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} - -.vsmall { font-size: x-small; } -.small { font-size: small; } -.medium { font-size: medium; } -.larger { font-size: larger; } -.large { font-size: x-large; } -.space { letter-spacing: 0.2em; } -/* Poems */ -.poetry-container { text-align: center; - margin: 0; } - .poem - { - display: inline-block; - text-align: left; - font-size: medium; - line-height: 1.2em; /* set spacing between lines in stanza */ - margin-top: 0; - } -.poem .stanza { margin: 1em 0em 0em 0em;} -.stanza br { /* br's generated by Guiguts ignored by CSS browsers */ - display: none; /* Lynx doesn't see this, so executes br */ - } -.poem .i0 { display:block; margin-left: 2em;}/* default (non-indented) line */ - -.one { width: 5%; border: 1px solid; } -.two { width: 10%; border: 1px solid;} -.three { width: 20%; border: 1px solid;} -.four { width: 40%; border: 1px solid;} -.blkquot { margin-left: 10%; - margin-right: 10%; - font-size: 90%; - text-align: justify; - text-indent: 1em; } -.center { text-indent: 0; - text-align: center; } -.citation { text-align: right; - margin-right: 10%; } -.correction { border-bottom: 1px dashed red;} -.eq { margin-top: 0em; - } -.end { margin-bottom: 2em; - } -.greek { font-family: Palatino, serif; - } -.pagenum { font-size: 90%; - color: red; } -.sc { font-variant: small-caps; } -div.chapter { page-break-before: always;} -div.book { margin-left: 7%; - margin-right: 7%;} -#tnote { border: 1px dotted black; - padding: 1em; - max-width: 40em; - margin: auto;} -#tnote p { font-size: medium; } -.nobreak { page-break-before: avoid;} - /* ]]> */ </style> - </head> -<body> -<p style='text-align:center; font-size:1.2em; font-weight:bold'>The Project Gutenberg eBook of Novum organon renovatum, by William Whewell</p> -<div style='display:block; margin:1em 0'> -This eBook is for the use of anyone anywhere in the United States and -most other parts of the world 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 <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you -are not located in the United States, you will have to check the laws of the -country where you are located before using this eBook. -</div> - -<p style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Title: Novum organon renovatum</p> -<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Author: William Whewell</p> -<p style='display:block; text-indent:0; margin:1em 0'>Release Date: January 10, 2023 [eBook #69764]</p> -<p style='display:block; text-indent:0; margin:1em 0'>Language: English</p> - <p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em; text-align:left'>Produced by: Ed Brandon from materials kindly provided by the Internet Archive, and with help gratefully received from various voluntary sources.</p> -<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK NOVUM ORGANON RENOVATUM ***</div> -<h1><span class="space">NOVUM ORGANON<br/> -RENOVATU</span>M.</h1> -<p class="center large"> -<span class="sc">By</span> WILLIAM WHEWELL, D.D.,</p> -<p class="center vsmall end"> -MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND<br/> -CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE.</p> -<p class="center small end"> -BEING THE SECOND PART OF THE PHILOSOPHY<br/> -OF THE INDUCTIVE SCIENCES.</p> -<p class="center small end"> -<i>THE THIRD EDITION, WITH LARGE ADDITIONS.</i><br/></p> -<div class="center"> -<img src="images/whand.jpg" alt="Hand passing torch to hand" /> -</div> -<p class="center small"> -ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ</p> -<p class="center medium end"> -LONDON:<br/> -JOHN W. PARKER AND SON, WEST STRAND.<br/> -1858.</p> -<div class="book"> -<div class="chapter"> -<p class="blkquot">It is to our immortal countryman; Bacon, that we owe the -broad announcement of this grand and fertile principle; and the -developement of the idea, that the whole of natural philosophy -consists entirely of a series of inductive generalizations, -commencing with the most circumstantially stated particulars, and -carried up to universal laws, or axioms, which comprehend in -their statements every subordinate degree of generality; and of -a corresponding series of inverted reasoning from generals to -particulars, by which these axioms are traced back into their -remotest consequences, and all particular propositions deduced -from them; as well those by whose immediate considerations we -rose to their discovery, as those of which we had no previous -knowledge.</p> -<p class="citation small eq end"><span class="sc">Herschel</span>, -<i>Discourse on Natural Philosophy</i>, Art. 96.</p> -<hr class="four" /> -<p class="center vsmall end"> -CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.</p> -</div> -<div class="chapter"> -<p><span class="pagenum" id="pageiii"></span></p> -<h3 class="nobreak">PREFACE.</h3> -<hr class="two end" /> -</div> -<p><span class="sc">Even</span> if Bacon’s <i>Novum Organon</i> had possessed the -character to which it aspired as completely as was -possible in its own day, it would at present need renovation: -and even if no such book had ever been written, it would be -a worthy undertaking to determine -the machinery, intellectual, social and material, by -which human knowledge can best be augmented. -Bacon could only divine how sciences might be constructed; -we can trace, in their history, how their -construction has taken place. However sagacious were -his conjectures, the facts which have really occurred -must give additional instruction: however large were -his anticipations, the actual progress of science since -his time has illustrated them in all their extent. And -as to the structure and operation of the <em>Organ</em> by -which truth is to be collected from nature,—that is, -the Methods by which science is to be promoted—we -know that, though Bacon’s general maxims are sagacious -and animating, his particular precepts failed in -his hands, and are now practically useless. This, -perhaps, was not wonderful, seeing that they were, as -I have said, mainly derived from conjectures respecting -knowledge and the progress of knowledge; but -at <span class="pagenum" id="pageiv">iv</span> -the present day, when, in several provinces of knowledge, -we have a large actual progress of solid truth -to look back upon, we may make the like attempt -with the prospect of better success, at least on that -ground. It may be a task, not hopeless, to extract -from the past progress of science the elements of an -effectual and substantial method of Scientific Discovery. -The advances which have, during the last three -centuries, been made in the physical sciences;—in -Astronomy, in Physics, in Chemistry, in Natural History, -in Physiology;—these are allowed by all to be -real, to be great, to be striking; may it not be that -the steps of progress in these different cases have in -them something alike? May it not be that in each -advancing movement of such knowledge there is some -common principle, some common process? May it -not be that discoveries are made by an <em>Organ</em> which -has something uniform in its working? If we can -shew that this is so, we shall have the <em>New Organ</em>, -which Bacon aspired to construct, <em>renovated</em> according -to our advanced intellectual position and office.</p> -<p>It was with the view of opening the way to such -an attempt that I undertook that survey of the past -progress of physical knowledge, of which I have given -the results in the <i>History of the Sciences</i>, and the -<i>History of Scientific Ideas</i><a id="fnanchor1-P" href="#note1-P"><span class="fnanchor">1</span></a>; -the former containing -the history of the sciences, so far as it depends on -<span class="pagenum" id="pagev">v</span> -observed <em>Facts</em>; the latter containing the history of -those <em>Ideas</em> by which such Facts are bound into -Theories.</p> -<div class="footnote"><span class="label"> -<a id="note1-P" href="#fnanchor1-P">1</a></span> Published in -two former editions as part of the <i>Philosophy of the -Inductive Sciences</i> (b. i–x.). -</div> -<p>It can hardly happen that a work which treats of -Methods of Scientific Discovery, shall not seem to -fail in the positive results which it offers. For an -Art of Discovery is not possible. At each step of the -investigation are needed Invention, Sagacity, Genius,—elements -which no art can give. We may hope in -vain, as Bacon hoped, for an Organ which shall enable -all men to construct Scientific Truths, as a pair of -compasses enables all men to construct exact -circles<a id="fnanchor2-P" href="#note2-P"><span class="fnanchor">2</span></a>. -This cannot be. The practical results of the Philosophy of Science -must be rather classification and -analysis of what has been done, than precept and -method for future doing. Yet I think that the methods of discovery -which I have to recommend, though -gathered from a wider survey of scientific history, -both as to subjects and as to time, than (so far as I am -aware) has been elsewhere attempted, are quite as -definite and practical as any others which have been -proposed; with the great additional advantage of being -the methods by which all great discoveries in science -have really been made. This may be said, for instance, -of <i>the Method of Gradation</i> and <i>the Method of Natural -Classification</i>, spoken of <a href="#page220">b. iii. c. viii</a>; and in a narrower -sense, of <i>the Method of Curves</i>, <i>the Method -of</i> <span class="pagenum" id="pagevi">vi</span> -<i>Means</i>, <i>the Method of Least Squares</i> and <i>the Method -of Residues</i>, spoken of in <a href="#page202">chap. vii.</a> of the same Book. -Also the Remarks on the <i>Use of Hypotheses</i> and on -the <i>Tests of Hypotheses</i> (<a href="#page186">b. ii. c. v.</a>) point out features -which mark the usual course of discovery.</p> -<div class="footnote"><span class="label"> -<a id="note2-P" href="#fnanchor2-P">2</a></span> <i>Nov. Org.</i> lib. i. aph. 61. -</div> -<p>But one of the principal lessons resulting from our -views is undoubtedly this:—that different sciences -may be expected to advance by different modes of -procedure, according to their present condition; and -that in many of these sciences, an Induction performed -by any of the methods which have just been referred -to is not the next step which we may expect to see -made. Several of the sciences may not be in a condition -which fits them for such a <i>Colligation of Facts</i>; -(to use the phraseology to which the succeeding analysis -has led me). The Facts may, at the present -time, require to be more fully observed, or the Idea -by which they are to be colligated may require to be -more fully unfolded.</p> -<p>But in this point also, our speculations are far from -being barren of practical results. The examination -to which we have subjected each science, gives us the -means of discerning whether what is needed for the -further progress of the science, has its place in the -Observations, or in the Ideas, or in the union of the -two. If observations be wanted, the Methods of Observation, -given in <a href="#page145">b. iii. c. ii.</a> may be referred to. If -those who are to make the next discoveries need, for -that purpose, a developement of their Ideas, the modes -in which such a developement has usually taken <span class="pagenum" id="pagevii">vii</span> -place are treated of in Chapters <a href="#page164">iii.</a> and <a href="#page180">iv.</a> -of that Book.</p> -<p>No one who has well studied the history of science -can fail to see how important a part of that history -is the explication, or as I might call it, the <i>clarification</i> -of men’s Ideas. This, the metaphysical aspect of -each of the physical sciences, is very far from being, -as some have tried to teach, an aspect which it passes -through at an early period of progress, and previously -to the stage of positive knowledge. On the contrary, -the metaphysical movement is a necessary part of the -inductive movement. This, which is evidently so by -the nature of the case, was proved by a copious collection -of historical evidences, in the <i>History of Scientific -Ideas</i>. The ten Books of that History contain an -account of the principal philosophical controversies -which have taken place in all the physical sciences, -from Mathematics to Physiology. These controversies, -which must be called <i>metaphysical</i> if anything be so -called, have been conducted by the greatest discoverers -in each science, and have been an essential part of the -discoveries made. Physical discoverers have differed -from barren speculators, not by having <em>no</em> metaphysics -in their heads, but by having <em>good</em> metaphysics in -their heads while their adversaries had bad; and by -binding their metaphysics to their physics, instead of -keeping the two asunder. I trust that the <i>History of -Scientific Ideas</i> is of some value, even as a record of a -number of remarkable controversies; but I conceive -that it also contains an indisputable proof that -there <span class="pagenum" id="pageviii">viii</span> -is, in progressive science, a metaphysical as well as a -physical element;—ideas as well as facts;—thoughts -as well as things. Metaphysics is the process of ascertaining -that thought is consistent with itself: and -if it be not so, our supposed knowledge is not knowledge.</p> -<p>In <a href="#page97">Chapter vi.</a> of the Second Book, I have spoken of -<i>the Logic of Induction</i>. Several -writers<a id="fnanchor3-P" href="#note3-P"><span class="fnanchor">3</span></a> have quoted -very emphatically my assertion that the Logic of Induction -does not exist in previous writers: using it as an -introduction to Logical Schemes of their own. They -seem to have overlooked the fact that at the same time -that I noted the deficiency, I offered a scheme which I -think fitted to supply this want. And I am obliged to -say that I do not regard the schemes proposed by any -of those gentlemen as at all satisfactory for the purpose. -But I must defer to a future occasion any criticism of -authors who have written on the subjects here treated. -A critical notice of such authors formed the Twelfth -Book of the former edition of the <i>Philosophy of the -Sciences</i>. I have there examined the opinions concerning -the Nature of Real Knowledge and the mode of -acquiring it, which have been promulgated in all ages, -from Plato and Aristotle, to Roger Bacon, to Francis -Bacon, to Newton, to Herschel. Such a survey, with -the additions which I should now have to make to it, -may hereafter be put forth as a separate book: -but I <span class="pagenum" id="pageix">ix</span> -have endeavoured to confine the present volume to such -positive teaching regarding Knowledge and Science as -results from the investigations pursued in the other -works of this series. But with regard to this matter, -of the <i>Logic of Induction</i>, I may venture to say, that -we shall not find anything deserving the name explained -in the common writers on Logic, or exhibited -under the ordinary Logical Forms. <em>That</em> in previous -writers which comes the nearest to the notice of such a -Logic as the history of science has suggested and verified, -is the striking declaration of Bacon in two of his -Aphorisms (b. i. aph. civ. cv.).</p> -<div class="footnote"><span class="label"> -<a id="note3-P" href="#fnanchor3-P">3</a></span> Apelt <i>Die -Theorie der Induction</i>: Gratry <i>Logique</i>. -</div> -<p>“There will be good hopes for the Sciences then, -and not till then, when by a true <span class="sc">scale</span> or Ladder, -and by successive steps, following continuously without -gaps or breaks, men shall ascend from particulars to -the narrower Propositions, from those to intermediate -ones, rising in order one above another, and at last to -the most general.</p> -<p>“But in establishing such propositions, we must devise -some other <span class="sc">Form of Induction</span> than has hitherto -been in use; and this must be one which serves not -only to prove and discover <em>Principles</em>, (as very general -Propositions are called,) but also the narrower and the -intermediate, and in short, all true Propositions.”</p> -<p>And he elsewhere speaks of successive <span class="sc">Floors</span> of -Induction.</p> -<p>All the truths of an extensive science form a Series -of such Floors, connected by such Scales or Ladders; -and a part of the Logic of Induction consists, as -I <span class="pagenum" id="pagex">x</span> -conceive, in the construction of a <em>Scheme</em> of such -Floors. Converging from a wide basis of various -classes of particulars, at last to one or a few general -truths, these schemes necessarily take the shape of -a Pyramid. I have constructed such Pyramids for -Astronomy and for Optics<a id="fnanchor4-P" href="#note4-P"><span class="fnanchor">4</span></a>; -and the illustrious Von -Humboldt in speaking of the former subject, does me -the honour to say that my attempt in that department -is perfectly successful<a id="fnanchor5-P" href="#note5-P"><span class="fnanchor">5</span></a>. -The Logic of Induction -contains other portions, which may be seen in the -following work, <a href="#page97">b. ii. c. vi.</a></p> -<div class="footnote"><span class="label"> -<a id="note4-P" href="#fnanchor4-P">4</a></span> See the Tables at the end of book ii. -</div> -<div class="footnote"><span class="label"> -<a id="note5-P" href="#fnanchor5-P">5</a></span> <i>Cosmos</i>, vol. ii. n. 35. -</div> -<p>I have made large additions to the present edition, -especially in what regards the Application of Science, -(<a href="#page233">b. iii. c. ix.</a>) and the Language of Science. The -former subject I am aware that I have treated very -imperfectly. It would indeed, of itself, furnish material -for a large work; and would require an acquaintance -with practical arts and manufactures of the most -exact and extensive kind. But even a general observer -may see how much more close the union of Art -with Science is now than it ever was before; and what -large and animating hopes this union inspires, both -for the progress of Art and of Science. On another -subject also I might have dilated to a great extent,—what -I may call (as I have just now called it) the -<i>social</i> machinery for the advancement of science. There -can be no doubt that at certain stages of -sciences, <span class="pagenum" id="pagexi">xi</span> -Societies and Associations may do much to promote -their further progress; by combining their observations, -comparing their views, contributing to provide -material means of observation and calculation, and -dividing the offices of observer and generalizer. We -have had in Europe in general, and especially in this -country, very encouraging examples of what may be -done by such Associations. For the present I have -only ventured to propound one Aphorism on the subject, -namely this; (Aph. LV.) That it is worth considering -whether a continued and connected system of -observation and calculation, like that of Astronomy, -might not be employed in improving our knowledge -of other subjects; as Tides, Currents, Winds, Clouds, -Rain, Terrestrial Magnetism, Aurora Borealis, composition -of crystals, and the like. In saying this, I have -mentioned those subjects which are, as appears to -me, most likely to profit by continued and connected -observations.</p> -<p>I have thrown the substance of my results into -Aphorisms, as Bacon had done in his <i>Novum Organum</i>. -This I have done, not in the way of delivering dogmatic -assertions or oracular sentences; for -the Aphorisms are all supported by reasoning, and -were, in fact, written after the reasoning, and extracted -from it. I have adopted this mode of gathering results -into compact sentences, because it seems to -convey lessons with additional clearness and emphasis.</p> -<p>I have only to repeat what I have already said; that -this task of adapting the <i>Novum Organum</i> to -the <span class="pagenum" id="pagexii">xii</span> -present state of Physical Science, and of constructing a -<i>Newer Organ</i> which may answer the purposes at which -Bacon aimed, seems to belong to the present generation; -and being here founded upon a survey of the -past history and present condition of the Physical -Sciences, will I hope, not be deemed presumptuous.</p> -<p class="bigind"><span class="sc">Trinity Lodge</span>,</p> -<p class="vbigind">1 <i>November</i>, 1858.</p> -<div class="chapter"> -<p class="end"><span class="pagenum" id="pagexiii"></span></p> -<h2 class="nobreak">TABLE OF CONTENTS.</h2> -<hr class="two end" /> -</div> -<table> -<tr><th class="pag"> </th><th colspan="3"> </th><th class="pag">PAGE</th></tr> -<tr><td class="cht" colspan="4">Preface</td><td class="pag"><a -href="#pageiii"><span class="correction" title="emended from v">iii</span></a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5"><span class="larger">BOOK I.</span></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5">APHORISMS CONCERNING IDEAS.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="chn"><span class="sc">Aphorisms</span> I.</td><td class="line">—</td><td class="left">XVIII.</td> -<td class="ch">Ideas in general</td><td class="pag"><a href="#page5">5</a>—7 </td></tr> -<tr><td class="chn">XIX.</td><td class="line">—</td><td class="left">XLIV.</td> -<td class="ch">Ideas in the Pure Sciences</td><td class="pag"><a href="#page8">8</a>—12</td></tr> -<tr><td class="chn">XLV.</td><td class="line">—</td><td class="left">LV.</td> -<td class="ch">Ideas in the Mechanical Sciences</td><td class="pag"><a href="#page13">13</a>—15</td></tr> -<tr><td class="chn">LVI.</td><td class="line">—</td><td class="left">LXXI.</td> -<td class="ch">Ideas in the Secondary Mechanical -Sciences</td><td class="pag"><a href="#page15">15</a>—18</td></tr> -<tr><td class="chn">LXXII.</td><td class="line">—</td><td class="left"><span class="correction" title="emended from LXX.">LXXIII.</span></td> -<td class="ch">Ideas in the Mechanico-chemical -Sciences</td><td class="pag"><a href="#page18">18</a></td></tr> -<tr><td class="chn">LXXIV.</td><td class="line">—</td><td class="left">LXXIX.</td> -<td class="ch">Ideas in Chemistry</td><td class="pag"><a href="#page18">18</a></td></tr> -<tr><td class="chn">LXXX.</td><td class="line">—</td><td class="left">LXXXI.</td> -<td class="ch">Ideas in Morphology</td><td class="pag"><a href="#page19">19</a></td></tr> -<tr><td class="chn"><span class="correction" title="emended from LXXXV.">LXXXII.</span></td><td class="line">—</td><td class="left">C.</td> -<td class="ch">Ideas in Classificatory Science</td><td class="pag"><a href="#page20">20</a>—23</td></tr> -<tr><td class="chn">CI.</td><td class="line">—</td><td class="left">CVI.</td> -<td class="ch">Ideas in Biology</td><td class="pag"><a href="#page23">23</a>—24</td></tr> -<tr><td class="chn">CVII.</td><td class="line">—</td><td class="left">CXVII.</td> -<td class="ch">Ideas in Palæontology</td><td class="pag"><a href="#page24">24</a>—26</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5"><span class="larger">BOOK II.</span></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5">OF KNOWLEDGE.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. I.</td><td class="cht" colspan="3">Of Two Principal Processes by which Science is -constructed</td><td class="pag"><a -href="#page27">27</a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. II.</td><td class="cht" colspan="3">Of the Explication of Conceptions</td><td class="pag"><a -href="#page30">30</a></td></tr> -<tr><td class="ccn"><i>Sect.</i> I.</td><td class="ch" colspan="4"><i>The Historical Progress.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c2a1">1.</a></td><td class="ch" colspan="3">The Explication of Conceptions,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a2">2.</a></td><td class="ch" colspan="3">Has taken place historically by discussions.</td></tr> -<tr><td class="ccn" colspan="5">{xiv}</td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c2a3">3.</a></td><td class="ch" colspan="3">False Doctrines when exposed appear impossible:</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a4">4.</a></td><td class="ch" colspan="3">But were plausible before</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a5">5.</a></td><td class="ch" colspan="3">Men’s Minds gradually cleared.</td></tr> -<tr><td class="ccn"><i>Sect.</i> II.</td><td class="ch" colspan="4"><i>Use of definitions.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c2a6">6.</a></td><td class="ch" colspan="3">Controversies about Definitions.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a7">7.</a></td><td class="ch" colspan="3">Not arbitrary Definitions.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a8">8.</a></td><td class="ch" colspan="3">Attention to Facts requisite.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a9">9.</a></td><td class="ch" colspan="3">Definition is not essential.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a10">10.</a></td><td class="ch" colspan="3">The omission of Definition not always blameable.</td></tr> -<tr><td class="ccn"><i>Sect.</i> III.</td><td class="ch" colspan="4"><i>Use of Axioms.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c2a11">11.</a></td><td class="ch" colspan="3">Axioms serve to express Ideas.</td></tr> -<tr><td class="ccn"><i>Sect.</i> IV.</td><td class="ch" colspan="4"><i>Clear and appropriate Ideas.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c2a12">12.</a></td><td class="ch" colspan="3">We must see the Axioms clearly.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a13">13.</a></td><td class="ch" colspan="3">Inappropriate Ideas cannot lead to Truth.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a14">14.</a></td><td class="ch" colspan="3">The fault is in the Conceptions.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a15">15.</a></td><td class="ch" colspan="3">Rules cannot teach Discovery;</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a16">16.</a></td><td class="ch" colspan="3">But are not useless.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a17">17.</a></td><td class="ch" colspan="3">Discussion as well as Facts needed.</td></tr> -<tr><td class="ccn"><i>Sect.</i> V.</td><td class="ch" colspan="4"><i>Accidental Discoveries.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c2a18">18.</a></td><td class="ch" colspan="3">No Scientific Discovery is accidental.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a19">19.</a></td><td class="ch" colspan="3">Such accidents do not happen to common Men.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a20">20.</a></td><td class="ch" colspan="3">Examples.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c2a21">21.</a></td><td class="ch" colspan="3">So far Explication of Conceptions.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. III.</td><td class="cht" colspan="3">Of Facts as the Materials of Science</td><td class="pag"><a href="#page50">50</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c3a1">1.</a></td><td class="ch" colspan="3">Facts must be true.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a2">2.</a></td><td class="ch" colspan="3">Facts not separable from Ideas.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a3">3.</a></td><td class="ch" colspan="3">The Ideas must be distinct.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a4">4.</a></td><td class="ch" colspan="3">Conceptions of the Intellect only to be admitted.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a5">5.</a></td><td class="ch" colspan="3">Facts are to be observed with reference to -Space and Time:</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a6">6.</a></td><td class="ch" colspan="3">And also to other Ideas.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a7">7.</a></td><td class="ch" colspan="3">The Decomposition of Facts.</td></tr> -<tr><td class="ccn" colspan="5">{xv}</td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c3a8">8.</a></td><td class="ch" colspan="3">This step is not sufficient.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a9">9.</a></td><td class="ch" colspan="3">It introduces Technical Terms,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a10">10.</a></td><td class="ch" colspan="3">And Classification.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c3a11">11.</a></td><td class="ch" colspan="3">The materials of Science.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. IV.</td><td class="cht" colspan="3">Of the Colligation of Facts</td><td class="pag"><a href="#page59">59</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c4a1">1.</a></td><td class="ch" colspan="3">Facts are colligated by Conceptions.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a2">2.</a></td><td class="ch" colspan="3">Science begins with common Observation.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a3">3.</a></td><td class="ch" colspan="3">Facts must be decomposed.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a4">4.</a></td><td class="ch" colspan="3">What Ideas first give Sciences.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a5">5.</a></td><td class="ch" colspan="3">Facts must be referred to Ideas.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a6">6.</a></td><td class="ch" colspan="3">Sagacity needed.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a7">7.</a></td><td class="ch" colspan="3">Discovery made by Guesses.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a8">8.</a></td><td class="ch" colspan="3">False Hypotheses preluding to true ones.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a9">9.</a></td><td class="ch" colspan="3">New Hypotheses not mere modifications of old ones.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a10">10.</a></td><td class="ch" colspan="3">Hypotheses may have superfluous parts.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a11">11.</a></td><td class="ch" colspan="3">Hypotheses to be compared with Facts.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c4a12">12.</a></td><td class="ch" colspan="3">Secondary Steps.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. V.</td><td class="cht" colspan="3">Of certain Characteristics of Scientific Induction</td><td class="pag"><a href="#page70">70</a></td></tr> -<tr><td class="ccn"><i>Sect.</i> I.</td><td class="ch" colspan="4"><i>Invention a part of Induction.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c4a1">1.</a></td><td class="ch" colspan="3">Induction the source of Knowledge.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a2">2.</a></td><td class="ch" colspan="3">Induction involves a New Element.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a3">3.</a></td><td class="ch" colspan="3">Meaning of Induction.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a4">4.</a></td><td class="ch" colspan="3">The New Element is soon forgotten.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a5">5.</a></td><td class="ch" colspan="3">Induction includes a Definition and a Proposition.</td></tr> -<tr><td class="ccn"><i>Sect.</i> II.</td><td class="ch" colspan="4"><i>Use of Hypotheses.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c5a6">6.</a></td><td class="ch" colspan="3">Discoveries made by Guesses,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a7">7.</a></td><td class="ch" colspan="3">Which must be compared with Facts.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a8">8.</a></td><td class="ch" colspan="3">Hypotheses are suspected.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a9">9.</a></td><td class="ch" colspan="3">Hypotheses may be useful though inaccurate.</td></tr> -<tr><td class="ccn"><i>Sect.</i> III.</td><td class="ch" colspan="4"><i>Tests of Hypotheses.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c5a10">10.</a></td><td class="ch" colspan="3">True Hypotheses foretel Phenomena,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a11">11.</a></td><td class="ch" colspan="3">Even of different kinds.—Consilience of -Inductions.</td></tr> -<tr><td class="ccn" colspan="5">{xvi}</td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c5a12">12.</a></td><td class="ch" colspan="3">True Theories tend to Simplicity.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c5a13">13.</a></td><td class="ch" colspan="3">Connexion of the last Tests.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. VI.</td><td class="cht" colspan="3">Of the Logic of Induction</td><td class="pag"><a href="#page97">97</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c6a1">1.</a></td><td class="ch" colspan="3">Steps of Generalization,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a2">2.</a></td><td class="ch" colspan="3">May be expressed by <i>Tables</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a3">3.</a></td><td class="ch" colspan="3">Which exhibit Inductive Steps;</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a4">4.</a></td><td class="ch" colspan="3">And the Consilience of Inductions;</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a5">5.</a></td><td class="ch" colspan="3">And the tendency to Simplicity;</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a6">6.</a></td><td class="ch" colspan="3">And the names of Discoverers;</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a7">7.</a></td><td class="ch" colspan="3">And the Verifications of Theory;</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a8">8.</a></td><td class="ch" colspan="3">By means of several easy steps.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a9">9.</a></td><td class="ch" colspan="3">This resembles Book-keeping.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a10">10.</a></td><td class="ch" colspan="3">The Logic of Induction.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a11">11.</a></td><td class="ch" colspan="3">Attention at each step required.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a12">12.</a></td><td class="ch" colspan="3">General Truths are not mere additions of -particulars:</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a13">13.</a></td><td class="ch" colspan="3">But a new view is introduced.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a14">14.</a></td><td class="ch" colspan="3">Formula of Inductive Logic:</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a15">15.</a></td><td class="ch" colspan="3">May refer to Definition.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a16">16.</a></td><td class="ch" colspan="3">Formula inadequate.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a17">17.</a></td><td class="ch" colspan="3">Deductive Connexion of Steps.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a18">18.</a></td><td class="ch" colspan="3">Relation of Deductive and Inductive Reasoning.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a19">19.</a></td><td class="ch" colspan="3">The Criterion of Truth.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a20">20.</a></td><td class="ch" colspan="3">Theory and Fact.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c6a21">21.</a></td><td class="ch" colspan="3">Higher and Lower Generalizations.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. VII.</td><td class="cht" colspan="3">Of Laws of Phenomena and of Causes</td><td class="pag"><a href="#page118">118</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c7a1">1.</a></td><td class="ch" colspan="3">Knowledge of Laws of Phenomena.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c7a2">2.</a></td><td class="ch" colspan="3"><i>Formal</i> and <i>Physical</i> Sciences.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c7a3">3.</a></td><td class="ch" colspan="3">Causes in Astronomy.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c7a4">4.</a></td><td class="ch" colspan="3">Different Mechanical Causes in other Sciences.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c7a5">5.</a></td><td class="ch" colspan="3">Chemical and Vital Forces as Causes.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c7a6">6.</a></td><td class="ch" colspan="3">Difference of these kinds of Force.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c7a7">7.</a></td><td class="ch" colspan="3">Difficulty of conceiving new Causes.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c7a8">8.</a></td><td class="ch" colspan="3">Men willingly take old Causes.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c7a9">9.</a></td><td class="ch" colspan="3">Is the Magnetic Fluid real? -<tr><td class="chn" colspan="2"><a href="#b2c7a10">10.</a></td><td class="ch" colspan="3">Are Causes to be sought? (Comte’s Doctrine.) -<tr><td class="chn" colspan="2"><a href="#b2c7a11">11.</a></td><td class="ch" colspan="3">Both Laws and Causes to be studied.</td></tr> -<tr><td class="ccn" colspan="5">{xvii}</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. VIII.</td><td class="cht" colspan="3">Of Art and Science</td><td class="pag"><a href="#page129">129</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c8a1">1.</a></td><td class="ch" colspan="3">Art precedes Science.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c8a2">2.</a></td><td class="ch" colspan="3">Contrast of Art and Science.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c8a3">3.</a></td><td class="ch" colspan="3">Instinct and Insight.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c8a4">4.</a></td><td class="ch" colspan="3">Difference of Art and Instinct.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c8a5">5.</a></td><td class="ch" colspan="3">Does Art involve Science? -<tr><td class="chn" colspan="2"><a href="#b2c8a6">6.</a></td><td class="ch" colspan="3">Science unfolds Principles.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c8a7">7.</a></td><td class="ch" colspan="3">Science may improve Art.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c8a8">8.</a></td><td class="ch" colspan="3">Arts not classified with Sciences.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. IX.</td><td class="cht" colspan="3">Of the Classification of Sciences</td><td class="pag"><a href="#page136">136</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b2c9a1">1.</a></td><td class="ch" colspan="3">Use and Limits of such Classification.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c9a2">2.</a></td><td class="ch" colspan="3">Classification depends on the Ideas.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c9a3">3.</a></td><td class="ch" colspan="3">This points out Transitions.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b2c9a4">4.</a></td><td class="ch" colspan="3">The Classification.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht" colspan="4">Inductive Table of Astronomy</td><td class="pag"><a href="#page140a">140</a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht" colspan="4">Inductive Table of Optics</td><td class="pag"><a href="#page140b">140</a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5"><span class="larger">BOOK III.</span></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5">OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. I.</td><td class="cht" colspan="3">Introduction</td><td class="pag"><a href="#page141">141</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c1a1">1.</a></td><td class="ch" colspan="3">Object of this Book.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c1a2">2.</a></td><td class="ch" colspan="3">An Art of Discovery not possible.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c1a3">3.</a></td><td class="ch" colspan="3">Use of Methods.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c1a4">4.</a></td><td class="ch" colspan="3">Series of Six Processes.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c1a5">5.</a></td><td class="ch" colspan="3">Methods of Observation and Induction.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. II.</td><td class="cht" colspan="3">Of Methods of Observation</td><td class="pag"><a href="#page145">145</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c2a1">1.</a></td><td class="ch" colspan="3">Referring to Number, Space, and Time.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a2">2.</a></td><td class="ch" colspan="3">Observations are never perfect.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a3">3.</a></td><td class="ch" colspan="3">(I.) <i>Number is naturally exact</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a4">4.</a></td><td class="ch" colspan="3">(II.) <i>Measurement of Space</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a5">5.</a></td><td class="ch" colspan="3">Instruments Invented in Astronomy,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a6">6.</a></td><td class="ch" colspan="3">And improved.</td></tr> -<tr><td class="ccn" colspan="5">{xviii}</td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c2a7">7.</a></td><td class="ch" colspan="3">Goniometer.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a8">8.</a></td><td class="ch" colspan="3">Standard of Length.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a10">10.</a></td><td class="ch" colspan="3">(III.) <i>Measurement of Time</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a11">11.</a></td><td class="ch" colspan="3">Unit of Time.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a12">12.</a></td><td class="ch" colspan="3">Transit Instrument.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a13">13.</a></td><td class="ch" colspan="3">Chronometers.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a14">14.</a></td><td class="ch" colspan="3">(IV.) <i>Conversion of Space and Time</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a15">15.</a></td><td class="ch" colspan="3">Space may Measure Time.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a16">16.</a></td><td class="ch" colspan="3">Time may Measure Space.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a17">17.</a></td><td class="ch" colspan="3">(V.) <i>The Method of Repetition</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a18">18.</a></td><td class="ch" colspan="3">The Method of Coincidences.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a19">19.</a></td><td class="ch" colspan="3">Applied to Pendulums.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a20">20.</a></td><td class="ch" colspan="3">(VI.) <i>Measurement of Weight</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a21">21.</a></td><td class="ch" colspan="3">Standard of Weight.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a22">22.</a></td><td class="ch" colspan="3">(VII.) <i>Measurement of Secondary Qualities</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a23">23.</a></td><td class="ch" colspan="3">“The Howl” in Harmonics.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a24">24.</a></td><td class="ch" colspan="3">(VIII.) <i>Manipulation</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a25">25.</a></td><td class="ch" colspan="3">Examples in Optics.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a26">26.</a></td><td class="ch" colspan="3">(IX.) <i>The Education of the Senses</i>,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a27">27.</a></td><td class="ch" colspan="3">By the Study of Natural History.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c2a28">28.</a></td><td class="ch" colspan="3">Preparation for Ideas.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. III.</td><td class="cht" colspan="3">Of Methods of Acquiring clear Scientific Ideas; <span style="font-variant: -normal"><i>and first</i></span> of Intellectual Education</td><td class="pag"><a href="#page164">164</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c3a1">1.</a></td><td class="ch" colspan="3">(I.) <i>Idea of Space</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a2">2.</a></td><td class="ch" colspan="3">Education by Geometry.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a3">3.</a></td><td class="ch" colspan="3">(II.) <i>Idea of Number</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a4">4.</a></td><td class="ch" colspan="3">Effect of the usual Education.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a5">5.</a></td><td class="ch" colspan="3">(III.) <i>Idea of Force</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a6">6.</a></td><td class="ch" colspan="3">Study of Mechanics needed,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a7">7.</a></td><td class="ch" colspan="3">To make Newton intelligible.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a8">8.</a></td><td class="ch" colspan="3">No <i>Popular</i> Road.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a9">9.</a></td><td class="ch" colspan="3">(IV.) <i>Chemical Ideas</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a10">10.</a></td><td class="ch" colspan="3">(V.) <i>Natural History Ideas</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a11">11.</a></td><td class="ch" colspan="3">Natural Classes to be taught.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a12">12.</a></td><td class="ch" colspan="3">Mathematical Prejudices,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a13">13.</a></td><td class="ch" colspan="3">To be corrected by Natural History.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a14">14.</a></td><td class="ch" colspan="3">Method of Natural History,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a15">15.</a></td><td class="ch" colspan="3">Resembles common language.</td></tr> -<tr><td class="ccn" colspan="5">{xix}</td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c3a16">16.</a></td><td class="ch" colspan="3">Its Lessons.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a17">17.</a></td><td class="ch" colspan="3">(VI.) <i>Well-established Ideas alone to be used</i>.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c3a18">18.</a></td><td class="ch" colspan="3">How are Ideas cleared? -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. IV.</td><td class="cht" colspan="3">Of Methods of Acquiring Clear Scientific Ideas, <span style="font-variant: -normal"><i>continued</i></span>.—Of the Discussion of Ideas</td><td class="pag"><a href="#page180">180</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c4a1">1.</a></td><td class="ch" colspan="3">Successive Clearness,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c4a2">2.</a></td><td class="ch" colspan="3">Produced by Discussion.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c4a3">3.</a></td><td class="ch" colspan="3">Examples.</td></tr> -<tr><td class="chn" colspan="2">4.</td><td class="ch" colspan="3">Disputes not useless,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c4a5">5.</a></td><td class="ch" colspan="3">Although “metaphysical.” -<tr><td class="chn" colspan="2"><a href="#b3c4a6">6.</a></td><td class="ch" colspan="3">Connected with Facts.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. V.</td><td class="cht" colspan="3">Analysis of the Process of Induction</td><td class="pag"><a href="#page186">186</a></td></tr> -<tr><td class="ccn"><i>Sect.</i> I.</td><td class="ch" colspan="4"><i>The Three Steps of Induction.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c5a1">1.</a></td><td class="ch" colspan="3">Methods may be useful.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c5a2">2.</a></td><td class="ch" colspan="3">The three Steps.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c5a3">3.</a></td><td class="ch" colspan="3">Examples.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c5a4">4.</a></td><td class="ch" colspan="3">Mathematical names of the Steps.</td></tr> -<tr><td class="ccn"><i>Sect.</i> II.</td><td class="ch" colspan="4"><i>Of the Selection of the Fundamental Idea.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c5a5">5.</a></td><td class="ch" colspan="3">Examples.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c5a6">6.</a></td><td class="ch" colspan="3">The Idea to be found by trying,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c5a7">7.</a></td><td class="ch" colspan="3">Till the Discovery is made;</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c5a8">8.</a></td><td class="ch" colspan="3">Preluded by Guesses.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c5a9">9.</a></td><td class="ch" colspan="3">Idea and Facts homogeneous.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c5a10">10.</a></td><td class="ch" colspan="3">Idea tested by the Facts.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. VI.</td><td class="cht" colspan="3">General Rules for the Construction of the -Conception</td><td class="pag"><a href="#page195">195</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c6a1">1.</a></td><td class="ch" colspan="3">First: for Quantity.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c6a2">2.</a></td><td class="ch" colspan="3">Formula and Coefficients found together.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c6a3">3.</a></td><td class="ch" colspan="3">Example. Law of Cooling.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c6a4">4.</a></td><td class="ch" colspan="3">Determined by Experiment.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c6a5">5.</a></td><td class="ch" colspan="3">Progressive Series of Numbers.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c6a6">6.</a></td><td class="ch" colspan="3">Recurrent Series.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c6a7">7.</a></td><td class="ch" colspan="3">Use of Hypotheses.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c6a8">8.</a></td><td class="ch" colspan="3">Even with this there are difficulties.</td></tr> -<tr><td class="ccn" colspan="5">{xv}</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. VII.</td><td class="cht" colspan="3">Special Methods of Induction Applicable to -Quantity</td><td class="pag"><a href="#page202">202</a></td></tr> -<tr><td class="ccn"><i>Sect.</i> I.</td><td class="ch" colspan="4"><i>The Method of Curves.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c7a1">1.</a></td><td class="ch" colspan="3">Its Process.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a2">2.</a></td><td class="ch" colspan="3">Its Use.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a3">3.</a></td><td class="ch" colspan="3">With imperfect Observations.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a4">4.</a></td><td class="ch" colspan="3">It corrects Observations.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a5">5.</a></td><td class="ch" colspan="3"><i>Obstacles</i>. (I.) Ignorance of the argument.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a6">6.</a></td><td class="ch" colspan="3">(II.) Combination of Laws.</td></tr> -<tr><td class="ccn"><i>Sect.</i> II.</td><td class="ch" colspan="4"><i>The Method of Means.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c7a7">7.</a></td><td class="ch" colspan="3">Its Relation to the Method of Curves.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a8">8.</a></td><td class="ch" colspan="3">Its process.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a9">9.</a></td><td class="ch" colspan="3"><i>Argument</i> required to be known.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a10">10.</a></td><td class="ch" colspan="3">Use of the Method.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a11">11.</a></td><td class="ch" colspan="3">Large masses of Observations used.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a12">12.</a></td><td class="ch" colspan="3">Proof of the Use of the Method.</td></tr> -<tr><td class="ccn"><i>Sect.</i> III.</td><td class="ch" colspan="4"><i>The Method of Least Squares.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c7a13">13.</a></td><td class="ch" colspan="3">Is a Method of Means.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a14">14.</a></td><td class="ch" colspan="3">Example.</td></tr> -<tr><td class="ccn"><i>Sect.</i> IV.</td><td class="ch" colspan="4"><i>The Method of Residues.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c7a15">15.</a></td><td class="ch" colspan="3">Occasion for its Use.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a16">16.</a></td><td class="ch" colspan="3">Its Process.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a17">17.</a></td><td class="ch" colspan="3">Examples.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a18">18.</a></td><td class="ch" colspan="3">Its Relation to the Method of Means.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a19">19.</a></td><td class="ch" colspan="3">Example.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c7a20">20.</a></td><td class="ch" colspan="3">“Residual Phenomena.” -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. VIII.</td><td class="cht" colspan="3">Methods of Induction Depending on Resemblance</td><td class="pag"><a href="#page220">220</a></td></tr> -<tr><td class="ccn"><i>Sect.</i> I.</td><td class="ch" colspan="4"><i>The Law of Continuity.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c8a1">1.</a></td><td class="ch" colspan="3">Its Nature and Application,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a2">2.</a></td><td class="ch" colspan="3">To Falling Bodies,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a3">3.</a></td><td class="ch" colspan="3">To Hard Bodies,</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a4">4.</a></td><td class="ch" colspan="3">To Gravitation.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a5">5.</a></td><td class="ch" colspan="3">The Evidence.</td></tr> -<tr><td class="ccn" colspan="5">{xxi}</td></tr> -<tr><td class="ccn"><i>Sect.</i> II.</td><td class="ch" colspan="4"><i>The Method of Gradation.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c8a6">6.</a></td><td class="ch" colspan="3">Occasions of its Use.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a7">7.</a></td><td class="ch" colspan="3">Examples.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a8">8.</a></td><td class="ch" colspan="3">Not enjoined by Bacon.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a9">9.</a></td><td class="ch" colspan="3">Other Examples.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a10">10.</a></td><td class="ch" colspan="3">Its Value in Geology.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a11">11.</a></td><td class="ch" colspan="3">Limited Results.</td></tr> -<tr><td class="ccn"><i>Sect.</i> III.</td><td class="ch" colspan="4"><i>The Method of Natural Classification.</i></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c8a12">12.</a></td><td class="ch" colspan="3">Examples of its Use.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a13">13.</a></td><td class="ch" colspan="3">Its Process.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a14">14.</a></td><td class="ch" colspan="3">Negative Results.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a15">15.</a></td><td class="ch" colspan="3">Is opposed to Arbitrary Definitions.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a16">16.</a></td><td class="ch" colspan="3">Propositions and Definitions correlative.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c8a17">17.</a></td><td class="ch" colspan="3">Definitions only provisional.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. IX.</td><td class="cht" colspan="3">Of the Application of Inductive Truths</td><td class="pag"><a href="#page233">233</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c9a1">1.</a></td><td class="ch" colspan="3">This forms the Sequel of Discovery.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c9a2">2.</a></td><td class="ch" colspan="3">Systematic Verification of Discoveries.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c9a3">3.</a></td><td class="ch" colspan="3">Correction of Coefficients.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c9a4">4.</a></td><td class="ch" colspan="3">Astronomy a Model.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c9a5">5.</a></td><td class="ch" colspan="3">Verification by new cases.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c9a6">6.</a></td><td class="ch" colspan="3">Often requires fresh calculation.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c9a7">7.</a></td><td class="ch" colspan="3">Cause of Dew.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c9a8">8.</a></td><td class="ch" colspan="3">Useful Applications.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht">Chap. X.</td><td class="cht" colspan="3">Of the Induction of Causes</td><td class="pag"><a href="#page247">247</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b3c10a1">1.</a></td><td class="ch" colspan="3">Is to be pursued.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c10a2">2.</a></td><td class="ch" colspan="3">Induction of Substance.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c10a3">3.</a></td><td class="ch" colspan="3">Induction of Force.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c10a4">4.</a></td><td class="ch" colspan="3">Induction of Polarity.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c10a5">5.</a></td><td class="ch" colspan="3">Is Gravity Polar? -<tr><td class="chn" colspan="2"><a href="#b3c10a6">6.</a></td><td class="ch" colspan="3">Induction of Ulterior Causes.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b3c10a7">7.</a></td><td class="ch" colspan="3">Of the Supreme Cause.</td></tr> -<tr><td class="ccn" colspan="5">{xxii}</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5"><span class="larger">BOOK IV.</span></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5">OF THE LANGUAGE OF SCIENCE.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht" colspan="4">Introduction</td><td class="pag"><a href="#page257">257</a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="cht" colspan="5"> Aphorisms concerning the Language of Science.</td></tr> -<tr><td class="ch" colspan="2"><i>Aphorism</i> I.</td><td class="ch" colspan="2">Relative to the Ancient Period</td><td class="pag"><a href="#page258">258</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b4a1a1">1.</a></td><td class="ch" colspan="3">Common Words.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a1a2">2.</a></td><td class="ch" colspan="3">Descriptive Terms.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a1a3">3.</a></td><td class="ch" colspan="3">Theoretical Terms.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ch" colspan="2"><i>Aphorism</i> II.</td><td class="ch" colspan="2">Relative to the Modern Period</td><td class="pag"><a href="#page269">269</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b4a2a1">1.</a></td><td class="ch" colspan="3">Systematic Nomenclature.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a2a2">2.</a></td><td class="ch" colspan="3">Systematic Terminology.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a2a3">3.</a></td><td class="ch" colspan="3">Systematic Modification.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ch" style="padding-left: 7em; text-indent: -6em" colspan="4"><i>Aphorisms</i> (III. IV. V. VI. VII.) relative to the -Application of Common Words</td><td class="pag"><a href="#page278">278</a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ch" style="padding-left: 7em; text-indent: -6em" colspan="4"><i>Aphorisms</i> (VIII. IX. X. XI. XII. XIII.) relative to the -Construction of New Terms</td><td class="pag"><a href="#page285">285</a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ch" colspan="2"><i>Aphorism</i> XIV.</td><td class="ch" colspan="2">Binary Nomenclature</td><td class="pag"><a href="#page307">307</a></td></tr> -<tr><td class="chn" colspan="2">XV.</td><td class="ch" colspan="2">Linnæan Maxims</td><td class="pag"><a href="#page308">308</a></td></tr> -<tr><td class="chn" colspan="2">XVI.</td><td class="ch" colspan="2">Numerical Names</td><td class="pag"><a href="#page309">309</a></td></tr> -<tr><td class="chn" colspan="2">XVII.</td><td class="ch" colspan="2">Names of more than two Steps</td><td class="pag"><a href="#page310">310</a></td></tr> -<tr><td class="chn" colspan="2">XVIII.</td><td class="ch" colspan="2">No arbitrary <i>Terms</i></td><td class="pag"><a href="#page311">311</a></td></tr> -<tr><td class="chn" colspan="2">XIX.</td><td class="ch" colspan="2">Forms fixed by Convention</td><td class="pag"><a href="#page314">314</a></td></tr> -<tr><td class="chn" colspan="2">XX.</td><td class="ch" colspan="2"><i>Form</i> of Terms</td><td class="pag"><a href="#page318">318</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b4a20a1">1.</a></td><td class="ch" colspan="3">Terms derived from Latin and Greek.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a20a2">2.</a></td><td class="ch" colspan="3">German Terms.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a20a3">3.</a></td><td class="ch" colspan="3">Descriptive Terms.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a20a4">4.</a></td><td class="ch" colspan="3">Nomenclature. Zoology.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a20a5">5.</a></td><td class="ch" colspan="3">—————— Mineralogy.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a20a6">6.</a></td><td class="ch" colspan="3">—————— Botany.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a20a7">7.</a></td><td class="ch" colspan="3">—————— Chemistry.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a20a8">8.</a></td><td class="ch" colspan="3">—————— Crystallography.</td></tr> -<tr><td class="ccn" colspan="5">{xxiii}</td></tr> -<tr><td class="ch" colspan="2"><i>Aphorism</i> XXI.</td><td class="ch" colspan="2"> Philological Rules</td><td class="pag"><a href="#page328">328</a></td></tr> -<tr><td class="chn"><i>Art.</i></td><td class="chn"><a href="#b4a21a1">1.</a></td><td class="ch" colspan="3">Hybrids.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a21a2">2.</a></td><td class="ch" colspan="3">Terminations of Substantives.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a21a3">3.</a></td><td class="ch" colspan="3">Formations of Substantives (names of things).</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a21a4">4.</a></td><td class="ch" colspan="3">Abstract Substantives.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a21a5">5.</a></td><td class="ch" colspan="3">Rules of derivation from Greek and Latin.</td></tr> -<tr><td class="chn" colspan="2"><a href="#b4a21a6">6.</a></td><td class="ch" colspan="3">Modification of Terminations.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ch" colspan="2"><i>Aphorism</i> XXII.</td><td class="ch" colspan="2"> Introduction of Changes</td><td class="pag"><a href="#page341">341</a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5">FURTHER ILLUSTRATIONS OF THE APHORISMS ON SCIENTIFIC -LANGUAGE, FROM THE RECENT COURSE OF SCIENCES.</td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5">1. <span class="sc">Botany.</span></td></tr> -<tr><td class="ch" colspan="2"><i>Aphorism</i> XXIII.</td><td class="ch" colspan="2">Multiplication of Genera</td><td class="pag"><a href="#page346">346</a></td></tr> -<tr><td colspan="5"> </td></tr> -<tr><td class="ccn" colspan="5">2. <span class="sc">Comparative Anatomy.</span></td></tr> -<tr><td class="ch" colspan="2"><i>Aphorism</i> XXIV.</td><td class="ch" colspan="2">Single Names to be used</td><td class="pag"><a href="#page353">353</a></td></tr> -<tr><td class="chn" colspan="2">XXV.</td><td class="ch" colspan="2">The History of Science is the History -of its Language</td><td class="pag"><a href="#page355">355</a></td></tr> -<tr><td class="chn" colspan="2">XXVI.</td><td class="ch" colspan="2">Algebraical Symbols</td><td class="pag"><a href="#page357">357</a></td></tr> -<tr><td class="chn" colspan="2">XXVII.</td><td class="ch" colspan="2">Algebraical Analogies</td><td class="pag"><a href="#page364">364</a></td></tr> -<tr><td class="chn" colspan="2">XXVIII.</td><td class="ch" colspan="2">Capricious Derivations</td><td class="pag"><a href="#page365">365</a></td></tr> -<tr><td class="chn" colspan="2">XXIX.</td><td class="ch" colspan="2">Inductions are our Definitions</td><td class="pag"><a href="#page368">368</a></td></tr> -</table> -<div class="chapter"> -<p><span class="pagenum" id="page1"></span></p> -<p class="h2 end">NOVUM ORGANON<br /> -RENOVATUM.</p> -<p class="blkquot"> -<span class="sc">De</span> Scientiis tum demum bene sperandum est, quando per -<span class="sc">Scalam</span> veram et per gradus continuos, et non intermissos aut -hiulcos, a particularibus ascendetur ad Axiomata minora, et -deinde ad media, alia aliis superiora, et postremo demum ad -generalissima.</p> -<p class="blkquot">In constituendo autem Axiomate, -Forma <span class="sc">Inductionis</span> alia -quam adhuc in usu fuit, excogitanda est; et quæ non ad Principia -tantum (quæ vocant) probanda et invenienda, sed etiam ad -Axiomata minora, et media, denique omnia.</p> -<p class="citation small eq end"><span class="sc">Bacon</span>, <i>Nov. Org.</i>, Aph. civ. cv.</p> -</div> -<div class="chapter"> -<p><span class="pagenum" id="page3"></span></p> -<h3 class="nobreak">NOVUM ORGANON RENOVATUM.</h3> -</div> -<hr class="two end" /> -<p><span class="sc">The</span> name <i>Organon</i> was applied to the works of -Aristotle which treated of Logic, that is, of the method -of establishing and proving knowledge, and of refuting -errour, by means of Syllogisms. Francis Bacon, holding -that this method was insufficient and futile for -the augmentation of real and useful knowledge, published -his <i>Novum Organon</i>, in which he proposed for -that purpose methods from which he promised a better -success. Since his time real and useful knowledge has -made great progress, and many Sciences have been -greatly extended or newly constructed; so that even -if Bacon’s method had been the right one, and had -been complete as far as the progress of Science up to -his time could direct it, there would be room for the -revision and improvement of the methods of arriving -at scientific knowledge.</p> -<p>Inasmuch as we have gone through the <i>Histories</i> -of the principal <i>Sciences</i>, from the earliest up to the -present time, in a previous work, and have also traced -the <i>History of Scientific Ideas</i> in another work, it -may perhaps be regarded as not too presumptuous if -we attempt this revision and improvement of the -methods by which Sciences must rise and grow. -This <span class="pagenum" id="page4">4</span> -is our task in the present volume; and to mark the -reference of this undertaking to the work of Bacon, we -name our book <i>Novum Organon Renovatum</i>.</p> -<p class="end">Bacon has delivered his precepts in Aphorisms, -some of them stated nakedly, others expanded into -dissertations. The general results at which we have -arrived by tracing the history of Scientific Ideas are -the groundwork of such Precepts as we have to give: -and I shall therefore begin by summing up these -results in Aphorisms, referring to the former work -for the historical proof that these Aphorisms are true.</p> -<div class="chapter"> -<p><span class="pagenum" id="page5"></span></p> -<p class="h2 end">NOVUM ORGANON RENOVATUM.</p> -<hr class="three" /> -<h2 class="nobreak">BOOK I.</h2> -<p class="center end">APHORISMS CONCERNING IDEAS DERIVED FROM -THE HISTORY OF IDEAS.</p> -<hr class="one" /> -</div> -<p class="center">I.</p> -<p><i>MAN is the Interpreter of Nature, Science the right -interpretation.</i> (<i>History of Scientific Ideas</i>: -Book <span class="sc">i.</span> Chapter 1.)</p> -<p class="center">II.</p> -<p><i>The</i> Senses <i>place before us the</i> Characters <i>of the Book -of Nature; but these convey no knowledge to us, till we -have discovered the Alphabet by which they are to be read.</i> -(Ibid. <span class="sc">i.</span> 2.)</p> -<p class="center" id="b1a3">III.</p> -<p><i>The</i> Alphabet, <i>by means of which we interpret Phenomena, -consists of the</i> Ideas <i>existing in our own minds; for -these give to the phenomena that coherence and significance -which is not an object of sense.</i> (<span class="sc">i.</span> 2.)</p> -<p class="center">IV.</p> -<p><i>The antithesis of</i> Sense <i>and</i> Ideas <i>is the foundation of -the Philosophy of Science. No knowledge can exist without -the union, no philosophy without the separation, of these two -elements.</i> (<span class="sc">i.</span> 2.) -<span class="pagenum" id="page6">6</span></p> -<p class="center">V.</p> -<p>Fact <i>and</i> Theory <i>correspond to Sense on the one hand, -and to Ideas on the other, so far as we are</i> conscious <i>of our -Ideas: but all facts involve ideas</i> unconsciously; <i>and thus -the distinction of Facts and Theories is not tenable, as that -of Sense and Ideas is.</i> (<span class="sc">i.</span> 2.)</p> -<p class="center">VI.</p> -<p><i>Sensations and Ideas in our knowledge are like Matter -and Form in bodies. Matter cannot exist without Form, -nor Form without Matter: yet the two are altogether distinct -and opposite. There is no possibility either of separating, -or of confounding them. The same is the case with -Sensations and Ideas.</i> (<span class="sc">i.</span> 2.)</p> -<p class="center">VII.</p> -<p><i>Ideas are not</i> trans<i>formed, but</i> in<i>formed Sensations; for -without ideas, sensations have no form.</i> (<span class="sc">i.</span> 2.)</p> -<p class="center">VIII.</p> -<p><i>The Sensations are the</i> Objective, <i>the Ideas the</i> Subjective -<i>part of every act of perception or knowledge.</i> (<span class="sc">i.</span> 2.)</p> -<p class="center">IX.</p> -<p><i>General Terms denote</i> Ideal Conceptions, <i>as a</i> circle, <i>an</i> -orbit, <i>a</i> rose. <i>These are not</i> Images <i>of real things, as was -held by the Realists, but Conceptions: yet they are conceptions, not bound -together by mere</i> Name, <i>as the Nominalists -held, but by an Idea.</i> (<span class="sc">i.</span> 2.)</p> -<p class="center">X.</p> -<p><i>It has been said by some, that all Conceptions are merely</i> -states <i>or</i> feelings of the mind, <i>but this assertion only tends -to confound what it is our business to distinguish.</i> (<span class="sc">i.</span> 2.)</p> -<p class="center">XI.</p> -<p><i>Observed Facts are connected so as to produce new truths, -by superinducing upon them an Idea: and such truths are -obtained</i> by Induction. (<span class="sc">i.</span> 2.) -<span class="pagenum" id="page7">7</span></p> -<p class="center">XII.</p> -<p><i>Truths once obtained by legitimate Induction are Facts: -these Facts may be again connected, so as to produce higher -truths: and thus we advance to</i> Successive Generalizations. -(<span class="sc">i.</span> 2.)</p> -<p class="center">XIII.</p> -<p><i>Truths obtained by Induction are made compact and -permanent by being expressed in</i> Technical Terms. (<span class="sc">i.</span> 3.)</p> -<p class="center">XIV.</p> -<p><i>Experience cannot conduct us to universal and necessary -truths:—Not to universal, because she has not tried all -cases:—Not to necessary, because necessity is not a matter -to which experience can testify.</i> (<span class="sc">i.</span> 5.)</p> -<p class="center">XV.</p> -<p><i>Necessary truths derive their necessity from the</i> Ideas -<i>which they involve; and the existence of necessary truths -proves the existence of Ideas not generated by experience.</i> -(<span class="sc">i.</span> 5.)</p> -<p class="center">XVI.</p> -<p><i>In Deductive Reasoning, we cannot have any truth in -the conclusion which is not virtually contained in the -premises.</i> (<span class="sc">i.</span> 6.)</p> -<p class="center">XVII.</p> -<p><i>In order to acquire any exact and solid knowledge, the -student must possess with perfect precision the ideas -appropriate to that part of knowledge: and this precision is -tested by the student’s</i> perceiving <i>the axiomatic evidence of -the</i> axioms <i>belonging to each</i> Fundamental Idea. (<span class="sc">i.</span> 6.)</p> -<p class="center">XVIII.</p> -<p><i>The Fundamental Ideas which it is most important to -consider, as being the Bases of the Material Sciences, are the -Ideas of</i> Space, Time (<i>including Number</i>), Cause -(<i>including Force and Matter</i>), Outness <i>of Objects, and</i> Media <i>of -Perception of Secondary Qualities,</i> Polarity (<i>Contrariety</i>), -<span class="pagenum" id="page8">8</span> -<i>Chemical</i> Composition <i>and</i> Affinity, Substance, Likeness -<i>and Natural</i> Affinity, Means and Ends (<i>whence the Notion -of Organization</i>), Symmetry, <i>and the Ideas of</i> Vital Powers. -(<span class="sc">i.</span> 8.)</p> -<p class="center">XIX.</p> -<p><i>The Sciences which depend upon the Ideas of Space and -Number are</i> Pure <i>Sciences, not</i> Inductive <i>Sciences: they do -not infer special Theories from Facts, but deduce the conditions -of all theory from Ideas. The Elementary Pure -Sciences, or Elementary Mathematics, are Geometry, Theoretical -Arithmetic and Algebra.</i> (<span class="sc">ii.</span> 1.)</p> -<p class="center">XX.</p> -<p><i>The Ideas on which the Pure Sciences depend, are those -of</i> Space <i>and</i> Number; <i>but Number is a modification of -the conception of Repetition, which belongs to the Idea of</i> -Time. (<span class="sc">ii.</span> 1.)</p> -<p class="center">XXI.</p> -<p><i>The</i> Idea of Space <i>is not derived from experience, for -experience of external objects</i> pre<i>supposes bodies to exist in -Space, Space is a condition under which the mind receives -the impressions of sense, and therefore the relations of space -are necessarily and universally true of all perceived objects. -Space is a</i> form <i>of our perceptions, and regulates them, -whatever the</i> matter <i>of them may be.</i> (<span class="sc">ii.</span> 2.)</p> -<p class="center">XXII.</p> -<p><i>Space is not a General Notion collected by abstraction -from particular cases; for we do not speak of</i> Spaces <i>in -general, but of universal or absolute</i> Space. <i>Absolute Space -is infinite. All special spaces are</i> in <i>absolute space, and are -parts of it.</i> (<span class="sc">ii.</span> 3.)</p> -<p class="center">XXIII.</p> -<p><i>Space is not a real object or thing, distinct from the -objects which exist in it; but it is a real condition of the -existence of external objects.</i> (<span class="sc">ii.</span> 3.) -<span class="pagenum" id="page9">9</span></p> -<p class="center">XXIV.</p> -<p><i>We have an</i> Intuition <i>of objects in space; that is, we -contemplate objects as</i> made up <i>of spatial parts, and -apprehend their spatial relations by the same act by which we -apprehend the objects themselves.</i> (<span class="sc">ii.</span> 3.)</p> -<p class="center">XXV.</p> -<p>Form <i>or Figure is space limited by boundaries. Space -has necessarily</i> three <i>dimensions, length, breadth, depth; and -no others which cannot be resolved into these.</i> (<span class="sc">ii.</span> 3.)</p> -<p class="center">XXVI.</p> -<p><i>The Idea of Space is exhibited for scientific purposes, by -the</i> Definitions <i>and</i> Axioms <i>of Geometry; such, for instance, -as these:—the</i> Definition of a Right Angle, <i>and</i> of a Circle;—<i>the</i> -Definition of Parallel Lines, <i>and the</i> Axiom <i>concerning them;—the</i> -Axiom <i>that</i> two straight lines cannot -inclose a space. <i>These Definitions are necessary, not arbitrary; -and the Axioms are needed as well as the Definitions, -in order to express the necessary conditions which the Idea of -Space imposes.</i> (<span class="sc">ii.</span> 4.)</p> -<p class="center">XXVII.</p> -<p><i>The Definitions and Axioms of Elementary Geometry do -not</i> completely <i>exhibit the Idea of Space. In proceeding -to the Higher Geometry, we may introduce other additional -and independent Axioms; such as that of Archimedes, that</i> -a curve line which joins two points is less than any -broken line joining the same points and including the -curve line. (<span class="sc">ii.</span> 4.)</p> -<p class="center">XXVIII.</p> -<p><i>The perception of a</i> solid object <i>by sight requires that act -of mind by which, from figure and shade, we infer distance -and position in space. The perception of</i> figure <i>by sight -requires that act of mind by which we give an outline -to each object.</i> (<span class="sc">ii.</span> 6.) -<span class="pagenum" id="page10">10</span></p> -<p class="center">XXIX.</p> -<p><i>The perception of Form by touch is not an impression on -the passive sense, but requires an act of our muscular frame -by which we become aware of the position of our own limbs. -The perceptive faculty involved in this act has been called</i> -the muscular sense. (<span class="sc">ii.</span> 6.)</p> -<p class="center">XXX.</p> -<p><i>The</i> Idea of Time <i>is not derived from experience, for -experience of changes</i> pre<i>supposes occurrences to take place in -Time. Time is a condition under which the mind receives -the impressions of sense, and therefore the relations of time -are necessarily and universally true of all perceived occurrences. -Time is a</i> form <i>of our perceptions, and regulates -them, whatever the</i> matter <i>of them may be.</i> (<span class="sc">ii.</span> 7.)</p> -<p class="center">XXXI.</p> -<p><i>Time is not a General Notion collected by abstraction -from particular cases. For we do not speak of particular</i> -Times <i>as examples of time in general, but as parts of a -single and infinite</i> Time. (<span class="sc">ii.</span> 8.)</p> -<p class="center">XXXII.</p> -<p><i>Time, like Space, is a form, not only of perception, but -of</i> Intuition. <i>We consider the whole of any time as</i> equal -<i>to the</i> sum <i>of the parts; and an occurrence as</i> coinciding -<i>with the portion of time which it occupies.</i> (<span class="sc">ii.</span> 8.)</p> -<p class="center">XXXIII.</p> -<p><i>Time is analogous to Space of</i> one dimension: <i>portions -of both have a beginning and an end, are long or short. -There is nothing in Time which is analogous to Space of -two, or of three, dimensions, and thus nothing which corresponds -to Figure.</i> (<span class="sc">ii.</span> 8.)</p> -<p class="center">XXXIV.</p> -<p><i>The Repetition of a set of occurrences, as, for example, -strong and weak, or long and short sounds, according -to a</i> <span class="pagenum" id="page11">11</span> -<i>steadfast order, produces</i> Rhythm, <i>which is a conception -peculiar to Time, as Figure is to Space.</i> (<span class="sc">ii.</span> 8.)</p> -<p class="center">XXXV.</p> -<p><i>The simplest form of Repetition is that in which there is -no variety, and thus gives rise to the conception of</i> Number. -(<span class="sc">ii.</span> 8.)</p> -<p class="center">XXXVI.</p> -<p><i>The simplest numerical truths are seen by Intuition; when -we endeavour to deduce the more complex from these simplest, -we employ such maxims as these</i>:—If equals be added -to equals the wholes are equal:—If equals be subtracted -from equals the remainders are equal:—The whole is -equal to the sum of all its parts. (<span class="sc">ii.</span> 9.)</p> -<p class="center">XXXVII.</p> -<p><i>The Perception of Time involves a constant and latent -kind of memory, which may be termed a</i> Sense of Succession. -<i>The Perception of Number also involves this Sense of -Succession, although in small numbers we appear to apprehend -the units simultaneously and not successively.</i> (<span class="sc">ii.</span> 10.)</p> -<p class="center">XXXVIII.</p> -<p><i>The Perception of Rhythm is not an impression on the -passive sense, but requires an act of thought by which we -connect and group the strokes which form the Rhythm.</i> -(<span class="sc">ii.</span> 10.)</p> -<p class="center">XXXIX.</p> -<p>Intuitive <i>is opposed to</i> Discursive <i>reason. In intuition, -we obtain our conclusions by dwelling upon</i> one <i>aspect of -the fundamental Idea; in discursive reasoning, we combine</i> -several <i>aspects of the Idea,</i> (<i>that is, several axioms,</i>) <i>and -reason from the combination.</i> (<span class="sc">ii.</span> 11.)</p> -<p class="center">XL.</p> -<p><i>Geometrical deduction</i> (<i>and deduction in general</i>) <i>is called</i> -Synthesis, <i>because we introduce, at successive steps, -the</i> <span class="pagenum" id="page12">12</span> -<i>results of new principles. But in reasoning on the relations -of space, we sometimes go on</i> separating <i>truths into their -component truths, and these into other component truths; and -so on: and this is geometrical</i> Analysis. (<span class="sc">ii.</span> 11.)</p> -<p class="center">XLI.</p> -<p><i>Among the foundations of the Higher Mathematics, is the</i> -Idea of Symbols <i>considered as general</i> Signs <i>of Quantity. -This idea of a Sign is distinct from, and independent of -other ideas. The Axiom to which we refer in reasoning by -means of Symbols of quantity is this</i>:—The interpretation -of such symbols must be perfectly general. <i>This Idea -<span class="correction" title="emended from 'of' [2nd ed.]">and</span> -Axiom are the bases of Algebra in its most general form.</i> -(<span class="sc">ii.</span> 12.)</p> -<p class="center">XLII.</p> -<p><i>Among the foundations of the Higher Mathematics is -also the</i> Idea of a Limit. <i>The Idea of a Limit cannot be -superseded by any other definitions or Hypotheses, The -Axiom which we employ in introducing this Idea into our -reasoning is this</i>:—What is true up to the Limit is true -at the Limit. <i>This Idea and Axiom are the bases of all -Methods of Limits, Fluxions, Differentials, Variations, and -the like.</i> (<span class="sc">ii.</span> 12.)</p> -<p class="center">XLIII.</p> -<p><i>There is a</i> pure <i>Science of Motion, which does not depend -upon observed facts, but upon the Idea of motion. It may -also be termed</i> Pure Mechanism, <i>in opposition to Mechanics -Proper, or</i> Machinery, <i>which involves the mechanical conceptions of -force and matter. It has been proposed to name -this Pure Science of Motion,</i> Kinematics. (<span class="sc">ii.</span> 13.)</p> -<p class="center">XLIV.</p> -<p><i>The pure Mathematical Sciences must be successfully cultivated, -in order that the progress of the principal Inductive -Sciences may take place. This appears in the case of Astronomy, -in which Science, both in ancient and in modern -times, each advance of the theory has depended upon -the</i> <span class="pagenum" id="page13">13</span> <i>previous -solution of problems in pure mathematics. It appears -also inversely in the Science of the Tides, in which, at present, -we cannot advance in the theory, because we cannot -solve the requisite problems in the Integral Calculus.</i> (<span class="sc">ii.</span> 14.)</p> -<p class="center">XLV.</p> -<p><i>The</i> Idea of Cause, <i>modified into the conceptions of -mechanical cause, or Force, and resistance to force, or Matter, -is the foundation of the Mechanical Sciences; that is, Mechanics,</i> -(<i>including Statics and Dynamics,</i>) <i>Hydrostatics, -and Physical Astronomy.</i> (<span class="sc">iii.</span> 1.)</p> -<p class="center">XLVI.</p> -<p><i>The Idea of Cause is not derived from experience; for in -judging of occurrences which we contemplate, we consider -them as being, universally and necessarily, Causes and Effects, -which a finite experience could not authorize us to do. -The Axiom, that every event must have a cause, is true -independently of experience, and beyond the limits of -experience.</i> (<span class="sc">iii.</span> 2.)</p> -<p class="center">XLVII.</p> -<p><i>The Idea of Cause is expressed for purposes of science by -these three Axioms</i>:—Every Event must have a Cause:—Causes -are measured by their Effects:—Reaction is equal -and opposite to Action. (<span class="sc">iii.</span> 4.)</p> -<p class="center">XLVIII.