="#Page_119">119</a> et seq., <a href="#Page_130">130</a>, <a href="#Page_223">223</a>;</span></li> +<li><span style="margin-left: 1em;">relation of, with heat, <a href="#Page_162">162</a>, <a href="#Page_245">245</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">amount required to develop electricity, <a href="#Page_131">131</a> et seq.;</span></li> +<li><span style="margin-left: 1em;">produces various physical changes, <a href="#Page_139">139</a>;</span></li> +<li><span style="margin-left: 1em;">substantial conception of, <a href="#Page_183">183</a>-<a href="#Page_184">184</a>.</span></li> +<li><span style="margin-left: 1em;">See <i>Energy</i>.</span></li> + +<li>World, the, what it consists of, <a href="#Page_208">208</a>.</li> + +<li>World-particles, <a href="#Page_203">203</a>.</li> + +<li>Wronsky, <a href="#Page_172">172</a>.</li> + +<li>Wundt, on causality and the axioms of physics, <a href="#Page_157">157</a>-<a href="#Page_159">159</a>; <a href="#Page_359">359</a> footnote.</li> + +</ul> + +<ul class="IX"><li>Xenophon, <a href="#Page_49">49</a>, footnote.</li> + +</ul> + +<ul class="IX"><li>Young, Thomas, on energy, <a href="#Page_173">173</a>.</li> + +</ul> + +<ul class="IX"><li>Zelter, <a href="#Page_35">35</a>.</li> + +<li>Zeuner, <a href="#Page_171">171</a>.</li> + +<li>Zoölogy, comparison in, <a href="#Page_239">239</a>.</li></ul> + +<p><span class="pagenum"><a name="Page_412" id="Page_412">[Pg 412]</a><br /><a name="Page_413" id="Page_413">[Pg 413]</a></span></p> + +<hr class="chap" /> + + +<h2>THE SCIENCE OF MECHANICS.</h2> + +<p class="center">A CRITICAL AND HISTORICAL EXPOSITION OF ITS +PRINCIPLES.</p> + +<p class="center bold">By DR. ERNST MACH.</p> + +<p class="center small">PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE +UNIVERSITY OF VIENNA.</p> + +<p class="center">Translated from the Second German Edition<br /> +<span class="bold">By THOMAS J. McCORMACK.</span></p> + +<hr/> +<p class="center">250 Cuts. 534 Pages. Half Morocco, Gilt Top, Marginal Analyses.<br/> +Exhaustive Index. Price $2.50.</p> + + +<hr/> + +<h3><a name="TABLE_OF_CONTENTS2" id="TABLE_OF_CONTENTS2">TABLE OF CONTENTS.</a></h3> + + +<p><span class="smcap">Statics.</span></p> + +<ul class="IX"><li>The Lever.</li> + +<li>The Inclined Plane.</li> + +<li>The Composition of Forces.</li> + +<li>Virtual Velocities.</li> + +<li>Statics in Their Application to Fluids.</li> + +<li>Statics in Their Application to Gases.</li></ul> + + + +<p><span class="smcap">Dynamics.</span></p> + +<ul class="IX"><li>Galileo's Achievements.</li> + +<li>Achievements of Huygens.</li> + +<li>Achievements of Newton.</li> + +<li>Principle of Reaction.</li> + +<li>Criticism of the Principle of Reaction +and of the Concept of Mass.</li> + +<li>Newton's Views of Time, Space, and +Motion.</li> + +<li>Critique of the Newtonian Enunciations.</li> + +<li>Retrospect of the Development of +Dynamics.</li></ul> + + + +<p><span class="smcap">The Extension of the Principles of Mechanics.</span></p> + +<ul class="IX"><li>Scope of the Newtonian Principles.</li> + +<li>Formulæ and Units of Mechanics.</li> + +<li>Conservation of Momentum, Conservation +of the Centre of Gravity, +and Conservation of Areas.</li> + +<li>Laws of Impact.</li> + +<li>D'Alembert's Principle.</li> + +<li>Principle of <i>Vis Viva</i>.</li> + +<li>Principle of Least Constraint.</li> + +<li>Principle of Least Action.</li> + +<li>Hamilton's Principle.</li> + +<li>Hydrostatic and Hydrodynamic +Questions.</li></ul> + + + +<p><span class="smcap">Formal Development of Mechanics.</span></p> + +<ul class="IX"><li>The Isoperimetrical Problems.</li> + +<li>Theological, Animistic, and Mystical +Points of View in Mechanics.</li> + +<li>Analytical Mechanics.</li> + +<li>The Economy of Science.</li></ul> + + +<p><span class="smcap">The Relation of Mechanics to Other Departments of Knowledge.</span></p> + +<ul class="IX"> +<li>Relations of Mechanics to Physics.</li> + +<li>Relations of Mechanics to Physiology.</li></ul> + + +<p><span class="pagenum"><a name="Page_414" id="Page_414">[Pg 414]</a></span></p> + + + + +<h2><a name="PRESS_NOTICES" id="PRESS_NOTICES">PRESS NOTICES.</a></h2> + + +<p>"The appearance of a translation into English of this remarkable book +should serve to revivify in this country [England] the somewhat stagnating +treatment of its subject, and should call up the thoughts which puzzle us when +we think of them, and that is not sufficiently often.... Professor Mach is a +striking instance of the combination of great mathematical knowledge with +experimental skill, as exemplified not only by the elegant illustrations of mechanical +principles which abound in this treatise, but also from his brilliant +experiments on the photography of bullets.... A careful study of Professor +Mach's work, and a treatment with more experimental illustration, on the +lines laid down in the interesting diagrams of his <i>Science of Mechanics</i>, will +do much to revivify theoretical mechanical science, as developed from the +elements by rigorous logical treatment."—Prof. A. G. Greenhill, in <i>Nature</i>, +London.</p> + +<p>"Those who are curious to learn how the principles of mechanics have +been evolved, from what source they take their origin, and how far they can +be deemed of positive and permanent value, will find Dr. Mach's able treatise +entrancingly interesting.... The book is a remarkable one in many respects, +while the mixture of history with the latest scientific principles and +absolute mathematical deductions makes it exceedingly attractive."—<i>Mechanical +World</i>, Manchester and London, England.</p> + +<p>"Mach's Mechanics is unique. It is not a text-book, but forms a useful +supplement to the ordinary text-book. The latter is usually a skeleton outline, +full of mathematical symbols and other abstractions. Mach's book has +'muscle and clothing,' and being written from the historical standpoint, introduces +the leading contributors in succession, tells what they did and how +they did it, and often what manner of men they were. Thus it is that the +pages glow, as it were, with a certain humanism, quite delightful in a scientific +book.... The book is handsomely printed, and deserves a warm reception +from all interested in the progress of science."—<i>The Physical Review</i>, New +York and London.</p> + +<p>"Mr. T. J. McCormack, by his effective translation, where translation +was no light task, of this masterly treatise upon the earliest and most fundamental +of the sciences, has rendered no slight service to the English speaking +student. The German and English languages are generally accounted +second to none in their value as instruments for the expression of scientific +thought; but the conversion bodily of an abstruse work from one into the +other, so as to preserve all the meaning and spirit of the original and to set it +easily and naturally into its new form, is a task of the greatest difficulty, and<span class="pagenum"><a name="Page_415" id="Page_415">[Pg 415]</a></span> +when performed so well as in the present instance, merits great commendation. +Dr. Mach has created for his own works the severest possible standard +of judgment. To expect no more from the books of such a master than from +the elementary productions of an ordinary teacher in the science would be +undue moderation. Our author has lifted what, to many of us, was at one +time a course of seemingly unprofitable mental gymnastics, encompassed +only at vast expenditure of intellectual effort, into a study possessing a deep +philosophical value and instinct with life and interest. 'No profit grows +where is no pleasure ta'en,' and the emancipated collegian will turn with +pleasure from the narrow methods of the text-book to where the science is +made to illustrate, by a treatment at once broad and deep, the fundamental +connexion between all the physical sciences, taken together."—<i>The Mining +Journal</i>, London, England.</p> + +<p>"As a history of mechanics, the work is admirable."—<i>The Nation</i>, New +York.</p> + +<p>"An excellent book, admirably illustrated."—<i>The Literary World</i>, London, +England.</p> + +<p>"Sets forth the elements of its subject with a lucidity, clearness, and +force unknown in the mathematical text-books ... is admirably fitted to +serve students as an introduction on historical lines to the principles of mechanical +science."—<i>Canadian Mining and Mechanical Review</i>, Ottawa, Can.</p> + +<p>"A masterly book.... To any one who feels that he does not know as +much as he ought to about physics, we can commend it most heartily as a +scholarly and able treatise ... both interesting and profitable."—A. M. +Wellington, in <i>Engineering News</i>, New York.</p> + +<p>"The book as a whole is unique, and is a valuable addition to any library +of science or philosophy.... Reproductions of quaint old portraits and +vignettes give piquancy to the pages. The numerous marginal titles form a +complete epitome of the work; and there is that invaluable adjunct, a good +index. Altogether the publishers are to be congratulated upon producing a +technical work that is thoroughly attractive in its make-up."—Prof. D. W. +Hering, in <i>Science</i>.</p> + +<p>"There is one other point upon which this volume should be commended, +and that is the perfection of the translation. It is a common fault that books +of the greatest interest and value in the original are oftenest butchered or +made ridiculous by a clumsy translator. The present is a noteworthy exception."—<i>Railway +Age</i>.</p><p><span class="pagenum"><a name="Page_416" id="Page_416">[Pg 416]</a></span></p> + +<p>"The book is admirably printed and bound.... The presswork is unexcelled +by any technical books that have come to our hands for some time, +and the engravings and figures are all clearly and well executed."—<i>Railroad +Gazette</i>.</p> + + + + +<h2><a name="TESTIMONIALS_OF_PROMINENT_EDUCATORS" id="TESTIMONIALS_OF_PROMINENT_EDUCATORS">TESTIMONIALS OF PROMINENT EDUCATORS.</a></h2> + + +<p>"I am delighted with Professor Mach's <i>Science of Mechanics</i>."—<i>M. E. +Cooley</i>, Professor of Mechanical Engineering, Ann Arbor, Mich.</p> + +<p>"You have done a good service to science in publishing Mach's <i>Science +of Mechanics</i> in English. I shall take every opportunity to recommend it to +young students as a source of much interesting information and inspiration."—<i>M. +I. Pupin</i>, Professor of Mechanics, Columbia College, New York.</p> + +<p>"Mach's <i>Science of Mechanics</i> is an admirable ... book."—<i>Prof. E. A. +Fuertes</i>, Director of the College of Civil Engineering of Cornell University, +Ithaca, N. Y.</p> + +<p>"I congratulate you upon producing the work in such good style and in +so good a translation. I bought a copy of it a year ago, very shortly after you +issued it. The book itself is deserving of the highest admiration; and you +are entitled to the thanks of all English-speaking physicists for the publication +of this translation."—<i>D. W. Hering</i>, Professor of Physics, University of +the City of New York, New York.</p> + +<p>"I have read Mach's <i>Science of Mechanics</i> with great pleasure. The book +is exceedingly interesting."—<i>W. F. Magie</i>, Professor of Physics, Princeton +University, Princeton, N. J.</p> + +<p>"The <i>Science of Mechanics</i> by Mach, translated by T. J. McCormack, I +regard as a most valuable work, not only for acquainting the student with the +history of the development of Mechanics, but as serving to present to him +most favorably the fundamental ideas of Mechanics and their rational connexion +with the highest mathematical developments. It is a most profitable +book to read along with the study of a text-book of Mechanics, and I shall +take pleasure in recommending its perusal by my students."—<i>S. W. Robinson</i>, +Professor of Mechanical Engineering, Ohio State University, Columbus, Ohio.</p> + +<p>"I am delighted with Mach's 'Mechanics.' I will call the attention to +it of students and instructors who have the Mechanics or Physics to study or +teach."—<i>J. E. Davies</i>, University of Wisconsin, Madison, Wis.</p> + +<p>"There can be but one opinion as to the value of Mach's work in this +translation. No instructor in physics should be without a copy of it."—<i>Henry +Crew</i>, Professor of Physics in the Northwestern University, Evanston, Ill.</p><hr class="chap" /><p><span class="pagenum"><a name="Page_417" id="Page_417">[Pg 417]</a></span></p> + + + + +<h2><a name="POPULAR_SCIENTIFIC_LECTURES" id="POPULAR_SCIENTIFIC_LECTURES">POPULAR SCIENTIFIC LECTURES.</a></h2> + +<p class="center">A PORTRAYAL OF THE SPIRIT AND METHODS +OF SCIENCE.</p> + +<p class="center bold">By DR. ERNST MACH.</p> + +<p class="small center">PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE +UNIVERSITY OF VIENNA.</p> + +<p class="center bold">Translated by THOMAS J. McCORMACK.</p> + +<p class="center"><i>Third Edition, Revised Throughout and Greatly Enlarged.</i></p> + +<hr/> + +<p class="center">Cloth, Gilt Top. Exhaustively Indexed. Pages, 415. Cuts, 59. Price, $1.50.</p> + +<hr/> + + +<h3><a name="TITLES_OF_THE_LECTURES" id="TITLES_OF_THE_LECTURES">TITLES OF THE LECTURES.</a></h3> + + +<ul class="IX"><li>The Forms of Liquids.</li> + +<li>The Fibres of Corti.</li> + +<li>On the Causes of Harmony.</li> + +<li>On the Velocity of Light.</li> + +<li>Why Has Man Two Eyes?</li> + +<li>On Symmetry.</li> + +<li>On the Fundamental Concepts of Static Electricity.</li> + +<li>On the Principle of the Conservation of Energy.</li> + +<li>On the Economical Nature of Physical Inquiry.</li> + +<li>On the Principle of Comparison in Physics.</li> + +<li>On the Part Played by Accident in Invention and Discovery.</li> + +<li>On Sensations of Orientation.</li> + +<li>On the Relative Educational Value of the Classics and the Mathematico-Physical Sciences.</li> + +<li>A Contribution to the History of Acoustics.</li> + +<li>Remarks on the Theory of Spatial Vision.</li> + +<li>On Transformation and Adaptation in Scientific Thought.</li></ul> + + + +<h2>PRESS NOTICES.</h2> + +<p>"A most fascinating volume, treating of phenomena in which all are interested, +in a delightful style and with wonderful clearness. For lightness +of touch and yet solid value of information the chapter 'Why Has Man Two +Eyes?' has scarcely a rival in the whole realm of popular scientific writing."—<i>The +Boston Traveller</i>.</p> + +<p>"Truly remarkable in the insight they give into the relationship of the +various fields cultivated under the name of Physics.... A vein of humor is +met here and there reminding the reader of Heaviside, never offending one's +taste. These features, together with the lightness of touch with which Mr. +McCormack has rendered them, make the volume one that may be fairly +called rare. The spirit of the author is preserved in such attractive, really +delightful, English that one is assured nothing has been lost by translation."—Prof. +Henry Crew, in <i>The Astrophysical Journal</i>.</p><p><span class="pagenum"><a name="Page_418" id="Page_418">[Pg 418]</a></span></p> + +<p>"A very delightful and useful book.... The author treats some of the +most recondite problems of natural science, in so charmingly untechnical a +way, with such a wealth of bright illustration, as makes his meaning clear to +the person of ordinary intelligence and education.... This is a work that +should find a place in every library, and that people should be encouraged to +read."—<i>Daily Picayune</i>, New Orleans.</p> + +<p>"In his translation Mr. McCormack has well preserved the frank, simple, +and pleasing style of this famous lecturer on scientific topics. Professor +Mach deals with the live facts, the salient points of science, and not with its +mysticism or dead traditions. He uses the simplest of illustrations and expresses +himself clearly, tersely, and with a delightful freshness that makes +entertaining reading of what in other hands would be dull and prosy."—<i>Engineering +News</i>, N. Y.</p> + +<p>"The general reader is led by plain and easy steps along a delightful way +through what would be to him without such a help a complicated maze of +difficulties. Marvels are invented and science is revealed as the natural foe +to mysteries."—<i>The Chautauquan</i>.</p> + +<p>"The beautiful quality of the work is not marred by abstruse discussions +which would require a scientist to fathom, but is so simple and so clear that +it brings us into direct contact with the matter treated."—<i>The Boston Post</i>.</p> + +<p>"A masterly exposition of important scientific truths."—<i>Scotsman</i>, Edinburgh.</p> + +<p>"These lectures by Dr. Mach are delightfully simple and frank; there is +no dryness or darkness of technicalities, and science and common life do not +seem separated by a gulf.... The style is admirable, and the whole volume +seems gloriously alive and human."—<i>Providence Journal</i>, R. I.</p> + +<p>"The non-scientific reader who desires to learn something of modern +scientific theories, and the reasons for their existence, cannot do better than +carefully study these lectures. The English is excellent throughout, and reflects +great credit on the translator."—<i>Manufacturer and Builder</i>.</p> + +<p>"We like the quiet, considerate intelligence of these lectures."—<i>Independent</i>, +New York.