</p> -<p><i>The Conception of Force involves the Idea of Cause, as -applied to the motion and rest of bodies. The conception of</i> -force <i>is suggested by muscular action exerted: the conception -of</i> matter <i>arises from muscular action resisted. We necessarily -ascribe to all bodies solidity and inertia, since we -conceive Matter as that which cannot be compressed or moved -without resistance.</i> (<span class="sc">iii.</span> 5.)</p> -<p class="center">XLIX.</p> -<p><i>Mechanical Science depends on the Conception of Force; -and is divided into</i> Statics, <i>the doctrine of Force preventing</i> -<span class="pagenum" id="page14">14</span> <i>motion, and</i> -Dynamics, <i>the doctrine of Force producing -motion.</i> (<span class="sc">iii.</span> 6.)</p> -<p class="center">L.</p> -<p><i>The Science of Statics depends upon the Axiom, that Action and -Reaction are equal, which in Statics assumes this -form</i>:—When two equal weights are supported on the -middle point between them, the pressure on the fulcrum -is equal to the sum of the weights. (<span class="sc">iii.</span> 6.)</p> -<p class="center">LI.</p> -<p><i>The Science of Hydrostatics depends upon the Fundamental -Principle that</i> fluids press equally in all directions. -<i>This principle necessarily results from the conception of a -Fluid, as a body of which the parts are perfectly moveable -in all directions. For since the Fluid is a body, it can -transmit pressure; and the transmitted pressure is equal to -the original pressure, in virtue of the Axiom that Reaction -is equal to Action. That the Fundamental Principle is not -derived from experience, is plain both from its evidence and -from its history.</i> (<span class="sc">iii.</span> 6.)</p> -<p class="center">LII.</p> -<p><i>The Science of Dynamics depends upon the three Axioms -above stated respecting Cause. The First Axiom,—that every -change must have a Cause,—gives rise to the First Law of -Motion,—that</i> a body not acted upon by a force will move -with a uniform velocity in a straight line. <i>The Second -Axiom,—that Causes are measured by their Effects,—gives -rise to the Second Law of Motion,—that</i> when a force acts -upon a body in motion, the effect of the force is compounded -with the previously existing motion. <i>The Third -Axiom,—that</i> Reaction is equal and opposite to Action,—<i>gives -rise to the Third Law of Motion, which is expressed -in the same terms as the Axiom; Action and Reaction -being understood to signify momentum gained and lost.</i> -(<span class="sc">iii.</span> 7.) <span class="pagenum" id="page15">15</span></p> -<p class="center">LIII.</p> -<p><i>The above Laws of Motion, historically speaking, were -established by means of experiment: but since they have been -discovered and reduced to their simplest form, they have been -considered by many philosophers as self-evident. This result -is principally due to the introduction and establishment of -terms and definitions, which enable us to express the Laws in -a very simple manner.</i> (<span class="sc">iii.</span> 7.)</p> -<p class="center">LIV.</p> -<p><i>In the establishment of the Laws of Motion, it happened, -in several instances, that Principles were assumed as self-evident -which do not now appear evident, but which have -since been demonstrated from the simplest and most evident -principles. Thus it was assumed that</i> a perpetual motion -is impossible;—<i>that</i> the velocities of bodies acquired by -falling down planes or curves of the same vertical height -are equal;—<i>that</i> the actual descent of the center of gravity -is equal to its potential ascent. <i>But we are not hence -to suppose that these assumptions were made without ground: -for since they really follow from the laws of motion, they -were probably, in the minds of the discoverers, the results of -undeveloped demonstrations which their sagacity led them to -divine.</i> (<span class="sc">iii.</span> 7.)</p> -<p class="center">LV.</p> -<p><i>It is a</i> Paradox <i>that Experience should lead us to truths -confessedly universal, and apparently necessary, such as the -Laws of Motion are. The</i> Solution <i>of this paradox is, -that these laws are interpretations of the Axioms of Causation. -The axioms are universally and necessarily true, but -the right interpretation of the terms which they involve, is -learnt by experience. Our Idea of Cause supplies the</i> Form, -<i>Experience, the</i> Matter, <i>of these Laws.</i> (<span class="sc">iii.</span> 8.)</p> -<p class="center">LVI.</p> -<p>Primary <i>Qualities of Bodies are those which we can conceive -as directly perceived;</i> Secondary <i>Qualities are -those</i> <span class="pagenum" id="page16">16</span> -<i>which we conceive as perceived by means of a -Medium.</i> (<span class="sc">iv.</span> 1.)</p> -<p class="center">LVII.</p> -<p><i>We necessarily perceive bodies as</i> without <i>us; the Idea of</i> -Externality <i>is one of the conditions of perception.</i> (<span class="sc">iv.</span> 1.)</p> -<p class="center">LVIII.</p> -<p><i>We necessarily assume a</i> Medium <i>for the perceptions of -Light, Colour, Sound, Heat, Odours, Tastes; and this Medium</i> must <i>convey -impressions by means of its mechanical attributes.</i> (<span class="sc">iv.</span> 1.)</p> -<p class="center">LIX.</p> -<p><i>Secondary Qualities are not</i> extended <i>but</i> intensive: -<i>their effects are not augmented by addition of parts, but by -increased operation of the medium. Hence they are not -measured directly, but by</i> scales; <i>not by</i> units, <i>but by</i> -degrees. (<span class="sc">iv.</span> 4.)</p> -<p class="center">LX.</p> -<p><i>In the Scales of Secondary Qualities, it is a condition</i> -(<i>in order that the scale may be complete,</i>) <i>that every example -of the quality must either</i> agree <i>with one of the degrees of -the Scale, or lie between two</i> contiguous <i>degrees.</i> (<span class="sc">iv.</span> 4.)</p> -<p class="center">LXI.</p> -<p><i>We perceive</i> by means of <i>a medium and</i> by means of -<i>impressions on the nerves: but we do not</i> (<i>by our senses</i>) <i>perceive -either the medium or the impressions on the nerves.</i> (<span class="sc">iv.</span> 1.)</p> -<p class="center">LXII.</p> -<p><i>The</i> Prerogatives of the Sight <i>are, that by this sense we -necessarily and immediately apprehend the</i> position <i>of its -objects: and that from visible circumstances, we</i> infer <i>the</i> -distance <i>of objects from us, so readily that we seem to perceive -and not to infer.</i> (<span class="sc">iv.</span> 2.) -<span class="pagenum" id="page17">17</span></p> -<p class="center">LXIII.</p> -<p><i>The</i> Prerogatives of the Hearing <i>are, that by this sense -we perceive relations perfectly precise and definite between -two notes, namely,</i> Musical Intervals (<i>as an</i> Octave, <i>a</i> -Fifth); <i>and that when two notes are perceived together, they -are comprehended as distinct,</i> (<i>a</i> Chord,) <i>and as having a -certain relation,</i> (Concord <i>or</i> Discord.) (<span class="sc">iv.</span> 2.)</p> -<p class="center">LXIV.</p> -<p><i>The Sight cannot decompose a compound colour into -simple colours, or distinguish a compound from a simple -colour. The Hearing cannot directly perceive the place, still -less the distance, of its objects: we infer these obscurely and -vaguely from audible circumstances.</i> (<span class="sc">iv.</span> 2.)</p> -<p class="center">LXV.</p> -<p><i>The</i> First Paradox of Vision <i>is, that we see objects</i> upright, -<i>though the images on the retina are</i> inverted. <i>The -solution is, that we do not see the image on the retina at all, -we only see by means of it.</i> (<span class="sc">iv.</span> 2.)</p> -<p class="center">LXVI.</p> -<p><i>The</i> Second Paradox of Vision <i>is, that we see objects</i> -single, <i>though there are two images on the retinas, one in -each eye. The explanation is, that it is a Law of Vision -that we see</i> (<i>small or distant</i>) <i>objects single, when their images -fall on</i> corresponding points <i>of the two retinas.</i> (<span class="sc">iv.</span> 2.)</p> -<p class="center">LXVII.</p> -<p><i>The law of single vision for</i> near <i>objects is this:—When -the two images in the two eyes are situated, part for part, -nearly but not exactly, upon corresponding points, the object -is apprehended as single and solid if the two objects are such -as would be produced by a single solid object seen by the eyes -separately.</i> (<span class="sc">iv.</span> 2.)</p> -<p class="center">LXVIII.</p> -<p><i>The ultimate object of each of the Secondary Mechanical -Sciences is, to determine the nature and laws of the -processes</i> <span class="pagenum" id="page18">18</span> -<i>by which the impression of the Secondary Quality treated of -is conveyed: but before we discover the cause, it may be -necessary to determine the</i> laws <i>of the phenomena; and for -this purpose a</i> Measure <i>or</i> Scale <i>of each quality is necessary.</i> -(<span class="sc">iv.</span> 4.)</p> -<p class="center">LXIX.</p> -<p><i>Secondary qualities are measured by means of such effects -as can be estimated in number or space.</i> (<span class="sc">iv.</span> 4.)</p> -<p class="center">LXX.</p> -<p><i>The Measure of Sounds, as high or low, is the</i> Musical -Scale, <i>or</i> Harmonic Canon. (<span class="sc">iv.</span> 4.)</p> -<p class="center">LXXI.</p> -<p><i>The Measures of Pure Colours are the</i> Prismatic Scale; -<i>the same, including</i> Fraunhofer’s Lines; <i>and</i> Newton’s -Scale <i>of Colours. The principal Scales of Impure Colours -are</i> Werner’s Nomenclature <i>of Colours, and</i> Merimée’s -Nomenclature <i>of Colours</i>. (<span class="sc">iv.</span> 4.)</p> -<p class="center">LXXII.</p> -<p><i>The Idea of</i> Polarity <i>involves the conception of contrary -properties in contrary directions:—the properties being, for -example, attraction and repulsion, darkness and light, synthesis and -analysis; and the contrary directions being those -which are directly opposite, or, in some cases, those which are -at right angles.</i> (<span class="sc">v.</span> 1.)</p> -<p class="center">LXXIII. (Doubtful.)</p> -<p><i>Coexistent polarities are fundamentally identical.</i> (<span class="sc">v.</span> 2.)</p> -<p class="center">LXXIV.</p> -<p><i>The Idea of Chemical</i> Affinity, <i>as implied in Elementary -Composition, involves peculiar conceptions. It is not properly -expressed by assuming the qualities of bodies to</i> resemble -<i>those of the elements, or to depend on the</i> figure <i>of the elements, -or on their</i> attractions. (<span class="sc">vi.</span> 1.) -<span class="pagenum" id="page19">19</span></p> -<p class="center">LXXV.</p> -<p><i>Attractions take place between bodies, Affinities between -the particles of a body. The former may be compared to the -alliances of states, the latter to the ties of family.</i> (<span class="sc">vi.</span> 2.)</p> -<p class="center">LXXVI.</p> -<p><i>The governing principles of Chemical Affinity are, that it -is</i> elective; <i>that it is</i> definite; <i>that it</i> determines the properties -<i>of the compound; and that</i> analysis is possible. (<span class="sc">vi.</span> 2.)</p> -<p class="center">LXXVII.</p> -<p><i>We have an idea of</i> Substance: <i>and an axiom involved -in this Idea is, that</i> the weight of a body is the sum of the -weights of all its elements. (<span class="sc">vi.</span> 3.)</p> -<p class="center">LXXVIII.</p> -<p><i>Hence Imponderable Fluids are not to be admitted as -chemical elements.</i> (<span class="sc">vi.</span> 4.)</p> -<p class="center">LXXIX.</p> -<p><i>The Doctrine of Atoms is admissible as a mode of expressing -and calculating laws of nature; but is not proved by any -fact, chemical or physical, as a philosophical truth.</i> (<span class="sc">vi.</span> 5.)</p> -<p class="center">LXXX.</p> -<p><i>We have an Idea of</i> Symmetry; <i>and an axiom involved -in this Idea is, that in a symmetrical natural body, if there -be a tendency to modify any member in any manner, there is -a tendency to modify all the corresponding members in the -same manner.</i> (<span class="sc">vii.</span> 1.)</p> -<p class="center">LXXXI.</p> -<p><i>All hypotheses respecting the manner in which the elements -of inorganic bodies are arranged in space, must be constructed -with regard to the general facts of crystallization.</i> -(<span class="sc">vii.</span> 3.) <span class="pagenum" id="page20">20</span></p> -<p class="center">LXXXII.</p> -<p><i>When we consider any object as</i> One, <i>we give unity to it -by an act of thought. The condition which determines what -this unity shall include, and what it shall exclude, is this;—that -assertions concerning the one thing shall be possible.</i> (<span class="sc">viii.</span> 1.)</p> -<p class="center">LXXXIII.</p> -<p><i>We collect individuals into</i> Kinds <i>by applying to them -the Idea of Likeness. Kinds of things are not determined -by definitions, but by this condition:—that general assertions -concerning such kinds of things shall be possible.</i> (<span class="sc">viii.</span> 1.)</p> -<p class="center">LXXXIV.</p> -<p><i>The</i> Names <i>of kinds of things are governed by their use; -and that may be a right name in one use which is not so in -another. A whale is not a</i> fish <i>in natural history, but it is -a</i> fish <i>in commerce and law.</i> (<span class="sc">viii.</span> 1.)</p> -<p class="center">LXXXV.</p> -<p><i>We take for granted that each kind of things has a special</i> -character <i>which may be expressed by a Definition. The -ground of our assumption is this;—that reasoning must be -possible.</i> (<span class="sc">viii.</span> 1.)</p> -<p class="center">LXXXVI.</p> -<p><i>The “Five Words,”</i> Genus, Species, Difference, Property, Accident, -<i>were used by the Aristotelians, in order to -express the subordination of Kinds, and to describe the nature -of Definitions and Propositions. In modern times, these -technical expressions have been more referred to by Natural -Historians than by Metaphysicians.</i> (<span class="sc">viii.</span> 1.)</p> -<p class="center">LXXXVII.</p> -<p><i>The construction of a Classificatory Science includes</i> -Terminology, <i>the formation of a descriptive language;</i>—Diataxis, -<i>the Plan of the System of Classification, called</i> -<span class="pagenum" id="page21">21</span> -<i>also the</i> Systematick;—Diagnosis, <i>the Scheme of the Characters -by which the different Classes are known, called also -the</i> Characteristick. Physiography <i>is the knowledge which -the System is employed to convey. Diataxis includes</i> Nomenclature. -(<span class="sc">viii.</span> 2.)</p> -<p class="center" id="a88">LXXXVIII.</p> -<p>Terminology <i>must be conventional, precise, constant; -copious in words, and minute in distinctions, according to -the needs of the science. The student must understand the -terms,</i> directly <i>according to the convention, not through the -medium of explanation or comparison.</i> (<span class="sc">viii.</span> 2.)</p> -<p class="center">LXXXIX.</p> -<p><i>The</i> Diataxis,<i> or Plan of the System, may aim at a -Natural or at an Artificial System. But no classes can be -absolutely artificial, for if they were, no assertions could be -made concerning them.</i> (<span class="sc">viii.</span> 2.)</p> -<p class="center">XC.</p> -<p><i>An</i> Artificial System <i>is one in which the</i> smaller <i>groups</i> -(<i>the Genera</i>) <i>are</i> natural; <i>and in which the</i> wider <i>divisions</i> -(<i>Classes, Orders</i>) <i>are constructed by the</i> peremptory <i>application -of selected Characters;</i> (<i>selected, however, so as not to -break up the smaller groups.</i>) (<span class="sc">viii.</span> 2.)</p> -<p class="center">XCI.</p> -<p><i>A</i> Natural System <i>is one which attempts to make</i> all <i>the -divisions</i> natural, <i>the widest as well as the narrowest; and -therefore applies</i> no <i>characters</i> peremptorily. (<span class="sc">viii.</span> 2.)</p> -<p class="center">XCII.</p> -<p><i>Natural Groups are best described, not by any Definition -which marks their boundaries, but by a</i> Type <i>which marks -their center. The Type of any natural group is an example -which possesses in a marked degree all the leading characters -of the class.</i> (<span class="sc">viii.</span> 2.) -<span class="pagenum" id="page22">22</span></p> -<p class="center">XCIII.</p> -<p><i>A Natural Group is steadily fixed, though not precisely -limited; it is given in position, though not circumscribed; it -is determined, not by a boundary without, but by a central -point within;—not by what it strictly excludes, but by what -it eminently includes;—by a Type, not by a Definition.</i> -(<span class="sc">viii.</span> 2.)</p> -<p class="center">XCIV.</p> -<p><i>The prevalence of Mathematics as an element of education -has made us think Definition the philosophical mode -of fixing the meaning of a word: if</i> (<i>Scientific</i>) <i>Natural -History were introduced into education, men might become -familiar with the fixation of the signification of words by</i> -Types; <i>and this process agrees more nearly with the common -processes by which words acquire their significations.</i> -(<span class="sc">viii.</span> 2.)</p> -<p class="center">XCV.</p> -<p><i>The attempts at Natural Classification are of three sorts; -according as they are made by the process of</i> blind trial, <i>of</i> -general comparison, <i>or of</i> subordination of characters. -<i>The process of Blind Trial professes to make its classes by -attention to all the characters, but without proceeding methodically. -The process of General Comparison professes to -enumerate all the characters, and forms its classes by the</i> -majority. <i>Neither of these methods can really be carried -into effect. The method of Subordination of Characters -considers some characters as</i> more important <i>than others; -and this method gives more consistent results than the others. -This method, however, does not depend upon the Idea of -Likeness only, but introduces the Idea of Organization or -Function.</i> (<span class="sc">viii.</span> 2.)</p> -<p class="center">XCVI.</p> -<p><i>A</i> Species <i>is a collection of individuals, which are descended -from a common stock, or which resemble such a -collection as much as these resemble each other: the resemblance -being opposed to a</i> definite <i>difference.</i> -(<span class="sc">viii.</span> 2.) <span class="pagenum" id="page23">23</span></p> -<p class="center">XCVII.</p> -<p><i>A</i> Genus <i>is a collection of species which resemble each -other more than they resemble other species: the resemblance -being opposed to a</i> definite <i>difference.</i> (<span class="sc">viii.</span> 2.)</p> -<p class="center" id="a98">XCVIII.</p> -<p><i>The</i> Nomenclature <i>of a Classificatory Science is the collection -of the names of the Species, Genera, and other divisions. -The</i> binary <i>nomenclature, which denotes a species by -the</i> generic <i>and</i> specific <i>name, is now commonly adopted in -Natural History.</i> (<span class="sc">viii.</span> 2.)</p> -<p class="center">XCIX.</p> -<p><i>The</i> Diagnosis, <i>or Scheme of the Characters, comes, in -the order of philosophy, after the Classification. The characters -do not</i> make <i>the classes, they only enable us to</i> recognize <i>them. -The Diagnosis is an Artificial Key to a Natural -System.</i> (<span class="sc">viii.</span> 2.)</p> -<p class="center">C.</p> -<p><i>The basis of all Natural Systems of Classification is the -Idea of Natural Affinity. The Principle which this Idea -involves is this:—Natural arrangements, obtained from</i> -different <i>sets of characters, must</i> coincide <i>with each other.</i> -(<span class="sc">viii.</span> 4.)</p> -<p class="center">CI.</p> -<p><i>In order to obtain a Science of Biology, we must analyse -the Idea of Life. It has been proved by the biological speculations -of past time, that Organic Life cannot rightly be -solved into Mechanical or Chemical Forces, or the operation -of a Vital Fluid, or of a Soul.</i> (<span class="sc">ix.</span> 2.)</p> -<p class="center">CII.</p> -<p><i>Life is a System of Vital Forces; and the conception of -such Forces involves a peculiar Fundamental Idea.</i> -(<span class="sc">ix.</span> 3.) <span class="pagenum" id="page24">24</span></p> -<p class="center">CIII.</p> -<p><i>Mechanical, chemical, and vital Forces form an ascending -progression, each including the preceding. Chemical Affinity -includes in its nature Mechanical Force, and may often be -practically resolved into Mechanical Force.</i> (<i>Thus the ingredients -of gunpowder, liberated from their chemical union, -exert great mechanical Force: a galvanic battery acting by -chemical process does the like.</i>) <i>Vital Forces include in -their nature both chemical Affinities and mechanical Forces: -for Vital Powers produce both chemical changes,</i> (<i>as digestion,</i>) -<i>and motions which imply considerable mechanical -force,</i> (<i>as the motion of the sap and of the blood.</i>) (<span class="sc">ix.</span> 4.)</p> -<p class="center">CIV.</p> -<p><i>In</i> voluntary <i>motions, Sensations produce Actions, and -the connexion is made by means of Ideas: in</i> reflected -<i>motions, the connexion neither seems to be nor is made by -means of Ideas: in</i> instinctive <i>motions, the connexion is -such as requires Ideas, but we cannot believe the Ideas to -exist.</i> (<span class="sc">ix.</span> 5.)</p> -<p class="center">CV.</p> -<p><i>The Assumption of a Final Cause in the structure of each -part of animals and plants is as inevitable as the assumption -of an Efficient Cause for every event. The maxim that in -organized bodies nothing is</i> in vain, <i>is as necessarily true as -the maxim that nothing happens</i> by chance. (<span class="sc">ix.</span> 6.)</p> -<p class="center">CVI.</p> -<p><i>The Idea of living beings as subject to</i> disease <i>includes a -recognition of a Final Cause in organization; for disease is -a state in which the vital forces do not attain their</i> proper -ends. (<span class="sc">ix.</span> 7.)</p> -<p class="center">CVII.</p> -<p><i>The Palætiological Sciences depend upon the Idea of -Cause: but the leading conception which they involve is that -of</i> historical cause, <i>not mechanical cause.</i> -(<span class="sc">x.</span> 1.) <span class="pagenum" id="page25">25</span></p> -<p class="center">CVIII.</p> -<p><i>Each Palætiological Science, when complete, must possess -three members: the</i> Phenomenology, <i>the</i> Ætiology, <i>and the</i> -Theory. (<span class="sc">x.</span> 2.)</p> -<p class="center">CIX.</p> -<p><i>There are, in the Palætiological Sciences, two antagonist -doctrines:</i> Catastrophes <i>and</i> Uniformity. <i>The doctrine -of a</i> uniform course of nature <i>is tenable only when we -extend the nation of Uniformity so far that it shall include Catastrophes.</i> -(<span class="sc">x.</span> 3.)</p> -<p class="center">CX.</p> -<p><i>The Catastrophist constructs Theories, the Uniformitarian -demolishes them. The former adduces evidence of an Origin, -the latter explains the evidence away. The Catastrophist’s -dogmatism is undermined by the Uniformitarian’s skeptical -hypotheses. But when these hypotheses are asserted dogmatically -they cease to be consistent with the doctrine of Uniformity.</i> (<span class="sc">x.</span> 3.)</p> -<p class="center">CXI.</p> -<p><i>In each of the Palætiological Sciences, we can ascend to -remote periods by a chain of causes, but in none can we -ascend to a</i> beginning <i>of the chain.</i> (<span class="sc">x.</span> 3.)</p> -<p class="center">CXII.</p> -<p><i>Since the Palætiological sciences deal with the conceptions -of historical cause,</i> History, <i>including</i> Tradition, <i>is -an important source of materials for such sciences.</i> (<span class="sc">x.</span> 4.)</p> -<p class="center">CXIII.</p> -<p><i>The history and tradition which present to us the providential -course of the world form a</i> Sacred Narrative; <i>and -in reconciling the Sacred Narrative with the results of science, -arise inevitable difficulties which disturb the minds of -those who reverence the Sacred Narrative.</i> -(<span class="sc">x.</span> 4.) <span class="pagenum" id="page26">26</span></p> -<p class="center">CXIV.</p> -<p><i>The disturbance of reverent minds, arising from scientific -views, ceases when such views become familiar, the Sacred -Narrative being then interpreted anew in accordance with -such views.</i> (<span class="sc">x.</span> 4.)</p> -<p class="center">CXV.</p> -<p><i>A new interpretation of the Sacred Narrative, made for -the purpose of reconciling it with doctrines of science, should -not be insisted on till such doctrines are clearly proved; and -when they are so proved, should be frankly accepted, in the -confidence that a reverence for the Sacred Narrative is consistent -with a reverence for the Truth.</i> (<span class="sc">x.</span> 4.)</p> -<p class="center">CXVI.</p> -<p><i>In contemplating the series of causes and effects which -constitutes the world, we necessarily assume a</i> First Cause -<i>of the whole series.</i> (<span class="sc">x.</span> 5.)</p> -<p class="center">CXVII.</p> -<p><i>The Palætiological Sciences point backwards with lines -which are broken, but which all converge to the</i> same <i>invisible -point: and this point is the Origin of the Moral and -Spiritual, as well as of the Natural World.</i> (<span class="sc">x.</span> 5.)</p> -<div class="chapter"> -<p class="h2">NOVUM ORGANON RENOVATUM.</p><br /><br /> -<hr class="three" /> -<h2 class="nobreak">BOOK II.</h2> -<p class="center end">OF THE CONSTRUCTION OF SCIENCE.</p><br /> -<hr class="one" /> -<p><span class="pagenum" id="page27"></span></p> -<h3 class="nobreak">CHAPTER I.<br /><br /> -<span class="sc">Of two principal Processes by which Science is constructed.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism I.</span></p> -<p><i>THE two processes by which Science is constructed are -the</i> Explication of Conceptions, <i>and the</i> Colligation of -Facts.</p> -<p class="drop"><span class="sc">TO</span> the subject of the present and next Book all that -has preceded is subordinate and preparatory. In -former works we have treated of the History of Scientific -Discoveries and of the History of Scientific Ideas. We -have now to attempt to describe the manner in which -discoveries are made, and in which Ideas give rise to -knowledge. It has already been stated that Knowledge -requires us to possess both Facts and Ideas;—that -every step in our knowledge consists in applying the -Ideas and Conceptions furnished by our minds to the -Facts which observation and experiment offer to us. -When our Conceptions are clear and distinct, when our -Facts are certain and sufficiently numerous, and when -the Conceptions, being suited to the nature of the <span class="pagenum" id="page28">28</span> -Facts, are applied to them so as to produce an exact -and universal accordance, we attain knowledge of a -precise and comprehensive kind, which we may term -<i>Science</i>. And we apply this term to our knowledge -still more decidedly when, Facts being thus included -in exact and general Propositions, such Propositions -are, in the same manner, included with equal rigour -in Propositions of a higher degree of Generality; and -these again in others of a still wider nature, so as to -form a large and systematic whole.</p> -<p>But after thus stating, in a general way, the nature -of science, and the elements of which it consists, we -have been examining with a more close and extensive -scrutiny, some of those elements; and we must now -return to our main subject, and apply to it the results -of our long investigation. We have been exploring -the realm of Ideas; we have been passing in review -the difficulties in which the workings of our own minds -involve us when we would make our conceptions consistent -with themselves: and we have endeavoured to -get a sight of the true solutions of these difficulties. -We have now to inquire how the results of these long -and laborious efforts of thought find their due place in -the formation of our Knowledge. What do we gain -by these attempts to make our notions distinct and -consistent; and in what manner is the gain of which -we thus become possessed, carried to the general treasure-house -of our permanent and indestructible knowledge? After all this -battling in the world of ideas, -all this struggling with the shadowy and changing -forms of intellectual perplexity, how do we secure to -ourselves the fruits of our warfare, and assure ourselves -that we have really pushed forwards the frontier of -the empire of Science? It is by such an appropriation, -that the task which we have had in our hands -during the two previous works, (the <i>History of the -Inductive Sciences</i> and the <i>History of Scientific Ideas</i>,) -must acquire its real value and true place in our design.</p> -<p class="end">In order to do this, we must reconsider, in a more -definite and precise shape, the doctrine which has -already been laid down;—that our Knowledge consists <span class="pagenum" id="page29">29</span> -in applying Ideas to Facts; and that the conditions of -real knowledge are that the ideas be distinct and appropriate, -and exactly applied to clear and certain -facts. The steps by which our knowledge is advanced -are those by which one or the other of these two processes -is rendered more complete;—by which <em>Conceptions</em> are <em>made more -clear</em> in themselves, or by which -the Conceptions more strictly <em>bind together the Facts</em>. -These two processes may be considered as together constituting -the whole formation of our knowledge; and -the principles which have been established in the History of -Scientific Ideas bear principally upon the former -of these two operations;—upon the business of elevating -our conceptions to the highest possible point of precision -and generality. But these two portions of the -progress of knowledge are so clearly connected with -each other, that we shall deal with them in immediate -succession. And having now to consider these operations -in a more exact and formal manner than it was -before possible to do, we shall designate them by certain -constant and technical phrases. We shall speak -of the two processes by which we arrive at science, as -<i>the Explication of Conceptions</i> and <i>the Colligation of -Facts</i>: we shall show how the discussions in which we -have been engaged have been necessary in order to -promote the former of these offices; and we shall -endeavour to point out modes, maxims, and principles -by which the second of the two tasks may also be furthered.</p> -<div class="chapter"> -<p><span class="pagenum" id="page30"></span></p> -<h3 class="nobreak">CHAPTER II.<br /><br /> -<span class="sc">Of the Explication of Conceptions.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> II.</p> -<p><i>The Explication of Conceptions, as requisite for the progress -of science, has been effected by means of discussions and -controversies among scientists; often by debates concerning -definitions; these controversies have frequently led to the -establishment of a Definition; but along with the Definition, -a corresponding Proposition has always been expressed or -implied. The essential requisite for the advance of science -is the clearness of the Conception, not the establishment of a -Definition. The construction of an exact Definition is often -very difficult. The requisite conditions of clear Conceptions -may often be expressed by Axioms as well as by Definitions.</i></p> -<p class="center"><span class="sc">Aphorism</span> III.</p> -<p class="end"><i>Conceptions, for purposes of science, must be</i> appropriate -<i>as well as clear: that is, they must be modifications of</i> that -<i>Fundamental Idea, by which the phenomena can really be interpreted. -This maxim may warn us from errour, though -it may not lead to discovery. Discovery depends upon the -previous cultivation or natural clearness of the appropriate -Idea, and therefore</i> no discovery is the work of accident.</p> -<p class="center"><span class="sc">Sect. I.</span>—<i>Historical Progress of the Explication of Conceptions.</i></p> -<p class="noind" id="b2c2a1"> -<span class="dropcap"><span class="dsmall">1.</span> W</span>E have given the appellation of <i>Ideas</i> to certain -comprehensive forms of thought,—as -<i>space</i>, <i>number</i>, <i>cause</i>, <i>composition</i>, <i>resemblance</i>,—which -we apply to the phenomena which we contemplate. -But the special modifications of these ideas which are <span class="pagenum" id="page31">31</span> -exemplified in particular facts, we have termed <i>Conceptions</i>; -as <i>a circle</i>, <i>a square number</i>, <i>an accelerating -force</i>, <i>a neutral combination</i> of elements, a <i>genus</i>. -Such Conceptions involve in themselves certain necessary and -universal relations derived from the Ideas -just enumerated; and these relations are an indispensable -portion of the texture of our knowledge. But to -determine the contents and limits of this portion of -our knowledge, requires an examination of the Ideas -and Conceptions from which it proceeds. The Conceptions must -be, as it were, carefully <em>unfolded</em>, so as -to bring into clear view the elements of truth with -which they are marked from their ideal origin. This -is one of the processes by which our knowledge is extended -and made more exact; and this I shall describe -as the <i>Explication of Conceptions</i>.</p> -<p>In the several Books of the History of Ideas we -have discussed a great many of the Fundamental Ideas -of the most important existing sciences. We have, in -those Books, abundant exemplifications of the process -now under our consideration. We shall here add a -few general remarks, suggested by the survey which -we have thus made.</p> -<p id="b2c2a2">2. Such discussions as those in which we have been -engaged concerning our fundamental Ideas, have been -the course by which, historically speaking, those Conceptions -which the existing sciences involve have been -rendered so clear as to be fit elements of exact knowledge. -Thus, the disputes concerning the various kinds -and measures of <i>Force</i> were an important part of the -progress of the science of Mechanics. The struggles by -which philosophers attained a right general conception -of <i>plane</i>, of <i>circular</i>, of <i>elliptical Polarization</i>, were -some of the most difficult steps in the modern discoveries -of Optics. A Conception of the <i>Atomic Constitution</i> -of bodies, such as shall include what we know, -and assume nothing more, is even now a matter of -conflict among Chemists. The debates by which, in -recent times, the Conceptions of <i>Species</i> and <i>Genera</i> -have been rendered more exact, have improved the -science of Botany: the imperfection of the science of <span class="pagenum" id="page32">32</span> -Mineralogy arises in a great measure from the circumstance, -that in that subject, the Conception of a <i>Species</i> -is not yet fixed. In Physiology, what a vast advance -would that philosopher make, who should establish a -precise, tenable, and consistent Conception of <i>Life</i>!</p> -<p>Thus discussions and speculations concerning the -import of very abstract and general terms and notions, -may be, and in reality have been, far from useless and -barren. Such discussions arose from the desire of men -to impress their opinions on others, but they had the -effect of making the opinions much more clear and distinct. -In trying to make others understand them, they -learnt to understand themselves. Their speculations -were begun in twilight, and ended in the full brilliance -of day. It was not easily and at once, without expenditure -of labour or time, that men arrived at those -notions which now form the elements of our knowledge; -on the contrary, we have, in the history of -science, seen how hard, discoverers, and the forerunners -of discoverers, have had to struggle with the indistinctness -and obscurity of the intellect, before they could -advance to the critical point at which truth became -clearly visible. And so long as, in this advance, some -speculators were more forward than others, there was -a natural and inevitable ground of difference of opinion, -of argumentation, of wrangling. But the tendency of all -such controversy is to diffuse truth and to -dispel errour. Truth is consistent, and can bear the -tug of war; Errour is incoherent, and falls to pieces -in the struggle. True Conceptions can endure the -sun, and become clearer as a fuller light is obtained; -confused and inconsistent notions vanish like visionary -spectres at the break of a brighter day. And thus -all the controversies concerning such Conceptions as -science involves, have ever ended in the establishment -of the side on which the truth was found.</p> -<p id="b2c2a3">3. Indeed, so complete has been the victory of -truth in most of these instances, that at present we -can hardly imagine the struggle to have been necessary. -The very essence of these triumphs is that they -lead us to regard the views we reject as not only false, <span class="pagenum" id="page33">33</span> -but inconceivable. And hence we are led rather to -look back upon the vanquished with contempt than -upon the victors with gratitude. We now despise those -who, in the Copernican controversy, could not conceive -the apparent motion of the sun on the heliocentric -hypothesis;—or those who, in opposition to Galileo, -thought that a uniform force might be that which -generated a velocity proportional to the space;—or -those who held there was something absurd in Newton’s -doctrine of the different refrangibility of differently -coloured rays;—or those who imagined that -when elements combine, their sensible qualities must -be manifest in the compound;—or those who were -reluctant to give up the distinction of vegetables into -herbs, shrubs, and trees. We cannot help thinking that -men must have been singularly dull of comprehension, -to find a difficulty in admitting what is to us so plain -and simple. We have a latent persuasion that we in -their place should have been wiser and more clear-sighted;—that -we should have taken the right side, -and given our assent at once to the truth.</p> -<p id="b2c2a4">4. Yet in reality, such a persuasion is a mere delusion. -The persons who, in such instances as the above, -were on the losing side, were very far, in most cases, -from being persons more prejudiced, or stupid, or narrow-minded, -than the greater part of mankind now -are; and the cause for which they fought was far -from being a manifestly bad one, till it had been so -decided by the result of the war. It is the peculiar -character of scientific contests, that what is only an -epigram with regard to other warfare is a truth in -this;—They who are defeated are really in the wrong. -But they may, nevertheless, be men of great subtilty, -sagacity, and genius; and we nourish a very foolish -self-complacency when we suppose that we are their -superiors. That this is so, is proved by recollecting -that many of those who have made very great discoveries -have laboured under the imperfection of thought -which was the obstacle to the next step in knowledge. -Though Kepler detected with great acuteness the -Numerical Laws of the solar system, he laboured in <span class="pagenum" id="page34">34</span> -vain to conceive the very simplest of the Laws of -Motion by which the paths of the planets are governed. -Though Priestley made some important steps in chemistry, -he could not bring his mind to admit the doctrine -of a general Principle of Oxidation. How many ingenious -men in the last century rejected the Newtonian Attraction -as an impossible chimera! How -many more, equally intelligent, have, in the same manner, -in our own time, rejected, I do not now mean as -false, but as inconceivable, the doctrine of Luminiferous -Undulations! To err in this way is the lot, not -only of men in general, but of men of great endowments, -and very sincere love of truth.</p> -<p id="b2c2a5">5. And those who liberate themselves from such -perplexities, and who thus go on in advance of their -age in such matters, owe their superiority in no small -degree to such discussions and controversies as those -to which we now refer. In such controversies, the -Conceptions in question are turned in all directions, -examined on all sides; the strength and the weakness -of the maxims which men apply to them are fully tested; -the light of the brightest minds is diffused to other -minds. Inconsistency is unfolded into self-contradiction; -axioms are built up into a system of necessary -truths; and ready exemplifications are accumulated of -that which is to be proved or disproved, concerning -the ideas which are the basis of the controversy.</p> -<p class="end">The History of Mechanics from the time of Kepler -to that of Lagrange, is perhaps the best exemplification -of the mode in which the progress of a science -depends upon such disputes and speculations as give -clearness and generality to its elementary conceptions. -This, it is to be recollected, is the kind of progress of -which we are now speaking; and this is the principal -feature in the portion of scientific history which we -have mentioned. For almost all that was to be done -by reference to observation, was executed by Galileo -and his disciples. What remained was the task of -generalization and simplification. And this was promoted -in no small degree by the various controversies -which took place within that period concerning <span class="pagenum" id="page35">35</span> mechanical -conceptions:—as, for example, the question -concerning the measure of the Force of Percussion;—the -war of the <i>Vis Viva</i>;—the controversy of the -Center of Oscillation;—of the independence of Statics and -Dynamics;—of the principle of Least Action;—of the -evidence of the Laws of Motion;—and of the number -of Laws really distinct. None of these discussions was -without its influence in giving generality and clearness -to the mechanical ideas of mathematicians: and therefore, -though remote from general apprehension, and -dealing with very abstract notions, they were of eminent -use in the perfecting the science of Mechanics. -Similar controversies concerning fundamental notions, -those, for example, which Galileo himself had to maintain, -were no less useful in the formation of the science -of Hydrostatics. And the like struggles and conflicts, -whether they take the form of controversies between -several persons, or only operate in the efforts and -fluctuations of the discoverer’s mind, are always requisite, -before the conceptions acquire that clearness which -makes them flt to appear in the enunciation of scientific -truth. This, then, was one object of the History -of Ideas;—to bring under the reader’s notice the main -elements of the controversies which have thus had so -important a share in the formation of the existing -body of science, and the decisions on the controverted -points to which the mature examination of the subject -has led; and thus to give an abundant exhibition of -that step which we term the Explication of Conceptions.</p> -<p class="center"><span class="sc">Sect. II.</span>—<i>Use of Definitions.</i></p> -<p id="b2c2a6">6. The result of such controversies as we have -been speaking of, often appears to be summed up in a -<i>Definition</i>; and the controversy itself has often assumed -the form of a battle of definitions. For example, the -inquiry concerning the Laws of Falling -Bodies led to the question whether the proper Definition -of a <i>uniform force</i> is, that it generates a velocity -proportional to the <i>space</i> from rest, or to the <i>time</i>. -The controversy of the <i>Vis Viva</i> was, what was the <span class="pagenum" id="page36">36</span> -proper Definition of the <i>measure of force</i>. A principal -question in the classification of minerals is, what is -the Definition of a <i>mineral species</i>. Physiologists have -endeavoured to throw light on their subject, by -Defining <i>organization</i>, or some similar term.</p> -<p id="b2c2a7">7. It is very important for us to observe, that -these controversies have never been questions of insulated -and <em>arbitrary</em> Definitions, as men seem often -tempted to suppose them to have been. In all cases -there is a tacit assumption of some Proposition which -is to be expressed by means of the Definition, and -which gives it its importance. The dispute concerning -the Definition thus acquires a real value, and becomes -a question concerning true and false. Thus in the discussion -of the question, What is a Uniform Force? it -was taken for granted that ‘gravity is a uniform -force:’—in the debate of the <i>Vis Viva</i>, it was assumed -that ‘in the mutual action of bodies the whole effect -of the force is unchanged:’—in the zoological definition -of Species, (that it consists of individuals which have, -or may have, sprung from the same parents,) it is presumed -that ‘individuals so related resemble each other -more than those which are excluded by such a definition;’ or -perhaps, that ‘species so defined have permanent and definite -differences.’ A definition of Organization, or of any other -term, which was not employed to express some principle, -would be of no value.</p> -<p>The establishment, therefore, of a right Definition -of a Term may be a useful step in the Explication of -our Conceptions; but this will be the case <em>then</em> only -when we have under our consideration some Proposition -in which the Term is employed. For then the -question really is, how the Conception shall be understood -and defined in order that the Proposition may be -true.</p> -<p id="b2c2a8">8. The establishment of a Proposition requires an -attention to observed Facts, and can never be rightly -derived from our Conceptions alone. We must hereafter -consider the necessity which exists that the Facts -should be rightly bound together, as well as that our -Conceptions should be clearly employed, in order to <span class="pagenum" id="page37">37</span> -lead us to real knowledge. But we may observe here -that, in such cases at least as we are now considering, -the two processes are co-ordinate. To unfold our Conceptions -by the means of Definitions, has never been -serviceable to science, except when it has been associated -with an immediate <em>use</em> of the Definitions. The -endeavour to define a uniform Force was combined -with the assertion that ‘gravity is a uniform force:’ -the attempt to define Accelerating Force was immediately -followed by the doctrine that ‘accelerating -forces may be compounded:’ the process of defining -Momentum was connected with the principle that -‘momenta gained and lost are equal:’ naturalists would -have given in vain the Definition of Species which we -have quoted, if they had not also given the ‘characters’ -of species so separated. Definition and Proposition -are the two handles of the instrument by which we -apprehend truth; the former is of no use without the -latter. Definition may be the best mode of explaining -our Conception, but that which alone makes it worth -while to explain it in any mode, is the opportunity of -using it in the expression of Truth. When a Definition -is propounded to us as a useful step in knowledge, -we are always entitled to ask what Principle it -serves to enunciate. If there be no answer to this inquiry, -we define and give clearness to our conceptions -in vain. While we labour at such a task, we do but -light up a vacant room;—we sharpen a knife with -which we have nothing to cut;—we take exact aim, -while we load our artillery with blank cartridge;—we -apply strict rules of grammar to sentences which -have no meaning.</p> -<p>If, on the other hand, we have under our consideration -a proposition probably established, every step -which we can make in giving distinctness and exactness -to the Terms which this proposition involves, is -an important step towards scientific truth. In such -cases, any improvement in our Definition is a real -advance in the explication of our Conception. The -clearness of our impressions casts a light upon the -Ideas which we contemplate and convey to others. <span class="pagenum" id="page38">38</span></p> -<p id="b2c2a9">9. But though <i>Definition</i> may be subservient to a -right explication of our conceptions, it is <em>not essential</em> -to that process. It is absolutely necessary to every -advance in our knowledge, that those by whom such -advances are made should possess clearly the conceptions -which they employ: but it is by no means necessary that -they should unfold these conceptions in the -words of a formal Definition. It is easily seen, by -examining the course of Galileo’s discoveries, that he -had a distinct conception of the <i>Moving Force</i> which -urges bodies downwards upon an inclined plane, while -he still hesitated whether to call it <i>Momentum</i>, <i>Energy</i>, -<i>Impetus</i>, or <i>Force</i>, and did not venture to offer -a Definition of the thing which was the subject of his -thoughts. The Conception of <i>Polarization</i> was clear -in the minds of many optical speculators, from the -time of Huyghens and Newton to that of Young and -Fresnel. This Conception we have defined to be -‘Opposite properties depending upon opposite positions;’ -but this notion was, by the discoverers, though constantly -assumed and expressed by means of superfluous -hypotheses, never clothed in definite language. And -in the mean time, it was the custom, among subordinate -writers on the same subjects, to say, that the -term <i>Polarization</i> had no definite meaning, and was -merely an expression of our ignorance. The Definition -which was offered by Haüy and others of a <i>Mineralogical -Species</i>;—‘The same elements combined in the -same proportions, with the same fundamental form;’—was -false, inasmuch as it was incapable of being rigorously -applied to any one case; but this defect did not -prevent the philosophers who propounded such a Definition -from making many valuable additions to mineralogical -knowledge, in the way of identifying some -species and distinguishing others. The right Conception -which they possessed in their minds prevented -their being misled by their own very erroneous Definition. -The want of any precise Definitions of <i>Strata</i>, -and <i>Formations</i>, and <i>Epochs</i>, among geologists, has -not prevented the discussions which they have carried -on upon such subjects from being highly serviceable <span class="pagenum" id="page39">39</span> -in the promotion of geological knowledge. For however -much the apparent vagueness of these terms -might leave their arguments open to cavil, there was a -general understanding prevalent among the most intelligent -cultivators of the science, as to what was -meant in such expressions; and this common understanding -sufficed to determine what evidence should -be considered conclusive and what inconclusive, in -these inquiries. And thus the distinctness of Conception, -which is a real requisite of scientific progress, -existed in the minds of the inquirers, although Definitions, -which are a partial and accidental evidence -of this distinctness, had not yet been hit upon. The -Idea had been developed in men’s minds, although a -clothing of words had not been contrived for it, nor, -perhaps, the necessity of such a vehicle felt: and thus -that essential condition of the progress of knowledge, -of which we are here speaking, existed; while it was -left to the succeeding speculators to put this unwritten -Rule in the form of a verbal Statute.</p> -<p class="end" id="b2c2a10">10. Men are often prone to consider it as a thoughtless -<em>omission</em> of an essential circumstance, and as a -<em>neglect</em> which involves some blame, when knowledge -thus assumes a form in which Definitions, or rather -Conceptions, are implied but are not expressed. But in -such a judgment, they assume <em>that</em> to be a matter of -choice requiring attention only, which is in fact as -difficult and precarious as any other portion of the task -of discovery. To <em>define</em>, so that our Definition shall -have any scientific value, requires no small portion of -that sagacity by which truth is detected. As we have -already said, Definitions and Propositions are co-ordinate -in their use and in their origin. In many cases, -perhaps in most, the Proposition which contains a -scientific truth, is apprehended with confidence, but -with some vagueness and vacillation, before it is put in -a positive, distinct, and definite form.—It is thus known -to be true, before it can be enunciated in terms each of -which is rigorously defined. The business of Definition is -part of the business of discovery. When it has -been clearly seen what ought to be our Definition, it <span class="pagenum" id="page40">40</span> -must be pretty well known what truth we have to -state. The Definition, as well as the discovery, supposes -a decided step in our knowledge to have been -made. The writers on Logic in the middle ages, made -Definition the last stage in the progress of knowledge; -and in this arrangement at least, the history of science, -and the philosophy derived from the history, confirm -their speculative views. If the Explication of our -Conceptions ever assume the form of a Definition, this -will come to pass, not as an arbitrary process, or as a -matter of course, but as the mark of one of those happy -efforts of sagacity to which all the successive advances -of our knowledge are owing.</p> -<p class="center"><span class="sc">Sect. III.</span>—<i>Use of Axioms.</i></p> -<p class="end" id="b2c2a11">11. Our Conceptions, then, even when they become -so clear as the progress of knowledge requires, are not -adequately expressed, or necessarily expressed at all, by -means of Definitions. We may ask, then, whether there -is any <em>other mode</em> of expression in which we may look -for the evidence and exposition of that peculiar exactness -of thought which the formation of Science demands. -And in answer to this inquiry, we may refer to the -discussions respecting many of the Fundamental Ideas -of the sciences contained in our <i>History</i> of such Ideas. -It has there been seen that these Ideas involve many -elementary truths which enter into the texture of our -knowledge, introducing into it connexions and relations -of the most important kind, although these elementary -truths cannot be deduced from any verbal definition of -the idea. It has been seen that these elementary truths -may often be enunciated by means of <em>Axioms</em>, stated in -addition to, or in preference to, Definitions. For example, -the Idea of Cause, which forms the basis of the -science of Mechanics, makes its appearance in our elementary -mechanical reasonings, not as a Definition, but by -means of the Axioms that ‘Causes are measured by -their effects,’ and that ‘Reaction is equal and opposite -to action.’ Such axioms, tacitly assumed or <span class="pagenum" id="page41">41</span> occasionally -stated, as maxims of acknowledged validity, -belong to all the Ideas which form the foundations of -the sciences, and are constantly employed in the reasoning -and speculations of those who think clearly on -such subjects. It may often be a task of some difficulty -to detect and enunciate in words the Principles -which are thus, perhaps silently and unconsciously, -taken for granted by those who have a share in the -establishment of scientific truth: but inasmuch as -these Principles are an essential element in our knowledge, -it is very important to our present purpose -to separate them from the associated materials, and -to trace them to their origin. This accordingly I -attempted to do, with regard to a considerable number -of the most prominent of such Ideas, in the <i>History</i>. -The reader will there find many of these Ideas -resolved into Axioms and Principles by means of -which their effect upon the elementary reasonings of -the various sciences may be expressed. That Work -is intended to form, in some measure, a representation -of the Ideal Side of our physical knowledge;—a Table -of those contents of our Conceptions which are not -received directly from facts;—an exhibition of Rules -to which we know that truth must conform.</p> -<p class="center"><span class="sc">Sect. IV.</span>—<i>Clear and appropriate Ideas.</i></p> -<p id="b2c2a12">12. In order, however, that we may see the necessary -cogency of these rules, we must possess, clearly and -steadily, the Ideas from which the rules flow. In order -to perceive the necessary relations of the Circles of the -Sphere, we must possess clearly the Idea of Solid -Space:—in order that we may see the demonstration of -the composition of forces, we must have the Idea of -Cause moulded into a distinct Conception of Statical -Force. This is that <em>Clearness of Ideas</em> which we -stipulate for in any one’s mind, as the first essential -condition of his making any new step in the discovery of -truth. And we now see what answer we are able to -give, if we are asked for a Criterion of this Clearness of <span class="pagenum" id="page42">42</span> -Idea. The Criterion is, that the person shall <em>see</em> the -necessity of the Axioms belonging to each Idea;—shall -accept them in such a manner as to perceive the cogency -of the reasonings founded upon them. Thus, a person -has a clear Idea of Space who follows the reasonings of -geometry and fully apprehends their conclusiveness. -The Explication of Conceptions, which we are speaking -of as an essential part of real knowledge, is the process -by which we bring the Clearness of our Ideas to bear -upon the Formation of our knowledge. And this is -done, as we have now seen, not always, nor generally, -nor principally, by laying down a Definition of the -Conception; but by acquiring such a possession of it -in our minds as enables, indeed compels us, to admit, -along with the Conception, all the Axioms and Principles -which it necessarily implies, and by which it -produces its effect upon our reasonings.</p> -<p id="b2c2a13">13. But in order that we may make any real advance -in the discovery of truth, our Ideas must not only be -clear, they must also be <em>appropriate</em>. Each science has -for its basis a different class of Ideas; and the steps -which constitute the progress of one science can never -be made by employing the Ideas of another kind of -science. No genuine advance could ever be obtained -in Mechanics by applying to the subject the Ideas of -Space and Time merely:—no advance in Chemistry, by -the use of mere Mechanical Conceptions:—no discovery -in Physiology, by referring facts to mere Chemical and -Mechanical Principles. Mechanics must involve the -Conception of <i>Force</i>;—Chemistry, the Conception of -<i>Elementary Composition</i>;—Physiology, the Conception -of <i>Vital Powers</i>. Each science must advance by means -of its appropriate Conceptions. Each has its own field, -which extends as far as its principles can be applied. I -have already noted the separation of several of these -fields by the divisions of the Books of the <i>History</i> of Ideas. -The Mechanical, the Secondary Mechanical, the Chemical, the -Classificatory, the Biological Sciences form so -many great Provinces in the Kingdom of knowledge, -each in a great measure possessing its own peculiar -fundamental principles. Every attempt to build up a <span class="pagenum" id="page43">43</span> -new science by the application of principles which -belong to an old one, will lead to frivolous and barren -speculations.</p> -<p>This truth has been exemplified in all the instances -in which subtle speculative men have failed in their -attempts to frame new sciences, and especially in the -essays of the ancient schools of philosophy in Greece, -as has already been stated in the History of Science. -Aristotle and his followers endeavoured in vain to -account for the mechanical relation of forces in the -lever by applying the <em>inappropriate</em> geometrical conceptions -of the properties of the circle:—they speculated to no -purpose about the elementary composition -of bodies, because they assumed the <em>inappropriate</em> -conception of <em>likeness</em> between the elements and the -compound, instead of the genuine notion of elements -merely <em>determining</em> the qualities of the compound. And -in like manner, in modern times, we have seen, in the -history of the fundamental ideas of the physiological -sciences, how all the <em>inappropriate</em> mechanical and -chemical and other ideas which were applied in succession -to the subject failed in bringing into view any -genuine physiological truth.</p> -<p id="b2c2a14">14. That the real cause of the failure in the instances -above mentioned lay in the <i>Conceptions</i>, is -plain. It was not ignorance of the facts which in -these cases prevented the discovery of the truth. Aristotle -was as well acquainted with the fact of the proportion -of the weights which balance on a Lever as Archimedes -was, although Archimedes alone gave the true mechanical -reason for the proportion.</p> -<p>With regard to the doctrine of the Four Elements -indeed, the inapplicability of the conception of -composition of qualities, required, perhaps, to be proved by -some reference to facts. But this conception was -devised at first, and accepted by succeeding times, in a -blind and gratuitous manner, which could hardly have -happened if men had been awake to the necessary -condition of our knowledge;—that the conceptions -which we introduce into our doctrines are not arbitrary -or accidental notions, but certain peculiar modes of <span class="pagenum" id="page44">44</span> -apprehension strictly determined by the subject of our -speculations.</p> -<p id="b2c2a15">15. It may, however, be said that this injunction -that we are to employ <em>appropriate</em> Conceptions only in -the formation of our knowledge, cannot be of practical -use, because we can only determine what Ideas <em>are</em> -appropriate, by finding that they truly combine the -facts. And this is to a certain extent true. Scientific -discovery must ever depend upon some happy thought, -of which we cannot trace the origin;—some fortunate -cast of intellect, rising above all rules. No maxims -can be given which inevitably lead to discovery. No -precepts will elevate a man of ordinary endowments -to the level of a man of genius: nor will an inquirer -of truly inventive mind need to come to the teacher -of inductive philosophy to learn how to exercise the -faculties which nature has given him. Such persons -as Kepler or Fresnel, or Brewster, will have their -powers of discovering truth little augmented by any -injunctions respecting Distinct and Appropriate Ideas; -and such men may very naturally question the utility -of rules altogether.</p> -<p id="b2c2a16">16. But yet the opinions which such persons may -entertain, will not lead us to doubt concerning the -value of the attempts to analyse and methodize the -process of discovery. Who would attend to Kepler if -he had maintained that the speculations of Francis -Bacon were worthless? Notwithstanding what has -been said, we may venture to assert that the Maxim -which points out the necessity of Ideas appropriate -as well as clear, for the purpose of discovering truth, is -not without its use. It may, at least, have a value as -a caution or prohibition, and may thus turn us away -from labours certain to be fruitless. We have already -seen, in the <i>History</i> of Ideas, that this maxim, if duly -attended to, would have at once condemned, as wrongly -directed, the speculations of physiologists of the -mathematical, mechanical, chemical, and vital-fluid schools; -since the Ideas which the teachers of these schools -introduce, cannot suffice for the purposes of physiology, -which seeks truths respecting the vital powers. Again, <span class="pagenum" id="page45">45</span> -it is clear from similar considerations that no definition -of a mineralogical species by chemical characters alone -can answer the end of science, since we seek to make -mineralogy, not an analytical but a classificatory science<a id="fnanchor1-2" href="#note1-2"><span class="fnanchor">1</span></a>. -Even before the appropriate conception is matured in -men’s minds so that they see clearly what it is, they -may still have light enough to see what it is not.</p> -<div class="footnote"><span class="label"><a id="note1-2" href="#fnanchor1-2">1</a></span> This agrees with what M. Necker has well -observed in his <i>Règne Mineral</i>, that those who have treated -mineralogy as a merely chemical science, have substituted the -analysis of substances for the classification of individuals. See -<i>History of Ideas</i>, b. viii. chap. iii. -</div> -<p id="b2c2a17">17. Another result of this view of the necessity -of appropriate Ideas, combined with a survey of the -history of science is, that though for the most part, as -we shall see, the progress of science consists in accumulating -and combining Facts rather than in debating -concerning Definitions; there are still certain periods -when the <em>discussion</em> of Definitions may be the most -useful mode of cultivating some special branch of -science. This discussion is of course always to be conducted -by the light of facts; and, as has already been -said, along with the settlement of every good Definition -will occur the corresponding establishment of -some Proposition. But still at particular periods, the -want of a Definition, or of the clear conceptions which -Definition supposes, may be peculiarly felt. A good -and tenable Definition of <i>Species</i> in Mineralogy would -at present be perhaps the most important step which -the science could make. A just conception of the -nature of <i>Life</i>, (and if expressed by means of a -Definition, so much the better,) can hardly fail to give its -possessor an immense advantage in the speculations -which now come under the considerations of physiologists. -And controversies respecting Definitions, in -these cases, and such as these, may be very far from -idle and unprofitable.</p> -<p class="end">Thus the knowledge that Clear and Appropriate -Ideas are requisite for discovery, although it does not -lead to any very precise precepts, or supersede the -value of natural sagacity and inventiveness, may still <span class="pagenum" id="page46">46</span> -be of use to us in our pursuit after truth. It may -show us what course of research is, in each stage of -science, recommended by the general analogy of the -history of knowledge; and it may both save us from -hopeless and barren paths of speculation, and make us -advance with more courage and confidence, to know -that we are looking for discoveries in the manner in -which they have always hitherto been made.</p> -<p class="center"><span class="sc">Sect. V.</span>—<i>Accidental Discoveries.</i></p> -<p id="b2c2a18">18. Another consequence follows from the views -presented in this Chapter, and it is the last I shall at -present mention. <em>No scientific discovery</em> can, with any -justice, be considered <em>due to accident</em>. In whatever -manner facts may be presented to the notice of a discoverer, -they can never become the materials of exact -knowledge, except they find his mind already provided -with precise and suitable conceptions by which they may -be analysed and connected. Indeed, as we have already -seen, facts cannot be observed as Facts, except in virtue -of the Conceptions which the -observer<a id="fnanchor2-2" href="#note2-2"><span class="fnanchor">2</span></a> -himself unconsciously -supplies; and they are not Facts of Observation for any purpose -of Discovery, except these familiar -and unconscious acts of thought be themselves of a -just and precise kind. But supposing the Facts to be -adequately observed, they can never be combined into -any new Truth, except by means of some new Conceptions, -clear and appropriate, such as I have endeavoured -to characterize. When the observer’s mind is prepared with -such instruments, a very few facts, or it -may be a single one, may bring the process of discovery -into action. But in such cases, this previous -condition of the intellect, and not the single fact, is -really the main and peculiar cause of the success. The -fact is merely the occasion by which the engine of -discovery is brought into play sooner or later. It is, -as I have elsewhere said, only the spark which discharges -a gun already loaded and pointed; and there <span class="pagenum" id="page47">47</span> -is little propriety in speaking of such an accident as -the cause why the bullet hits the mark. If it were -true that the fall of an apple was the occasion of Newton’s -pursuing the train of thought which led to the -doctrine of universal gravitation, the habits and -constitution of Newton’s intellect, and not the apple, were -the real source of this great event in the progress of -knowledge. The common love of the marvellous, and -the vulgar desire to bring down the greatest achievements -of genius to our own level, may lead men to -ascribe such results to any casual circumstances which -accompany them; but no one who fairly considers the -real nature of great discoveries, and the intellectual -processes which they involve, can seriously hold the -opinion of their being the effect of accident.</p> -<div class="footnote"><span class="label"> -<a id="note2-2" href="#fnanchor2-2">2</a></span> -B. i. of this vol. Aphorism <a href="#b1a3">III.</a> -</div> -<p id="b2c2a19">19. Such accidents never happen to common men. -Thousands of men, even of the most inquiring and -speculative men, had seen bodies fall; but who, except -Newton, ever followed the accident to such consequences? -And in fact, how little of his train of -thought was contained in, or even directly suggested -by, the fall of the apple! If the apple fall, said the -discoverer, ‘why should not the moon, the planets, the -satellites, fall?’ But how much previous thought,—what -a steady conception of the universality of the -laws of motion gathered from other sources,—were -requisite, that the inquirer should see any connexion -in these cases! Was it by accident that he saw in the -apple an image of the moon, and of every body in the -solar system?</p> -<p id="b2c2a20">20. The same observations may be made with regard to -the other cases which are sometimes adduced -as examples of accidental discovery. It has been said, -‘By the accidental placing of a rhomb of calcareous -spar upon a book or line Bartholinus discovered the -property of the <i>Double Refraction</i> of light.’ But -Bartholinus could have seen no such consequence in the -accident if he had not previously had a clear conception -of <em>single refraction</em>. A lady, in describing an -optical experiment which had been shown her, said of -her teacher, ‘He told me to <em>increase and diminish</em> <span class="pagenum" id="page48">48</span> -<em>the angle of refraction</em>, and at last I found that he only -meant me to move my head up and down.’ At any -rate, till the lady had acquired the notions which the -technical terms convey, she could not have made -Bartholinus’s discovery by means of his accident. ‘By -accidentally combining two rhombs in different positions,’ -it is added, ‘Huyghens discovered the <i>Polarization</i> of -Light.’ Supposing that this experiment had -been made without design, what Huyghens really -observed was, that the images appeared and disappeared -alternately as he turned one of the rhombs -round. But was it an easy or an obvious business to -analyze this curious alternation into the circumstances -of the rays of light having <i>sides</i>, as Newton expressed -it, and into the additional hypotheses which are implied -in the term ‘polarization’? Those will be able -to answer this question, who have found how far from -easy it is to understand clearly what is meant by -‘polarization’ in this case, now that the property is -fully established. Huyghens’s success depended on his -clearness of thought, for this enabled him to perform -the intellectual analysis, which never would have occurred -to most men, however often they had ‘accidentally -combined two rhombs in different positions.’ ‘By accidentally -looking through a prism of the same substance, and turning -it round, Malus discovered the -polarization of light by reflection.’ Malus saw that, -in some positions of the prism, the light reflected -from the windows of the Louvre thus seen through -the prism, became dim. A common man would have -supposed this dimness the result of accident; but -Malus’s mind was differently constituted and disciplined. -He considered the position of the window, -and of the prism; repeated the experiment over and -over; and in virtue of the eminently distinct conceptions -of space which he possessed, resolved the phenomena into -its geometrical conditions. A believer in -accident would not have sought them; a person of -less clear ideas would not have found them. A person -must have a strange confidence in the virtue of chance, -and the worthlessness of intellect, who can say that <span class="pagenum" id="page49">49</span> -‘in all these fundamental discoveries appropriate ideas -had no share,’ and that the discoveries ‘might have -been made by the most ordinary observers.’</p> -<p class="end" id="b2c2a21">21. I have now, I trust, shown in various ways, -how the <i>Explication of Conceptions</i>, including in this -term their clear development from Fundamental Ideas -in the discoverer’s mind, as well as their precise expression -in the form of Definitions or Axioms, when -that can be done, is an essential part in the establishment -of all exact and general physical truths. In doing -this, I have endeavoured to explain in what sense the -possession of clear and appropriate ideas is a main -requisite for every step in scientific discovery. That it -is far from being the only step, I shall soon have to -show; and if any obscurity remain on the subject -treated of in the present chapter, it will, I hope, be -removed when we have examined the other elements -which enter into the constitution of our knowledge.</p> -<div class="chapter"> -<p><span class="pagenum" id="page50"></span></p> -<h3 class="nobreak">CHAPTER III.<br /><br /> -<span class="sc">Of Facts as the Materials of Science.</span></h3> -<hr class="two" /> -</div> -<p class="center"><span class="sc">Aphorism</span> IV.</p> -<p><i>Facts are the materials of science, but all Facts involve -Ideas. Since in observing Facts, we cannot exclude Ideas, -we must, for the purposes of science, take care that the Ideas -are clear and rigorously applied.</i></p> -<p class="center"><span class="sc">Aphorism</span> V.</p> -<p><i>The last Aphorism leads to such Rules as the following:—That -Facts, for the purposes of material science, must involve -Conceptions of the Intellect only, and not Emotions:—That -Facts must be observed with reference to our most exact conceptions, -Number, Place, Figure, Motion:—That they must -also be observed with reference to any other exact conceptions -which the phenomena suggest, as Force, in mechanical phenomena, -Concord, in musical.</i></p> -<p class="center"><span class="sc">Aphorism</span> VI.</p> -<p><i>The resolution of complex Facts into precise and measured -partial Facts, we call the</i> Decomposition of Facts. <i>This -process is requisite for the progress of science, but does not -necessarily lead to progress.</i></p> -<p class="noind" id="b2c3a1"> -<span class="dropcap"><span class="dsmall">1.</span> W</span>E -have now to examine how Science is built -up by the combination of Facts. In doing this, -we suppose that we have already attained a supply of -definite and certain Facts, free from obscurity and doubt. -We must, therefore, first consider under what conditions -Facts can assume this character.</p> -<p>When we inquire what Facts are to be made the -materials of Science, perhaps the answer which we <span class="pagenum" id="page51">51</span> -should most commonly receive would be, that they -must be <em>True Facts</em>, as distinguished from any mere -inferences or opinions of our own. We should probably be told -that we must be careful in such a case to -consider as Facts, only what we really observe;—that -we must assert only what we see; and believe nothing -except upon the testimony of our senses.</p> -<p>But such maxims are far from being easy to apply, -as a little examination will convince us.</p> -<p id="b2c3a2">2. It has been explained, in preceding works, -that all perception of external objects and occurrences -involves an active as well as a passive process -of the mind;—includes not only Sensations, but also -Ideas by which Sensations are bound together, and -have a unity given to them. From this it follows, that -there is a difficulty in separating in our perceptions -what we receive from without, and what we ourselves -contribute from within;—what we perceive, and what -we infer. In many cases, this difficulty is obvious to -all: as, for example, when we witness the performances -of a juggler or a ventriloquist. In these instances, we -imagine ourselves to see and to hear what certainly we -do not see and hear. The performer takes advantage -of the habits by which our minds supply interruptions -and infer connexions; and by giving us fallacious -indications, he leads us to perceive as an actual fact, what -does not happen at all. In these cases, it is evident -that we ourselves assist in making the fact; for we -make one which does not really exist. In other cases, -though the fact which we perceive be true, we can -easily see that a large portion of the perception is our -own act; as when, from the sight of a bird of prey we -infer a carcase, or when we read a half-obliterated inscription. -In the latter case, the mind supplies the -meaning, and perhaps half the letters; yet we do not -hesitate to say that we actually <em>read</em> the inscription. -Thus, in many cases, our own inferences and interpretations -enter into our facts. But this happens in -many instances in which it is at first sight less obvious. -When any one has seen an oak-tree blown down by a -strong gust of wind, he does not think of the occurrence <span class="pagenum" id="page52">52</span> -any otherwise than as a <em>Fact</em> of which he is assured by -his senses. Yet by what sense does he perceive the -Force which he thus supposes the wind to exert? By -what sense does he distinguish an Oak-tree from all -other trees? It is clear upon reflexion, that in such -a case, his own mind supplies the conception of extraneous -impulse and pressure, by which he thus interprets the motions -observed, and the distinction of -different kinds of trees, according to which he thus -names the one under his notice. The Idea of Force, -and the idea of definite Resemblances and Differences, -are thus combined with the impressions on our senses, -and form an undistinguished portion of that which we -consider as the Fact. And it is evident that we can in -no other way perceive Force, than by seeing motion; -and cannot give a Name to any object, without not -only seeing a difference of single objects, but supposing -a difference of classes of objects. When we speak as -if we saw impulse and attraction, things and classes, -we really see only objects of various forms and colours, -more or less numerous, variously combined. But do -we really perceive so much as this? When we see the -form, the size, the number, the motion of objects, are -these really mere impressions on our senses, unmodified -by any contribution or operation of the mind -itself? A very little attention will suffice to convince -us that this is not the case. When we see a windmill -turning, it may happen, as we have elsewhere -noticed<a id="fnanchor3-2" href="#note3-2"><span class="fnanchor">3</span></a>, -that we mistake the direction in which the sails turn: -when we look at certain diagrams, they may appear -either convex or concave: when we see the moon first -in the horizon and afterwards high up in the sky, we -judge her to be much larger in the former than in the -latter position, although to the eye she subtends the -same angle. And in these cases and the like, it has -been seen that the errour and confusion which we thus -incur arise from the mixture of acts of the mind itself -with impressions on the senses. But such acts are, as -we have also seen, <em>inseparable</em> portions of the process <span class="pagenum" id="page53">53</span> -of perception. A certain activity of the mind is involved, -not only in seeing objects erroneously, but in -seeing them at all. With regard to solid objects, this -is generally acknowledged. When we seem to see an -edifice occupying space in all dimensions, we really see -only a representation of it as it appears referred by -perspective to a surface. The inference of the solid -form is an operation of our own, alike when we look at -a reality and when we look at a picture. But we may -go further. Is plane Figure really a mere Sensation? -If we look at a decagon, do we see at once that it has -ten sides, or is it not necessary for us to count them: -and is not counting an act of the mind? All objects -are seen in space; all objects are seen as one or many: -but are not the Idea of Space and the Idea of Number -requisite in order that we may thus apprehend what -we see? That these Ideas of Space and Number involve a -connexion derived from the mind, and not from -the senses, appears, as we have already seen, from this, -that those Ideas afford us the materials of universal -and necessary truths:—such truths as the senses cannot -possibly supply. And thus, even the perception of -such facts as the size, shape, and number of objects, -cannot be said to be impressions of sense, distinct from -all acts of mind, and cannot be expected to be free -from errour on the ground of their being mere observed -Facts.</p> -<div class="footnote"><span class="label"> -<a id="note3-2" href="#fnanchor3-2">3</a></span> <i>History of Ideas</i>, B. ii. c. vi. s. 6. -</div> -<p>Thus the difficulty which we have been illustrating, -of distinguishing Facts from inferences and from -interpretations of facts, is not only great, but amounts to an -impossibility. The separation at which we aimed in -the outset of this discussion, and which was supposed -to be necessary in order to obtain a firm groundwork -for science, is found to be unattainable. We cannot -obtain a sure basis of Facts, by rejecting all inferences -and judgments of our own, for such inferences and -judgments form an unavoidable element in all Facts. -We cannot exclude our Ideas from our Perceptions, -for our Perceptions involve our Ideas.</p> -<p id="b2c3a3">3. But still, it cannot be doubted that in selecting -the Facts which are to form the foundation of Science, <span class="pagenum" id="page54">54</span> -we must reduce them to their most simple and certain -form; and must reject everything from which doubt or -errour may arise. Now since this, it appears, cannot -be done, by rejecting the Ideas which all Facts involve, -in what manner are we to conform to the obvious maxim, -that the Facts which form the basis of -Science must be perfectly definite and certain?</p> -<p>The analysis of facts into Ideas and Sensations, -which we have so often referred to, suggests the answer -to this inquiry. We are not able, nor need we -endeavour, to exclude Ideas from our Facts; but we -may be able to discern, with perfect distinctness, the -Ideas which we include. We cannot observe any phenomena -without applying to them such Ideas as Space -and Number, Cause and Resemblance, and usually, -several others; but we may avoid applying these Ideas -in a wavering or obscure manner, and confounding -Ideas with one another. We cannot read any of the -inscriptions which nature presents to us, without -interpreting them by means of some language which we -ourselves are accustomed to speak; but we may make -it our business to acquaint ourselves perfectly with the -language which we thus employ, and to interpret it -according to the rigorous rules of grammar and analogy.</p> -<p>This maxim, that when Facts are employed as the -basis of Science, we must distinguish clearly the Ideas -which they involve, and must apply these in a distinct -and rigorous manner, will be found to be a more precise -guide than we might perhaps at first expect. We -may notice one or two Rules which flow from it.</p> -<p id="b2c3a4">4. In the first place. Facts, when used as the materials -of physical Science, must be <em>referred to Conceptions -of the Intellect only</em>, all emotions of fear, admiration, -and the like, being rejected or subdued. Thus, -the observations of phenomena which are related as -portents and prodigies, striking terrour and boding -evil, are of no value for purposes of science. The tales -of armies seen warring in the sky, the sound of arms -heard from the clouds, fiery dragons, chariots, swords -seen in the air, may refer to meteorological phenomena; -but the records of phenomena observed in the <span class="pagenum" id="page55">55</span> -state of mind which these descriptions imply can be -of no scientific value. We cannot make the poets our -observers.</p> -<div class="poetry-container"> - <div class="poem"> - <div class="stanza"> - <span class="i0">Armorum sonitum toto Germania cœlo</span><br /> - <span class="i0">Audiit; insolitis tremuerunt motibus Alpes.</span><br /> - <span class="i0">Vox quoque per lucos vulgo exaudita silentes</span><br /> - <span class="i0">Ingens; et simulacra modis pallentia miris</span><br /> - <span class="i0">Visa sub obscurum noctis: pecudesque locutæ.</span><br /> - </div> - </div> -</div> -<p class="noind">The mixture of fancy and emotion with the observation -of facts has often disfigured them to an extent which -is too familiar to all to need illustration. We have an -example of this result, in the manner in which Comets -are described in the treatises of the middle ages. In -such works, these bodies are regularly distributed into -several classes, accordingly as they assume the form of -a sword, of a spear, of a cross, and so on. When such -resemblances had become matters of interest, the -impressions of the senses were governed, not by the -rigorous conceptions of form and colour, but by these -assumed images; and under these circumstances, we can -attach little value to the statement of what was seen.</p> -<p>In all such phenomena, the reference of the objects -to the exact Ideas of Space, Number, Position, Motion, -and the like, is the first step of Science: and accordingly, -this reference was established at an early period -in those sciences which made an early progress, as, for -instance, Astronomy. Yet even in astronomy there -appears to have been a period when the predominant -conceptions of men in regarding the heavens and the -stars pointed to mythical story and supernatural influence, -rather than to mere relations of space, time, -and motion: and of this primeval condition of those -who gazed at the stars, we seem to have remnants in -the Constellations, in the mythological Names of the -Planets, and in the early prevalence of Astrology. It -was only at a later period, when men had begun to -measure the places, or at least to count the revolutions -of the stars, that Astronomy had its birth.</p> -<p id="b2c3a5">5. And thus we are led to another Rule:—that in -collecting Facts which are to be made the basis of <span class="pagenum" id="page56">56</span> -Science, the Facts are to be observed, as far as possible, -<i>with reference to place</i>, <i>figure</i>, -<i>number</i>, <i>motion</i>, and the -like Conceptions; which, depending upon the Ideas of -Space and Time, are the most universal, exact, and -simple of our conceptions. It was by early attention to -these relations in the case of the heavenly bodies, that -the ancients formed the science of Astronomy: it was -by not making precise observations of this kind in the -case of terrestrial bodies, that they failed in framing a -science of the Mechanics of Motion. They succeeded -in Optics as far as they made observations of this nature; -but when they ceased to trace the geometrical -paths of rays in the actual experiment, they ceased to -go forwards in the knowledge of this subject.</p> -<p id="b2c3a6">6. But we may state a further Rule:—that though -these relations of Time and Space are highly important -in almost all Facts, we are not to confine ourselves to -these: but are to consider the phenomena <em>with reference -to other Conceptions also</em>: it being always understood -that these conceptions are to be made as exact and -rigorous as those of geometry and number. Thus the -science of Harmonics arose from considering sounds -with reference to <em>Concords</em> and <em>Discords</em>; the science -of Mechanics arose from not only observing motions as -they take place in Time and Space, but further, referring -them to <em>Force</em> as their <em>Cause</em>. And in like manner, other -sciences depend upon other Ideas, which, as -I have endeavoured to show, are not less fundamental -than those of Time and Space; and like them, capable -of leading to rigorous consequences.</p> -<p id="b2c3a7">7. Thus the Facts which we assume as the basis of -Science are to be freed from all the mists which -imagination and passion throw round them; and to be -separated into those elementary Facts which exhibit -simple and evident relations of Time, or Space, or -Cause, or some other Ideas equally clear. We resolve -the complex appearances which nature offers to us, -and the mixed and manifold modes of looking at these -appearances which rise in our thoughts, into limited, -definite, and clearly-understood portions. This process -we may term the <i>Decomposition of Facts</i>. It is the <span class="pagenum" id="page57">57</span> -beginning of exact knowledge,—the first step in the -formation of all Science. This Decomposition of Facts -into Elementary Facts, clearly understood and surely -ascertained, must precede all discovery of the laws of -nature.</p> -<p id="b2c3a8">8. But though this step is necessary, it is not infallibly -sufficient. It by no means follows that when we -have thus decomposed Facts into Elementary Truths -of observation, we shall soon be able to combine these, -so as to obtain Truths of a higher and more speculative -kind. We have examples which show us how -far this is from being a necessary consequence of the -former step. Observations of the weather, made and -recorded for many years, have not led to any general -truths, forming a science of Meteorology: and although -great numerical precision has been given to such -observations by means of barometers, thermometers, and -other instruments, still, no general laws regulating the -cycles of change of such phenomena have yet been -discovered. In like manner the faces of crystals, and -the sides of the polygons which these crystals form, -were counted, and thus numerical facts were obtained, -perfectly true and definite, but still of no value for -purposes of science. And when it was discovered -what Element of the form of crystals it was important -to observe and measure, namely, the Angle made by -two faces with each other, this discovery was a step of -a higher order, and did not belong to that department, -of mere exact observation of manifest Facts, -with which we are here concerned.</p> -<p id="b2c3a9">9. When the Complex Facts which nature offers to -us are thus decomposed into Simple Facts, the -decomposition, in general, leads to the introduction of <em>Terms</em> -and Phrases, more or less technical, by which these -Simple Facts are described. When Astronomy was -thus made a science of measurement, the things measured -were soon described as <i>Hours</i>, and <i>Days</i>, and -<i>Cycles</i>, <i>Altitude</i> and <i>Declination</i>, -<i>Phases</i> and <i>Aspects</i>. -In the same manner, in Music, the concords had names -assigned them, as <i>Diapente</i>, <i>Diatessaron</i>, <i>Diapason</i>; in -studying Optics, the <i>Rays</i> of light were spoken of as <span class="pagenum" id="page58">58</span> -having their course altered by <i>Reflexion</i> and <i>Refraction</i>; -and when useful observations began to be made -in Mechanics, the observers spoke of <i>Force</i>, <i>Pressure</i>, -<i>Momentum</i>, <i>Inertia</i>, and the like.</p> -<p id="b2c3a10">10. When we take phenomena in which the leading Idea is -Resemblance, and resolve them into precise -component Facts, we obtain some kind of Classification; -as, for instance, when we lay down certain Rules -by which particular trees, or particular animals are to -be known. This is the earliest form of Natural History; -and the Classification which it involves is that -which corresponds, nearly or exactly, with the usual -Names of the objects thus classified.</p> -<p class="end" id="b2c3a11">11. Thus the first attempts to render observation -certain and exact, lead to a decomposition of the obvious -facts into Elementary Facts, connected by the -Ideas of Space, Time, Number, Cause, Likeness, and -others: and into a Classification of the Simple Facts; -a classification more or less just, and marked by Names -either common or technical. Elementary Facts, and -Individual Objects, thus observed and classified, form -the materials of Science; and any improvement in -Classification or Nomenclature, or any discovery of a -Connexion among the materials thus accumulated, -leads us fairly within the precincts of Science. We -must now, therefore, consider the manner in which -Science is built up of such materials;—the process by -which they are brought into their places, and the -texture of the bond which unites and cements them.</p> -<div class="chapter"> -<p><span class="pagenum" id="page59"></span></p> -<h3 class="nobreak">CHAPTER IV.<br /><br /> -<span class="sc">Of the Colligation of Facts.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> VII.</p> -<p><i>Science begins with</i> common <i>observation of facts; but -even at this stage, requires that the observations be precise. -Hence the sciences which depend upon space and number -were the earliest formed. After common observation, come -Scientific</i> Observation <i>and</i> Experiment.</p> -<p class="center"><span class="sc">Aphorism</span> VIII.</p> -<p><i>The Conceptions by which Facts are bound together, are -suggested by the sagacity of discoverers. This sagacity cannot -be taught. It commonly succeeds by guessing; and this -success seems to consist in framing several</i> tentative -hypotheses <i>and selecting the right one. But a supply of -appropriate hypotheses cannot be constructed by rule, nor without -inventive talent.</i></p> -<p class="center"><span class="sc">Aphorism</span> IX.</p> -<p><i>The truth of tentative hypotheses must be tested by their -application to facts. The discoverer must be ready, carefully -to try his hypotheses in this manner, and to reject -them if they will not bear the test, in spite of indolence and -vanity.</i></p> -<p class="noind" id="b2c4a1"> -<span class="dropcap"><span class="dsmall">1.</span> F</span>ACTS -such as the last Chapter speaks of are, by -means of such Conceptions as are described in -the preceding Chapter, bound together so as to give -rise to those general Propositions of which Science -consists. Thus the Facts that the planets revolve <span class="pagenum" id="page60">60</span> -about the sun in certain periodic times and at certain -distances, are included and connected in Kepler’s Law, -by means of such Conceptions as the <i>squares of numbers</i>, -the <i>cubes of distances</i>, and the <i>proportionality</i> of -these quantities. Again the existence of this proportion -in the motions of any two planets, forms a set of -Facts which may all be combined by means of the -Conception of a certain <i>central accelerating force</i>, as -was proved by Newton. The whole of our physical -knowledge consists in the establishment of such -propositions; and in all such cases, Facts are bound -together by the aid of suitable Conceptions. This part -of the formation of our knowledge I have called the -<i>Colligation of Facts</i>: and we may apply this term to -every case in which, by an act of the intellect, we -establish a precise connexion among the phenomena -which are presented to our senses. The knowledge of -such connexions, accumulated and systematized, is -Science. On the steps by which science is thus collected -from phenomena we shall proceed now to make -a few remarks.</p> -<p id="b2c4a2">2. Science begins with <em>Common</em> Observation of -facts, in which we are not conscious of any peculiar -discipline or habit of thought exercised in observing. -Thus the common perceptions of the appearances and -recurrences of the celestial luminaries, were the first -steps of Astronomy: the obvious cases in which bodies -fall or are supported, were the beginning of Mechanics; -the familiar aspects of visible things, were the origin -of Optics; the usual distinctions of well-known plants, -first gave rise to Botany. Facts belonging to such -parts of our knowledge are noticed by us, and accumulated -in our memories, in the common course of our -habits, almost without our being aware that we are -observing and collecting facts. Yet such facts may -lead to many scientific truths; for instance, in the first -stages of Astronomy (as we have shown in the <i>History</i>) -such facts led to Methods of Intercalation and Rules -of the Recurrence of Eclipses. In succeeding stages -of science, more especial attention and preparation on -the part of the observer, and a selection of certain <span class="pagenum" id="page61">61</span> -<em>kinds</em> of facts, becomes necessary; but there is an early -period in the progress of knowledge at which man is -a physical philosopher, without seeking to be so, or -being aware that he is so.</p> -<p id="b2c4a3">3. But in all stages of the progress, even in that -early one of which we have just spoken, it is necessary, -in order that the facts may be fit materials of -any knowledge, that they should be decomposed into -Elementary Facts, and that these should be observed -with precision. Thus, in the first infancy of astronomy, -the recurrence of phases of the moon, of places -of the sun’s rising and setting, of planets, of eclipses, -was observed to take place at intervals of certain definite -numbers of days, and in a certain exact order; -and thus it was, that the observations became portions -of astronomical science. In other cases, although the -facts were equally numerous, and their general aspect -equally familiar, they led to no science, because their -exact circumstances were not apprehended. A vague -and loose mode of looking at facts very easily observable, -left men for a long time under the belief that a -body, ten times as heavy as another, falls ten times as -fast;—that objects immersed in water are always magnified, -without regard to the form of the surface;—that -the magnet exerts an irresistible force;—that -crystal is always found associated with ice;—and the -like. These and many others are examples how blind -and careless men can be, even in observation of the -plainest and commonest appearances; and they show -us that the mere faculties of perception, although -constantly exercised upon innumerable objects, may long -fail in leading to any exact knowledge.</p> -<p id="b2c4a4">4. If we further inquire what was the favourable -condition through which some special classes of facts -were, from the first, fitted to become portions of science, -we shall find it to have been principally this;—that -these facts were considered with reference to the -Ideas of Time, Number, and Space, which are Ideas -possessing peculiar definiteness and precision; so that -with regard to them, confusion and indistinctness are -hardly possible. The interval from new moon to new <span class="pagenum" id="page62">62</span> -moon was always a particular number of days: the -sun in his yearly course rose and set near to a known -succession of distant objects: the moon’s path passed -among the stars in a certain order:—these are observations -in which mistake and obscurity are not likely -to occur, if the smallest degree of attention is bestowed -upon the task. To count a number is, from the first -opening of man’s mental faculties, an operation which -no science can render more precise. The relations of -space are nearest to those of number in obvious and -universal evidence. Sciences depending upon these -Ideas arise with the first dawn of intellectual civilization. -But few of the other Ideas which man employs -in the acquisition of knowledge possess this clearness -in their common use. The Idea of <i>Resemblance</i> may -be noticed, as coming next to those of Space and Number -in original precision; and the Idea of <i>Cause</i>, in a -certain vague and general mode of application, sufficient -for the purposes of common life, but not for the -ends of science, exercises a very extensive influence -over men’s thoughts. But the other Ideas on which -science depends, with the Conceptions which arise out -of them, are not unfolded till a much later period of -intellectual progress; and therefore, except in such -limited cases as I have noticed, the observations of -common spectators and uncultivated nations, however -numerous or varied, are of little or no effect in giving -rise to Science.</p> -<p id="b2c4a5">5. Let us now suppose that, besides common everyday -perception of facts, we turn our attention to some -other occurrences and appearances, with a design of -obtaining from them speculative knowledge. This -process is more peculiarly called <i>Observation</i>, or, when -we ourselves occasion the facts, <i>Experiment</i>. But the -same remark which we have already made, still holds -good here. These facts can be of no value, except -they are resolved into those exact Conceptions which -contain the essential circumstances of the case. They -must be determined, not indeed necessarily, as has -sometimes been said, ‘according to Number, Weight, -and Measure;’ for, as we have endeavoured to show <span class="pagenum" id="page63">63</span> -in the preceding Books<a id="fnanchor4-2" href="#note4-2"><span class="fnanchor">4</span></a>, -there are many other -Conceptions to which phenomena may be subordinated, -quite different from these, and yet not at all less -definite and precise. But in order that the facts obtained -by observation and experiment may be capable of -being used in furtherance of our exact and solid knowledge, -they must be apprehended and analysed according to some -Conceptions which, applied for this purpose, give distinct -and definite results, such as can be -steadily taken hold of and reasoned from; that is, the -facts must be referred to Clear and Appropriate Ideas, -according to the manner in which we have already explained -this condition of the derivation of our knowledge. The -phenomena of light, when they are such -as to indicate sides in the ray, must be referred to the -Conception of <i>polarization</i>; the phenomena of mixture, -when there is an alteration of qualities as well -as quantities, must be combined by a Conception of -<i>elementary composition</i>. And thus, when mere position, -and number, and resemblance, will no longer answer the -purpose of enabling us to connect the facts, -we call in other Ideas, in such cases more efficacious, -though less obvious.</p> -<div class="footnote"><span class="label"><a id="note4-2" href="#fnanchor4-2">4</a></span> -<i>Hist. of Sci. Id.</i> Bs. v. vi. vii. viii. ix. x. -</div> -<p id="b2c4a6">6. But how are we, in these cases, to discover such -Ideas, and to judge which will be efficacious, in leading -to a scientific combination of our experimental data? -To this question, we must in the first place answer, -that the first and great instrument by which facts, so -observed with a view to the formation of exact knowledge, -are combined into important and permanent -truths, is that peculiar Sagacity which belongs to the -genius of a Discoverer; and which, while it supplies -those distinct and appropriate Conceptions which lead -to its success, cannot be limited by rules, or expressed -in definitions. It would be difficult or impossible to -describe in words the habits of thought which led Archimedes -to refer the conditions of equilibrium on the -Lever to the Conception of <i>pressure</i>, while Aristotle -could not see in them anything more than the results <span class="pagenum" id="page64">64</span> -of the strangeness of the properties of the circle;—or -which impelled Pascal to explain by means of the -Conception of the <i>weight of air</i>, the facts which his -predecessors had connected by the notion of nature’s -horrour of a vacuum;—or which caused Vitello and -Roger Bacon to refer the magnifying power of a convex lens -to the bending of the rays of light towards -the perpendicular by <i>refraction</i>, while others conceived -the effect to result from the matter of medium, with -no consideration of its form. These are what are commonly -spoken of as felicitous and inexplicable strokes -of inventive talent; and such, no doubt, they are. No -rules can ensure to us similar success in new cases; or -can enable men who do not possess similar endowments, -to make like advances in knowledge.</p> -<p id="b2c4a7">7. Yet still, we may do something in tracing the -process by which such discoveries are made; and this -it is here our business to do. We may observe that -these, and the like discoveries, are not improperly -described as happy <i>Guesses</i>; and that Guesses, in these -as in other instances, imply various suppositions made, -of which some one turns out to be the right one. We -may, in such cases, conceive the discoverer as inventing -and trying many conjectures, till he finds one -which answers the purpose of combining the scattered -facts into a single rule. The discovery of general -truths from special facts is performed, commonly at -least, and more commonly than at first appears, by -the use of a series of Suppositions, or <i>Hypotheses</i>, -which are looked at in quick succession, and of which -the one which really leads to truth is rapidly detected, -and when caught sight of, firmly held, verified, and -followed to its consequences. In the minds of most -discoverers, this process of invention, trial, and -acceptance or rejection of the hypothesis, goes on so rapidly -that we cannot trace it in its successive steps. But in -some instances, we can do so; and we can also see that -the other examples of discovery do not differ essentially -from these. The same intellectual operations -take place in other cases, although this often happens -so instantaneously that we lose the trace of the <span class="pagenum" id="page65">65</span> -progression. In the discoveries made by Kepler, we have -a curious and memorable exhibition of this process in -its details. Thanks to his communicative disposition, -we know that he made nineteen hypotheses with regard -to the motion of Mars, and calculated the results -of each, before he established the true doctrine, that -the planet’s path is an ellipse. We know, in like manner, -that Galileo made wrong suppositions respecting -the laws of falling bodies, and Mariotte, concerning -the motion of water in a siphon, before they hit upon -the correct view of these cases.</p> -<p id="b2c4a8">8. But it has very often happened in the history of -science, that the erroneous hypotheses which preceded -the discovery of the truth have been made, not by the -discoverer himself, but by his precursors; to whom he -thus owed the service, often an important one in such -cases, of exhausting the most tempting forms of errour. -Thus the various fruitless suppositions by which Kepler -endeavoured to discover the law of reflection, led -the way to its real detection by Snell; Kepler’s numerous -imaginations concerning the forces by which the -celestial motions are produced,—his ‘physical reasonings’ -as he termed them,—were a natural prelude to -the truer physical reasonings of Newton. The various -hypotheses by which the suspension of vapour in air -had been explained, and their failure, left the field -open for Dalton with his doctrine of the mechanical -mixture of gases. In most cases, if we could truly -analyze the operation of the thoughts of those who -make, or who endeavour to make discoveries in science, -we should find that many more suppositions pass -through their minds than those which are expressed -in words; many a possible combination of conceptions -is formed and soon rejected. There is a constant -invention and activity, a perpetual creating and selecting -power at work, of which the last results only are -exhibited to us. Trains of hypotheses are called up and -pass rapidly in review; and the judgment makes its -choice from the varied group.</p> -<p id="b2c4a9">9. It would, however, be a great mistake to suppose -that the hypotheses, among which our choice thus <span class="pagenum" id="page66">66</span> -lies, are constructed by an enumeration of obvious -cases, or by a wanton alteration of relations which -occur in some first hypothesis. It may, indeed, sometimes -happen that the proposition which is finally -established is such as may be formed, by some slight -alteration, from those which are justly rejected. Thus -Kepler’s elliptical theory of Mars’s motions, involved -relations of lines and angles much of the same nature -as his previous false suppositions: and the true law of -refraction so much resembles those erroneous ones -which Kepler tried, that we cannot help wondering -how he chanced to miss it. But it more frequently -happens that new truths are brought into view by the -application of new Ideas, not by new modifications of -old ones. The cause of the properties of the Lever -was learnt, not by introducing any new <em>geometrical</em> -combination of lines and circles, but by referring the -properties to genuine <em>mechanical</em> Conceptions. When -the Motions of the Planets were to be explained, this -was done, not by merely improving the previous notions, -of cycles of time, but by introducing the new -conception of <em>epicycles</em> in space. The doctrine of the -Four Simple Elements was expelled, not by forming -any new scheme of elements which should impart, -according to new rules, their sensible qualities to their -compounds, but by considering the elements of bodies -as <em>neutralizing</em> each other. The Fringes of Shadows -could not be explained by ascribing new properties to -the single rays of light, but were reduced to law by -referring them to the <em>interference</em> of several rays.</p> -<p>Since the true supposition is thus very frequently -something altogether diverse from all the obvious -conjectures and combinations, we see here how far we are -from being able to reduce discovery to rule, or to give -any precepts by which the want of real invention and -sagacity shall be supplied. We may warn and encourage -these faculties when they exist, but we cannot -create them, or make great discoveries when they are -absent.</p> -<p id="b2c4a10">10. The Conceptions which a true theory requires -are very often clothed in a <i>Hypothesis</i> which connects <span class="pagenum" id="page67">67</span> -with them several superfluous and irrelevant circumstances. -Thus the Conception of the Polarization of -Light was originally represented under the image of -particles of light having their poles all turned in the -same direction. The Laws of Heat may be made out -perhaps most conveniently by conceiving Heat to be -a <i>Fluid</i>. The Attraction of Gravitation might have -been successfully applied to the explanation of facts, if -Newton had throughout treated Attraction as the result of -an <i>Ether</i> diffused through space; a supposition -which he has noticed as a possibility. The doctrine of -Definite and Multiple Proportions may be conveniently -expressed by the hypothesis of <i>Atoms</i>. In such cases, -the Hypothesis may serve at first to facilitate the -introduction of a new Conception. Thus a pervading -Ether might for a time remove a difficulty, which some -persons find considerable, of imagining a body to exert -force at a distance. A Particle with Poles is more -easily conceived than Polarization in the abstract. -And if hypotheses thus employed will really explain -the facts by means of a few simple assumptions, the -laws so obtained may afterwards be reduced to a simpler -form than that in which they were first suggested. -The general laws of Heat, of Attraction, of Polarization, -of Multiple Proportions, are now certain, whatever image -we may form to ourselves of their ultimate causes.</p> -<p id="b2c4a11">11. In order, then, to discover scientific truths, -suppositions consisting either of new Conceptions, or of -new Combinations of old ones, are to be made, till we -find one supposition which succeeds in binding together -the Facts. But how are we to find this? How is the -trial to be made? What is meant by ‘success’ in these -cases? To this we reply, that our inquiry must be, -whether the Facts have the same relation in the Hypothesis -which they have in reality;—whether the results -of our suppositions agree with the phenomena which -nature presents to us. For this purpose, we must -both carefully observe the phenomena, and steadily -trace the consequences of our assumptions, till we can <span class="pagenum" id="page68">68</span> -bring the two into comparison. The Conceptions which -our hypotheses involve, being derived from certain -Fundamental Ideas, afford a basis of rigorous reasoning, -as we have shown in the Books of the <i>History</i> of those -Ideas. And the results to which this reasoning leads, -will be susceptible of being verified or contradicted by -observation of the facts. Thus the Epicyclical Theory -of the Moon, once assumed, determined what the -moon’s place among the stars ought to be at any given -time, and could therefore be tested by actually observing -the moon’s places. The doctrine that musical -strings of the same length, stretched with weights of -1, 4, 9, 16, would give the musical intervals of an octave, -a fifth, a fourth, in succession, could be put to the -trial by any one whose ear was capable of appreciating -those intervals: and the inference which follows from -this doctrine by numerical reasoning,—that there must -be certain imperfections in the concords of every musical -scale,—could in like manner be confirmed by trying -various modes of <i>Temperament</i>. In like manner -all received theories in science, up to the present time, -have been established by taking up some supposition, -and comparing it, directly or by means of its remoter -consequences, with the facts it was intended to embrace. -Its agreement, under certain cautions and conditions, -of which we may hereafter speak, is held to be the -evidence of its truth. It answers its genuine purpose, -the Colligation of Facts.</p> -<p id="b2c4a12">12. When we have, in any subject, succeeded in one -attempt of this kind, and obtained some true Bond of -Unity by which the phenomena are held together, the -subject is open to further prosecution; which ulterior -process may, for the most part, be conducted in a more -formal and technical manner. The first great outline -of the subject is drawn; and the finishing of the -resemblance of nature demands a more minute pencilling, -but perhaps requires less of genius in the master. In -the pursuance of this task, rules and precepts may be -given, and features and leading circumstances pointed -out, of which it may often be useful to the inquirer to -be aware. <span class="pagenum" id="page69">69</span></p> -<p>Before proceeding further, I shall speak of some -characteristic marks which belong to such scientific -processes as are now the subject of our consideration, -and which may sometimes aid us in determining when -the task has been rightly executed.</p> -<div class="chapter"> -<p><span class="pagenum" id="page70"></span></p> -<h3 class="nobreak">CHAPTER V.<br /><br /> -<span class="sc">Of Certain Characteristics of Scientific Induction.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism X.</span></p> -<p><i>The process of scientific discovery is cautious and rigorous, -not by abstaining from hypotheses, but by rigorously comparing -hypotheses with facts, and by resolutely rejecting all -which the comparison does not confirm.</i></p> -<p class="center"><span class="sc">Aphorism XI.</span></p> -<p><i>Hypotheses may be useful, though involving much that is -superfluous, and even erroneous: for they may supply the -true bond of connexion of the facts; and the superfluity and -errour may afterwards be pared away.</i></p> -<p class="center"><span class="sc">Aphorism XII.</span></p> -<p><i>It is a test of true theories not only to account for, but to -predict phenomena.</i></p> -<p class="center"><span class="sc">Aphorism XIII.</span></p> -<p>Induction <i>is a term applied to describe the process of a -true Colligation of Facts by means of an exact and appropriate -Conception.</i> An Induction <i>is also employed to denote -the</i> proposition <i>which results from this process.</i></p> -<p class="center"><span class="sc">Aphorism XIV.</span></p> -<p>The Consilience of Inductions <i>takes place when an -Induction, obtained from one class of facts, coincides with -an Induction, obtained from another different class. This</i> <span class="pagenum" id="page71">71</span> -<i>Consilience is a test of the truth of the Theory in which it -occurs.</i></p> -<p class="center"><span class="sc">Aphorism XV.</span></p> -<p><i>An Induction is not the mere</i> sum <i>of the Facts which are -colligated. The Facts are not only brought together, but seen -in a new point of view. A new mental Element is</i> superinduced; -<i>and a peculiar constitution and discipline of mind -are requisite in order to make this Induction.</i></p> -<p class="center"><span class="sc">Aphorism XVI.</span></p> -<p class="end"><i>Although in Every Induction a new conception is superinduced -upon the Facts; yet this once effectually done, the -novelty of the conception is overlooked, and the conception is -considered as a part of the fact.</i></p> -<p class="center"><span class="sc">Sect. I.</span>—<i>Invention a part of Induction.</i></p> -<p class="noind" id="b2c5a1"> -<span class="dropcap"><span class="dsmall">1.</span> T</span>HE -two operations spoken of in the preceding -chapters,—the Explication of the Conceptions -of our own minds, and the Colligation of observed Facts -by the aid of such Conceptions,—are, as we have just -said, inseparably connected with each other. When -united, and employed in collecting knowledge from the -phenomena which the world presents to us, they constitute -the mental process of <i>Induction</i>; which is usually and -justly spoken of as the genuine source of all -our <em>real general knowledge</em> respecting the external -world. And we see, from the preceding analysis of -this process into its two constituents, from what origin -it derives each of its characters. It is <em>real</em>, because it -arises from the combination of Real Facts, but it is -<em>general</em>, because it implies the possession of General -Ideas. Without the former, it would not be knowledge of the -External World; without the latter, it -would not be Knowledge at all. When Ideas and -Facts are separated from each other, the neglect of -Facts gives rise to empty speculations, idle subtleties, -visionary inventions, false opinions concerning the laws -of phenomena, disregard of the true aspect of nature: <span class="pagenum" id="page72">72</span> -while the want of Ideas leaves the mind overwhelmed, -bewildered, and stupified by particular sensations, with -no means of connecting the past with the future, the -absent with the present, the example with the rule; -open to the impression of all appearances, but capable -of appropriating none. Ideas are the <em>Form</em>, facts the -<em>Material</em>, of our structure. Knowledge does not -consist in the empty mould, or in the brute mass of matter, -but in the rightly-moulded substance. Induction -gathers general truths from particular facts;—and in -her harvest, the corn and the reaper, the solid ears and -the binding band, are alike requisite. All our knowledge -of nature is obtained by Induction; the term -being understood according to the explanation we have -now given. And our knowledge is then most complete, then -most truly deserves the name of Science, -when both its elements are most perfect;—when the -Ideas which have been concerned in its formation have, -at every step, been clear and consistent; and when -they have, at every step also, been employed in binding -together real and certain Facts. Of such Induction, -I have already given so many examples and illustrations -in the two preceding chapters, that I need not -now dwell further upon the subject.</p> -<p id="b2c5a2">2. Induction is familiarly spoken of as the process -by which we collect a <i>General Proposition</i> from a number -of <i>Particular Cases</i>: and it appears to be frequently -imagined that the general proposition results -from a mere juxta-position of the cases, or at most, from -merely conjoining and extending them. But if we -consider the process more closely, as exhibited in the -cases lately spoken of, we shall perceive that this is an -inadequate account of the matter. The particular -facts are not merely brought together, but there is a -New Element added to the combination by the very -act of thought by which they are combined. There is -a Conception of the mind introduced in the general -proposition, which did not exist in any of the observed -facts. When the Greeks, after long observing the -motions of the planets, saw that these motions might -be rightly considered as produced by the motion of one <span class="pagenum" id="page73">73</span> -wheel revolving in the inside of another wheel, these -Wheels were Creations of their minds, added to the -Facts which they perceived by sense. And even if the -wheels were no longer supposed to be material, but -were reduced to mere geometrical spheres or circles, -they were not the less products of the mind alone,—something -additional to the facts observed. The same -is the case in all other discoveries. The facts are -known, but they are insulated and unconnected, till -the discoverer supplies from his own stores a Principle -of Connexion. The pearls are there, but they will not -hang together till some one provides the String. The -distances and periods of the planets were all so many -separate facts; by Kepler’s Third Law they are connected -into a single truth: but the Conceptions which -this law involves were supplied by Kepler’s mind, and -without these, the facts were of no avail. The planets -described ellipses round the sun, in the contemplation -of others as well as of Newton; but Newton conceived -the deflection from the tangent in these elliptical -motions in a new light,—as the effect of a Central Force -following a certain law; and then it was, that such a -force was discovered truly to exist.</p> -<p>Thus<a id="fnanchor5-2" href="#note5-2"><span class="fnanchor">5</span></a> -in each inference made by Induction, there is -introduced some General Conception, which is given, -not by the phenomena, but by the mind. The conclusion -is not contained in the premises, but includes -them by the introduction of a New Generality. In -order to obtain our inference, we travel beyond the -cases which we have before us; we consider them as -mere exemplifications of some Ideal Case in which the -relations are complete and intelligible. We take a -Standard, and measure the facts by it; and this -Standard is constructed by us, not offered by Nature. -We assert, for example, that a body left to itself will -move on with unaltered velocity; not because our -senses ever disclosed to us a body doing this, but -because (taking this as our Ideal Case) we find that all <span class="pagenum" id="page74">74</span> -actual cases are intelligible and explicable by means of -the Conception of <i>Forces</i>, causing change and motion, -and exerted by surrounding bodies. In like manner, -we see bodies striking each other, and thus moving and -stopping, accelerating and retarding each other: but -in all this, we do not perceive by our senses that -abstract quantity, <i>Momentum</i>, which is always lost by -one body as it is gained by another. This Momentum -is a creation of the mind, brought in among the facts, -in order to convert their apparent confusion into order, -their seeming chance into certainty, their perplexing -variety into simplicity. This the Conception of <i>Momentum -gained and lost</i> does: and in like manner, in -any other case in which a truth is established by Induction, -some Conception is introduced, some Idea is -applied, as the means of binding together the facts, -and thus producing the truth.</p> -<div class="footnote"><span class="label"><a id="note5-2" href="#fnanchor5-2">5</a></span> -I repeat here remarks made at the end of the <i>Mechanical Euclid</i>, p. 178. -</div> -<p id="b2c5a3">3. Hence in every inference by Induction, there is -some Conception <em>superinduced</em> upon the Facts: and -we may henceforth conceive this to be the peculiar -import of the term <i>Induction</i>. I am not to be understood -as asserting that the term was originally or -anciently employed with this notion of its meaning; -for the peculiar feature just pointed out in Induction -has generally been overlooked. This appears by the -accounts generally given of Induction. ‘Induction,’ -says Aristotle<a id="fnanchor6-2" href="#note6-2"><span class="fnanchor">6</span></a>, -‘is when by means of one extreme -term<a id="fnanchor7-2" href="#note7-2"><span class="fnanchor">7</span></a> we -infer the other extreme term to be true of -the middle term.’ Thus, (to take such exemplifications -as belong to our subject,) from knowing that Mercury, -Venus, Mars, describe ellipses about the Sun, we infer -that all Planets describe ellipses about the Sun. In -making this inference syllogistically, we assume that -the evident proposition, ‘Mercury, Venus, Mars, do -what all Planets do,’ may be taken <em>conversely</em>, ‘All <span class="pagenum" id="page75">75</span> -Planets do what Mercury, Venus, Mars, do.’ But we -may remark that, in this passage, Aristotle (as was -natural in his line of discussion) turns his attention -entirely to the <em>evidence</em> of the inference; and overlooks -a step which is of far more importance to our knowledge, -namely, the <em>invention</em> of the second extreme -term. In the above instance, the particular luminaries, -Mercury, Venus, Mars, are one logical <i>Extreme</i>; the -general designation Planets is the <i>Middle Term</i>; but -having these before us, how do we come to think of -<i>description of ellipses</i>, which is the other Extreme -of the syllogism? When we have once invented this -‘second Extreme Term,’ we may, or may not, be satisfied -with the evidence of the syllogism; we may, or -may not, be convinced that, so far as this property -goes, the extremes are co-extensive with the middle -term<a id="fnanchor8-2" href="#note8-2"><span class="fnanchor">8</span></a>; -but the <em>statement</em> of the syllogism is the -important step in science. We know how long Kepler -laboured, how hard he fought, how many devices he -tried, before he hit upon this <em>Term</em>, the Elliptical -Motion. He rejected, as we know, many other ‘second -extreme Terms,’ for example, various combinations of -epicyclical constructions, because they did not represent -with sufficient accuracy the special facts of observation. -When he had established his premiss, that ‘Mars -does describe an Ellipse about the Sun,’ he does not -hesitate to <em>guess</em> at least that, in this respect, he might -<em>convert</em> the other premiss, and assert that ‘All the -Planets do what Mars does.’ But the main business -was, the inventing and verifying the proposition -respecting the Ellipse. The Invention of the Conception -was the great step in the <em>discovery</em>; the Verification of -the Proposition was the great step in the <em>proof</em> of the -discovery. If Logic consists in pointing out the conditions -of proof, the Logic of Induction must consist in -showing what are the conditions of proof, in such -inferences as this: but this subject must be pursued in the -next chapter; I now speak principally of the act of <span class="pagenum" id="page76">76</span> -<i>Invention</i>, which is requisite in every inductive inference.</p> -<div class="footnote"><span class="label"><a id="note6-2" href="#fnanchor6-2">6</a></span> -<i>Analyt. Prior.</i> lib. ii. c. xxiii. <span class="greek">Περὶ τῆς ἐπαγωγῆς</span>. -</div> -<div class="footnote"><span class="label"> -<a id="note7-2" href="#fnanchor7-2">7</a></span> The syllogism here alluded to would -be this:—<br /> -  Mercury, Venus, Mars, describe ellipses about the Sun;<br /> -  All Planets do what Mercury, Venus, Mars, do;<br /> -  Therefore all Planets describe ellipses about the Sun. -</div> -<div class="footnote"><span class="label"> -<a id="note8-2" href="#fnanchor8-2">8</a></span> -<span class="greek">Εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β καὶ μὴ ὑπερτείνει τὸ μέσον</span>.—Aristot. <i>Ibid.</i> -</div> -<p id="b2c5a4">4. Although in every inductive inference, an act of -invention is requisite, the act soon slips out of notice. -Although we bind together facts by superinducing -upon them a new Conception, this Conception, once -introduced and applied, is looked upon as inseparably -connected with the facts, and necessarily implied in -them. Having once had the phenomena bound together in -their minds in virtue of the Conception, men -can no longer easily restore them back to the detached -and incoherent condition in which they were before -they were thus combined. The pearls once strung, -they seem to form a chain by their nature. Induction -has given them a unity which it is so far from costing -us an effort to preserve, that it requires an effort to -imagine it dissolved. For instance, we usually represent -to ourselves the Earth as <em>round</em>, the Earth and -the Planets as <em>revolving</em> about the Sun, and as <em>drawn</em> -to the Sun by a Central Force; we can hardly understand -how it could cost the Greeks, and Copernicus, -and Newton, so much pains and trouble to arrive at a -view which to us is so familiar. These are no longer -to us Conceptions caught hold of and kept hold of by -a severe struggle; they are the simplest modes of -conceiving the facts: they are really Facts. We are -willing to <em>own</em> our obligation to those discoverers, but we -hardly <em>feel</em> it: for in what other manner (we ask in -our thoughts) could we represent the facts to ourselves?</p> -<p>Thus we see why it is that this step of which we -now speak, the Invention of a new Conception in -every inductive inference, is so generally overlooked -that it has hardly been noticed by preceding philosophers. -When once performed by the discoverer, it -takes a fixed and permanent place in the understanding -of every one. It is a thought which, once breathed -forth, permeates all men’s minds. All fancy they -nearly or quite knew it before. It oft was thought, or -almost thought, though never till now expressed. Men -accept it and retain it, and know it cannot be taken <span class="pagenum" id="page77">77</span> -from them, and look upon it as their own. They will not -and cannot part with it, even though they may deem -it trivial and obvious. It is a secret, which once -uttered, cannot be recalled, even though it be despised -by those to whom it is imparted. As soon as the leading -term of a new theory has been pronounced and -understood, all the phenomena change their aspect. -There is a standard to which we cannot help referring -them. We cannot fall back into the helpless and -bewildered state in which we gazed at them when we -possessed no principle which gave them unity. Eclipses -arrive in mysterious confusion: the notion of a <i>Cycle</i> -dispels the mystery. The Planets perform a tangled -and mazy dance; but <i>Epicycles</i> reduce the maze to -order. The Epicycles themselves run into confusion; -the conception of an <i>Ellipse</i> makes all clear and simple. -And thus from stage to stage, new elements of intelligible -order are introduced. But this intelligible order -is so completely adopted by the human understanding, -as to seem part of its texture. Men ask Whether -Eclipses follow a Cycle; Whether the Planets describe -Ellipses; and they imagine that so long as they do not -<em>answer</em> such questions rashly, they take nothing for -granted. They do not recollect how much they assume -in <em>asking</em> the question:—how far the conceptions of -Cycles and of Ellipses are beyond the visible surface of -the celestial phenomena:—how many ages elapsed, -how much thought, how much observation, were -needed, before men’s thoughts were fashioned into the -words which they now so familiarly use. And thus -they treat the subject, as we have seen Aristotle treating -it; as if it were a question, not of invention, but -of proof; not of substance, but of form: as if the main -thing were not <em>what</em> we assert, but <em>how</em> we assert it. -But for our purpose, it is requisite to bear in mind the -feature which we have thus attempted to mark; and -to recollect that, in every inference by induction, there -is a Conception supplied by the mind and superinduced -upon the Facts.</p> -<p class="end" id="b2c5a5">5. In collecting scientific truths by Induction, we -often find (as has already been observed) a Definition <span class="pagenum" id="page78">78</span> -and a Proposition established at the same time,—introduced -together, and mutually dependent on each -other. The combination of the two constitutes the -Inductive act; and we may consider the Definition as -representing the superinduced Conception, and the -Proposition as exhibiting the Colligation of Facts.</p> -<p class="center"><span class="sc">Sect. II.</span>—<i>Use of Hypotheses.</i></p> -<p id="b2c5a6">6. To discover a Conception of the mind which will -justly represent a train of observed facts is, in some -measure, a process of conjecture, as I have stated already; -and as I then observed, the business of conjecture is -commonly conducted by calling up before our -minds several suppositions, and selecting that one which -most agrees with what we know of the observed facts. -Hence he who has to discover the laws of nature may -have to invent many suppositions before he hits upon -the right one; and among the endowments which lead -to his success, we must reckon that fertility of invention -which ministers to him such imaginary schemes, -till at last he finds the one which conforms to the true -order of nature. A facility in devising hypotheses, -therefore, is so far from being a fault in the intellectual -character of a discoverer, that it is, in truth, a -faculty indispensable to his task. It is, for his purposes, -much better that he should be too ready in contriving, -too eager in pursuing systems which promise -to introduce law and order among a mass of unarranged -facts, than that he should be barren of such inventions -and hopeless of such success. Accordingly, as we have -already noticed, great discoverers have often invented -hypotheses which would not answer to all the facts, as -well as those which would; and have fancied themselves -to have discovered laws, which a more careful -examination of the facts overturned.</p> -<p>The tendencies of our speculative -nature<a id="fnanchor9-2" href="#note9-2"><span class="fnanchor">9</span></a>, -carrying <span class="pagenum" id="page79">79</span> -us onwards in pursuit of symmetry and rule, and thus -producing all true theories, perpetually show their -vigour by overshooting the mark. They obtain something, -by aiming at much more. They detect the order -and connexion which exist, by conceiving imaginary -relations of order and connexion which have no existence. -Real discoveries are thus mixed with baseless -assumptions; profound sagacity is combined with fanciful -conjecture; not rarely, or in peculiar instances, -but commonly, and in most cases; probably in all, if we -could read the thoughts of discoverers as we read the -books of Kepler. To try wrong guesses is, with most -persons, the only way to hit upon right ones. The -character of the true philosopher is, not that he never -conjectures hazardously, but that his conjectures are -clearly conceived, and brought into rigid contact with -facts. He sees and compares distinctly the Ideas and -the Things;—the relations of his notions to each other -and to phenomena. Under these conditions, it is not -only excusable, but necessary for him, to snatch at -every semblance of general rule,—to try all promising -forms of simplicity and symmetry.</p> -<div class="footnote"><span class="label"><a id="note9-2" href="#fnanchor9-2">9</a></span> -I here take the liberty of characterizing inventive -minds in general in the same phraseology which, in the History -of Science, I have employed in reference to particular examples. -These expressions are what I have used in speaking of the -discoveries of Copernicus.—<i>Hist. Ind. Sc.</i> b. v. c. ii. -</div> -<p>Hence advances in -knowledge<a id="fnanchor10-2" href="#note10-2"><span class="fnanchor">10</span></a> -are not commonly -made without the previous exercise of some boldness -and license in guessing. The discovery of new truths -requires, undoubtedly, minds careful and scrupulous in -examining what is suggested; but it requires, no less, -such as are quick and fertile in suggesting. What is -Invention, except the talent of rapidly calling before us -the many possibilities, and selecting the appropriate -one? It is true, that when we have rejected all the -inadmissible suppositions, they are often quickly forgotten; -and few think it necessary to dwell on these -discarded hypotheses, and on the process by which they -were condemned. But all who discover truths, must -have reasoned upon many errours to obtain each truth; <span class="pagenum" id="page80">80</span> -every accepted doctrine must have been one chosen -out of many candidates. If many of the guesses of -philosophers of bygone times now appear fanciful and -absurd, because time and observation have refuted them, -others, which were at the time equally gratuitous, have -been conformed in a manner which makes them appear -marvellously sagacious. To form hypotheses, and then -to employ much labour and skill in refuting them, if -they do not succeed in establishing them, is a part of -the usual process of inventive minds. Such a proceeding -belongs to the <em>rule</em> of the genius of discovery, -rather than (as has often been taught in modern times) -to the <em>exception</em>.</p> -<div class="footnote"><span class="label"><a id="note10-2" href="#fnanchor10-2">10</a></span> -These observations are made on occasion of -Kepler’s speculations, and are illustrated by reference to his -discoveries.—<i>Hist. Ind. Sc.</i> b. v. c. iv. sect. 1. -</div> -<p id="b2c5a7">7. But if it be an advantage for the discoverer of -truth that he be ingenious and fertile in inventing -hypotheses which may connect the phenomena of nature, -it is indispensably requisite that he be diligent -and careful in comparing his hypotheses with the facts, -and ready to abandon his invention as soon as it appears -that it does not agree with the course of actual -occurrences. This constant comparison of his own -conceptions and supposition with observed facts under -all aspects, forms the leading employment of the -discoverer: this candid and simple love of truth, which -makes him willing to suppress the most favourite -production of his own ingenuity as soon as it appears to -be at variance with realities, constitutes the first -characteristic of his temper. He must have neither the -blindness which cannot, nor the obstinacy which will -not, perceive the discrepancy of his fancies and his -facts. He must allow no indolence, or partial views, -or self-complacency, or delight in seeming demonstration, -to make him tenacious of the schemes which he -devises, any further than they are confirmed by their -accordance with nature. The framing of hypotheses -is, for the inquirer after truth, not the end, but the -beginning of his work. Each of his systems is invented, -not that he may admire it and follow it into -all its consistent consequences, but that he may make -it the occasion of a course of active experiment and -observation. And if the results of this process -<span class="pagenum" id="page81">81</span> contradict -his fundamental assumptions, however ingenious, -however symmetrical, however elegant his system may -be, he rejects it without hesitation. He allows no -natural yearning for the offspring of his own mind to -draw him aside from the higher duty of loyalty to his -sovereign, Truth: to her he not only gives his -affections and his wishes, but strenuous labour and -scrupulous minuteness of attention.</p> -<p>We may refer to what we have said of Kepler, Newton, -and other eminent philosophers, for illustrations -of this character. In Kepler we have -remarked<a id="fnanchor11-2" href="#note11-2"><span class="fnanchor">11</span></a> the -courage and perseverance with which he undertook and -executed the task of computing his own hypotheses: -and, as a still more admirable characteristic, that he -never allowed the labour he had spent upon any conjecture -to produce any reluctance in abandoning the -hypothesis, as soon as he had evidence of its inaccuracy. -And in the history of Newton’s discovery -that the moon is retained in her orbit by the force of -gravity, we have noticed the same moderation in maintaining -the hypothesis, after it had once occurred to -the author’s mind. The hypothesis required that the -moon should fall from the tangent of her orbit every -second through a space of sixteen feet; but according -to his first calculations it appeared that in fact she only -fell through a space of thirteen feet in that time. The -difference seems small, the approximation encouraging, -the theory plausible; a man in love with his own fancies -would readily have discovered or invented some -probable cause of the difference. But Newton acquiesced -in it as a disproof of his conjecture, and ‘laid -aside at that time any further thoughts of this -matter<a id="fnanchor12-2" href="#note12-2"><span class="fnanchor">12</span></a>.’</p> -<div class="footnote"><span class="label"><a id="note11-2" href="#fnanchor11-2">11</a></span> -<i>Hist. Ind. Sc.</i> b. v. c. iv. sect. 1. -</div> -<div class="footnote"><span class="label"><a id="note12-2" href="#fnanchor12-2">12</a></span> -<i>Hist. Ind. Sc.</i> b. vii. c. ii. sect. 3. -</div> -<p id="b2c5a8">8. It has often happened that those who have undertaken -to instruct mankind have not possessed this pure -love of truth and comparative indifference to the -maintenance of their own inventions. Men have frequently -adhered with great tenacity and vehemence to the hypotheses -which they have once framed; and in their <span class="pagenum" id="page82">82</span> -affection for these, have been prone to overlook, to -distort, and to misinterpret facts. In this manner, <i>Hypotheses</i> -have so often been prejudicial to the genuine -pursuit of truth, that they have fallen into a kind of -obloquy; and have been considered as dangerous temptations -and fallacious guides. Many warnings have -been uttered against the fabrication of hypotheses, by -those who profess to teach philosophy; many disclaimers -of such a course by those who cultivate science.</p> -<p>Thus we shall find Bacon frequently discommending -this habit, under the name of ‘anticipation of the mind,’ -and Newton thinks it necessary to say emphatically -‘hypotheses non fingo.’ It has been constantly urged -that the inductions by which sciences are formed must -be <em>cautious</em> and <em>rigorous</em>; and the various imaginations -which passed through Kepler’s brain, and to which he -has given utterance, have been blamed or pitied, as -lamentable instances of an unphilosophical frame of -mind. Yet it has appeared in the preceding remarks -that hypotheses rightly used are among the helps, far -more than the dangers, of science;—that scientific -induction is not a ‘cautious’ or a ‘rigorous’ process in -the sense of <em>abstaining from</em> such suppositions, but in -<em>not adhering</em> to them till they are confirmed by fact, and -in carefully seeking from facts confirmation or refutation. -Kepler’s distinctive character was, not that he was -peculiarly given to the construction of hypotheses, but -that he narrated with extraordinary copiousness and -candour the course of his thoughts, his labours, and -his feelings. In the minds of most persons, as we have -said, the inadmissible suppositions, when rejected, are -soon forgotten: and thus the trace of them vanishes -from the thoughts, and the successful hypothesis alone -holds its place in our memory. But in reality, many -other transient suppositions must have been made by -all discoverers;—hypotheses which are not afterwards -asserted as true systems, but entertained for an -instant;—‘tentative hypotheses,’ as they have been -called. Each of these hypotheses is followed by its -corresponding train of observations, from which it -derives its power of leading to truth. The hypothesis is <span class="pagenum" id="page83">83</span> -like the captain, and the observations like the soldiers -of an army: while he appears to command them, and -in this way to work his own will, he does in fact derive -all his power of conquest from their obedience, and -becomes helpless and useless if they mutiny.</p> -<p class="end">Since the discoverer has thus constantly to work his -way onwards by means of hypotheses, false and true, -it is highly important for him to possess talents and -means for rapidly <em>testing</em> each supposition as it offers -itself. In this as in other parts of the work of discovery, -success has in general been mainly owing to the -native ingenuity and sagacity of the discoverer’s mind. -Yet some Rules tending to further this object have -been delivered by eminent philosophers, and some -others may perhaps be suggested. Of these we shall -here notice only some of the most general, leaving for -a future chapter the consideration of some more -limited and detailed processes by which, in certain -cases, the discovery of the laws of nature may be -materially assisted.</p> -<p class="center"><span class="sc">Sect. III.</span>—<i>Tests of Hypotheses.</i></p> -<p id="b2c5a9">9. A maxim which it may be useful to recollect is -this;—that <i>hypotheses may often be of service to science, -when they involve a certain portion of incompleteness, -and even of errour</i>. The object of such inventions is to -bind together facts which without them are loose and -detached; and if they do this, they may lead the way -to a perception of the true rule by which the phenomena -are associated together, even if they themselves -somewhat misstate the matter. The imagined arrangement -enables us to contemplate, as a whole, a collection -of special cases which perplex and overload our minds -when they are considered in succession; and if our -scheme has so much of truth in it as to conjoin what is -really connected, we may afterwards duly correct or -limit the mechanism of this connexion. If our hypothesis -renders a reason for the agreement of cases -really similar, we may afterwards find this reason to be <span class="pagenum" id="page84">84</span> -false, but we shall be able to translate it into the -language of truth.</p> -<p>A conspicuous example of such an hypothesis,—one -which was of the highest value to science, though very -incomplete, and as a representation of nature altogether -false,—is seen in the <i>Doctrine of epicycles</i> by -which the ancient astronomers explained the motions -of the sun, moon, and planets. This doctrine connected the -places and velocities of these bodies at particular times -in a manner which was, in its general -features, agreeable to nature. Yet this doctrine was -erroneous in its assertion of the <em>circular</em> nature of all -the celestial motions, and in making the heavenly -bodies revolve <em>round the earth</em>. It was, however, of -immense value to the progress of astronomical science; -for it enabled men to express and reason upon many -important truths which they discovered respecting the -motion of the stars, up to the time of Kepler. Indeed -we can hardly imagine that astronomy could, in its -outset, have made so great a progress under any other -form, as it did in consequence of being cultivated in -this shape of the incomplete and false <i>epicyclical hypothesis</i>.</p> -<p>We may notice another instance of an exploded -hypothesis, which is generally mentioned only to be -ridiculed, and which undoubtedly is both false in the -extent of its assertion, and unphilosophical in its -expression; but which still, in its day, was not without -merit. I mean the doctrine of <i>Nature’s horrour -of a vacuum</i> (<i>fuga vacui</i>), by which the action of -siphons and pumps and many other phenomena were -explained, till Mersenne and Pascal taught a truer -doctrine. This hypothesis was of real service; for it -brought together many facts which really belong to -the same class, although they are very different in their -first aspect. A scientific writer of modern -times<a id="fnanchor13-2" href="#note13-2"><span class="fnanchor">13</span></a> -appears to wonder that men did not at once divine the -weight of the air, from which the phenomena formerly -ascribed to the <i>fuga vacui</i> really result. ‘Loaded, <span class="pagenum" id="page85">85</span> -compressed by the atmosphere,’ he says, ‘they did not -recognize its action. In vain all nature testified that -air was elastic and heavy; they shut their eyes to her -testimony. The water rose in pumps and flowed in -siphons at that time, as it does at this day. They -could not separate the boards of a pair of bellows of -which the holes were stopped; and they could not -bring together the same boards without difficulty, if -they were at first separated. Infants sucked the milk -of their mothers; air entered rapidly into the lungs -of animals at every inspiration; cupping-glasses produced -tumours on the skin; and in spite of all these -striking proofs of the weight and elasticity of the air, -the ancient philosophers maintained resolutely that air -was light, and explained all these phenomena by the -horrour which they said nature had for a vacuum.’ -It is curious that it should not have occurred to the -author while writing this, that if these facts, so -numerous and various, can all be accounted for by <em>one</em> -principle, there is a strong presumption that the -principle is not altogether baseless. And in reality is it -not true that nature <em>does</em> abhor a vacuum, and does all -she can to avoid it? No doubt this power is not unlimited; -and moreover we can trace it to a mechanical -cause, the pressure of the circumambient air. But the -tendency, arising from this pressure, which the bodies -surrounding a space void of air have to rush into it, -may be expressed, in no extravagant or unintelligible -manner, by saying that nature has a repugnance to a -vacuum.</p> -<div class="footnote"><span class="label"><a id="note13-2" href="#fnanchor13-2">13</a> -</span> Deluc, <i>Modifications de l’Atmosphère</i>, Partie 1. -</div> -<p>That imperfect and false hypotheses, though they -may thus explain <em>some</em> phenomena, and may be useful -in the progress of science, cannot explain <em>all</em> phenomena;—and -that we are never to rest in our labours -or acquiesce in our results, till we have found some -view of the subject which <em>is</em> consistent with <em>all</em> the -observed facts;—will of course be understood. We shall -afterwards have to speak of the other steps of such a -progress.</p> -<p id="b2c5a10">10. Thus the hypotheses which we accept ought to -explain phenomena which we have observed. But they <span class="pagenum" id="page86">86</span> -ought to do more than this: our hypotheses ought to -<em>foretel</em> phenomena which have not yet been observed; -at least all phenomena of the same kind as those which -the hypothesis was invented to explain. For our assent -to the hypothesis implies that it is held to be true of all -particular instances. That these cases belong to past or -to future times, that they have or have not already -occurred, makes no difference in the applicability of the -rule to them. Because the rule prevails, it includes all -cases; and will determine them all, if we can only calculate -its real consequences. Hence it will predict the -results of new combinations, as well as explain the -appearances which have occurred in old ones. And that -it does this with certainty and correctness, is one mode -in which the hypothesis is to be verified as right and -useful.</p> -<p>The scientific doctrines which have at various periods -been established have been verified in this manner. -For example, the <i>Epicyclical Theory</i> of the heavens -was confirmed by its <em>predicting</em> truly eclipses of the -sun and moon, configurations of the planets, and other -celestial phenomena; and by its leading to the construction -of Tables by which the places of the heavenly -bodies were given at every moment of time. The truth -and accuracy of these predictions were a proof that the -hypothesis was valuable, and, at least to a great extent, -true; although, as was afterwards found, it involved a -false representation of the structure of the heavens. -In like manner, the discovery of the <i>Laws of Refraction</i> -enabled mathematicians to <em>predict</em>, by calculation, -what would be the effect of any new form or combination of -transparent lenses. Newton’s hypothesis of -<i>Fits of Easy Transmission and Easy Reflection</i> in the -particles of light, although not confirmed by other -kinds of facts, involved a true statement of the law of -the phenomena which it was framed to include, and -served to <em>predict</em> the forms and colours of thin plates -for a wide range of given cases. The hypothesis that -Light operates by <i>Undulations</i> and <i>Interferences</i>, -afforded the means of <em>predicting</em> results under a still -larger extent of conditions. In like manner in the <span class="pagenum" id="page87">87</span> -progress of chemical knowledge, the doctrine of <i>Phlogiston</i> -supplied the means of <em>foreseeing</em> the consequence -of many combinations of elements, even before they -were tried; but the <i>Oxygen Theory</i>, besides affording -predictions, at least equally exact, with regard to the -general results of chemical operations, included all the -facts concerning the relations of weight of the elements -and their compounds, and enabled chemists to <em>foresee</em> -such facts in untried cases. And the Theory of <i>Electromagnetic -Forces</i>, as soon as it was rightly understood, -enabled those who had mastered it to <em>predict</em> motions -such as had not been before observed, which were -accordingly found to take place.</p> -<p>Men cannot help believing that the laws laid down -by discoverers must be in a great measure identical -with the real laws of nature, when the discoverers thus -determine effects beforehand in the same manner in -which nature herself determines them when the occasion -occurs. Those who can do this, must, to a considerable -extent, have detected nature’s secret;—must -have fixed upon the conditions to which she attends, -and must have seized the rules by which she applies -them. Such a coincidence of untried facts with speculative -assertions cannot be the work of chance, but implies some -large portion of truth in the principles on -which the reasoning is founded. To trace order and -law in that which has been observed, may be considered -as interpreting what nature has written down for us, -and will commonly prove that we understand her -alphabet. But to predict what has not been observed, -is to attempt ourselves to use the legislative phrases of -nature; and when she responds plainly and precisely -to that which we thus utter, we cannot but suppose -that we have in a great measure made ourselves masters -of the meaning and structure of her language. The -prediction of results, even of the same kind as those -which have been observed, in new cases, is a proof of -real success in our inductive processes.</p> -<p id="b2c5a11">11. We have here spoken of the prediction of -facts <em>of the same kind</em> as those from which our rule -was collected. But the evidence in favour of our <span class="pagenum" id="page88">88</span> -induction is of a much higher and more forcible character -when it enables us to explain and determine -cases of a <em>kind different</em> from those which were contemplated -in the formation of our hypothesis. The -instances in which this has occurred, indeed, impress -us with a conviction that the truth of our hypothesis -is certain. No accident could give rise to such an -extraordinary coincidence. No false supposition could, -after being adjusted to one class of phenomena, exactly -represent a different class, where the agreement was -unforeseen and uncontemplated. That rules springing -from remote and unconnected quarters should thus -leap to the same point, can only arise from <em>that</em> being -the point where truth resides.</p> -<p>Accordingly the cases in which inductions from -classes of facts altogether different have thus <em>jumped -together</em>, belong only to the best established theories -which the history of science contains. And as I shall -have occasion to refer to this peculiar feature in their -evidence, I will take the liberty of describing it by a -particular phrase; and will term it the <i>Consilience of -Inductions</i>.</p> -<p>It is exemplified principally in some of the greatest -discoveries. Thus it was found by Newton that the -doctrine of the Attraction of the Sun varying according -to the Inverse Square of this distance, which explained -Kepler’s <i>Third Law</i>, of the proportionality of -the cubes of the distances to the squares of the periodic -times of the planets, explained also his <i>First</i> and -<i>Second Laws</i>, of the elliptical motion of each planet; -although no connexion of these laws had been visible -before. Again, it appeared that the force of universal -Gravitation, which had been inferred from the <i>Perturbations</i> -of the moon and planets by the sun and by -each other, also accounted for the fact, apparently -altogether dissimilar and remote, of the <i>Precession of -the equinoxes</i>. Here was a most striking and surprising -coincidence, which gave to the theory a stamp -of truth beyond the power of ingenuity to counterfeit. -In like manner in Optics; the hypothesis of alternate -Fits of easy Transmission and Reflection would explain <span class="pagenum" id="page89">89</span> -the colours of thin plates, and indeed was devised and -adjusted for that very purpose; but it could give no -account of the phenomena of the fringes of shadows. -But the doctrine of Interferences, constructed at first -with reference to phenomena of the nature of the -<i>Fringes</i>, explained also the <i>Colours of thin plates</i> better -than the supposition of the Fits invented for that very -purpose. And we have in Physical Optics another -example of the same kind, which is quite as striking -as the explanation of Precession by inferences from the -facts of Perturbation. The doctrine of Undulations -propagated in a Spheroidal Form was contrived at first -by Huyghens, with a view to explain the laws of -<i>Double Refraction</i> in calc-spar; and was pursued with -the same view by Fresnel. But in the course of the -investigation it appeared, in a most unexpected and -wonderful manner, that this same doctrine of spheroidal -undulations, when it was so modified as to -account for the <em>directions</em> of the two refracted rays, -accounted also for the positions of their <i>Planes of -Polarization</i><a id="fnanchor14-2" href="#note14-2"><span class="fnanchor">14</span></a>, -a phenomenon which, taken by itself, -it had perplexed previous mathematicians, even to -represent.</p> -<div class="footnote"><span class="label"><a id="note14-2" href="#fnanchor14-2">14</a> -</span> <i>Hist. Ind. Sc.</i> b. ix. c. xi. sect. 4. -</div> -<p>The Theory of Universal Gravitation, and of the -Undulatory Theory of Light, are, indeed, full of examples -of this Consilience of Inductions. With regard to -the latter, it has been justly asserted by Herschel, that -the history of the undulatory theory was a succession -of <em>felicities</em><a id="fnanchor15-2" href="#note15-2"><span class="fnanchor">15</span></a>. -And it is precisely the unexpected -coincidences of results drawn from distant parts of the -subject which are properly thus described. Thus the -Laws of the <i>Modification of polarization</i> to which -Fresnel was led by his general views, accounted for -the Rule respecting the <i>Angle at which light is polarized</i>, -discovered by Sir D. -Brewster<a id="fnanchor16-2" href="#note16-2"><span class="fnanchor">16</span></a>. -The conceptions of the -theory pointed out peculiar <i>Modifications</i> -of the phenomena when <i>Newton’s rings</i> were produced -by polarised light, which modifications were <span class="pagenum" id="page90">90</span> ascertained -to take place in fact, by Arago and -Airy<a id="fnanchor17-2" href="#note17-2"><span class="fnanchor">17</span></a>. -When the beautiful phenomena of <i>Dipolarized light</i> -were discovered by Arago and Biot, Young was able -to declare that they were reducible to the general laws -of <i>Interference</i> which he had already -established<a id="fnanchor18-2" href="#note18-2"><span class="fnanchor">18</span></a>. -And what was no less striking a confirmation of the -truth of the theory, <i>Measures</i> of the same element -deduced from various classes of facts were found to -coincide. Thus the <i>Length</i> of a luminiferous undulation, -calculated by Young from the measurement of -<i>Fringes</i> of shadows, was found to agree very nearly -with the previous calculation from the colours of <i>Thin -plates</i><a id="fnanchor19-2" href="#note19-2"><span class="fnanchor">19</span></a>.</p> -<div class="footnote"><span class="label"><a id="note15-2" href="#fnanchor15-2">15</a></span> -See <i>Hist. Ind. Sc.</i> b. ix. c. xii. -</div> -<div class="footnote"><span class="label"><a id="note16-2" href="#fnanchor16-2">16</a></span> -<i>Ib.</i> c. xi. sect. 4. -</div> -<div class="footnote"><span class="label"><a id="note17-2" href="#fnanchor17-2">17</a></span> -See <i>Hist. Ind. Sc.</i> b. ix. c. xiii. sect. 6. -</div> -<div class="footnote"><span class="label"><a id="note18-2" href="#fnanchor18-2">18</a></span> -<i>Ib.</i> c. xi. sect. 5. -</div> -<div class="footnote"><span class="label"><a id="note19-2" href="#fnanchor19-2">19</a></span> -<i>Ib.</i> c. xi. sect. 2. -</div> -<p>No example can be pointed out, in the whole history of science, -so far as I am aware, in which this -Consilience of Inductions has given testimony in -favour of an hypothesis afterwards discovered to be -false. If we take one class of facts only, knowing the -law which they follow, we may construct an hypothesis, -or perhaps several, which may represent them: -and as new circumstances are discovered, we may often -adjust the hypothesis so as to correspond to these also. -But when the hypothesis, of itself and without adjustment -for the purpose, gives us the rule and reason of a -class of facts not contemplated in its construction, we -have a criterion of its reality, which has never yet -been produced in favour of falsehood.</p> -<p id="b2c5a12">12. In the preceding Article I have spoken of the -hypothesis with which we compare our facts as being -framed <em>all at once</em>, each of its parts being included in -the original scheme. In reality, however, it often happens -that the various suppositions which our system -contains are <em>added</em> upon occasion of different researches. -Thus in the Ptolemaic doctrine of the heavens, new epicycles -and eccentrics were added as new -inequalities of the motions of the heavenly bodies were -discovered; and in the Newtonian doctrine of material -rays of light, the supposition that these rays had <span class="pagenum" id="page91">91</span> -‘fits,’ was added to explain the colours of thin plates; -and the supposition that they had ‘sides’ was introduced -on occasion of the phenomena of polarization. -In like manner other theories have been built up of -parts devised at different times.</p> -<p>This being the mode in which theories are often -framed, we have to notice a distinction which is found -to prevail in the progress of true and false theories. -In the former class all the additional suppositions <em>tend -to simplicity</em> and harmony; the new suppositions resolve -themselves into the old ones, or at least require -only some easy modification of the hypothesis first -assumed: the system becomes more coherent as it is -further extended. The elements which we require for -explaining a new class of facts are already contained -in our system. Different members of the theory run -together, and we have thus a constant convergence to -unity. In false theories, the contrary is the case. The -new suppositions are something altogether additional;—not -suggested by the original scheme; perhaps difficult to -reconcile with it. Every such addition adds to -the complexity of the hypothetical system, which at -last becomes unmanageable, and is compelled to surrender -its place to some simpler explanation.</p> -<p>Such a false theory, for example, was the ancient -doctrine of eccentrics and epicycles. It explained the -general succession of the Places of the Sun, Moon, -and Planets; it would not have explained the proportion -of their Magnitudes at different times, if these -could have been accurately observed; but this the ancient -astronomers were unable to do. When, however, -Tycho and other astronomers came to be able to observe -the planets accurately in all positions, it was -found that <em>no</em> combination of <em>equable</em> circular motions -would exactly represent all the observations. We may -see, in Kepler’s works, the many new modifications of -the epicyclical hypothesis which offered themselves to -him; some of which would have agreed with the phenomena -with a certain degree of accuracy, but not with -so great a degree as Kepler, fortunately for the progress -of science, insisted upon obtaining. After these <span class="pagenum" id="page92">92</span> -epicycles had been thus accumulated, they all disappeared -and gave way to the simpler conception of an -<em>elliptical</em> motion. In like manner, the discovery of new -inequalities in the Moon’s motions encumbered her -system more and more with new machinery, which was -at last rejected all at once in favour of the <i>elliptical</i> -theory. Astronomers could not but suppose themselves in -a wrong path, when the prospect grew darker -and more entangled at every step.