</p> + +<p>"Professor Mach's lectures are so pleasantly written and illumined with +such charm of illustration that they have all the interest of lively fiction."—<i>New +York Com. Advertiser</i>.</p> + +<p>"The literary and philosophical suggestiveness of the book is very rich." +<i>Hartford Seminary Record</i>.</p><p><span class="pagenum"><a name="Page_419" id="Page_419">[Pg 419]</a></span></p> + +<p>"All are presented so skilfully that one can imagine that Professor Mach's +hearers departed from his lecture-room with the conviction that science was +a matter for abecedarians. Will please those who find the fairy tales of +science more absorbing than fiction."—<i>The Pilot</i>, Boston.</p> + +<p>"Professor Mach ... is a master in physics.... His book is a good one +and will serve a good purpose, both for instruction and suggestion."—Prof. +A. E. Dolbear, in <i>The Dial</i>.</p> + +<p>"The most beautiful ideas are unfolded in the exposition."—<i>Catholic +World</i>, New York.</p> + + + + +<h2><a name="THE_ANALYSIS_OF_THE_SENSATIONS" id="THE_ANALYSIS_OF_THE_SENSATIONS">THE ANALYSIS OF THE SENSATIONS</a></h2> + +<p class="center bold">By DR. ERNST MACH.</p> + +<p class="center small">PROFESSOR OF THE HISTORY AND THEORY OF INDUCTIVE SCIENCE IN THE +UNIVERSITY OF VIENNA.</p> + +<hr/> + +<p class="center">Pages, 208. Illustrations, 37. Indexed.</p> + +<p class="center">(Price, Cloth, $1.25.)</p> + +<hr/> + + +<h3><a name="CONTENTS" id="CONTENTS">CONTENTS.</a></h3> + + +<ul class="IX"><li>Introductory: Antimetaphysical.</li> + +<li>The Chief Points of View for the Investigation +of the Senses.</li> + +<li>The Space-Sensations of the Eye.</li> + +<li>Space-Sensation, Continued.</li> + +<li>The Relations of the Sight-Sensations +to One Another and to the +Other Psychical Elements.</li> + +<li>The Sensation of Time.</li> + +<li>The Sensation of Sound.</li> + +<li>Influence of the Preceding Investigations +on the Mode of Conceiving +Physics.</li></ul> + +<hr/> + +<p>"A wonderfully original little book. Like everything he writes a work of +genius."—<i>Prof. W. James</i> of Harvard.</p> + +<p>"I consider each work of Professor Mach a distinct acquisition to a +library of science."—<i>Prof. D. W. Hering</i>, New York University.</p> + +<p>"There is no work known to the writer which, in its general scientific +bearings, is more likely to repay richly thorough study. We are all interested +in nature in one way or another, and our interests can only be heightened +and clarified by Mach's wonderfully original and wholesome book. It is not +saying too much to maintain that every intelligent person should have a copy +of it,—and should study that copy."—<i>Prof. J. E. Trevor</i>, Cornell.</p> + +<p>"Students may here make the acquaintance of some of the open questions +of sensation and at the same time take a lesson in the charm of scientific +modesty that can hardly be excelled."—<i>Prof. E. C. Sanford</i>, Clark University.</p> + +<p>"It exhibits keen observation and acute thought, with many new and interesting +experiments by way of illustration. Moreover, the style is light +and even lively—a rare merit in a German prose work, and still rarer in a +translation of one."—<i>The Literary World</i>, London.</p> + +<hr/> + +<p class="center">CHICAGO:<br /> +<span class="bold">The Open Court Publishing Company</span><br /> +324 DEARBORN STREET.</p> + +<p class="center">LONDON: Kegan Paul, Trench, Trübner, & Company.</p><hr class="chap" /> +<p><span class="pagenum"><a name="Page_420" id="Page_420">[Pg 420]</a></span></p> + + + + +<h2><a name="CATALOGUE_OF_PUBLICATIONS" id="CATALOGUE_OF_PUBLICATIONS">CATALOGUE OF PUBLICATIONS</a></h2> + +<p class="center small">OF THE<br /> +<span class="big">OPEN COURT PUBLISHING CO.</span></p> + +<hr/> + +<p>COPE, E. D.</p> + +<blockquote><p>THE PRIMARY FACTORS OF ORGANIC EVOLUTION.</p></blockquote> + +<blockquote><p>121 cuts. Pp., xvi, 547. Cloth, $2.00, net.</p></blockquote> + +<p>MÜLLER, F. MAX.</p> + +<blockquote><p>THREE INTRODUCTORY LECTURES ON THE SCIENCE OF THOUGHT.</p></blockquote> + +<blockquote><p>With 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.</p></blockquote> + +<blockquote><p>THREE LECTURES ON THE SCIENCE OF LANGUAGE.</p></blockquote> + +<blockquote><p>The Oxford University Extension Lectures, with a Supplement, "My Predecessors." 112 pages. 2nd Edition. Cloth, 75 cents. Paper, 25c.</p></blockquote> + +<p>ROMANES, GEORGE JOHN.</p> + +<blockquote><p>DARWIN AND AFTER DARWIN.</p></blockquote> + +<blockquote><p>An Exposition of the Darwinian Theory and a Discussion of Post-Darwinian Questions. Three Vols., $4.00. Singly, as follows:</p> + +<p>1. <span class="smcap">The Darwinian Theory.</span> 460 pages. 125 illustrations. Cloth, $2.00.</p> + +<p>2. <span class="smcap">Post-Darwinian Questions.</span> Heredity and Utility. Pp. 338. $1.50.</p> + +<p>3. <span class="smcap">Post-Darwinian Questions.</span> Isolation and Physiological Selection. Pp. 181. $1.00.</p></blockquote> + +<blockquote><p>AN EXAMINATION OF WEISMANNISM.</p></blockquote> + +<blockquote><p>236 pages. Cloth, $1.00. Paper, 35c.</p></blockquote> + +<blockquote><p>THOUGHTS ON RELIGION.</p></blockquote> + +<blockquote><p>Edited by Charles Gore, M. A., Canon of Westminster. Third Edition, Pages, 184. Cloth, gilt top, $1.25.</p></blockquote> + +<p>RIBOT, TH.</p> + +<blockquote><p>THE PSYCHOLOGY OF ATTENTION.</p> + +<p>THE DISEASES OF PERSONALITY.</p> + +<p>THE DISEASES OF THE WILL.</p></blockquote> + +<blockquote><p>Authorised translations. Cloth, 75 cents each. Paper, 25 cents. <i>Full set, cloth, $1.75, net.</i></p></blockquote> + +<p>MACH, ERNST.</p> + +<blockquote><p>THE SCIENCE OF MECHANICS.</p></blockquote> + +<blockquote><p><span class="smcap">A Critical and Historical Exposition of its Principles.</span> Translated by <span class="smcap">T. J. McCormack</span>. 250 cuts. 534 pages. 1/2 m., gilt top. $2.50.</p></blockquote> + +<blockquote><p>POPULAR SCIENTIFIC LECTURES.</p></blockquote> + +<blockquote><p>Third Edition. 415 pages. 59 cuts. Cloth, gilt top. Net, $1.50.</p></blockquote> + +<blockquote><p>THE ANALYSIS OF THE SENSATIONS.</p></blockquote> + +<blockquote><p>Pp. 208. 37 cuts. Cloth, $1.25, net.</p></blockquote> + +<p>GOODWIN, REV. T. A.</p> + +<blockquote><p>LOVERS THREE THOUSAND YEARS AGO.</p></blockquote> + +<blockquote><p>As Indicated by the Song of Solomon. Pp. 41. Boards, 50c.</p></blockquote> + +<p>HOLYOAKE, G. J.</p> + +<blockquote><p>ENGLISH SECULARISM. <span class="smcap">A Confession of Belief.</span></p></blockquote> + +<blockquote><p>Pp. 146. Cloth, 50c., net.</p></blockquote> + +<p>CORNILL, CARL HEINRICH.</p> + +<blockquote><p>THE PROPHETS OF ISRAEL.</p></blockquote> + +<blockquote><p>Popular Sketches from Old Testament History. Pp., 200. Cloth, $1.00.</p></blockquote> + +<blockquote><p>THE RISE OF THE PEOPLE OF ISRAEL.</p></blockquote> + +<blockquote><p>See <i>Epitomes of Three Sciences</i>, below.</p></blockquote> + +<p>BINET, ALFRED.</p> + +<blockquote><p>THE PSYCHIC LIFE OF MICRO-ORGANISMS.</p></blockquote> + +<blockquote><p>Authorised translation. 135 pages. Cloth, 75 cents; Paper, 25 cents.</p></blockquote> + +<blockquote><p>ON DOUBLE CONSCIOUSNESS.</p></blockquote> + +<blockquote><p>Studies in Experimental Psychology. 93 pages. Paper, 15 cents.</p></blockquote><p><span class="pagenum"><a name="Page_421" id="Page_421">[Pg 421]</a></span></p> + +<p>WAGNER, RICHARD</p> + +<blockquote><p>A PILGRIMAGE TO BEETHOVEN.</p></blockquote> + +<blockquote><p>A Novelette. Frontispiece, portrait of Beethoven. Pp. 40. Boards, 50c.</p></blockquote> + +<p>WEISMANN, AUGUST.</p> + +<blockquote><p>GERMINAL SELECTION. <span class="smcap">As a Source of Definite Variation.</span></p></blockquote> + +<blockquote><p>Pp. 73. Paper, 25c.</p></blockquote> + +<p>NOIRÉ, LUDWIG.</p> + +<blockquote><p>ON THE ORIGIN OF LANGUAGE. Pp. 57. Paper, 15c.</p></blockquote> + +<p>FREYTAG, GUSTAV.</p> + +<blockquote><p>THE LOST MANUSCRIPT. A Novel.</p></blockquote> + +<blockquote><p>2 vols. 953 pages. Extra cloth, $4.00. One vol., cl., $1.00; paper, 75c.</p></blockquote> + +<blockquote><p>MARTIN LUTHER.</p></blockquote> + +<blockquote><p>Illustrated. Pp. 130. Cloth, $1.00. Paper, 25c.</p></blockquote> + +<p>HERING, EWALD.</p> + +<blockquote><p>ON MEMORY, and THE SPECIFIC ENERGIES OF THE NERVOUS +SYSTEM. Pp. 50. Paper, 15c.</p></blockquote> + +<p>TRUMBULL, M. M.</p> + +<blockquote><p>THE FREE TRADE STRUGGLE IN ENGLAND.</p></blockquote> + +<blockquote><p>Second Edition. 296 pages. Cloth, 75 cents; paper, 25 cents.</p></blockquote> + +<blockquote><p>WHEELBARROW: <span class="smcap">Articles and Discussions on the Labor Question</span>.</p></blockquote> + +<blockquote><p>With portrait of the author. 303 pages. Cloth, $1.00; paper, 35 cents.</p></blockquote> + +<blockquote><p>EARL GREY ON RECIPROCITY AND CIVIL SERVICE REFORM.</p></blockquote> + +<blockquote><p>With Comments by Gen. M. M. Trumbull. Price, 10 cents.</p></blockquote> + +<p>GOETHE AND SCHILLER'S XENIONS.</p> + +<blockquote><p>Selected and translated by Paul Carus. Album form. Pp., 162. Cl., $1.00</p></blockquote> + +<p>OLDENBERG, H.</p> + +<blockquote><p>ANCIENT INDIA: ITS LANGUAGE AND RELIGIONS.</p></blockquote> + +<blockquote><p>Pp. 100. Cloth, 50c. Paper, 25c.</p></blockquote> + +<p>CARUS, PAUL.</p> + +<blockquote><p>THE ETHICAL PROBLEM.</p></blockquote> + +<blockquote><p>90 pages. Cloth, 50 cents; Paper, 30 cents.</p></blockquote> + +<blockquote><p>FUNDAMENTAL PROBLEMS.</p></blockquote> + +<blockquote><p>Second edition, enlarged and revised. 372 pp. Cl., $1.50. Paper, 50c.</p></blockquote> + +<blockquote><p>HOMILIES OF SCIENCE.</p></blockquote> + +<blockquote><p>317 pages. Cloth, Gilt Top, $1.50.</p></blockquote> + +<blockquote><p>THE IDEA OF GOD.</p></blockquote> + +<blockquote><p>Fourth edition. 32 pages. Paper, 15 cents.</p></blockquote> + +<blockquote><p>THE SOUL OF MAN.</p></blockquote> + +<blockquote><p>With 152 cuts and diagrams. 458 pages. Cloth, $3.00.</p></blockquote> + +<blockquote><p>TRUTH IN FICTION. <span class="smcap">Twelve Tales with a Moral.</span></p></blockquote> + +<blockquote><p>Fine laid paper, white and gold binding, gilt edges. Pp. 111. $1.00.</p></blockquote> + +<blockquote><p>THE RELIGION OF SCIENCE.</p></blockquote> + +<blockquote><p>Second, extra edition. Price, 50 cents. R. S. L. edition, 25c. Pp. 103.</p></blockquote> + +<blockquote><p>PRIMER OF PHILOSOPHY.</p></blockquote> + +<blockquote><p>240 pages. Second Edition. Cloth, $1.00. Paper, 25c.</p></blockquote> + +<blockquote><p>THREE LECTURES: (1) <span class="smcap">The Philosophy of the Tool.</span> Pages, 24. Paper, +10c. (2) <span class="smcap">Our Need of Philosophy.</span> Pages, 14. Paper, 5c. (3) <span class="smcap">Science +a Religious Revelation.</span> Pages, 21. Paper, 5c.</p></blockquote> + +<blockquote><p>THE GOSPEL OF BUDDHA. According to Old Records.</p></blockquote> + +<blockquote><p>4th Edition. Pp., 275. Cloth, $1.00. Paper, 35 cents. In German, $1.25.</p></blockquote> + +<blockquote><p>BUDDHISM AND ITS CHRISTIAN CRITICS.</p></blockquote> + +<blockquote><p>Pages, 311. Cloth, $1.25.</p></blockquote> + +<blockquote><p>KARMA. <span class="smcap">A Story of Early Buddhism.</span></p></blockquote> + +<blockquote><p>Illustrated by Japanese artists. 2nd Edition. Crêpe paper, 75 cents.</p></blockquote> + +<p>GARBE, RICHARD.</p> + +<blockquote><p>THE REDEMPTION OF THE BRAHMAN. <span class="smcap">A Tale of Hindu Life.</span></p></blockquote> + +<blockquote><p>Laid paper. Gilt top. 96 pages. Price, 75c. Paper, 25c.</p></blockquote> + +<blockquote><p>THE PHILOSOPHY OF ANCIENT INDIA.</p></blockquote> + +<blockquote><p>Pp. 89. Cloth, 50c. Paper, 25c.</p></blockquote> + +<p>EPITOMES OF THREE SCIENCES.</p> + +<blockquote><p>1. <span class="smcap">The Study of Sanskrit.</span> By <i>H. Oldenberg</i>. 2. <span class="smcap">Experimental Psychology.</span> +By <i>Joseph Jastrow</i>. 3. <span class="smcap">The Rise of the People of Israel.</span> By +<i>C. H. Cornill</i>. 140 pages. Cloth, reduced to 50 cents.</p></blockquote><p><span class="pagenum"><a name="Page_422" id="Page_422">[Pg 422]</a></span></p> + + + + +<h2><a name="The_Religion_of_Science_Library" id="The_Religion_of_Science_Library">The Religion of Science Library.</a></h2> + + +<p>A collection of bi-monthly publications, most of which are reprints of +books published by The Open Court Publishing Company. Yearly, $1.50. +Separate copies according to prices quoted. The books are printed upon +good paper, from large type.</p> + +<p>The Religion of Science Library, by its extraordinarily reasonable price, +will place a large number of valuable books within the reach of all readers.</p> + +<p>The following have already appeared in the series:</p> + +<blockquote><p>No. 1. <i>The Religion of Science.</i> By <span class="smcap">Paul Carus</span>. 25c.</p> + +<p>2. <i>Three Introductory Lectures on the Science of Thought.</i> By <span class="smcap">F. Max Müller</span>. 25c.</p> + +<p>3. <i>Three Lectures on the Science of Language.</i> By <span class="smcap">F. Max Müller</span>. 25c.</p> + +<p>4. <i>The Diseases of Personality.</i> By <span class="smcap">Th. Ribot</span>. 25c.</p> + +<p>5. <i>The Psychology of Attention.</i> By <span class="smcap">Th. Ribot</span>. 25c.</p> + +<p>6. <i>The Psychic Life of Micro-Organisms.</i> By <span class="smcap">Alfred Binet</span>. 25c.</p> + +<p>7. <i>The Nature of the State.</i> By <span class="smcap">Paul Carus</span>. 15c.</p> + +<p>8. <i>On Double Consciousness.</i> By <span class="smcap">Alfred Binet</span>. 15c.</p> + +<p>9. <i>Fundamental Problems.</i> By <span class="smcap">Paul Carus</span>. 50c.</p> + +<p>10. <i>The Diseases of the Will.</i> By <span class="smcap">Th. Ribot</span>. 25c.</p> + +<p>11. <i>The Origin of Language.</i> By <span class="smcap">Ludwig Noire</span>. 15c.</p> + +<p>12. <i>The Free Trade Struggle in England.</i> By <span class="smcap">M. M. Trumbull</span>. 25c.</p> + +<p>13. <i>Wheelbarrow on the Labor Question.</i> By <span class="smcap">M. M. Trumbull</span>. 35c.</p> + +<p>14. <i>The Gospel of Buddha.</i> By <span class="smcap">Paul Carus</span>. 35c.</p> + +<p>15. <i>The Primer of Philosophy.</i> By <span class="smcap">Paul Carus</span>. 25c.</p> + +<p>16. <i>On Memory</i>, and <i>The Specific Energies of the Nervous System</i>. By <span class="smcap">Prof. Ewald Hering</span>. 15c.</p> + +<p>17. <i>The Redemption of the Brahman.</i> A Tale of Hindu Life. By <span class="smcap">Richard Garbe</span>. 25c.</p> + +<p>18. <i>An Examination of Weismannism.</i> By <span class="smcap">G. J. Romanes</span>. 35c.</p> + +<p>19. <i>On Germinal Selection.</i> By <span class="smcap">August Weismann</span>. 25c.</p> + +<p>20. <i>Lovers Three Thousand Years Ago.</i> By <span class="smcap">T. A. Goodwin</span>. 15c.</p> + +<p>21. <i>Popular Scientific Lectures.</i> By <span class="smcap">Ernst Mach</span>. 50c.</p> + +<p>22. <i>Ancient India: Its Language and Religions.</i> By <span class="smcap">H. Oldenberg</span>. 25c.</p> + +<p>23. <i>The Prophets of Ancient Israel.</i> By <span class="smcap">Prof. C. H. Cornill</span>. 25c.</p> + +<p>24. <i>Homilies of Science.</i> By <span class="smcap">Paul Carus</span>. 35c.</p> + +<p>25. <i>Thoughts on Religion.</i> By <span class="smcap">G. J. Romanes</span>. 50 cents.</p> + +<p>26. <i>The Philosophy of Ancient India.</i> By <span class="smcap">Prof. Richard Garbe</span>. 25c.</p> + +<p>27. <i>Martin Luther.</i> By <span class="smcap">Gustav Freytag</span>. 25c.</p> + +<p>28. <i>English Secularism.</i> By <span class="smcap">George Jacob Holyoake</span>. 25c.</p> + +<p>29. <i>On Orthogenesis.</i> By <span class="smcap">Th. Eimer</span>. 25c.</p> + +<p>30. <i>Chinese Philosophy.</i> By <span class="smcap">Paul Carus</span>. 25c.</p> + +<p>31. <i>The Lost Manuscript.</i> By <span class="smcap">Gustav Freytag</span>. 60c.</p></blockquote> +<p><span class="pagenum"><a name="Page_423" id="Page_423">[Pg 423]</a></span></p> +<hr class="tb" /> + +<p class="center">THE OPEN COURT PUBLISHING CO.</p> + +<p class="center"><span class="smcap">324 Dearborn Street, Chicago, Ill.</span><br /> +LONDON: Kegan Paul, Trench, Trübner & Co</p> + +<hr class="chap" /> + + +<h2><a name="THE_OPEN_COURT" id="THE_OPEN_COURT">THE OPEN COURT</a></h2> + +<p class="center small">A MONTHLY MAGAZINE</p> + +<p class="center bold">Devoted to the Science of Religion, the Religion of Science, and +the Extension of the Religious Parliament Idea.</p> + + +<p><i>THE OPEN COURT</i> does not understand by religion any creed or dogmatic +belief, but man's world-conception in so far as it regulates his conduct.</p> + +<p>The old dogmatic conception of religion is based upon the science of past +ages; to base religion upon the maturest and truest thought of the present +time is the object of <i>The Open Court</i>. Thus, the religion of <i>The Open Court</i> is +the Religion of Science, that is, the religion of verified and verifiable truth.</p> + +<p>Although opposed to irrational orthodoxy and narrow bigotry, <i>The Open +Court</i> does not attack the properly religious element of the various religions. +It criticises their errors unflinchingly but without animosity, and endeavors +to preserve of them all that is true and good.