</p> -<p>Again; the Cartesian system of Vortices might be -said to explain the primary phenomena of the revolutions -of planets about the sun, and satellites about -planets. But the elliptical form of the orbits required -new suppositions. Bernoulli ascribed this curve to the -shape of the planet, operating on the stream of the -vortex in a manner similar to the rudder of a boat. -But then the motions of the aphelia, and of the nodes,—the -perturbations,—even the action of gravity towards the -earth,—could not be accounted for without -new and independent suppositions. Here was none of -the simplicity of truth. The theory of Gravitation, -on the other hand, became more simple as the facts to -be explained became more numerous. The attraction -of the sun accounted for the motions of the planets; -the attraction of the planets was the cause of the motion -of the satellites. But this being assumed, the -perturbations, and the motions of the nodes and aphelia, -only made it requisite to extend the attraction of the -sun to the satellites, and that of the planets to each -other:—the tides, the spheroidal form of the earth, -the precession, still required nothing more than that -the moon and sun should attract the parts of the earth, -and that these should attract each other;—so that -all the suppositions resolved themselves into the single -one, of the universal gravitation of all matter. It is -difficult to imagine a more convincing manifestation of -simplicity and unity.</p> -<p>Again, to take an example from another science;—the -doctrine of Phlogiston brought together many facts -in a very plausible manner,—combustion, acidification, -and others,—and very naturally prevailed for a while. <span class="pagenum" id="page93">93</span> -But the balance came to be used in chemical operations, -and the facts of weight as well as of combination -were to be accounted for. On the phlogistic theory, it -appeared that this could not be done without a new -supposition, and <em>that</em>, a very strange one;—that -phlogiston was an element not only not heavy, but -absolutely light, so that it diminished the weight of the -compounds into which it entered. Some chemists for a -time adopted this extravagant view, but the wiser of -them saw, in the necessity of such a supposition to the -defence of the theory, an evidence that the hypothesis -of an element <i>phlogiston</i> was erroneous. And the -opposite hypothesis, which taught that oxygen was -subtracted, and not phlogiston added, was accepted -because it required no such novel and inadmissible -assumption.</p> -<p>Again, we find the same evidence of truth in the -progress of the Undulatory Theory of light, in the -course of its application from one class of facts to another. -Thus we explain Reflection and Refraction by -undulations; when we come to Thin Plates, the requisite -‘fits’ are already involved in our fundamental -hypothesis, for they are the length of an undulation: -the phenomena of Diffraction also require such intervals; -and the intervals thus required agree exactly -with the others in magnitude, so that no new property -is needed. Polarization for a moment appears to require -some new hypothesis; yet this is hardly the case; -for the direction of our vibrations is hitherto arbitrary:—we -allow polarization to decide it, and we suppose -the undulations to be transverse. Having done this -for the sake of Polarization, we turn to the phenomena -of Double Refraction, and inquire what new hypothesis -they require. But the answer is, that they require -none: the supposition of transverse vibrations, which -we have made in order to explain Polarization, gives -us also the law of Double Refraction. Truth may give -rise to such a coincidence; falsehood cannot. Again, -the facts of Dipolarization come into view. But they -hardly require any new assumption; for the difference -of optical elasticity of crystals in different directions, <span class="pagenum" id="page94">94</span> -which is already assumed in uniaxal -crystals<a id="fnanchor20-2" href="#note20-2"><span class="fnanchor">20</span></a>, -is extended to biaxal exactly according to the law of symmetry; -and this being done, the laws of the phenomena, curious and -complex as they are, are fully -explained. The phenomena of Circular Polarization -by internal reflection, instead of requiring a new hypothesis, -are found to be given by an interpretation of -an apparently inexplicable result of an old hypothesis. -The Circular Polarization of Quartz and the Double -Refraction does indeed appear to require a new assumption, -but still not one which at all disturbs the form -of the theory; and in short, the whole history of this -theory is a progress, constant and steady, often striking -and startling, from one degree of evidence and consistence -to another of a higher order.</p> -<div class="footnote"><span class="label"><a id="note20-2" href="#fnanchor20-2">20</a></span> -<i>Hist. Ind. Sc.</i> b. ix. c. xi. sect. 5. -</div> -<p>In the Emission Theory, on the other hand, as in -the theory of solid epicycles, we see what we may -consider as the natural course of things in the career -of a false theory. Such a theory may, to a certain -extent, explain the phenomena which it was at first -contrived to meet; but every new class of facts requires -a new supposition—an addition to the machinery: and -as observation goes on, these incoherent appendages -accumulate, till they overwhelm and upset the original -frame-work. Such has been the hypothesis of the -Material Emission of light. In its original form, it -explained Reflection and Refraction: but the colours -of Thin Plates added to it the Fits of easy Transmission and -Reflection; the phenomena of Diffraction -further invested the emitted particles with complex -laws of Attraction and Repulsion; Polarization gave -them Sides: Double Refraction subjected them to -peculiar Forces emanating from the axes of the crystal: -Finally, Dipolarization loaded them with the complex -and unconnected contrivance of Moveable Polarization: -and even when all this had been done, additional -mechanism was wanting. There is here no unexpected -success, no happy coincidence, no convergence of -principles from remote quarters. The philosopher builds <span class="pagenum" id="page95">95</span> -the machine, but its parts do not fit. They hold -together only while he presses them. This is not the -character of truth.</p> -<p>As another example of the application of the Maxim -now under consideration, I may perhaps be allowed to -refer to the judgment which, in the History of Thermotics, -I have ventured to give respecting Laplace’s -Theory of Gases. I have stated<a id="fnanchor21-2" href="#note21-2"><span class="fnanchor">21</span></a>, -that we cannot help -forming an unfavourable judgment of this theory, by -looking for that great characteristic of true theory; -namely, that the hypotheses which were assumed to -account for <em>one class</em> of facts are found to explain -<em>another class</em> of a different nature. Thus Laplace’s first -suppositions explain the connexion of Compression -with Density, (the law of Boyle and Mariotte,) and -the connexion of Elasticity with Heat, (the law of -Dalton and Gay Lussac). But the theory requires -other assumptions when we come to Latent Heat; and -yet these new assumptions produce no effect upon the -calculations in any application of the theory. When -the hypothesis, constructed with reference to the Elasticity -and Temperature, is applied to another class of -facts, those of Latent Heat, we have no Simplification -of the Hypothesis, and therefore no evidence of the -truth of the theory.</p> -<div class="footnote"><span class="label"><a id="note21-2" href="#fnanchor21-2">21</a></span> -<i>Hist. Ind. Sc.</i> b. x. c. iv. -</div> -<p id="b2c5a13">13. The last two sections of this chapter direct our -attention to two circumstances, which tend to prove, in -a manner which we may term irresistible, the truth of -the theories which they characterize:—the <i>Consilience -of Inductions</i> from different and separate classes of -facts;—and the progressive <i>Simplification of the Theory</i> -as it is extended to new cases. These two Characters -are, in fact, hardly different; they are exemplified by -the same cases. For if these Inductions, collected from -one class of facts, supply an unexpected explanation of -a new class, which is the case first spoken of, there -will be no need for new machinery in the hypothesis -to apply it to the newly-contemplated facts; and thus, -we have a case in which the system does not become <span class="pagenum" id="page96">96</span> -more complex when its application is extended to a -wider field, which was the character of true theory -in its second aspect. The Consiliences of our Inductions -give rise to a constant Convergence of our Theory -towards Simplicity and Unity.</p> -<p class="end">But, moreover, both these cases of the extension of -the theory, without difficulty or new suppositions, to a -wider range and to new classes of phenomena, may be -conveniently considered in yet another point of view; -namely, as successive steps by which we gradually -ascend in our speculative views to a higher and higher -point of generality. For when the theory, either by -the concurrence of two indications, or by an extension -without complication, has included a new range of -phenomena, we have, in fact, a new induction of a -more general kind, to which the inductions formerly -obtained are subordinate, as particular cases to a general -proposition. We have in such examples, in short, -an instance of <i>successive generalization</i>. This is a -subject of great importance, and deserving of being well -illustrated; it will come under our notice in the next -chapter.</p> -<div class="chapter"> -<p><span class="pagenum" id="page97"></span></p> -<h3 class="nobreak">CHAPTER VI.<br /><br /> -<span class="sc">Of the Logic of Induction.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XVII.</p> -<p><i>The</i> Logic of Induction <i>consists in stating the Facts and -the Inference in such a manner, that the Evidence of the Inference -is manifest: just as the Logic of Deduction consists -in stating the Premises and the Conclusion in such a manner -that the Evidence of the Conclusion is manifest.</i></p> -<p class="center"><span class="sc">Aphorism</span> XVIII. -<p><i>The Logic of Deduction is exhibited by means of a certain -Formula; namely, a Syllogism; and every train of deductive -reasoning, to be demonstrative, must be capable of resolution -into a series of such Formulæ legitimately constructed. In -like manner, the Logic of Induction may be exhibited by -means of certain</i> Formulæ; <i>and every train of inductive -inference to be sound, must be capable of resolution into a -scheme of such Formulæ, legitimately constructed.</i></p> -<p class="center"><span class="sc">Aphorism</span> XIX. -<p><i>The</i> inductive act of thought <i>by which several Facts are -colligated into one Proposition, may be expressed by saying:</i> -The several Facts are exactly expressed as one Fact, if, -and only if, we adopt the Conceptions and the Assertion -<i>of the Proposition.</i></p> -<p class="center"><span class="sc">Aphorism</span> XX. -<p><i>The One Fact, thus inductively obtained from several -Facts, may be combined with other Facts, and colligated -with them by a new act of Induction. This process may be</i> <span class="pagenum" id="page98">98</span> -<i>indefinitely repeated: and these successive processes are the</i> -Steps <i>of Induction, or of</i> Generalization, <i>from the lowest to -the highest.</i></p> -<p class="center"><span class="sc">Aphorism</span> XXI. -<p><i>The relation of the successive Steps of Induction may be -exhibited by means of an</i> Inductive Table, <i>in which the -several Facts are indicated, and tied together by a Bracket, -and the Inductive Inference placed on the other side of the -Bracket; and this arrangement repeated, so as to form a -genealogical Table of each Induction, from the lowest to the -highest.</i></p> -<p class="center"><span class="sc">Aphorism</span> XXII. -<p><i>The Logic of Induction is the</i> Criterion of Truth <i>inferred -from Facts, as the Logic of Deduction is the Criterion of -Truth deduced from necessary Principles. The Inductive -Table enables us to apply such a Criterion; for we can determine -whether each Induction is verified and justified by -the Facts which its Bracket includes; and if each induction -in particular be sound, the highest, which merely combines -them all, must necessarily be sound also.</i></p> -<p class="center"><span class="sc">Aphorism</span> XXIII. -<p><i>The distinction of</i> Fact <i>and</i> Theory <i>is only relative. -Events and phenomena, considered as Particulars which may -be colligated by Induction, are</i> Facts; <i>considered as Generalities -already obtained by colligation of other Facts, they are</i> -Theories. <i>The same event or phenomenon is a Fact or a -Theory, according as it is considered as standing on one side -or the other of the Inductive Bracket.</i></p> -<p class="noind" id="b2c6a1"> -<span class="dropcap"><span class="dsmall">1.</span> T</span>HE -subject to which the present chapter refers -is described by phrases which are at the present -day familiarly used in speaking of the progress of -knowledge. We hear very frequent mention of <i>ascending -from particular to general</i> propositions, and -from these to propositions still more general;—of <span class="pagenum" id="page99">99</span> -truths <i>included</i> in other truths of a higher degree of -generality;—of different <i>stages of generalization</i>;—and -of the <i>highest step</i> of the process of discovery, to -which all others are subordinate and preparatory. As -these expressions, so familiar to our ears, especially -since the time of Francis Bacon, denote, very significantly, -processes and relations which are of great importance in -the formation of science, it is necessary for -us to give a clear account of them, illustrated with -general exemplifications; and this we shall endeavour -to do.</p> -<p>We have, indeed, already explained that science consists -of Propositions which include the Facts from which -they were collected; and other wider Propositions, collected -in like manner from the former, and including -them. Thus, that the stars, the moon, the sun, rise, -culminate, and set, are facts <em>included</em> in the proposition -that the heavens, carrying with them all the celestial -bodies, have a diurnal revolution about the axis of the -earth. Again, the observed monthly motions of the -moon, and the annual motions of the sun, are <em>included</em> -in certain propositions concerning the movements of -those luminaries with respect to the stars. But all -these propositions are really <em>included</em> in the doctrine -that the earth, revolving on its axis, moves round the -sun, and the moon round the earth. These movements, again, -considered as facts, are explained and -<em>included</em> in the statement of the forces which the earth -exerts upon the moon, and the sun upon the earth. -Again, this doctrine of the forces of these three bodies -is <em>included</em> in the assertion, that all the bodies of the -solar system, and all parts of matter, exert forces, each -upon each. And we might easily show that all the -leading facts in astronomy are comprehended in the -same generalization. In like manner with regard to -any other science, so far as its truths have been well -established and fully developed, we might show that it -consists of a gradation of propositions, proceeding from -the most special facts to the most general theoretical -assertions. We shall exhibit this gradation in some of -the principal branches of science. <span class="pagenum" id="page100">100</span></p> -<p id="b2c6a2">2. This gradation of truths, successively included -in other truths, may be conveniently represented by -Tables resembling the genealogical tables by which the -derivation of descendants from a common ancestor is -exhibited; except that it is proper in this case to invert -the form of the Table, and to make it converge to -unity downwards instead of upwards, since it has for -its purpose to express, not the derivation of many from -one, but the collection of one truth from many things. -Two or more co-ordinate facts or propositions may be -ranged side by side, and joined by some mark of connexion, -(a bracket, as <sub>⏟</sub> or <sup>⎵</sup>,) beneath -which may be placed the more general proposition -which is collected by induction from the former. Again, -propositions co-ordinate with this more general one -may be placed on a level with it; and the combination -of these, and the result of the combination, may be -indicated by brackets in the same manner; and so on, -through any number of gradations. By this means -the streams of knowledge from various classes of facts -will constantly run together into a smaller and smaller -number of channels; like the confluent rivulets of a -great river, coming together from many sources, uniting -their ramifications so as to form larger branches, these -again uniting in a single trunk. The <i>genealogical tree</i> -of each great portion of science, thus formed, will -contain all the leading truths of the science arranged -in their due co-ordination and subordination. Such -Tables, constructed for the sciences of Astronomy and -of Optics, will be given at the end of this chapter.</p> -<p id="b2c6a3">3. The union of co-ordinate propositions into a proposition -of a higher order, which occurs in this Tree of -Science wherever two twigs unite in one branch, is, in -each case, an example of <i>Induction</i>. The single proposition -is collected by the process of induction from -its several members. But here we may observe, that -the image of a mere <em>union</em> of the parts at each of these -points, which the figure of a tree or a river presents, is -very inadequate to convey the true state of the case; -for in Induction, as we have seen, besides mere collection -of particulars, there is always a <em>new conception</em>, a <span class="pagenum" id="page101">101</span> -principle of connexion and unity, supplied by the -mind, and superinduced upon the particulars. There -is not merely a juxta-position of materials, by which -the new proposition contains all that its component -parts contained; but also a formative act exerted by -the understanding, so that these materials are contained -in a new shape. We must remember, therefore, that our -Inductive Tables, although they represent the elements -and the order of these inductive -steps, do not fully represent the whole signification of -the process in each case.</p> -<p id="b2c6a4">4. The principal features of the progress of science -spoken of in the last chapter are clearly exhibited in -these Tables; namely, the <i>Consilience of Inductions</i> -and the constant Tendency to Simplicity observable in -true theories. Indeed in all cases in which, from -propositions of considerable generality, propositions of a -still higher degree are obtained, there is a convergence -of inductions; and if in one of the lines which thus -converge, the steps be rapidly and suddenly made in -order to meet the other line, we may consider that we -have an example of Consilience. Thus when Newton -had collected, from Kepler’s Laws, the Central Force of -the sun, and from these, combined with other facts, -the Universal Force of all the heavenly bodies, he -suddenly turned round to include in his generalization -the Precession of the Equinoxes, which he declared to -arise from the attraction of the sun and moon upon -the protuberant part of the terrestrial spheroid. The -apparent remoteness of this fact, in its nature, from the -other facts with which he thus associated it, causes this -part of his reasoning to strike us as a remarkable example -of <i>Consilience</i>. Accordingly, in the Table of -Astronomy we find that the columns which contain -the facts and theories relative to the <i>sun</i> and <i>planets</i>, -after exhibiting several stages of induction within -themselves, are at length suddenly connected with -a column till then quite distinct, containing the -<i>precession of the equinoxes</i>. In like manner, in the Table -of Optics, the columns which contain the facts and -theories relative to <i>double refraction</i>, and those which -<span class="pagenum" id="page102">102</span> include -<i>polarization by crystals</i>, each go separately -through several stages of induction; and then these -two sets of columns are suddenly connected by Fresnel’s -mathematical induction, that double refraction and -polarization arise from the same cause: thus -exhibiting a remarkable <i>Consilience</i>.</p> -<p id="b2c6a5">5. The constant <i>Tendency to Simplicity</i> in the -sciences of which the progress is thus represented, -appears from the form of the Table itself; for the -single trunk into which all the branches converge, -contains in itself the substance of all the propositions -by means of which this last generalization was arrived -at. It is true, that this ultimate result is sometimes -not so simple as in the Table it appears: for instance, -the ultimate generalization of the Table exhibiting the -progress of Physical Optics,—namely, that Light consists -in Undulations,—must be understood as including some other -hypotheses; as, that the undulations -are transverse, that the ether through which they are -propagated has its elasticity in crystals and other -transparent bodies regulated by certain laws; and the -like. Yet still, even acknowledging all the complication -thus implied, the Table in question evidences -clearly enough the constant advance towards unity, -consistency, and simplicity, which have marked the -progress of this Theory. The same is the case in the -Inductive Table of Astronomy in a still greater -degree.</p> -<p id="b2c6a6">6. These Tables naturally afford the opportunity of -assigning to each of the distinct steps of which the -progress of science consists, the name of the <i>Discoverer</i> -to whom it is due. Every one of the inductive -processes which the brackets of our Tables mark, -directs our attention to some person by whom the induction -was first distinctly made. These names I -have endeavoured to put in their due places in the -Tables; and the Inductive Tree of our knowledge in -each science becomes, in this way, an exhibition of the -claims of each discoverer to distinction, and, as it -were, a Genealogical Tree of scientific nobility. It is -by no means pretended that such a tree includes the <span class="pagenum" id="page103">103</span> -names of all the meritorious labourers in each department -of science. Many persons are most usefully -employed in collecting and verifying truths, who do -not advance to any new truths. The labours of a -number of such are included in each stage of our -ascent. But such Tables as we have now before us -will present to us the names of all the most eminent -discoverers: for the main steps of which the progress -of science consists, are transitions from more particular -to more general truths, and must therefore be -rightly given by these Tables; and those must be the -greatest names in science to whom the principal events -of its advance are thus due.</p> -<p id="b2c6a7">7. The Tables, as we have presented them, exhibit -the course by which we pass from Particular to General -through various gradations, and so to the most general. -They display the order of <i>discovery</i>. But by reading -them in an inverted manner, beginning at the single -comprehensive truths with which the Tables end, and -tracing these back into the more partial truths, and -these again into special facts, they answer another -purpose;—they exhibit the process of <i>verification</i> of -discoveries once made. For each of our general propositions -is true in virtue of the truth of the narrower -propositions which it involves; and we cannot satisfy -ourselves of its truth in any other way than by ascertaining -that these its constituent elements are true. -To assure ourselves that the sun attracts the planets -with forces varying inversely as the square of the distance, -we must analyse by geometry the motion of a -body in an ellipse about the focus, so as to see that such -a motion does imply such a force. We must also verify -those calculations by which the observed places of each -planet are stated to be included in an ellipse. These -calculations involve assumptions respecting the path which -the earth describes about the sun, which assumptions -must again be verified by reference to observation. And -thus, proceeding from step to step, we resolve the most -general truths into their constituent parts; and these -again into their parts; and by testing, at each step, both -the reality of the asserted ingredients and the propriety <span class="pagenum" id="page104">104</span> -of the conjunction, we establish the whole system of -truths, however wide and various it may be.</p> -<p id="b2c6a8">8. It is a very great advantage, in such a mode of -exhibiting scientific truths, that it resolves the verification -of the most complex and comprehensive theories, -into a number of small steps, of which almost any one -falls within the reach of common talents and industry. -That <em>if</em> the particulars of any one step be true, the -generalization also is true, any person with a mind -properly disciplined may satisfy himself by a little -study. That each of these particular propositions <em>is</em> -true, may be ascertained, by the same kind of attention, -when this proposition is resolved into <em>its</em> constituent -and more special propositions. And thus we -may proceed, till the most general truth is broken up -into small and manageable portions. Of these portions, -each may appear by itself narrow and easy; and -yet they are so woven together, by hypothesis and conjunction, -that the truth of the parts necessarily assures -us of the truth of the whole. The verification is of -the same nature as the verification of a large and complex -statement of great sums received by a mercantile -office on various accounts from many quarters. The -statement is separated into certain comprehensive heads, -and these into others less extensive; and these again -into smaller collections of separate articles, each of -which can be inquired into and reported on by separate -persons. And thus at last, the mere addition of -numbers performed by these various persons, and the -summation of the results which they obtain, executed -by other accountants, is a complete and entire security -that there is no errour in the whole of the process.</p> -<p id="b2c6a9">9. This comparison of the process by which we -verify scientific truth to the process of Book-keeping -in a large commercial establishment, may appear to -some persons not sufficiently dignified for the subject. -But, in fact, the possibility of giving this formal and -business-like aspect to the evidence of science, as -involved in the process of successive generalization, is an -inestimable advantage. For if no one could pronounce -concerning a wide and profound theory except he who <span class="pagenum" id="page105">105</span> -could at once embrace in his mind the whole range of -inference, extending from the special facts up to the -most general principles, none but the greatest geniuses -would be entitled to judge concerning the truth or -errour of scientific discoveries. But, in reality, we -seldom need to verify more than one or two steps of -such discoveries at one time; and this may commonly -be done (when the discoveries have been fully established -and developed,) by any one who brings to the -task clear conceptions and steady attention. The progress -of science is gradual: the discoveries which are -successively made, are also verified successively. We -have never any very large collections of them on our -hands at once. The doubts and uncertainties of any -one who has studied science with care and perseverance -are generally confined to a few points. If he can -satisfy himself upon these, he has no misgivings respecting -the rest of the structure; which has indeed -been repeatedly verified by other persons in like manner. -The fact that science is capable of being resolved -into separate processes of verification, is that which -renders it possible to form a great body of scientific -truth, by adding together a vast number of truths, of -which many men, at various times and by multiplied -efforts, have satisfied themselves. The treasury of -Science is constantly rich and abundant, because it -accumulates the wealth which is thus gathered by so -many, and reckoned over by so many more: and the -dignity of Knowledge is no more lowered by the multiplicity -of the tasks on which her servants are employed, and the -narrow field of labour to which some -confine themselves, than the rich merchant is degraded -by the number of offices which it is necessary for him -to maintain, and the minute articles of which he requires -an exact statement from his accountants.</p> -<p id="b2c6a10">10. The analysis of doctrines inductively obtained, -into their constituent facts, and the arrangement of -them in such a form that the conclusiveness of the -induction may be distinctly seen, may be termed the -<i>Logic of Induction</i>. By <i>Logic</i> has generally been -meant a system which teaches us so to arrange our <span class="pagenum" id="page106">106</span> -reasonings that their truth or falsehood shall be evident -in their form. In <em>deductive</em> reasonings, in which -the general principles are assumed, and the question is -concerning their application and combination in particular -cases, the device which thus enables us to judge -whether our reasonings are conclusive is the <i>Syllogism</i>; -and this <i>form</i>, along with the rules which belong to it, -does in fact supply us with a criterion of deductive or -demonstrative reasoning. The <i>Inductive Table</i>, such -as it is presented in the present chapter, in like manner -supplies the means of ascertaining the truth of our -inductive inferences, so far as the form in which our -reasoning may be stated can afford such a criterion. Of -course some care is requisite in order to reduce a train -of demonstration into the form of a series of syllogisms; -and certainly not less thought and attention are required -for resolving all the main doctrines of any great -department of science into a graduated table of co-ordinate -and subordinate inductions. But in each -case, when this task is once executed, the evidence or -want of evidence of our conclusions appears immediately -in a most luminous manner. In each step of -induction, our Table enumerates the particular facts, -and states the general theoretical truth which includes -these and which these constitute. The special act of -attention by which we satisfy ourselves that the facts -<em>are</em> so included,—that the general truth <em>is</em> so -constituted,—then affords little room for errour, with -moderate attention and clearness of thought.</p> -<p id="b2c6a11">11. We may find an example of this <i>act of attention</i> -thus required, at any one of the steps of induction -in our Tables; for instance, at the step in the early -progress of astronomy at which it was inferred, that -the earth is a globe, and that the sphere of the heavens -(relatively) performs a diurnal revolution round this -globe of the earth. How was this established in the belief -of the Greeks, and how is it fixed in our conviction? -As to the globular form, we find that as we travel to -the north, the apparent pole of the heavenly motions, -and the constellations which are near it, seem to mount -higher, and as we proceed southwards they descend. <span class="pagenum" id="page107">107</span> -Again, if we proceed from two different points considerably -to the east and west of each other, and travel -directly northwards from each, as from the south of -Spain to the north of Scotland, and from Greece to -Scandinavia, these two north and south lines will be -much nearer to each other in their northern than in -their southern parts. These and similar facts, as soon -as they are clearly estimated and connected in the -mind, are <em>seen to be consistent</em> with a convex surface of -the earth, and with no other: and this notion is further -confirmed by observing that the boundary of the earth’s -shadow upon the moon is always circular; it being -supposed to be already established that the moon receives -her light from the sun, and that lunar eclipses -are caused by the interposition of the earth. As for -the assertion of the (relative) diurnal revolution of the -starry sphere, it is merely putting the visible phenomena -in an exact geometrical form: and thus we establish and -verify the doctrine of the revolution of the sphere of -the heavens about the globe of the earth, by contemplating -it so as to see that it does really and exactly -include the particular facts from which it is collected.</p> -<p>We may, in like manner, illustrate this mode of -verification by any of the other steps of the same Table. -Thus if we take the great Induction of Copernicus, the -heliocentric scheme of the solar system, we find it in the -Table exhibited as including and explaining, <i>first</i>, the -diurnal revolution just spoken of; <i>second</i>, the motions -of the moon among the fixed stars; <i>third</i>, the motions -of the planets with reference to the fixed stars and the -sun; <i>fourth</i>, the motion of the sun in the ecliptic. -And the scheme being clearly conceived, we <em>see</em> that all -the particular facts <em>are</em> faithfully represented by it; -and this agreement, along with the simplicity of the -scheme, in which respect it is so far superior to any -other conception of the solar system, persuade us that -it is really the plan of nature.</p> -<p>In exactly the same way, if we attend to any of the -several remarkable discoveries of Newton, which form -the principal steps in the latter part of the Table, as -for instance, the proposition that the sun attracts all <span class="pagenum" id="page108">108</span> -the planets with a force which varies inversely as the -square of the distance, we find it proved by its including -three other propositions previously established;—<i>first</i>, -that the sun’s mean force on different planets -follows the specified variation (which is proved from -Kepler’s third law); <i>second</i>, that the force by which -each planet is acted upon in different parts of its orbit -tends to the sun (which is proved by the equable description -of areas); <i>third</i>, that this force in different -parts of the same orbit is also inversely as the square -of the distance (which is proved from the elliptical -form of the orbit). And the Newtonian generalization, -when its consequences are mathematically traced, -is <em>seen</em> to agree with each of these particular propositions, -and thus is fully established.</p> -<p id="b2c6a12">12. But when we say that the more general proposition -<em>includes</em> the several more particular ones, we -must recollect what has before been said, that these -particulars form the general truth, not by being merely -enumerated and added together, but by being seen <em>in a -new light</em>. No mere verbal recitation of the particulars -can decide whether the general proposition is true; -a special act of thought is requisite in order to determine -how truly each is included in the supposed induction. -In this respect the Inductive Table is not -like a mere schedule of accounts, where the rightness -of each part of the reckoning is tested by mere addition -of the particulars. On the contrary, the Inductive -truth is never the mere <em>sum</em> of the facts. It is made -into something more by the introduction of a new -mental element; and the mind, in order to be able to -supply this element, must have peculiar endowments -and discipline. Thus looking back at the instances -noticed in the last article, how are we to see that a -convex surface of the earth is necessarily implied by -the convergence of meridians towards the north, or by -the visible descent of the north pole of the heavens as -we travel south? Manifestly the student, in order to -see this, must have clear conceptions of the relations -of space, either naturally inherent in his mind, or -established there by geometrical cultivation,—by <span class="pagenum" id="page109">109</span> -studying the properties of circles and spheres. When he -is so prepared, he will feel the force of the expressions -we have used, that the facts just mentioned are <em>seen to -be consistent</em> with a globular form of the earth; but -without such aptitude he will not see this consistency: -and if this be so, the mere assertion of it in words -will not avail him in satisfying himself of the truth of -the proposition.</p> -<p>In like manner, in order to perceive the force of the -Copernican induction, the student must have his mind -so disciplined by geometrical studies, or otherwise, that -he sees clearly how absolute motion and relative motion -would alike produce apparent motion. He must have -learnt to cast away all prejudices arising from the seeming -fixity of the earth; and then he will see that there -is nothing which stands in the way of the induction, -while there is much which is on its side. And in the -same manner the Newtonian induction of the law of -the sun’s force from the elliptical form of the orbit, -will be evidently satisfactory to him only who has such -an insight into Mechanics as to see that a curvilinear -path must arise from a constantly deflecting force; -and who is able to follow the steps of geometrical -reasoning by which, from the properties of the ellipse, -Newton proves this deflection to be in the proportion -in which he asserts the force to be. And thus in all -cases the inductive truth must indeed be verified by -comparing it with the particular facts; but then this -comparison is possible for him only whose mind is -properly disciplined and prepared in the use of those -conceptions, which, in addition to the facts, the act of -induction requires.</p> -<p id="b2c6a13">13. In the Tables some indication is given, at -several of the steps, of the act which the mind must -thus perform, besides the mere conjunction of facts, in -order to attain to the inductive truth. Thus in the -cases of the Newtonian inductions just spoken of, the -inferences are stated to be made ‘By Mechanics;’ -and in the case of the Copernican induction, it is said -that, ‘By the nature of motion, the apparent motion is -the same, whether the heavens or the earth have a <span class="pagenum" id="page110">110</span> -diurnal motion; and the latter is more simple.’ But -these verbal statements are to be understood as mere -hints<a id="fnanchor22-2" href="#note22-2"><span class="fnanchor">22</span></a>: -they cannot supersede the necessity of the student’s -contemplating for himself the mechanical principles and the -nature of motion thus referred to.</p> -<div class="footnote"><span class="label"><a id="note22-2" href="#fnanchor22-2">22</a> -</span> In the Inductive Tables they are marked by an asterisk. -</div> -<p id="b2c6a14">14. In the common or Syllogistic Logic, a certain -<i>Formula</i> of language is used in stating the reasoning, -and is useful in enabling us more readily to apply the -Criterion of Form to alleged demonstrations. This -formula is the usual Syllogism; with its members, -Major Premiss, Minor Premiss, and Conclusion. It -may naturally be asked whether in Inductive Logic -there is any such Formula? whether there is any -standard form of words in which we may most properly -express the inference of a general truth from -particular facts?</p> -<p>At first it might be supposed that the formula of -Inductive Logic need only be of this kind: ‘These -particulars, and all known particulars of the same -kind, are exactly included in the following general -proposition.’ But a moment’s reflection on what has -just been said will show us that this is not sufficient: -for the particulars are not merely <em>included</em> in the -general proposition. It is not enough that they appertain -to it by enumeration. It is, for instance, no adequate -example of Induction to say, ‘Mercury describes -an elliptical path, so does Venus, so do the Earth, -Mars, Jupiter, Saturn, Uranus; therefore all the -Planets describe elliptical paths.’ This is, as we have -seen, the mode of stating the <em>evidence</em> when the proposition -is once suggested; but the Inductive step consists in the -<em>suggestion</em> of a conception not before -apparent. When Kepler, after trying to connect the -observed places of the planet Mars in many other -ways, found at last that the conception of an <i>ellipse</i> -would include them all, he obtained a truth by induction: -for this conclusion was not obviously included -in the phenomena, and had not been applied to these <span class="pagenum" id="page111">111</span> -facts previously. Thus in our Formula, besides stating -that the particulars are included in the general proposition, -we must also imply that the generality is constituted by -a new Conception,—new at least in its -application.</p> -<p>Hence our Inductive Formula might be something -like the following: ‘These particulars, and all known -particulars of the same kind, are exactly expressed by -adopting the Conceptions and Statement of the following -Proposition.’ It is of course requisite that the -Conceptions should be perfectly clear, and should precisely -embrace the facts, according to the explanation -we have already given of those conditions.</p> -<p id="b2c6a15">15. It may happen, as we have already stated, that -the Explication of a Conception, by which it acquires -its due distinctness, leads to a Definition, which Definition -may be taken as the summary and total result -of the intellectual efforts to which this distinctness is -due. In such cases, the Formula of Induction may be -modified according to this condition; and we may state -the inference by saying, after an enumeration and -analysis of the appropriate facts, ‘These facts are -completely and distinctly expressed by adopting the -following Definition and Proposition.’</p> -<p>This Formula has been adopted in stating the Inductive -Propositions which constitute the basis of the -science of Mechanics, in a work intitled <i>The Mechanical -Euclid</i>. The fundamental truths of the subject -are expressed in <i>Inductive Pairs</i> of Assertions, consisting -each of a Definition and a Proposition, such as -the following:<br /> - <span class="sc">Def.</span>—A <i>Uniform Force</i> -is that which acting in the -direction of the body’s motion, adds or subtracts equal -velocities in equal times.<br /> - <span class="sc">Prop.</span>—Gravity is a Uniform Force.<br /> - Again,<br /> - <span class="sc">Def.</span>—Two <i>Motions</i> are -<i>compounded</i> when each -produces its separate effect in a direction parallel to -itself.<br /> - <span class="sc">Prop.</span>—When any Force acts upon a body in motion, -the motion which the Force would produce in the <span class="pagenum" id="page112">112</span> -body at rest is compounded with the previous motion -of the body.<br /> - And in like manner in other cases.</p> -<p>In these cases the proposition is, of course, established, -and the definition realized, by an enumeration -of the facts. And in the case of inferences made in -such a form, the Definition of the Conception and the -Assertion of the Truth are both requisite and are correlative -to one another. Each of the two steps contains the verification -and justification of the other. -The Proposition derives its meaning from the Definition; -the Definition derives its reality from the Proposition. -If they are separated, the Definition is arbitrary or empty, -the Proposition vague or ambiguous.</p> -<p id="b2c6a16">16. But it must be observed that neither of the -preceding Formulæ expresses the full cogency of the -inductive proof. They declare only that the results -can be clearly explained and rigorously deduced by the -employment of a certain Definition and a certain Proposition. -But in order to make the conclusion demonstrative, which in -perfect examples of Induction it is, -we ought to be able to declare that the results can be -clearly explained and rigorously declared <em>only</em> by the -Definition and Proposition which we adopt. And in -reality, the conviction of the sound inductive reasoner -does reach to this point. The Mathematician asserts -the Laws of Motion, seeing clearly that they (or laws -equivalent to them) afford the only means of clearly -expressing and deducing the actual facts. But this -conviction, that the inductive inference is not only -consistent with the facts, but necessary, finds its place -in the mind gradually, as the contemplation of the -consequences of the proposition, and the various relations -of the facts, becomes steady and familiar. It -is scarcely possible for the student at once to satisfy -himself that the inference is thus inevitable. And -when he arrives at this conviction, he sees also, in -many cases at least, that there may be other ways of -expressing the substance of the truth established, -besides that special Proposition which he has under -his notice. <span class="pagenum" id="page113">113</span></p> -<p>We may, therefore, without impropriety, renounce -the undertaking of conveying in our formula this final -conviction of the necessary truth of our inference. We -may leave it to be thought, without insisting upon saying it, -that in such cases what <em>can</em> be true, <em>is</em> true. -But if we wish to express the ultimate significance of -the Inductive Act of thought, we may take as our -Formula for the Colligation of Facts by Induction, -this:—‘The several Facts are exactly expressed as one -Fact if, <em>and only if</em>, we adopt the Conception and the -Assertion’ of the inductive inference.</p> -<p id="b2c6a17">17. I have said that the mind must be properly -disciplined in order that it may see the necessary -connexion between the facts and the general proposition -in which they are included. And the perception of -this connexion, though treated as <em>one step</em> in our -inductive inference, may imply <em>many steps</em> of demonstrative -proof. The connexion is this, that the particular case -is included in the general one, that is, may -be <em>deduced</em> from it: but this deduction may often -require many links of reasoning. Thus in the case of -the inference of the law of the force from the elliptical -form of the orbit by Newton, the proof that in the -ellipse the deflection from the tangent is inversely as -the square of the distance from the focus of the ellipse, -is a ratiocination consisting of several steps, and -involving several properties of Conic Sections; these -properties being supposed to be previously established by -a geometrical system of demonstration on the special -subject of the Conic Sections. In this and similar -cases the Induction involves many steps of Deduction. -And in such cases, although the Inductive Step, the -Invention of the Conception, is really the most important, -yet since, when once made, it occupies a -familiar place in men’s minds; and since the Deductive -Demonstration is of considerable length and requires -intellectual effort to follow it at every step; men often -admire the deductive part of the proposition, the geometrical -or algebraical demonstration, far more than -that part in which the philosophical merit really resides. <span class="pagenum" id="page114">114</span></p> -<p id="b2c6a18">18. Deductive reasoning is virtually a collection of -syllogisms, as has already been stated: and in such -reasoning, the general principles, the Definitions and -Axioms, necessarily stand at the <em>beginning</em> of the -demonstration. In an inductive inference, the Definitions -and Principles are the <em>final result</em> of the reasoning, -the ultimate effect of the proof. Hence when an -Inductive Proposition is to be established by a proof -involving several steps of demonstrative reasoning, the -enunciation of the Proposition will contain, explicitly -or implicitly, principles which the demonstration proceeds -upon as axioms, but which are really inductive -inferences. Thus in order to prove that the force -which retains a planet in an ellipse varies inversely as -the square of the distance, it is taken for granted that -the Laws of Motion are true, and that they apply to -the planets. Yet the doctrine that this is so, as well -as the law of the force, were established only by this and -the like demonstrations. The doctrine which is the -<em>hypothesis</em> of the deductive reasoning, is the <em>inference</em> -of the inductive process. The special facts which are -the basis of the inductive inference, are the conclusion -of the train of deduction. And in this manner the -deduction establishes the induction. The principle -which we gather from the facts is true, because the -facts can be derived from it by rigorous demonstration. -Induction moves upwards, and deduction downwards, -on the same stair.</p> -<p>But still there is a great difference in the character -of their movements. Deduction descends steadily and -methodically, step by step: Induction mounts by a -leap which is out of the reach of method. She bounds -to the top of the stair at once; and then it is the -business of Deduction, by trying each step in order, to -establish the solidity of her companion’s footing. Yet -these must be processes of the same mind. The Inductive -Intellect makes an assertion which is subsequently -justified by demonstration; and it shows its -sagacity, its peculiar character, by enunciating the -proposition when as yet the demonstration does not <span class="pagenum" id="page115">115</span> -exist: but then it shows that it <em>is</em> sagacity, by also -producing the demonstration.</p> -<p>It has been said that inductive and deductive reasoning -are contrary in their scheme; that in Deduction -we infer particular from general truths; while in -Induction we infer general from particular: that -Deduction consists of many steps, in each of which we apply -known general propositions in particular cases; while -in Induction we have a single step, in which we pass -from many particular truths to one general proposition. -And this is truly said; but though contrary -in their motions, the two are the operation of the same -mind travelling over the same ground. Deduction is -a necessary part of Induction. Deduction justifies by -calculation what Induction had happily guessed. Induction -recognizes the ore of truth by its weight; -Deduction confirms the recognition by chemical analysis. -Every step of Induction must be confirmed by -rigorous deductive reasoning, followed into such detail -as the nature and complexity of the relations (whether -of quantity or any other) render requisite. If not so -justified by the supposed discoverer, it is <em>not</em> Induction.</p> -<p id="b2c6a19">19. Such Tabular arrangements of propositions as -we have constructed may be considered as the <i>Criterion -of Truth</i> for the doctrines which they include. They -are the Criterion of Inductive Truth, in the same -sense in which Syllogistic Demonstration is the Criterion -of Necessary Truth,—of the certainty of conclusions, -depending upon evident First Principles. -And that such Tables are really a Criterion of the -truth of the propositions which they contain, will be -plain by examining their structure. For if the connexion -which the inductive process assumes be ascertained -to be in each case real and true, the assertion of -the general proposition merely collects together -ascertained truths; and in like manner each of those more -particular propositions is true, because it merely -expresses collectively more special facts: so that the most -general theory is only the assertion of a great body -of facts, duly classified and subordinated. When we <span class="pagenum" id="page116">116</span> -assert the truth of the Copernican theory of the motions -of the solar system, or of the Newtonian theory of the -forces by which they are caused, we merely assert the -groups of propositions which, in the Table of Astronomical -Induction, are included in these doctrines; and -ultimately, we may consider ourselves as merely asserting -at once so many Facts, and therefore, of course, -expressing an indisputable truth.</p> -<p id="b2c6a20">20. At any one of these steps of Induction in the -Table, the inductive proposition is a <em>Theory</em> with -regard to the Facts which it includes, while it is to be -looked upon as a <em>Fact</em> with respect to the higher -generalizations in which it is included. In any other -sense, as was formerly shown, the opposition of <em>Fact</em> -and <em>Theory</em> is untenable, and leads to endless perplexity -and debate. Is it a Fact or a Theory that the -planet Mars revolves in an Ellipse about the Sun? -To Kepler, employed in endeavouring to combine the -separate observations by the Conception of an Ellipse, -it is a Theory; to Newton, engaged in inferring the -law of force from a knowledge of the elliptical motion, -it is a Fact. There are, as we have already seen, no -special attributes of Theory and Fact which distinguish -them from one another. Facts are phenomena apprehended -by the aid of conceptions and mental acts, as -Theories also are. We commonly call our observations -<i>Facts</i>, when we apply, without effort or consciousness, -conceptions perfectly familiar to us: while we speak of -Theories, when we have previously contemplated the -Facts and the connecting Conception separately, and -have made the connexion by a conscious mental act. -The real difference is a difference of relation; as the -same proposition in a demonstration is the <em>premiss</em> of -one syllogism and the <em>conclusion</em> in another;—as the -same person is a father and a son. Propositions are -Facts and Theories, according as they stand above or -below the Inductive Brackets of our Tables.</p> -<p id="b2c6a21">21. To obviate mistakes I may remark that the -terms <i>higher</i> and <i>lower</i>, when used of generalizations, -are unavoidably represented by their opposites in our -Inductive Tables. The highest generalization is that <span class="pagenum" id="page117">117</span> -which includes all others; and this stands the lowest -on our page, because, reading downwards, that is the -place which we last reach.</p> -<p class="end">There is a distinction of the knowledge acquired by -Scientific Induction into two kinds, which is so important -that we shall consider it in the succeeding -chapter.</p> -<div class="chapter"> -<p><span class="pagenum" id="page118"></span></p> -<h3 class="nobreak">CHAPTER VII.<br /><br /> -<span class="sc">Of Laws of Phenomena and of Causes.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XXIV.</p> -<p><i>Inductive truths are of two kinds</i>, Laws of Phenomena, -<i>and</i> Theories of Causes. <i>It is necessary to begin in every -science with the Laws of Phenomena; but it is impossible that -we should be satisfied to stop short of a Theory of Causes. In -Physical Astronomy, Physical Optics, Geology, and other -sciences, we have instances showing that we can make a great -advance in inquiries after true Theories of Causes.</i></p> -<p class="noind" id="b2c7a1"> -<span class="dropcap"><span class="dsmall">1.</span> I</span>N -the first attempts at acquiring an exact and -connected knowledge of the appearances and operations -which nature presents, men went no further -than to learn <em>what</em> takes place, not <em>why</em> it occurs. -They discovered an Order which the phenomena follow, -Rules which they obey; but they did not come in -sight of the Powers by which these rules are determined, -the Causes of which this order is the effect. -Thus, for example, they found that many of the celestial -motions took place as if the sun and stars were -carried round by the revolutions of certain celestial -spheres; but what causes kept these spheres in constant -motion, they were never able to explain. In -like manner in modern times, Kepler discovered that -the planets describe ellipses, before Newton explained -why they select this particular curve, and describe it -in a particular manner. The laws of reflection, refraction, -dispersion, and other properties of light have -long been known; the causes of these laws are at -present under discussion. And the same might be <span class="pagenum" id="page119">119</span> -said of many other sciences. The discovery of <i>the -Laws of Phenomena</i> is, in all cases, the first step in -exact knowledge; these Laws may often for a long -period constitute the whole of our science; and it is -always a matter requiring great talents and great efforts, -to advance to a knowledge of the <i>Causes</i> of the -phenomena.</p> -<p>Hence the larger part of our knowledge of nature, -at least of the certain portion of it, consists of the -knowledge of the Laws of Phenomena. In Astronomy -indeed, besides knowing the rules which guide the appearances, -and resolving them into the real motions -from which they arise, we can refer these motions to -the forces which produce them. In Optics, we have -become acquainted with a vast number of laws by -which varied and beautiful phenomena are governed; -and perhaps we may assume, since the evidence of the -Undulatory Theory has been so fully developed, that -we know also the Causes of the Phenomena. But in -a large class of sciences, while we have learnt many -Laws of Phenomena, the causes by which these are -produced are still unknown or disputed. Are we to -ascribe to the operation of a fluid or fluids, and if so, -in what manner, the facts of heat, magnetism, electricity, -galvanism? What are the forces by which the -elements of chemical compounds are held together? -What are the forces, of a higher order, as we cannot -help believing, by which the course of vital action in -organized bodies is kept up? In these and other cases, -we have extensive departments of science; but we are -as yet unable to trace the effects to their causes; and -our science, so far as it is positive and certain, consists -entirely of the laws of phenomena.</p> -<p id="b2c7a2">2. In those cases in which we have a division of -the science which teaches us the doctrine of the causes, -as well as one which states the rules which the effects -follow, I have, in the <i>History</i>, distinguished the two -portions of the science by certain terms. I have thus -spoken of <i>Formal</i> Astronomy and <i>Physical</i> Astronomy. -The latter phrase has long been commonly employed to -describe that department of Astronomy which deals with <span class="pagenum" id="page120">120</span> -those forces by which the heavenly bodies are guided in -their motions; the former adjective appears well suited -to describe a collection of rules depending on those ideas -of space, time, position, number, which are, as we have -already said, the <i>forms</i> of our apprehension of phenomena. -The laws of phenomena may be considered as -<i>formulæ</i>, expressing results in terms of those ideas. -In like manner, I have spoken of Formal Optics and -Physical Optics; the latter division including all -speculations concerning the machinery by which the -effects are produced. Formal Acoustics and Physical -Acoustics may be distinguished in like manner, although -these two portions of science have been a good -deal mixed together by most of those who have treated -of them. Formal Thermotics, the knowledge of the -laws of the phenomena of heat, ought in like manner -to lead to Physical Thermotics, or the Theory of Heat -with reference to the cause by which its effects are -produced;—a branch of science which as yet can hardly -be said to exist.</p> -<p id="b2c7a3">3. What <em>kinds of cause</em> are we to admit in science? -This is an important, and by no means an easy question. -In order to answer it, we must consider in what -manner our progress in the knowledge of causes has -hitherto been made. By far the most conspicuous instance -of success in such researches, is the discovery -of the causes of the motions of the heavenly bodies. -In this case, after the formal laws of the motions,—their -conditions as to space and time,—had become -known, men were enabled to go a step further; to reduce -them to the familiar and general cause of motion—mechanical -force; and to determine the laws which -this force follows. That this was a step in addition to -the knowledge previously possessed, and that it was a -real and peculiar truth, will not be contested. And a -step in any other subject which should be analogous to -this in astronomy;—a discovery of causes and forces -as certain and clear as the discovery of universal -gravitation;—would undoubtedly be a vast advance upon -a body of science consisting only of the laws of phenomena. <span class="pagenum" id="page121">121</span></p> -<p id="b2c7a4">4. But although physical astronomy may well be -taken as a standard in estimating the value and magnitude -of the advance from the knowledge of phenomena to the -knowledge of causes; the peculiar features -of the transition from formal to physical science in -that subject must not be allowed to limit too narrowly -our views of the nature of this transition in other -cases. We are not, for example, to consider that the -step which leads us to the knowledge of causes in any -province of nature must necessarily consist in the -discovery of centers of forces, and collections of -such centers, by which the effects are produced. The discovery -of the causes of phenomena may imply the detection -of a fluid by whose undulations, or other operations, -the results are occasioned. The phenomena of acoustics -are, we know, produced in this manner by the air; -and in the cases of light, heat, magnetism, and others, -even if we reject all the theories of such fluids which -have hitherto been proposed, we still cannot deny that -such theories are intelligible and possible, as the -discussions concerning them have shown. Nor can it be -doubted that if the assumption of such a fluid, in any -case, were as well evidenced as the doctrine of universal -gravitation is, it must be considered as a highly -valuable theory.</p> -<p id="b2c7a5">5. But again; not only must we, in aiming at the -formation of a Causal Section in each Science of Phenomena, -consider Fluids and their various modes of -operation admissible, as well as centers of mechanical -force; but we must be prepared, if it be necessary, to -consider the forces, or powers to which we refer the -phenomena, under still more general aspects, and invested -with characters different from mere mechanical -force. For example; the forces by which the chemical -elements of bodies are bound together, and from which -arise, both their sensible texture, their crystalline form, -and their chemical composition, are certainly forces of -a very different nature from the mere attraction of -matter according to its mass. The powers of assimilation -and reproduction in plants and animals are obviously -still more removed from mere mechanism; yet <span class="pagenum" id="page122">122</span> -these powers are not on that account less real, nor a -less fit and worthy subject of scientific inquiry.</p> -<p id="b2c7a6">6. In fact, these forces—mechanical, chemical and -vital,—as we advance from one to the other, each bring -into our consideration new characters; and what these -characters are, has appeared in the historical survey -which we made of the Fundamental Ideas of the various -sciences. It was then shown that the forces by which -chemical effects are produced necessarily involve the -Idea of Polarity,—they are polar forces; the particles -tend together in virtue of opposite properties which in -the combination neutralize each other. Hence, in attempting -to advance to a theory of Causes in chemistry, -our task is by no means to invent laws of <i>mechanical</i> -force, and collections of forces, by which the effects -may be produced. We know beforehand that no such -attempt can succeed. Our aim must be to conceive -such new kinds of force, including Polarity among -their characters, as may best render the results intelligible.</p> -<p id="b2c7a7">7. Thus in advancing to a Science of Cause in any -subject, the labour and the struggle is, not to analyse -the phenomena according to any preconceived and -already familiar ideas, but to form distinctly new -conceptions, such as do really carry us to a more intimate -view of the processes of nature. Thus in the case of -astronomy, the obstacle which deferred the discovery -of the true causes from the time of Kepler to that of -Newton, was the difficulty of taking hold of mechanical -conceptions and axioms with sufficient clearness and -steadiness; which, during the whole of that interval, -mathematicians were learning to do. In the question -of causation which now lies most immediately in the -path of science, that of the causes of electrical and -chemical phenomena, the business of rightly fixing and -limiting the conception of polarity, is the proper object -of the efforts of discoverers. Accordingly a large portion -of Mr Faraday’s recent -labours<a id="fnanchor23-2" href="#note23-2"><span class="fnanchor">23</span></a> -is directed, not to <span class="pagenum" id="page123">123</span> -the attempt at discovering new laws of phenomena, but -to the task of throwing light upon the conception of -polarity, and of showing how it must be understood, so -that it shall include electrical induction and other phenomena, -which have commonly been ascribed to forces -acting mechanically at a distance. He is by no means -content, nor would it answer the ends of science that -he should be, with stating the results of his experiments; -he is constantly, in every page, pointing out -the interpretation of his experiments, and showing how -the conception of Polar Forces enters into this interpretation. -‘I shall,’ he says<a id="fnanchor24-2" href="#note24-2"><span class="fnanchor">24</span></a>, -‘use every opportunity -which presents itself of returning to that strong test of -truth, experiment; but,’ he adds, ‘I shall necessarily -have occasion to speak theoretically, and even hypothetically.’ -His hypothesis that electrical inductive -action always takes place by means of a continuous line -of polarized particles, and not by attraction and repulsion -at a distance, if established, cannot fail to be a -great step on our way towards a knowledge of causes, -as well as phenomena, in the subjects under his consideration.</p> -<div class="footnote"><span class="label"> -<a id="note23-2" href="#fnanchor23-2">23</a></span> Eleventh, Twelfth, -and Thirteenth Series of Researches, <i>Phil. Trans.</i> 1837 and 8. -</div> -<div class="footnote"><span class="label"> -<a id="note24-2" href="#fnanchor24-2">24</a></span> Art. 1318. -</div> -<p id="b2c7a8">8. The process of obtaining new conceptions is, to -most minds, far more unwelcome than any labour in -employing old ideas. The effort is indeed painful and -oppressive; it is feeling in the dark for an object which -we cannot find. Hence it is not surprising that we -should far more willingly proceed to seek for new causes -by applying conceptions borrowed from old ones. Men -were familiar with solid frames, and with whirlpools of -fluid, when they had not learnt to form any clear conception -of attraction at a distance. Hence they at -first imagined the heavenly motions to be caused by -Crystalline Spheres, and by Vortices. At length they -were taught to conceive Central Forces, and then they -reduced the solar system to these. But having done -this, they fancied that all the rest of the machinery of -nature must be central forces. We find Newton <span class="pagenum" id="page124">124</span> -expressing this conviction<a id="fnanchor25-2" href="#note25-2"><span class="fnanchor">25</span></a>, -and the mathematicians of -the last century acted upon it very extensively. We -may especially remark Laplace’s labours in this field. -Having explained, by such forces, the phenomena of -capillary attraction, he attempted to apply the same -kind of explanation to the reflection, refraction, and -double refraction of light;—to the constitution of -gases;—to the operation of heat. It was soon seen that -the explanation of refraction was arbitrary, and that -of double refraction illusory; while polarization entirely -eluded the grasp of this machinery. Centers of force -would no longer represent the modes of causation -which belonged to the phenomena. Polarization required -some other contrivance, such as the undulatory -theory supplied. No theory of light can be of any -avail in which the fundamental idea of Polarity is not -clearly exhibited.</p> -<div class="footnote"><span class="label"><a id="note25-2" href="#fnanchor25-2">25</a></span> -Multa me movent, &c.,—Pref. to the <i>Principia</i>, already quoted in the -<i>History</i>. -</div> -<p id="b2c7a9">9. The sciences of magnetism and electricity have -given rise to theories in which this relation of polarity -is exhibited by means of two opposite -fluids<a id="fnanchor26-2" href="#note26-2"><span class="fnanchor">26</span></a>;—a -positive and a negative fluid, or a vitreous and a resinous, -for electricity, and a boreal and an austral fluid -for magnetism. The hypothesis of such fluids gives -results agreeing in a remarkable manner with the -facts and their measures, as Coulomb and others have -shown. It may be asked how far we may, in such a -case, suppose that we have discovered the true cause of -the phenomena, and whether it is sufficiently proved -that these fluids really exist. The right answer seems -to be, that the hypothesis certainly represents the -truth so far as regards the polar relation of the two -energies, and the laws of the attractive and repulsive -forces of the particles in which these energies reside; -but that we are not entitled to assume that the vehicles -of these energies possess other attributes of material -fluids, or that the forces thus ascribed to the -particles are the primary elementary forces from which <span class="pagenum" id="page125">125</span> -the action originates. We are the more bound to -place this cautious limit to our acceptance of the Coulombian -theory, since in electricity Faraday has in -vain endeavoured to bring into view one of the polar -fluids without the other: whereas such a result ought -to be possible if there were two separable fluids. The -impossibility of this separate exhibition of one fluid -appears to show that the fluids are <em>real</em> only so far as -they are <em>polar</em>. And Faraday’s view above mentioned, -according to which the attractions at a distance are -resolved into the action of lines of polarized particles -of air, appears still further to show that the conceptions -hitherto entertained of electrical forces, according -to the Coulombian theory, do not penetrate to the real -and intimate nature of the causation belonging to this -case.</p> -<div class="footnote"><span class="label"><a id="note26-2" href="#fnanchor26-2">26</a></span> -<i>Hist. Ind. Sc.</i> b. xi. c. ii. -</div> -<p id="b2c7a10">10. Since it is thus difficult to know when we have -seized the true cause of the phenomena in any department -of science, it may appear to some persons that -physical inquirers are imprudent and unphilosophical -in undertaking this Research of Causes; and that it -would be safer and wiser to confine ourselves to the -investigation of the laws of phenomena, in which field -the knowledge which we obtain is definite and certain. -Hence there have not been wanting those who have -laid it down as a maxim that ‘science must study only -the laws of phenomena, and never the mode of -production<a id="fnanchor27-2" href="#note27-2"><span class="fnanchor">27</span></a>.’ -But it is easy to see that such a maxim would -confine the breadth and depth of scientific inquiries to -a most scanty and miserable limit. Indeed, such a -rule would defeat its own object; for the laws of phenomena, -in many cases, cannot be even expressed or -understood without some hypothesis respecting their -mode of production. How could the phenomena of -polarization have been conceived or reasoned upon, -except by imagining a polar arrangement of particles, -or transverse vibrations, or some equivalent hypothesis? -The doctrines of fits of easy transmission, the doctrine -of moveable polarization, and the like, even when <span class="pagenum" id="page126">126</span> -erroneous as representing the whole of the phenomena, -were still useful in combining some of them into laws; -and without some such hypotheses the facts could not -have been followed out. The doctrine of a fluid caloric -may be false; but without imagining such a fluid, how -could the movement of heat from one part of a body to -another be conceived? It may be replied that Fourier, -Laplace, Poisson, who have principally cultivated the -Theory of Heat, have not conceived it as a fluid, but -have referred conduction to the radiation of the molecules -of bodies, which they suppose to be separate points. -But this molecular constitution of bodies is itself an -assumption of the mode in which the phenomena are -produced; and the radiation of heat suggests inquiries -concerning a fluid emanation, no less than its conduction -does. In like manner, the attempts to connect -the laws of phenomena of heat and of gases, have led -to hypotheses respecting the constitution of gases, and -the combination of their particles with those of caloric, -which hypotheses may be false, but are probably the -best means of discovering the truth.</p> -<div class="footnote"><span class="label"><a id="note27-2" href="#fnanchor27-2">27</a> -</span> Comte, <i>Philosophie Positive</i>. -</div> -<p>To debar science from inquiries like these, on the -ground that it is her business to inquire into facts, -and not to speculate about causes, is a curious example -of that barren caution which hopes for truth without -daring to venture upon the quest of it. This temper -would have stopped with Kepler’s discoveries, and -would have refused to go on with Newton to inquire -into the mode in which the phenomena are produced. -It would have stopped with Newton’s optical facts, -and would have refused to go on with him and his -successors to inquire into the mode in which these -phenomena are produced. And, as we have abundantly -shown, it would, on that very account, have failed in -seeing what the phenomena really are.</p> -<p>In many subjects the attempt to study the laws of -phenomena, independently of any speculations respecting -the causes which have produced them, is neither -possible for human intelligence nor for human temper. -Men cannot contemplate the phenomena without -clothing them in terms of some hypothesis, and will <span class="pagenum" id="page127">127</span> -not be schooled to suppress the questionings which at -every moment rise up within them concerning the -causes of the phenomena. Who can attend to the -appearances which come under the notice of the geologist;—strata -regularly bedded, full of the remains of -animals such as now live in the depths of the ocean, -raised to the tops of mountains, broken, contorted, -mixed with rocks such as still flow from the mouths of -volcanos,—who can see phenomena like these, and -imagine that he best promotes the progress of our -knowledge of the earth’s history, by noting down the -facts, and abstaining from all inquiry whether these -are really proof of past states of the earth and of -subterraneous forces, or merely an accidental imitation of -the effects of such causes? In this and similar cases, -to proscribe the inquiry into causes would be to annihilate the science.</p> -<p>Finally, this caution does not even gain its own -single end, the escape from hypotheses. For, as we -have said, those who will not seek for new and appropriate -causes of newly-studied phenomena, are almost -inevitably led to ascribe the facts to modifications of -causes already familiar. They may declare that they -will not hear of such causes as vital powers, elective -affinities, electric, or calorific, or luminiferous ethers or -fluids; but they will not the less on that account -assume hypotheses equally unauthorized;—for instance—universal -mechanical forces; a molecular constitution of bodies; -solid, hard, inert matter;—and will -apply these hypotheses in a manner which is arbitrary -in itself as well as quite insufficient for its purpose.</p> -<p id="b2c7a11">11. It appears, then, to be required, both by the -analogy of the most successful efforts of science in past -times and by the irrepressible speculative powers of -the human mind, that we should attempt to discover -both the <em>laws of phenomena</em>, and their <em>causes</em>. In every -department of science, when prosecuted far enough, -these two great steps of investigation must succeed -each other. The laws of phenomena must be known -before we can speculate concerning causes; the causes -must be inquired into when the phenomena have been <span class="pagenum" id="page128">128</span> -reduced to rule. In both these speculations the suppositions -and conceptions which occur must be constantly tested by -reference to observation and experiment. In both we must, -as far as possible, devise -hypotheses which, when we thus test them, display -those characters of truth of which we have already -spoken;—an agreement with facts such as will stand -the most patient and rigid inquiry; a provision for -predicting truly the results of untried cases; a consilience -of inductions from various classes of facts; and -a progressive tendency of the scheme to simplicity and -unity.</p> -<p class="end">We shall attempt hereafter to give several rules of a -more precise and detailed kind for the discovery of the -causes, and still more, of the laws of phenomena. But -it will be useful in the first place to point out the -Classification of the Sciences which results from the -principles already established in this -<span class="correction" title="emended from word">work</span>. And for -this purpose we must previously decide the question, -whether the practical Arts, as Medicine and Engineering, -must be included in our list of Sciences.</p> -<div class="chapter"> -<p><span class="pagenum" id="page129"></span></p> -<h3 class="nobreak">CHAPTER VIII.<br /><br /> -<span class="sc">Of Art and Science.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XXV.</p> -<p><i>Art and Science differ. The object of Science is Knowledge; -the objects of Art, are Works. In Art, truth is a -means to an end; in Science, it is the only end. Hence the -Practical Arts are not to be classed among the Sciences.</i></p> -<p class="center"><span class="sc">Aphorism</span> XXVI.</p> -<p><i>Practical Knowledge, such as Art implies, is not Knowledge -such as Science includes. Brute animals have a practical -knowledge of relations of space and force; but they have -no knowledge of Geometry or Mechanics.</i></p> -<p class="noind" id="b2c8a1"> -<span class="dropcap"><span class="dsmall">1.</span> T</span>HE -distinction of Arts and Sciences very materially -affects all classifications of the departments -of Human Knowledge. It is often maintained, expressly or -tacitly, that the Arts are a part of our -knowledge, in the same sense in which the Sciences -are so; and that Art is the application of Science to the -purposes of practical life. It will be found that these -views require some correction, when we understand -<i>Science</i> in the exact sense in which we have throughout -endeavoured to contemplate it, and in which alone -our examination of its nature can instruct us in the -true foundations of our knowledge.</p> -<p>When we cast our eyes upon the early stages of -the histories of nations, we cannot fail to be struck -with the consideration, that in many countries the -Arts of life already appear, at least in some rude form -or other, when, as yet, nothing of science exists. A <span class="pagenum" id="page130">130</span> -practical knowledge of Astronomy, such as enables them -to reckon months and years, is found among all nations -except the mere savages. A practical knowledge of -Mechanics must have existed in those nations which -have left us the gigantic monuments of early architecture. -The pyramids and temples of Egypt and Nubia, -the Cyclopean walls of Italy and Greece, the temples -of Magna Græcia and Sicily, the obelisks and edifices -of India, the cromlechs and Druidical circles of countries -formerly Celtic,—must have demanded no small -practical mechanical skill and power. Yet those -modes of reckoning time must have preceded the rise -of speculative Astronomy; these structures must have -been erected before the theory of Mechanics was -known. To suppose, as some have done, a great body -of science, now lost, to have existed in the remote -ages to which these remains belong, is not only quite -gratuitous, and contrary to all analogy, but is a -supposition which cannot be extended so far as to explain -all such cases. For it is impossible to imagine that -<em>every</em> art has been preceded by the science which -renders a reason for its processes. Certainly men formed -wine from the grape, before they possessed a Science of -Fermentation; the first instructor of every artificer in -brass and iron can hardly be supposed to have taught -the Chemistry of metals as a Science; the inventor -of the square and the compasses had probably no more -knowledge of demonstrated Geometry than have the -artisans who now use those implements; and finally, -the use of speech, the employment of the inflections -and combinations of words, must needs be assumed as -having been prior to any general view of the nature -and analogy of Language. Even at this moment, the -greater part of the arts which exist in the world are -not accompanied by the sciences on which they theoretically -depend. Who shall state to us the general -chemical truths to which the manufactures of glass, -and porcelain, and iron, and brass, owe their existence? -Do not almost all artisans practise many successful -artifices long before science explains the ground of the -process? Do not arts at this day exist, in a high state <span class="pagenum" id="page131">131</span> -of perfection, in countries in which there is no science, -as China and India? These countries and many others -have no theories of mechanics, of optics, of chemistry, -of physiology; yet they construct and use mechanical -and optical instruments, make chemical combinations, -take advantage of physiological laws. It is too evident -to need further illustration that Art may exist without -Science;—that the former has usually been anterior to -the latter, and even now commonly advances independently, -leaving science to follow as it can.</p> -<p id="b2c8a2">2. We here mean by <i>Science</i>, that exact, general, -speculative knowledge, of which we have, throughout -this work, been endeavouring to exhibit the nature -and rules. Between such Science and the <i>practical -Arts</i> of life, the points of difference are sufficiently -manifest. The object of Science is <em>Knowledge</em>; the -object of Art are <em>Works</em>. The latter is satisfied with -producing its material results; to the former, the -operations of matter, whether natural or artificial, are -interesting only so far as they can be embraced by -intelligible principles. The End of Art is the Beginning -of Science; for when it is seen <em>what</em> is done, then -comes the question <em>why</em> it is done. Art may have -fixed general rules, stated in words; but she has -these merely as means to an end: to Science, the propositions -which she obtains are each, in itself, a sufficient end of -the effort by which it is acquired. When -Art has brought forth her product, her task is finished; -Science is constantly led by one step of her path to -another: each proposition which she obtains impels -her to go onwards to other propositions more general, -more profound, more simple. Art puts elements together, -without caring to know what they are, or why -they coalesce. Science analyses the compound, and at -every such step strives not only to perform, but to -understand the analysis. Art advances in proportion -as she becomes able to bring forth products more -multiplied, more complex, more various; but Science, -straining her eyes to penetrate more and more deeply -into the nature of things, reckons her success in -proportion as she sees, in all the phenomena, however <span class="pagenum" id="page132">132</span> -multiplied; complex, and varied, the results of one or -two simple and general laws.</p> -<p id="b2c8a3">3. There are many acts which man, as well as -animals, performs by the guidance of nature, without -seeing or seeking the reason why he does so; as, the -acts by which he balances himself in standing or -moving, and those by which he judges of the form and -position of the objects around him. These actions -have their reason in the principles of geometry and -mechanics; but of such reasons he who thus acts is -unaware: he works blindly, under the impulse of an -unknown principle which we call <i>Instinct</i>. When -man’s speculative nature seeks and finds the reasons -why he should act thus or thus;—why he should -stretch out his arm to prevent his falling, or assign a -certain position to an object in consequence of the -angles under which it is seen;—he may perform the -same actions as before, but they are then done by the -aid of a different faculty, which, for the sake of -distinction, we may call <i>Insight</i>. Instinct is a purely -active principle; it is seen in deeds alone; it has no -power of looking inwards; it asks no questions; it has -no tendency to discover reasons or rules; it is the -opposite of Insight.</p> -<p id="b2c8a4">4. Art is not identical with Instinct: on the contrary, -there are broad differences. Instinct is stationary; -Art is progressive. Instinct is mute; it acts, -but gives no rules for acting: Art can speak; she can -lay down rules. But though Art is thus separate -from Instinct, she is not essentially combined with -Insight. She can see what to do, but she needs not -to see why it is done. She may lay down Rules, but it -is not her business to give Reasons. When man makes -<em>that</em> his employment, he enters upon the domain of -Science. Art takes the phenomena and laws of nature -as she finds them: that they are multiplied, complex, -capricious, incoherent, disturbs her not. She is content -that the rules of nature’s operations should be -perfectly arbitrary and unintelligible, provided they -are constant, so that she can depend upon their effects. -But Science is impatient of all appearance of caprice, <span class="pagenum" id="page133">133</span> -inconsistency, irregularity, in nature. She will not -believe in the existence of such characters. She resolves -one apparent anomaly after another; her task is -not ended till every thing is so plain and simple, that -she is tempted to believe that she sees that it could by -no possibility have been otherwise than it is.</p> -<p id="b2c8a5">5. It may be said that, after all, Art does really -involve the knowledge which Science delivers;—that -the artisan who raises large weights, practically <em>knows</em> -the properties of the mechanical powers;—that he -who manufactures chemical compounds is virtually -acquainted with the laws of chemical combination. -To this we reply, that it might on the same grounds -be asserted, that he who acts upon the principle that -two sides of a triangle are greater than the third is -really acquainted with geometry; and that he who -balances himself on one foot knows the properties of -the center of gravity. But this is an acquaintance -with geometry and mechanics which even brute animals -possess. It is evident that it is not of such -knowledge as this that we have here to treat. It is -plain that this mode of possessing principles is -altogether different from that contemplation of them on -which science is founded. We neglect the most essential -and manifest differences, if we confound our unconscious -assumptions with our demonstrative reasonings.</p> -<p id="b2c8a6">6. The real state of the case is, that the principles -which Art <em>involves</em>, Science alone <em>evolves</em>. The truths -on which the success of Art depends, lurk in the -artist’s mind in an undeveloped state; guiding his -hand, stimulating his invention, balancing his judgment; -but not appearing in the form of enunciated -Propositions. Principles are not to him direct objects -of meditation: they are secret Powers of Nature, to -which the forms which tenant the world owe their -constancy, their movements, their changes, their luxuriant -and varied growth, but which he can nowhere -directly contemplate. That the creative and directive -Principles which have their lodgment in the artist’s -mind, when <em>unfolded</em> by our speculative powers into <span class="pagenum" id="page134">134</span> -systematic shape, become Science, is true; but it is -precisely this process of <em>development</em> which gives to -them their character of Science. In practical Art, -principles are unseen guides, leading us by invisible -strings through paths where the end alone is looked -at: it is for Science to direct and purge our vision so -that these airy ties, these principles and laws, -generalizations and theories, become distinct objects of vision. -Many may feel the intellectual monitor, but it is only -to her favourite heroes that the Goddess of Wisdom -visibly reveals herself.</p> -<p id="b2c8a7">7. Thus Art, in its earlier stages at least, is widely -different from Science, is independent of it, and is -anterior to it. At a later period, no doubt, Art may borrow -aid from Science; and the discoveries of the philosopher -may be of great value to the manufacturer and -the artist. But even then, this application forms no -essential part of the science: the interest which belongs -to it is not an intellectual interest. The augmentation -of human power and convenience may impel -or reward the physical philosopher; but the processes -by which man’s repasts are rendered more delicious, -his journeys more rapid, his weapons more terrible, -are not, therefore, Science. They may involve principles -which are of the highest interest to science; but -as the advantage is not practically more precious because -it results from a beautiful theory, so the theoretical -principle has no more conspicuous place in science -because it leads to convenient practical consequences. -The nature of Science is purely intellectual; Knowledge -alone,—exact general Truth,—is her object; and we -cannot mix with such material, as matters of the same -kind, the merely Empirical maxims of Art, without -introducing endless confusion into the subject, and -making it impossible to attain any solid footing in our -philosophy.</p> -<p class="end" id="b2c8a8">8. I shall therefore not place, in our Classification -of the Sciences, the Arts, as has generally been done; -nor shall I notice the applications of sciences to art, -as forming any separate portion of each science. The -sciences, considered as bodies of general speculative <span class="pagenum" id="page135">135</span> -truths, are what we are here concerned with; and -applications of such truths, whether useful or useless, -are important to us only as illustrations and examples. -Whatever place in human knowledge the Practical -Arts may hold, they are not Sciences. And it is only -by this rigorous separation of the Practical from the -Theoretical, that we can arrive at any solid conclusions -respecting the nature of Truth, and the mode of arriving -at it, such as it is our object to attain.</p> -<div class="chapter"> -<p><span class="pagenum" id="page136"></span></p> -<h3 class="nobreak">CHAPTER IX.<br /><br /> -<span class="sc">Of the Classification of Sciences.</span></h3> -</div> -<hr class="two" /> -<p class="noind" id="b2c9a1"> -<span class="dropcap"><span class="dsmall">1.</span> T</span>HE -Classification of Sciences has its chief use in -pointing out to us the extent of our powers of -arriving at truth, and the analogies which may obtain -between those certain and lucid portions of knowledge -with which we are here concerned, and those other -portions, of a very different interest and evidence, -which we here purposely abstain to touch upon. The -classification of human knowledge will, therefore, have -a more peculiar importance when we can include in it -the moral, political, and metaphysical, as well as the -physical portions of our knowledge. But such a survey -does not belong to our present undertaking: and -a general view of the connexion and order of the -branches of sciences which our review has hitherto included, -will even now possess some interest; and may -serve hereafter as an introduction to a more complete -scheme of the general body of human knowledge.</p> -<p id="b2c9a2">2. In this, as in any other case, a sound classification -must be the result, not of any assumed principles -imperatively applied to the subject, but of an examination -of the objects to be classified;—of an analysis of -them into the principles in which they agree and differ. -The Classification of Sciences must result from the -consideration of their nature and contents. Accordingly, -that review of the Sciences in which the <i>History</i> of -the Sciences engaged us, led to a Classification, of which -the main features are indicated in that work. The -Classification thus obtained, depends neither upon the -faculties of the mind to which the separate parts of -our knowledge owe their origin, nor upon the objects -which each science contemplates; but upon a more <span class="pagenum" id="page137">137</span> -natural and fundamental element;—namely, the <em>Ideas</em> -which each science involves. The Ideas regulate and -connect the facts, and are the foundations of the reasoning, -in each science: and having in another work -more fully examined these <i>Ideas</i>, we are now prepared -to state here the classification to which they lead. If -we have rightly traced each science to the Conceptions -which are really fundamental <em>with regard to it</em>, and -which give rise to the first principles on which it -depends, it is not necessary for our purpose that we -should decide whether these Conceptions are absolutely -ultimate principles of thought, or whether, on the contrary, -they can be further resolved into other Fundamental Ideas. -We need not now suppose it determined whether or not <i>Number</i> -is a mere modification -of the Idea of Time, and <i>Force</i> a mere modification of -the Idea of Cause: for however this may be, our Conception -of Number is the foundation of Arithmetic, -and our Conception of Force is the foundation of Mechanics. -It is to be observed also that in our classification, -each Science may involve, not only the Ideas -or Conceptions which are placed opposite to it in the -list, but also all which <em>precede</em> it. Thus Formal Astronomy -involves not only the Conception of Motion, but -also those which are the foundation of Arithmetic and -Geometry. In like manner. Physical Astronomy employs the -Sciences of Statics and Dynamics, and thus, -rests on their foundations; and they, in turn, depend -upon the Ideas of Space and of Time, as well as of -Cause.</p> -<p id="b2c9a3">3. We may further observe, that this arrangement -of Sciences according to the Fundamental Ideas which -they involve, points out the transition from those parts -of human knowledge which have been included in our -History and Philosophy, to other regions of speculation -into which we have not entered. We have repeatedly -found ourselves upon the borders of inquiries of a -psychological, or moral, or theological nature. Thus -the History of Physiology<a id="fnanchor28-2" href="#note28-2"><span class="fnanchor">28</span></a> -led us to the consideration <span class="pagenum" id="page138">138</span> -of Life, Sensation, and Volition; and at these Ideas we -stopped, that we might not transgress the boundaries of -our subject as then predetermined. It is plain that -the pursuit of such conceptions and their consequences, -would lead us to the sciences (if we are allowed to call -them sciences) which contemplate not only animal, but -human principles of action, to Anthropology, and Psychology. -In other ways, too, the Ideas which we hare -examined, although manifestly the foundations of sciences -such as we have here treated of also plainly -pointed to speculations of a different order; thus the -Idea of a Final Cause is an indispensable guide in -Biology, as we have seen; but the conception of Design -as directing the order of nature, once admitted, soon -carries us to higher contemplations. Again, the Class -of Palætiological Sciences which we were in the <i>History</i> -led to construct, although we there admitted only -one example of the Class, namely Geology, does in -reality include many vast lines of research; as the -history and causes of the division of plants and animals, -the history of languages, arts, and consequently -of civilization. Along with these researches, comes -the question how far these histories point backwards to -a natural or a supernatural origin; and the Idea of a -First Cause is thus brought under our consideration. -Finally, it is not difficult to see that as the Physical -Sciences have their peculiar governing Ideas, which -support and shape them, so the Moral and Political -Sciences also must similarly have their fundamental -and formative Ideas, the source of universal and certain -truths, each of their proper kind. But to follow -out the traces of this analogy, and to verify the -existence of those Fundamental Ideas in Morals and -Politics, is a task quite out of the sphere of the work -in which we are here engaged.</p> -<div class="footnote"><span class="label"><a id="note28-2" href="#fnanchor28-2">28</a> -</span> <i>Hist. Ind. Sc.</i> b. xvii. c. v. sect. 2. -</div> -<p id="b2c9a4">4. We may now place before the reader our Classification -of the Sciences. I have added to the list of -Sciences, a few not belonging to our present subject, -that the nature of the transition by which we are to -extend our philosophy into a wider and higher region -may be in some measure perceived. <span class="pagenum" id="page139">139</span></p> -<p>The Classification of the Sciences is given over leaf.</p> -<p>A few remarks upon it offer themselves.</p> -<p>The <i>Pure</i> Mathematical Sciences can hardly be called -<i>Inductive</i> Sciences. Their principles are not obtained -by Induction from Facts, but are necessarily assumed -in reasoning upon the subject matter which those -sciences involve.</p> -<p>The Astronomy of the Ancients aimed only at explaining -the motions of the heavenly bodies, as a <i>mechanism</i>. -Modern Astronomy, explains these motions on -the principles of Mechanics.</p> -<p>The term <i>Physics</i>, when confined to a peculiar -class of Sciences, is usually understood to exclude the -Mechanical Sciences on the one side, and Chemistry -on the other; and thus embraces the Secondary Mechanical -and Analytico-Mechanical Sciences. But the adjective -<i>Physical</i> applied to any science and opposed -to <i>Formal</i>, as in Astronomy and Optics, implies those -speculations in which we consider not only the Laws -of Phenomena but their Causes; and generally, as -in those cases, their Mechanical Causes.</p> -<p class="end">The term <i>Metaphysics</i> is applied to subjects in which -the Facts examined are emotions, thoughts and mental -conditions; subjects not included in our present survey. <span class="pagenum" id="page140">140</span></p> -<table> -<tr> -<th class="small">Fundamental Ideas or<br /> -Conceptions.</th><th class="small">Sciences.</th><th></th><th class="small">Classification.</th> -</tr> -<tr> -<td>Space</td><td>Geometry</td><td>⎫</td><td></td> -</tr> -<tr> -<td>Time</td><td></td><td>⎪</td><td>Pure Mathematical</td> -</tr> -<tr> -<td><i>Number</i></td><td>Arithmetic</td><td>⎬</td><td></td> -</tr> -<tr> -<td>Sign</td><td>Algebra</td><td>⎪</td><td> Sciences.</td> -</tr> -<tr> -<td>Limit</td><td>Differentials</td><td>⎭</td><td></td> -</tr> -<tr> -<td><i>Motion</i></td><td>Pure Mechanism</td><td>⎱</td><td>Pure Motional</td> -</tr> -<tr> -<td></td><td>Formal Astronomy</td><td>⎰</td><td>Sciences.</td> -</tr> -<tr> -<td colspan="4"></td> -</tr> -<tr> -<td>Cause</td><td colspan="3"></td> -</tr> -<tr> -<td><i>Force</i></td><td>Statics</td><td>⎫</td><td></td> -</tr> -<tr> -<td><i>Matter</i></td><td>Dynamics</td><td>⎪</td><td>Mechanical</td> -</tr> -<tr> -<td><i>Inertia</i></td><td> Hydrostatics</td><td>⎬</td><td></td> -</tr> -<tr> -<td><i>Fluid Pressure</i></td><td>Hydrodynamics</td><td>⎪</td><td>Sciences.</td> -</tr> -<tr> -<td></td><td>Physical Astronomy</td><td>⎭</td><td></td> -</tr> -<tr> -<td>Outness</td><td colspan="3"></td> -</tr> -<tr> -<td>Medium <i>of Sensation</i></td><td>Acoustics</td><td>⎫</td><td></td> -</tr> -<tr> -<td>Intensity <i>of Qualities</i></td><td>Formal Optics</td><td>⎪</td><td>Secondary</td> -</tr> -<tr> -<td><i>Scales of Qualities</i></td><td>Physical Optics</td><td>⎬</td><td>Mechanical</td> -</tr> -<tr> -<td></td><td>Thermotics</td><td>⎪</td><td>Sciences.</td> -</tr> -<tr> -<td></td><td>Atmology</td><td>⎭</td><td>(<i>Physics</i>.)</td> -</tr> -<tr> -<td>Polarity</td><td>Electricity</td><td>⎫</td><td>Analytico-Mecha-</td> -</tr> -<tr> -<td></td><td>Magnetism</td><td>⎬</td><td>nical Sciences.</td> -</tr> -<tr> -<td></td><td>Galvanism</td><td>⎭</td><td>(<i>Physics</i>.)</td> -</tr> -<tr> -<td>Element (<i>Composition</i>)</td><td colspan="3"></td> -</tr> -<tr> -<td><i>Chemical</i> Affinity</td><td colspan="3"></td> -</tr> -<tr> -<td>Substance (<i>Atoms</i>)</td><td>Chemistry</td><td></td><td>Analytical Science.</td> -</tr> -<tr> -<td>Symmetry</td><td>Crystallography</td><td>⎱</td><td>Analytico-Classifi-</td> -</tr> -<tr> -<td>Likeness</td><td>Systematic Mineralogy</td><td>⎰</td><td>catory Sciences.</td> -</tr> -<tr> -<td><i>Degrees of Likeness</i></td><td>Systematic Botany</td><td>⎫</td><td>Classificatory</td> -</tr> -<tr> -<td></td><td>Systematic Zoology</td><td>⎬</td><td></td> -</tr> -<tr> -<td><i>Natural</i> Affinity</td><td>Comparative Anatomy</td><td>⎭</td><td>Sciences.</td> -</tr> -<tr> -<td>(<i>Vital Powers</i>)</td><td colspan="3"></td> -</tr> -<tr> -<td>Assimilation</td><td colspan="3"></td> -</tr> -<tr> -<td>Irritability</td><td colspan="3"></td> -</tr> -<tr> -<td>(<i>Organization</i>)</td><td>Biology</td><td></td><td>Organical Sciences.</td> -</tr> -<tr> -<td>Final Cause</td><td colspan="3"></td> -</tr> -<tr> -<td>Instinct</td><td colspan="3"></td> -</tr> -<tr> -<td>Emotion</td><td>Psychology</td><td></td><td>(<i>Metaphysics</i>.)</td> -</tr> -<tr> -<td>Thought</td><td colspan="3"></td> -</tr> -<tr> -<td>Historical Causation</td><td>Geology</td><td>⎫</td><td></td> -</tr> -<tr> -<td></td><td>Distribution of</td><td>⎪</td><td>Palætiological</td> -</tr> -<tr> -<td></td><td> Plants and Animals</td><td>⎬</td><td></td> -</tr> -<tr> -<td></td><td>Glossology</td><td>⎪</td><td>Sciences.</td> -</tr> -<tr> -<td></td><td>Ethnography</td><td>⎭</td><td></td> -</tr> -<tr> -<td>First Cause</td><td>Natural Theology.</td><td colspan="2"></td> -</tr> -</table> -<div class="chapter"> -<p class="end"><span class="pagenum"><a id="page140a"></a></span></p> -<p class="h2">INDUCTIVE CHARTS</p> -</div> -<p class="end">[<i>Transcriber's note</i>: Two large charts were inserted into the book at this point. Here -they have been reproduced as tables. But since the originals were much wider than the book -pages they are somewhat unwieldy tables. They are omitted in ePub and Kindle files. -In the lines containing brackets, vertical lines -are used to indicate the range of columns thus brought together, where this is not obvious. -To move on to the text of Book III., click <a href="#page141">here</a>.]</p> -</div> -<p class="h2 end x-ebookmaker-drop">INDUCTIVE TABLE OF ASTRONOMY</p> -<table class="chart x-ebookmaker-drop"> - <colgroup span="15"></colgroup> - <tr> - <td class="t l"><span class="sc">The Earth</span> appears to be immovable.</td> - <td class="t l"><span class="sc">The Stars</span> keep their relative places in the vault of the sky, - and with the <span class="sc">Sun</span> and <span class="sc">Moon</span>, rise, move, and set.</td> - <td class="t l"><span class="sc">The Moon’s</span> bright part is of the shape of a ball enlightened by the Sun.</td> - <td class="t l"><span class="sc">The Moon’s Eclipses</span> occur when she is full.</td> - <td class="t l"><span class="sc">Eclipses of the Sun and Moon</span> often occur.</td> - <td class="t l"><span class="sc">The Moon</span> rises and sets at different times and places. Her course among the Stars varies.</td> - <td class="t l" colspan="2"><span class="sc">The Planets</span> are morning and evening Stars: are direct, stationary, and retrograde.</td> - <td class="t l" colspan="2"><span class="sc">The Sun</span> rises, culminates, - and sets in different times and places at different seasons: different <span class="sc">Constellations</span> are visible at night.</td> - <td class="t"></td> - <td class="t l"><span class="sc">The Tides</span> ebb and flow.</td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t l"></td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z" colspan="2">⏟</td> - <td class="c l z" colspan="2">⏟</td> - <td class="t"></td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t l"></td> - <td class="t"><span class="red">Chald<sup>ns</sup>.</span> <i>The Sphere of the Heavens appears to make a Diurnal Revolution.</i></td> - <td class="t"><span class="red">Greeks.</span> The Moon receives her light <i>from the Sun</i>.</td> - <td class="t"><span class="red">Greeks.</span> The Moon’s Eclipses are caused by the <i>Earth’s shadow.</i></td> - <td class="t"><span class="red">Chald<sup>ns</sup>.</span> The Moon’s Eclipses follow certain cycles.</td> - <td class="t"><span class="red">Greeks.</span> The Moon appears to revolve monthly in an <i>oblique orbit</i>, which has <i>Nodes</i> and an <i>Apogee</i>.</td> - <td class="t" colspan="2"><span class="red">Chaldeans.</span> The Planets have proper motions and certain <i>Cycles</i>.</td> - <td class="t" colspan="2"><span class="red">Pythagoras.</span> The Sun appears to move annually in an <i>Ecliptic</i> oblique to the diurnal motion.</td> - <td class="t l">The places of Stars are determined by their <span class="sc">Longitude</span> measured from the Equinox.</td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t l">The forms and dist<sup>s</sup> of known parts of the earth are such as fit a convex surface.</td> - <td class="t">The visible Pole of the Heavens rises or drops as we travel N. or S.</td> - <td class="t"></td> - <td class="t">The boundary of the Earth’s shadow is always circular.</td> - <td class="t l" colspan="2">By observations of Eclipses, the Moon’s Nodes and Apogee revolve, and her motion is unequal according to certain laws.</td> - <td class="t l" colspan="2">By observations of the Planets, their progressions, stations, and retrogradations.</td> - <td class="t l" colspan="2">By observations of the Sun, his motion is unequal according to certain laws.</td> - <td class="t l">By observations, Longitudes of Stars increase.</td> - <td class="t l">By observations, the Tides depend on the Moon and Sun.</td> - <td class="t"></td> - <td class="t" colspan="2"></td> - </tr> - <tr> - <td class="c l z" colspan="4">⏟</td> - <td class="c l z" colspan="2">⏟</td> - <td class="c l z" colspan="2">⏟</td> - <td class="c l z" colspan="2">⏟</td> - <td class="c l z">⏟</td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="c" colspan="4"><span class="red">Aristotle?</span> The Earth is a <i>Globe</i>, about which the Sphere of the Heavens performs a <i>Diurnal Revolution</i>.</td> - <td class="t" colspan="2"><span class="red">Hipparchus.</span> The Moon appears to move in an <i>Epicycle</i> carried by a Deferent: the <i>Velocity of Apogee</i> and <i>Nodes</i> determined.</td> - <td class="t" colspan="2"><span class="red">Eudoxus.</span> The Planets appear to move in Epicycles carried by <i>Deferents</i>.</td> - <td class="t" colspan="2"><span class="red">Hipparchus.</span> The Sun appears to move in an <i>Eccentric</i>, his <i>Apogee</i> being fixed.</td> - <td class="t"><span class="red">Hippar.</span> There is a <i>Precession of the Equinoxes</i>.</td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="t l" colspan="2">By additional observations, the Moon’s motion has another inequality. Evection.</td> - <td class="t l" colspan="2">By additional observations, the Planets’ motions in their Epicycles are unequal according to certain laws.</td> - <td class="t" colspan="2">By additional observations, the Sun’s Apogee moves. <span class="red">Albategnius.</span></td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="c l z" colspan="2">⏟</td> - <td class="c l z" colspan="2">⏟</td> - <td class="t" colspan="2"></td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="t" colspan="2"><span class="red">Ptolemy.</span> The Moon appears to move in an <i>Epicycle</i> carried by an <i>Eccentric</i>.</td> - <td class="t" colspan="2"><span class="red">Ptolemy.</span> The Planets appear to move in <i>Epicycles</i> carried by <i>Eccentrics</i>.</td> - <td class="t" colspan="2"></td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t l" colspan="3">* <i>By the nature of motion</i>, the apparent motion is the same whether the Heavens or the Earth have a diurnal revolution: the latter is <i>simpler</i>.</td> - <td class="t" colspan="3"></td> - <td class="t" colspan="2">* <i>By the nature of motion</i>, the apparent motion is the same if the Planets revolve about the Sun: this is <i>simpler</i>.</td> - <td class="t" colspan="2">* <i>By the nature of motion</i>, the apparent motion of the Sun is the same if the Earth revolve round the Sun: this is <i>simpler</i>.</td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td colspan="9" class="c l"><sup>—————</sup><sub>⏟</sub><sup>—————</sup></td> - <td class="t"></td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="c" colspan="8"><span class="red">* Copernicus.</span> The Earth and Planets revolve about the Sun as a center in Orbits nearly circular. The Earth - revolves about its axis inclined to the Ecliptic in a constant position, and the Moon revolves about the Earth. The <i>Heliocentric Theory</i> governs - subsequent speculations.</td> - <td class="t" colspan="2"></td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="c" colspan="2"><sup>——⏞——</sup></td> - <td class="h" colspan="9"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="t l" colspan="2">Retaining Moon’s Eccentric and Epicycle;<br />By additional observations, the Moon’s motion has other inequalities.</td> - <td class="t" colspan="3">Retaining but referring to the Sun as center the Planets’ Epicycles and Eccentrics and the annual Orbit;</td> - <td class="t">Retaining obs<sup>ns</sup>. Earth’s Aphelion revolves.</td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t" colspan="3"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="c" colspan="2"><sup>——</sup>⏟<sup>——</sup></td> - <td colspan="9"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="t l" colspan="2"><span class="red">Tycho.</span> Moon’s <i>Variation</i>; <i>Unequal Motion of Node</i>; <i>Change of Inclination</i>.</td> - <td class="t l">By calc<sup>ns</sup>. of the periodic times and distances.</td> - <td class="t l">By additional observations and calculations.</td> - <td class="t l">By additional observations and calculations.</td> - <td class="t l">Planets’ Aphelia revolve.<br />Jupiter and Saturn’s motions have an inequality dep<sup>g</sup>. on their mutual positions.</td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t l">The <span class="sc">Weight</span> of bodies dimin<sup>s</sup> in going towards the Equator.</td> - <td class="t l" colspan="2"><span class="sc">The Satellites</span> of Jupiter and Saturn revolve according to Kepler’s Laws.</td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="c l z" colspan="2">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="l"></td> - <td class="l"></td> - <td class="l"></td> - <td class="c z">⏟</td> - <td class="l"></td> - <td></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="t" colspan="2"><span class="red">Horrox. Halley.</span> The Moon moves in an <i>Ellipse</i> with variable <i>axis</i> and <i>eccentricity</i>.</td> - <td class="t"> <span class="red">Kepler.</span> Distances cubed are as times squared.</td> - <td class="t"> <span class="red">Kepler.</span> Areas as described by Planets are as times.</td> - <td class="t"> <span class="red">Kepler.</span> Curves described by Planets are as ellipses.</td> - <td class="l"></td> - <td class="t l"></td> - <td class="t l"></td> - <td class="t"><span class="red">Newton.</span> Earth is oblate.</td> - <td class="l" colspan="2"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="t l">* By Mechanics.</td> - <td class="t l">* By Mechanics.</td> - <td class="t l">* By Mechanics.</td> - <td class="t l">* By Mechanics.</td> - <td class="t l">* By Mechanics.</td> - <td class="t l">* By Mechanics.</td> - <td class="t l">* By Mechanics.</td> - <td class="t l">* By Mechanics.</td> - <td class="t l">* By Mechanics.</td> - <td class="c l" colspan="2">* By Mechanics.</td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="c z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z"></td> - <td class="c l z"></td> - <td class="c l z"></td> - <td class="c z" colspan="2">⏟</td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="t l"><span class="red">* Newton.</span> Moon is attracted by the Earth.<br /><br />Fall of heavy bodies. </td> - <td class="t l"><span class="red">* Newton.</span> Moon‘s inequalities produced by attraction of Sun.</td> - <td class="t l"><span class="red">* Newton. Wren. Hooke.</span> Sun’s force on different Planets is invers. as square of distance.</td> - <td class="t"><span class="red">* Newton.</span> Planets are attracted by the Sun.</td> - <td class="t"><span class="red">* Newton.</span> Sun attracts Planets invers. as square of distance.</td> - <td class="t l"><span class="red">* Newton.</span> These inequalities are produced by mutual attraction of the Planets.</td> - <td class="t l">Precession of Equinoxes is produced by attraction of Moon and Sun on oblate Earth.</td> - <td class="t l">Tides are produced by attraction of Moon and Sun on Sea.<br /><span class="red">Explanation imperfect.</span></td> - <td class="t l">Diminution of gravity and oblateness of Earth arise from attractions of parts.</td> - <td class="t" colspan="2"><span class="red">* Newton.</span> Jupiter and Saturn attract their Satellites inversely as the square of the distance, and the Sun attracts Planets and Satellites alike.</td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="c z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z" colspan="3">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="c z" colspan="2"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="t l"><span class="red">Newton.</span> Earth attracts Moon invers. as square of distance.</td> - <td class="t l"><span class="red">Newton.</span> Sun attracts Moon.</td> - <td class="t" colspan="3"><span class="red">Newton.</span> Sun attracts Planets inversely as the square of the distance.</td> - <td class="t"><span class="red">Newton.</span> Planets attract each other.</td> - <td class="t"><span class="red">* Newton.</span> Moon and Sun attract parts of the Earth.</td> - <td class="t"><span class="red">* Newton.</span> Moon and Sun attract the Ocean.</td> - <td class="t"><span class="red">* Newton.</span> Parts of the Earth attract each other.</td> - <td colspan="2"></td> - </tr> - <tr> - <td class="t" colspan="5"></td> - <td class="l"></td> - <td class="c z" colspan="8"><sup>————</sup>⏟<sup>————</sup></td> - <td class="r"></td> - </tr> - <tr> - <td class="t" colspan="5"></td> - <td class="c" colspan="9"><span class="red">Newton.</span> All parts of the Earth, Sun, Moon. and Planets attract <i>each other</i> with Forces inversely as the square of the distance.</td> - <td class="r"></td> - </tr> - <tr> - <td class="t" colspan="4"></td> - <td class="l"></td> - <td class="c z" colspan="9"><sup>————</sup>⏟<sup>————</sup></td> - <td class="r"></td> - </tr> - <tr> - <td class="t" colspan="5"></td> - <td class="c" colspan="10"><span class="red">Newton.</span> <span class="sc">THE THEORY OF UNIVERSAL GRAVITATION.</span><br />(All bodies attract each other with a Force of <i>Gravity</i> which is inversely as the squares of the distances.)</td> - </tr> - </table> -<div class="chapter x-ebookmaker-drop"> -<p><span class="pagenum"><a id="page140b"></a></span></p> -<p class="h2 x-ebookmaker-drop">INDUCTIVE TABLE OF OPTICS</p> -</div> -<p class="bigind x-ebookmaker-drop">First Facts. The common and obvious Phænomena of Light and Vision.</p> -<p class="vbigind x-ebookmaker-drop">By the <i>Idea of a Medium</i> Light and Vision take place by means of something intermediate.</p> -<p class="bigind x-ebookmaker-drop">First Law of Phænomena. The effects take place in straight lines denoted by the Term <i>Rays</i>.</p><br /> -<table class="chart x-ebookmaker-drop"> - <colgroup span="25"></colgroup> - <tr> - <td class="c">Facts of</td> - <td class="c">.........</td> - <td class="c">.........</td> - <td class="c">.........</td> - <td class="c">.........</td> - <td class="c">.........</td> - <td class="c">.........</td> - <td colspan="13"></td> - <td class="c">.........</td> - <td class="c">.........</td> - <td class="c">.........</td> - <td class="c">.........</td> - <td class="c">.........</td> - </tr> - <tr> - <td class="t l">Rays falling on water, specula, &c.</td> - <td class="t l">Rays passing through water, glass, &c. Measures.<br /><span class="red">Ptolemy.</span></td> - <td class="t l">Colours seen by prisms, in rainbow, &c.</td> - <td class="t">Colours in diff. transp. Substances. Optical instrum<sup>ts</sup>.</td> - <td class="t l">Two Images in Rhomb. of Calcspar.</td> - <td class="t">Two Images in other crystals.</td> - <td class="t l b">Two Rhombs of Calcspar make 4 images alternately appear and disappear.</td> - <td class="b"> <br /></td> - <td class="b"> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td class="t l">Fringes of shadows.<br /><span class="red">Grimaldi.<br />Hook.<br />Newton.</span></td> - <td class="t">Spectra of gratings. <br /><span class="red">Fraunhofer.</span></td> - <td class="t">Colours of striated surfaces. Coventry’s Micromet<sup>r</sup>. Barton’s Buttons.<br /><span class="red">Young.</span></td> - <td class="t l">Colours of <i>thick Plates</i>.<br /><span class="red">Newton.</span></td> - <td class="t">Colours of <i>thin Plates</i>.<br /><span class="red">Hook.<br /> Newton.</span></td> - </tr> - <tr> - <td class="c l z">⏟</td> - <td class="c l z">⏟</td> - <td class="l"></td> - <td></td> - <td class="l"></td> - <td></td> - <td colspan="4" class="c l"><sup>—————</sup><sub>⏟</sub><sup>—————</sup></td> - <td colspan="10"></td> - <td class="l"> <br /></td> - <td colspan="2"></td> - <td class="l" colspan="2"></td> - </tr> - <tr> - <td class="t"><span class="red">Euclid.</span><br /> Ang. Inc. equals Ang. Reflection.</td> - <td class="t l b"><span class="red">Snell.</span> Sin. Refr. to Sin. Inc. in giv. <i>Ratio</i> in same med.</td> - <td class="t l b">By measures of Refraction.</td> - <td class="t">Dispersion of colours is same when Refr. is diff.<br /> Measures.<br /><span class="red">Dollond.</span></td> - <td class="l"> <br /></td> - <td> <br /></td> - <td class="t" colspan=11><span class="red">Huyghens.</span> Rays of light have four Sides with regard to which their properties alternate.<br /> - <span class="red">Newton.</span> Idea of <i>Polarization</i> introduced, which governs subsequent observations. <i>Dipolarization</i> with Colours.</td> - <td> <br /></td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> <br /></td> - <td colspan="2"></td> - <td class="l" colspan="2"></td> - </tr> - <tr> - <td></td> - <td colspan="2" class="c l"><sup>—</sup><sub>⏟</sub><sup>—</sup></td> - <td class="t l"></td> - <td class="l" colspan="2"></td> - <td colspan="9" class="c"><sub>⏞</sub></td> - <td> <br /></td> - <td> <br /></td> - <td><br /></td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> <br /></td> - <td colspan="2"></td> - <td class="l" colspan="2"></td> - </tr> - <tr> - <td> <br /></td> - <td class="t b" colspan=2><span class="red">Newt.</span> Refr. R<sup>o</sup>. is diff. for diff. colours, but in same med. is const. for each colour.</td> - <td class="b"></td> - <td class="t l">Measures. <span class="red">Huyghens.</span></td> - <td class="t">Double Refr. in biaxal crystals.<br /><span class="red">Brewster.</span></td> - <td class="t h l">Rays are polarized by Calcspar, Quartz, &c. </td> - <td class="t h l">Rays are polarized by biaxal crystals.</td> - <td class="t h l">Rays are polarized by Tourmaline, Agate, &c.</td> - <td class="t h l">Rays are polarised by Refl. at glass.</td> - <td class="t l">Rays are polarized by transmission through glass.</td> - <td class="t h l">Variable q<sup>y</sup>. of pol. refl. light paral. plane of Refl.<br /><span class="red">Arago.</span></td> - <td class="t h">Variable q<sup>y</sup>. of pol. refl. light perp. plane of Refl.</td> - <td class="t h">Whole light reflected by internal Refl.</td> - <td class="t h l">Pol. Rays through uniaxal crystals give colours. Rings. <span class="red">Wollaston</span>.</td> - <td class="t h">Pol. Rays through biaxal crystals give colours.<br /><span class="red">Arago.</span></td> - <td class="t h">Pol. Rays. through imperf. crystallized bodies give colours. (Glass strained, jellies prest.)<br /><span class="red">Brewster.</span></td> - <td class="t h">Pol. Rays in axis of Quartz give a peculiar set of colours.<br />Plane of Pol<sup>n</sup> twisted diff<sup>ly</sup>. for diff. colours.<br /><span class="red">Biot.<br />Arago.</span></td> - <td class="t h">Pol. Rays oblique in Quartz give peculiar rings, &c.</td> - <td class="t h">Pol. Rays through certain liquids give a peculiar set of colours.</td> - <td class="t l" colspan=3>The Laws of these Phænomena were never discovered till Theory had indicated them.</td> - <td class="t l" colspan=2><i>Newton’s Scale of Colours.</i><br /><br /><i>Fits</i> of Rays.<br /><span class="red">Newton.</span></td> - </tr> - <tr> - <td></td> - <td colspan="3" class="c l"><sup>——</sup><sub>⏟</sub><sup>——</sup></td> - <td class="c l">⏟</td> - <td> <br /></td> - <td class="l"> </td> - <td class="l"> </td> - <td class="l"> </td> - <td class="l"> </td> - <td class="l"> </td> - <td class="l"> </td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> </td> - <td> <br /></td> - <td> <br /></td> - <td></td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> </td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> </td> - <td> <br /></td> - </tr> - <tr> - <td class="l"> <br /></td> - <td></td> - <td class="t l"><span class="red">Dollond.</span> <br /></td> - <td class="t">Prop<sup>n</sup> of Ref. R<sup>s</sup> is diff. in diff. med.<br /><i>Achromatism</i>.</td> - <td class="t l"><span class="red">Huygh<sup>s</sup></span>.<br />Law of Double Ref. exp. by a spheroid.</td> - <td> <br /></td> - <td class="l"> </td> - <td class="l"> </td> - <td class="l"> </td> - <td class="l"> </td> - <td class="l"> </td> - <td class="l"> </td> - <td class="t">Change of plane of pol. by Refl.<br /><span class="red">Arago</span></td> - <td class="t">Light is <i>circularly pol.</i> by 2 Refl. in <i>Fresnel’s Rhomb.</i><br /><span class="red">Fresnel.</span></td> - <td class="l"> </td> - <td> <br /></td> - <td> <br /></td> - <td class="t">+ in dir<sup>n</sup> of plagihedral faces.<br /><span class="red">J. Herschel.</span></td> - <td> <br /></td> - <td class="t">Plane of Pol<sup>n</sup>. twisted.<br /><span class="red">Biot</span></td> - <td class="t l">Fringes obliterated by stopping light from one edge or interposing a glass.<br /><span class="red">Young.<br />Arago.</span></td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> </td> - <td> <br /></td> - </tr> - <tr> - <td class="l"> <br /></td> - <td> <br /></td> - <td class="l"> <br /></td> - <td> <br /></td> - <td colspan="2" class="c l"><sup>——</sup><sub>⏟</sub><sup>——</sup></td> - <td class="c">⏟</td> - <td class="c">⏟</td> - <td class="c">⏟</td> - <td class="c">⏟</td> - <td class="c">⏟</td> - <td class="l"> </td> - <td> <br /></td> - <td> <br /></td> - <td class="t l" colspan=2>Optical classification of crystals. <span class="red">Brewster.</span></td> - <td> <br /></td> - <td><br /></td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> </td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> </td> - <td> <br /></td> - </tr> - <tr> - <td class="l"> </td> - <td> <br /></td> - <td class="l"> </td> - <td class="t">Ratios not reconcilable. <i>Irrationality</i>.<br /><span class="red">Blair.</span></td> - <td class="t l"><span class="red">Fresnel.</span> <br /></td> - <td class="t" >Law exp. by surface of 4 dim<sup>s</sup>.</td> - <td class="t l"><span class="red">Newt. Malus.</span> Ray pol. in <i>principal plane</i> of Rhomb.; and perp. to it.</td> - <td class="t"><span class="red">Brews. Biot. Ray</span> pol. in plane bisecting ang.at axis; and perp. to it.</td> - <td class="t"><span class="red">Brews.</span> Ray pol. paral. to axis.</td> - <td class="t l"><span class="red">Malus.</span> Ray pol. in plane of Refl. for <i>given angle</i>.</td> - <td class="t"><span class="red">Malus.</span> Ray partially pol. in plane perp. to plane of Reflection.</td> - <td class="l"> </td> - <td class="t"><br />None Refl<sup>d</sup>. if tan. ang. equal Refr. R<sup>o</sup>.<br /><span class="red">Brewster.</span></td> - <td></td> - <td class="t l">Tint is as sq. of sin.<br /><span class="red">Biot.</span></td> - <td class="t">Tint is as sin. α sin. β.<br /><span class="red">Brewster.<br />Biot.</span><br />Lemniscates.<br /><span class="red">J. Herschel.</span></td> - <td> <br /></td> - <td class="t">* By interf. of resolved undul<sup>ns</sup>. of 2 rays circularly pol<sup>d</sup>. in opp. directions.<br /><span class="red">* Fresnel.</span></td> - <td class="t">* By interf. of resolved undul<sup>ns</sup>. of 2 rays elliptically pol<sup>d</sup>. in opp. directions.<br /><span class="red">* Airy.</span></td> - <td></td> - <td class="t l">* By interf. of rays from edges.<br /><span class="red">Young.</span></td> - <td> <br /></td> - <td> <br /></td> - <td class="l"> </td> - <td> <br /></td> - </tr> - <tr> - <td class="t l b">* Refl. produced by spherical undul<sup>ns</sup>.</td> - <td class="t">* Refr. produced by spherical undul<sup>ns</sup>. of diff. vel. for diff. colour.</td> - <td class="t l" colspan="2"><span class="red">† Explanation imperfect.</span></td> - <td class="t l b">* Refr. produced by spheroidal undul<sup>ns</sup>.</td> - <td class="t">* Refr. produced by curved surf. undul<sup>ns</sup>.</td> - <td class="t l b">* Pol<sup>n</sup>. being prod. by resolution of transv<sup>e</sup> undul<sup>ns</sup>.</td> - <td class="t">* Pol<sup>n</sup>. being prod. by resolution of transv<sup>e</sup> undul<sup>ns</sup>.</td> - <td class="t b"><span class="red">† Explan. imperfect.</span></td> - <td class="t l b" colspan="2">* Polarization being produced by resolution of transverse undulations.</td> - <td class="t l">* Undul<sup>ns</sup>. being com<sup>d</sup>. acc. to laws of elastic bodies.</td> - <td class="t">* Undul<sup>ns</sup>. being com<sup>d</sup>. acc. to a certain hypothesis.</td> - <td class="t b">* Impossible formulæ being interpreted by analogy.</td> - <td class="t l b">* By interf. of resolved parts of transverse undul<sup>ns</sup>.</td> - <td class="t">* By interf. of resolved parts of transverse undul<sup>ns</sup>.</td> - <td class="t"><span class="red">† Explan. imperfect.</span></td> - <td class="t b" colspan="2">* Same hypothesis explains separation of rays in axis and oblique.<br /> - <span class="red">† Explanation imperfect.<br />* Maccullagh.</span></td> - <td class="t"><span class="red">† Explan. wanting.</span></td> - <td class="t l b">* By interf. of rays from all parts.<br /><span class="red">* Young.<br />* Fresnel.</span></td> - <td class="t">* By interf. of undul<sup>ns</sup>. from all parts.<br /><span class="red">* Fraunhofer.</span></td> - <td class="t">* By interf. of rays from striæ.<br /><span class="red">* Young.</span></td> - <td class="t l">* By interf. of undul<sup>ns</sup>. from two surfaces.<br /><span class="red">* Young.</span></td> - <td class="t b">* By interf. of undul<sup>ns</sup>. from two surfaces.<br /><span class="red">* Young.</span></td> - </tr> - <tr> - <td colspan="5" class="c l"><sup>————</sup><sub>⏟</sub><sup>————</sup></td> - <td class="l"> <br /></td> - <td colspan="3" class="c l"><sup>———</sup><sub>⏟</sub><sup>———</sup></td> - <td colspan="5" class="c l"><sup>————</sup><sub>⏟</sub><sup>————</sup></td> - <td colspan="5" class="c l"><sup>————</sup><sub>⏟</sub><sup>————</sup></td> - <td class="l"> <br /></td> - <td colspan="5" class="c l"><sup>————</sup><sub>⏟</sub><sup>————</sup></td> - </tr> - <tr> - <td> <br /></td> - <td class="t"><span class="red">* Huyghens.</span></td> - <td class="t" colspan="3">Reflection and Refraction are propagation of undulations.</td> - <td> <br /></td> - <td class="t"><span class="red">* Young.<br />* Fresnel.</span></td> - <td class="t" colspan="2">Polarization in crystals is transverse undulations.</td> - <td class="t"><span class="red">* Fresnel.</span></td> - <td class="t" colspan="4">Polarization in Reflection and Refraction is transverse undulations.</td> - <td class="t"><span class="red">* Fresnel.<br />* Arago.</span></td> - <td class="t" colspan="4">Dipolarized Colours are produced by interference of Rays polarized in same plane; - length of undulation being different for different colours.</td> - <td></td> - <td class="t"><span class="red">* Young.<br />* Fresnel.</span></td> - <td class="t" colspan="4">Colours of Fringes, Gratings, Striæ, thick Plates, thin Plates &c. are produced - by interference of undulations; length of undulation being different for different colours.</td> - </tr> - <tr> - <td class="t l" colspan="4">* Undulations being propagated by the uniform elasticity of each medium.</td> - <td class="t">* Undul<sup>ns</sup>. prop. by el<sup>y</sup>. of medium diff. in 2 diff. dir<sup>ns</sup>, (<i>axis of crystal.</i>)</td> - <td class="t" colspan="2">* Undul<sup>ns</sup>. being prop. by elasticity of med. diff. in 3 diff. directions (<i>axes</i>).</td> - <td colspan="18"> <br /></td> - </tr> - <tr> - <td colspan="4" class="c"><sup>———</sup><sub>⏟</sub><sup>———</sup></td> - <td class="c">——⌟<br />⌞——</td> - <td colspan="2" class="c"><br /><sup>—</sup><sub>⏟</sub><sup>—</sup></td> - <td colspan="18" class="l"> <br /></td> - </tr> - <tr> - <td> <br /></td> - <td class="t" colspan="3"><span class="red">Young.</span> Reflection and double Refraction are propagation of undulations by crystalline elasticity.</td> - <td> <br /></td> - <td class="t" colspan="2"><span class="red">* Fresnel.</span> Double Refr. and Pol. arise from same cause.</td> - <td colspan="18"> <br /></td> - </tr> - <tr> - <td colspan="9" class="c l"><sup>—————</sup><sub>⏟</sub><sup>—————</sup></td> - <td colspan="5" class="c l"><sup>—————</sup><sub>⏟</sub><sup>—————</sup></td> - <td colspan="11" class="c l"><sup>—————</sup><sub>⏟</sub><sup>—————</sup></td> - </tr> - <tr> - <td> <br /></td> - <td class="t"><span class="red">Young.</span></td> - <td class="t"><span class="red">Fresnel.</span></td> - <td class="t" colspan="6">Light is transverse undulations propagated in media by elasticity dependent on axis, when crystalline.</td> - <td class="t"><span class="red">Fresnel.</span></td> - <td class="t" colspan="4">Light is transverse undul<sup>ns</sup>. transmitted from one med. to another according to probable hypotheses.</td> - <td class="t"><span class="red">Young.<br />Fresnel.</span></td> - <td class="t" colspan="10">Colours result from interferences, the lengths of undulation being different for different colours.</td> - </tr> - <tr> - <td colspan="3"></td> - <td colspan="12" class="c l"><sup>—————</sup><sub>⏟</sub><sup>—————</sup></td> - <td colspan="10" class="l"></td> - </tr> - <tr> - <td colspan="3"></td> - <td class="c" colspan="12">THE UNDULATORY THEORY OF LIGHT.</td> - <td colspan="10"></td> - </tr> -</table> -<div class="book"> -<div class="chapter"> -<p class="end"><span class="pagenum"><a id="page141"></a></span></p> -<p class="h2 end">NOVUM ORGANON RENOVATUM.</p> -<hr class="three" /> -<h2 class="nobreak">BOOK III.</h2> -<p class="center">OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE.</p><br /> -<hr class="one" /> -<h3 class="nobreak">CHAPTER I.<br /><br /> -<span class="sc">Introduction.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XXVII.</p> -<p><i>The Methods by which the construction of Science is promoted are,</i> -Methods of Observation, Methods of obtaining -clear Ideas, <i>and</i> Methods of Induction.</p> -<p class="noind" id="b3c1a1"> -<span class="dropcap"><span class="dsmall">1.</span> I</span>N the -preceding Book, we pointed out certain -general Characters of scientific knowledge which -may often serve to distinguish it from opinions of a -looser or vaguer kind. In the course of the progress -of knowledge from the earliest to the present time, men -have been led to a perception, more or less clear, of -these characteristics. Various philosophers, from Plato -and Aristotle in the ancient world, to Richard de Saint -Victor and Roger Bacon in the middle ages, Galileo -and Gilbert, Francis Bacon and Isaac Newton, in modern -times, were led to offer precepts and maxims, as fitted -to guide us to a real and fundamental knowledge of -nature. It may on another occasion be our business -to estimate the value of these precepts and maxims. -And other contributions of the same kind to the philosophy -of science might be noticed, and some which <span class="pagenum" id="page142">142</span> -contain still more valuable suggestions, and indicate a -more practical acquaintance with the subject. Among -these, I must especially distinguish Sir John Herschel’s -<i>Discourse on the Study of Natural Philosophy</i>. But my -object at present is not to relate the history, but to -present the really valuable results of preceding labours: and -I shall endeavour to collect, both from them and from -my own researches and reflections, such views and -such rules as seem best adapted to assist us in the -discovery and recognition of scientific truth; or, at -least, such as may enable us to understand the process -by which this truth is obtained. I would present -to the reader the Philosophy and, if possible, the Art -of Discovery.</p> -<p id="b3c1a2">2. But, in truth, we must acknowledge, before we -proceed with this subject, that, speaking with strictness, -an <em>Art of Discovery</em> is not possible;—that we can -give no Rules for the pursuit of truth which shall be -universally and peremptorily applicable;—and that the -helps which we can offer to the inquirer in such cases -are limited and precarious. Still, we trust it will be -found that aids may be pointed out which are neither -worthless nor uninstructive. The mere classification -of examples of successful inquiry, to which our rules -give occasion, is full of interest for the philosophical -speculator. And if our maxims direct the discoverer -to no operations which might not have occurred to -his mind of themselves, they may still concentrate our -attention on that which is most important and characteristic -in these operations, and may direct us to -the best mode of insuring their success. I shall, -therefore, attempt to resolve the Process of Discovery -into its parts, and to give an account as distinct as -may be of Rules and Methods which belong to each -portion of the process.</p> -<p id="b3c1a3">3. In <a href="#page27">Book II.</a> we considered the three main -parts of the process by which science is constructed: -namely, the Decomposition and Observation of Complex Facts; -the Explication of our Ideal Conceptions; and the -Colligation of Elementary Facts by -means of those Conceptions. The first and last of <span class="pagenum" id="page143">143</span> -these three steps are capable of receiving additional -accuracy by peculiar processes. They may further the -advance of science in a more effectual manner, when -directed by special technical <i>Methods</i>, of which in the -present Book we must give a brief view. In this more -technical form, the observation of facts involves the -<i>Measurement of Phenomena</i>; and the Colligation of -Facts includes all arts and rules by which the process -of Induction can be assisted. Hence we shall have -here to consider <i>Methods of Observation</i>, and <i>Methods -of Induction</i>, using these phrases in the widest sense. -The second of the three steps above mentioned, the -Explication of our Conceptions, does not admit of being -much assisted by methods, although something may -be done by Education and Discussion.</p> -<p id="b3c1a4">4. The Methods of Induction, of which we have to -speak, apply only to the first step in our ascent from -phenomena to laws of nature;—the discovery of <i>Laws -of Phenomena</i>. A higher and ulterior step remains -behind, and follows in natural order the discovery of -Laws of Phenomena; namely, the <i>Discovery of Causes</i>; -and this must be stated as a distinct and essential process -in a complete view of the course of science. Again, -when we have thus ascended to the causes of phenomena and -of their laws, we can often reason downwards from the cause -so discovered; and we are thus -led to suggestions of new phenomena, or to new explanations -of phenomena already known. Such proceedings may be termed -<i>Applications</i> of our Discoveries; -including in the phrase, <i>Verifications</i> of our Doctrines -by such an application of them to observed facts. -Hence we have the following series of processes concerned -in the formation of science.<br /> -  (1.) Decomposition of Facts;<br /> -  (2.) Measurement of Phenomena;<br /> -  (3.) Explication of Conceptions;<br /> -  (4.) Induction of Laws of Phenomena;<br /> -  (5.) Induction of Causes;<br /> -  (6.) Application of Inductive Discoveries.</p> -<p id="b3c1a5">5. Of these six processes, the methods by which -the second and fourth may be assisted are here our <span class="pagenum" id="page144">144</span> -peculiar object of attention. The treatment of these -subjects in the present work must necessarily be scanty -and imperfect, although we may perhaps be able to add -something to what has hitherto been systematically -taught on these heads. Methods of Observation and -of Induction might of themselves form an abundant -subject for a treatise, and hereafter probably will do -so, in the hands of future writers. A few remarks, -offered as contributions to this subject, may serve to -show how extensive it is, and how much more ready -it now is than it ever before was, for a systematic discussion.</p> -<p class="end">Of the above steps of the formation of science, the -first, the Decomposition of Facts, has already been -sufficiently explained in the last Book: for if we -pursue it into further detail and exactitude, we find -that we gradually trench upon some of the succeeding -parts. I, therefore, proceed to treat of the second -step, the Measurement of Phenomena;—of <i>Methods</i> -by which this work, in its widest sense, is executed, -and these I shall term Methods of Observation.</p> -<div class="chapter"> -<p><span class="pagenum" id="page145"></span></p> -<h3 class="nobreak">CHAPTER II.<br /><br /> -<span class="sc">Of Methods of Observation.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XXVIII.</p> -<p><i>The Methods of Observation of Quantity in general are</i>, -Numeration, <i>which is precise by the nature of Number; the</i> -Measurement of Space <i>and</i> of Time, <i>which are easily made -precise; the</i> Conversion of Space and Time, <i>by which each -aids the measurement of the other; the</i> Method of Repetition; -<i>the</i> Method of Coincidences <i>or</i> Interferences. <i>The -measurement of Weight is made precise by the</i> Method of -Double-weighing. <i>Secondary Qualities are measured by -means of</i> Scales of Degrees; <i>but in order to apply these -Scales, the student requires the</i> Education of the Senses. -<i>The Education of the Senses is forwarded by the practical -study of</i> Descriptive Natural History, Chemical Manipulation, -<i>and</i> Astronomical Observation.</p> -<p class="noind" id="b3c2a1"> -<span class="dropcap"><span class="dsmall">1.</span> I</span> -SHALL speak, in this chapter, of Methods -of exact and systematic observation, by which -such facts are collected as form the materials of precise -scientific propositions. These Methods are very various, -according to the nature of the subject inquired -into, and other circumstances: but a great portion of -them agree in being processes of measurement. These -I shall peculiarly consider: and in the first place those -referring to Number, Space, and Time, which are at -the same time objects and instruments of measurement.</p> -<p id="b3c2a2">2. But though we have to explain how observations -may be made as perfect as possible, we must not -forget that in most cases complete perfection is -unattainable. <em>Observations are never perfect.</em> -For we <span class="pagenum" id="page146">146</span> -observe phenomena by our senses, and measure their -relations in time and space; but our senses and our -measures are all, from various causes, inaccurate. If -we have to observe the exact place of the moon among -the stars, how much of instrumental apparatus is -necessary! This apparatus has been improved by -many successive generations of astronomers, yet it is -still far from being perfect. And the senses of man, -as well as his implements, are limited in their exactness. -Two different observers do not obtain precisely -the same measures of the time and place of a phenomenon; -as, for instance, of the moment at which the -moon occults a star, and the point of her <i>limb</i> at which -the occultation takes place. Here, then, is a source of -inaccuracy and errour, even in astronomy, where the -means of exact observation are incomparably more -complete than they are in any other department of -human research. In other cases, the task of obtaining -accurate measures is far more difficult. If we have -to observe the tides of the ocean when rippled with -waves, we can see the average level of the water first -rise and then fall; but how hard is it to select the exact -moment when it is at its greatest height, or the exact -highest point which it reaches! It is very easy, in such -a case, to err by many minutes in time, and by several -inches in space.</p> -<p>Still, in many cases, good Methods can remove very -much of this inaccuracy, and to these we now proceed.</p> -<p id="b3c2a3">3. (I.) <i>Number</i>.—Number is the first step of -measurement, since it measures itself, and does not, like -space and time, require an arbitrary standard. Hence -the first exact observations, and the first advances of -rigorous knowledge, appear to have been made by means -of number; as for example,—the number of days in a -month and in a year;—the cycles according to which -eclipses occur;—the number of days in the revolutions -of the planets; and the like. All these discoveries, as -we have seen in the History of Astronomy, go back to -the earliest period of the science, anterior to any -distinct tradition; and these discoveries presuppose a series, -probably a very long series, of observations, made <span class="pagenum" id="page147">147</span> -principally by means of number. Nations so rude as to -have no other means of exact measurement, have still -systems of numeration by which they can reckon to a -considerable extent. Very often, such nations have very -complex systems, which are capable of expressing numbers -of great magnitude. Number supplies the means -of measuring other quantities, by the assumption of a -<em>unit</em> of measure of the appropriate kind: but where -nature supplies the unit, number is applicable directly -and immediately. Number is an important element in -the Classificatory as well as in the Mathematical Sciences. -The History of those Sciences shows how the -formation of botanical systems was effected by the -adoption of number as a leading element, by Cæsalpinus; -and how afterwards the Reform of Linnæus in classification -depended in a great degree on his finding, in the -pistils and stamens, a better numerical basis than those -before employed. In like manner, the number of rays -in the membrane of the gills<a id="fnanchor1-3" href="#note1-3"><span class="fnanchor">1</span></a>, -and the number of rays -in the fins of fish, were found to be important elements -in ichthyological classification by Artedi and Linnæus. -There are innumerable instances, in all parts of Natural -History, of the importance of the observation of number. -And in this observation, no instrument, scale or -standard is needed, or can be applied; except the -scale of natural numbers, expressed either in words or -in figures, can be considered as an instrument.</p> -<div class="footnote"><span class="label"><a id="note1-3" href="#fnanchor1-3">1</a> -</span> <i>Hist. Ind. Sc.</i> b. xvi. c. vii. -</div> -<p id="b3c2a4">4. (II.) <i>Measurement of Space.</i>—Of quantities -admitting of <em>continuous</em> increase and decrease, -(for number is discontinuous,) space is the most simple in its -mode of measurement, and requires most frequently to -be measured. The obvious mode of measuring space is -by the repeated application of a material measure, as -when we take a foot-rule and measure the length of a -room. And in this case the foot-rule is the <em>unit</em> of -space, and the length of the room is expressed by the -number of such units which it contains: or, as it may -not contain an exact number, by a number with a -<i>fraction</i>. But besides this measurement of linear space, <span class="pagenum" id="page148">148</span> -there is another kind of space which, for purposes of -science, it is still more important to measure, namely, -angular space. The visible heavens being considered -as a sphere, the portions and paths of the heavenly -bodies are determined by drawing circles on the surface -of this sphere, and are expressed by means of the parts -of these circles thus intercepted: by such measures the -doctrines of astronomy were obtained in the very beginning -of the science. The arcs of circles thus measured, -are not like linear spaces, reckoned by means of an -<em>arbitrary</em> unit, for there is a <em>natural unit</em>, the total -circumference, to which all arcs may be referred. For -the sake of convenience, the whole circumference is -divided into 360 parts or <i>degrees</i>; and by means of -these degrees and their parts, all arcs are expressed. -The <em>arcs</em> are the measures of the <i>angles at the center</i>, -and the degrees may be considered indifferently as -measuring the one or the other of these quantities.</p> -<p id="b3c2a5">5. In the History of -Astronomy<a id="fnanchor2-3" href="#note2-3"><span class="fnanchor">2</span></a>, -I have described -the method of observation of celestial angles employed -by the Greeks. They determined the lines in which -the heavenly bodies were seen, by means either of -Shadows, or of Sights; and measured the angles between -such lines by arcs or rules properly applied to -them. The Armill, Astrolabe, Dioptra, and Parallactic -Instrument of the ancients, were some of the -instruments thus constructed. Tycho Brahe greatly -improved the methods of astronomical observation by -giving steadiness to the frame of his instruments, -(which were large <i>quadrants</i>,) and accuracy to the -divisions of the <i>limb</i><a id="fnanchor3-3" href="#note3-3"><span class="fnanchor">3</span></a>. -But the application of the -<i>telescope</i> to the astronomical quadrant and the fixation of -the center of the field by a <i>cross</i> of fine wires placed in -the focus, was an immense improvement of the instrument, -since it substituted a precise visual ray, pointing -to the star, instead of the coarse coincidence of Sights. -The accuracy of observation was still further increased <span class="pagenum" id="page149">149</span> -by applying to the telescope a <i>micrometer</i> which might -subdivide the smaller divisions of the arc.</p> -<div class="footnote"><span class="label"><a id="note2-3" href="#fnanchor2-3">2</a></span> -<i>Hist. Ind. Sc.</i> b. iii. c. iv. sect. 3. -</div> -<div class="footnote"><span class="label"><a id="note3-3" href="#fnanchor3-3">3</a></span> -<i>Ib.</i> b. vii. c. vi. sect. 1. -</div> -<p id="b3c2a6">6. By this means, the precision of astronomical observation -was made so great, that very minute angular -spaces could be measured: and it then became a question -whether discrepancies which appeared at first as -defects in the theory, might not arise sometimes from -a bending or shaking of the instrument, and from the -degrees marked on the limb being really somewhat -unequal, instead of being rigorously equal. Accordingly, -the framing and balancing of the instrument, so -as to avoid all possible tremor or flexure, and the exact -division of an arc into equal parts, became great objects -of those who wished to improve astronomical observations. -The observer no longer gazed at the stars from -a lofty tower, but placed his telescope on the solid -ground,—and braced and balanced it with various -contrivances. Instead of a quadrant, an entire circle was -introduced (by Ramsden;) and various processes were -invented for the dividing of instruments. Among -these we may notice Troughton’s method of dividing; -in which the visual ray of a microscope was substituted -for the points of a pair of compasses, and, by <i>stepping</i> -round the circle, the partial arcs were made to bear -their exact relation to the whole circumference.</p> -<p id="b3c2a7">7. Astronomy is not the only science which depends on -the measurement of angles. Crystallography -also requires exact measures of this kind; and the -<i>goniometer</i>, especially that devised by Wollaston, -supplies the means of obtaining such measures. The -science of Optics also, in many cases, requires the -measurement of angles.</p> -<p id="b3c2a8">8. In the measurement of linear space, there is no -natural standard which offers itself. Most of the common -measures appear to be taken from some part of -the human body; as a <i>foot</i>, a <i>cubit</i>, a <i>fathom</i>; but such -measures cannot possess any precision, and are altered -by convention: thus there were in ancient times many -kinds of cubits; and in modern Europe, there are a -great number of different standards of the foot, as the -Rhenish foot, the Paris foot, the English foot. It is <span class="pagenum" id="page150">150</span> -very desirable that, if possible, some permanent standard, -founded in nature, should be adopted; for the conventional -measures are lost in the course of ages; and -thus, dimensions expressed by means of them become -unintelligible. Two different natural standards have -been employed in modern times: the French have -referred their measures of length to the total -circumference of a meridian of the earth; a quadrant of this -meridian consists of ten million units or <i>metres</i>. The -English have fixed their linear measure by reference to -the length of a pendulum which employs an exact -second of time in its small oscillation. Both these -methods occasion considerable difficulties in carrying -them into effect; and are to be considered mainly as -means of recovering the standard if it should ever be -lost. For common purposes, some material standard is -adopted as authority for the time: for example, the -standard which in England possessed legal authority -up to the year 1835 was preserved in the House of -Parliament; and was lost in the conflagration which -destroyed that edifice. The standard of length now -generally referred to by men of science in England is -that which is in the possession of the Astronomical -Society of London.</p> -<p id="b3c2a9">9. A standard of length being established, the -artifices for applying it, and for subdividing it in the -most accurate manner, are nearly the same as in the -case of measures of arcs: as for instance, the employment -of the visual rays of microscopes instead of the -legs of compasses and the edges of rules; the use of -micrometers for minute measurements; and the like. -Many different modes of avoiding errour in such -measurements have been devised by various observers, -according to the nature of the cases with which they -had to deal<a id="fnanchor4-3" href="#note4-3"><span class="fnanchor">4</span></a>.</p> -<div class="footnote"><span class="label"> -<a id="note4-3" href="#fnanchor4-3">4</a></span> On the precautions employed in astronomical -instruments for the measure of space, see Sir J. Herschel’s -<i>Astronomy</i> (in the <i>Cabinet Cyclopædia</i>,) Arts. 103–110. -</div> -<p id="b3c2a10">10. (III.) <i>Measurement of Time</i>.—The methods of -measuring Time are not so obvious as the methods of <span class="pagenum" id="page151">151</span> -measuring space; for we cannot apply one portion of -time to another, so as to test their equality. We are -obliged to begin by assuming some change as the measure -of time. Thus the motion of the sun in the sky, -or the length and position of the shadows of objects, -were the first modes of measuring the parts of the day. -But what assurance had men, or what assurance could -they have, that the motion of the sun or of the shadow -was uniform? They could have no such assurance, -till they had adopted some measure of smaller times; -which smaller times, making up larger times by repetition, -they took as the standard of uniformity;—for -example, an hour-glass, or a clepsydra which answered -the same purpose among the ancients. There is no -apparent reason why the successive periods measured -by the emptying of the hour-glass should be unequal; -they are implicitly accepted as equal; and by reference -to these, the uniformity of the sun’s motion may be -verified. But the great improvement in the measurement -of time was the use of a pendulum for the purpose by -Galileo, and the application of this device to -clocks by Huyghens in 1656. For the successive -oscillations of a pendulum are rigorously equal, and a clock -is only a train of machinery employed for the purpose -of counting these oscillations. By means of this invention, -the measure of time in astronomical observations -became as accurate as the measure of space.</p> -<p id="b3c2a11">11. What is the <i>natural unit</i> of time? It was assumed -from the first by the Greek astronomers, that -the sidereal days, measured by the revolution of a star -from any meridian to the same meridian again, are -exactly equal; and all improvements in the measure of -time tended to confirm this assumption. The sidereal -day is therefore the natural standard of time. But the -solar day, determined by the diurnal revolution of the -sun, although not rigorously invariable, as the sidereal -day is, undergoes scarcely any perceptible variation; -and since the course of daily occurrences is regulated -by the sun, it is far more convenient to seek the basis -of our unit of time in <em>his</em> motions. Accordingly the -solar day (the <i>mean</i> solar day) is divided into 24 hours, <span class="pagenum" id="page152">152</span> -and these, into minutes and seconds; and this is our -scale of time. Of such time, the sidereal day has 23 -hours 56 minutes 4·09 seconds. And it is plain that -by such a statement the length of the hour is fixed, -with reference to a sidereal day. The <i>standard</i> of -time (and the standard of space in like manner) equally -answers its purpose, whether or not it coincides with -any <i>whole number</i> of units.</p> -<p id="b3c2a12">12. Since the sidereal day is thus the standard of -our measures of time, it becomes desirable to refer to -it, constantly and exactly, the instruments by which -time is measured, in order that we may secure ourselves -against errour. For this purpose, in astronomical -observatories, observations are constantly made of the -transit of stars across the meridian; the <i>transit instrument</i> -with which this is done being adjusted with -all imaginable regard to -accuracy<a id="fnanchor5-3" href="#note5-3"><span class="fnanchor">5</span></a>.</p> -<div class="footnote"><span class="label"><a id="note5-3" href="#fnanchor5-3">5</a> -</span> On the precautions employed in the measure of -time by astronomers, see Herschel’s <i>Astronomy</i>, Art. 115–127. -</div> -<p id="b3c2a13">13. When exact measures of time are required in -other than astronomical observations, the same instruments -are still used, namely, clocks and chronometers. -In chronometers, the regulating part is an oscillating -body; not, as in clocks, a pendulum oscillating by the -force of gravity, but a wheel swinging to and fro on -its center, in consequence of the vibrations of a slender -coil of elastic wire. To divide time into still -smaller portions than these vibrations, other artifices -are used; some of which will be mentioned under the -next head.</p> -<p id="b3c2a14">14. (IV.) <i>Conversion of Space and Time.</i>—Space -and time agree in being extended quantities, which are -made up and measured by the repetition of homogeneous -parts. If a body move uniformly, whether in -the way of revolving or otherwise, the <em>space</em> which any -point describes, is <em>proportional</em> to the <em>time</em> of its -motion; and the space and the time may each be -taken as a measure of the other. Hence in such cases, -by taking space instead of time, or time instead of <span class="pagenum" id="page153">153</span> -space, we may often obtain more convenient and precise -measures, than we can by measuring directly the -element with which we are concerned.</p> -<p>The most prominent example of such a conversion, -is the measurement of the Right Ascension of stars, -(that is, their angular distance from a standard -meridian<a id="fnanchor6-3" href="#note6-3"><span class="fnanchor">6</span></a> -on the celestial sphere,) by means of the time -employed in their coming to the meridian of the place -of observation. Since, as we have already stated, the -visible celestial sphere, carrying the fixed stars, -revolves with perfect uniformity about the pole; if we -observe the stars as they come in succession to a fixed -circle passing through the poles, the intervals of time -between these observations will be proportional to the -angles which the meridian circles passing through these -stars make at the poles where they meet; and hence, -if we have the means of measuring time with great -accuracy, we can, by watching the <em>times</em> of the transits -of successive stars across some visible mark in our own -meridian, determine the <em>angular distances</em> of the -meridian circles of all the stars from one another.</p> -<div class="footnote"><span class="label"><a id="note6-3" href="#fnanchor6-3">6</a> -</span> A <i>meridian</i> is a circle passing through the -poles about which the celestial sphere revolves. The meridian -<em>of any place</em> on the earth is that meridian which is -exactly over the place. -</div> -<p>Accordingly, now that the pendulum clock affords -astronomers the means of determining time exactly, a -measurement of the Right Ascensions of heavenly -bodies by means of a clock and a transit instrument, -is a part of the regular business of an observatory. If -the sidereal clock be so adjusted that it marks the -beginning of its scale of time when the first point of -Right Ascension is upon the visible meridian of our -observatory, the point of the scale at which the clock -points when any other star is in our meridian, will -truly represent the Right Ascension of the star.</p> -<p>Thus as the motion of the stars is our measure of -time, we employ time, conversely, as our measure of -the places of the stars. The celestial machine and our -terrestrial machines correspond to each other in their -movements; and the star steals silently and steadily <span class="pagenum" id="page154">154</span> -across our meridian line, just as the pointer of the -clock steals past the mark of the hour. We may judge -of the scale of this motion by considering that the full -moon employs about two minutes of time in sailing -across any fixed line seen against the sky, transverse -to her path: and all the celestial bodies, carried along -by the revolving sphere, travel at the same rate.</p> -<p id="b3c2a15">15. In this case, up to a certain degree, we render -our measures of astronomical angles more exact and -convenient by substituting time for space; but when, -in the very same kind of observation, we wish to proceed -to a greater degree of accuracy, we find that it -is best done by substituting space for time. In observing -the transit of a star across the meridian, if we -have the clock within hearing, we can count the beats -of the pendulum by the noise which they make, and -tell exactly at which second of time the passage of the -star across the visible thread takes place; and thus we -measure Right Ascension by means of time. But our -perception of time does not allow us to divide a second -into ten parts, and to pronounce whether the transit -takes place three-tenths, six-tenths, or seven-tenths of -a second after the preceding beat of the clock. This, -however, can be done by the usual mode of observing -the transit of a star. The observer, listening to the -beat of his clock, fastens his attention upon the star at -each beat, and especially at the one immediately before -and the one immediately after the passage of the -thread: and by this means he has these two positions -and the position of the thread so far present to his -intuition at once, that he can judge in what proportion -the thread is nearer to one position than the other, and -can thus divide the intervening second in its due proportion. -Thus if he observe that at the beginning of -the second the star is on one side of the thread, and at -the end of the second on the other side; and that the -two distances from the thread are as two to three, he -knows that the transit took place at two-fifths (or -four-tenths) of a second after the former beat. In this -way a second of time in astronomical observations -may, by a skilful observer, be divided into ten equal <span class="pagenum" id="page155">155</span> -parts; although when time is observed as time, a tenth -of a second appears almost to escape our senses. From -the above explanation, it will be seen that the reason -why the subdivision is possible in the way thus described, -is this:—that the moment of time thus to be -divided is so small, that the eye and the mind can -retain, to the end of this moment, the impression of -position which it received at the beginning. Though -the two positions of the star, and the intermediate -thread, are seen successively, they can be contemplated -by the mind as if they were seen simultaneously: and -thus it is precisely the smallness of this portion of -time which enables us to subdivide it by means of -space.</p> -<p id="b3c2a16">16. There is another case, of somewhat a different -kind, in which time is employed in measuring space; -namely, when space, or the standard of space, is defined -by the length of a pendulum oscillating in a given -time. We might in this way define any space by the -time which a pendulum of such a length would take -in oscillating; and thus we might speak, as was observed -by those who suggested this device, of five -minutes of cloth, or a rope half an hour long. We -may observe, however, that in this case, the space is -<em>not proportional</em> to the time. And we may add, that -though we thus appear to avoid the arbitrary standard of -space (for as we have seen, the standard of -measures of time is a natural one,) we do not do so in -fact: for we assume the invariableness of gravity, -which really varies (though very slightly,) from place -to place.</p> -<p id="b3c2a17">17. (V.) <i>The Method of Repetition in Measurement.</i>—In -many cases we can give great additional -accuracy to our measurements by repeatedly adding -to itself the quantity which we wish to measure. Thus -if we wished to ascertain the exact breadth of a thread, -it might not be easy to determine whether it was one-ninetieth, -or one-ninety-fifth, or one-hundredth part of -an inch; but if we find that ninety-six such threads -placed side by side occupy exactly an inch, we have -the precise measure of the breadth of the thread. In <span class="pagenum" id="page156">156</span> -the same manner, if two clocks are going nearly at the -same rate, we may not be able to distinguish the excess -of an oscillation of one of the pendulums over an -oscillation of the other: but when the two clocks have -gone for an hour, one of them may have gained ten -seconds upon the other; thus showing that the proportion -of their times of oscillation is 3610 to 3600.</p> -<p>In the latter of these instances, we have the principle -of repetition truly exemplified, because (as has been -justly observed by Sir J. Herschel<a id="fnanchor7-3" href="#note7-3"><span class="fnanchor">7</span></a>,) -there is then ‘a -juxtaposition of units without errour,’—‘one vibration -commences exactly where the last terminates, no part -of time being lost or gained in the addition of the -units so counted.’ In space, this juxtaposition of units -without errour cannot be rigorously accomplished, -since the units must be added together by material -contact (as in the above case of the threads,) or in -some equivalent manner. Yet the principle of repetition -has been applied to angular measurement with -considerable success in Borda’s Repeating Circle. In -this instrument, the angle between two objects which -we have to observe, is repeated along the graduated -limb of the circle by turning the telescope from one -object to the other, alternately fastened to the circle -(by its <i>clamp</i>) and loose from it (by unclamping). In -this manner the errours of graduation may (theoretically) -be entirely got rid of: for if an angle repeated -<i>nine</i> times be found to go twice round the circle, it -must be <em>exactly</em> eighty degrees: and where the repetition does -not give an exact number of circumferences, -it may still be made to subdivide the errour to any -required extent.