</p> + +<p>The current numbers of <i>The Open Court</i> contain valuable original articles +from the pens of distinguished thinkers. Accurate and authorised translations +are made in Philosophy, Science, and Criticism from the literature of +Continental Europe, and reviews of noteworthy recent investigations are presented. +Portraits of eminent philosophers and scientists are published, and +appropriate illustrations accompany some of the articles.</p> + +<p>Terms: $1.00 a year; $1.35 to foreign countries in the Postal Union. +Single Copies, 10 cents.</p> + + +<h2>THE MONIST</h2> + +<p class="center smalL">A QUARTERLY MAGAZINE OF</p> + +<p class="center">PHILOSOPHY AND SCIENCE.</p> + + +<p><i>THE MONIST</i> discusses the fundamental problems of Philosophy in +their practical relations to the religious, ethical, and sociological questions +of the day. The following have contributed to its columns:</p> + +<ul class="IX"> +<li><span class="smcap">Prof. Joseph Le Conte</span>,</li> +<li><span class="smcap">Dr. W. T. Harris</span>,</li> +<li><span class="smcap">M. D. Conway</span>,</li> +<li><span class="smcap">Charles S. Peirce</span>,</li> +<li><span class="smcap">Prof. F. Max Müller</span>,</li> +<li><span class="smcap">Prof. E. D. Cope</span>,</li> +<li><span class="smcap">Carus Sterne</span>,</li> +<li><span class="smcap">Mrs. C. Ladd Franklin</span>,</li> +<li><span class="smcap">Prof. Max Verworn</span>,</li> +<li><span class="smcap">Prof. Felix Klein</span>,</li> +<li><span class="smcap">Prof. G. J. Romanes</span>,</li> +<li><span class="smcap">Prof. C. Lloyd Morgan</span>,</li> +<li><span class="smcap">James Sully</span>,</li> +<li><span class="smcap">B. Bosanquet</span>,</li> +<li><span class="smcap">Dr. A. Binet</span>,</li> +<li><span class="smcap">Prof. Ernst Mach</span>,</li> +<li><span class="smcap">Rabbi Emil Hirsch</span>,</li> +<li><span class="smcap">Lester F. Ward</span>,</li> +<li><span class="smcap">Prof. H. Schubert</span>,</li> +<li><span class="smcap">Dr. Edm. Montgomery</span>,</li> +<li><span class="smcap">Prof. C. Lombroso</span>,</li> +<li><span class="smcap">Prof. E. Haeckel</span>,</li> +<li><span class="smcap">Prof. H. Höffding</span>,</li> +<li><span class="smcap">Dr. F. Oswald</span>,</li> +<li><span class="smcap">Prof. J. Delbœuf</span>,</li> +<li><span class="smcap">Prof. F. Jodl</span>,</li> +<li><span class="smcap">Prof. H. M. Stanley</span>,</li> +<li><span class="smcap">G. Ferrero</span>,</li> +<li><span class="smcap">J. Venn</span>,</li> +<li><span class="smcap">Prof. H. von Holst</span>.</li> +</ul> + + +<p>Per Copy, 50 cents; Yearly, $2.00. In England and all countries in U.P.U. +per Copy, 2s 6d; Yearly, 9s 6d.</p> + +<hr class="tb" /> + +<p class="center">CHICAGO</p> + +<p class="center big">THE OPEN COURT PUBLISHING CO.,</p> + +<p class="center">Monon Building, 324 Dearborn St.,<br /> +LONDON: Kegan Paul, Trench, Trübner & Co.</p> + +<hr class="tb" /> +<p>FOOTNOTES:</p> + +<div class="footnote"><p><a name="Footnote_1_1" id="Footnote_1_1"></a><a href="#FNanchor_1_1"><span class="label">[1]</span></a> <i>Statique expérimentale et théorique des liquids</i>, 1873. See also <i>The Science +of Mechanics</i>, p. 384 et seqq., The Open Court Publishing Co., Chicago, 1893.</p></div> + +<div class="footnote"><p><a name="Footnote_2_2" id="Footnote_2_2"></a><a href="#FNanchor_2_2"><span class="label">[2]</span></a> Compare Mach, <i>Ueber die Molecularwirkung der Flüssigkeiten</i>, Reports +of the Vienna Academy, 1862.</p></div> + +<div class="footnote"><p><a name="Footnote_3_3" id="Footnote_3_3"></a><a href="#FNanchor_3_3"><span class="label">[3]</span></a> In almost all branches of physics that are well worked out such maximal +and minimal problems play an important part.</p></div> + +<div class="footnote"><p><a name="Footnote_4_4" id="Footnote_4_4"></a><a href="#FNanchor_4_4"><span class="label">[4]</span></a> Compare Mach, <i>Vorträge über Psychophysik</i>, Vienna, 1863, page 41; <i>Compendium +der Physik für Mediciner</i>, Vienna, 1863, page 234; and also <i>The Science +of Mechanics</i>, Chicago, 1893, pp. 84 and 464.</p></div> + +<div class="footnote"><p><a name="Footnote_5_5" id="Footnote_5_5"></a><a href="#FNanchor_5_5"><span class="label">[5]</span></a> Like reflexions are found in Quételet, <i>Du système sociale</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_6_6" id="Footnote_6_6"></a><a href="#FNanchor_6_6"><span class="label">[6]</span></a> For the full development of this idea see the essay "On the Economical +Nature of Physical Inquiry," p. 186, and the chapter on "The Economy of +Science," in my <i>Mechanics</i> (Chicago: The Open Court Publishing Company, +1893), p. 481.</p></div> + +<div class="footnote"><p><a name="Footnote_7_7" id="Footnote_7_7"></a><a href="#FNanchor_7_7"><span class="label">[7]</span></a> Science may be regarded as a maximum or minimum problem, exactly +as the business of the merchant. In fact, the intellectual activity of natural +inquiry is not so greatly different from that exercised in ordinary life as is +usually supposed.</p></div> + +<div class="footnote"><p><a name="Footnote_8_8" id="Footnote_8_8"></a><a href="#FNanchor_8_8"><span class="label">[8]</span></a> This experiment, with its associated reflexions, is due to Galileo.</p></div> + +<div class="footnote"><p><a name="Footnote_9_9" id="Footnote_9_9"></a><a href="#FNanchor_9_9"><span class="label">[9]</span></a> A development of the theory of musical audition differing in many +points from the theory of Helmholtz here expounded, will be found in my +<i>Contributions to the Analysis of the Sensations</i> (English translation by C. M. +Williams), Chicago, The Open Court Publishing Company, 1897.</p></div> + +<div class="footnote"><p><a name="Footnote_10_10" id="Footnote_10_10"></a><a href="#FNanchor_10_10"><span class="label">[10]</span></a> Sauveur also set out from Leibnitz's idea, but arrived by independent +researches at a different theory, which was very near to that of Helmholtz. +Compare on this point Sauveur, <i>Mémoires de l'Académie des Sciences</i>, Paris, +1700-1705, and R. Smith, <i>Harmonics</i>, Cambridge, 1749. (See <i>Appendix</i>, p. 346.)</p></div> + +<div class="footnote"><p><a name="Footnote_11_11" id="Footnote_11_11"></a><a href="#FNanchor_11_11"><span class="label">[11]</span></a> According to Mr. Jules Andrieu, the idea that nature must be tortured +to reveal her secrets is preserved in the name <i>crucible</i>—from the Latin <i>crux</i>, +a cross. But, more probably, <i>crucible</i> is derived from some Old French or +Teutonic form, as <i>cruche</i>, <i>kroes</i>, <i>krus</i>, etc., a pot or jug (cf. Modern English +<i>crock</i>, <i>cruse</i>, and German <i>Krug</i>).—<i>Trans.</i></p></div> + +<div class="footnote"><p><a name="Footnote_12_12" id="Footnote_12_12"></a><a href="#FNanchor_12_12"><span class="label">[12]</span></a> Xenophon, Memorabilia iv, 7, puts into the mouth of Socrates these +words: οὔτε γὰρ εὑρετὰ ἀνθρώποις αὐτὰ ἐνόμιζεν εἶναι, οὔτε χαρίζεσθαι +θεοῖς ἂν ἡγεῖτο τὸν ζητοῦντα ἃ ἐκεῖνοι σαφηνίσαι οὐκ ἐβουλήθησαν.</p></div> + +<div class="footnote"><p><a name="Footnote_13_13" id="Footnote_13_13"></a><a href="#FNanchor_13_13"><span class="label">[13]</span></a> Galilei, <i>Discorsi e dimostrazione matematiche</i>. Leyden, 1638. <i>Dialogo +Primo.</i></p></div> + +<div class="footnote"><p><a name="Footnote_14_14" id="Footnote_14_14"></a><a href="#FNanchor_14_14"><span class="label">[14]</span></a> In the same way, the pitch of a locomotive-whistle is higher as the +locomotive rapidly approaches an observer, and lower when rapidly leaving +him than if the locomotive were at rest.—<i>Trans.</i></p></div> + +<div class="footnote"><p><a name="Footnote_15_15" id="Footnote_15_15"></a><a href="#FNanchor_15_15"><span class="label">[15]</span></a> A kilometre is 0.621 or nearly five-eighths of a statute mile.</p></div> + +<div class="footnote"><p><a name="Footnote_16_16" id="Footnote_16_16"></a><a href="#FNanchor_16_16"><span class="label">[16]</span></a> Observe, also, the respect in which the wheel is held in India, Japan +and other Buddhistic countries, as the emblem of power, order, and law, and +of the superiority of mind over matter. The consciousness of the importance of +this invention seems to have lingered long in the minds of these nations.—<i>Tr.</i></p></div> + +<div class="footnote"><p><a name="Footnote_17_17" id="Footnote_17_17"></a><a href="#FNanchor_17_17"><span class="label">[17]</span></a> This effect is particularly noticeable in the size of workmen on high +chimneys and church-steeples—"steeple Jacks." When the cables were slung +from the towers of the Brooklyn bridge (277 feet high), the men sent out in +baskets to paint them, appeared, against the broad background of heaven and +water, like flies.—<i>Trans.</i></p></div> + +<div class="footnote"><p><a name="Footnote_18_18" id="Footnote_18_18"></a><a href="#FNanchor_18_18"><span class="label">[18]</span></a> See Joh. Müller, <i>Vergleichende Physiologie des Gesichtssinnes</i>, Leipsic, +1826.</p></div> + +<div class="footnote"><p><a name="Footnote_19_19" id="Footnote_19_19"></a><a href="#FNanchor_19_19"><span class="label">[19]</span></a> Delivered before the German Casino of Prague, in the winter of 1871. +</p> +<p> +A fuller treatment of the problems of this lecture will be found in my <i>Contributions +to the Analysis of the Sensations</i> (Jena, 1886), English Translation, +Chicago, 1895. J. P. Soret, <i>Sur la perception du beau</i> (Geneva, 1892), also regards +repetition as a principle of æsthetics. His discussions of the <i>æsthetical</i> +side of the subject are much more detailed than mine. But with respect to +the psychological and physiological foundation of the principle, I am convinced +that the <i>Contributions to the Analysis of the Sensations</i> go deeper.—<span class="smcap">Mach</span> +(1894).</p></div> + +<div class="footnote"><p><a name="Footnote_20_20" id="Footnote_20_20"></a><a href="#FNanchor_20_20"><span class="label">[20]</span></a> Kant, in his <i>Prolegomena zu jeder künftigen Metaphysik</i>, also refers to +this fact, but for a different purpose.</p></div> + +<div class="footnote"><p><a name="Footnote_21_21" id="Footnote_21_21"></a><a href="#FNanchor_21_21"><span class="label">[21]</span></a> Compare Mach, <i>Fichte's Zeitschrift für Philosophie</i>, 1864, p. 1.</p></div> + +<div class="footnote"><p><a name="Footnote_22_22" id="Footnote_22_22"></a><a href="#FNanchor_22_22"><span class="label">[22]</span></a> The fact that the first and second differential coefficients of a curve are +directly seen, but the higher coefficients not, is very simply explained. The +first gives the position of the tangent, the declination of the straight line from +the position of symmetry, the second the declination of the curve from the +straight line. It is, perhaps, not unprofitable to remark here that the ordinary +method of testing rulers and plane surfaces (by reversed applications) +ascertains the deviation of the object from symmetry to itself.</p></div> + +<div class="footnote"><p><a name="Footnote_23_23" id="Footnote_23_23"></a><a href="#FNanchor_23_23"><span class="label">[23]</span></a> See the lecture <i>On the Causes of Harmony</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_24_24" id="Footnote_24_24"></a><a href="#FNanchor_24_24"><span class="label">[24]</span></a> A. von Oettingen, <i>Harmoniesystem in dualer Entwicklung</i>. Leipsic and +Dorpat, 1866.</p></div> + +<div class="footnote"><p><a name="Footnote_25_25" id="Footnote_25_25"></a><a href="#FNanchor_25_25"><span class="label">[25]</span></a> Compare Mach's <i>Zur Theorie des Gehörorgans</i>, Vienna Academy, 1863.</p></div> + +<div class="footnote"><p><a name="Footnote_26_26" id="Footnote_26_26"></a><a href="#FNanchor_26_26"><span class="label">[26]</span></a> A lecture delivered at the International Electrical Exhibition, in Vienna, +on September 4, 1883.</p></div> + +<div class="footnote"><p><a name="Footnote_27_27" id="Footnote_27_27"></a><a href="#FNanchor_27_27"><span class="label">[27]</span></a> If the two bodies were oppositely electrified they would exert attractions +upon each other.</p></div> + +<div class="footnote"><p><a name="Footnote_28_28" id="Footnote_28_28"></a><a href="#FNanchor_28_28"><span class="label">[28]</span></a> The quantity which flows off is in point of fact less than <i>q</i>. It would be +equal to the quantity <i>q</i> only if the inner coating of the jar were wholly encompassed +by the outer coating.</p></div> + +<div class="footnote"><p><a name="Footnote_29_29" id="Footnote_29_29"></a><a href="#FNanchor_29_29"><span class="label">[29]</span></a> Rigorously, of course, this is not correct. First, it is to be noted that the +jar <i>L</i> is discharged simultaneously with the electrode of the machine. The +jar <i>F</i>, on the other hand, is always discharged simultaneously with the outer +coating of the jar <i>L</i>. Hence, if we call the capacity of the electrode of the +machine <i>E</i>, that of the unit jar <i>L</i>, that of the outer coating of <i>L</i>, <i>A</i>, and that of +the principal jar <i>F</i>, then this equation would exist for the example in the text: +(<i>F</i> + <i>A</i>)/(<i>L</i> + <i>E</i>) = 5. A cause of further departure from absolute exactness is +the residual charge.</p></div> + +<div class="footnote"><p><a name="Footnote_30_30" id="Footnote_30_30"></a><a href="#FNanchor_30_30"><span class="label">[30]</span></a> Making allowance for the corrections indicated in the preceding footnote, +I have obtained for the dielectric constant of sulphur the number 3.2, +which agrees practically with the results obtained by more delicate methods. +For the highest attainable precision one should by rights immerse the two +plates of the condenser first wholly in air and then wholly in sulphur, if the +ratio of the capacities is to correspond to the dielectric constant. In point of +fact, however, the error which arises from inserting simply a plate of sulphur +that exactly fills the space between the two plates, is of no consequence.</p></div> + +<div class="footnote"><p><a name="Footnote_31_31" id="Footnote_31_31"></a><a href="#FNanchor_31_31"><span class="label">[31]</span></a> As this definition in its simple form is apt to give rise to misunderstandings, +elucidations are usually added to it. It is clear that we cannot lift a +quantity of electricity to <i>K</i>, without changing the distribution on <i>K</i> and the +potential on <i>K</i>. Hence, the charges on <i>K</i> must be conceived as fixed, and so +small a quantity raised that no appreciable change is produced by it. Taking +the work thus expended as many times as the small quantity in question is +contained in the unit of quantity, we shall obtain the potential. The potential +of a body <i>K</i> may be briefly and precisely defined as follows: If we expend +the element of work <i>dW</i> to raise the element of positive quantity <i>dQ</i> from the +earth to the conductor, the potential of a conductor <i>K</i> will be given by <i>V</i> = +<i>dW</i>/<i>dQ</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_32_32" id="Footnote_32_32"></a><a href="#FNanchor_32_32"><span class="label">[32]</span></a> In this article the solidus or slant stroke is used for the usual fractional +sign of division. Where plus or minus signs occur in the numerator or denominator, +brackets or a vinculum is used.—<i>Tr.</i></p></div> + +<div class="footnote"><p><a name="Footnote_33_33" id="Footnote_33_33"></a><a href="#FNanchor_33_33"><span class="label">[33]</span></a> A sort of agreement exists between the notions of thermal and electrical +capacity, but the difference between the two ideas also should be carefully +borne in mind. The thermal capacity of a body depends solely upon that body +itself. The electrical capacity of a body <i>K</i> is influenced by all bodies in its +vicinity, inasmuch as the charge of these bodies is able to alter the potential +of <i>K</i>. To give, therefore, an unequivocal significance to the notion of the capacity +(<i>C</i>) of a body <i>K</i>, <i>C</i> is defined as the relation <i>Q</i>/<i>V</i> for the body <i>K</i> in a +certain given position of all neighboring bodies, and during connexion of all +neighboring conductors with the earth. In practice the situation is much +simpler. The capacity, for example, of a jar, the inner coating of which is +almost enveloped by its outer coating, communicating with the ground, is not +sensibly affected by charged or uncharged adjacent conductors.</p></div> + +<div class="footnote"><p><a name="Footnote_34_34" id="Footnote_34_34"></a><a href="#FNanchor_34_34"><span class="label">[34]</span></a> These formulæ easily follow from Newton's theorem that a homogeneous +spherical shell, whose elements obey the law of the inverse squares, exerts no +force whatever on points within it but acts on points without as if the whole +mass were concentrated at its centre. The formulæ next adduced also flow +from this proposition.</p></div> + +<div class="footnote"><p><a name="Footnote_35_35" id="Footnote_35_35"></a><a href="#FNanchor_35_35"><span class="label">[35]</span></a> The energy of a sphere of radius <i>r</i> charged with the quantity <i>q</i> is +1/2(<i>q</i><sup>2</sup>/<i>r</i>). If the radius increase by the space <i>dr</i> a loss of energy occurs, and +the work done is 1/2(<i>q</i><sup>2</sup>/<i>r</i><sup>2</sup>)<i>dr</i>. Letting <i>p</i> denote the uniform electrical pressure +on unit of surface of the sphere, the work done is also 4<i>r</i><sup>2</sup>π<i>pdr</i>. Hence +<i>p</i> = (1/8<i>r</i><sup>2</sup>π)(<i>q</i><sup>2</sup>/<i>r</i><sup>2</sup>). Subjected to the same superficial pressure on all sides, +say in a fluid, our half sphere would be an equilibrium. Hence we must make +the pressure <i>p</i> act on the surface of the great circle to obtain the effect on the +balance, which is <i>r</i><sup>2</sup>π<i>p</i> = 1/8(<i>q</i><sup>2</sup>/<i>r</i><sup>2</sup>) = 1/8<i>V</i><sup>2</sup>.