</p> -<div class="footnote"><span class="label"><a id="note7-3" href="#fnanchor7-3">7</a> -</span> <i>Disc. Nat. Phil.</i> art. 121. -</div> -<p id="b3c2a18">18. Connected with the principle of repetition, is -the <i>Method of coincidences</i> or <i>interferences</i>. If we have -two Scales, on one of which an inch is divided into 10, -and on the other into 11 equal parts; and if, these -Scales being placed side by side, it appear that the -beginning of the latter Scale is between the 2nd and -3rd division of the former, it may not be apparent <span class="pagenum" id="page157">157</span> -what fraction added to 2 determines the place of beginning -of the second Scale as measured on the first. But -if it appear also that the 3rd division of the second -Scale <em>coincides</em> with a certain division of the first, (the -5th,) it is certain that 2 and <em>three-tenths</em> is the <em>exact</em> -place of the beginning of the second Scale, measured -on the first Scale. The 3rd division of the 11 Scale -will coincide (or interfere with) a division of the 10 -Scale, when the beginning or <i>zero</i> of the 11 divisions -is three-tenths of a division beyond the preceding line -of the 10 Scale; as will be plain on a little consideration. -And if we have two Scales of equal units, in -which each unit is divided into nearly, but not quite, -the same number of equal parts (as 10 and 11, 19 and -20, 29 and 30,) and one sliding on the other, it will -always happen that some one or other of the division -lines will coincide, or very nearly coincide; and thus -the exact position of the beginning of one unit, measured -on the other scale, is determined. A sliding -scale, thus divided for the purpose of subdividing the -units of that on which it slides, is called a <i>Vernier</i>, -from the name of its inventor.</p> -<p id="b3c2a19">19. The same Principle of Coincidence or Interference -is applied to the exact measurement of the length -of time occupied in the oscillation of a pendulum. If -a detached pendulum, of such a length as to swing in -little less than a second, be placed before the seconds’ -pendulum of a clock, and if the two pendulums begin -to move together, the former will gain upon the latter, -and in a little while their motions will be quite discordant. -But if we go on watching, we shall find -them, after a time, to agree again exactly; namely, -when the detached pendulum has gained one complete -oscillation (back and forwards,) upon the clock pendulum, -and again coincides with it in its motion. If this -happen after 5 minutes, we know that the times of -oscillation of the two pendulums are in the proportion -of 300 to 302, and therefore the detached pendulum -oscillates in <span style="font-size: 80%"><sup>150</sup>⁄<sub>151</sub></span> -of a second. The accuracy which can -be obtained in the measure of an oscillation by this -means is great; for the clock can be compared (by <span class="pagenum" id="page158">158</span> -observing transits of the stars or otherwise) with -the natural standard of time, the sidereal day. And -the moment of coincidence of the two pendulums -may, by proper arrangements, be very exactly determined.</p> -<p>We have hitherto spoken of methods of measuring -time and space, but other elements also may be very -precisely measured by various means.</p> -<p id="b3c2a20">20. (VI.) <i>Measurement of Weight.</i>—Weight, like -space and time, is a quantity made up by addition of -parts, and may be measured by similar methods. The -principle of repetition is applicable to the measurement -of weight; for if two bodies be simultaneously put in -the same pan of a balance, and if they balance pieces in -the other pan, their weights are exactly added.</p> -<p>There may be difficulties of practiced workmanship -in carrying into effect the mathematical conditions of -a perfect balance; for example, in securing an exact -equality of the effective arms of the beam in all positions. -These difficulties are evaded by the <i>Method of -double weighing</i>; according to which the standard -weights, and the body which is to be weighed, are -successively put in the <em>same</em> pan, and made to balance by -a third body in the opposite scale. By this means the -different lengths of the arms of the beam, and other -imperfections of the balance, become of no -consequence<a id="fnanchor8-3" href="#note8-3"><span class="fnanchor">8</span></a>.</p> -<div class="footnote"><span class="label"><a id="note8-3" href="#fnanchor8-3">8</a> -</span> For other methods of measuring weights accurately, -see Faraday’s <i>Chemical Manipulation</i>, p. 25. -</div> -<p id="b3c2a21">21. There is no natural <i>Standard</i> of weight. The -conventional weight taken as the standard, is the -weight of a given bulk of some known substance; for -instance, a <i>cubic foot of water</i>. But in order that this -may be definite, the water must not contain any portion -of heterogeneous substance: hence it is required -that the water be <em>distilled</em> water.</p> -<p id="b3c2a22">22. (VII.) <i>Measurement of Secondary Qualities.</i>—We -have already seen<a id="fnanchor9-3" href="#note9-3"><span class="fnanchor">9</span></a> that -secondary qualities are -estimated by means of conventional Scales, which refer <span class="pagenum" id="page159">159</span> -them to space, number, or some other definite expression. -Thus the Thermometer measures heat; the -Musical Scale, with or without the aid of number, expresses -the pitch of a note; and we may have an exact -and complete Scale of Colours, pure and impure. We -may remark, however, that with regard to sound and -colour, the estimates of the ear and the eye are not -superseded, but only assisted: for if we determine -what a note is, by comparing it with an instrument -known to be in tune, we still leave the ear to decide -when the note is <em>in unison</em> with one of the notes of the -instrument. And when we compare a colour with our -chromatometer, we judge by the eye which division -of the chromatometer it <em>matches</em>. Colour and sound -have their Natural Scales, which the eye and ear -habitually apply; what science requires is, that those -scales should be systematized. We have seen that -several conditions are requisite in such scales of -qualities: the observer’s skill and ingenuity are mainly -shown in devising such scales and methods of applying -them.</p> -<div class="footnote"><span class="label"> -<a id="note9-3" href="#fnanchor9-3">9</a></span> -<a href="#page145">B. iii. c. ii.</a> Of the Measure of Secondary Qualities. -</div> -<p id="b3c2a23">23. The Method of Coincidences is employed in -harmonics: for if two notes are nearly, but not quite, -in unison, the coincidences of the vibrations produce -an audible undulation in the note, which is called the -<i>howl</i>; and the exactness of the unison is known by -this howl vanishing.</p> -<p id="b3c2a24">24. (VIII.) <i>Manipulation.</i>—The process of applying -practically methods of experiment and observation, is -termed Manipulation; and the value of observations -depends much upon the proficiency of the -observer in this art. This skill appears, as we have -said, not only in devising means and modes in measuring -results, but also in inventing and executing arrangements -by which elements are subjected to such -conditions as the investigation requires: in finding and -using some material combination by which nature shall -be asked the question which we have in our minds. -To do this in any subject may be considered as a -peculiar Art, but especially in Chemistry; where ‘many -experiments, and even whole trains of research, are <span class="pagenum" id="page160">160</span> -essentially dependent for success on mere -manipulation<a id="fnanchor10-3" href="#note10-3"><span class="fnanchor">10</span></a>.’ -The changes which the chemist has to study,—compositions, -decompositions, and mutual actions, -affecting the internal structure rather than the external -form and motion of bodies,—are not familiarly -recognized by common observers, as those actions are -which operate upon the total mass of a body: and -hence it is only when the chemist has become, to a -certain degree, familiar with his science, that he has -the power of observing. He must learn to interpret -the effects of mixture, heat, and other Chemical agencies, -so as to see in them those facts which chemistry -makes the basis of her doctrines. And in learning to -interpret this language, he must also learn to call it -forth;—to place bodies under the requisite conditions, -by the apparatus of his own laboratory and the operations -of his own fingers. To do this with readiness -and precision, is, as we have said, an Art, both of the -mind and of the hand, in no small degree recondite -and difficult. A person may be well acquainted with -all the doctrines of chemistry, and may yet fail in the -simplest experiment. How many precautions and observances, -what resource and invention, what delicacy -and vigilance, are requisite in <i>Chemical Manipulation</i>, -may be seen by reference to Dr. Faraday’s work on -that subject.</p> -<div class="footnote"><span class="label"><a id="note10-3" href="#fnanchor10-3">10</a></span> -Faraday’s <i>Chemical Manipulation</i>, p. 3. -</div> -<p id="b3c2a25">25. The same qualities in the observer are requisite -in some other departments of science; for example, -in the researches of Optics: for in these, after the first -broad facts have been noticed, the remaining features -of the phenomena are both very complex and very -minute; and require both ingenuity in the invention -of experiments, and a keen scrutiny of their results. -We have instances of the application of these qualities -in most of the optical experimenters of recent times, -and certainly in no one more than Sir David Brewster. -Omitting here all notice of his succeeding labours, his -<i>Treatise on New Philosophical Instruments</i>, published -in 1813, is an excellent model of the kind of resource <span class="pagenum" id="page161">161</span> -and skill of which we now speak. I may mention as -an example of this skill, his mode of determining the -refractive power of an <em>irregular</em> fragment of any -transparent substance. At first this might appear an -impossible problem; for it would seem that a regular and -smooth surface are requisite, in order that we may -have any measurable refraction. But Sir David Brewster -overcame the difficulty by immersing the fragment -in a combination of fluids, so mixed, that they had the -same refractive power as the specimen. The question, -<em>when</em> they had this power, was answered by noticing -when the fragment became so transparent that its surface -could hardly be seen; for this happened when, the -refractive power within and without the fragment being -the same, there was no refraction at the surface. And this -condition being obtained, the refractive power of the fluid, -and therefore of the fragment, was easily ascertained.</p> -<p id="b3c2a26">26. (IX.) <i>The Education of the Senses.</i>—Colour -and Musical Tone are, as we have seen, determined by -means of the Senses, whether or not Systematical Scales -are used in expressing the observed fact. Systematical -Scales of sensible qualities, however, not only give -precision to the record, but to the observation. But for -this purpose such an Education of the Senses is requisite -as may enable us to apply the scale immediately. -The memory must retain the sensation or perception -to which the technical term or degree of the scale -refers. Thus with regard to colour, as we have said -already<a id="fnanchor11-3" href="#note11-3"><span class="fnanchor">11</span></a>, -when we find such terms as <i>tin-white</i> or -<i>pinchbeck-brown</i>, the metallic colour so denoted ought -to occur at once to our recollection without delay or -search. The observer’s senses, therefore, must be educated, -at first by an actual exhibition of the standard, -and afterwards by a familiar use of it, to understand -readily and clearly each phrase and degree of the scales -which in his observations he has to apply. This is not -only the best, but in many cases the only way in which -the observation can be expressed. Thus <i>glassy lustre</i>, -<i>fatty lustre</i>, <i>adamantine lustre</i>, denote -certain kinds of <span class="pagenum" id="page162">162</span> -shining in minerals, which appearances we should -endeavour in vain to describe by periphrasis; and -which the terms, if considered as terms in common -language, would by no means clearly discriminate: for -who, in common language, would say that coal has a -fatty lustre? But these terms, in their conventional -sense, are perfectly definite; and when the eye is once -familiarized with this application of them, are easily -and clearly intelligible.</p> -<div class="footnote"><span class="label"> -<a id="note11-3" href="#fnanchor11-3">11</a></span> B. viii. c. iii. Terminology. -[Please see Transcriber’s <a href="#tnote">Notes</a>.] -</div> -<p id="b3c2a27">27. The education of the senses, which is thus -requisite in order to understand well the terminology -of any science, must be acquired by an inspection of -the objects which the science deals with; and is, perhaps, -best promoted by the practical study of Natural -History. In the different departments of Natural -History, the descriptions of species are given by means -of an extensive technical <i>terminology</i>: and that education -of which we now speak, ought to produce the effect -of making the observer as familiar with each of the terms -of this terminology as we are with the words of our -common language. The technical terms have a much -more precise meaning than other terms, since they are -defined by express convention, and not learnt by common -usage merely. Yet though they are thus defined, -not the definition, but the perception itself, is that -which the term suggests to the proficient.</p> -<p>In order to use the terminology to any good purpose, -the student must possess it, not as a dictionary, -but as a language. The terminology of his sciences -must be the natural historian’s most familiar tongue. -He must learn to think in such language. And when -this is achieved, the terminology, as I have elsewhere -said, though to an uneducated eye cumbrous and -pedantical, is felt to be a useful implement, not an -oppressive burden<a id="fnanchor12-3" href="#note12-3"><span class="fnanchor">12</span></a>. -The impatient schoolboy looks upon -his grammar and vocabulary as irksome and burdensome; -but the accomplished student who has learnt -the language by means of them, knows that they have -given him the means of expressing what he thinks, and <span class="pagenum" id="page163">163</span> -even of thinking more precisely. And as the study of -language thus gives precision to the thoughts, the study -of Natural History, and especially of the descriptive -part of it, gives precision to the senses.</p> -<div class="footnote"><span class="label"><a id="note12-3" href="#fnanchor12-3">12</a> -</span> <i>Hist. Ind. Sc.</i> b. xvi. c. iv. sect. 2. -</div> -<p>The Education of the Senses is also greatly promoted -by the practical pursuit of any science of experiment -and observation, as chemistry or astronomy. -The methods of manipulating, of which we have just -spoken, in chemistry, and the methods of measuring -extremely minute portions of space and time which are -employed in astronomy, and which are described in -the former part of this chapter, are among the best -modes of educating the senses for purposes of scientific -observation.</p> -<p class="end" id="b3c2a28">28. By the various Methods of precise observation -which we have thus very briefly described, facts are -collected, of an exact and definite kind; they are then -bound together in general laws, by the aid of general -ideas and of such methods as we have now to consider. -It is true, that the ideas which enable us to combine -facts into general propositions, do commonly operate in -our minds while we are still engaged in the office of -observing. Ideas of one kind or other are requisite to -connect our phenomena into facts, and to give meaning -to the terms of our descriptions: and it frequently -happens, that long before we have collected all the -facts which induction requires, the mind catches the -suggestion which some of these ideas offer, and leaps -forwards to a conjectural law while the labour of observation -is yet unfinished. But though this actually -occurs, it is easy to see that the process of combining -and generalizing facts is, in the order of nature, posterior -to, and distinct from, the process of observing -facts. Not only is this so, but there is an intermediate -step which, though inseparable from all successful -generalization, may be distinguished from it in our -survey; and may, in some degree, be assisted by peculiar -methods. To the consideration of such methods -we now proceed.</p> -<div class="chapter"> -<p><span class="pagenum" id="page164"></span></p> -<h3 class="nobreak">CHAPTER III.<br /><br /> -<span class="sc">Of Methods of acquiring clear Scientific Ideas</span>; -<i>and first</i> <span class="sc">of Intellectual Education.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XXIX.</p> -<p><i>The Methods by which the acquisition of clear Scientific -Ideas is promoted, are mainly two</i>; Intellectual Education -<i>and</i> Discussion of Ideas.</p> -<p class="center"><span class="sc">Aphorism</span> XXX.</p> -<p><i>The Idea of Space becomes more clear by studying</i> Geometry; -<i>the Idea of Force, by studying</i> Mechanics; <i>the Ideas -of Likeness, of Kind, of Subordination of Classes, by studying</i> -Natural History.</p> -<p class="center"><span class="sc">Aphorism</span> XXXI.</p> -<p>Elementary Mechanics <i>should now form a part of intellectual -education, in order that the student may understand -the Theory of Universal Gravitation: for an intellectual -education should cultivate such ideas as enable the student to -understand the most complete and admirable portions of the -knowledge which the human race has attained to.</i></p> -<p class="center"><span class="sc">Aphorism</span> XXXII.</p> -<p>Natural History <i>ought to form a part of intellectual education, -in order to correct certain prejudices which arise from -cultivating the intellect by means of mathematics alone; and -in order to lead the student to see that the division of things -into Kinds, and the attribution and use of Names, are processes -susceptible of great precision.</i> <span class="pagenum" id="page165">165</span></p> -<p class="drop"><span class="sc">THE</span> -ways in which men become masters of those -clear and yet comprehensive conceptions which -the formation and reception of science require, are -mainly two; which, although we cannot reduce them -to any exact scheme, we may still, in a loose use of -the term, call <i>Methods</i> of acquiring clear Ideas. These -two ways are Education and Discussion.</p> -<p id="b3c3a1">1. (I.) <i>Idea of Space.</i>—It is easily seen that -Education may do at least something to render our ideas -distinct and precise. To learn Geometry in youth, -tends, manifestly, to render our idea of space clear and -exact. By such an education, all the relations, and all -the consequences of this idea, come to be readily and -steadily apprehended; and thus it becomes easy for us -to understand portions of science which otherwise we -should by no means be able to comprehend. The conception -of <i>similar triangles</i> was to be mastered, before -the disciples of Thales could see the validity of his -method of determining the height of lofty objects by -the length of their shadows. The conception of <i>the -sphere with its circles</i> had to become familiar, before -the annual motion of the sun and its influence upon -the lengths of days could be rightly traced. The -properties of circles, combined with the -<i>pure</i><a id="fnanchor13-3" href="#note13-3"><span class="fnanchor">13</span></a> -<i>doctrine of -motion</i>, were required as an introduction to the theory -of Epicycles: the properties of <i>conic sections</i> were -needed, as a preparation for the discoveries of Kepler. -And not only was it necessary that men should possess -a <em>knowledge</em> of certain figures and their properties; but -it was equally necessary that they should have the -<em>habit of reasoning</em> with perfect steadiness, precision, -and conclusiveness concerning the relations of space. -No small discipline of the mind is requisite, in most -cases, to accustom it to go, with complete insight and -security, through the demonstrations respecting intersecting -planes and lines, dihedral and trihedral angles, -which occur in solid geometry. Yet how absolutely -necessary is a perfect mastery of such reasonings, to -him who is to explain the motions of the moon in <span class="pagenum" id="page166">166</span> -latitude and longitude! How necessary, again, is the -same faculty to the student of crystallography! Without -mathematical habits of conception and of thinking, -these portions of science are perfectly inaccessible. But -the early study of plane and solid geometry gives to -all tolerably gifted persons, the habits which are thus -needed. The discipline of following the reasonings of -didactic works on this subject, till we are quite familiar -with them, and of devising for ourselves reasonings of -the same kind, (as, for instance, the solutions of problems -proposed,) soon gives the mind the power of <em>discoursing</em> -with perfect facility concerning the most -complex and multiplied relations of space, and enables -us to refer to the properties of all plane and solid -figures as surely as to the visible forms of objects. -Thus we have here a signal instance of the efficacy of -education in giving to our Conceptions that clearness, -which the formation and existence of science indispensably require.</p> -<div class="footnote"><span class="label"><a id="note13-3" href="#fnanchor13-3">13</a> -</span> See <i>Hist. Sc. Ideas</i>, b. ii. c. xiii. -</div> -<p id="b3c3a2">2. It is not my intention here to enter into the -details of the form which should be given to education, -in order that it may answer the purposes now contemplated. -But I may make a remark, which the above -examples naturally suggest, that in a mathematical -education, considered as a preparation for furthering -or understanding physical science, Geometry is to be -cultivated, far rather than Algebra:—the properties of -space are to be studied and reasoned upon as they are -in themselves, not as they are replaced and disguised -by symbolical representations. It is true, that when -the student is become quite familiar with elementary -geometry, he may often enable himself to deal in a -more rapid and comprehensive manner with the relations -of space, by using the language of symbols and -the principles of symbolical calculation: but this is an -ulterior step, which may be added to, but can never be -substituted for, the direct cultivation of geometry. -The method of symbolical reasoning employed upon -subjects of geometry and mechanics, has certainly -achieved some remarkable triumphs in the treatment -of the theory of the universe. These successful <span class="pagenum" id="page167">167</span> -applications of symbols in the highest problems of physical -astronomy appear to have made some teachers of mathematics -imagine that it is best to <em>begin</em> the pupil’s course -with such symbolical generalities. But this mode of -proceeding will be so far from giving the student clear -ideas of mathematical relations, that it will involve -him in utter confusion, and probably prevent his ever -obtaining a firm footing in geometry. To commence -mathematics in such a way, would be much as if we -should begin the study of a language by reading the -highest strains of its lyrical poetry.</p> -<p id="b3c3a3">3. (II.) <i>Idea of Number, &c.</i>—The study of -mathematics, as I need hardly observe, developes and renders -exact, our conceptions of the relations of number, as -well as of space. And although, as we have already -noticed, even in their original form the conceptions of -number are for the most part very distinct, they may -be still further improved by such discipline. In complex -cases, a methodical cultivation of the mind in such -subjects is needed: for instance, questions concerning -Cycles, and Intercalations, and Epacts, and the like, -require very great steadiness of arithmetical apprehension -in order that the reasoner may deal with them -rightly. In the same manner, a mastery of problems -belonging to the science of Pure Motion, or, as I have -termed it, <i>Mechanism</i>, requires either great natural -aptitude in the student, or a mind properly disciplined -by suitable branches of mathematical study.</p> -<p id="b3c3a4">4. Arithmetic and Geometry have long been standard -portions of the education of cultured persons throughout -the civilized world; and hence all such persons have -been able to accept and comprehend those portions of -science which depend upon the idea of space: for instance, -the doctrine of the globular form of the earth, -with its consequences, such as the measures of latitude -and longitude;—the heliocentric system of the universe -in modern, or the geocentric in ancient times;—the -explanation of the rainbow; and the like. In nations -where there is no such education, these portions of -science cannot exist as a part of the general stock of -the knowledge of society, however intelligently they <span class="pagenum" id="page168">168</span> -may be pursued by single philosophers dispersed here -and there in the community.</p> -<p id="b3c3a5">5. (III.) <i>Idea of Force.</i>—As the idea of Space is -brought out in its full evidence by the study of Geometry, -so the idea of Force is called up and developed -by the study of the science of Mechanics. It has -already been shown, in our scrutiny of the Ideas of the -Mechanical Sciences, that Force, the Cause of motion -or of equilibrium, involves an independent Fundamental -Idea, and is quite incapable of being resolved into any -mere modification of our conceptions of space, time, -and motion. And in order that the student may possess -this idea in a precise and manifest shape, he must -pursue the science of Mechanics in the mode which -this view of its nature demands;—that is, he must -study it as an independent science, resting on solid -elementary principles of its own, and not built upon -some other unmechanical science as its substructure. -He must trace the truths of Mechanics from their own -axioms and definitions; these axioms and definitions -being considered as merely means of bringing into -play the Idea on which the science depends. The conceptions -of force and matter, of action and reaction, of -momentum and inertia, with the reasonings in which -they are involved, cannot be evaded by any substitution -of lines or symbols for the conceptions. Any attempts -at such substitution would render the study of -Mechanics useless as a preparation of the mind for -physical science; and would, indeed, except counteracted -by great natural clearness of thought on such -subjects, fill the mind with confused and vague notions, -quite unavailing for any purposes of sound reasoning. -But, on the other hand, the study of Mechanics, in its -genuine form, as a branch of education, is fitted to give -a most useful and valuable precision of thought on -such subjects; and is the more to be recommended, -since, in the general habits of most men’s minds, the -mechanical conceptions are tainted with far greater -obscurity and perplexity than belongs to the conceptions -of number, space, and motion.</p> -<p id="b3c3a6">6. As habitually distinct conceptions of <i>space</i> and <span class="pagenum" id="page169">169</span> -<i>motion</i> were requisite for the reception of the doctrines -of formal astronomy, (the Ptolemaic and Copernican -system,) so a clear and steady conception of <i>force</i> -is indispensably necessary for understanding the Newtonian -system of physical astronomy. It may be objected -that the study of Mechanics as a science has not -commonly formed part of a liberal education in Europe, -and yet that educated persons have commonly accepted -the Newtonian system. But to this we reply, that although -most persons of good intellectual culture have -professed to assent to the Newtonian system of the universe, -yet they have, in fact, entertained it in so vague -and perplexed a manner as to show very clearly that a -better mental preparation than the usual one is necessary, -in order that such persons may really understand -the doctrine of universal attraction. I have elsewhere -spoken of the prevalent indistinctness of mechanical -conceptions<a id="fnanchor14-3" href="#note14-3"><span class="fnanchor">14</span></a>; -and need not here dwell upon the -indications, constantly occurring in conversation and in -literature, of the utter inaccuracy of thought on such -subjects which may often be detected; for instance, in -the mode in which many men speak of centrifugal and -centripetal forces;—of projectile and central forces;—of -the effect of the moon upon the waters of the ocean; -and the like. The incoherence of ideas which we -frequently witness on such points, shows us clearly -that, in the minds of a great number of men, well -educated according to the present standard, the -acceptance of the doctrine of Universal Gravitation is a result -of traditional prejudice, not of rational conviction. -And those who are Newtonians on such grounds, are -not at all more intellectually advanced by being -Newtonians in the nineteenth century, than they would -have been by being Ptolemaics in the fifteenth.</p> -<div class="footnote"><span class="label"><a id="note14-3" href="#fnanchor14-3">14</a> -</span> <i>Hist. Sc. Ideas</i>, b. iii. c. x. -</div> -<p id="b3c3a7">7. It is undoubtedly in the highest degree desirable -that all great advances in science should become the -common property of all cultivated men. And this can -only be done by introducing into the course of a liberal -education such studies as unfold and fix in men’s minds <span class="pagenum" id="page170">170</span> -the fundamental ideas upon which the new-discovered -truths rest. The progress made by the ancients in -geography, astronomy, and other sciences, led them to -assign, wisely and well, a place to arithmetic and -geometry among the steps of an ingenuous education. The -discoveries of modern times have rendered these steps -still more indispensable; for we cannot consider a man -as cultivated up to the standard of his times, if he is -not only ignorant of, but incapable of comprehending, -the greatest achievements of the human intellect. And -as innumerable discoveries of all ages have thus secured -to Geometry her place as a part of good education, so -the great discoveries of Newton make it proper to introduce -Elementary Mechanics as a part of the same -course. If the education deserve to be called <i>good</i>, -the pupil will not remain ignorant of those discoveries, -the most remarkable extensions of the field of human -knowledge which have ever occurred. Yet he cannot -by possibility comprehend them, except his mind be -previously disciplined by mechanical studies. The period -appears now to be arrived when we may venture, -or rather when we are bound to endeavour, to include -a new class of Fundamental Ideas in the elementary -discipline of the human intellect. This is indispensable, -if we wish to educe the powers which we know -that it possesses, and to enrich it with the wealth which -lies within its reach<a id="fnanchor15-3" href="#note15-3"><span class="fnanchor">15</span></a>.</p> -<div class="footnote"><span class="label"><a id="note15-3" href="#fnanchor15-3">15</a> -</span> The University of Cambridge has, by a recent law, -made an examination in Elementary Mechanics requisite for the -Degree of B.A. -</div> -<p id="b3c3a8">8. By the view which is thus presented to us of the -nature and objects of intellectual education, we are led -to consider the mind of man as undergoing a progress -from age to age. By the discoveries which are made, -and by the clearness and evidence which, after a time, -(not suddenly nor soon,) the truths thus discovered acquire, -one portion of knowledge after another becomes -<em>elementary</em>; and if we would really secure this progress, -and make men share in it, these new portions -must be treated as elementary in the constitution of a <span class="pagenum" id="page171">171</span> -liberal education. Even in the rudest forms of intelligence, -man is immeasurably elevated above the unprogressive -brute, for the idea of number is so far developed that -he can count his flock or his arrows. But -when number is contemplated in a speculative form, he -has made a vast additional progress; when he steadily -apprehends the relations of space, he has again advanced; -when in thought he carries these relations into -the vault of the sky, into the expanse of the universe, -he reaches a higher intellectual position. And when -he carries into these wide regions, not only the relations -of space and time, but of cause and effect, of -force and reaction, he has again made an intellectual -advance; which, wide as it is at first, is accessible to -all; and with which all should acquaint themselves, if -they really desire to prosecute with energy the ascending -path of truth and knowledge which lies before -them. This should be an object of exertion to all ingenuous -and hopeful minds. For, that exertion is -necessary,—that after all possible facilities have been -afforded, it is still a matter of toil and struggle to -appropriate to ourselves the acquisitions of great discoverers, -is not to be denied. Elementary mechanics, -like elementary geometry, is a study accessible to all: -but like that too, or perhaps more than that, it is a -study which requires effort and contention of mind,—a -forced steadiness of thought. It is long since one complained -of this labour in geometry; and was answered -that in that region there is no <em>Royal Road</em>. The same -is true of Mechanics, and must be true of all branches -of solid education. But we should express the truth -more appropriately in our days by saying that there is -no <em>Popular Road</em> to these sciences. In the mind, as -in the body, strenuous exercise alone can give strength -and activity. The art of exact thought can be acquired -only by the labour of close thinking.</p> -<p id="b3c3a9">9. (IV.) <i>Chemical Ideas.</i>—We appear then to have -arrived at a point of human progress in which a liberal -education of the scientific intellect should include, -besides arithmetic, elementary geometry and mechanics. <span class="pagenum" id="page172">172</span> -The question then occurs to us, whether there are any other -Fundamental Ideas, among those belonging to -other sciences, which ought also to be made part of -such an education;—whether, for example, we should -strive to develope in the minds of all cultured men -the ideas of <i>polarity</i>, mechanical and chemical, of which -we spoke in a former part of this work.</p> -<p>The views to which we have been conducted by the -previous inquiry lead us to reply that it would not be -well at present to make <i>chemical</i> Polarities, at any -rate, a subject of elementary instruction. For even -the most profound and acute philosophers who have -speculated upon this subject,—they who are leading -the van in the march of discovery,—do not seem yet -to have reduced their thoughts on this subject to a -consistency, or to have taken hold of this idea of Polarity -in a manner quite satisfactory to their own -minds. This part of the subject is, therefore, by no -means ready to be introduced into a course of general -elementary education; for, with a view to such a purpose, -nothing less than the most thoroughly luminous -and transparent condition of the idea will suffice. Its -whole efficacy, as a means and object of disciplinal -study, depends upon there being no obscurity, perplexity, -or indefiniteness with regard to it, beyond that -transient deficiency which at first exists in the learner’s -mind, and is to be removed by his studies. The -idea of chemical Polarity is not yet in this condition; -and therefore is not yet fit for a place in education. -Yet since this idea of Polarity is the most general idea -which enters into chemistry, and appears to be that -which includes almost all the others, it would be -unphilosophical, and inconsistent with all sound views of -science, to introduce into education some chemical -conceptions, and to omit those which depend upon this -idea: indeed such a partial adoption of the science -could hardly take place without not only omitting, but -misrepresenting, a great part of our chemical knowledge. -The conclusion to which we are necessarily -led, therefore, is this:—that at present chemistry <span class="pagenum" id="page173">173</span> -cannot with any advantage, form a portion of the general -intellectual education<a id="fnanchor16-3" href="#note16-3"><span class="fnanchor">16</span></a>.</p> -<div class="footnote"><span class="label"><a id="note16-3" href="#fnanchor16-3">16</a> -</span> I do not here stop to prove that an education -(if it be so called) in which the memory only retains the -verbal expression of results, while the mind does not apprehend -the principles of the subject, and therefore cannot even -understand the words in which its doctrines are expressed, -is of no value whatever to the intellect, but rather, is highly -hurtful to the habits of thinking and reasoning. -</div> -<p id="b3c3a10">10. (V.) <i>Natural-History Ideas.</i>—But there remains -still another class of Ideas, with regard to -which we may very properly ask whether they may -not advantageously form a portion of a liberal education: -I mean the Ideas of definite Resemblance and -Difference, and of one set of resemblances subordinate -to another, which form the bases of the classificatory -sciences. These Ideas are developed by the study of -the various branches of Natural History, as Botany, -and Zoology; and beyond all doubt, those pursuits, if -assiduously followed, very materially affect the mental -habits. There is this obvious advantage to be looked -for from the study of Natural History, considered as -a means of intellectual discipline:—that it gives us, in -a precise and scientific form, examples of the classing -and naming of objects; which operations the use of -common language leads us constantly to perform in a -loose and inexact way. In the usual habits of our -minds and tongues, things are distinguished or brought -together, and names are applied, in a manner very indefinite, -vacillating, and seemingly capricious: and we -may naturally be led to doubt whether such defects -can be avoided;—whether exact distinctions of things, -and rigorous use of words be possible. Now upon this -point we may receive the instruction of Natural History; -which proves to us, by the actual performance of -the task, that a precise classification and nomenclature -are attainable, at least for a mass of objects all of the -same kind. Further, we also learn from this study, -that there may exist, not only an exact distinction of -kinds of things, but a series of distinctions, one set -subordinate to another, and the more general including <span class="pagenum" id="page174">174</span> -the more special, so as to form a system of classification. -All these are valuable lessons. If by the study -of Natural History we evolve, in a clear and well defined form, -the conceptions of <i>genus</i>, <i>species</i>, and of -<i>higher</i> and <i>lower steps</i> of classification, -we communicate precision, clearness, and method to the intellect, -through a great range of its operations.</p> -<p id="b3c3a11">11. It must be observed, that in order to attain the -disciplinal benefit which the study of Natural History -is fitted to bestow, we must teach the <em>natural</em> not the -artificial <i>classifications</i>; or at least the natural as well -as the artificial. For it is important for the student to -perceive that there are classifications, not merely arbitrary, -founded upon some <em>assumed</em> character, but natural, recognized -by some <em>discovered</em> character: he ought -to see that our classes being collected according to one -mark, are confirmed by many marks not originally stated -in our scheme; and are thus found to be grouped -together, not by a single resemblance, but by a mass of -resemblances, indicating a natural affinity. That objects -may be collected into such groups, is a highly important -lesson, which Natural History alone, pursued -as the science of <i>natural classes</i>, can teach.</p> -<p id="b3c3a12">12. Natural History has not unfrequently been -made a portion of education: and has in some degree -produced such effects as we have pointed out. It -would appear, however, that its lessons have, for the -most part, been very imperfectly learnt or understood -by persons of ordinary education: and that there are -perverse intellectual habits very commonly prevalent -in the cultivated classes, which ought ere now to have -been corrected by the general teaching of Natural -History. We may detect among speculative men -many prejudices respecting the nature and rules of -reasoning, which arise from pure mathematics having -been so long and so universally the instrument of -intellectual cultivation. Pure Mathematics reasons from -definitions: whatever term is introduced into her -pages, as a <i>circle</i>, or a <i>square</i>, its definition comes along -with it: and this definition is supposed to supply all -that the reasoner needs to know, respecting the term. <span class="pagenum" id="page175">175</span> -If there be any doubt concerning the validity of the -conclusion, the doubt is resolved by recurring to the -definitions. Hence it has come to pass that in other -subjects also, men seek for and demand definitions as -the most secure foundation of reasoning. The definition -and the term defined are conceived to be so far -identical, that in all cases the one may be substituted -for the other; and such a substitution is held to be -the best mode of detecting fallacies.</p> -<p id="b3c3a13">13. It has already been shown that even geometry -is not founded upon definitions alone: and we shall -not here again analyse the fallacy of this belief in the -supreme value of definitions. But we may remark -that the study of Natural History appears to be the -proper remedy for this erroneous habit of thought. For -in every department of Natural History the object of -our study is <em>kinds</em> of things, not one of which kinds -can be rigorously defined, yet all of them are sufficiently -definite. In these cases we may indeed give a -specific description of one of the kinds, and may call it -a definition; but it is clear that such a definition does -not contain the essence of the thing. We -say<a id="fnanchor17-3" href="#note17-3"><span class="fnanchor">17</span></a> that the -Rose Tribe are ‘Polypetalous dicotyledons, with lateral -styles, superior simple ovaria, regular perigynous stamens, -exalbuminous definite seeds, and alternate stipulate leaves.’ -But no one would say that this was our -essential conception of a rose, to be substituted for it -in all cases of doubt or obscurity, by way of making -our reasonings perfectly clear. Not only so; but as -we have already seen<a id="fnanchor18-3" href="#note18-3"><span class="fnanchor">18</span></a>, -the definition does not even -apply to all the tribe. For the stipulæ are absent in -Lowea: the albumen is present in Neillia: the fruit of -Spiræa sorbifolia is capsular. If, then, we can possess -any certain knowledge in Natural History, (which no -cultivator of the subject will doubt,) it is evident that -our knowledge cannot depend on the possibility of laying -down exact definitions and reasoning from them.</p> -<div class="footnote"><span class="label"><a id="note17-3" href="#fnanchor17-3">17</a> -</span> Lindley’s <i>Nat. Syst. Bot.</i> p. 81. -</div> -<div class="footnote"><span class="label"><a id="note18-3" href="#fnanchor18-3">18</a> -</span> <i>Hist. Sc. Ideas,</i> b. viii. c. ii. sect. 3. -</div> -<p id="b3c3a14">14. But it may be asked, if we cannot define a <span class="pagenum" id="page176">176</span> -word, or a class of things which a word denotes, how -can we distinguish what it does mean from what it -does not mean? How can we say that it signifies one -thing rather than another, except we declare what is -its signification?</p> -<p>The answer to this question involves the general -principle of a natural method of classification, which -has already been stated<a id="fnanchor19-3" href="#note19-3"><span class="fnanchor">19</span></a> -and need not here be again -dwelt on. It has been shown that names of <em>kinds</em> of -things (<i>genera</i>) associate them according to total -resemblances, not partial characters. The principle -which connects a group of objects in natural history is -not a <em>definition</em>, but a <em>type</em>. Thus we take as the type -of the Rose family, it may be, the common <i>wild rose</i>; -all species which resemble this flower more than they -resemble any other group of species are also <i>roses</i>, and -form one <i>genus</i>. All genera which resemble Roses -more than they resemble any other group of genera -are of the same <i>family</i>. And thus the Rose family -is collected about some one species, which is the type -or central point of the group.</p> -<div class="footnote"><span class="label"><a id="note19-3" href="#fnanchor19-3">19</a> -</span> <i>Hist. Sc. Ideas,</i> b. viii. c. ii. sect. 3. -</div> -<p>In such an arrangement, it may readily be conceived -that though the nucleus of each group may cohere -firmly together, the outskirts of contiguous groups -may approach, and may even be intermingled, so that -some species may doubtfully adhere to one group or -another. Yet this uncertainty does not at all affect -the truths which we find ourselves enabled to assert -with regard to the general mass of each group. And -thus we are taught that there may be very important -differences between two groups of objects, although we -are unable to tell where the one group ends and where -the other begins; and that there may be propositions -of indisputable truth, in which it is impossible to give -unexceptionable definitions of the terms employed.</p> -<p id="b3c3a15">15. These lessons are of the highest value with -regard to all employments of the human mind; for the -mode in which words in common use acquire their -meaning, approaches far more nearly to the <i>Method of</i> -<span class="pagenum" id="page177">177</span> <i>Type</i> than -to the method of definition. The terms -which belong to our practical concerns, or to our spontaneous -and unscientific speculations, are rarely capable -of exact definition. They have been devised in order -to express assertions, often very important, yet very -vaguely conceived: and the signification of the word is -extended, as far as the assertion conveyed by it can be -extended, by apparent connexion or by analogy. And -thus, in all the attempts of man to grasp at knowledge, -we have an exemplification of that which we have -stated as the rule of induction, that Definition and -Proposition are mutually dependent, each adjusted so -as to give value and meaning to the other: and this is -so, even when both the elements of truth are defective -in precision: the Definition being replaced by an -incomplete description or a loose reference to a Type; -and the Proposition being in a corresponding degree -insecure.</p> -<p id="b3c3a16">16. Thus the study of Natural History, as a corrective -of the belief that definitions are essential to -substantial truth, might be of great use; and the advantage -which might thus be obtained is such as well -entitles this study to a place in a liberal education. -We may further observe, that in order that Natural -History may produce such an effect, it must be studied -by inspection of the <em>objects</em> themselves, and not by the -reading of books only. Its lesson is, that we must in -all cases of doubt or obscurity refer, not to words or -definitions, but to things. The Book of Nature is its -dictionary: it is there that the natural historian looks, -to find the meaning of the words which he -uses<a id="fnanchor20-3" href="#note20-3"><span class="fnanchor">20</span></a>. So -<span class="pagenum" id="page178">178</span> long as a plant, -in its most essential parts, is more <em>like</em> -a rose than any thing else, it <em>is</em> a rose. He knows no -other definition.</p> -<div class="footnote"><span class="label"><a id="note20-3" href="#fnanchor20-3">20</a> -</span> It is a curious example of the influence of the belief -in definitions, that elementary books have been written in which -Natural History is taught in the way of question and answer, and -consequently by means of words alone. In such a scheme, of course -all objects are <em>defined</em>: and we may easily anticipate -the value of the knowledge thus conveyed. Thus, ‘Iron is a -well-known hard metal, of a darkish gray colour, and very elastic:’ -‘Copper is an orange-coloured metal, more sonorous than any other, -and the most elastic of any except iron.’ This is to pervert -the meaning of education, and to make it a business of mere words. -</div> -<p id="b3c3a17">17. (VI.) <i>Well-established Ideas alone to be used.</i>—We -may assert in general what we have elsewhere, as -above, stated specially with reference to the fundamental -principles of chemistry:—no Ideas are suited to become -the elements of elementary education, till they have not -only become perfectly distinct and fixed in the minds -of the leading cultivators of the science to which they -belong; but till they have been so for some considerable -period. The entire clearness and steadiness of view -which is essential to sound science, must have time to -extend itself to a wide circle of disciples. The views -and principles which are detected by the most profound -and acute philosophers, are soon appropriated by all the -most intelligent and active minds of their own and of -the following generations; and when this has taken -place, (and not till then,) it is right, by a proper -constitution of our liberal education, to extend a general -knowledge of such principles to all cultivated persons. -And it follows, from this view of the matter, that we -are by no means to be in haste to adopt, into our -course of education, all new discoveries as soon as they -are made. They require some time, in order to settle -into their proper place and position in men’s minds, -and to show themselves under their true aspects; and -till this is done, we confuse and disturb, rather than -enlighten and unfold, the ideas of learners, by introducing -the discoveries into our elementary instruction. -Hence it was perhaps reasonable that a century should -elapse from the time of Galileo, before the rigorous -teaching of Mechanics became a general element of -intellectual training; and the doctrine of Universal -Gravitation was hardly ripe for such an employment till -the end of the last century. We must not direct the -unformed youthful mind to launch its little bark upon -the waters of speculation, till all the agitation of -discovery, with its consequent fluctuation and -controversy, has well subsided.</p> -<p id="b3c3a18">18. But it may be asked, How is it -that time <span class="pagenum" id="page179">179</span> operates -to give distinctness and evidence to scientific -ideas? In what way does it happen that views and -principles, obscure and wavering at first, after a while -become luminous and steady? Can we point out any -process, any intermediate steps, by which this result is -produced? If we can, this process must be an important -portion of the subject now under our consideration.</p> -<p class="end">To this we reply, that the transition from the hesitation -and contradiction with which true ideas are first -received, to the general assent and clear apprehension -which they afterwards obtain, takes place through -the circulation of various arguments for and against -them, and various modes of presenting and testing -them, all which we may include under the term <i>Discussion</i>, -which we have already mentioned as the -second of the two ways by which scientific views are -developed into full maturity.</p> -<div class="chapter"> -<p><span class="pagenum" id="page180"></span></p> -<h3 class="nobreak">CHAPTER IV.<br /><br /> -<span class="sc">Of Methods of acquiring clear Scientific Ideas,</span> -<i>continued.</i>—<span class="sc">Of the Discussion of Ideas.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XXXIII.</p> -<p><i>The conception involved in scientific truths have attained -the requisite degree of clearness by means of the</i> Discussions -<i>respecting ideas which have taken place among discoverers -and their followers. Such discussions are very far from -being unprofitable to science. They are</i> metaphysical, <i>and -must be so: the difference between discoverers and barren -reasoners is, that the former employ good, and the latter bad -metaphysics.</i></p> -<p class="noind" id="b3c4a1"> -<span class="dropcap"><span class="dsmall">1.</span> I</span>T -is easily seen that in every part of science, the -establishment of a new set of ideas has been accompanied -with much of doubt and dissent. And by -means of discussions so occasioned, the new conceptions, -and the opinions which involve them, have gradually become -definite and clear. The authors and -asserters of the new opinions, in order to make them -defensible, have been compelled to make them consistent: -in order to recommend them to others, they have -been obliged to make them more entirely intelligible -to themselves. And thus the Terms which formed the -main points of the controversy, although applied in a -loose and vacillating manner at first, have in the end -become perfectly definite and exact. The opinions discussed -have been, in their main features, the same -throughout the debate; but they have at first been -dimly, and at last clearly apprehended: like the objects -of a landscape, at which we look through a telescope -ill adjusted, till, by sliding the tube backwards and <span class="pagenum" id="page181">181</span> -forwards, we at last bring it into focus, and perceive -every feature of the prospect sharp and bright.</p> -<p id="b3c4a2">2. We have in the last -Book<a id="fnanchor21-3" href="#note21-3"><span class="fnanchor">21</span></a> fully exemplified -this gradual progress of conceptions from obscurity -to clearness by means of Discussion. We have -seen, too, that this mode of treating the subject has -never been successful, except when it has been associated -with an appeal to facts as well as to reasonings. -A combination of experiment with argument, of observation -with demonstration, has always been found -requisite in order that men should arrive at those -distinct conceptions which give them substantial truths. -The arguments used led to the rejection of undefined, -ambiguous, self-contradictory notions; but the reference -to facts led to the selection, or at least to the -retention, of the conceptions which were both true and -useful. The two correlative processes, definition and -true assertion, the formation of clear ideas and the -induction of laws, went on together.</p> -<div class="footnote"><span class="label"> -<a id="note21-3" href="#fnanchor21-3">21</a></span> <a href="#page30"> -B. <span class="correction" title="emended from i.">ii.</span> c. ii.</a> -Of the Explication of Conceptions. -</div> -<p>Thus those discussions by which scientific conceptions -are rendered ultimately quite distinct and fixed, -include both reasonings from Principles and illustrations -from Facts. At present we turn our attention -more peculiarly to the former part of the process; -according to the distinction already drawn, between the -Explication of Conceptions and the Colligation of Facts. -The Discussions of which we here speak, are the Method -(if they may be called a <i>method</i>) by which the -Explication of Conceptions is carried to the requisite -point among philosophers.</p> -<p id="b3c4a3">3. In the <i>History</i> of the Fundamental Ideas of the -Sciences which forms the Prelude to this work, and -in the <i>History of the Inductive Sciences</i>, I have, in -several instances, traced the steps by which, historically -speaking, these Ideas have obtained their ultimate and -permanent place in the minds of speculative -men. I have thus exemplified the reasonings and controversies -which constitute such Discussion as we now -speak of. I have stated, at considerable length, the <span class="pagenum" id="page182">182</span> -various attempts, failures, and advances, by which the -ideas which enter into the science of Mechanics were -evolved into their present evidence. In like manner -we have seen the conception of <i>refracted rays</i> of light, -obscure and confused in Seneca, growing clearer in -Roger Bacon, more definite in Descartes, perfectly -distinct in Newton. The <i>polarity</i> of light, at first -contemplated with some perplexity, became very distinct -to Malus, Young, and Fresnel; yet the phenomena of -<i>circular polarization</i>, and still more, the <i>circular -polarization of fluids</i>, leave us, even at present, some -difficulty in fully mastering this conception. The <i>related -polarities</i> of electricity and magnetism are not yet -fully comprehended, even by our greatest philosophers. -One of Mr. Faraday’s late papers (the Fourteenth Series of his -Researches) is employed in an experimental -discussion of this subject, which leads to no satisfactory -result. The controversy between MM. Biot and -Ampère<a id="fnanchor22-3" href="#note22-3"><span class="fnanchor">22</span></a>, -on the nature of the Elementary Forces in electro-dynamic -action, is another evidence that the discussion of this -subject has not yet reached its termination. -With regard to <i>chemical polarity</i>, I have already stated -that this idea is as yet very far from being brought to -an ultimate condition of definiteness; and the subject -of Chemical Forces, (for that whole subject must be included -in this idea of polarity,) which has already occasioned much -perplexity and controversy, may easily -occasion much more, before it is settled to the satisfaction -of the philosophical world. The ideas of the -<i>classificatory</i> sciences also have of late been undergoing -much, and very instructive discussion, in the controversies -respecting the relations and offices of the natural -and artificial methods. And with regard to <i>physiological</i> -ideas, it would hardly be too much to say, -that the whole history of physiology up to the present -time has consisted of the discussion of the fundamental -ideas of the science, such as Vital Forces, Nutrition, -Reproduction, and the like. We had before us at -some length, in the <i>History of Scientific Ideas</i>, a review -<span class="pagenum" id="page183">183</span> of -the opposite opinions which have been advanced -on this subject; and we attempted in some degree to -estimate the direction in which these ideas are permanently -settling. But without attaching any importance -to this attempt, the account there given may at least -serve to show, how important a share in the past progress -of this subject the <i>discussion</i> of its Fundamental -Ideas has hitherto had.</p> -<div class="footnote"><span class="label"><a id="note22-3" href="#fnanchor22-3">22</a> -</span> <i>Hist. Ind. Sc.</i> b. xiii. c. 6. -</div> -<p id="b3c4a4">4. There is one reflexion which is very pointedly -suggested by what has been said. The manner in -which our scientific ideas acquire their distinct and -ultimate form being such as has been described,—always -involving much abstract reasoning and analysis -of our conceptions, often much opposite argumentation -and debate;—how unphilosophical is it to speak of -abstraction and analysis, of dispute and controversy, as -frivolous and unprofitable processes, by which true -science can never be benefitted; and how erroneous -to put such employments in antithesis with the study -of facts!</p> -<p>Yet some writers are accustomed to talk with contempt -of all past controversies, and to wonder at the -blindness of those who did not <em>at first</em> take the view -which was established <em>at last</em>. Such persons forget -that it was precisely the controversy, which established -among speculative men that final doctrine which they -themselves have quietly accepted. It is true, they -have had no difficulty in thoroughly adopting the -truth; but that has occurred because all dissentient -doctrines have been suppressed and forgotten; and because -systems, and books, and language itself, have -been accommodated peculiarly to the expression of -the accepted truth. To despise those who have, by -their mental struggles and conflicts, brought the subject -into a condition in which errour is almost out of -our reach, is to be ungrateful exactly in proportion to -the amount of the benefit received. It is as if a child, -when its teacher had with many trials and much -trouble prepared a telescope so that the vision through -it was distinct, should wonder at his stupidity in -pushing the tube of the eye-glass out and in so often. <span class="pagenum" id="page184">184</span></p> -<p id="b3c4a5">5. Again, some persons condemn all that we have -here spoken of as the discussion of ideas, terming it -<i>metaphysical</i>: and in this spirit, one -writer<a id="fnanchor23-3" href="#note23-3"><span class="fnanchor">23</span></a> has -spoken of the ‘metaphysical period’ of each science, -as preceding the period of ‘positive knowledge.’ But -as we have seen, that process which is here termed -‘metaphysical,’—the analysis of our conceptions and -the exposure of their inconsistencies,—(accompanied -with the study of facts,)—has always gone on most -actively in the most prosperous periods of each science. -There is, in Galileo, Kepler, Gassendi, and the other -fathers of mechanical philosophy, as much of <em>metaphysics</em> -as in their adversaries. The main difference -is, that the metaphysics is of a better kind; it is more -conformable to metaphysical truth. And the same is -the case in other sciences. Nor can it be otherwise. -For all truth, before it can be consistent with <em>facts</em>, -must be consistent with <em>itself</em>: and although this rule -is of undeniable authority, its application is often far -from easy. The perplexities and ambiguities which -arise from our having the same idea presented to us -under different aspects, are often difficult to -disentangle: and no common acuteness and steadiness of -thought must be expended on the task. It would be -easy to adduce, from the works of all great discoverers, -passages more profoundly metaphysical than any which -are to be found in the pages of barren <i>à priori</i> reasoners.</p> -<div class="footnote"><span class="label"><a id="note23-3" href="#fnanchor23-3">23</a> -</span> M. Auguste Comte, <i>Cours de Philosophie Positive</i>. -</div> -<p id="b3c4a6">6. As we have said, these metaphysical discussions -are not to be put in opposition to the study of facts; -but are to be stimulated, nourished and directed by a -constant recourse to experiment and observation. The -cultivation of ideas is to be conducted as having for -its object the connexion of facts; never to be pursued -as a mere exercise of the subtilty of the mind, striving -to build up a world of its own, and neglecting that -which exists about us. For although man may in this -way please himself, and admire the creations of his -own brain, he can never, by this course, hit upon the <span class="pagenum" id="page185">185</span> -real scheme of nature. With his ideas unfolded by -education, sharpened by controversy, rectified by metaphysics, -he may <em>understand</em> the natural world, but he -cannot <em>invent</em> it. At every step, he must try the value -of the advances he has made in thought, by applying -his thoughts to things. The Explication of Conceptions -must be carried on with a perpetual reference to -the Colligation of Facts.</p> -<p class="end">Having here treated of Education and Discussion as -the methods by which the former of these two processes -is to be promoted, we have now to explain the -methods which science employs in order most successfully -to execute the latter. But the Colligation of -Facts, as already stated, may offer to us two steps of -a very different kind,—the laws of Phenomena, and -their Causes. We shall first describe some of the -methods employed in obtaining truths of the former of -these two kinds.</p> -<div class="chapter"> -<p><span class="pagenum" id="page186"></span></p> -<h3 class="nobreak">CHAPTER V.<br /><br /> -<span class="sc">Analysis of the Process of Induction.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XXXIV.</p> -<p><i>The Process of Induction may be resolved into three steps; -the</i> Selection of the Idea, <i>the</i> Construction of the Conception, -<i>and the</i> Determination of the Magnitudes.</p> -<p class="center"><span class="sc">Aphorism</span> XXXV.</p> -<p><i>These three steps correspond to the determination of the</i> -Independent Variable, <i>the</i> Formula, <i>and the</i> Coefficients, -<i>in mathematical investigations; or to the</i> Argument, <i>the</i> -Law, <i>and the</i> Numerical Data, <i>in a Table of an astronomical -or other</i> Inequality.</p> -<p class="center"><span class="sc">Aphorism</span> XXXVI.</p> -<p><i>The Selection of the Idea depends mainly upon inventive -sagacity: which operates by suggesting and trying various -hypotheses. Some inquirers try erroneous hypotheses; and -thus, exhausting the forms of errour, form the Prelude to -Discovery.</i></p> -<p class="center"><span class="sc">Aphorism</span> XXXVII.</p> -<p class="end"><i>The following Rules may be given, in order to the selection -of the Idea for purposes of Induction:—the Idea and the -Facts must be</i> homogeneous; <i>and the Rule must be</i> tested -by the Facts.</p> -<p class="center"><span class="sc">Sect. I.</span>—<i>The Three Steps of Induction.</i></p> -<p class="noind" id="b3c5a1"> -<span class="dropcap"><span class="dsmall">1.</span> W</span>HEN -facts have been decomposed and phenomena measured, -the philosopher endeavours to combine them into general laws, -by the aid of <span class="pagenum" id="page187">187</span> Ideas and Conceptions; these being -illustrated and regulated by such means as we have spoken of in the last -two chapters. In this task, of gathering laws of nature -from observed facts, as we have already -said<a id="fnanchor24-3" href="#note24-3"><span class="fnanchor">24</span></a>, the natural -sagacity of gifted minds is the power by which -the greater part of the successful results have been -obtained; and this power will probably always be more -efficacious than any Method can be. Still there are -certain methods of procedure which may, in such investigations, -give us no inconsiderable aid, and these I -shall endeavour to expound.</p> -<div class="footnote"><span class="label"> -<a id="note24-3" href="#fnanchor24-3">24</a></span> <a href="#page97">B. ii. c. vi.</a> -</div> -<p id="b3c5a2">2. For this purpose, I remark that the Colligation -of ascertained Facts into general Propositions may be -considered as containing three steps, which I shall -term the <i>Selection of the Idea</i>, <i>the Construction of the -Conception</i>, and <i>the Determination of the Magnitudes</i>. -It will be recollected that by the word <i>Idea</i>, -(or Fundamental Idea,) used in a peculiar sense, I mean certain -wide and general fields of intelligible relation, such as -Space, Number, Cause, Likeness; while by <i>Conception</i> -I denote more special modifications of these ideas, as a -<i>circle</i>, a <i>square number</i>, a <i>uniform force</i>, a <i>like form</i> of -flower. Now in order to establish any law by reference -to facts, we must select the <i>true Idea</i> and the <i>true -Conception</i>. For example; when Hipparchus -found<a id="fnanchor25-3" href="#note25-3"><span class="fnanchor">25</span></a> -that the distance of the bright star Spica Virginis from -the equinoxial point had increased by two degrees in -about two hundred years, and desired to reduce this -change to a law, he had first to assign, if possible, the -<em>idea</em> on which it depended;—whether it was regulated -for instance, by <em>space</em>, or by <em>time</em>; whether it was determined -by the positions of other stars at each moment, or went on -progressively with the lapse of ages. -And when there was found reason to select <em>time</em> as the -regulative <em>idea</em> of this change, it was then to be determined -how the change went on with the time;—whether uniformly, -or in some other manner: the <em>conception</em>, or the rule -of the progression, was to be <span class="pagenum" id="page188">188</span> rightly constructed. -Finally, it being ascertained that -the change did go on uniformly, the question then -occurred what was its <em>amount</em>:—whether exactly a -degree in a century, or more, or less, and how much: -and thus the determination of the <em>magnitude</em> completed -the discovery of the law of phenomena respecting this star.</p> -<div class="footnote"><span class="label"> -<a id="note25-3" href="#fnanchor25-3">25</a></span> <i>Hist. Ind. Sc.</i> b. iii. c. iv. sect. 3. -</div> -<p id="b3c5a3">3. Steps similar to these three may be discerned -in all other discoveries of laws of nature. Thus, in -investigating the laws of the motions of the sun, moon -or planets, we find that these motions may be resolved, -besides a uniform motion, into a series of partial motions, -or Inequalities; and for each of these Inequalities, -we have to learn upon what it directly depends, whether -upon the progress of time only, or upon some configuration -of the heavenly bodies in space; then, we have -to ascertain its law; and finally, we have to determine -what is its amount. In the case of such Inequalities, -the fundamental element on which the Inequality depends, -is called by mathematicians the <i>Argument</i>. And -when the Inequality has been fully reduced to known -rules, and expressed in the form of a Table, the Argument -is the fundamental Series of Numbers which -stands in the margin of the Table, and by means of -which we refer to the other Numbers which express -the Inequality. Thus, in order to obtain from a Solar -Table the Inequality of the sun’s annual motion, the -Argument is the Number which expresses the day of -the year; the Inequalities for each day being (in the -Table) ranged in a line corresponding to the days. -Moreover, the Argument of an Inequality being assumed -to be known, we must, in order to calculate the -Table, that is, in order to exhibit the law of nature, -know also the <em>Law</em> of the Inequality, and its <em>Amount</em>. -And the investigation of these three things, the Argument, -the Law, and the Amount of the Inequality, -represents the three steps above described, the -Selection of the Idea, the Construction of the Conception, -and the Determination of the Magnitude.</p> -<p id="b3c5a4">4. In a great body of cases, <i>mathematical</i> language -and calculation are used to express the -connexion <span class="pagenum" id="page189">189</span> between -the general law and the special facts. And when -this is done, the three steps above described may be -spoken of as the Selection of the <i>Independent Variable</i>, -the Construction of the <i>Formula</i>, and the Determination -of the <i>Coefficients</i>. It may be worth our while to -attend to an exemplification of this. Suppose then, -that, in such observations as we have just spoken of, -namely, the shifting of a star from its place in the -heavens by an unknown law, astronomers had, at the -end of three successive years, found that the star had -removed by 3, by 8, and by 15 minutes from its original place. -Suppose it to be ascertained also, by -methods of which we shall hereafter treat, that this -change depends upon the time; we must then take the -<em>time</em>, (which we may denote by the symbol <i>t</i>,) for the -<em>independent variable</em>. But though the star changes -its place <em>with</em> the time, the change is not <em>proportional</em> -to the time; for its motion which is only 3 minutes in -the first year, is 5 minutes in the second year, and 7 -in the third. But it is not difficult for a person a little -versed in mathematics to perceive that the series 3, 8, -15, may be obtained by means of two terms, one of -which is proportional to the time, and the other to the -square of the time; that is, it is expressed by the <i>formula at + btt</i>. -The question then occurs, what are the -values of the <em>coefficients</em> <i>a</i> and <i>b</i>; -and a little examination of the case shows us that <i>a</i> must be 2, -and <i>b</i>, 1: so that the formula is 2<i>t</i> + <i>tt</i>. -Indeed if we add together the series 2, 4, 6, which expresses a change -proportional to the time, and 1, 4, 9, which is proportional -to the square of the time, we obtain the series -3, 8, 15, which is the series of numbers given by observation. -And thus the three steps which give us the -Idea, the Conception, and the Magnitudes; or the -Argument, the Law, and the Amount, of the change; -give us the Independent Variable, the Formula, and -the Coefficients, respectively.</p> -<p class="end">We now proceed to offer some suggestions of methods -by which each of these steps may be in some degree -promoted. <span class="pagenum" id="page190">190</span></p> -<p class="center"><span class="sc">Sect. II.</span>—<i>Of the -Selection of the Fundamental Idea.</i></p> -<p id="b3c5a5">5. When we turn our thoughts upon any assemblage of -facts, with a view of collecting from them -some connexion or law, the most important step, and -at the same time that in which rules can least aid us, is -the Selection of the Idea by which they are to be -collected. So long as this idea has not been detected, -all seems to be hopeless confusion or insulated facts; -when the connecting idea has been caught sight of, we -constantly regard the facts with reference to their -connexion, and wonder that it should be possible for -any one to consider them in any other point of view.</p> -<p>Thus the different seasons, and the various aspects -of the heavenly bodies, might at first appear to be -direct manifestations from some superior power, which -man could not even understand: but it was soon found -that the ideas of time and space, of motion and recurrence, -would give coherency to many of the phenomena. Yet this -took place by successive steps. Eclipses, -for a long period, seemed to follow no law; and being -very remarkable events, continued to be deemed the -indications of a supernatural will, after the common -motions of the heavens were seen to be governed by -relations of time and space. At length, however, the -Chaldeans discovered that, after a period of eighteen -years, similar sets of eclipses recur; and, thus selecting -the idea of <em>time</em>, simply, as that to which these events -were to be referred, they were able to reduce them to -rule; and from that time, eclipses were recognized as -parts of a regular order of things. We may, in the -same manner, consider any other course of events, and -may enquire by what idea they are bound together. -For example, if we take the weather, years peculiarly -wet or dry, hot and cold, productive and unproductive, -follow each other in a manner which, at first sight at -least, seems utterly lawless and irregular. Now can we -in any way discover some rule and order in these -occurrences? Is there, for example, in these events, -as in eclipses, a certain cycle of years, after which like <span class="pagenum" id="page191">191</span> -seasons come round again? or does the weather depend -upon the force of some extraneous body—for instance, -the moon—and follow in some way her aspects? or -would the most proper way of investigating this subject -be to consider the effect of the moisture and heat of -various tracts of the earth’s surface upon the ambient -air? It is at our choice to <em>try</em> these and other modes -of obtaining a science of the weather: that is, we may -refer the phenomena to the idea of <em>time</em>, introducing -the conception of a cycle;—or to the idea of external -<em>force</em>, by the conception of the moon’s action;—or to the -idea of <em>mutual action</em>, introducing the conceptions of -thermotical and atmological agencies, operating between -different regions of earth, water, and air.</p> -<p id="b3c5a6">6. It may be asked, How are we to decide in such -alternatives? How are we to select the one right idea -out of several conceivable ones? To which we can only -reply, that this must be done by <em>trying</em> which will -succeed. If there really exist a cycle of the weather, as -well as of eclipses, this must be established by comparing -the asserted cycle with a good register of the seasons, -of sufficient extent. Or if the moon really influence -the meteorological conditions of the air, the asserted -influence must be compared with the observed facts, -and so accepted or rejected. When Hipparchus had -observed the increase of longitude of the stars, the idea -of a motion of the celestial sphere suggested itself as -the explanation of the change; but this thought was -<em>verified</em> only by observing several stars. -It was conceivable that each star should have an independent -motion, governed by time only, or by other circumstances, -instead of being regulated by its place in the -sphere; and this possibility could be rejected by trial -alone. In like manner, the original opinion of the -composition of bodies supposed the compounds to derive -their properties from the elements according to the law -of <em>likeness</em>; but this opinion was overturned by a -thousand facts; and thus the really applicable Idea -of Chemical Composition was introduced in modern -times. In what has already been said on the History -of Ideas, we have seen how each science was in a state <span class="pagenum" id="page192">192</span> -of confusion and darkness till the right idea was introduced.</p> -<p id="b3c5a7">7. No general method of evolving such ideas can be -given. Such events appear to result from a peculiar -sagacity and felicity of mind;—never without labour, -never without preparation;—yet with no constant dependence -upon preparation, or upon labour, or even -entirely upon personal endowments. Newton explained -the colours which refraction produces, by referring -each colour to a peculiar <em>angle of refraction</em>, -thus introducing the right idea. But when the same philosopher -tried to explain the colours produced by diffraction, he -erred, by attempting to apply the same idea, (<i>the course -of a single ray</i>,) instead of applying the truer idea, of -the <em>interference of two rays</em>. Newton gave a wrong -rule for the double refraction of Iceland spar, by -making the refraction depend on the <em>edges</em> of the rhombohedron: -Huyghens, more happy, introduced the -idea of the <em>axis of symmetry</em> of the solid, and thus was -able to give the true law of the phenomena.</p> -<p id="b3c5a8">8. Although the selected idea is proved to be the -right one, only when the true law of nature is established -by means of it, yet it often happens that there -prevails a settled conviction respecting the relation -which must afford the key to the phenomena, before -the selection has been confirmed by the laws to which -it leads. Even before the empirical laws of the tides -were made out, it was not doubtful that these laws -depended upon the places and motions of the sun and -moon. We know that the crystalline form of a body -must depend upon its chemical composition, though -we are as yet unable to assign the law of this dependence.</p> -<p>Indeed in most cases of great discoveries, the right -idea to which the facts were to be referred, was selected -by many philosophers, before the decisive demonstration -that it was the right idea, was given by the -discoverer. Thus Newton showed that the motions of -the planets might be explained by means of a central -force in the sun: but though he established, he did not -first select the idea involved in the conception of a <span class="pagenum" id="page193">193</span> -central force. The idea had already been sufficiently -pointed out, dimly by Kepler, more clearly by Borelli, -Huyghens, Wren, and Hooke. Indeed this anticipation of -the true idea is always a principal part of that -which, in the <i>History of the Sciences</i>, we have termed -the <i>Prelude</i> of a Discovery. The two steps of <em>proposing</em> -a philosophical problem, and of <em>solving</em> it, are, as -we have elsewhere said, both important, and are often -performed by different persons. The former step is, in -fact, the Selection of the Idea. In explaining any -change, we have to discover first the <em>Argument</em>, and -then the <em>Law</em> of the change. The selection of the -Argument is the step of which we here speak; and is -that in which inventiveness of mind and justness of -thought are mainly shown.</p> -<p id="b3c5a9">9. Although, as we have said, we can give few precise directions -for this cardinal process, the Selection of -the Idea, in speculating on phenomena, yet there is -one Rule which may have its use: it is this:—<em>The idea -and the facts must be homogeneous</em>: the elementary -Conceptions, into which the facts have been decomposed, -must be of the same nature as the Idea by -which we attempt to collect them into laws. Thus, if -facts have been observed and measured by reference to -space, they must be bound together by the idea of -space: if we would obtain a knowledge of mechanical -forces in the solar system, we must observe mechanical -phenomena. Kepler erred against this rule in his -attempts at obtaining physical laws of the system; for -the facts which he took were the <em>velocities</em>, not the -<em>changes of velocity</em>, which are really the mechanical -facts. Again, there has been a transgression of this -Rule committed by all chemical philosophers who have -attempted to assign the relative position of the elementary -particles of bodies in their component molecules. For their -purpose has been to discover the -<em>relations</em> of the particles in <em>space</em>; and yet they have -neglected the only facts in the constitution of bodies -which have a reference to space—namely, <em>crystalline -form</em>, and <em>optical properties</em>. No progress can be made -in the theory of the elementary structure of bodies, <span class="pagenum" id="page194">194</span> -without making these classes of facts the main basis of -our speculations.</p> -<p id="b3c5a10">10. The only other Rule which I have to offer on -this subject, is that which I have already given:—<em>the -Idea must be tested by the facts</em>. It must be tried by -applying to the facts the conceptions which are derived -from the idea, and not accepted till some of these succeed -in giving the law of the phenomena. The justice -of the suggestion cannot be known otherwise than by -making the trial. If we can discover a <em>true law</em> by -employing any conceptions, the idea from which these -conceptions are derived is the <em>right</em> one; nor can there -be any proof of its rightness so complete and satisfactory, -as that we are by it led to a solid and permanent -truth.</p> -<p>This, however, can hardly be termed a Rule; for -when we would know, to conjecture and to try the -truth of our conjecture by a comparison with the facts, -is the natural and obvious dictate of common sense.</p> -<p class="end">Supposing the Idea which we adopt, or which we -would try, to be now fixed upon, we still have before -us the range of many Conceptions derived from it; -many Formulæ may be devised depending on the same -Independent Variable, and we must now consider how -our selection among these is to be made.</p> -<div class="chapter"> -<p><span class="pagenum" id="page195"></span></p> -<h3 class="nobreak">CHAPTER VI.<br /><br /> -<span class="sc">General Rules for the Construction of the Conception.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XXXVIII.</p> -<p><i>The Construction of the Conception very often includes, in -a great measure, the Determination of the Magnitudes.</i></p> -<p class="center"><span class="sc">Aphorism</span> XXXIX.</p> -<p><i>When a series of</i> progressive <i>numbers is given as the -result of observation, it may generally be reduced to law by -combinations of arithmetical and geometrical progressions.</i></p> -<p class="center"><span class="sc">Aphorism</span> XL.</p> -<p><i>A true formula for a progressive series of numbers cannot -commonly be obtained from a</i> narrow range <i>of observations.</i></p> -<p class="center"><span class="sc">Aphorism</span> XLI.</p> -<p>Recurrent <i>series of numbers must, in most cases, be expressed -by circular formulæ.</i></p> -<p class="center"><span class="sc">Aphorism</span> XLII.</p> -<p><i>The true construction of the conception is frequently suggested -by some hypothesis; and in these cases, the hypothesis -may be useful, though containing superfluous parts.</i></p> -<p class="noind" id="b3c6a1"> -<span class="dropcap"><span class="dsmall">1.</span> I</span>N -speaking of the discovery of laws of nature, -those which depend upon <em>quantity</em>, as number, -space, and the like, are most prominent and most easily -conceived, and therefore in speaking of such researches, -we shall often use language which applies peculiarly to <span class="pagenum" id="page196">196</span> -the cases in which quantities numerically measurable -are concerned, leaving it for a subsequent task to extend -our principles to ideas of other kinds.</p> -<p>Hence we may at present consider the Construction -of a Conception which shall include and connect the -facts, as being the construction of a Mathematical Formula, -coinciding with the numerical expression of the -facts; and we have to consider how this process can be -facilitated, it being supposed that we have already before -us the numerical measures given by observation.</p> -<p id="b3c6a2">2. We may remark, however, that the construction -of the right Formula for any such case, and the determination -of the Coefficients of such formula, which we -have spoken of as two separate steps, are in practice -almost necessarily simultaneous; for the near coincidence -of the results of the theoretical rule with the -observed facts confirms at the same time the Formula -and its Coefficients. In this case also, the mode of -arriving at truth is to try various hypotheses;—to -modify the hypotheses so as to approximate to the -facts, and to multiply the facts so as to test the hypotheses.</p> -<p>The Independent Variable, and the Formula which -we would try, being once selected, mathematicians have -devised certain special and technical processes by which -the value of the coefficients may be determined. These -we shall treat of in the <a href="#page202">next</a> Chapter; but in the mean -time we may note, in a more general manner, the mode -in which, in physical researches, the proper formula -may be obtained.</p> -<p id="b3c6a3">3. A person somewhat versed in mathematics, having before -him a series of numbers, will generally be -able to devise a formula which approaches near to -those numbers. If, for instance, the series is constantly -progressive, he will be able to see whether it -more nearly resembles an arithmetical or a geometrical -progression. For example, MM. Dulong and Petit, in -their investigation of the law of cooling of bodies, -obtained the following series of measures. A thermometer, -made hot, was placed in an enclosure of which -the temperature was 0 degrees, and the rapidity of <span class="pagenum" id="page197">197</span> -cooling of the thermometer was noted for many temperatures. -It was found that</p> -<table> -<tr> -<td>For the temperature </td><td>240</td><td>the rapidity of cooling was</td><td class="chn">10·69</td></tr> -<tr><td class="ccn">〃</td><td>220</td><td class="ccn">〃</td><td class="chn">8·81</td></tr> -<tr><td class="ccn">〃</td><td>200</td><td class="ccn">〃</td><td class="chn">7·40</td></tr> -<tr><td class="ccn">〃</td><td>180</td><td class="ccn">〃</td><td class="chn">6·10</td></tr> -<tr><td class="ccn">〃</td><td>160</td><td class="ccn">〃</td><td class="chn">4·89</td></tr> -<tr><td class="ccn">〃</td><td>140</td><td class="ccn">〃</td><td class="chn">3·88</td></tr> -</table> -<p class="noind eq">and so on. Now this series of numbers manifestly increases -with greater rapidity as we proceed from the -lower to the higher parts of the scale. The numbers -do not, however, form a geometrical series, as we may -easily ascertain. But if we were to take the differences -of the successive terms we should find them to be—</p> -<p class="eq center">1·88, 1·41, 1·30, 1·21, 1·01, &c.</p> -<p class="noind eq">and these numbers are very nearly the terms of a geometric -series. For if we divide each term by the succeeding one, -we find these numbers,</p> -<p class="eq center">1·33, 1·09, 1·07, 1·20, 1·27,</p> -<p class="noind eq">in which there does not appear to be any constant tendency -to diminish or increase. And we shall find that -a geometrical series in which the ratio is 1·165, may be -made to approach very near to this series, the deviations -from it being only such as may be accounted for -by conceiving them as errours of observation. In this -manner a certain formula<a id="fnanchor26-3" href="#note26-3"><span class="fnanchor">26</span></a> -is obtained, giving results <span class="pagenum" id="page198">198</span> -which very nearly coincide with the observed facts, as -may be seen in the margin.</p> -<div class="footnote"><span class="label"><a id="note26-3" href="#fnanchor26-3">26</a> -</span> The formula is <i>v</i> = 2·037(<i>a<sup>t</sup></i> − 1) where -<i>v</i> is the velocity of cooling, <i>t</i> the -temperature of the thermometer expressed in degrees, and <i>a</i> is the -quantity, 1·0077.<br /> - The degree of coincidence is as follows:—<br /> -<table> -<tr> -<th class="small">Excess of temperature of <br />the thermometer, or<br />values of <i>t</i>.</th> -<th class="small">Observed <br />values<br />of <i>v</i>.</th> -<th class="small">Calculated <br />values<br />of <i>v.</i></th></tr> -<tr><td class="ccn">240</td><td class="ccn">10·69</td><td class="ccn">10·68</td></tr> -<tr><td class="ccn">220</td><td class="ccn"> 8·81 </td><td class="ccn"> 8·89</td></tr> -<tr><td class="ccn">200</td><td class="ccn"> 7·40 </td><td class="ccn"> 7·34</td></tr> -<tr><td class="ccn">180</td><td class="ccn"> 6·10</td><td class="ccn"> 6·03</td></tr> -<tr><td class="ccn">160</td><td class="ccn"> 4·89 </td><td class="ccn"> 4·87</td></tr> -<tr><td class="ccn">140</td><td class="ccn"> 3·88</td><td class="ccn"> 3·89</td></tr> -<tr><td class="ccn">120</td><td class="ccn"> 3·02</td><td class="ccn"> 3·05</td></tr> -<tr><td class="ccn">100</td><td class="ccn"> 2·30 </td><td class="ccn"> 2·33</td></tr> -<tr><td class="ccn"> 80</td><td class="ccn"> 1·74 </td><td class="ccn"> 1·72</td></tr> -</table> -</div> -<p>The physical law expressed by the formula just -spoken of is this:—that when a body is cooling in an -empty inclosure which is kept at a constant temperature, -the quickness of the cooling, for excesses of temperature -in arithmetical progression, increases as the -terms of a geometrical progression, diminished by a -constant number.</p> -<p id="b3c6a4">4. In the actual investigation of Dulong and Petit, -however, the formula was not obtained in precisely the -manner just described. For the quickness of cooling -depends upon two elements, the temperature of the hot -body and the temperature of the inclosure; not merely -upon the <em>excess</em> of one of these over the other. And -it was found most convenient, first, to make such experiments -as should exhibit the dependence of the velocity of cooling -upon the temperature of the enclosure; -which dependence is contained in the following law:—The -quickness of cooling of a thermometer in vacuo -for a constant excess of temperature, increases in geometric -progression, when the temperature of the inclosure increases -in arithmetic progression. From this -law the preceding one follows by necessary -consequence<a id="fnanchor27-3" href="#note27-3"><span class="fnanchor">27</span></a>.</p> -<div class="footnote"><span class="label"><a id="note27-3" href="#fnanchor27-3">27</a> -</span> For if <i>θ</i> be the temperature of the inclosure, -and <i>t</i> the excess of temperature of the hot body, it appears, -by this law, that the radiation of heat is as <i>a<sup>θ</sup></i>. And hence -the quickness of cooling, which is as the excess of radiation, -is as <span style="white-space: nowrap;"><i>a<sup>θ + t</sup></i> − <i>a<sup>θ</sup></i></span>; -that is, as <span style="white-space: nowrap;"><i>a<sup>θ</sup></i>(<i>a<sup>t</sup></i> − 1)</span> -which agrees with the formula given in the last note.<br /> - The whole of this series of researches of Dulong and Petit is -full of the most beautiful and instructive artifices for the -construction of the proper formulæ in physical research. -</div> -<p>This example may serve to show the nature of the -artifices which may be used for the construction of -formulæ, when we have a constantly progressive series -of numbers to represent. We must not only endeavour -by trial to contrive a formula which will answer the -conditions, but we must vary our experiments so as to -determine, first one factor or portion of the formula, -and then the other; and we must use the most -<span class="pagenum" id="page199">199</span> probable -hypothesis as means of suggestion for our formulæ.</p> -<p id="b3c6a5">5. In a <em>progressive</em> series of numbers, unless the -formula which we adopt be really that which expresses -the law of nature, the deviations of the formula from -the facts will generally become enormous, when the -experiments are extended into new parts of the scale. -True formulæ for a progressive series of results can -hardly ever be obtained from a very limited range of -experiments: just as the attempt to guess the general -course of a road or a river, by knowing two or three -points of it in the neighbourhood of one another, would -generally fail. In the investigation respecting the -laws of the cooling of bodies just noticed, one great -advantage of the course pursued by the experimenters -was, that their experiments included so great a range -of temperatures. The attempts to assign the law of -elasticity of steam deduced from experiments made -with moderate temperatures, were found to be enormously -wrong, when very high temperatures were -made the subject of experiment. It is easy to see that -this must be so: an arithmetical and a geometrical -series may nearly coincide for a few terms moderately -near each other: but if we take remote corresponding -terms in the two series, one of these will be very many -times the other. And hence, from a narrow range of -experiments, we may infer one of these series when we -ought to infer the other; and thus obtain a law which -is widely erroneous.</p> -<p id="b3c6a6">6. In Astronomy, the series of observations which -we have to study are, for the most part, not progressive, -but <em>recurrent</em>. The numbers observed do not go on -constantly increasing; but after increasing up to a certain -amount they diminish; then, after a certain space, -increase again; and so on, changing constantly through -certain <em>cycles</em>. In cases in which the observed numbers -are of this kind, the formula which expresses them -must be a <em>circular function</em>, of some sort or other; -involving, for instance, sines, tangents, and other forms -of calculation, which have recurring values when the -angle on which they depend goes on constantly <span class="pagenum" id="page200">200</span> -increasing. The main business of formal astronomy consists -in resolving the celestial phenomena into a series -of <i>terms</i> of this kind, in detecting their <i>arguments</i>, and -in determining their <i>coefficients</i>.</p> -<p id="b3c6a7">7. In constructing the formulæ by which laws of -nature are expressed, although the first object is to -assign the Law of the Phenomena, philosophers have, -in almost all cases, not proceeded in a purely empirical -manner, to connect the observed numbers by some expression -of calculation, but have been guided, in the -selection of their formula, by some <em>Hypothesis</em> -respecting the mode of connexion of the facts. -Thus the formula of Dulong and Petit above given was suggested -by the Theory of Exchanges; the first attempts at the -resolution of the heavenly motions into circular functions -were clothed in the hypothesis of Epicycles. And -this was almost inevitable. ‘We must confess,’ says -Copernicus<a id="fnanchor28-3" href="#note28-3"><span class="fnanchor">28</span></a>, -‘that the celestial motions are circular, -or compounded of several circles, since their inequalities -observe a fixed law, and recur in value at certain -intervals, which could not be except they were circular: -for a circle alone can make that quantity which -has occurred recur again.’ In like manner the first -publication of the <i>Law of the Sines</i>, the true formula of -optical refraction, was accompanied by Descartes with -an hypothesis, in which an explanation of the law was -pretended. In such cases, the mere comparison of -observations may long fail in suggesting the true formulæ. -The fringes of shadows and other diffracted -colours were studied in vain by Newton, Grimaldi, -Comparetti, the elder Herschel, and Mr. Brougham, -so long as these inquirers attempted merely to trace -the laws of the facts as they appeared in themselves; -while Young, Fresnel, Fraunhofer, Schwerdt, and -others, determined these laws in the most rigorous -manner, when they applied to the observations the -Hypothesis of Interferences.</p> -<div class="footnote"><span class="label"><a id="note28-3" href="#fnanchor28-3">28</a> -</span> <i>De Rev.</i> l. i. c. iv. -</div> -<p id="b3c6a8">8. But with all the aid that Hypotheses and Calculation -can afford, the construction of true formulæ, in <span class="pagenum" id="page201">201</span> -those cardinal discoveries by which the progress of -science has mainly been caused, has been a matter of -great labour and difficulty, and of good fortune added -to sagacity. In the <i>History of Science</i>, we have seen -how long and how hard Kepler laboured, before he -converted the formula for the planetary motions, from -an <em>epicyclical</em> combination, to a simple <em>ellipse</em>. The same -philosopher, labouring with equal zeal and perseverance -to discover the formula of optical refraction, which -now appears to us so simple, was utterly foiled. Malus -sought in vain the formula determining the Angle at -which a transparent surface polarizes light: Sir D. -Brewster<a id="fnanchor29-3" href="#note29-3"><span class="fnanchor">29</span></a>, -with a happy sagacity, discovered -the formula to be simply this, that the <em>index</em> of refraction is -the <em>tangent</em> of the angle of polarization.</p> -<div class="footnote"><span class="label"><a id="note29-3" href="#fnanchor29-3">29</a> -</span> <i>Hist. Ind. Sc.</i> b. ix. c. vi. -</div> -<p class="end">Though we cannot give rules which will be of -much service when we have thus to divine the general -form of the relation by which phenomena are connected, -there are certain methods by which, in a narrower field, -our investigations may be materially promoted;—certain -special methods of obtaining laws -from Observations. Of these we shall now proceed to -treat.</p> -<div class="chapter"> -<p><span class="pagenum" id="page202"></span></p> -<h3 class="nobreak">CHAPTER VII.<br /><br /> -<span class="sc">Special Methods of Induction applicable to Quantity.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XLIII.</p> -<p><i>There are special Methods of Induction applicable to -Quantity; of which the principal are, the</i> Method of Curves, -<i>the</i> Method of Means, <i>the</i> Method of Least Squares, <i>and -the</i> Method of Residues.</p> -<p class="center"><span class="sc">Aphorism</span> XLIV.</p> -<p>The Method of Curves <i>consists in drawing a curve of -which the observed quantities are the Ordinates, the quantity -on which the change of these quantities depends being the -Abscissa. The efficacy of this Method depends upon the -faculty which the eye possesses, of readily detecting regularity -and irregularity in forms. The Method may be used -to detect the Laws which the observed quantities follow: and -also, when the Observations are inexact, it may be used to correct -these Observations, so as to obtain data more true than the -observed facts themselves.</i></p> -<p class="center"><span class="sc">Aphorism</span> XLV.</p> -<p>The Method of Means <i>gets rid of irregularities by taking -the arithmetical mean of a great number of observed quantities. -Its efficacy depends upon this; that in cases in which -observed quantities are affected by other inequalities, besides -that of which we wish to determine the law, the excesses</i> above -<i>and defects</i> below <i>the quantities which the law in question -would produce, will, in a collection of</i> many <i>observations</i>, -balance <i>each other.</i> <span class="pagenum" id="page203">203</span></p> -<p class="center"><span class="sc">Aphorism</span> XLVI.</p> -<p>The Method of Least Squares <i>is a Method of Means, in -which the mean is taken according to the condition, that the -sum of the squares of the errours of observation shall be the -least possible which the law of the facts allows. It appears, -by the Doctrine of Chances, that this is the</i> most probable -<i>mean.</i></p> -<p class="center"><span class="sc">Aphorism</span> XLVII.</p> -<p>The Method of Residues <i>consists in subtracting, from -the quantities given by Observation, the quantity given by any -Law already discovered; and then examining the remainder, -or</i> Residue, <i>in order to discover the leading Law which it -follows. When this second Law has been discovered, the -quantity given by it may be subtracted from the first Residue; -thus giving a</i> Second Residue, <i>which may be examined in -the same manner; and so on. The efficacy of this method -depends principally upon the circumstance of the Laws of -variation being successively smaller and smaller in amount -(or at least in their mean effect); so that the ulterior undiscovered -Laws do not prevent the Law in question from being</i> -prominent <i>in the observations.</i></p> -<p class="center"><span class="sc">Aphorism</span> XLVIII.</p> -<p class="end"><i>The Method of Means and the Method of Least Squares -cannot be applied without our</i> knowing the Arguments <i>of -the Inequalities which we seek. The Method of Curves and -the Method of Residues, when the Arguments of the principal -Inequalities are known, often make it easy to find the others.</i></p> -<p class="drop end"><span class="sc">IN</span> cases where the phenomena admit of numerical -measurement and expression, certain mathematical methods -may be employed to facilitate and give -accuracy to the determination of the formula by which -the observations are connected into laws. Among the -most usual and important of these Methods are the -following:— <span class="pagenum" id="page204">204</span><br /> -    I. The Method of Curves.<br /> -     II. <a href="#b3c7a7">The Method of Means</a>.<br /> -    III. <a href="#b3c7a13">The Method of Least Squares</a>.<br /> -    IV. <a href="#b3c7a15">The Method of Residues</a>.</p> -<p class="center"><span class="sc">Sect. I.</span>—<i>The Method of Curves.</i></p> -<p id="b3c7a1">1. <span class="sc">The</span> Method of Curves proceeds upon this basis; -that when one quantity undergoes a series of changes -depending on the progress of another quantity, (as, for -instance, the Deviation of the Moon from her equable -place depends upon the progress of Time,) this dependence -may be expressed by means of a <i>curve</i>. In the -language of mathematicians, the variable quantity, -whose changes we would consider, is made the <i>ordinate</i> -of the curve, and the quantity on which the -changes depend is made the <i>abscissa</i>. In this manner, -the curve will exhibit in its form a series of undulations, -rising and falling so as to correspond with the -alternate Increase and Diminution of the quantity represented, -at intervals of Space which correspond to -the intervals of Time, or other quantity by which the -changes are regulated. Thus, to take another example, -if we set up, at equal intervals, a series of ordinates -representing the Height of all the successive High Waters -brought by the tides at a given place, for a year, the -curve which connects the summits of all these ordinates -will exhibit a series of undulations, ascending -and descending once in about each Fortnight; since, in -that interval, we have, in succession, the high spring -tides and the low neap tides. The curve thus drawn -offers to the eye a picture of the order and magnitude -of the changes to which the quantity under contemplation, -(the height of high water,) is subject.</p> -<p id="b3c7a2">2. Now the peculiar facility and efficacy of the -Method of Curves depends upon this circumstance;—that -order and regularity are more readily and clearly -recognized, when thus exhibited to the eye in a picture, -than they are when presented to the mind in any other -manner. To detect the relations of Number considered -directly as Number, is not easy: and we might <span class="pagenum" id="page205">205</span> -contemplate for a long time a Table of recorded Numbers -without perceiving the order of their increase and -diminution, even if the law were moderately simple; -as any one may satisfy himself by looking at a Tide -Table. But if these Numbers are expressed by the -magnitude of <i>Lines</i>, and if these Lines are arranged in -regular order, the eye readily discovers the rule of -their changes: it follows the curve which runs along -their extremities, and takes note of the order in which -its convexities and concavities succeed each other, if -any order be readily discoverable. The separate observations -are in this manner compared and generalized -and reduced to rule by the eye alone. And the eye, -so employed, detects relations of order and succession -with a peculiar celerity and evidence. If, for example, -we thus arrive as ordinates the prices of corn in each -year for a series of years, we shall see the order, -rapidity, and amount of the increase and decrease of price, -far more clearly than in any other manner. And if -there were any recurrence of increase and decrease at -stated intervals of years, we should in this manner -perceive it. The eye, constantly active and busy, and -employed in making into shapes the hints and traces -of form which it contemplates, runs along the curve -thus offered to it; and as it travels backwards and -forwards, is ever on the watch to detect some resemblance -or contrast between one part and another. And -these resemblances and contrasts, when discovered, are -the images of Laws of Phenomena; which are made -manifest at once by this artifice, although the mind -could not easily catch the indications of their existence, -if they were not thus reflected to her in the clear -mirror of Space.</p> -<p>Thus when we have a series of good Observations, -and know the argument upon which their change of -magnitude depends, the Method of Curves enables us to -ascertain, almost at a glance, the law of the change; and -by further attention, may be made to give us a formula -with great accuracy. The Method enables us to perceive, -among our observations, an order, which without the -method, is concealed in obscurity and perplexity. <span class="pagenum" id="page206">206</span></p> -<p id="b3c7a3">3. But the Method of Curves not only enables us -to obtain laws of nature from <em>good</em> Observations, but -also, in a great degree, from observations which are -very <em>imperfect</em>. For the imperfection of observations -may in part be corrected by this consideration;—that -though they may appear irregular, the correct facts -which they imperfectly represent, are really regular. -And the Method of Curves enables us to remedy this -apparent irregularity, at least in part. For when -Observations thus imperfect are laid down as Ordinates, -and their extremities connected by a line, we obtain, -not a smooth and flowing curve, such as we should -have if the observations contained only the rigorous -results of regular laws; but a broken and irregular -line, full of sudden and capricious twistings, and -bearing on its face marks of irregularities dependent, not -upon law, but upon chance. Yet these irregular and -abrupt deviations in the curve are, in most cases, but -small in extent, when compared with those bendings -which denote the effects of regular law. And this -circumstance is one of the great grounds of advantage -in the Method of Curves. For when the observations -thus laid down present to the eye such a broken and -irregular line, we can still see, often with great ease -and certainty, what twistings of the line are probably -due to the irregular errours of observation; and can -at once reject these, by drawing a more regular curve, -cutting off all such small and irregular sinuosities, -leaving some to the right and some to the left; and -then proceeding as if this regular curve, and not the -irregular one, expressed the observations. In this -manner, we suppose the errours of observation to -balance each other; some of our corrected measures -being too great and others too small, but with no great -preponderance either way. We draw our main regular -curve, not <em>through</em> the points given by our observations, -but <em>among</em> them: drawing it, as has been said -by one of the philosophers<a id="fnanchor30-3" href="#note30-3"><span class="fnanchor">30</span></a> -who first systematically -used this method, ‘with a bold but careful hand.’ <span class="pagenum" id="page207">207</span> -The regular curve which we thus obtain, thus freed -from the casual errours of observation, is that in which -we endeavour to discover the laws of change and succession.</p> -<div class="footnote"><span class="label"><a id="note30-3" href="#fnanchor30-3">30</a> -</span> Sir J. Herschel, <i>Ast. Soc. Trans.</i> vol. v. p. 1. -</div> -<p id="b3c7a4">4. By this method, thus getting rid at once, in a -great measure, of errours of observation, we obtain -data which are <em>more true than the</em> individual <em>facts -themselves</em>. The philosopher’s business is to compare -his hypotheses with facts, as we have often said. But -if we make the comparison with separate special facts, -we are liable to be perplexed or misled, to an unknown -amount, by the errours of observation; which may -cause the hypothetical and the observed result to agree, -or to disagree, when otherwise they would not do so. -If, however, we thus take the <em>whole mass of the facts</em>, -and remove the errours of actual -observation<a id="fnanchor31-3" href="#note31-3"><span class="fnanchor">31</span></a>, by -making the curve which expresses the supposed observation -regular and smooth, we have the separate facts -corrected by their general tendency. We are put in -possession, as we have said, of something more true -than any fact by itself is.</p> -<div class="footnote"><span class="label"> -<a id="note31-3" href="#fnanchor31-3">31</a></span> <i>Ib.</i> vol. v. p. 4. -</div> -<p>One of the most admirable examples of the use of -this Method of Curves is found in Sir John Herschel’s -<i>Investigation of the Orbits of Double -Stars</i><a id="fnanchor32-3" href="#note32-3"><span class="fnanchor">32</span></a>. The author -there shows how far inferior the direct observations of -the angle of position are, to the observations corrected -by a curve in the manner above stated. ‘This curve -once drawn,’ he says, ‘must represent, it is evident, -the law of variation of the angle of position, with the -time, not only for instants intermediate between the -dates of observations, but even at the moments of -observation themselves, much better than the individual -<em>raw</em> observations can possibly (on an average) do. -It is only requisite to try a case or two, to be satisfied -that by substituting the curve for the points, we have -made a nearer approach to nature, and in a great -measure eliminated errours of observation.’ ‘In -following the graphical process,’ he adds, ‘we have a -conviction almost approaching to moral certainty that <span class="pagenum" id="page208">208</span> -we cannot be greatly misled.’ Again, having thus -corrected the raw observations, he makes another use -of the graphical method, by trying whether an ellipse -can be drawn ‘if not <em>through</em>, at least <em>among</em> the -points, so as to approach tolerably near them all; and -thus approaching to the orbit which is the subject of -investigation.’</p> -<div class="footnote"><span class="label"> -<a id="note32-3" href="#fnanchor32-3">32</a></span> <i>Ib.</i> -</div> -<p id="b3c7a5">5. The <em>Obstacles</em> which principally impede the -application of the Method of Curves are (I.) our <em>ignorance -of the arguments</em> of the changes, and (II.) the <em>complication -of several laws</em> with one another.</p> -<p>(I.) If we do not know on what quantity those -changes depend which we are studying, we may fail -entirely in detecting the law of the changes, although -we throw the observations into curves. For the true -<em>argument</em> of the change should, in fact, be made the -<em>abscissa</em> of the curve. If we were to express, by a -series of ordinates, the <em>hour</em> of high water on -successive days, we should not obtain, or should obtain very -imperfectly, the law which these times follow; for the -real argument of this change is not the <em>solar hour</em>, but -the <em>hour</em> at which the <em>moon</em> passes the meridian. But -if we are supposed to be aware that <em>this</em> is the <em>argument</em>, -(which theory suggests and trial instantly confirms) we then do -immediately obtain the primary -Rules of the Time of High Water, by throwing a series -of observations into a Curve, with the Hour of the -Moon’s Transit for the abscissa.</p> -<p>In like manner, when we have obtained the first -great or Semi-mensual Inequality of the tides, if we -endeavour to discover the laws of other Inequalities by -means of curves, we must take from theory the suggestion -that the Arguments of such inequalities will -probably be the <em>parallax</em> and the <em>declination</em> of the -moon. This suggestion again is confirmed by trial; -but if we were supposed to be entirely ignorant of the -dependence of the changes of the tide on the Distance -and Declination of the moon, the curves would exhibit -unintelligible and seemingly capricious changes. For -by the effect of the Inequality arising from the Parallax, -the convexities of the curves which belong to the <span class="pagenum" id="page209">209</span> -spring tides, are in some years made alternately greater -and less all the year through; while in other years -they are made all nearly equal. This difference does -not betray its origin, till we refer it to the Parallax; -and the same difficulty in proceeding would arise if we -were ignorant that the moon’s Declination is one of the -Arguments of tidal changes.</p> -<p>In like manner, if we try to reduce to law any meteorological -changes, those of the Height of the Barometer for instance, -we find that we can make little -progress in the investigation, precisely because we do -not know the Argument on which these changes depend. -That there is a certain regular <em>diurnal</em> change -of small amount, we know; but when we have abstracted -this Inequality, (of which the Argument is the <em>time of -day</em>,) we find far greater Changes left behind, from day -to day and from hour to hour; and we express these -in curves, but we cannot reduce them to Rule, because -we cannot discover on what numerical quantity they -depend. The assiduous study of barometrical observations, -thrown into curves, may perhaps hereafter point -out to us what are the relations of time and space by -which these variations are determined; but in the -mean time, this subject exemplifies to us our remark, -that the method of curves is of comparatively small -use, so long as we are in ignorance of the real -Arguments of the Inequalities.</p> -<p id="b3c7a6">6. (II.) In the next place, I remark that a difficulty -is thrown in the way of the Method of Curves by -<i>the Combination of several laws</i> one with another. It -will readily be seen that such a cause will produce a -complexity in the curves which exhibit the succession -of facts. If, for example, we take the case of the Tides, -the Height of high water increases and diminishes with -the Approach of the sun to, and its Recess from, the -syzygies of the moon. Again, this Height increases -and diminishes as the moon’s Parallax increases and -diminishes; and again, the Height diminishes when -the Declination increases, and <i>vice versa</i>; and all these -Arguments of change, the Distance from Syzygy, the -Parallax, the Declination, complete their circuit and <span class="pagenum" id="page210">210</span> -return into themselves in different periods. Hence -the curve which represents the Height of high water -has not any periodical interval in which it completes -its changes and commences a new cycle. The sinuosity -which would arise from each Inequality separately -considered, interferes with, disguises, and conceals the -others; and when we first cast our eyes on the curve -of observation, it is very far from offering any obvious -regularity in its form. And it is to be observed that -we have not yet enumerated <em>all</em> the elements of this -complexity: for there are changes of the tide depending -upon the Parallax and Declination of the Sun as -well as of the Moon. Again; besides these changes, of -which the Arguments are obvious, there are others, as -those depending upon the Barometer and the Wind, -which follow no known regular law, and which constantly -affect and disturb the results produced by other -laws.</p> -<p class="end">In the Tides, and in like manner in the motions of -the Moon, we have very eminent examples of the way -in which the discovery of laws may be rendered difficult -by the number of laws which operate to affect the -same quantity. In such cases, the Inequalities are -generally picked out in succession, nearly in the order -of their magnitudes. In this way there were successively -collected, from the study of the Moon’s motions -by a series of astronomers, those Inequalities which we -term the <i>Equation of the Center</i>, the <i>Evection</i>, the -<i>Variation</i>, and the <i>Annual Equation</i>. -These Inequalities were not, in fact, obtained by the application of -the Method of Curves; but the Method of Curves -might have been applied to such a case with great advantage. -The Method has been applied with great -industry and with remarkable success to the investigation -of the laws of the Tides; and by the use of it, -a series of Inequalities both of the Times and of the -Heights of high water has been detected, which explain -all the main features of the observed facts. <span class="pagenum" id="page211">211</span></p> -<p class="center" id="b3c7a7"><span class="sc">Sect.</span> II.—<i>The Method of Means.</i></p> -<p>7. The Method of Curves, as we have endeavoured -to explain above, frees us from the casual and extraneous -irregularities which arise from the imperfection -of observation; and thus lays bare the results of the -laws which really operate, and enables us to proceed in -search of those laws. But the Method of Curves is -not the only one which effects such a purpose. The -errours arising from detached observations may be got -rid of, and the additional accuracy which multiplied -observations give may be obtained, by operations upon -the observed numbers, without expressing them by -spaces. The process of curves assumes that the errours -of observation balance each other;—that the accidental -excesses and defects are nearly equal in amount;—that -the true quantities which would have been observed -if all accidental causes of irregularity were removed, -are obtained, exactly or nearly, by selecting quantities, -upon the whole, equally distant from the extremes of -great and small, which our imperfect observations offer -to us. But when, among a number of unequal quantities, -we take a quantity equally distant from the -greater and the smaller, this quantity is termed the -<i>Mean</i> of the unequal quantities. Hence the correction -of our observations by the method of curves consists in -taking the Mean of the observations.</p> -<p id="b3c7a8">8. Now without employing curves, we may proceed -arithmetically to take the Mean of all the observed -numbers of each class. Thus, if we wished to know -the Height of the spring tide at a given place, and if -we found that four different spring tides were measured -as being of the height of ten, thirteen, eleven, -and fourteen feet, we should conclude that the true -height of the tide was the <i>Mean</i> of these numbers,—namely, -twelve feet; and we should suppose that the -deviation from this height, in the individual cases, -arose from the accidents of weather, the imperfections -of observation, or the operation of other laws, besides -the alternation of spring and neap tides. <span class="pagenum" id="page212">212</span></p> -<p>This process of finding the Mean of an assemblage of -observed numbers is much practised in discovering, -and still more in confirming and correcting, laws of -phenomena. We shall notice a few of its peculiarities.</p> -<p id="b3c7a9">9. The Method of Means requires a knowledge of -the <em>Argument</em> of the changes which we would study; -for the numbers must be arranged in certain Classes, -before we find the Mean of each Class; and the principle -on which this arrangement depends is the Argument. This -knowledge of the Argument is more indispensably necessary -in the Method of Means than in -the Method of Curves; for when Curves are drawn, the -eye often spontaneously detects the law of recurrence in -their sinuosities; but when we have collections of -Numbers, we must divide them into classes by a selection -of our own. Thus, in order to discover the law -which the heights of the tide follow, in the progress -from spring to neap, we arrange the observed tides -according to the <em>day of the moon’s age</em>; and we then -take the mean of all those which thus happen at the -<em>same period</em> of the Moon’s Revolution. In this manner -we obtain the law which we seek; and the process is -very nearly the same in all other applications of this -Method of Means. In all cases, we begin by assuming -the Classes of measures which we wish to compare, the -Law which we could confirm or correct, the Formula -of which we would determine the coefficients.</p> -<p id="b3c7a10">10. The Argument being thus assumed, the Method -of Means is very efficacious in ridding our inquiry of -errours and irregularities which would impede and perplex -it. Irregularities which are altogether accidental, -or at least accidental with reference to some law which -we have under consideration, compensate each other in -a very remarkable way, when we take the Means of -<em>many</em> observations. If we have before us a collection -of observed tides, some of them may be elevated, some -depressed by the wind, some noted too high and some -too low by the observer, some augmented and some -diminished by uncontemplated changes in the moon’s -distance or motion: but in the course of a year or two -at the longest, all these causes of irregularity balance <span class="pagenum" id="page213">213</span> -each other; and the law of succession, which runs -through the observations, comes out as precisely as if -those disturbing influences did not exist. In any particular -case, there appears to be no possible reason why -the deviation should be in one way, or of one moderate -amount, rather than another. But taking the mass of -observations together, the deviations in opposite ways -will be of equal amount, with a degree of exactness -very striking. This is found to be the case in all -inquiries where we have to deal with observed numbers -upon a large scale. In the progress of the population -of a country, for instance, what can appear more -inconstant, in detail, than the causes which produce births -and deaths? yet in each country, and even in each -province of a country, the proportions of the whole -numbers of births and deaths remain nearly constant. -What can be more seemingly beyond the reach of rule -than the occasions which produce letters that cannot -find their destination? yet it appears that the number -of ‘dead letters’ is nearly the same from year to year. -And the same is the result when the deviations arise, -not from mere accident, but from laws perfectly regular, -though not contemplated in our -investigation<a id="fnanchor33-3" href="#note33-3"><span class="fnanchor">33</span></a>. -Thus the effects of the Moon’s Parallax upon the Tides, -sometimes operating one way and sometimes another, -according to certain rules, are quite eliminated by -taking the Means of a long series of observations; the -excesses and defects neutralizing each other, so far as -concerns the effect upon any law of the tides which we -would investigate.</p> -<div class="footnote"><span class="label"><a id="note33-3" href="#fnanchor33-3">33</a> -</span> Provided the argument of the law which we -neglect have no coincidence with the argument of the law -which we would determine. -</div> -<p id="b3c7a11">11. In order to obtain very great accuracy, very -large masses of observations are often employed by -philosophers, and the accuracy of the result increases -with the multitude of observations. The immense collections -of astronomical observations which have in -this manner been employed in order to form and correct -the Tables of the celestial motions are perhaps -the most signal instances of the attempts to obtain <span class="pagenum" id="page214">214</span> -accuracy by this accumulation of observations. Delambre’s -Tables of the Sun are founded upon nearly 3000 -observations; Burg’s Tables of the Moon upon above -4000.</p> -<p>But there are other instances hardly less remarkable. -Mr. Lubbock’s first investigations of the laws of -the tides of London<a id="fnanchor34-3" href="#note34-3"><span class="fnanchor">34</span></a>, -included above 13,000 observations, -extending through nineteen years; it being considered -that this large number was necessary to remove -the effects of accidental causes<a id="fnanchor35-3" href="#note35-3"><span class="fnanchor">35</span></a>. -And the attempts -to discover the laws of change in the barometer have -led to the performance of labours of equal amount: -Laplace and Bouvard examined this question by means -of observations made at the Observatory of Paris, four -times every day for eight years.</p> -<div class="footnote"><span class="label"> -<a id="note34-3" href="#fnanchor34-3">34</a></span> <i>Phil. Trans.</i> 1831. -</div> -<div class="footnote"><span class="label"><a id="note35-3" href="#fnanchor35-3">35</a> -</span> This period of nineteen years was also selected for -a reason which is alluded to in a former <a href="#note33-3">note</a>. It was thought -that this period secured the inquirer from the errours -which might be produced by the partial coincidence of the -Arguments of different irregularities; for example, -those due to the moon’s Parallax and to the moon’s Declination. It has -since been found (<i>Phil. Tr.</i> 1838. <i>On the Determination -of the Laws of the Tides from Short Series of Observations</i>), -that with regard to Parallax at least, the Means of one year give -sufficient accuracy. -</div> -<p class="end" id="b3c7a12">12. We may remark one striking evidence of the -accuracy thus obtained by employing large masses of -observations. In this way we may often detect inequalities -much smaller than the errours by which they are -encumbered and concealed. Thus the Diurnal Oscillations -of the Barometer were discovered by the comparison of -observations of many days, classified according to the -hours of the day; and the result was a clear -and incontestable proof of the existence of such oscillations -although the differences which these oscillations -produce at different hours of the day are far smaller -than the casual changes, hitherto reduced to no law, -which go on from hour to hour and from day to day. -The effect of law, operating incessantly and steadily, -makes itself more and more felt as we give it a longer -range; while the effect of accident, followed out in the <span class="pagenum" id="page215">215</span> -same manner, is to annihilate itself, and to disappear -altogether from the result.</p> -<p class="center" id="b3c7a13"><span class="sc">Sect.</span> III.—<i>The Method of Least Squares.</i></p> -<p>13. The Method of Least Squares is in fact a -method of means, but with some peculiar characters. -Its object is to determine the <em>best Mean</em> of a number -of observed quantities; or the <em>most probable Law</em> -derived from a number of observations, of which some, -or all, are allowed to be more or less imperfect. And -the method proceeds upon this supposition;—that all -errours are not <em>equally</em> probable, but that small -errours are more probable than large ones. By reasoning -mathematically upon this ground, we find that -the best result is obtained (since we cannot obtain a -result in which the errours vanish) by making, not the -<em>Errours</em> themselves, but the <em>Sum of their Squares</em>, of -the <em>smallest</em> possible amount.</p> -<p id="b3c7a14">14. An example may illustrate this. Let a quantity which -is known to increase uniformly, (as the distance of a star -from the meridian at successive instants,) be measured at -equal intervals of time, and be -found to be successively 4, 12, 14. It is plain, upon -the face of these observations, that they are erroneous; -for they ought to form an arithmetical progression, but -they deviate widely from such a progression. But the -question then occurs, what arithmetical progression do -they <em>most probably</em> represent: for we may assume -several arithmetical progressions which more or less -approach the observed series; as for instance, these -three; 4, 9, 14; 6, 10, 14; 5, 10, 15. Now in order -to see the claims of each of these to the truth, we may -tabulate them thus.</p> -<table> -<tr> -<th><span style="font-weight: normal">Observation</span></th><th><span style="font-weight: normal"> 4, 12, 14</span></th><th class="small"> Errours</th> -<th class="small"> Sums of<br /> Errours</th><th class="small"> Sums of Squares<br />  of Errours</th> -</tr> -<tr><td class="ccn">Series (1)</td><td> 4,  9, 14 </td><td>  0, 3, 0 </td><td class="ccn"> 3</td><td class="ccn"> 9</td></tr> -<tr><td class="ccn"> 〃  (2)</td><td> 6, 10, 14 </td><td>  2, 2, 0 </td><td class="ccn">4</td><td class="ccn"> 8</td></tr> -<tr><td class="ccn"> 〃  (3)</td><td> 5, 10, 15 </td><td>  1, 2, 1 </td><td class="ccn">4 </td><td class="ccn">6</td></tr> -</table> -<p class="noind eq">Here, although the first series gives the sum of the <span class="pagenum" id="page216">216</span> -errours less than the others, the third series gives the -sum of the squares of the errours least; and is therefore, -by the proposition on which this Method depends, -the <em>most probable</em> series of the three.</p> -<p class="end">This Method, in more extensive and complex cases, -is a great aid to the calculator in his inferences from -facts, and removes much that is arbitrary in the Method -of Means.</p> -<p class="center" id="b3c7a15"><span class="sc">Sect.</span> IV.—<i>The Method of Residues.</i></p> -<p>15. By either of the preceding Methods we obtain, -from observed facts, such Laws as readily offer themselves; -and by the Laws thus discovered, the most prominent -changes of the observed quantities are accounted -for. But in many cases we have, as we have noticed -already, <em>several</em> Laws of nature operating at the same -time, and combining their influences to modify those -quantities which are the subjects of observation. In -these cases we may, by successive applications of the -Methods already pointed out, detect such Laws one -after another: but this successive process, though only -a repetition of what we have already described, offers -some peculiar features which make it convenient to -consider it in a separate Section, as the Method of -Residues.</p> -<p id="b3c7a16">16. When we have, in a series of changes of -a variable quantity, discovered <em>one</em> Law which the -changes follow, detected its Argument, and determined -its Magnitude, so as to explain most clearly the course -of observed facts, we may still find that the observed -changes are not fully accounted for. When we compare -the results of our Law with the observations, -there may be a difference, or as we may term it, a -<i>Residue</i>, still unexplained. But this Residue being -thus detached from the rest, may be examined and -scrutinized in the same manner as the whole observed -quantity was treated at first: and we may in this way -detect in <em>it</em> also a Law of change. If we can do this, -we must accommodate this new found Law as nearly -as possible to the Residue to which it belongs; and <span class="pagenum" id="page217">217</span> -this being done, the difference of our Rule and of the -Residue itself, forms a <i>Second Residue</i>. This Second -Residue we may again bring under our consideration; -and may perhaps in <em>it</em> also discover some Law of change -by which its alterations may be in some measure accounted for. -If this can be done, so as to account for -a large portion of this Residue, the remaining unexplained part -forms a <i>Third Residue</i>; and so on.</p> -<p id="b3c7a17">17. This course has really been followed in various -inquiries, especially in those of Astronomy and Tidology. -The <i>Equation of the Center</i>, for the Moon, was -obtained out of the <i>Residue</i> of the Longitude, which -remained when the <i>Mean Anomaly</i> was taken away. -This Equation being applied and disposed of, the <i>Second -Residue</i> thus obtained, gave to Ptolemy the <i>Evection</i>. -The <i>Third Residue</i>, left by the Equation of the Center -and the Evection, supplied to Tycho the <i>Variation</i> -and the <i>Annual Equation</i>. And the Residue, remaining -from these, has been exhausted by other Equations, -of various arguments, suggested by theory or by observation. -In this case, the successive generations of -astronomers have gone on, each in its turn executing -some step in this Method of Residues. In the examination -of the Tides, on the other hand, this method -has been applied systematically and at once. The -observations readily gave the <i>Semimensual Inequality</i>; -the <i>Residue</i> of this supplied the corrections due to the -Moon’s <i>Parallax</i> and <i>Declination</i>; and when these -were determined, the <i>remaining Residue</i> was explored -for the law of the Solar Correction.</p> -<p id="b3c7a18">18. In a certain degree, the Method of Residues and -the Method of Means are <em>opposite</em> to each other. For -the Method of Residues extricates Laws from their -combination, <em>bringing them into view in succession</em>; -while the Method of Means discovers each Law, not by -bringing the others into view, but by <em>destroying their -effect</em> through an accumulation of observations. By -the Method of Residues we should <em>first</em> extract the -Law of the Parallax Correction of the Tides, and <em>then</em>, -from the Residue left by this, obtain the Declination -Correction. But we might at once employ the Method <span class="pagenum" id="page218">218</span> -of Means, and put together all the cases in which the -Declination was the same; not allowing for the Parallax -in each case, but taking for granted that the -Parallaxes belonging to the same Declination would -neutralize each other; as many falling above as below -the mean Parallax. In cases like this, where the -Method of Means is not impeded by a partial coincidence -of the Arguments of different unknown Inequalities, -it may be employed with almost as much success -as the Method of Residues. But still, when the Arguments -of the Laws are clearly known, as in this instance, -the Method of Residues is more clear and -direct, and is the rather to be recommended.</p> -<p id="b3c7a19">19. If for example, we wish to learn whether the -Height of the Barometer exerts any sensible influence -on the Height of the Sea’s Surface, it would appear -that the most satisfactory mode of proceeding, must be -to subtract, in the first place, what we know to be the -effects of the Moon’s Age, Parallax and Declination, -and other ascertained causes of change; and to search -in the <em>unexplained Residue</em> for the effects of -barometrical pressure. The contrary course has, however, -been adopted, and the effect of the Barometer on the -ocean has been investigated by the direct application -of the Method of Means, classing the observed heights -of the water according to the corresponding heights of -the Barometer without any previous reduction. In -this manner, the suspicion that the tide of the sea is -affected by the pressure of the atmosphere, has been -confirmed. This investigation must be looked upon -as a remarkable instance of the efficacy of the Method -of Means, since the amount of the barometrical effect -is much smaller than the other changes from among -which it was by this process extricated. But an -application of the Method of Residues would still -be desirable on a subject of such extent and difficulty.</p> -<p id="b3c7a20">20. Sir John Herschel, in his <i>Discourse on the -Study of Natural Philosophy</i> (Articles 158–161), has -pointed out the mode of making discoveries by studying -Residual Phenomena; and has given several illustrations -of the process. In some of these, he has also <span class="pagenum" id="page219">219</span> -considered this method in a wider sense than we have -done; treating it as not applicable to quantity only, -but to properties and relations of different kinds.</p> -<p class="end">We likewise shall proceed to offer a few remarks on -Methods of Induction applicable to other relations than -those of quantity.</p> -<div class="chapter"> -<p><span class="pagenum" id="page220"></span></p> -<h3 class="nobreak">CHAPTER VIII.<br /><br /> -<span class="sc">Methods of Induction depending on Resemblance.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> XLIX.</p> -<p>The Law of Continuity <i>is this:—that a quantity cannot -pass from one amount to another by any change of conditions, -without passing through all intermediate magnitudes -according to the intermediate conditions. This Law may -often be employed to disprove distinctions which have no real -foundation.</i></p> -<p class="center"><span class="sc">Aphorism</span> L.</p> -<p>The Method of Gradation <i>consists in taking a number of -stages of a property in question, intermediate between two -extreme cases which appear to be different. This Method is -employed to determine whether the extreme cases are really -distinct or not.</i></p> -<p class="center"><span class="sc">Aphorism</span> LI.</p> -<p><i>The Method of Gradation, applied to decide the question, -whether the existing</i> geological <i>phenomena arise from existing -causes, leads to this result:—That the phenomena do appear -to arise from Existing Causes, but that the action of existing -causes may, in past times, have transgressed, to any extent, -their</i> recorded <i>limits of intensity.</i></p> -<p class="center"><span class="sc">Aphorism</span> LII.</p> -<p class="end">The Method of Natural Classification <i>consists in classing -cases, not according to any</i> assumed <i>Definition, but according -to the connexion of the facts themselves, so as to make them -the means of asserting general truths.</i> <span class="pagenum" id="page221">221</span></p> -<p class="center"><span class="sc">Sect.</span> I.—<i>The Law of Continuity.</i></p> -<p class="noind" id="b3c8a1"> -<span class="dropcap"><span class="dsmall">1.</span> T</span>HE -Law of Continuity is applicable to quantity -primarily, and therefore might be associated -with the methods treated of in the last chapter: but -inasmuch as its inferences are made by a transition from -one degree to another among contiguous cases, it will -be found to belong more properly to the Methods of -Induction of which we have now to speak.</p> -<p>The <i>Law of Continuity</i> consists in this proposition,—That -a quantity cannot pass from one amount to -another by any change of conditions, without passing -through all intermediate degrees of magnitude according -to the intermediate conditions. And this law may -often be employed to correct inaccurate inductions, -and to reject distinctions which have no real foundation -in nature. For example, the Aristotelians made -a distinction between motions according to nature, (as -that of a body falling vertically downwards,) and motions -contrary to nature, (as that of a body moving -along a horizontal plane:) the former, they held, became -naturally quicker and quicker, the latter naturally -slower and slower. But to this it might be replied, -that a horizontal line may pass, by gradual motion, -through various inclined positions, to a vertical -position: and thus the retarded motion may pass into the -accelerated; and hence there must be some inclined -plane on which the motion downwards is naturally -uniform: which is false, and therefore the distinction -of such kinds of motion is unfounded. Again, the -proof of the First Law of Motion depends upon the -Law of Continuity: for since, by diminishing the -resistance to a body moving on a horizontal plane, we -diminish the retardation, and this without limit, the -law of continuity will bring us at the same time to -the case of no resistance and to the case of no retardation.</p> -<p id="b3c8a2">2. The Law of Continuity is asserted by Galileo -in a particular application; and the assertion which it <span class="pagenum" id="page222">222</span> -suggests is by him referred to -Plato;—namely<a id="fnanchor36-3" href="#note36-3"><span class="fnanchor">36</span></a> that a -moveable body cannot pass from rest to a determinate -degree of velocity without passing through all smaller -degrees of velocity. This law, however, was first asserted -in a more general and abstract form by -Leibnitz<a id="fnanchor37-3" href="#note37-3"><span class="fnanchor">37</span></a>: -and was employed by him to show that the laws -of motion propounded by Descartes must be false. The -Third Cartesian Law of Motion was -this<a id="fnanchor38-3" href="#note38-3"><span class="fnanchor">38</span></a>: that when -one moving body meets another, if the first body have -a less momentum than the second, it will be reflected -with its whole motion: but if the first have a greater -momentum than the second, it will lose a part of its -motion, which it will transfer to the second. Now -each of these cases leads, by the Law of Continuity, to -the case in which the two bodies have <em>equal</em> momentums: -but in this case, by the first part of the law the -body would <em>retain all</em> its motion; and by the second -part of the law it would <em>lose</em> a portion of it: hence the -Cartesian Law is false.</p> -<div class="footnote"><span class="label"><a id="note36-3" href="#fnanchor36-3">36</a> -</span> <i>Dialog.</i> iii. 150. iv. 32. -</div> -<div class="footnote"><span class="label"><a id="note37-3" href="#fnanchor37-3">37</a> -</span> <i>Opera</i>, i. 366. -</div> -<div class="footnote"><span class="label"><a id="note38-3" href="#fnanchor38-3">38</a> -</span> Cartes, <i>Prin.</i> p. 35. -</div> -<p id="b3c8a3">3. I shall take another example of the application -of this Law from Professor Playfair’s Dissertation on -the History of Mathematical and Physical -Science<a id="fnanchor39-3" href="#note39-3"><span class="fnanchor">39</span></a>. -‘The Academy of Sciences at Paris having (in 1724) -proposed, as a Prize Question, the Investigation of the -Laws of the Communication of Motion, John Bernoulli -presented an Essay on the subject very ingenious and -profound; in which, however, he denied the existence -of hard bodies, because in the collision of such bodies, -a finite change of motion must take place in an instant: -an event which, on the principle just explained, he -maintained to be impossible.’ And this reasoning -was justifiable: for we can form a <em>continuous</em> -transition from cases in which the impact manifestly -occupies a finite time, (as when we strike a large soft -body) to cases in which it is apparently instantaneous. -Maclaurin and others are disposed, in order to avoid -the conclusion of Bernoulli, to reject the Law of <span class="pagenum" id="page223">223</span> -Continuity. This, however, would not only be, as Playfair -says, to deprive ourselves of an auxiliary, commonly -useful though sometimes deceptive; but what is much -worse, to acquiesce in false propositions, from the want -of clear and patient thinking. For the Law of Continuity, -when rightly interpreted, is <em>never</em> violated in -actual fact. There are not really any such bodies as -have been termed <i>perfectly hard</i>: and if we approach -towards such cases, we must learn the laws of motion -which rule them by attending to the Law of Continuity, -not by rejecting it.</p> -<div class="footnote"><span class="label"><a id="note39-3" href="#fnanchor39-3">39</a> -</span> In the <i>Encyc. Brit.</i> p. 537. -</div> -<p id="b3c8a4">4. Newton used the Law of Continuity to suggest, -but not to prove, the doctrine of universal gravitation. -Let, he said, a terrestrial body be carried as high as -the moon: will it not still fall to the earth? and does -not the moon fall by the same force<a id="fnanchor40-3" href="#note40-3"><span class="fnanchor">40</span></a>? -Again: if any -one says that there is a material ether which does not -gravitate<a id="fnanchor41-3" href="#note41-3"><span class="fnanchor">41</span></a>, -this kind of matter, by condensation, may -be gradually transmuted to the density of the most -intensely gravitating bodies: and these gravitating -bodies, by taking the internal texture of the condensed -ether, may cease to gravitate; and thus the weight of -bodies depends, not on their quantity of matter, but -on their texture; which doctrine Newton conceived he -had disproved by experiment.</p> -<div class="footnote"><span class="label"><a id="note40-3" href="#fnanchor40-3">40</a> -</span> <i>Principia</i>, lib. iii. prop. 6. -</div> -<div class="footnote"><span class="label"><a id="note41-3" href="#fnanchor41-3">41</a> -</span> <i>Ib.</i> cor. 2. -</div> -<p id="b3c8a5">5. The evidence of the Law of Continuity resides -in the universality of those Ideas, which enter into -our apprehension of Laws of Nature. When, of two -quantities, one depends upon the other, the Law of -Continuity necessarily governs this dependence. Every -philosopher has the power of applying this law, in -proportion as he has the faculty of apprehending the Ideas -which he employs in his induction, with the same -clearness and steadiness which belong to the fundamental -ideas of Quantity, Space and Number. To those -who possess this faculty, the Law is a Rule of very wide -and decisive application. Its use, as has appeared in the -above examples, is seen rather in the disproof of erroneous -views, and in the correction of false propositions, <span class="pagenum" id="page224">224</span> -than in the invention of new truths. It is a test of -truth, rather than an instrument of discovery.</p> -<p class="end">Methods, however, approaching very near to the -Law of Continuity may be employed as positive means -of obtaining new truths; and these I shall now describe.</p> -<p class="center"><span class="sc">Sect.</span> II.—<i>The Method of Gradation.</i></p> -<p id="b3c8a6">6. To gather together the cases which resemble -each other, and to separate those which are essentially -distinct, has often been described as the main business -of science; and may, in a certain loose and vague -manner of speaking, pass for a description of some of -the leading procedures in the acquirement of knowledge. -The selection of instances which agree, and of -instances which differ, in some prominent point or -property, are important steps in the formation of -science. But when classes of things and properties -have been established in virtue of such comparisons, it -may still be doubtful whether these classes are separated -by distinctions of opposites, or by differences of -degree. And to settle such questions, the <i>Method of -Gradation</i> is employed; which consists in taking -intermediate stages of the properties in question, so as to -ascertain by experiment whether, in the transition -from one class to another, we have to leap over a -manifest gap, or to follow a continuous road.</p> -<p id="b3c8a7">7. Thus for instance, one of the early <i>Divisions</i> -established by electrical philosophers was that of <i>Electrics</i> -and <i>Conductors</i>. But this division Dr. Faraday -has overturned as an essential opposition. He -takes<a id="fnanchor42-3" href="#note42-3"><span class="fnanchor">42</span></a> a -<i>Gradation</i> which carries him from Conductors to -Non-conductors. Sulphur, or Lac, he says, are held to be -non-conductors, but are not rigorously so. Spermaceti -is a bad conductor: ice or water better than spermaceti: -metals so much better that they are put in a -different class. But even in metals the transit of the -electricity is not instantaneous: we have in them proof -of a retardation of the electric current: ‘and what <span class="pagenum" id="page225">225</span> -reason,” Mr. Faraday asks, “why this retardation -should not be of the same kind as that in spermaceti, -or in lac, or sulphur? But as, in them, retardation is -insulation, [and insulation is -induction<a id="fnanchor43-3" href="#note43-3"><span class="fnanchor">43</span></a>] why should -we refuse the same relation to the same exhibitions of -force in the metals?”</p> -<div class="footnote"><span class="label"><a id="note42-3" href="#fnanchor42-3">42</a> -</span> <i>Researches</i>, 12th series, art. 1328. -</div> -<div class="footnote"><span class="label"><a id="note43-3" href="#fnanchor43-3">43</a> -</span> These words refer to another proposition, -also established by the Method of Gradation. -</div> -<p>The process employed by the same sagacious philosopher -to show the <em>identity</em> of Voltaic and Franklinic -electricity, is another example of the same kind<a id="fnanchor44-3" href="#note44-3"><span class="fnanchor">44</span></a>. -Machine [Franklinic] electricity was made to exhibit the -same phenomena as Voltaic electricity, by causing the -discharge to pass through a bad conductor, into a very -extensive discharging train: and thus it was clearly -shown that Franklinic electricity, not so conducted, -differs from the other kinds, only in being in a state -of successive tension and explosion instead of a state -of continued current.</p> -<div class="footnote"><span class="label"><a id="note44-3" href="#fnanchor44-3">44</a> -</span> <i>Hist. Ind. Sc.</i> b. xiv. c. ix. sect. 2. -</div> -<p>Again; to show that the decomposition of bodies in -the Voltaic circuit was not due to the <em>Attraction</em> of the -Poles<a id="fnanchor45-3" href="#note45-3"><span class="fnanchor">45</span></a>, -Mr. Faraday devised a beautiful series of -experiments, in which these supposed <em>Poles</em> were made to -assume all possible electrical conditions:—in some cases -the decomposition took place against air, which according -to common language is not a conductor, nor is decomposed;—in -others, against the metallic poles, which -are excellent conductors but undecomposable;—and so -on: and hence he infers that the decomposition cannot -justly be considered as due to the Attraction, or Attractive -Powers, of the Poles.</p> -<div class="footnote"><span class="label"><a id="note45-3" href="#fnanchor45-3">45</a> -</span> <i>Ibid. Researches</i>, art. 497. -</div> -<p id="b3c8a8">8. The reader of the <i>Novum Organon</i> may perhaps, -in looking at such examples of the Rule, be reminded -of some of Bacon’s Classes of Instances, as his <i>instantiæ -absentiæ in proximo</i>, and his <i>instantiæ migrantes</i>. -But we may remark that Instances classed -and treated as Bacon recommends in those parts of -his work, could hardly lead to scientific truth. His <span class="pagenum" id="page226">226</span> -processes are vitiated by his proposing to himself the -<em>form</em> or <em>cause</em> of the property before him, as the object -of his inquiry; instead of being content to obtain, in -the first place, the <em>law of phenomena</em>. Thus his -example<a id="fnanchor46-3" href="#note46-3"><span class="fnanchor">46</span></a> -of a Migrating Instance is thus given. “Let -the <em>Nature inquired into</em> be that of Whiteness; -an Instance Migrating to the production of this property is -glass, first whole, and then pulverized; or plain water, -and water agitated into a foam; for glass and water -are transparent, and not white; but glass powder and -foam are white, and not transparent. Hence we must -inquire what has happened to the glass or water in -that Migration. For it is plain that the <em>Form of -Whiteness</em> is conveyed and induced by the crushing -of the glass and shaking of the water.” No real -knowledge has resulted from this line of reasoning:—from -taking the Natures and Forms of things and of -their qualities for the primary subject of our researches.</p> -<div class="footnote"><span class="label"><a id="note46-3" href="#fnanchor46-3">46</a> -</span> <i>Nov. Org.</i> lib. ii. Aph. 28. -</div> -<p id="b3c8a9">9. We may easily give examples from other subjects in -which the Method of Gradation has been used -to establish, or to endeavour to establish, very extensive -propositions. Thus Laplace’s Nebular Hypothesis,—that -systems like our solar system are formed by -gradual condensation from diffused masses, such as the -nebulæ among the stars,—is founded by him upon an -application of this Method of Gradation. We see, he -conceives, among these nebulæ, instances of all degrees -of condensation, from the most loosely diffused fluid, -to that separation and solidification of parts by which -suns, and satellites, and planets are formed: and thus -we have before us instances of systems in all their -stages; as in a forest we see trees in every period of -growth. How far the examples in this case satisfy the -demands of the Method of Gradation, it remains for -astronomers and philosophers to examine.</p> -<p>Again; this method was used with great success by -Macculloch and others to refute the opinion, put in -currency by the Wernerian school of geologists, that <span class="pagenum" id="page227">227</span> -the rocks called <i>trap rocks</i> must be classed with those -to which a <em>sedimentary</em> origin is ascribed. For it was -shown that a gradual <em>transition</em> might be traced from -those examples in which trap rocks most resembled -stratified rocks, to the lavas which have been recently -ejected from volcanoes: and that it was impossible to -assign a different origin to one portion, and to the -other, of this kind of mineral masses; and as the -volcanic rocks were certainly not sedimentary, it followed, -that the trap rocks were not of that nature.</p> -<p>Again; we have an attempt of a still larger kind -made by Sir C. Lyell, to apply this Method of Gradation -so as to disprove all distinction between the causes by -which geological phenomena have been produced, and -the causes which are now acting at the earth’s surface. -He has collected a very remarkable series of changes -which have taken place, and are still taking place, by -the action of water, volcanoes, earthquakes, and other -terrestrial operations; and he conceives he has shown -in these a <em>gradation</em> which leads, with no wide chasm -or violent leap, to the state of things of which geological -researches have supplied the evidence.</p> -<p id="b3c8a10">10. Of the value of this Method in geological speculations, -no doubt can be entertained. Yet it must still -require a grave and profound consideration, in so vast -an application of the Method as that attempted by -Sir C. Lyell, to determine what extent we may allow to -the steps of our <em>gradation</em>; and to decide how far the -changes which have taken place in distant parts of the -series may exceed those of which we have historical -knowledge, without ceasing to be of the <em>same kind</em>. -Those who, dwelling in a city, see, from time to time, -one house built and another pulled down, may say that -such <em>existing causes</em>, operating through past time, -sufficiently explain the existing condition of the city. Yet -we arrive at important political and historical truths, -by considering the <em>origin</em> of a city as an event of a -<em>different order</em> from those daily changes. The causes -which are now working to produce geological results, -may be supposed to have been, at some former epoch, -so far exaggerated in their operation, that the changes <span class="pagenum" id="page228">228</span> -should be paroxysms, not degrees;—that they should -violate, not continue, the gradual series. And we -have no kind of evidence whether the duration of our -historical times is sufficient to give us a just measure -of the limits of such degrees;—whether the terms -which we have under our notice enable us to ascertain -the average rate of progression.</p> -<p id="b3c8a11">11. The result of such considerations seems to be -this:—that we may apply the Method of Gradation in -the investigation of geological causes, provided we -leave the Limits of the Gradation undefined. But, -then, this is equivalent to the admission of the opposite -hypothesis: for a continuity of which the successive -intervals are not limited, is not distinguishable from -discontinuity. The geological sects of recent times -have been distinguished as <i>uniformitarians</i> and <i>catastrophists</i>: -the Method of Gradation seems to prove the -doctrine of the uniformitarians; but then, at the same -time that it does this, it breaks down the distinction -between them and the catastrophists.</p> -<p class="end">There are other exemplifications of the use of gradations -in Science which well deserve notice: but some -of them are of a kind somewhat different, and may be -considered under a separate head.</p> -<p class="center"><span class="sc">Sect.</span> III. <i>The Method of Natural Classification.</i></p> -<p id="b3c8a12">12. The Method of Natural Classification consists, as -we have seen, in grouping together objects, not according -to any selected properties, but according to their -most important resemblances; and in combining such -grouping with the assignation of certain marks of the -classes thus formed. The examples of the successful -application of this method are to be found in the -Classificatory Sciences through their whole extent; as, -for example, in framing the Genera of plants and animals. -The same method, however, may often be extended to other -sciences. Thus the classification of -Crystalline Forms, according to their Degree of Symmetry, -(which is really an important distinction,) as introduced -by Mohs and Weiss, was a great improvement <span class="pagenum" id="page229">229</span> -upon Haüy’s arbitrary division according to certain -assumed primary forms. Sir David Brewster was led -to the same distinction of crystals by the study of -their optical properties; and the scientific value of the -classification was thus strongly exhibited. Mr. Howard’s -classification of Clouds appears to be founded in -their real nature, since it enables him to express the -laws of their changes and successions. As we have -elsewhere said, the criterion of a true classification is, -that it makes general propositions possible. One of -the most prominent examples of the beneficial influence -of a right classification, is to be seen in the -impulse given to geology by the distinction of strata -according to the organic fossils which they -contain<a id="fnanchor47-3" href="#note47-3"><span class="fnanchor">47</span></a>: -which, ever since its general adoption, has been a -leading principle in the speculations of geologists.</p> -<div class="footnote"><span class="label"><a id="note47-3" href="#fnanchor47-3">47</a> -</span> <i>Hist. Ind. Sc.</i> b. xviii. c. ii. sect. 3. -</div> -<p id="b3c8a13">13. The mode in which, in this and in other cases, -the Method of Natural Classification directs the researches -of the philosopher, is this:—his arrangement -being adopted, at least as an instrument of inquiry and -trial, he follows the course of the different members of -the classification, according to the guidance which Nature -herself offers; not prescribing beforehand the -marks of each part, but distributing the facts according -to the total resemblances, or according to those -resemblances which he finds to be most important. -Thus, in tracing the course of a series of strata from -place to place, we identify each stratum, not by any -single character, but by all taken together;—texture, -colour, fossils, position, and any other circumstances -which offer themselves. And if, by this means, we -come to ambiguous cases, where different indications -appear to point different ways, we decide so as best to -preserve undamaged those general relations and truths -which constitute the value of our system. Thus -although we consider the organic fossils in each stratum -as its most important characteristic, we are not -prevented, by the disappearance of some fossils, or the -addition of others, or by the total absence of fossils, <span class="pagenum" id="page230">230</span> -from identifying strata in distant countries, if the -position and other circumstances authorize us to do so. -And by this Method of Classification, the doctrine of -<i>Geological Equivalents</i><a id="fnanchor48-3" href="#note48-3"><span class="fnanchor">48</span></a> -has been applied to a great -part of Europe.</p> -<div class="footnote"><span class="label"><a id="note48-3" href="#fnanchor48-3">48</a> -</span> <i>Hist. Ind. Sc.</i> b. xviii. c. iii. sect. 4. -</div> -<p id="b3c8a14">14. We may further observe, that the same method -of natural classification which thus enables us to -identify strata in remote situations, notwithstanding that -there may be great differences in their material and -contents, also forbids us to assume the identity of the -series of rocks which occur in different countries, when -this identity has not been verified by such a continuous -exploration of the component members of the -series. It would be in the highest degree unphilosophical -to apply the special names of the English or -German strata to the rocks of India, or America, or -even of southern Europe, till it has appeared that in -those countries the geological series of northern Europe -really exists. In each separate country, the divisions -of the formations which compose the crust of the -earth must be made out, by applying the Method of -Natural Arrangement <em>to that particular case</em>, and not -by arbitrarily extending to it the nomenclature -belonging to another case. It is only by such precautions, -that we can ever succeed in obtaining geological -propositions, at the same time true and comprehensive; or -can obtain any sound general views respecting the -physical history of the earth.</p> -<p id="b3c8a15">15. The Method of Natural Classification, which -we thus recommend, falls in with those mental habits -which we formerly described as resulting from the -study of Natural History. The method was then termed -the <i>Method of Type</i>, and was put in opposition to the -<i>Method of Definition</i>.</p> -<p>The Method of Natural Classification is directly -opposed to the process in which we assume and apply -<em>arbitrary</em> definitions; for in the former Method, we -find our classes in nature, and do not make them by -marks of our own imposition. Nor can any advantage <span class="pagenum" id="page231">231</span> -to the progress of knowledge be procured, by laying -down our characters when our arrangements are as yet -quite loose and unformed. Nothing was gained by -the attempts to <em>define</em> Metals by their weight, their -hardness, their ductility, their colour; for to all these -marks, as fast as they were proposed, exceptions were -found, among bodies which still could not be excluded -from the list of Metals. It was only when -elementary substances were divided into <em>Natural -Classes</em>, of which classes Metals were one, that a true -view of their distinctive characters was obtained. -Definitions in the outset of our examination of nature are -almost always, not only useless, but prejudicial.</p> -<p id="b3c8a16">16. When we obtain a Law of Nature by induction -from phenomena, it commonly happens, as we have -already seen, that we introduce, at the same time, a -Proposition and a Definition. In this case, the two -are correlative, each giving a real value to the other. -In such cases, also, the Definition, as well as the -Proposition, may become the basis of rigorous reasoning, -and may lead to a series of deductive truths. We have -examples of such Definitions and Propositions in the -Laws of Motion, and in many other cases.