</p></div> + +<div class="footnote"><p><a name="Footnote_36_36" id="Footnote_36_36"></a><a href="#FNanchor_36_36"><span class="label">[36]</span></a> The arrangement described is for several reasons not fitted for the actual +measurement of potential. Thomson's absolute electrometer is based upon +an ingenious modification of the electrical balance of Harris and Volta. Of +two large plane parallel plates, one communicates with the earth, while the +other is brought to the potential to be measured. A small movable superficial +portion <i>f</i> of this last hangs from the balance for the determination of the +attraction <i>P</i>. The distance of the plates from each other being <i>D</i> we get <i>V</i> = +<i>D</i>√(8π<i>P</i>/<i>f</i>).</p></div> + +<div class="footnote"><p><a name="Footnote_37_37" id="Footnote_37_37"></a><a href="#FNanchor_37_37"><span class="label">[37]</span></a> This moment of torsion needs a supplementary correction, on account of +the vertical electric attraction of the excited disks. This is done by changing +the weight of the disk by means of additional weights and by making a second +reading of the angles of deflexion.</p></div> + +<div class="footnote"><p><a name="Footnote_38_38" id="Footnote_38_38"></a><a href="#FNanchor_38_38"><span class="label">[38]</span></a> The jar in our experiment acts like an accumulator, being charged by a +dynamo machine. The relation which obtains between the expended and the +available work may be gathered from the following simple exposition. A +Holtz machine <i>H</i> (Fig. 40) is charging a unit jar <i>L</i>, which after <i>n</i> discharges +of quantity <i>q</i> and potential <i>v</i>, charges the jar <i>F</i> with the quantity <i>Q</i> at the potential +<i>V</i>. The energy of the unit-jar discharges is lost and that of the jar <i>F</i> +alone is left. Hence the ratio of the available work to the total work expended +is +</p> +<p> +<i>½QV/[½QV + (n/2)qv]</i> and as <i>Q</i> = <i>nq</i>, also <i>V/(V + v)</i>. +</p> + +<p> +If, now, we interpose no unit jar, still the parts of the machine and the wires +of conduction are themselves virtually such unit jars and the formula still +subsists <i>V</i>/(<i>V</i> + Σ<i>v</i>), in which Σ<i>v</i> represents the sum of all the successively introduced +differences of potential in the circuit of connexion.</p></div> + +<div class="footnote"><p><a name="Footnote_39_39" id="Footnote_39_39"></a><a href="#FNanchor_39_39"><span class="label">[39]</span></a> Published in Vol. 5, No. I, of <i>The Monist</i>, October, 1894, being in part +a re-elaboration of the treatise <i>Ueber die Erhaltung der Arbeit</i>, Prague, 1872.</p></div> + +<div class="footnote"><p><a name="Footnote_40_40" id="Footnote_40_40"></a><a href="#FNanchor_40_40"><span class="label">[40]</span></a> <i>On Matter, Living Force, and Heat</i>, Joule: <i>Scientific Papers</i>, London, +1884, I, p. 265.</p></div> + +<div class="footnote"><p><a name="Footnote_41_41" id="Footnote_41_41"></a><a href="#FNanchor_41_41"><span class="label">[41]</span></a> "Atqui hoc si sit, globorum series sive corona eundem situm cum priore +habebit, eademque de causa octo globi sinistri ponderosiores erunt sex dextris, +ideoque rursus octo illi descendent, sex illi ascendent, istique globi ex sese +<i>continuum et aeternum motum efficient, quod est falsum</i>."</p></div> + +<div class="footnote"><p><a name="Footnote_42_42" id="Footnote_42_42"></a><a href="#FNanchor_42_42"><span class="label">[42]</span></a> "A igitur, (si ullo modo per naturam fieri possit) locum sibi tributum +non servato, ac delabatur in <i>D</i>; quibus positis aqua quae ipsi <i>A</i> succedit eandem +ob causam deffluet in <i>D</i>, eademque ab alia istinc expelletur, atque adeo +aqua haec (cum ubique eadem ratio sit) <i>motum instituet perpetuum, quod absurdum +fuerit</i>."</p></div> + +<div class="footnote"><p><a name="Footnote_43_43" id="Footnote_43_43"></a><a href="#FNanchor_43_43"><span class="label">[43]</span></a> "Accipio, gradus velocitatis ejusdem mobilis super diversas planorum +inclinationes acquisitos tunc esse aequales, cum eorundum planorum elevationes +aequales sint."</p></div> + +<div class="footnote"><p><a name="Footnote_44_44" id="Footnote_44_44"></a><a href="#FNanchor_44_44"><span class="label">[44]</span></a> "Voi molto probabilmente discorrete, ma oltre al veri simile voglio con +una esperienza crescer tanto la probabilità, che poco gli manchi all'agguagliarsi +ad una ben necessaria dimostrazione. Figuratevi questo foglio essere +una parete eretta all'orizzonte, e da un chiodo fitto in essa pendere una palla +di piombo d'un'oncia, o due, sospesa dal sottil filo <i>AB</i> lungo due, o tre braccia +perpendicolare all'orizzonte, e nella parete segnate una linea orizontale <i>DC</i> +segante a squadra il perpendicolo <i>AB</i>, il quale sia lontano dalla parete due +dita in circa, trasferendo poi il filo <i>AB</i> colla palla in <i>AC</i>, lasciata essa palla in +libertà, la quale primieramente vedrete scendere descrivendo l'arco <i>CBD</i>, e +di tanto trapassare il termine <i>B</i>, che scorrendo per l'arco <i>BD</i> sormonterà fino +quasi alla segnata parallela <i>CD</i>, restando di per vernirvi per piccolissimo intervallo, +toltogli il precisamente arrivarvi dall'impedimento dell'aria, e del +filo. Dal che possiamo veracemente concludere, che l'impeto acquistato nel +punto <i>B</i> dalla palla nello scendere per l'arco <i>CB</i>, fu tanto, che bastò a risospingersi +per un simile arco <i>BD</i> alla medesima altezza; fatta, e più volte reiterata +cotale esperienza, voglio, che fiechiamo nella parete rasente al perpendicolo +<i>AB</i> un chiodo come in <i>E</i>, ovvero in <i>F</i>, che sporga in fuori cinque, o +sei dita, e questo acciocchè il filo <i>AC</i> tornando come prima a riportar la palla +<i>C</i> per l'arco <i>CB</i>, giunta che ella sia in <i>B</i>, inoppando il filo nel chiodo <i>E</i>, sia +costretta a camminare per la circonferenza <i>BG</i> descritta in torno al centro <i>E</i>, +dal che vedremo quello, che potrà far quel medesimo impeto, che dianzi concepizo +nel medesimo termine <i>B</i>, sospinse l'istesso mobile per l'arco <i>ED</i> all'altezza +dell'orizzonale <i>CD</i>. Ora, Signori, voi vedrete con gusto condursi la +palla all'orizzontale nel punto <i>G</i>, e l'istesso accadere, l'intoppo si metesse +più basso, come in <i>F</i>, dove la palla descriverebbe l'arco <i>BJ</i>, terminando sempre +la sua salita precisamente nella linea <i>CD</i>, e quando l'intoppe del chiodo +fusse tanto basso, che l'avanzo del filo sotto di lui non arivasse all'altezza di +<i>CD</i> (il che accaderebbe, quando fusse più vicino al punto <i>B</i>, che al segamento +dell' <i>AB</i> coll'orizzontale <i>CD</i>), allora il filo cavalcherebbe il chiodo, e +segli avolgerebbe intorno. Questa esperienza non lascia luogo di dubitare +della verità del supposto: imperocchè essendo li due archi <i>CB</i>, <i>DB</i> equali e +similmento posti, l'acquisto di momento fatto per la scesa nell'arco <i>CB</i>, è il +medesimo, che il fatto per la scesa dell'arco <i>DB</i>; ma il momento acquistato +in <i>B</i> per l'arco <i>CB</i> è potente a risospingere in su il medesimo mobile per l'arco +<i>BD</i>; adunque anco il momento acquistato nella scesa <i>DB</i> è eguale a quello, +che sospigne l'istesso mobile pel medesimo arco da <i>B</i> in <i>D</i>, sicche universal-mente +ogni memento acquistato per la scesa d'un arco è eguale a quello, che +può far risalire l'istesso mobile pel medesimo arco: ma i momenti tutti che +fanno resalire per tutti gli archi <i>BD</i>, <i>BG</i>, <i>BJ</i> sono eguali, poichè son fatti +dal istesso medesimo momento acquistato per la scesa <i>CB</i>, come mostra +l'esperienza: adunque tutti i momenti, che si acquistano per le scese negli +archi <i>DB</i>, <i>GB</i>, <i>JB</i> sono eguali."</p></div> + +<div class="footnote"><p><a name="Footnote_45_45" id="Footnote_45_45"></a><a href="#FNanchor_45_45"><span class="label">[45]</span></a> "Constat jam, quod mobile ex quiete in <i>A</i> descendens per <i>AB</i>, gradus +acquirit velocitatis juxta temporis ipsius incrementum: gradum vero in <i>B</i> +esse maximum acquisitorum, et suapte natura immutabiliter impressum, sublatis +scilicet causis accelerationis novae, aut retardationis: accelerationis inquam, +si adhuc super extenso plano ulterius progrederetur; retardationis +vero, dum super planum acclive <i>BC</i> fit reflexio: in horizontali autem <i>GH</i> +aequabilis motus juxta gradum velocitatis ex <i>A</i> in <i>B</i> acquisitae in infinitum +extenderetur."</p></div> + +<div class="footnote"><p><a name="Footnote_46_46" id="Footnote_46_46"></a><a href="#FNanchor_46_46"><span class="label">[46]</span></a> "Si gravitas non esset, neque aër motui corporum officeret, unumquodque +eorum, acceptum semel motum continuaturum velocitate aequabili, secundum +lineam rectam."</p></div> + +<div class="footnote"><p><a name="Footnote_47_47" id="Footnote_47_47"></a><a href="#FNanchor_47_47"><span class="label">[47]</span></a> "Si pondera quotlibet, vi gravitatis suae, moveri incipiant; non posse +centrum gravitatis ex ipsis compositae altius, quam ubi incipiente motu reperiebatur, +ascendere. +</p> +<p> +"Ipsa vero hypothesis nostra quominus scrupulum moveat, nihil aliud +sibi velle ostendemus, quam, quod nemo unquam negavit, gravia nempe sursum +non ferri.—Et sane, si hac eadem uti scirent novorum operum machinatores, +qui motum perpetuum irrito conatu moliuntur, facile suos ipsi errores +deprehenderent, intelligerentque rem eam mechanica ratione haud quaquam +possibilem esse."</p></div> + +<div class="footnote"><p><a name="Footnote_48_48" id="Footnote_48_48"></a><a href="#FNanchor_48_48"><span class="label">[48]</span></a> "Si pendulum e pluribus ponderibus compositum, atque e quiete dimissum, +partem quamcunque oscillationis integrae confecerit, atque inde porro +intelligantur pondera ejus singula, relicto communi vinculo, celeritates acquisitas +sursum convertere, ac quousque possunt ascendere; hoc facto centrum +gravitatis ex omnibus compositae, ad eandem altitudinem reversum erit, quam +ante inceptam oscillationem obtinebat."</p></div> + +<div class="footnote"><p><a name="Footnote_49_49" id="Footnote_49_49"></a><a href="#FNanchor_49_49"><span class="label">[49]</span></a> "Notato autem hic illud staticum axioma etiam locum habere: +</p> + +<div class="poem"><div class="stanza"> +<span class="i0">"Ut spatium agentis ad spatium patientis<br /></span> +<span class="i0">Sic potentia patientis ad potentiam agentis."<br /></span> +</div></div> +</div> + +<div class="footnote"><p><a name="Footnote_50_50" id="Footnote_50_50"></a><a href="#FNanchor_50_50"><span class="label">[50]</span></a> "Cependant, comme dans cet ouvrage on ne fut d'abord attentif qu'à +considérer ce beau développement de la mécanique qui semblait sortir tout +entière d'une seule et même formule, on crut naturellement que la science etait +faite, et qu'il ne restait plus qu'à chercher la démonstration du principe des +vitesses virtuelles. Mais cette recherche ramena toutes les difficultés qu'on +avait franchies par le principe même. Cette loi si générale, où se mêlent des +idées vagues et étrangères de mouvements infinement petits et de perturbation +d'équilibre, ne fit en quelque sorte que s'obsurcir à l'examen; et le livre de +Lagrange n'offrant plus alors rien de clair que la marche des calculs, on vit +bien que les nuages n'avaient paru levé sur le cours de la mécanique que +parcequ'ils étaient, pour ainsi dire, rassemblés à l'origine même do cette +science. +</p> +<p> +"Une démonstration générale du principe des vitesses virtuelles devait +au fond revenir a établir le mécanique entière sur une autre base: car la demonstration +d'une loi qui embrasse toute une science ne peut être autre chose +qua la reduction de cette science à une autre loi aussi générale, mais évidente, +ou du moins plus simple que la première, et qui partant la rende inutile."</p></div> + +<div class="footnote"><p><a name="Footnote_51_51" id="Footnote_51_51"></a><a href="#FNanchor_51_51"><span class="label">[51]</span></a> <i>Traité de la lumière</i>, Leyden, 1690, p. 2.</p></div> + +<div class="footnote"><p><a name="Footnote_52_52" id="Footnote_52_52"></a><a href="#FNanchor_52_52"><span class="label">[52]</span></a> "L'on ne sçaurait douter que la lumière ne consiste dans le <i>mouvement</i> de +certaine matière. Car soit qu'on regarde sa production, on trouve qu'içy sur +la terre c'est principalement le feu et la flamme qui l'engendrent, lesquels +contient sans doute des corps qui sont dans un mouvement rapide, puis qu'ils +dissolvent et fondent plusieurs autres corps des plus solides: soit qu'on regarde +ses effets, on voit que quand la lumière est ramasseé, comme par des +miroires concaves, elle a la vertu de brûler comme le feu. c-est-à-dire qu'elle +desunit les parties des corps; ce qui marque assurément du <i>mouvement</i>, au +moins dans la <i>vraye Philosophie</i>, dans laquelle on conçoit la cause de tous les +effets naturels par des raisons de <i>mechanique</i>. Ce qu'il faut faire à mon avis, +ou bien renoncer à tout espérance de jamais rien comprendre dans la Physique."</p></div> + +<div class="footnote"><p><a name="Footnote_53_53" id="Footnote_53_53"></a><a href="#FNanchor_53_53"><span class="label">[53]</span></a> <i>Sur la puissance motrice du feu</i>. (Paris, 1824.)</p></div> + +<div class="footnote"><p><a name="Footnote_54_54" id="Footnote_54_54"></a><a href="#FNanchor_54_54"><span class="label">[54]</span></a> "On objectra peut-être ici que le mouvement perpétuel, démontré impossible +par les <i>seules actions mécaniques</i>, ne l'est peut-être pas lorsqu'on +emploie l'influence soit de la <i>chaleur</i>, soit de l'électricité; mais pent-on concevoir +les phénomènes de la chaleur et de l'électricité comme dus à autre +chose qu'à des <i>mouvements quelconques des corps</i> et comme tels ne doivent-ils +pas être soumis aux lois générales de la mécanique?"</p></div> + +<div class="footnote"><p><a name="Footnote_55_55" id="Footnote_55_55"></a><a href="#FNanchor_55_55"><span class="label">[55]</span></a> By this is meant the temperature of a Celsius scale, the zero of which is +273° below the melting-point of ice.</p></div> + +<div class="footnote"><p><a name="Footnote_56_56" id="Footnote_56_56"></a><a href="#FNanchor_56_56"><span class="label">[56]</span></a> I first drew attention to this fact in my treatise <i>Ueber die Erhaltung der +Arbeit</i>, Prague, 1872. Before this, Zeuner had pointed out the analogy between +mechanical and thermal energy. I have given a more extensive development +of this idea in a communication to the <i>Sitzungsberichte der Wiener</i> +<i>Akademie</i>, December, 1892, entitled <i>Geschichte und Kritik des Carnot'schen +Wärmegesetzes</i>. Compare also the works of Popper (1884), Helm (1887), +Wronsky (1888), and Ostwald (1892).</p></div> + +<div class="footnote"><p><a name="Footnote_57_57" id="Footnote_57_57"></a><a href="#FNanchor_57_57"><span class="label">[57]</span></a> Sir William Thomson first consciously and intentionally introduced +(1848, 1851) a <i>mechanical</i> measure of temperature similar to the electric measure +of potential.</p></div> + +<div class="footnote"><p><a name="Footnote_58_58" id="Footnote_58_58"></a><a href="#FNanchor_58_58"><span class="label">[58]</span></a> Compare my <i>Analysis of the Sensations</i>, Jena, 1886: English translation, +Chicago, 1897.</p></div> + +<div class="footnote"><p><a name="Footnote_59_59" id="Footnote_59_59"></a><a href="#FNanchor_59_59"><span class="label">[59]</span></a> A better terminology appears highly desirable in the place of the usual +misleading one. Sir William Thomson (1852) appears to have felt this need, +and it has been clearly expressed by F. Wald (1889). We should call the work +which corresponds to a vanished quantity of heat its mechanical substitution-value; +while that work which can be <i>actually</i> performed in the passage of a +thermal condition <i>A</i> to a condition <i>B</i>, alone deserves the name of the <i>energy-value</i> +of this change of condition. In this way the <i>arbitrary</i> substantial conception +of the processes would be preserved and misapprehensions forestalled.</p></div> + +<div class="footnote"><p><a name="Footnote_60_60" id="Footnote_60_60"></a><a href="#FNanchor_60_60"><span class="label">[60]</span></a> An address delivered before the anniversary meeting of the Imperial +Academy of Sciences, at Vienna, May 25, 1882.</p></div> + +<div class="footnote"><p><a name="Footnote_61_61" id="Footnote_61_61"></a><a href="#FNanchor_61_61"><span class="label">[61]</span></a> <i>Primitive Culture.</i></p></div> + +<div class="footnote"><p><a name="Footnote_62_62" id="Footnote_62_62"></a><a href="#FNanchor_62_62"><span class="label">[62]</span></a> Tylor, <i>loc. cit.</i></p></div> + +<div class="footnote"><p><a name="Footnote_63_63" id="Footnote_63_63"></a><a href="#FNanchor_63_63"><span class="label">[63]</span></a> <i>Essai philosophique sur les probabilités</i>. 6th Ed. Paris, 1840, p. 4. The +necessary consideration of the initial velocities is lacking in this formulation.</p></div> + +<div class="footnote"><p><a name="Footnote_64_64" id="Footnote_64_64"></a><a href="#FNanchor_64_64"><span class="label">[64]</span></a> <i>Principien der Wirthschaftslehre</i>, Vienna, 1873.</p></div> + +<div class="footnote"><p><a name="Footnote_65_65" id="Footnote_65_65"></a><a href="#FNanchor_65_65"><span class="label">[65]</span></a> It is clear from this that all so-called elementary (differential) laws involve +a relation to the whole.</p></div> + +<div class="footnote"><p><a name="Footnote_66_66" id="Footnote_66_66"></a><a href="#FNanchor_66_66"><span class="label">[66]</span></a> If it be objected, that in the case of perturbations of the velocity of rotation +of the earth, we could be sensible of such perturbations, and being obliged +to have some measure of time, we should resort to the period of vibration of +the waves of sodium light,—all that this would show is that for practical reasons +we should select that event which best served us as the <i>simplest</i> common +measure of the others.</p></div> + +<div class="footnote"><p><a name="Footnote_67_67" id="Footnote_67_67"></a><a href="#FNanchor_67_67"><span class="label">[67]</span></a> Measurement, in fact, is the definition of one phenomenon by another +(standard) phenomenon.</p></div> + +<div class="footnote"><p><a name="Footnote_68_68" id="Footnote_68_68"></a><a href="#FNanchor_68_68"><span class="label">[68]</span></a> I have represented the point of view here taken for more than thirty +years and developed it in various writings (<i>Erhaltung der Arbeit</i>, 1872, parts +of which are published in the article on <i>The Conservation of Energy</i> in this +collection; <i>The Forms of Liquids</i>, 1872, also published in this collection; and +the <i>Bewegungsempfindungen</i>, 1875). The idea, though known to philosophers, +is unfamiliar to the majority of physicists. It is a matter of deep regret to me, +therefore, that the title and author of a small tract which accorded with my +views in numerous details and which I remember having caught a glance of +in a very busy period (1879-1880), have so completely disappeared from my +memory that all efforts to obtain a clue to them have hitherto been fruitless.</p></div> + +<div class="footnote"><p><a name="Footnote_69_69" id="Footnote_69_69"></a><a href="#FNanchor_69_69"><span class="label">[69]</span></a> Inaugural Address, delivered on assuming the Rectorate of the University +of Prague, October 18, 1883. +</p> +<p> +The idea presented in this essay is neither new nor remote. I have touched +upon it myself on several occasions (first in 1867), but have never made it the +subject of a formal disquisition. Doubtless, others, too, have treated it; it +lies, so to speak, in the air. However, as many of my illustrations were well +received, although known only in an imperfect form from the lecture itself +and the newspapers, I have, contrary to my original intention, decided to +publish it. It is not my intention to trespass here upon the domain of biology. +My statements are to be taken merely as the expression of the fact that no one +can escape the influence of a great and far-reaching idea.</p></div> + +<div class="footnote"><p><a name="Footnote_70_70" id="Footnote_70_70"></a><a href="#FNanchor_70_70"><span class="label">[70]</span></a> At first sight an apparent contradiction arises from the admission of both +heredity and adaptation; and it is undoubtedly true that a strong disposition +to heredity precludes great capability of adaptation. But imagine the organism +to be a plastic mass which retains the form transmitted to it by former +influences until new influences modify it; the <i>one</i> property of <i>plasticity</i> will +then represent capability of adaptation as well as power of heredity. Analogous +to this is the case of a bar of magnetised steel of high coercive force: +the steel retains its magnetic properties until a new force displaces them. +Take also a body in motion: the body retains the velocity acquired in (<i>inherited</i> +from) the interval of time just preceding, except it be changed in the +next moment by an accelerating force. In the case of the body in motion the +<i>change</i> of velocity (<i>Abänderung</i>) was looked upon as a matter of course, while +the discovery of the principle of <i>inertia</i> (or persistence) created surprise; in +Darwin's case, on the contrary, <i>heredity</i> (or persistence) was taken for granted, +while the principle of <i>variation</i> (<i>Abänderung</i>) appeared novel. +</p> +<p> +Fully adequate views are, of course, to be reached only by a study of the +original facts emphasised by Darwin, and not by these analogies. The example +referring to motion, if I am not mistaken, I first heard, in conversation, +from my friend J. Popper, Esq., of Vienna. +</p> +<p> +Many inquirers look upon the stability of the species as something settled, +and oppose to it the Darwinian theory. But the stability of the species is itself +a "theory." The essential modifications which Darwin's views also are +undergoing will be seen from the works of Wallace [and Weismann], but more +especially from a book of W. H. Rolph, <i>Biologische Probleme</i>, Leipsic, 1882. +Unfortunately, this last talented investigator is no longer numbered among +the living.</p></div> + +<div class="footnote"><p><a name="Footnote_71_71" id="Footnote_71_71"></a><a href="#FNanchor_71_71"><span class="label">[71]</span></a> Written in 1883.</p></div> + +<div class="footnote"><p><a name="Footnote_72_72" id="Footnote_72_72"></a><a href="#FNanchor_72_72"><span class="label">[72]</span></a> See Pfaundler, <i>Pogg. Ann., Jubelband</i>, p. 182.</p></div> + +<div class="footnote"><p><a name="Footnote_73_73" id="Footnote_73_73"></a><a href="#FNanchor_73_73"><span class="label">[73]</span></a> See the beautiful discussions of this point in Hering's <i>Memory as a General +Function of Organised Matter</i> (1870), Chicago, The Open Court Publishing +Co., 1887. Compare also Dubois, <i>Ueber die Uebung</i>, Berlin, 1881.</p></div> + +<div class="footnote"><p><a name="Footnote_74_74" id="Footnote_74_74"></a><a href="#FNanchor_74_74"><span class="label">[74]</span></a> Spencer, <i>The Principles of Psychology</i>. London, 1872.</p></div> + +<div class="footnote"><p><a name="Footnote_75_75" id="Footnote_75_75"></a><a href="#FNanchor_75_75"><span class="label">[75]</span></a> See the article <i>The Velocity of Light</i>, page 63.</p></div> + +<div class="footnote"><p><a name="Footnote_76_76" id="Footnote_76_76"></a><a href="#FNanchor_76_76"><span class="label">[76]</span></a> I am well aware that the endeavor to confine oneself in natural research +to <i>facts</i> is often censured as an exaggerated fear of metaphysical spooks. +But I would observe, that, judged by the mischief which they have wrought, +the metaphysical, of all spooks, are the least fabulous. It is not to be denied +that many forms of thought were not originally acquired by the individual, but +were antecedently formed, or rather prepared for, in the development of the +species, in some such way as Spencer, Haeckel, Hering, and others have +supposed, and as I myself have hinted on various occasions.</p></div> + +<div class="footnote"><p><a name="Footnote_77_77" id="Footnote_77_77"></a><a href="#FNanchor_77_77"><span class="label">[77]</span></a> Compare, for example, <i>Schiller, Zerstreute Betrachtungen über verschiedene +ästhetische Gegenstände</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_78_78" id="Footnote_78_78"></a><a href="#FNanchor_78_78"><span class="label">[78]</span></a> We must not be deceived in imagining that the happiness of other people +is not a very considerable and essential portion of our own. It is common +capital, which cannot be created by the individual, and which does not perish +with him. The formal and material limitation of the <i>ego</i> is necessary and sufficient +only for the crudest practical objects, and cannot subsist in a broad conception. +Humanity in its entirety may be likened to a polyp-plant. The +material and organic bonds of individual union have, indeed, been severed; +they would only have impeded freedom of movement and evolution. But the +ultimate aim, the psychical connexion of the whole, has been attained in a +much higher degree through the richer development thus made possible.</p></div> + +<div class="footnote"><p><a name="Footnote_79_79" id="Footnote_79_79"></a><a href="#FNanchor_79_79"><span class="label">[79]</span></a> C. E. von Baer, the subsequent opponent of Darwin and Haeckel, has +discussed in two beautiful addresses (<i>Das allgemeinste Gesetz der Natur in +aller Entwickelung</i>, and <i>Welche Auffassung der lebenden Natur ist die richtige, +und wie ist diese Auffassung auf die Entomologie anzuwenden</i>?) the +narrowness of the view which regards an animal in its existing state as +finished and complete, instead of conceiving it as a phase in the series of evolutionary +forms and regarding the species itself as a phase of the development +of the animal world in general.</p></div> + +<div class="footnote"><p><a name="Footnote_80_80" id="Footnote_80_80"></a><a href="#FNanchor_80_80"><span class="label">[80]</span></a> An address delivered before the General Session of the German Association +of Naturalists and Physicians, at Vienna, Sept. 24, 1894.</p></div> + +<div class="footnote"><p><a name="Footnote_81_81" id="Footnote_81_81"></a><a href="#FNanchor_81_81"><span class="label">[81]</span></a> Inaugural lecture delivered on assuming the Professorship of the History +and Theory of Inductive Science in the University of Vienna, October +21, 1895.</p></div> + +<div class="footnote"><p><a name="Footnote_82_82" id="Footnote_82_82"></a><a href="#FNanchor_82_82"><span class="label">[82]</span></a> The phrase is, <i>Er hat das Pulver nicht erfunden</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_83_83" id="Footnote_83_83"></a><a href="#FNanchor_83_83"><span class="label">[83]</span></a> "Quod si quis tanta industria exstitisset, ut ex naturae principiis at geometria +hanc rem eruere potuisset, eum ego supra mortalium sortem ingenio +valuisse dicendum crederem. Sed hoc tantum abest, ut fortuito reperti artificii +rationem non adhuc satis explicari potuerint viri doctissimi."—Hugenii +Dioptrica (de telescopiis).</p></div> + +<div class="footnote"><p><a name="Footnote_84_84" id="Footnote_84_84"></a><a href="#FNanchor_84_84"><span class="label">[84]</span></a> I must not be understood as saying that the fire-drill has played no part +in the worship of fire or of the sun.</p></div> + +<div class="footnote"><p><a name="Footnote_85_85" id="Footnote_85_85"></a><a href="#FNanchor_85_85"><span class="label">[85]</span></a> Compare on this point the extremely interesting remarks of Dr. Paul +Carus in his <i>Philosophy of the Tool</i>, Chicago, 1893.</p></div> + +<div class="footnote"><p><a name="Footnote_86_86" id="Footnote_86_86"></a><a href="#FNanchor_86_86"><span class="label">[86]</span></a> Möbius, <i>Naturwissenschaftlicher Verein für Schleswig-Holstein</i>, Kiel, +1893, p. 113 et seq.</p></div> + +<div class="footnote"><p><a name="Footnote_87_87" id="Footnote_87_87"></a><a href="#FNanchor_87_87"><span class="label">[87]</span></a> I am indebted for this observation to Professor Hatscheck.</p></div> + +<div class="footnote"><p><a name="Footnote_88_88" id="Footnote_88_88"></a><a href="#FNanchor_88_88"><span class="label">[88]</span></a> Cf. Hoppe, <i>Entdecken und Finden</i>, 1870.</p></div> + +<div class="footnote"><p><a name="Footnote_89_89" id="Footnote_89_89"></a><a href="#FNanchor_89_89"><span class="label">[89]</span></a> See the lecture "Sensations of Orientation," p. 282 et seq.</p></div> + +<div class="footnote"><p><a name="Footnote_90_90" id="Footnote_90_90"></a><a href="#FNanchor_90_90"><span class="label">[90]</span></a> This story was related to me by Jolly, and subsequently repeated in a +letter from him.</p></div> + +<div class="footnote"><p><a name="Footnote_91_91" id="Footnote_91_91"></a><a href="#FNanchor_91_91"><span class="label">[91]</span></a> I do not know whether Swift's academy of schemers in Lagado, in +which great discoveries and inventions were made by a sort of verbal game +of dice, was intended as a satire on Francis Bacon's method of making discoveries +by means of huge synoptic tables constructed by scribes. It certainly +would not have been ill-placed.</p></div> + +<div class="footnote"><p><a name="Footnote_92_92" id="Footnote_92_92"></a><a href="#FNanchor_92_92"><span class="label">[92]</span></a> "Crescunt disciplinae lente tardeque; per varios errores sero pervenitur +ad veritatem. Omnia praeparata esse debent diuturno et assiduo labore +ad introitum veritatis novae. Jam illa certo temporis momento divina quadam +necessitate coacta emerget." +</p> +<p> +Quoted by Simony, <i>In ein ringförmiges Band einen Knoten zu machen</i>, +Vienna, 1881, p. 41.</p></div> + +<div class="footnote"><p><a name="Footnote_93_93" id="Footnote_93_93"></a><a href="#FNanchor_93_93"><span class="label">[93]</span></a> A lecture delivered on February 24, 1897, before the <i>Verein zur Verbreitung +naturwissenschaftlicher Kenntnisse in Wien</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_94_94" id="Footnote_94_94"></a><a href="#FNanchor_94_94"><span class="label">[94]</span></a> Wollaston, <i>Philosophical Transactions, Royal Society</i>, 1810. In the same +place Wollaston also describes and explains the creaking of the muscles. +My attention was recently called to this work by Dr. W. Pascheles.—Cf. also +Purkinje, <i>Prager medicin</i>. <i>Jahrbücher</i>, Bd. 6, Wien, 1820.</p></div> + +<div class="footnote"><p><a name="Footnote_95_95" id="Footnote_95_95"></a><a href="#FNanchor_95_95"><span class="label">[95]</span></a> Similarly many external forces do not act at once on all parts of the +earth, and the internal forces which produce deformations act at first immediately +only upon limited parts. If the earth were a feeling being, the tides +and other terrestrial events would provoke in it similar sensations to those +of our movements. Perhaps the slight alterations of the altitude of the +pole which are at present being studied are connected with the continual +slight deformations of the central ellipsoid occasioned by seismical happenings.</p></div> + +<div class="footnote"><p><a name="Footnote_96_96" id="Footnote_96_96"></a><a href="#FNanchor_96_96"><span class="label">[96]</span></a> For the popular explanation by unconscious inference the matter is extremely +simple. We regard the railway carriage as vertical and unconsciously +infer the inclination of the trees. Of course the opposite conclusion that we +regard the trees as vertical and infer the inclination of the carriage, unfortunately, +is equally clear on this theory.</p></div> + +<div class="footnote"><p><a name="Footnote_97_97" id="Footnote_97_97"></a><a href="#FNanchor_97_97"><span class="label">[97]</span></a> It will be observed that my way of thinking and experimenting here is +related to that which led Knight to the discovery and investigation of the +geotropism of plants. <i>Philosophical Transactions</i>, January 9, 1806. The relations +between vegetable and animal geotropism have been more recently investigated +by J. Loeb.</p></div> + +<div class="footnote"><p><a name="Footnote_98_98" id="Footnote_98_98"></a><a href="#FNanchor_98_98"><span class="label">[98]</span></a> This experiment is doubtless related to the galvanotropic experiment +with the larvæ of frogs described ten years later by L. Hermann. Compare +on this point my remarks in the <i>Anzeiger der Wiener Akademie</i>, 1886, No. 21. +Recent experiments in galvanotropism are due to J. Loeb.</p></div> + +<div class="footnote"><p><a name="Footnote_99_99" id="Footnote_99_99"></a><a href="#FNanchor_99_99"><span class="label">[99]</span></a> <i>Wiener Akad.</i>, 6 November, 1873.</p></div> + +<div class="footnote"><p><a name="Footnote_100_100" id="Footnote_100_100"></a><a href="#FNanchor_100_100"><span class="label">[100]</span></a> <i>Wiener Gesellschaft der Aerzte</i>, 14 November, 1874.</p></div> + +<div class="footnote"><p><a name="Footnote_101_101" id="Footnote_101_101"></a><a href="#FNanchor_101_101"><span class="label">[101]</span></a> I have made a contribution to this last question in my <i>Analysis of the +Sensations</i>, (1886), English translation, 1897.</p></div> + +<div class="footnote"><p><a name="Footnote_102_102" id="Footnote_102_102"></a><a href="#FNanchor_102_102"><span class="label">[102]</span></a> In my <i>Grundlinien der Lehre von den Bewegungsempfindungen</i>, 1875, +the matter occupying lines 4 to 13 of page 20 from below, which rests on an +error, is, as I have also elsewhere remarked, to be stricken out. For another +experiment related to that of Foucault, compare my <i>Mechanics</i>, p. 303.</p></div> + +<div class="footnote"><p><a name="Footnote_103_103" id="Footnote_103_103"></a><a href="#FNanchor_103_103"><span class="label">[103]</span></a> <i>Anzeiger der Wiener Akad.</i>, 30 December, 1875.</p></div> + +<div class="footnote"><p><a name="Footnote_104_104" id="Footnote_104_104"></a><a href="#FNanchor_104_104"><span class="label">[104]</span></a> The experiment was specially interesting for me as I had already attempted +in 1874, although with very little confidence and without success, to +excite electromagnetically my own labyrinth through which I had caused a +current to pass.</p></div> + +<div class="footnote"><p><a name="Footnote_105_105" id="Footnote_105_105"></a><a href="#FNanchor_105_105"><span class="label">[105]</span></a> Perhaps the discussion concerning the peculiarity of cats always falling +on their feet, which occupied the Parisian Academy, and, incidentally, Parisian +society a few years ago, will be remembered here. I believe that the +questions which arose are disposed of by the considerations advanced in my +<i>Bewegungsempfindungen</i> (1875). I also partly gave, as early as 1866, the apparatus +conceived by the Parisian scientists to illustrate the phenomena in +question. One difficulty was left untouched in the Parisian debate. The +otolith apparatus of the cat can render it no service in <i>free</i> descent. The +cat, however, while at rest, doubtless knows its position in space and is instinctively +conscious of the amount of movement which will put it on its feet.</p></div> + +<div class="footnote"><p><a name="Footnote_106_106" id="Footnote_106_106"></a><a href="#FNanchor_106_106"><span class="label">[106]</span></a> See the Appendix to the English edition of my <i>Analysis of the Sensations</i>, +Chicago, 1897.</p></div> + +<div class="footnote"><p><a name="Footnote_107_107" id="Footnote_107_107"></a><a href="#FNanchor_107_107"><span class="label">[107]</span></a> Compare my <i>Analysis of Sensations</i>, p. 123 ff.</p></div> + +<div class="footnote"><p><a name="Footnote_108_108" id="Footnote_108_108"></a><a href="#FNanchor_108_108"><span class="label">[108]</span></a> E. H. Weber, <i>De aure et auditu hominis et animalium</i>, Lipsiae, 1820.</p></div> + +<div class="footnote"><p><a name="Footnote_109_109" id="Footnote_109_109"></a><a href="#FNanchor_109_109"><span class="label">[109]</span></a> Störensen, <i>Journ. Anat. Phys.</i>, London, Vol. 29 (1895).</p></div> + +<div class="footnote"><p><a name="Footnote_110_110" id="Footnote_110_110"></a><a href="#FNanchor_110_110"><span class="label">[110]</span></a> A lecture delivered on Nov. 10, 1897.</p></div> + +<div class="footnote"><p><a name="Footnote_111_111" id="Footnote_111_111"></a><a href="#FNanchor_111_111"><span class="label">[111]</span></a> Christiansen, <i>Wiedemann's Annalen</i>, XXIII. S. 298, XXIV., p. 439 (1884-1885).</p></div> + +<div class="footnote"><p><a name="Footnote_112_112" id="Footnote_112_112"></a><a href="#FNanchor_112_112"><span class="label">[112]</span></a> The German phrase is <i>Schlierenmethode</i>, by which term the method is +known even by American physicists. It is also called in English the "shadow-method." +But a term is necessary which will cover all the derivatives, and +so we have employed alternatively the words <i>striate</i> and <i>differential</i>. The +etymology of <i>schlieren</i>, it would seem, is uncertain. Its present use is derived +from its technological signification in glass-manufacturing, where by <i>die +Schlieren</i> are meant the wavy streaks and imperfections in glass. Hence its +application to the method for detecting small optical <i>differences</i> and faults +generally. Professor Crew of Evanston suggests to the translator that <i>schlieren</i> +may be related to our <i>slur</i> (L. G., <i>slüren</i>, to trail, to draggle), a conjecture +which is doubtless correct and agrees both with the meaning of <i>schlieren</i> as +given in the large German dictionaries and with the intransitive use of our +own verb <i>slur</i>, the faults in question being conceived as "trailings," "streakings," +etc.—<i>Trans.</i></p></div> + +<div class="footnote"><p><a name="Footnote_113_113" id="Footnote_113_113"></a><a href="#FNanchor_113_113"><span class="label">[113]</span></a> An address delivered before the Congress of Delegates of the German +Realschulmännerverein, at Dortmund, April 16, 1886. The full title of the +address reads: "On the Relative Educational Value of the Classics and the +Mathematico-Physical Sciences in Colleges and High Schools." +</p> +<p> +Although substantially contained in an address which I was to have made +at the meeting of Natural Scientists at Salzburg in 1881 (deferred on account +of the Paris Exposition), and in the Introduction to a course of lectures on +"Physical Instruction in Preparatory Schools," which I delivered in 1883, the +invitation of the German Realschulmännerverein afforded me the first opportunity +of putting my views upon this subject before a large circle of readers. +Owing to the place and circumstances of delivery, my remarks apply of course, +primarily, only to German schools, but, with slight modifications, made in +this translation, are not without force for the institutions of other countries. +In giving here expression to a strong personal conviction formed long ago, it +is a matter of deep satisfaction to me to find that they agree in many points +with the views recently advanced in independent form by Paulsen (<i>Geschichte +des gelehrten Unterrichts</i>, Leipsic, 1885) and Frary (<i>La question du latin</i>, +Paris, Cerf, 1885). It is not my desire nor effort here to say much that is new, +but merely to contribute my mite towards bringing about the inevitable revolution +now preparing in the world of elementary instruction. In the opinion +of experienced educationists the first result of that revolution will be to make +Greek and mathematics alternately optional subjects in the higher classes of +the German Gymnasium and in the corresponding institutions of other countries, +as has been done in the splendid system of instruction in Denmark. The +gap between the German classical Gymnasium and the German Realgymnasium, +or between classical and scientific schools generally, can thus be bridged +over, and the remaining inevitable transformations will then be accomplished +in relative peace and quiet. (Prague, May, 1886.)</p></div> + +<div class="footnote"><p><a name="Footnote_114_114" id="Footnote_114_114"></a><a href="#FNanchor_114_114"><span class="label">[114]</span></a> Maupertuis, <i>Œuvres</i>, Dresden, 1752, p. 339.</p></div> + +<div class="footnote"><p><a name="Footnote_115_115" id="Footnote_115_115"></a><a href="#FNanchor_115_115"><span class="label">[115]</span></a> F. Paulsen, <i>Geschichte des gelehrten Unterrichts</i>, Leipsic, 1885.</p></div> + +<div class="footnote"><p><a name="Footnote_116_116" id="Footnote_116_116"></a><a href="#FNanchor_116_116"><span class="label">[116]</span></a> There is a peculiar irony of fate in the fact that while Leibnitz was casting +about for a new vehicle of universal linguistic intercourse, the Latin language +which still subserved this purpose the best of all, was dropping more +and more out of use, and that Leibnitz himself contributed not the least to +this result.</p></div> + +<div class="footnote"><p><a name="Footnote_117_117" id="Footnote_117_117"></a><a href="#FNanchor_117_117"><span class="label">[117]</span></a> As a rule, the human brain is too much, and wrongly, burdened with +things which might be more conveniently and accurately preserved in books +where they could be found at a moment's notice. In a recent letter to me +from Düsseldorf, Judge Hartwich writes: +</p> +<p> +"A host of words exist which are out and out Latin or Greek, yet are employed +with perfect correctness by people of good education who never had +the good luck to be taught the ancient languages. For example, words like +'dynasty.' ... The child learns such words as parts of the common stock of +speech, or even as parts of his mother-tongue, just as he does the words +'father,' 'mother,' 'bread,' 'milk.' Does the ordinary mortal know the etymology +of these Saxon words? Did it not require the almost incredible +industry of the Grimms and other Teutonic philologists to throw the merest +glimmerings of light upon the origin and growth of our own mother-tongue? +Besides, do not thousands of people of so-called classical education use +every moment hosts of words of foreign origin whose derivation they do not +know? Very few of them think it worth while to look up such words in the +dictionaries, although they love to maintain that people should study the +ancient languages for the sake of etymology alone."</p></div> + +<div class="footnote"><p><a name="Footnote_118_118" id="Footnote_118_118"></a><a href="#FNanchor_118_118"><span class="label">[118]</span></a> Standing remote from the legal profession I should not have ventured to +declare that the study of Greek was not necessary for the jurists; yet this +view was taken in the debate that followed this lecture by professional jurists +of high standing. According to this opinion, the preparatory education obtained +in the German Realgymnasium would also be sufficient for the future +jurists and insufficient only for theologians and philologists. [In England and +America not only is Greek not necessary, but the law-Latin is so peculiar that +even persons of <i>good</i> classical education cannot understand it.—<i>Tr.</i>]</p></div> + +<div class="footnote"><p><a name="Footnote_119_119" id="Footnote_119_119"></a><a href="#FNanchor_119_119"><span class="label">[119]</span></a> In emphasising here the weak sides of the writings of Plato and Aristotle, +forced on my attention while reading them in German translations, I, of +course, have no intention of underrating the great merits and the high historical +importance of these two men. Their importance must not be measured +by the fact that our speculative philosophy still moves to a great extent +in their paths of thought. The more probable conclusion is that this branch +has made very little progress in the last two thousand years. Natural science +also was implicated for centuries in the meshes of the Aristotelian thought, +and owes its rise mainly to having thrown off those fetters.</p></div> + +<div class="footnote"><p><a name="Footnote_120_120" id="Footnote_120_120"></a><a href="#FNanchor_120_120"><span class="label">[120]</span></a> I would not for a moment contend that we derive exactly the same profit +from reading a Greek author in a translation as from reading him in the original; +but the difference, the excess of gain in the second case, appears to me, +and probably will to most men who are not professional philologists, to be +too dearly bought with the expenditure of eight years of valuable time.</p></div> + +<div class="footnote"><p><a name="Footnote_121_121" id="Footnote_121_121"></a><a href="#FNanchor_121_121"><span class="label">[121]</span></a> "The temptation," Judge Hartwich writes, "to regard the 'taste' of the +ancients as so lofty and unsurpassable appears to me to have its chief origin +in the fact that the ancients were unexcelled in the representation of the +nude. First, by their unremitting care of the human body they produced +splendid models; and secondly, in their gymnasiums and in their athletic +games they had these models constantly before their eyes. No wonder, then, +that their statues still excite our admiration! For the form, the ideal of the +human body has not changed in the course of the centuries. But with intellectual +matters it is totally different; they change from century to century, +nay, from decennium to decennium. It is very natural now, that people +should unconsciously apply what is thus so easily seen, namely, the works of +sculpture, as a universal criterion of the highly developed taste of the ancients—a +fallacy against which people cannot, in my judgment, be too strongly +warned."</p></div> + +<div class="footnote"><p><a name="Footnote_122_122" id="Footnote_122_122"></a><a href="#FNanchor_122_122"><span class="label">[122]</span></a> English: "In the beginning God created the heaven and the earth. +And the earth was without form and void; and darkness was upon the face +of the deep. And the spirit of God moved upon the face of the waters."—Dutch: +"In het begin schiep God den hemel en de aarde. De aarde nu was +woest en ledig, en duisternis was op den afgrond; en de Geest Gods zwefde +op de wateren."—Danish: "I Begyndelsen skabte Gud Himmelen og Jorden. +Og Jorden var ode og tom, og der var morkt ovenover Afgrunden, og +Guds Aand svoevede ovenover Vandene."—Swedish: "I begynnelsen skapade +Gud Himmel och Jord. Och Jorden war öde och tom, och mörker war +pä djupet, och Gods Ande swäfde öfwer wattnet."—German: "Am Anfang +schuf Gott Himmel und Erde. Und die Erde war wüst und leer, und es war +finster auf der Tiefe; und der Geist Gottes schwebte auf dem Wasser."</p></div> + +<div class="footnote"><p><a name="Footnote_123_123" id="Footnote_123_123"></a><a href="#FNanchor_123_123"><span class="label">[123]</span></a> Compare Herzen's excellent remarks, <i>De l'enseignement secondaire dans +la Suisse romande</i>, Lausanne, 1886.</p></div> + +<div class="footnote"><p><a name="Footnote_124_124" id="Footnote_124_124"></a><a href="#FNanchor_124_124"><span class="label">[124]</span></a> <i>Geschichte der Mathematik</i>, Leipsic, 1874.</p></div> + +<div class="footnote"><p><a name="Footnote_125_125" id="Footnote_125_125"></a><a href="#FNanchor_125_125"><span class="label">[125]</span></a> <i>Geometrische Analyse</i>, Ulm, 1886.</p></div> + +<div class="footnote"><p><a name="Footnote_126_126" id="Footnote_126_126"></a><a href="#FNanchor_126_126"><span class="label">[126]</span></a> In his text-books of elementary mathematics</p></div> + +<div class="footnote"><p><a name="Footnote_127_127" id="Footnote_127_127"></a><a href="#FNanchor_127_127"><span class="label">[127]</span></a> <i>Abhandlungen aus dem Gebiete der Mathematik</i>, Würzburg, 1883.</p></div> + +<div class="footnote"><p><a name="Footnote_128_128" id="Footnote_128_128"></a><a href="#FNanchor_128_128"><span class="label">[128]</span></a> My idea here is an appropriate selection of readings from Galileo, Huygens, +Newton, etc. The choice is so easily made that there can be no question +of difficulties. The contents would be discussed with the students, and +the original experiments performed with them. Those scholars alone should +receive this instruction in the upper classes who did not look forward to systematical +instruction in the physical sciences. I do not make this proposition +of reform here for the first time. I have no doubt, moreover, that such radical +changes will only be slowly introduced.</p></div> + +<div class="footnote"><p><a name="Footnote_129_129" id="Footnote_129_129"></a><a href="#FNanchor_129_129"><span class="label">[129]</span></a> <i>Die Mathematik als Lehrgegenstand des Gymnasiums</i>, Berlin, 1883.</p></div> + +<div class="footnote"><p><a name="Footnote_130_130" id="Footnote_130_130"></a><a href="#FNanchor_130_130"><span class="label">[130]</span></a> Wrong as it is to burden future physicians and scientists with Greek for +the sake of the theologians and philologists, it would be just as wrong to compel +theologians and philologists, on account of the physicians, to study such +subjects as analytical geometry. Moreover, I cannot believe that ignorance +of analytical geometry would be a serious hindrance to a physician that was +otherwise well versed in quantitative thought. No special advantage generally +is observable in the graduates of the Austrian gymnasiums, all of whom have +studied analytical geometry. [Refers to an assertion of Dubois-Reymond.]</p></div> + +<div class="footnote"><p><a name="Footnote_131_131" id="Footnote_131_131"></a><a href="#FNanchor_131_131"><span class="label">[131]</span></a> Compare M. Cantor, <i>Geschichte der Mathematik</i>, Leipsic, 1880, Vol. I. p. +193.</p></div> + +<div class="footnote"><p><a name="Footnote_132_132" id="Footnote_132_132"></a><a href="#FNanchor_132_132"><span class="label">[132]</span></a> Compare Paulsen, <i>l. c.</i>, pp. 607, 688.</p></div> + +<div class="footnote"><p><a name="Footnote_133_133" id="Footnote_133_133"></a><a href="#FNanchor_133_133"><span class="label">[133]</span></a> It is to be hoped that the Americans will jealously guard their schools +and universities against the influence of the State.</p></div> + +<div class="footnote"><p><a name="Footnote_134_134" id="Footnote_134_134"></a><a href="#FNanchor_134_134"><span class="label">[134]</span></a> This article, which appeared in the Proceedings of the German Mathematical +Society of Prague for the year 1892, is printed as a supplement to the +article on "The Causes of Harmony," at page 32.</p></div> + +<div class="footnote"><p><a name="Footnote_135_135" id="Footnote_135_135"></a><a href="#FNanchor_135_135"><span class="label">[135]</span></a> The present exposition is taken from the volumes for 1700 (published in +1703) and for 1701 (published in 1704), and partly also from the <i>Histoire de +l'Académie</i> and partly from the <i>Mémoires</i>. Sauveur's later works enter less +into consideration here.</p></div> + +<div class="footnote"><p><a name="Footnote_136_136" id="Footnote_136_136"></a><a href="#FNanchor_136_136"><span class="label">[136]</span></a> Euler, <i>Tentamen novae theoriae musicae</i>, Petropoli, 1739.</p></div> + +<div class="footnote"><p><a name="Footnote_137_137" id="Footnote_137_137"></a><a href="#FNanchor_137_137"><span class="label">[137]</span></a> In attempting to perform his experiment of beats before the Academy, +Sauveur was not quite successful. <i>Histoire de l'Académie</i>, Année 1700, p. 136.</p></div> + +<div class="footnote"><p><a name="Footnote_138_138" id="Footnote_138_138"></a><a href="#FNanchor_138_138"><span class="label">[138]</span></a> <i>Histoire de l'Académie</i>, Année 1701, p. 134.</p></div> + +<div class="footnote"><p><a name="Footnote_139_139" id="Footnote_139_139"></a><a href="#FNanchor_139_139"><span class="label">[139]</span></a> <i>Ibid.</i>, p. 298.</p></div> + +<div class="footnote"><p><a name="Footnote_140_140" id="Footnote_140_140"></a><a href="#FNanchor_140_140"><span class="label">[140]</span></a> <i>Histoire de l'Académie</i>, Année 1702, p. 91.</p></div> + +<div class="footnote"><p><a name="Footnote_141_141" id="Footnote_141_141"></a><a href="#FNanchor_141_141"><span class="label">[141]</span></a> From the <i>Histoire de l'Académie</i>, Année 1700, p. 139.</p></div> + +<div class="footnote"><p><a name="Footnote_142_142" id="Footnote_142_142"></a><a href="#FNanchor_142_142"><span class="label">[142]</span></a> Because all octaves in use in music offer too great differences of rates +of vibration.</p></div> + +<div class="footnote"><p><a name="Footnote_143_143" id="Footnote_143_143"></a><a href="#FNanchor_143_143"><span class="label">[143]</span></a> "Les battemens ne plaisent pas à l'Oreille, à cause de l'inégalité du son, +et l'on peut croire avec beaucoup d'apparence que ce qui rend les Octaves si +agréables, c'est qu'on n'y entend jamais de battemens. +</p> +<p> +"En suivant cette idée, on trouve que les accords dont on ne peut entendre +les battemens, sont justement ceux que les Musiciens traitent de Consonances, +et que ceux dont les battemens se font sentir, sont les Dissonances, et que +quand un accord est Dissonance dans une certaine octave et Consonance +dans une autre, c'est qu'il bat dans l'une, et qu'il ne bat pas dans l'autre. +Aussi est il traité de Consonance imparfaite. Il est fort aisé par les principes +de Mr. Sauveur qu'on a établis ici, de voir quels accords battent, et dans +quelles Octaves au-dessus on au-dessous du son fixe. Si cette hypothèse est +vraye, elle découvrira la véritable source des Règles de la composition, inconnue +jusqu'à présent à la Philosophie, qui s'en remettait presque entièrement +au jugement de l'Oreille. Ces sortes de jugemens naturels, quelque +bisarres qu'ils paroissent quelquefois, ne le sont point, ils ont des causes +très réelles, dont la connaissance appartient à la Philosophie, pourvue qu'elle +s'en puisse mettre en possession."</p></div> + +<div class="footnote"><p><a name="Footnote_144_144" id="Footnote_144_144"></a><a href="#FNanchor_144_144"><span class="label">[144]</span></a> <i>Harmonics or the Philosophy of Musical Sounds</i>, Cambridge, 1749. I saw +this book only hastily in 1864 and drew attention to it in a work published in +1866. I did not come into its actual possession until three years ago and then +only did I learn its exact contents.</p></div> + +<div class="footnote"><p><a name="Footnote_145_145" id="Footnote_145_145"></a><a href="#FNanchor_145_145"><span class="label">[145]</span></a> <i>Harmonics</i>, pp. 118 and 243.</p></div> + +<div class="footnote"><p><a name="Footnote_146_146" id="Footnote_146_146"></a><a href="#FNanchor_146_146"><span class="label">[146]</span></a> "Short cycle" is the period in which the same phases of the two co-operant +tones are repeated.</p></div> + +<div class="footnote"><p><a name="Footnote_147_147" id="Footnote_147_147"></a><a href="#FNanchor_147_147"><span class="label">[147]</span></a> This article, designed to illustrate historically that on Symmetry, at +page 89, first appeared in Fichte's <i>Zeitschrift für Philosophie</i>, for 1865.</p></div> + +<div class="footnote"><p><a name="Footnote_148_148" id="Footnote_148_148"></a><a href="#FNanchor_148_148"><span class="label">[148]</span></a> Comp. Cornelius, <i>Ueber das Sehen</i>; Wundt, <i>Theorie der Sinneswahrnehmung</i>.</p></div> + +<div class="footnote"><p><a name="Footnote_149_149" id="Footnote_149_149"></a><a href="#FNanchor_149_149"><span class="label">[149]</span></a> Comp. Mach, <i>Ueber das Sehen von Lagen and Winkeln</i>. <i>Sitzungsb. der +Wiener Akademie</i>, 1861.</p></div> + +<div class="footnote"><p><a name="Footnote_150_150" id="Footnote_150_150"></a><a href="#FNanchor_150_150"><span class="label">[150]</span></a> Comp. Mach, <i>Zur Theorie des Gehörorgans</i>. <i>Sitsungsber, der Wiener +Akad.</i>, 1863.—<i>Ueber einige Erscheinungen der physiolog. Akustik.</i> <i>Ibid.</i>, 1864.</p></div> + + + + + + + + + +<pre> + + + + + +End of Project Gutenberg's Popular scientific lectures, by Ernst Mach + +*** END OF THIS PROJECT GUTENBERG EBOOK POPULAR SCIENTIFIC LECTURES *** + +***** This file should be named 39508-h.htm or 39508-h.zip ***** +This and all associated files of various formats will be found in: + http://www.gutenberg.org/3/9/5/0/39508/ + +Produced by Anna Hall, Albert László and the Online +Distributed Proofreading Team at http://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive) + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. Special rules, +set forth in the General Terms of Use part of this license, apply to +copying and distributing Project Gutenberg-tm electronic works to +protect the PROJECT GUTENBERG-tm concept and trademark. Project +Gutenberg is a registered trademark, and may not be used if you +charge for the eBooks, unless you receive specific permission. If you +do not charge anything for copies of this eBook, complying with the +rules is very easy. You may use this eBook for nearly any purpose +such as creation of derivative works, reports, performances and +research. They may be modified and printed and given away--you may do +practically ANYTHING with public domain eBooks. Redistribution is +subject to the trademark license, especially commercial +redistribution. + + + +*** START: FULL LICENSE *** + +THE FULL PROJECT GUTENBERG LICENSE +PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK + +To protect the Project Gutenberg-tm mission of promoting the free +distribution of electronic works, by using or distributing this work +(or any other work associated in any way with the phrase "Project +Gutenberg"), you agree to comply with all the terms of the Full Project +Gutenberg-tm License (available with this file or online at +http://gutenberg.org/license). + + +Section 1. General Terms of Use and Redistributing Project Gutenberg-tm +electronic works + +1.A. By reading or using any part of this Project Gutenberg-tm +electronic work, you indicate that you have read, understand, agree to +and accept all the terms of this license and intellectual property +(trademark/copyright) agreement. If you do not agree to abide by all +the terms of this agreement, you must cease using and return or destroy +all copies of Project Gutenberg-tm electronic works in your possession. +If you paid a fee for obtaining a copy of or access to a Project +Gutenberg-tm electronic work and you do not agree to be bound by the +terms of this agreement, you may obtain a refund from the person or +entity to whom you paid the fee as set forth in paragraph 1.E.8. + +1.B. "Project Gutenberg" is a registered trademark. It may only be +used on or associated in any way with an electronic work by people who +agree to be bound by the terms of this agreement. There are a few +things that you can do with most Project Gutenberg-tm electronic works +even without complying with the full terms of this agreement. See +paragraph 1.C below. There are a lot of things you can do with Project +Gutenberg-tm electronic works if you follow the terms of this agreement +and help preserve free future access to Project Gutenberg-tm electronic +works. See paragraph 1.E below. + +1.C. The Project Gutenberg Literary Archive Foundation ("the Foundation" +or PGLAF), owns a compilation copyright in the collection of Project +Gutenberg-tm electronic works. Nearly all the individual works in the +collection are in the public domain in the United States. If an +individual work is in the public domain in the United States and you are +located in the United States, we do not claim a right to prevent you from +copying, distributing, performing, displaying or creating derivative +works based on the work as long as all references to Project Gutenberg +are removed. Of course, we hope that you will support the Project +Gutenberg-tm mission of promoting free access to electronic works by +freely sharing Project Gutenberg-tm works in compliance with the terms of +this agreement for keeping the Project Gutenberg-tm name associated with +the work. You can easily comply with the terms of this agreement by +keeping this work in the same format with its attached full Project +Gutenberg-tm License when you share it without charge with others. + +1.D. The copyright laws of the place where you are located also govern +what you can do with this work. Copyright laws in most countries are in +a constant state of change. If you are outside the United States, check +the laws of your country in addition to the terms of this agreement +before downloading, copying, displaying, performing, distributing or +creating derivative works based on this work or any other Project +Gutenberg-tm work. The Foundation makes no representations concerning +the copyright status of any work in any country outside the United +States. + +1.E. Unless you have removed all references to Project Gutenberg: + +1.E.1. The following sentence, with active links to, or other immediate +access to, the full Project Gutenberg-tm License must appear prominently +whenever any copy of a Project Gutenberg-tm work (any work on which the +phrase "Project Gutenberg" appears, or with which the phrase "Project +Gutenberg" is associated) is accessed, displayed, performed, viewed, +copied or distributed: + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + +1.E.2. If an individual Project Gutenberg-tm electronic work is derived +from the public domain (does not contain a notice indicating that it is +posted with permission of the copyright holder), the work can be copied +and distributed to anyone in the United States without paying any fees +or charges. If you are redistributing or providing access to a work +with the phrase "Project Gutenberg" associated with or appearing on the +work, you must comply either with the requirements of paragraphs 1.E.1 +through 1.E.7 or obtain permission for the use of the work and the +Project Gutenberg-tm trademark as set forth in paragraphs 1.E.8 or +1.E.9. + +1.E.3. If an individual Project Gutenberg-tm electronic work is posted +with the permission of the copyright holder, your use and distribution +must comply with both paragraphs 1.E.1 through 1.E.7 and any additional +terms imposed by the copyright holder. Additional terms will be linked +to the Project Gutenberg-tm License for all works posted with the +permission of the copyright holder found at the beginning of this work. + +1.E.4. Do not unlink or detach or remove the full Project Gutenberg-tm +License terms from this work, or any files containing a part of this +work or any other work associated with Project Gutenberg-tm. + +1.E.5. Do not copy, display, perform, distribute or redistribute this +electronic work, or any part of this electronic work, without +prominently displaying the sentence set forth in paragraph 1.E.1 with +active links or immediate access to the full terms of the Project +Gutenberg-tm License. + +1.E.6. You may convert to and distribute this work in any binary, +compressed, marked up, nonproprietary or proprietary form, including any +word processing or hypertext form. However, if you provide access to or +distribute copies of a Project Gutenberg-tm work in a format other than +"Plain Vanilla ASCII" or other format used in the official version +posted on the official Project Gutenberg-tm web site (www.gutenberg.org), +you must, at no additional cost, fee or expense to the user, provide a +copy, a means of exporting a copy, or a means of obtaining a copy upon +request, of the work in its original "Plain Vanilla ASCII" or other +form. Any alternate format must include the full Project Gutenberg-tm +License as specified in paragraph 1.E.1. + +1.E.7. Do not charge a fee for access to, viewing, displaying, +performing, copying or distributing any Project Gutenberg-tm works +unless you comply with paragraph 1.E.8 or 1.E.9. + +1.E.8. You may charge a reasonable fee for copies of or providing +access to or distributing Project Gutenberg-tm electronic works provided +that + +- You pay a royalty fee of 20% of the gross profits you derive from + the use of Project Gutenberg-tm works calculated using the method + you already use to calculate your applicable taxes. The fee is + owed to the owner of the Project Gutenberg-tm trademark, but he + has agreed to donate royalties under this paragraph to the + Project Gutenberg Literary Archive Foundation. Royalty payments + must be paid within 60 days following each date on which you + prepare (or are legally required to prepare) your periodic tax + returns. Royalty payments should be clearly marked as such and + sent to the Project Gutenberg Literary Archive Foundation at the + address specified in Section 4, "Information about donations to + the Project Gutenberg Literary Archive Foundation." + +- You provide a full refund of any money paid by a user who notifies + you in writing (or by e-mail) within 30 days of receipt that s/he + does not agree to the terms of the full Project Gutenberg-tm + License. You must require such a user to return or + destroy all copies of the works possessed in a physical medium + and discontinue all use of and all access to other copies of + Project Gutenberg-tm works. + +- You provide, in accordance with paragraph 1.F.3, a full refund of any + money paid for a work or a replacement copy, if a defect in the + electronic work is discovered and reported to you within 90 days + of receipt of the work. + +- You comply with all other terms of this agreement for free + distribution of Project Gutenberg-tm works. + +1.E.9. If you wish to charge a fee or distribute a Project Gutenberg-tm +electronic work or group of works on different terms than are set +forth in this agreement, you must obtain permission in writing from +both the Project Gutenberg Literary Archive Foundation and Michael +Hart, the owner of the Project Gutenberg-tm trademark. Contact the +Foundation as set forth in Section 3 below. + +1.F. + +1.F.1. Project Gutenberg volunteers and employees expend considerable +effort to identify, do copyright research on, transcribe and proofread +public domain works in creating the Project Gutenberg-tm +collection. Despite these efforts, Project Gutenberg-tm electronic +works, and the medium on which they may be stored, may contain +"Defects," such as, but not limited to, incomplete, inaccurate or +corrupt data, transcription errors, a copyright or other intellectual +property infringement, a defective or damaged disk or other medium, a +computer virus, or computer codes that damage or cannot be read by +your equipment. + +1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the "Right +of Replacement or Refund" described in paragraph 1.F.3, the Project +Gutenberg Literary Archive Foundation, the owner of the Project +Gutenberg-tm trademark, and any other party distributing a Project +Gutenberg-tm electronic work under this agreement, disclaim all +liability to you for damages, costs and expenses, including legal +fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT +LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE +PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE +TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE +LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR +INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH +DAMAGE. + +1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a +defect in this electronic work within 90 days of receiving it, you can +receive a refund of the money (if any) you paid for it by sending a +written explanation to the person you received the work from. If you +received the work on a physical medium, you must return the medium with +your written explanation. The person or entity that provided you with +the defective work may elect to provide a replacement copy in lieu of a +refund. If you received the work electronically, the person or entity +providing it to you may choose to give you a second opportunity to +receive the work electronically in lieu of a refund. If the second copy +is also defective, you may demand a refund in writing without further +opportunities to fix the problem. + +1.F.4. Except for the limited right of replacement or refund set forth +in paragraph 1.F.3, this work is provided to you 'AS-IS' WITH NO OTHER +WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO +WARRANTIES OF MERCHANTIBILITY OR FITNESS FOR ANY PURPOSE. + +1.F.5. Some states do not allow disclaimers of certain implied +warranties or the exclusion or limitation of certain types of damages. +If any disclaimer or limitation set forth in this agreement violates the +law of the state applicable to this agreement, the agreement shall be +interpreted to make the maximum disclaimer or limitation permitted by +the applicable state law. The invalidity or unenforceability of any +provision of this agreement shall not void the remaining provisions. + +1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the +trademark owner, any agent or employee of the Foundation, anyone +providing copies of Project Gutenberg-tm electronic works in accordance +with this agreement, and any volunteers associated with the production, +promotion and distribution of Project Gutenberg-tm electronic works, +harmless from all liability, costs and expenses, including legal fees, +that arise directly or indirectly from any of the following which you do +or cause to occur: (a) distribution of this or any Project Gutenberg-tm +work, (b) alteration, modification, or additions or deletions to any +Project Gutenberg-tm work, and (c) any Defect you cause. + + +Section 2. Information about the Mission of Project Gutenberg-tm + +Project Gutenberg-tm is synonymous with the free distribution of +electronic works in formats readable by the widest variety of computers +including obsolete, old, middle-aged and new computers. It exists +because of the efforts of hundreds of volunteers and donations from +people in all walks of life. + +Volunteers and financial support to provide volunteers with the +assistance they need, are critical to reaching Project Gutenberg-tm's +goals and ensuring that the Project Gutenberg-tm collection will +remain freely available for generations to come. In 2001, the Project +Gutenberg Literary Archive Foundation was created to provide a secure +and permanent future for Project Gutenberg-tm and future generations. +To learn more about the Project Gutenberg Literary Archive Foundation +and how your efforts and donations can help, see Sections 3 and 4 +and the Foundation web page at http://www.pglaf.org. + + +Section 3. Information about the Project Gutenberg Literary Archive +Foundation + +The Project Gutenberg Literary Archive Foundation is a non profit +501(c)(3) educational corporation organized under the laws of the +state of Mississippi and granted tax exempt status by the Internal +Revenue Service. The Foundation's EIN or federal tax identification +number is 64-6221541. Its 501(c)(3) letter is posted at +http://pglaf.org/fundraising. Contributions to the Project Gutenberg +Literary Archive Foundation are tax deductible to the full extent +permitted by U.S. federal laws and your state's laws. + +The Foundation's principal office is located at 4557 Melan Dr. S. +Fairbanks, AK, 99712., but its volunteers and employees are scattered +throughout numerous locations. Its business office is located at +809 North 1500 West, Salt Lake City, UT 84116, (801) 596-1887, email +business@pglaf.org. Email contact links and up to date contact +information can be found at the Foundation's web site and official +page at http://pglaf.org + +For additional contact information: + Dr. Gregory B. Newby + Chief Executive and Director + gbnewby@pglaf.org + + +Section 4. Information about Donations to the Project Gutenberg +Literary Archive Foundation + +Project Gutenberg-tm depends upon and cannot survive without wide +spread public support and donations to carry out its mission of +increasing the number of public domain and licensed works that can be +freely distributed in machine readable form accessible by the widest +array of equipment including outdated equipment. Many small donations +($1 to $5,000) are particularly important to maintaining tax exempt +status with the IRS. + +The Foundation is committed to complying with the laws regulating +charities and charitable donations in all 50 states of the United +States. Compliance requirements are not uniform and it takes a +considerable effort, much paperwork and many fees to meet and keep up +with these requirements. We do not solicit donations in locations +where we have not received written confirmation of compliance. To +SEND DONATIONS or determine the status of compliance for any +particular state visit http://pglaf.org + +While we cannot and do not solicit contributions from states where we +have not met the solicitation requirements, we know of no prohibition +against accepting unsolicited donations from donors in such states who +approach us with offers to donate. + +International donations are gratefully accepted, but we cannot make +any statements concerning tax treatment of donations received from +outside the United States. U.S. laws alone swamp our small staff. + +Please check the Project Gutenberg Web pages for current donation +methods and addresses. Donations are accepted in a number of other +ways including checks, online payments and credit card donations. +To donate, please visit: http://pglaf.org/donate + + +Section 5. General Information About Project Gutenberg-tm electronic +works. + +Professor Michael S. Hart is the originator of the Project Gutenberg-tm +concept of a library of electronic works that could be freely shared +with anyone. For thirty years, he produced and distributed Project +Gutenberg-tm eBooks with only a loose network of volunteer support. + + +Project Gutenberg-tm eBooks are often created from several printed +editions, all of which are confirmed as Public Domain in the U.S. +unless a copyright notice is included. Thus, we do not necessarily +keep eBooks in compliance with any particular paper edition. + + +Most people start at our Web site which has the main PG search facility: + + http://www.gutenberg.org + +This Web site includes information about Project Gutenberg-tm, +including how to make donations to the Project Gutenberg Literary +Archive Foundation, how to help produce our new eBooks, and how to +subscribe to our email newsletter to hear about new eBooks. + + +</pre> + +</body> +</html> diff --git a/39508-h/images/i_015.jpg b/39508-h/images/i_015.jpg Binary files differnew file mode 100644 index 0000000..7184545 --- /dev/null +++ b/39508-h/images/i_015.jpg diff --git a/39508-h/images/i_016.jpg b/39508-h/images/i_016.jpg Binary files differnew file mode 100644 index 0000000..794479e --- /dev/null +++ b/39508-h/images/i_016.jpg diff --git a/39508-h/images/i_021-1.jpg b/39508-h/images/i_021-1.jpg Binary files differnew file mode 100644 index 0000000..2f77a8f --- /dev/null +++ b/39508-h/images/i_021-1.jpg diff --git a/39508-h/images/i_021.jpg b/39508-h/images/i_021.jpg Binary files differnew file mode 100644 index 0000000..c7c58bf --- /dev/null +++ b/39508-h/images/i_021.jpg diff --git a/39508-h/images/i_022.jpg b/39508-h/images/i_022.jpg Binary files differnew file mode 100644 index 0000000..af77c84 --- /dev/null +++ b/39508-h/images/i_022.jpg diff --git a/39508-h/images/i_028.jpg b/39508-h/images/i_028.jpg Binary files differnew file mode 100644 index 0000000..af6449f --- /dev/null +++ b/39508-h/images/i_028.jpg diff --git a/39508-h/images/i_029.jpg b/39508-h/images/i_029.jpg Binary files differnew file mode 100644 index 0000000..5c524fc --- /dev/null +++ b/39508-h/images/i_029.jpg diff --git a/39508-h/images/i_035.jpg b/39508-h/images/i_035.jpg Binary files differnew file mode 100644 index 0000000..8824a31 --- /dev/null +++ b/39508-h/images/i_035.jpg diff --git a/39508-h/images/i_047-1.jpg b/39508-h/images/i_047-1.jpg Binary files differnew file mode 100644 index 0000000..6f977a6 --- /dev/null +++ b/39508-h/images/i_047-1.jpg diff --git a/39508-h/images/i_047.jpg b/39508-h/images/i_047.jpg Binary files differnew file mode 100644 index 0000000..6a24ad7 --- /dev/null +++ b/39508-h/images/i_047.jpg diff --git a/39508-h/images/i_048.jpg b/39508-h/images/i_048.jpg Binary files differnew file mode 100644 index 0000000..3b6159a --- /dev/null +++ b/39508-h/images/i_048.jpg diff --git a/39508-h/images/i_052.jpg b/39508-h/images/i_052.jpg Binary files differnew file mode 100644 index 0000000..f45957d --- /dev/null +++ b/39508-h/images/i_052.jpg diff --git a/39508-h/images/i_060.jpg b/39508-h/images/i_060.jpg Binary files differnew file mode 100644 index 0000000..8a53199 --- /dev/null +++ b/39508-h/images/i_060.jpg diff --git a/39508-h/images/i_062.jpg b/39508-h/images/i_062.jpg Binary files differnew file mode 100644 index 0000000..4b9913a --- /dev/null +++ b/39508-h/images/i_062.jpg diff --git a/39508-h/images/i_063.jpg b/39508-h/images/i_063.jpg Binary files differnew file mode 100644 index 0000000..d25b3d8 --- /dev/null +++ b/39508-h/images/i_063.jpg diff --git a/39508-h/images/i_065.jpg b/39508-h/images/i_065.jpg Binary files differnew file mode 100644 index 0000000..04fba17 --- /dev/null +++ b/39508-h/images/i_065.jpg diff --git a/39508-h/images/i_069-1.jpg b/39508-h/images/i_069-1.jpg Binary files differnew file mode 100644 index 0000000..195c0a1 --- /dev/null +++ b/39508-h/images/i_069-1.jpg diff --git a/39508-h/images/i_069.jpg b/39508-h/images/i_069.jpg Binary files differnew file mode 100644 index 0000000..ea6e9c1 --- /dev/null +++ b/39508-h/images/i_069.jpg diff --git a/39508-h/images/i_070.jpg b/39508-h/images/i_070.jpg Binary files differnew file mode 100644 index 0000000..143dd12 --- /dev/null +++ b/39508-h/images/i_070.jpg diff --git a/39508-h/images/i_078.jpg b/39508-h/images/i_078.jpg Binary files differnew file mode 100644 index 0000000..932d392 --- /dev/null +++ b/39508-h/images/i_078.jpg diff --git a/39508-h/images/i_081.jpg b/39508-h/images/i_081.jpg Binary files differnew file mode 100644 index 0000000..7983973 --- /dev/null +++ b/39508-h/images/i_081.jpg diff --git a/39508-h/images/i_090.jpg b/39508-h/images/i_090.jpg Binary files differnew file mode 100644 index 0000000..012fc1a --- /dev/null +++ b/39508-h/images/i_090.jpg diff --git a/39508-h/images/i_093.jpg b/39508-h/images/i_093.jpg Binary files differnew file mode 100644 index 0000000..48b869d --- /dev/null +++ b/39508-h/images/i_093.jpg diff --git a/39508-h/images/i_094.jpg b/39508-h/images/i_094.jpg Binary files differnew file mode 100644 index 0000000..371e689 --- /dev/null +++ b/39508-h/images/i_094.jpg diff --git a/39508-h/images/i_102.jpg b/39508-h/images/i_102.jpg Binary files differnew file mode 100644 index 0000000..05adadc --- /dev/null +++ b/39508-h/images/i_102.jpg diff --git a/39508-h/images/i_112.jpg b/39508-h/images/i_112.jpg Binary files differnew file mode 100644 index 0000000..64eb1f4 --- /dev/null +++ b/39508-h/images/i_112.jpg diff --git a/39508-h/images/i_119-1.jpg b/39508-h/images/i_119-1.jpg Binary files differnew file mode 100644 index 0000000..3a330a2 --- /dev/null +++ b/39508-h/images/i_119-1.jpg diff --git a/39508-h/images/i_119-2.jpg b/39508-h/images/i_119-2.jpg Binary files differnew file mode 100644 index 0000000..23bb257 --- /dev/null +++ b/39508-h/images/i_119-2.jpg diff --git a/39508-h/images/i_124-1.jpg b/39508-h/images/i_124-1.jpg Binary files differnew file mode 100644 index 0000000..03e4c3f --- /dev/null +++ b/39508-h/images/i_124-1.jpg diff --git a/39508-h/images/i_124-2.jpg b/39508-h/images/i_124-2.jpg Binary files differnew file mode 100644 index 0000000..4d1f094 --- /dev/null +++ b/39508-h/images/i_124-2.jpg diff --git a/39508-h/images/i_125.jpg b/39508-h/images/i_125.jpg Binary files differnew file mode 100644 index 0000000..ac0615d --- /dev/null +++ b/39508-h/images/i_125.jpg diff --git a/39508-h/images/i_126.jpg b/39508-h/images/i_126.jpg Binary files differnew file mode 100644 index 0000000..1d58512 --- /dev/null +++ b/39508-h/images/i_126.jpg diff --git a/39508-h/images/i_127-1.jpg b/39508-h/images/i_127-1.jpg Binary files differnew file mode 100644 index 0000000..3872636 --- /dev/null +++ b/39508-h/images/i_127-1.jpg diff --git a/39508-h/images/i_127-s.jpg b/39508-h/images/i_127-s.jpg Binary files differnew file mode 100644 index 0000000..ea63d6e --- /dev/null +++ b/39508-h/images/i_127-s.jpg diff --git a/39508-h/images/i_129.jpg b/39508-h/images/i_129.jpg Binary files differnew file mode 100644 index 0000000..248aa6e --- /dev/null +++ b/39508-h/images/i_129.jpg diff --git a/39508-h/images/i_134.jpg b/39508-h/images/i_134.jpg Binary files differnew file mode 100644 index 0000000..5f0b48b --- /dev/null +++ b/39508-h/images/i_134.jpg diff --git a/39508-h/images/i_135.jpg b/39508-h/images/i_135.jpg Binary files differnew file mode 100644 index 0000000..7fb5d52 --- /dev/null +++ b/39508-h/images/i_135.jpg diff --git a/39508-h/images/i_139-1.jpg b/39508-h/images/i_139-1.jpg Binary files differnew file mode 100644 index 0000000..5855e4e --- /dev/null +++ b/39508-h/images/i_139-1.jpg diff --git a/39508-h/images/i_139-2.jpg b/39508-h/images/i_139-2.jpg Binary files differnew file mode 100644 index 0000000..5757a23 --- /dev/null +++ b/39508-h/images/i_139-2.jpg diff --git a/39508-h/images/i_143.jpg b/39508-h/images/i_143.jpg Binary files differnew file mode 100644 index 0000000..f6da678 --- /dev/null +++ b/39508-h/images/i_143.jpg diff --git a/39508-h/images/i_150.jpg b/39508-h/images/i_150.jpg Binary files differnew file mode 100644 index 0000000..3fe8750 --- /dev/null +++ b/39508-h/images/i_150.jpg diff --git a/39508-h/images/i_151.jpg b/39508-h/images/i_151.jpg Binary files differnew file mode 100644 index 0000000..7d7d09a --- /dev/null +++ b/39508-h/images/i_151.jpg diff --git a/39508-h/images/i_155.jpg b/39508-h/images/i_155.jpg Binary files differnew file mode 100644 index 0000000..c176372 --- /dev/null +++ b/39508-h/images/i_155.jpg diff --git a/39508-h/images/i_157.jpg b/39508-h/images/i_157.jpg Binary files differnew file mode 100644 index 0000000..7e11669 --- /dev/null +++ b/39508-h/images/i_157.jpg diff --git a/39508-h/images/i_296.jpg b/39508-h/images/i_296.jpg Binary files differnew file mode 100644 index 0000000..5530bf1 --- /dev/null +++ b/39508-h/images/i_296.jpg diff --git a/39508-h/images/i_298.jpg b/39508-h/images/i_298.jpg Binary files differnew file mode 100644 index 0000000..5c04137 --- /dev/null +++ b/39508-h/images/i_298.jpg diff --git a/39508-h/images/i_302.jpg b/39508-h/images/i_302.jpg Binary files differnew file mode 100644 index 0000000..e042c74 --- /dev/null +++ b/39508-h/images/i_302.jpg diff --git a/39508-h/images/i_304.jpg b/39508-h/images/i_304.jpg Binary files differnew file mode 100644 index 0000000..31ddd76 --- /dev/null +++ b/39508-h/images/i_304.jpg diff --git a/39508-h/images/i_324.jpg b/39508-h/images/i_324.jpg Binary files differnew file mode 100644 index 0000000..147f999 --- /dev/null +++ b/39508-h/images/i_324.jpg diff --git a/39508-h/images/i_325.jpg b/39508-h/images/i_325.jpg Binary files differnew file mode 100644 index 0000000..4ce01c3 --- /dev/null +++ b/39508-h/images/i_325.jpg diff --git a/39508-h/images/i_331.jpg b/39508-h/images/i_331.jpg Binary files differnew file mode 100644 index 0000000..52e7352 --- /dev/null +++ b/39508-h/images/i_331.jpg diff --git a/39508-h/images/i_333.jpg b/39508-h/images/i_333.jpg Binary files differnew file mode 100644 index 0000000..c0a8bcd --- /dev/null +++ b/39508-h/images/i_333.jpg diff --git a/39508-h/images/i_334.jpg b/39508-h/images/i_334.jpg Binary files differnew file mode 100644 index 0000000..6c1e1ea --- /dev/null +++ b/39508-h/images/i_334.jpg diff --git a/39508-h/images/i_336.jpg b/39508-h/images/i_336.jpg Binary files differnew file mode 100644 index 0000000..9d983af --- /dev/null +++ b/39508-h/images/i_336.jpg diff --git a/39508-h/images/i_338.jpg b/39508-h/images/i_338.jpg Binary files differnew file mode 100644 index 0000000..17b4638 --- /dev/null +++ b/39508-h/images/i_338.jpg diff --git a/39508-h/images/i_341.jpg b/39508-h/images/i_341.jpg Binary files differnew file mode 100644 index 0000000..8c9d22b --- /dev/null +++ b/39508-h/images/i_341.jpg diff --git a/39508-h/images/i_342.jpg b/39508-h/images/i_342.jpg Binary files differnew file mode 100644 index 0000000..4337f2a --- /dev/null +++ b/39508-h/images/i_342.jpg diff --git a/39508-h/images/i_399.jpg b/39508-h/images/i_399.jpg Binary files differnew file mode 100644 index 0000000..baf1fe3 --- /dev/null +++ b/39508-h/images/i_399.jpg diff --git a/39508-h/images/i_400.jpg b/39508-h/images/i_400.jpg Binary files differnew file mode 100644 index 0000000..c57c580 --- /dev/null +++ b/39508-h/images/i_400.jpg diff --git a/39508-h/music/112a.mid b/39508-h/music/112a.mid Binary files differnew file mode 100644 index 0000000..982b03a --- /dev/null +++ b/39508-h/music/112a.mid diff --git a/39508-h/music/112b.mid b/39508-h/music/112b.mid Binary files differnew file mode 100644 index 0000000..5b5b558 --- /dev/null +++ b/39508-h/music/112b.mid diff --git a/39508-h/music/112c.mid b/39508-h/music/112c.mid Binary files differnew file mode 100644 index 0000000..6d0c313 --- /dev/null +++ b/39508-h/music/112c.mid diff --git a/39508-h/music/112d.mid b/39508-h/music/112d.mid Binary files differnew file mode 100644 index 0000000..c0ecab1 --- /dev/null +++ b/39508-h/music/112d.mid diff --git a/39508-h/music/112e.mid b/39508-h/music/112e.mid Binary files differnew file mode 100644 index 0000000..6715b69 --- /dev/null +++ b/39508-h/music/112e.mid diff --git a/39508-h/music/112f.mid b/39508-h/music/112f.mid Binary files differnew file mode 100644 index 0000000..e4215b1 --- /dev/null +++ b/39508-h/music/112f.mid diff --git a/39508-h/music/112g.mid b/39508-h/music/112g.mid Binary files differnew file mode 100644 index 0000000..9296f35 --- /dev/null +++ b/39508-h/music/112g.mid diff --git a/39508-h/music/112h.mid b/39508-h/music/112h.mid Binary files differnew file mode 100644 index 0000000..0b7e000 --- /dev/null +++ b/39508-h/music/112h.mid |