</p> -<p id="b3c8a17">17. When we have established Natural Classes of -objects, we seek for Characters of our classes; and -these Characters may, to a certain extent, be called the -<i>Definitions</i> of our classes. This is to be understood, -however, only in a limited sense: for these Definitions -are not absolute and permanent. They are liable to -be modified and superseded. If we find a case which -manifestly belongs to our Natural Class, though violating -our Definition, we do not shut out the case, but -alter our definition. Thus, when we have made it -part of our Definition of the <i>Rose</i> family, that they -have <i>alternate stipulate leaves</i>, we do not, therefore, -exclude from the family the genus <i>Lowæa</i>, which has -<em>no stipulæ</em>. In Natural Classifications, our -Definitions are to be considered as temporary and -provisional only. When Sir C. Lyell established the -distinctions of the tertiary strata, which he termed <i>Eocene</i>, -<i>Miocene</i>, and <i>Pliocene</i>, he took a numerical criterion <span class="pagenum" id="page232">232</span> -(the proportion of recent species of shells contained in -those strata) as the basis of his division. But now -that those kinds of strata have become, by their -application to a great variety of cases, a series of Natural -Classes, we must, in our researches, keep in view the -natural connexion of the formations themselves in different -places; and must by no means allow ourselves -to be governed by the numerical proportions which -were originally contemplated; or even by any amended -numerical criterion equally arbitrary; for however -amended, Definitions in natural history are never immortal. -The etymologies of <i>Pliocene</i> and <i>Miocene</i> -may, hereafter, come to have merely an historical interest; -and such a state of things will be no more inconvenient, -provided the natural connexions of each class -are retained, than it is to call a rock <i>oolite</i> or -<i>porphyry</i>, when it has no roelike structure and no fiery -spots.</p> -<p class="end">The Methods of Induction which are treated of in -this and the preceding chapter, and which are specially -applicable to causes governed by relations of Quantity -or of Resemblance, commonly lead us to <i>Laws of Phenomena</i> -only. Inductions founded upon other ideas, -those of Substance and Cause for example, appear to -conduct us somewhat further into a knowledge of the -essential nature and real connexions of things. But -before we speak of these, we shall say a few words -respecting the way in which inductive propositions, -once obtained, may be verified and carried into effect -by their application.</p> -<div class="chapter"> -<p><span class="pagenum" id="page233"></span></p> -<h3 class="nobreak">CHAPTER IX.<br /><br /> -<span class="sc">Of the Application of Inductive Truths.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> LIII.</p> -<p><i>When the theory of any subject is established, the observations -and experiments which are made in applying the -science to use and to instruction, supply a perpetual</i> verification -<i>of the theory.</i></p> -<p class="center"><span class="sc">Aphorism</span> LIV.</p> -<p><i>Such observations and experiments, when numerous and -accurate, supply also</i> corrections <i>of the</i> constants <i>involved -in the theory; and sometimes</i>, (<i>by the Method of Residues</i>,) -additions <i>to the theory.</i></p> -<p class="center"><span class="sc">Aphorism</span> LV.</p> -<p><i>It is worth considering, whether a continued and connected -system of observation and calculation, like that of -astronomy, might not be employed with advantage in improving -our knowledge of other subjects; as Tides, Currents, -Winds, Clouds, Rain, Terrestrial Magnetism, Aurora Borealis, -Composition of Crystals, and many other subjects.</i></p> -<p class="center"><span class="sc">Aphorism</span> LVI.</p> -<p><i>An</i> extension <i>of a well-established theory to the explanation -of new facts excites admiration as a discovery; but it is a -discovery of a lower order than the theory itself.</i></p> -<p class="center"><span class="sc">Aphorism</span> LVII.</p> -<p><i>The practical inventions which are most important in -Art may be either unimportant parts of Science, or results -not explained by Science.</i> <span class="pagenum" id="page234">234</span></p> -<p class="center"><span class="sc">Aphorism</span> LVIII.</p> -<p><i>In modern times, in many departments. Art is constantly -guided, governed and advanced by Science.</i></p> -<p class="center"><span class="sc">Aphorism</span> LIX.</p> -<p><i>Recently several New Arts have been invented, which may -be regarded as notable verifications of the anticipations of -material benefits to be derived to man from the progress of -Science.</i></p> -<p class="noind" id="b3c9a1"> -<span class="dropcap"><span class="dsmall">1.</span> B</span>Y the -application of inductive truths, we here -mean, according to the arrangement given in -chap. I. of this book, those steps, which in the natural -order of science, follow the discovery of each truth. -These steps are, the <em>verification</em> of the discovery by additional -experiments and reasonings, and its <em>extension</em> -to new cases, not contemplated by the original discoverer. -These processes occupy that period, which, -in the history of each great discovery, we have termed -the <i>Sequel</i> of the epoch; as the collection of facts, and -the elucidation of conceptions, form its Prelude.</p> -<p id="b3c9a2">2. It is not necessary to dwell at length on the -processes of the Verification of Discoveries. When the -Law of Nature is once stated, it is far easier to devise -and execute experiments which prove it, than it was -to discern the evidence before. The truth becomes -one of the standard doctrines of the science to which it -belongs, and is verified by all who study or who teach -the science experimentally. The leading doctrines of -Chemistry are constantly exemplified by each chemist -in his <i>Laboratory</i>; and an amount of verification is -thus obtained of which books give no adequate conception. -In Astronomy, we have a still stronger example -of the process of verifying discoveries. Ever since the -science assumed a systematic form, there have been -<i>Observatories</i>, in which the consequences of the theory -were habitually compared with the results of observation. -And to facilitate this comparison, <i>Tables</i> of -great extent have been calculated, with immense labour, -from each theory, showing the place which the <span class="pagenum" id="page235">235</span> -theory assigned to the heavenly bodies at successive -times; and thus, as it were, challenging nature to -deny the truth of the discovery. In this way, as I -have elsewhere stated, the continued prevalence of an -errour in the systematic parts of astronomy is -impossible<a id="fnanchor49-3" href="#note49-3"><span class="fnanchor">49</span></a>. -An errour, if it arise, makes its way into the -tables, into the ephemeris, into the observer’s nightly -list, or his sheet of reductions; the evidence of sense -flies in its face in a thousand Observatories; the -discrepancy is traced to its source, and soon disappears -for ever.</p> -<div class="footnote"><span class="label"><a id="note49-3" href="#fnanchor49-3">49</a> -</span> <i>Hist. Ind. Sc.</i> b. vii. c. vi. sect. 6. -</div> -<p id="b3c9a3">3. In these last expressions, we suppose the theory, -not only to be tested, but also to be <em>corrected</em> when it -is found to be imperfect. And this also is part of the -business of the observing astronomer. From his accumulated -observations, he deduces more exact values than -had previously been obtained, of the <i>Constants</i> or -<i>Coefficients</i> of these Inequalities of which the <i>Argument</i> is -already known. This he is enabled to do by the methods -explained in the <a href="#page186">fifth</a> chapter of this book; the <a href="#b3c7a7">Method -of Means</a>, and especially the <a href="#b3c7a13">Method of Least Squares</a>. -In other cases, he finds, by the <a href="#b3c7a15">Method of Residues</a>, -some new Inequality; for if no change of the Coefficients -will bring the Tables and the observation to a -coincidence, he knows that a new Term is wanting in -his formula. He obtains, as far as he can, the law of -this unknown Term; and when its existence and its -law have been fully established, there remains the -task of tracing it to its cause.</p> -<p id="b3c9a4">4. The condition of the science of Astronomy, with -regard to its security and prospect of progress, is one of -singular felicity. It is a question well worth our consideration, -as regarding the interests of science, whether, in other branches -of knowledge also, <i>a continued -and corrected system, of observation and calculation</i>, -imitating the system employed by astronomers, might -not be adopted. But the discussion of this question -would involve us in a digression too wide for the present occasion. <span class="pagenum" id="page236">236</span></p> -<p id="b3c9a5">5. There is another mode of application of true -theories after their discovery, of which we must also -speak; I mean the process of showing that facts, not -included in the original induction, and apparently of a -different kind, are explained by reasonings founded -upon the theory:—<i>extensions</i> of the theory as we may -call them. The history of physical astronomy is full -of such events. Thus after Bradley and Wargentin -had observed a certain cycle among the perturbations -of Jupiter’s satellites, Laplace explained this cycle by -the doctrine of universal -gravitation<a id="fnanchor50-3" href="#note50-3"><span class="fnanchor">50</span></a>. The long -inequality of Jupiter and Saturn, the diminution of the -obliquity of the ecliptic, the acceleration of the moon’s -mean motion, were in like manner accounted for by -Laplace. The coincidence of the nodes of the moon’s -equator with those of her orbit was proved to result -from mechanical principles by Lagrange. The motions -of the recently-discovered planets, and of comets, shown -by various mathematicians to be in exact accordance -with the theory, are Verifications and Extensions still -more obvious.</p> -<div class="footnote"><span class="label"><a id="note50-3" href="#fnanchor50-3">50</a> -</span> <i>Hist. Ind. Sc.</i> b. vii. c. iv. sect. 3. -</div> -<p id="b3c9a6">6. In many of the cases just noticed, the consistency -between the theory, and the consequences thus proved -to result from it, is so far from being evident, that the -most consummate command of all the powers and aids -of mathematical reasoning is needed, to enable the philosopher -to arrive at the result. In consequence of -this circumstance, the labours just referred to, of Laplace, -Lagrange, and others, have been the object of -very great and very just admiration. Moreover, the -necessary connexion of new facts, at first deemed inexplicable, -with principles already known to be true;—a -connexion utterly invisible at the outset, and yet at -last established with the certainty of demonstration;—strikes -us with the delight of a new discovery; and at -first sight appears no less admirable than an original -induction. Accordingly, men sometimes appear tempted -to consider Laplace and other great mathematicians as -persons of a kindred genius to Newton. We must not <span class="pagenum" id="page237">237</span> -forget, however, that there is a great and essential difference -between inductive and deductive processes of -the mind. The discovery of a <em>new</em> theory, which is -true, is a step widely distinct from any mere development -of the consequences of a theory already invented -and established.</p> -<p id="b3c9a7">7. In the other sciences also, which have been -framed by a study of natural phenomena, we may find -examples of the explanation of new phenomena by -applying the principles of the science when once -established. Thus, when the laws of the reflection -and refraction of light had been established, a new -and poignant exemplification of them was found in -the explanation of the Rainbow by the reflection and -refraction of light in the spherical drops of a shower; -and again, another, no less striking, when the intersecting -Luminous Circles and Mock Suns, which are -seen in cold seasons, were completely explained by the -hexagonal crystals of ice which float in the upper -regions of the atmosphere. The Darkness of the space -between the primary and secondary rainbow is another -appearance which optical theory completely explains. -And when we further include in our optical theory -the doctrine of interferences, we find the explanation -of other phenomena; for instance, the Supernumerary -Rainbows which accompany the primary rainbow on -its inner side, and the small Halos which often surround -the sun and moon. And when we come to -optical experiments, we find many instances in which -the doctrine of interferences and of undulations have -been applied to explain the phenomena by calculations -almost as complex as those which we have mentioned -in speaking of astronomy: with results as little foreseen -at first and as entirely satisfactory in the end. -Such are Schwerdt’s explanation of the diffracted -images of a triangular aperture by the doctrine of -interferences, and the explanation of the coloured -Lemniscates seen by polarized light in biaxal crystals, -given by Young and by Herschel: and still more -marked is another case, in which the curves are -unsymmetrical, namely, the curves seen by passing polarized <span class="pagenum" id="page238">238</span> -light through plates of quartz, which agree in a wonderful manner -with the calculations of Airy. To these -we may add the curious phenomena, and equally -curious mathematical explanation, of Conical Refraction, -as brought to view by Professor Lloyd and Sir -W. Hamilton. Indeed, the whole history both of -Physical Optics and of Physical Astronomy is a series -of <em>felicities</em> of this kind, as we have elsewhere -observed. Such applications of theory, and unforeseen -explanations of new facts by complicated trains of reasoning -necessarily flowing from the theory, are strong proof -of the truth of the theory, while it is in the course of -being established; but we are here rather speaking of -them as applications of the theory after it has been -established.</p> -<p>Those who thus apply principles already discovered -are not to be ranked in their intellectual achievements -with those who discover new principles; but still, -when such applications are masked by the complex -relations of space and number, it is impossible not to -regard with admiration the clearness and activity of -intellect which thus discerns in a remote region the -rays of a central truth already unveiled by some great -discoverer.</p> -<p id="b3c9a8">8. As examples in other fields of the application -of a scientific discovery to the explanation of natural -phenomena, we may take the identification of Lightning -with electricity by Franklin, and the explanation -of Dew by Wells. For Wells’s <i>Inquiry into the -Cause of Dew</i>, though it has sometimes been praised -as an original discovery, was, in fact, only resolving -the phenomenon into principles already discovered. -The atmologists of the last century were -aware<a id="fnanchor51-3" href="#note51-3"><span class="fnanchor">51</span></a> that -the vapour which exists in air in an invisible state -may be condensed into water by cold; and they had -noticed that there is always a certain temperature, -lower than that of the atmosphere, to which if we -depress bodies, water forms upon them in fine drops. -This temperature is the limit of that which -is <span class="pagenum" id="page239">239</span> necessary -to constitute vapour, and is hence called the <i>constituent -temperature</i>. But these principles were not -generally familiar in England till Dr. Wells introduced -them into his <i>Essay on Dew</i>, published in 1814; having -indeed been in a great measure led to them by his -own experiments and reasonings. His explanation of -Dew,—that it arises from the coldness of the bodies -on which it settles,—was established with great ingenuity; -and is a very elegant confirmation of the Theory -of Constituent Temperature.</p> -<div class="footnote"><span class="label"><a id="note51-3" href="#fnanchor51-3">51</a> -</span><i>Hist. Ind. Sc.</i> b. x. c. iii. sect. 5. -</div> -<p>9. As other examples of such explanations of new -phenomena by a theory, we may point out Ampère’s -Theory that Magnetism is transverse voltaic currents, -applied to explain the rotation of a voltaic wire round -a magnet, and of a magnet round a voltaic wire. And -again, in the same subject, when it had been proved -that electricity might be converted into magnetism, it -seemed certain that magnetism might be converted -into electricity; and accordingly Faraday found under -what conditions this may be done; though indeed -here, the theory rather suggested the experiment than -explained it when it had been independently observed. -The production of an electric spark by a magnet was -a very striking exemplification of the theory of the -identity of these different polar agencies.</p> -<p>10. In Chemistry such applications of the principles of -the science are very frequent; for it is the -chemist’s business to account for the innumerable -changes which take place in material substances by -the effects of mixture, heat, and the like. As a marked -instance of such an application of the science, we -may take the explanation of the explosive force of -gunpowder<a id="fnanchor52-3" href="#note52-3"><span class="fnanchor">52</span></a>, -from the conversion of its materials -into gases. In Mineralogy also we have to apply the <span class="pagenum" id="page240">240</span> -principles of Chemistry to the analysis of bodies: and -I may mention, as a case which at the time excited -much notice, the analysis of a mineral called Heavy -Spar. It was found that different specimens of this -mineral differed in their crystalline angles about three -degrees and a half; a difference which was at variance -with the mineralogical discovery then recently made, -of the constancy of the angle of the same substance. -Vauquelin solved this difficulty by discovering that -the crystals with the different angles were really -minerals chemically different; the one kind being sulphate -of barytes, and the other, sulphate of strontian.</p> -<div class="footnote"><span class="label"><a id="note52-3" href="#fnanchor52-3">52</a> -</span> The explanation is, that the force is due to the -sudden development of a large volume of nitrogen and carbonic -acid gases, which at the ordinary temperature of the air would -occupy a space equal to about 300 times the bulk of the powder -used, but from the intense heat developed at the moment of the -explosion, the dilatation amounts to at least 1500 times -the volume of the gunpowder employed. -</div> -<p>11. In this way a scientific theory, when once established, -is perpetually finding new applications in the -phenomena of nature; and those who make such -applications, though, as we have said, they care not to -be ranked with the great discoverers who establish -theories new and true, often receive a more prompt -and general applause than great discoverers do; because -they have not to struggle with the perplexity -and averseness which often encounter the promulgation -of new truths.</p> -<p>12. Along with the verification and extension of -scientific truths, we are naturally led to consider the -useful application of them. The example of all the -best writers who have previously treated of the philosophy -of sciences, from Bacon to Herschel, draws our -attention to those instances of the application of scientific -truths, which are subservient to the uses of -practical life; to the support, the safety, the pleasure -of man. It is well known in how large a degree -the furtherance of these objects constituted the merit -of the <i>Novum Organon</i> in the eyes of its author; -and the enthusiasm with which men regard these -visible and tangible manifestations of the power and -advantage which knowledge may bring, has gone on -increasing up to our own day. And undoubtedly such -applications of the discoveries of science to promote -the preservation, comfort, power and dignity of man, -must always be objects of great philosophical as well -as practical interest. Yet we may observe that those <span class="pagenum" id="page241">241</span> -practical inventions which are of most importance in -the Arts, have not commonly, in the past ages of the -world, been the results of theoretical knowledge, nor -have they tended very greatly to the promotion of such -knowledge. The use of bread and of wine has existed -from the first beginning of man’s social history; yet men -have not had—we may question whether they yet have—a -satisfactory theory of the constitution and fabrication -of bread and of wine. From a very early period -there have been workers in metal: yet who could tell -upon what principles depended the purifying of gold -and silver by the fire, or the difference between iron -and steel? In some cases, as in the story of the brass -produced by the Corinthian conflagration, some particular -step in art is ascribed to a special accident; but -hardly ever to the thoughtful activity of a scientific -speculator. The Dyeing of cloths, the fabrication and -colouring of earthenware and glass vessels was carried -to a very high degree of completeness; yet who had -any sound theoretical knowledge respecting these processes? -Are not all these arts still practised with -a degree of skill which we can hardly or not at all -surpass, by nations which have, properly speaking, no -science? Till lately, at least, if even now the case -be different, the operations by which man’s comforts, -luxuries, and instruments were produced, were either -mere practical processes, which the artist practises, but -which the scientist cannot account for; or, as in astronomy -and optics, they depended upon a small portion -only of the theoretical sciences, and did not tend to -illustrate, or lead to, any larger truths. Bacon mentions -as recent discoveries, which gave him courage -and hope with regard to the future progress of human -knowledge, the invention of gunpowder, glass, and -printing, the introduction of silk, and the discovery of -America. Yet which of these can be said to have been -the results of a theoretical enlargement of human -knowledge? except perhaps the discovery of the New -World, which was in some degree the result of Columbus’s -conviction of the globular form of the earth. -This, however, was not a recent, but a very ancient <span class="pagenum" id="page242">242</span> -doctrine of all sound astronomers. And which of these -discoveries has been the cause of a great enlargement -of our theoretical knowledge?—except any one claims -such a merit for the discovery of printing; in which -sense the result is brought about in a very indirect -manner, in the same way in which the progress of -freedom and of religion may be ascribed as consequences -to the same discovery. However great or -striking, then, such discoveries have been, they have -not, generally speaking, produced any marked advance -of the Inductive Sciences in the sense in which we -here speak of them. They have increased man’s -power, it may be: that is, his power of adding to his -comforts and communicating with his fellow-men. -But they have not necessarily or generally increased -his theoretical knowledge. And, therefore, with whatever -admiration we may look upon such discoveries as -these, we are not to admire them as steps in Inductive -Science.</p> -<p>And on the other hand, we are not to ask of Inductive Science, -as a necessary result of her progress, -such additions as these to man’s means of enjoyment -and action. It is said, with a feeling of triumph, that -Knowledge is Power: but in whatever sense this may -truly be said, we value Knowledge, not because it is -Power but because it is Knowledge; and we estimate -wrongly both the nature and the dignity of that kind -of science with which we are here concerned, if we -expect that every new advance in theory will forthwith -have a market value:—that science will mark -the birth of a new Truth with some new birthday -present, such as a softer stuff to wrap our limbs, a -brighter vessel to grace our table, a new mode of -communication with our friends and the world, a new -instrument for the destruction of our enemies, or a new -region which may be the source of wealth and interest.</p> -<p>13. Yet though, as we have said, many of the most -remarkable processes which we reckon as the triumphs -of Art did not result from a previous progress of Science, -we have, at many points of the history of Science, -applications of new views, to enable man to <em>do</em> -as well <span class="pagenum" id="page243">243</span> -as to <em>see</em>. When Archimedes had obtained clear views -of the theory of machines, he forthwith expressed them -in his bold practical boast; ‘Give me whereon to stand, -and I will move the earth.’ And his machines with -which he is said to have handled the Roman ships -like toys, and his burning mirrors with which he is -reported to have set them on fire, are at least possible -applications of theoretical principles. When he saw -the waters rising in the bath as his body descended, -and rushed out crying, ‘I have found the way;’ what -he had found was the solution of the practical -question of the quantity of silver mixed with the gold of -Hiero’s crown. But the mechanical inventions of Hero -of Alexandria, which moved by the force of air or of -steam, probably involved no exact theoretical notions -of the properties of air or of steam. He devised a toy -which revolved by the action of steam; but by the force -of steam exerted in issuing from an orifice, not by its -pressure or condensation. And the Romans had no arts -derived from science in addition to those which they -inherited from the Greeks. They built aqueducts, not -indeed through ignorance of the principles of hydrostatics, -as has sometimes been said; for we, who know our -hydrostatics, build aqueducts still; but their practice -exemplified only Archimedean hydrostatics. Their -clepsydras or water-clocks were adjusted by trial only. -They used arches and vaults more copiously than the -Greeks had done, but the principle of the arch appears, -by the most recent researches, to have been known to -the Greeks. Domes and groined arches, such as we have -in the Pantheon and in the Baths of Caracalla, perhaps -they invented; certainly they practised them on -a noble scale. Yet this was rather practical skill -than theoretical knowledge; and it was pursued by -their successors in the middle ages in the same manner, -as practical skill rather than theoretical knowledge. -Thus were produced flying buttresses, intersecting -pointed vaults, and the other wonders of mediæval -architecture. The engineers of the fifteenth century, -as Leonardo da Vinci, began to convert their practical -into theoretical knowledge of Mechanics; but still <span class="pagenum" id="page244">244</span> -clocks and watches, flying machines and printing -presses involved no new mechanical principle.</p> -<p>14. But from this time the advances in Science -generally produced, as their result, new inventions of -a practical kind. Thus the doctrine of the weight of -air led to such inventions as the barometer used as -a Weather-glass, the Air-pump with its train of curious -experiments, the Diving-Bell, the Balloon. The -telescope was perhaps in some degree a discovery due -to accident, but its principles had been taught by -Roger Bacon, and still more clearly by Descartes. -Newton invented a steady thermometer by attending -to steady laws of nature. And in the case of the improvements -of the steam engine made by Watt, we -have an admirable example how superior the method -of improving Art by Science is, to the blind gropings -of mere practical habit.</p> -<p>Of this truth, the history of most of the useful arts -in our time offers abundant proofs and illustrations. -All improvements and applications of the forces and -agencies which man employs for his purposes are now -commonly made, not by blind trial but with the -clearest theoretical as well as practical insight which -he can obtain, into the properties of the agents which -he employs. In this way he has constructed, (using -theory and calculation at every step of his construction,) -steam engines, steam boats, screw-propellers, -locomotive engines, railroads and bridges and structures -of all kinds. Lightning-conductors have been -improved and applied to the preservation of buildings, -and especially of ships, with admirable effect, by Sir -Wm. Snow Harris, an experimenter who has studied -with great care the theory of electricity. The measurement -of the quantity of oxygen, that is, of vital -power, in air, has been taught by Cavendish, and by -Dr Ure a skilful chemist of our time. Methods for -measuring the bleaching power of a substance have -been devised by eminent chemical philosophers, Gay -Lussac and Mr Graham. Davy used his discoveries -concerning the laws of flame in order to construct his -Safety Lamp:—his discoveries concerning the galvanic <span class="pagenum" id="page245">245</span> -battery in order to protect ships’ bottoms from corrosion. -The skilled geologist has repeatedly given to -those who were about to dig for coal where it could -have no geological place, advice which has saved them -from ruinous expence. Sir Roderick Murchison, from -geological evidence, declared the likelihood of gold -being found abundantly in Australia, many years before -the diggings began.</p> -<p>Even the subtle properties of light as shewn in the -recent discoveries of its interference and polarization, -have been applied to useful purposes. Young invented -an <i>Eriometer</i>, an instrument which should measure the -fineness of the threads of wool by the coloured fringes -which they produce; and substances which it is important -to distinguish in the manufacture of sugar, -are discriminated by their effect in rotating the plane -of polarization of light. One substance has been termed -<i>Dextrin</i>, from its impressing a right-handed rotation -on the plane of polarization.</p> -<p>And in a great number of Arts and Manufactures, -the necessity of a knowledge of theory to the right -conduct of practice is familiarly acknowledged and -assumed. In the testing and smelting of metals, in the -fabrication of soap, of candles, of sugar; in the dyeing -and printing of woollen, linen, cotton and silken stuffs; -the master manufacturer has always the scientific chemist -at his elbow;—either a ‘consulting chemist’ to -whom he may apply on a special occasion, (for such is -now a regular profession;) or a chemist who day by -day superintends, controls, and improves the processes -which his workmen daily carry on. In these cases, -though Art long preceded Science, Science now guides, -governs and advances Art.</p> -<p>15. Other Arts and manufactures which have arisen -in modern times have been new creations produced by -Science, and requiring a complete acquaintance with -scientific processes to conduct them effectually and -securely. Such are the photographic Arts, now so -various in their form; beginning with those which, -from their authors, are called Daguerrotype and Talbotype. -Such are the Arts of Electrotype modelling <span class="pagenum" id="page246">246</span> -and Electrotype plating. Such are the Arts of preparing -fulminating substances; gun-cotton; fulminate -of silver, and of mercury; and the application of those -Arts to use, in the fabrication of percussion-caps for -guns. Such is the Art of Electric Telegraphy, from its -first beginning to its last great attempt, the electric -cord which connects England and America. Such is -the Art of imitating by the chemistry of the laboratory -the vegetable chemistry of nature, and thus producing -the flavour of the pear, the apple, the pine-apple, the -melon, the quince. Such is the Art of producing in -man a temporary insensibility to pain, which was -effected first through the means of sulphuric ether by -Dr Jackson of America, and afterwards through the -use of chloroform by Dr Simpson of Edinburgh. In -these cases and many others Science has endowed -man with New Arts. And though even in these Arts, -which are thus the last results of Science, there is -much which Science cannot fully understand and explain; -still, such cases cannot but be looked upon as -notable verifications of the anticipations of those who -in former times expected from the progress of Science -a harvest of material advantages to man.</p> -<p class="end">We must now conclude our task by a few words on -the subject of inductions involving Ideas ulterior to -those already considered.</p> -<div class="chapter"> -<p><span class="pagenum" id="page247"></span></p> -<h3 class="nobreak">CHAPTER X.<br /><br /> -<span class="sc">Of the Induction of Causes.</span></h3> -</div> -<hr class="two" /> -<p class="center"><span class="sc">Aphorism</span> LX.</p> -<p><i>In the</i> Induction of Causes <i>the principal Maxim is, that -we must be careful to possess, and to apply, with perfect -clearness, the Fundamental Idea on which the Induction depends.</i></p> -<p class="center"><span class="sc">Aphorism</span> LXI.</p> -<p><i>The Induction of Substance, of Force, of Polarity, go -beyond mere laws of phenomena, and may be considered as -the Induction of Causes.</i></p> -<p class="center"><span class="sc">Aphorism</span> LXII.</p> -<p><i>The Cause of certain phenomena being inferred, we are -led to inquire into the Cause of this Cause, which inquiry -must be conducted in the same manner as the previous one; -and thus we have the Induction of Ulterior Causes.</i></p> -<p class="center"><span class="sc">Aphorism</span> LXIII.</p> -<p><i>In contemplating the series of Causes which are themselves -the effects of other causes, we are necessarily led to assume a -Supreme Cause in the Order of Causation, as we assume a -First Cause in Order of Succession.</i></p> -<p class="noind" id="b3c10a1"> -<span class="dropcap"><span class="dsmall">1.</span> W</span>E -formerly<a id="fnanchor53-3" href="#note53-3"><span class="fnanchor">53</span></a> -stated the objects of the researches -of Science to be Laws of Phenomena and -Causes; and showed the propriety and the necessity of -not resting in the former object, but extending our <span class="pagenum" id="page248">248</span> -inquiries to the latter also. Inductions, in which phenomena -are connected by relations of Space, Time, -Number and Resemblance, belong to the former class; -and of the Methods applicable to such Inductions we -have treated already. In proceeding to Inductions -governed by any ulterior Ideas, we can no longer lay -down any Special Methods by which our procedure -may be directed. A few general remarks are all that -we shall offer.</p> -<div class="footnote"><span class="label"><a id="note53-3" href="#fnanchor53-3">53</a> -</span> <a href="#page118">B. ii. c. vii.</a> -</div> -<p>The principal Maxim in such cases of Induction is -the obvious one:—that we must be careful to possess -and to apply, with perfect clearness and precision, the -Fundamental Idea on which the Induction depends.</p> -<p>We may illustrate this in a few cases.</p> -<p id="b3c10a2">2. <i>Induction of Substance.</i>—The -Idea of Substance<a id="fnanchor54-3" href="#note54-3"><span class="fnanchor">54</span></a> -involves this axiom, that the weight of the whole compound -must be equal to the weights of the separate -elements, whatever changes the composition or separation -of the elements may have occasioned. The application -of this Maxim we may term the <i>Method of the -Balance</i>. We have seen<a id="fnanchor55-3" href="#note55-3"><span class="fnanchor">55</span></a> -elsewhere how the memorable -revolution in Chemistry, the overthrow of Phlogiston, -and the establishment of the Oxygen Theory, -was produced by the application of this Method. We -have seen too<a id="fnanchor56-3" href="#note56-3"><span class="fnanchor">56</span></a> -that the same Idea leads us to this -Maxim;—that <i>Imponderable Fluids</i> are not to be -admitted as <em>chemical</em> elements of bodies.</p> -<div class="footnote"><span class="label"><a id="note54-3" href="#fnanchor54-3">54</a> -</span> <i>Hist. Sc. Ideas</i>, Book vi. c. iii. -</div> -<div class="footnote"><span class="label"><a id="note55-3" href="#fnanchor55-3">55</a> -</span> <i>Ibid.</i> b. vi. c. iv. -</div> -<div class="footnote"><span class="label"><a id="note56-3" href="#fnanchor56-3">56</a> -</span> <i>Ibid.</i> -</div> -<p>Whether those which have been termed <i>Imponderable -Fluids</i>,—the supposed fluids which produce the -phenomena of Light, Heat, Electricity, Galvanism, -Magnetism,—really exist or no, is a question, not -merely of the <em>Laws</em>, but of the <em>Causes</em> of Phenomena. -It is, as has already been shown, a question which we -cannot help discussing, but which is at present involved -in great obscurity. Nor does it appear at all likely that -we shall obtain a true view of the cause of Light, -Heat, and Electricity, till we have discovered precise -and general laws connecting optical, thermotical, and <span class="pagenum" id="page249">249</span> -electrical <em>phenomena</em> with those chemical doctrines to -which the Idea of Substance is necessarily applied.</p> -<p id="b3c10a3">3. <i>Induction of Force.</i>—The inference of <i>Mechanical -Forces</i> from phenomena has been so abundantly -practised, that it is perfectly familiar among scientific -inquirers. From the time of Newton, it has been the -most common aim of mathematicians; and a persuasion -has grown up among them, that mechanical forces,—attraction -and repulsion,—are the only modes of -action of the particles of bodies which we shall ultimately -have to consider. I have attempted to show -that this mode of conception is inadequate to the purposes -of sound philosophy;—that the Particles of -crystals, and the Elements of chemical compounds, -must be supposed to be combined in some other way -than by mere mechanical attraction and repulsion. -Dr. Faraday has gone further in shaking the usual -conceptions of the force exerted, in well-known cases. -Among the most noted and conspicuous instances of -attraction and repulsion exerted at a distance, were -those which take place between electrized bodies. But -the eminent electrician just mentioned has endeavoured -to establish, by experiments of which it is very difficult -to elude the weight, that the action in these cases -does not take place at a distance, but is the result of -a chain of intermediate particles connected at every -point by forces of another kind.</p> -<p id="b3c10a4">4. <i>Induction of Polarity.</i>—The forces to which -Dr. Faraday ascribes the action in these cases are -<i>Polar Forces</i><a id="fnanchor57-3" href="#note57-3"><span class="fnanchor">57</span></a>. -We have already endeavoured -to explain the Idea of Polar Forces; which -implies<a id="fnanchor58-3" href="#note58-3"><span class="fnanchor">58</span></a> that at -every point forces exactly equal act in opposite directions; -and thus, in the greater part of their course, -neutralize and conceal each other; while at the extremities -of the line, being by some cause liberated, they -are manifested, still equal and opposite. And the -criterion by which this polar character of forces is -recognized, is implied in the reasoning of Faraday, on -the question of one or two electricities, of which we <span class="pagenum" id="page250">250</span> -formerly spoke<a id="fnanchor59-3" href="#note59-3"><span class="fnanchor">59</span></a>. -The maxim is this:—that in the -action of polar forces, along with every manifestation -of force or property, there exists a corresponding and -simultaneous manifestation of an equal and opposite -force or property.</p> -<div class="footnote"><span class="label"><a id="note57-3" href="#fnanchor57-3">57</a> -</span> <i>Researches</i>, 12th series. -</div> -<div class="footnote"><span class="label"><a id="note58-3" href="#fnanchor58-3">58</a> -</span> B. v. c. i. [For this and the following note, please -see the Transcriber’s <a href="#tnote">Notes</a>.] -</div> -<div class="footnote"><span class="label"><a id="note59-3" href="#fnanchor59-3">59</a> -</span> Book v. c. i. -</div> -<p id="b3c10a5">5. As it was the habit of the last age to reduce all -action to mechanical forces, the present race of physical -speculators appears inclined to reduce all forces to -polar forces. Mosotti has endeavoured to show that the -positive and negative electricities pervade all bodies, -and that gravity is only an apparent excess of one of -the kinds over the other. As we have seen, Faraday -has given strong experimental grounds for believing -that the supposed remote actions of electrized bodies -are really the effects of polar forces among contiguous -particles. If this doctrine were established with regard -to all electrical, magnetical, and chemical forces, -we might ask, whether, while all other forces are -polar, gravity really affords a single exception to the -universal rule? Is not the universe pervaded by an -omnipresent antagonism, a fundamental conjunction of -contraries, everywhere opposite, nowhere independent? -We are, as yet, far from the position in which Inductive -Science can enable us to answer such inquiries.</p> -<p id="b3c10a6">6. <i>Induction of Ulterior Causes.</i>—The first Induction -of a Cause does not close the business of scientific -inquiry. Behind proximate causes, there are ulterior -causes, perhaps a succession of such. Gravity is the -cause of the motions of the planets; but what is the -cause of gravity? This is a question which has occupied -men’s minds from the time of Newton to the present day. -Earthquakes and volcanoes are the causes -of many geological phenomena; but what is the cause -of those subterraneous operations? This inquiry after -ulterior causes is an inevitable result from the intellectual -constitution of man. He discovers mechanical -causes, but he cannot rest in them. He must needs -ask, whence it is that matter has its universal power of -attracting matter. He discovers polar forces: but even <span class="pagenum" id="page251">251</span> -if these be universal, he still desires a further insight -into the cause of this polarity. He sees, in organic -structures, convincing marks of adaptation to an end: -whence, he asks, is this adaptation? He traces in the -history of the earth a chain of causes and effects -operating through time: but what, he inquires, is the -power which holds the end of this chain?</p> -<p>Thus we are referred back from step to step in the -order of causation, in the same, manner as, in the palætiological -sciences, we were referred back in the order -of time. We make discovery after discovery in the -various regions of science; each, it may be, satisfactory, -and in itself complete, but none final. Something -always remains undone. The last question answered, -the answer suggests still another question. The strain -of music from the lyre of Science flows on, rich and -sweet, full and harmonious, but never reaches a close: -no cadence is heard with which the intellectual ear can -feel satisfied.</p> -<p id="b3c10a7"><i>Of the Supreme Cause.</i>—In the utterance of Science, -no cadence is heard with which the human mind can -feel satisfied. Yet we cannot but go on listening for -and expecting a satisfactory close. The notion of a -cadence appears to be essential to our relish of the -music. The idea of some closing strain seems to lurk -among our own thoughts, waiting to be articulated in -the notes which flow from the knowledge of external -nature. The idea of something ultimate in our philosophical -researches, something in which the mind can -acquiesce, and which will leave us no further questions -to ask, of <em>whence</em>, and <em>why</em>, and <em>by what power</em>, seems -as if it belongs to us:—as if we could not have it -withheld from us by any imperfection or incompleteness -in the actual performances of science. What is -the meaning of this conviction? What is the reality -thus anticipated? Whither does the developement of -this Idea conduct us?</p> -<p>We have already seen that a difficulty of the same -kind, which arises in the contemplation of causes and -effects considered as forming an historical series, drives -us to the assumption of a First Cause, as an Axiom <span class="pagenum" id="page252">252</span> -to which our Idea of Causation in time necessarily -leads. And as we were thus guided to a First Cause, -in order of Succession, the same kind of necessity -directs us to a Supreme Cause in order of Causation.</p> -<p>On this most weighty subject it is difficult to speak -fitly; and the present is not the proper occasion, even -for most of that which may be said. But there are -one or two remarks which flow from the general train -of the contemplations we have been engaged in, and -with which this Work must conclude.</p> -<p>We have seen how different are the kinds of cause -to which we are led by scientific researches. <i>Mechanical -Forces</i> are insufficient without <i>Chemical Affinities</i>; -Chemical Agencies fail us, and we are compelled -to have recourse to <i>Vital Powers</i>; Vital Powers cannot -be merely physical, and we must believe in something -hyperphysical, something of the nature of a <i>Soul</i>. -Not only do biological inquiries lead us to assume an -animal soul, but they drive us much further; they -bring before us <i>Perception</i>, and <i>Will</i> evoked -by Perception. Still more, these inquiries disclose to us <i>Ideas</i> -as the necessary forms of Perception, in the actions -of which we ourselves are conscious. We are aware, -we cannot help being aware, of our Ideas and our -Volitions as belonging to <em>us</em>, and thus we pass from -<em>things</em> to <em>persons</em>; we have the idea of <i>Personality</i> -awakened. And the idea of Design and <em>Purpose</em>, of -which we are conscious in our own minds, we find -reflected back to us, with a distinctness which we -cannot overlook, in all the arrangements which constitute -the frame of organized beings.</p> -<p>We cannot but reflect how widely diverse are the -kinds of principles thus set before us;—by what vast -strides we mount from the lower to the higher, as we -proceed through that series of causes which the range -of the sciences thus brings under our notice. Yet -we know how narrow is the range of these sciences -when compared with the whole extent of human knowledge. -We cannot doubt that on many other subjects, -besides those included in physical speculation, man has -made out solid and satisfactory trains of <span class="pagenum" id="page253">253</span> connexion;—has -discovered clear and indisputable evidence of causation. -It is manifest, therefore, that, if we are to -attempt to ascend to the Supreme Cause—if we are -to try to frame an idea of the Cause of all these subordinate -causes;—we must conceive it as more different from any -of them, than the most diverse are -from each other;—more elevated above the highest, -than the highest is above the lowest.</p> -<p>But further;—though the Supreme Cause must thus -be inconceivably different from all subordinate causes, -and immeasurably elevated above them all, it must -still include in itself all that is essential to each of -them, by virtue of that very circumstance that it is -the Cause of their Causality. Time and Space,—Infinite -Time and Infinite Space,—must be among its -attributes; for we cannot but conceive Infinite Time -and Space as attributes of the Infinite Cause of the -universe. Force and Matter must depend upon it -for their efficacy; for we cannot conceive the activity -of Force, or the resistance of Matter, to be independent -powers. But these are its lower attributes. The Vital -Powers, the Animal Soul, which are the Causes of the -actions of living things, are only the Effects of the -Supreme Cause of Life. And this Cause, even in the -lowest forms of organized bodies, and still more in -those which stand higher in the scale, involves a -reference to Ends and Purposes, in short, to manifest -Final Causes. Since this is so, and since, even when -we contemplate ourselves in a view studiously narrowed, -we still find that we have Ideas, and Will and -Personality, it would render our philosophy utterly -incoherent and inconsistent with itself, to suppose that -Personality, and Ideas, and Will, and Purpose, do not -belong to the Supreme Cause from which we derive -all that we have and all that we are.</p> -<p>But we may go a step further;—though, in our -present field of speculation, we confine ourselves -to knowledge founded on the facts which the external -world presents to us, we cannot forget, in speaking of -such a theme as that to which we have thus been led, -that these are but a small, and the least significant <span class="pagenum" id="page254">254</span> -portion of the facts which bear upon it. We cannot -fail to recollect that there are facts belonging to the -world within us, which more readily and strongly -direct our thoughts to the Supreme Cause of all -things. We can plainly discern that we have Ideas -elevated above the region of mechanical causation, of -animal existence, even of mere choice and will, which -still have a clear and definite significance, a permanent -and indestructible validity. We perceive as a fact, -that we have a Conscience, judging of Right and -Wrong; that we have Ideas of Moral Good and Evil, -that we are compelled to conceive the organization -of the moral world, as well as of the vital frame, to -be directed to an end and governed by a purpose. -And since the Supreme Cause is the cause of these -facts, the Origin of these Ideas, we cannot refuse to -recognize Him as not only the Maker, but the Governor -of the World; as not only a Creative, but a Providential -Power; as not only a Universal Father, but -an Ultimate Judge.</p> -<p>We have already passed beyond the boundary of -those speculations which we proposed to ourselves as -the basis of our conclusions. Yet we may be allowed -to add one other reflection. If we find in ourselves -Ideas of Good and Evil, manifestly bestowed upon us -to be the guides of our conduct, which guides we yet -find it impossible consistently to obey;—if we find -ourselves directed, even by our natural light, to aim at a -perfection of our moral nature from which we are constantly -deviating through weakness and perverseness; -if, when we thus lapse and err, we can find, in the -region of human philosophy, no power which can efface -our aberrations, or reconcile our actual with our ideal -being, or give us any steady hope and trust with regard -to our actions, after we have thus discovered their -incongruity with their genuine standard;—if we discern -that this is our condition, how can we fail to see -that it is in the highest degree consistent with all the -indications supplied by such a philosophy as that of -which we have been attempting to lay the foundations, -that the Supreme Cause, through whom man exists as <span class="pagenum" id="page255">255</span> -a moral being of vast capacities and infinite Hopes, -should have Himself provided a teaching for our ignorance, -a propitiation for our sin, a support for our -weakness, a purification and sanctification of our -nature?</p> -<p>And thus, in concluding our long survey of the -grounds and structure of science, and of the lessons -which the study of it teaches us, we find ourselves -brought to a point of view in which we can cordially -sympathize, and more than sympathize, with all the -loftiest expressions of admiration and reverence and -hope and trust, which have been uttered by those who -in former times have spoken of the elevated thoughts -to which the contemplation of the nature and progress -of human knowledge gives rise. We can not only hold -with Galen, and Harvey, and all the great physiologists, -that the organs of animals give evidence of a -purpose;—not only assert with Cuvier that this conviction -of a purpose can alone enable us to understand -every part of every living thing;—not only say with -Newton that ‘every true step made in philosophy -brings us nearer to the First Cause, and is on that -account highly to be valued;’—and that ‘the business -of natural philosophy is to deduce causes from effects, -till we come to the very First Cause, which certainly is -not mechanical;’—but we can go much farther, and -declare, still with Newton, that ‘this beautiful system -could have its origin no other way than by the purpose -and command of an intelligent and powerful Being, -who governs all things, not as the soul of the world, -but as the Lord of the Universe; who is not only God, -but Lord and Governor.’</p> -<p>When we have advanced so far, there yet remains -one step. We may recollect the prayer of one, the -master in this school of the philosophy of science: -‘This also we humbly and earnestly beg;—that human things -may not prejudice such as are divine;—neither that from -the unlocking of the gates of sense, and -the kindling of a greater natural light, anything may -arise of incredulity or intellectual night towards divine -mysteries; but rather that by our minds thoroughly <span class="pagenum" id="page256">256</span> -purged and cleansed from fancy and vanity, and yet -subject and perfectly given up to the divine oracles, -there may be given unto faith the things that are -faith’s.’ When we are thus prepared for a higher -teaching, we may be ready to listen to a greater than -Bacon, when he says to those who have sought their -God in the material universe, ‘Whom ye ignorantly -worship, him declare I unto you.’ And when we recollect -how utterly inadequate all human language has -been shown to be, to express the nature of that Supreme -Cause of the Natural, and Rational, and Moral, -and Spiritual world, to which our Philosophy points -with trembling finger and shaded eyes, we may receive, -with the less wonder but with the more reverence, -the declaration which has been vouchsafed to us:</p> -<p class="center end"><span class="greek">ΕΝ ΑΡΧΗ ΗΝ Ὁ ΛΟΓΟΣ, -ΚΑI Ὁ ΛΟΓΟΣ ΗΝ ΠΡΟΣ ΤΟΝ ΘΕΟΝ, ΚΑI ΘΕΟΣ ΗΝ Ὁ ΛΟΓΟΣ.</span></p> -<div class="chapter"> -<p><span class="pagenum" id="page257"></span></p> -<p class="h2">NOVUM ORGANON RENOVATUM.</p><br /><br /> -<hr class="three" /> -<h2 class="nobreak">BOOK IV.</h2> -<p class="center sc">of the language of science.</p><br /> -<hr class="one" /> -</div> -<p class="center sc">Introduction.</p> -<p class="drop"><span class="sc">IT</span> has been shown in the <i>History of the Sciences</i>, -and has further appeared in the course of the -<i>History of Ideas</i>, that almost every step in the progress -of science is marked by the formation or appropriation -of a technical term. Common language has, -in most cases, a certain degree of looseness and ambiguity; -as common knowledge has usually something of -vagueness and indistinctness. In common cases too, -knowledge usually does not occupy the intellect alone, -but more or less interests some affection, or puts in -action the fancy; and common language, accommodating itself -to the office of expressing such knowledge, contains, -in every sentence, a tinge of emotion -or of imagination. But when our knowledge becomes -perfectly exact and purely intellectual, we require a -language which shall also be exact and intellectual;—which -shall exclude alike vagueness and fancy, imperfection -and superfluity;—in which each term shall -convey a meaning steadily fixed and rigorously limited. -Such a language that of science becomes, through the -use of Technical Terms. And we must now endeavour -to lay down some maxims and suggestions, by attention -to which Technical Terms may be better fitted to -answer their purpose. In order to do this, we shall in <span class="pagenum" id="page258">258</span> -the first place take a rapid survey of the manner in -which Technical Terms have been employed from the -earliest periods of scientific history.</p> -<p class="end">The progress of the use of technical scientific language -offers to our notice two different and successive -periods; in the first of which, technical terms were -formed casually, as convenience in each case prompted; -while in the second period, technical language was -constructed intentionally, with set purpose, with a regard -to its connexion, and with a view of constructing a -system. Though the casual and the systematic formation -of technical terms cannot be separated by any -precise date of time, (for at all periods some terms in -some sciences have been framed unsystematically,) we -may, as a general description, call the former the <i>Ancient</i> -and the latter the <i>Modern</i> Period. In illustrating -the two following Aphorisms, I will give examples of -the course followed in each of these periods.</p> -<p class="center"><span class="sc">Aphorism</span> I.</p> -<p><i>In the Ancient Period of Sciences, Technical Terms were -formed in three different ways:—by appropriating common -words and fixing their meaning;—by constructing terms -containing a description;—by constructing terms containing -reference to a theory.</i></p> -<p><span class="sc">The</span> earliest sciences offer the earliest examples of -technical terms. These are Geometry, Arithmetic, and -Astronomy; to which we have soon after to add Harmonics, -Mechanics, and Optics. In these sciences, we -may notice the above-mentioned three different modes -in which technical terms were formed.</p> -<p id="b4a1a1">I. The simplest and first mode of acquiring technical -terms, is to take words current in common usage, -and by rigorously defining or otherwise fixing their -meaning, to fit them for the expression of scientific -truths. In this manner almost all the fundamental -technical terms of Geometry were formed. A <i>sphere</i>, -a <i>cone</i>, a <i>cylinder</i>, had among the Greeks, at first, <span class="pagenum" id="page259">259</span> -meanings less precise than those which geometers gave -to these words, and besides the mere designation of -form, implied some use or application. A <i>sphere</i> -(<span class="greek">σφαῖρα</span>) was a hand-ball used in games; a <i>cone</i> (<span class="greek">κῶνος</span>) -was a boy’s spinning-top, or the crest of a helmet; a -<i>cylinder</i> (<span class="greek">κύλινδρος</span>) was a roller; a <i>cube</i> (<span class="greek">κύβος</span>) was a -die: till these words were adopted by the geometers, -and made to signify among them pure modifications of -space. So an <i>angle</i> (<span class="greek">γωνία</span>) was only a corner; a <i>point</i> -(<span class="greek">σημεῖον</span>) was a signal; a <i>line</i> (<span class="greek">γραμμὴ</span>) was a mark; a -<i>straight</i> line (<span class="greek">εὐθεῖα</span>) was marked by an adjective which -at first meant only <i>direct</i>. A <i>plane</i> (<span class="greek">ἐπίπεδον</span>) is the -neuter form of an adjective, which by its derivation -means <i>on the ground</i>, and hence <i>flat</i>. In all these -cases, the word adopted as a term of science has its -sense rigorously fixed; and where the common use of -the term is in any degree vague, its meaning may be -modified at the same time that it is thus limited. -Thus a <i>rhombus</i> (<span class="greek">ῥόμβος</span>) by its derivation, might mean -any figure which is <i>twisted</i> out of a regular form; but -it is confined by geometers to that figure which has -four equal sides, its angles being oblique. In like -manner, a <i>trapezium</i> (<span class="greek">τραπέζιον</span>) originally signifies a -<i>table</i>, and thus might denote any form; but as the tables -of the Greeks had one side shorter than the opposite one, such a -figure was at first called a <i>trapezium</i>. -Afterwards the term was made to signify any figure -with four unequal sides; a name being more needful in -geometry for this kind of figure than for the original -form.</p> -<p>This class of technical terms, namely, words adopted -from common language, but rendered precise and -determinate for purposes of science, may also be -exemplified in other sciences. Thus, as was observed in the -early portion of the history of -astronomy<a id="fnanchor1-4" href="#note1-4"><span class="fnanchor">1</span></a>, -a <i>day</i>, a -<i>month</i>, a <i>year</i>, described at first portions of time marked -by familiar changes, but afterwards portions determined -by rigorous mathematical definitions. The conception -of the heavens as a revolving sphere, is so obvious, <span class="pagenum" id="page260">260</span> -that we may consider the terms which involve this -conception as parts of common language; as the <i>pole</i> -(<span class="greek">πόλος</span>); the <i>arctic circle</i>, which includes the stars that -never set<a id="fnanchor2-4" href="#note2-4"><span class="fnanchor">2</span></a>; -the <i>horizon</i> (<span class="greek">ὁρίζων</span>) a boundary, applied -technically to the circle bounding the visible earth -and sky. The <i>turnings of the sun</i> (<span class="greek">τροπαὶ ἠελίοιο</span>), -which are mentioned by Hesiod, gave occasion to the -term <i>tropics</i>, the circles at which the sun in his annual -motion turns back from his northward or southward -advance. The <i>zones</i> of the earth, (the <i>torrid</i>, -<i>temperate</i>, and <i>frigid</i>;) the <i>gnomon</i> of a dial; the <i>limb</i> (or -border) of the moon, or of a circular instrument, are -terms of the same class. An <i>eclipse</i> (<span class="greek">ἔκλειψις</span>) is -originally a deficiency or disappearance, and joined with -the name of the luminary, an <i>eclipse of the sun</i> or <i>of -the moon</i>, described the phenomenon; but when the -term became technical, it sufficed, without addition, to -designate the phenomenon.</p> -<div class="footnote"><span class="label"><a id="note1-4" href="#fnanchor1-4">1</a></span> -<i>Hist. Ind. Sci.</i> b. iii. c. i. -</div> -<div class="footnote"><span class="label"><a id="note2-4" href="#fnanchor2-4">2</a></span> -<i>Hist. Ast.</i> b. iii. c. i. sect. 8. -</div> -<p>In Mechanics, the Greeks gave a scientific precision -to very few words: we may mention <i>weights</i> (<span class="greek">βάρεα</span>), -the <i>arms of a lever</i> (<span class="greek">μήχεα</span>), its <i>fulcrum</i> -(<span class="greek">ὑπομόχλιον</span>), -and the verb <i>to balance</i> (<span class="greek">ἰσσοῤῥοπεῖν</span>). Other terms -which they used, as <i>momentum</i> (<span class="greek">ῥοπὴ</span>) -and <i>force</i> (<span class="greek">δύναμις</span>), -did not acquire a distinct and definite meaning till the -time of Galileo, or later. We may observe that all -abstract terms, though in their scientific application -expressing mere conceptions, were probably at first -derived from some word describing external objects. -Thus the Latin word for force, <i>vis</i>, seems to be connected -with a Greek word, <span class="greek">ἲς</span>, or -<span class="greek">ϝὶς</span>, which often has -nearly the same meaning; but originally, as it would -seem, signified a sinew or muscle, the obvious seat of -animal strength.</p> -<p>In later times, the limitation imposed upon a word -by its appropriation to scientific purposes, is often -more marked than in the cases above described. Thus -the <i>variation</i> is made to mean, in astronomy, the second -inequality of the moon’s motion; in magnetism, -the <i>variation</i> signifies the angular deviation of the <span class="pagenum" id="page261">261</span> -compass-needle from the north; in pure mathematics, -the <i>variation</i> of a quantity is the formula which expresses -the result of any small change of the most -general kind. In like manner, <i>parallax</i> (<span class="greek">παράλλαξις</span>) -denotes a <i>change</i> in general, but is used by astronomers -to signify the change produced by the spectator’s being -removed from the center of the earth, his theoretical -place, to the surface. <i>Alkali</i> at first denoted the ashes -of a particular plant, but afterwards, all bodies having -a certain class of chemical properties; and, in like -manner, <i>acid</i>, the class opposed to alkali, was modified -in signification by chemists, so as to refer no longer to -the taste.</p> -<p>Words thus borrowed from common language, and -converted by scientific writers into technical terms, -have some advantages and some disadvantages. They -possess this great convenience, that they are understood -after a very short explanation, and retained in -the memory without effort. On the other hand, they -lead to some inconvenience; for since they have a -meaning in common language, a careless reader is -prone to disregard the technical limitation of this -meaning, and to attempt to collect their import in scientific -books, in the same vague and conjectural manner in which he -collects the purpose of words in common cases. Hence the -language of science, when thus -resembling common language, is liable to be employed -with an absence of that scientific precision which alone -gives it value. Popular writers and talkers, when they -speak of <i>force</i>, <i>momentum</i>, <i>action and reaction</i>, and -the like, often afford examples of the inaccuracy thus -arising from the scientific appropriation of common -terms.</p> -<p id="b4a1a2">II. Another class of technical terms, which we -find occurring as soon as speculative science assumes a -distinct shape, consists of those which are intentionally -constructed by speculators, and which contain some -description or indication distinctive of the conception -to which they are applied. Such are a <i>parallelogram</i> -(<span class="greek">παραλληλόγραμμον</span>), which denotes a plane figure -bounded by two pairs of parallel lines; a <i>parallelopiped</i> -<span class="pagenum" id="page262">262</span> -(<span class="greek">παραλληλοπίπεδον</span>), which signifies a solid figure -bounded by three pairs of parallel planes. A <i>triangle</i> -(<span class="greek">τρίγωνος</span>, <i>trigon</i>) and a -<i>quadrangle</i> (<span class="greek">τετράγωνος</span>, -<i>tetragon</i>) were perhaps words invented independently of -the mathematicians: but such words extended to other -cases, <i>pentagon</i>, <i>decagon</i>, <i>heccædecagon</i>, <i>polygon</i>, are -inventions of scientific men. Such also are <i>tetrahedron</i>, -<i>hexahedron</i>, <i>dodecahedron</i>, <i>tesseracontaoctohedron</i>, -<i>polyhedron</i>, and the like. These words being constructed -by speculative writers, explain themselves, or -at least require only some conventional limitation, -easily adopted. Thus <i>parallelogram</i>, might mean a -figure bounded by any number of sets of parallel lines, -but it is conventionally restricted to a figure of <em>four</em> -sides. So a <i>great circle</i> in a sphere means one which -passes through the center of the sphere; and a <i>small -circle</i> is any other. So in trigonometry, we have the -hypotenuse (<span class="greek">ὑποτενοῦσα</span>), or <i>subtending</i> line, -to designate the line subtending an angle, and especially a -right angle. In this branch of mathematics we have -many invented technical terms; as <i>complement</i>, <i>supplement</i>, -<i>cosine</i>, <i>cotangent</i>, a <i>spherical angle</i>, the <i>pole of a -circle</i>, or of a sphere. The word <i>sine</i> itself appears to -belong to the class of terms already described as scientific -appropriations of common terms, although its -origin is somewhat obscure.</p> -<p>Mathematicians were naturally led to construct -these and many other terms by the progress of their -speculations. In like manner, when astronomy took -the form of a speculative science, words were invented -to denote distinctly the conceptions thus introduced. -Thus the sun’s annual path among the stars, in which -not only solar, but also all lunar eclipses occur, was -termed the <i>ecliptic</i>. The circle which the sun describes -in his diurnal motion, when the days and nights are -equal, the Greeks called the <i>equidiurnal</i> (<span class="greek">ἰσημερινὸς</span>,) -the Latin astronomers the <i>equinoctial</i>, and the corresponding -circle on the earth was the <i>equator</i>. The -ecliptic intersected the equinoctial in the <i>equinoctial -points</i>. The <i>solstices</i> (in Greek, <span class="greek">τροπαὶ</span>) were the times -when the sun arrested his motion northwards or -<span class="pagenum" id="page263">263</span> southwards; -and the <i>solstitial points</i> (<span class="greek">τὰ τροπικὰ σημεῖα</span>) -were the places, in the ecliptic where he then was. -The name of <i>meridians</i> was given to circles passing -through the poles of the equator; the <i>solstitial colure</i> -(<span class="greek">κόλουρος</span>, curtailed), was one of these circles, which -passes through the solstitial points, and is intercepted -by the horizon.</p> -<p>We have borrowed from the Arabians various astronomical terms, -as <i>Zenith</i>, <i>Nadir</i>, <i>Azimuth</i>, <i>Almacantar</i>. -And these words, which among the Arabians probably -belonged to the first class, of appropriated scientific -terms, are for us examples of the second class, invented -scientific terms; although they differ from most that -we have mentioned, in not containing an etymology -corresponding to their meaning in any language with -which European cultivators of science are generally -familiar. Indeed, the distinction of our two classes, -though convenient, is in a great measure, casual. Thus -most of the words we formerly mentioned, as <i>parallax</i>, -<i>horizon</i>, <i>eclipse</i>, though appropriated technical terms -among the Greeks, are to us invented technical terms.</p> -<p>In the construction of such terms as we are now considering, -those languages have a great advantage which -possess a power of forming words by composition. This -was eminently the case with the Greek language; and -hence most of the ancient terms of science in that language, -when their origin is once explained, are clearly -understood and easily retained. Of modern European -languages, the German possesses the greatest facility of -composition; and hence scientific authors in that language -are able to invent terms which it is impossible -to imitate in the other languages of Europe. Thus -Weiss distinguishes his various systems of crystals as -<i>zwei-und-zwei-gliedrig</i>, <i>ein-und-zwei-gliedrig</i>, -<i>drey-und-drey-gliedrig,</i> <i>&c.</i>, (two-and-two-membered, -one-and-two-membered, &c.) And Hessel, also a writer on -crystallography, speaks of <i>doubly-one-membered edges</i>, -<i>four-and-three spaced rays</i>, and the like.</p> -<p>How far the composition of words, in such cases, -may be practised in the English language, and the -general question, what are the best rules and artifices <span class="pagenum" id="page264">264</span> -in such cases, I shall afterwards consider. In the -mean time, I may observe that this list of invented -technical terms might easily be much enlarged. Thus -in harmonics we have the various intervals, as a <i>Fourth</i>, -a <i>Fifth</i>, an <i>Octave</i>, (<i>Diatessaron</i>, <i>Diapente</i>, <i>Diapason</i>,) a -<i>Comma</i>, which is the difference of a <i>Major</i> and <i>Minor -Tone</i>; we have the various <i>Moods</i> or <i>Keys</i>, and the -notes of various lengths, as <i>Minims</i>, <i>Breves</i>, <i>Semibreves</i>, -<i>Quavers</i>. In chemistry, <i>Gas</i> was at first a technical -term invented by Van Helmont, though it has now -been almost adopted into common language. I omit -many words which will perhaps suggest themselves to -the reader, because they belong rather to the next -class, which I now proceed to notice.</p> -<p id="b4a1a3">III. The third class of technical terms consists of -such as are constructed by men of science, and involve -some theoretical idea in the meaning which their derivation -implies. They do not merely describe, like the -class last spoken of, but describe with reference to -some doctrine or hypothesis which is accepted as a -portion of science. Thus <i>latitude</i> and <i>longitude</i>, according -to their origin, signify breadth and length; -they are used, however, to denote measures of the distance -of a place on the earth’s surface from the equator, -and from the first meridian, of which distances, one -cannot be called <i>length</i> more properly than the other. -But this appropriation of these words may be explained -by recollecting that the earth, as known to the ancient -geographers, was much further extended from east to -west than from north to south. The <i>Precession</i> of the -equinoxes is a term which implies that the stars are -fixed, while the point which is the origin of the measure -of celestial longitude moves backward. The <i>Right -Ascension</i> of a star is a measure of its position corresponding -to terrestrial longitude; this quantity is identical -with the angular ascent of the equinoctial point, -when the star is in the horizon in a <i>right</i> sphere; that -is, a sphere which supposes the spectator to be at the -equator. The <i>Oblique Ascension</i> (a term now little -used), is derived in like manner from an oblique sphere. -The motion of a planet is <i>direct</i> or <i>retrograde</i>, <i>in</i> <span class="pagenum" id="page265">265</span> -<i>consequentia</i> (<i>signa</i>), or <i>in antecedentia</i>, in reference to a -certain assumed standard direction for celestial motions, -namely, the direction opposite to that of the sun’s daily -motion, and agreeing with his annual motion among -the stars; or with what is much more evident, the -moon’s monthly motion. The <i>equation of time</i> is the -quantity which must be added to or subtracted from -the time marked by the sun, in order to reduce it to a -theoretical condition of equable progress. In like -manner the <i>equation of the center</i> of the sun or of the -moon is the angle which must be added to, or subtracted -from, the actual advance of the luminary in -the heavens, in order to make its motion equable. -Besides the equation of the center of the moon, which -represents the first and greatest of her deviations from -equable motion, there are many other <i>equations</i>, by -the application of which her motion is brought nearer -and nearer to perfect uniformity. The second of these -equations is called the <i>evection</i>, the third the <i>variation</i>, -the fourth the <i>annual equation</i>, The motion of the -sun as affected by its inequalities is called his <i>anomaly</i>, -which term denotes inequality. In the History of -Astronomy, we find that the inequable motions of the -sun, moon, and planets were, in a great measure, reduced -to rule and system by the Greeks, by the aid of -an hypothesis of circles, revolving, and carrying in -their motion other circles which also revolved. This -hypothesis introduced many technical terms, as <i>deferent</i>, -<i>epicycle</i>, <i>eccentric</i>. In like manner, the theories -which have more recently taken the place of the -theory of epicycles have introduced other technical -terms, as the <i>elliptical orbit</i>, the <i>radius vector</i>, and the -<i>equable description of areas</i> by this radius, which phrases -express the true laws of the planetary motions.</p> -<p>There is no subject on which theoretical views have -been so long and so extensively prevalent as astronomy, -and therefore no other science in which there are so -many technical terms of the kind we are now considering. -But in other subjects also, so far as theories have -been established, they have been accompanied by the -introduction or fixation of technical terms. Thus, as <span class="pagenum" id="page266">266</span> -we have seen in the examination of the foundations of -mechanics, the terms <i>force</i> and <i>inertia</i> derive their -precise meaning from a recognition of the first law of -motion; <i>accelerating force</i> and <i>composition of motion</i> -involve the second law; <i>moving force</i>, <i>momentum</i>, <i>action</i> -and <i>reaction</i>, are expressions which imply the third law. -The term <i>vis viva</i> was introduced to express a general -property of moving bodies; and other terms have been -introduced for like purposes, as <i>impetus</i> by Smeaton, -and <i>work done</i>, by other engineers. In the recent -writings of several French engineers, the term <i>travail</i> -is much employed, to express the work done and the -force which does it: this term has been rendered by -<i>labouring force</i>. The proposition which was termed -the <i>hydrostatic paradox</i> had this name in reference to -its violating a supposed law of the action of forces. -The verb to <i>gravitate</i>, and the abstract term <i>gravitation</i>, -sealed the establishment of Newton’s theory of -the solar system.</p> -<p>In some of the sciences, opinions, either false, or -disguised in very fantastical imagery, have prevailed; -and the terms which have been introduced during the -reign of such opinions, bear the impress of the time. -Thus in the days of alchemy, the substances with -which the operator dealt were personified; and a metal -when exhibited pure and free from all admixture was -considered as a little king, and was hence called a -<i>regulus</i>, a term not yet quite obsolete. In like manner, -a substance from which nothing more of any value -could be extracted, was dead, and was called a <i>caput -mortuum</i>. Quick silver, that is, live silver (<i>argentum -vivum</i>), was killed by certain admixtures, and was -<i>revived</i> when restored to its pure state.</p> -<p>We find a great number of medical terms which -bear the mark of opinions formerly prevalent among -physicians; and though these opinions hardly form a -part of the progress of science, and were not presented -in our History, we may notice some of these terms as -examples of the mode in which words involve in their -derivation obsolete opinions. Such words as <i>hysterics</i>, -<i>hypochondriac</i>, <i>melancholy</i>, <i>cholera</i>, <i>colic</i>, -<i>quinsey</i> <span class="pagenum" id="page267">267</span> -(<i>squinantia</i>, <span class="greek">συνάγχη</span>, a suffocation), <i>megrim</i>, -<i>migrane</i> (<i>hemicranium</i>, the middle of the skull), <i>rickets</i>, (<i>rachitis</i>, -from <span class="greek">ῥάχις</span>, the backbone), <i>palsy</i>, -(<i>paralysis</i>, <span class="greek">παράλυσις</span>,) -<i>apoplexy</i> (<span class="greek">ἀποπληξία</span>, a stroke), -<i>emrods</i>, (<span class="greek">αἱμοῤῥοΐδες</span>, -<i>hemorrhoids</i>, a flux of blood), <i>imposthume</i>, (corrupted -from <i>aposteme</i>, <span class="greek">ἀπόστημα</span>, an abscess), <i>phthisis</i> -(<span class="greek">φθίσις</span>, consumption), <i>tympanum</i> -(<span class="greek">τυμπανία</span>, swelling), -<i>dropsy</i> (<i>hydropsy</i>, <span class="greek">ὕδρωψ</span>,) -<i>sciatica</i>, isciatica (<span class="greek">ἰσκιαδικὴ</span>, -from <span class="greek">ἰσκίον</span>, the hip), <i>catarrh</i> -(<span class="greek">κατάῤῥους</span>, a flowing -down), <i>diarrhœa</i> (<span class="greek">διαῤῥοία</span>, -a flowing through), <i>diabetes</i> -(<span class="greek">διαβήτης</span>, a passing through), -<i>dysentery</i> (<span class="greek">δυσεντερία</span>, a -disorder of the entrails), <i>arthritic</i> pains (from <span class="greek">ἄρθρα</span>, -the joints), are names derived from the supposed or -real seat and circumstances of the diseases. The word -from which the first of the above names is derived -(<span class="greek">ὑστέρα</span>, the last place,) signifies the womb, according -to its order in a certain systematic enumeration of -parts. The second word, <i>hypochondriac</i>, means something -affecting the viscera below the cartilage of the -breastbone, which cartilage is called <span class="greek">χόνδρος</span>; -<i>melancholy</i> and <i>cholera</i> derive their names from supposed -affections of <span class="greek">χολὴ</span>, the bile. <i>Colic</i> is that which affects -the <i>colon</i> (<span class="greek">κῶλον</span>), the largest member of the bowels. -A disorder of the eye is called <i>gutta serena</i> (the ‘drop -serene’ of Milton), in contradistinction to <i>gutta turbida</i>, -in which the impediment to vision is perceptibly -opake. Other terms also record the opinions of the -ancient anatomists, as <i>duodenum</i>, a certain portion of -the intestines, which they estimated as twelve inches -long. We might add other allusions, as the <i>tendon of -Achilles</i>.</p> -<p>Astrology also supplied a number of words founded -upon fanciful opinions; but this study having been -expelled from the list of sciences, such words now -survive, only so far as they have found a place in common -language. Thus men were termed <i>mercurial</i>, <i>martial</i>, -<i>jovial</i>, or <i>saturnine</i>, accordingly as their characters -were supposed to be determined by the influence of the -planets, Mercury, Mars, Jupiter, or Saturn. Other -expressions, such as <i>disastrous</i>, <i>ill-starred</i>, <i>exorbitant</i>, -<i>lord of the ascendant</i>, and hence <i>ascendancy</i>, -<i>influence</i>, <span class="pagenum" id="page268">268</span> -a <i>sphere of action</i>, and the like, may serve to show -how extensively astrological opinions have affected -language, though the doctrine is no longer a recognized -science.</p> -<p>The preceding examples will make it manifest that -opinions, even of a recondite and complex kind, are -often implied in the derivation of words; and thus will -show how scientific terms, framed by the cultivators -of science, may involve received hypotheses and theories. -When terms are thus constructed, they serve -not only to convey with ease, but to preserve steadily -and to diffuse widely, the opinions which they thus -assume. Moreover, they enable the speculator to employ -these complex conceptions, the creations of science, -and the results of much labour and thought, as -readily and familiarly as if they were convictions -borrowed at once from the senses. They are thus powerful -instruments in enabling philosophers to ascend -from one step of induction and generalization to another; -and hereby contribute powerfully to the advance of knowledge and truth.</p> -<p>It should be noticed, before we proceed, that the -names of natural objects, when they come to be considered -as the objects of a science, are selected according to the -processes already enumerated. For the -most part, the natural historian adopts the common -names of animals, plants, minerals, gems, and the like, -and only endeavours to secure their steady and consistent -application. But many of these names imply some -peculiar, often fanciful, belief respecting the object.</p> -<p>Various plants derive their names from their supposed -virtues, as <i>herniaria</i>, <i>rupture-wort</i>; or from legends, -as <i>herba Sancti Johannis</i>, <i>St. John’s wort</i>. The -same is the case with minerals: thus the <i>topaz</i> was -asserted to come from an island so shrouded in mists -that navigators could only <i>conjecture</i> (<span class="greek">τοπάζειν</span>) where -it was. In these latter cases, however, the legend is -often not the true origin of the name, but is suggested -by it.</p> -<p>The privilege of constructing names where they are -wanted, belongs to natural historians no less than to <span class="pagenum" id="page269">269</span> -the cultivators of physical science; yet in the ancient -world, writers of the former class appear rarely to -have exercised this privilege, even when they felt the -imperfections of the current language. Thus Aristotle -repeatedly mentions classes of animals which have no -name, as co-ordinate with classes that have names; -but he hardly ventures to propose names which may -supply these defects<a id="fnanchor3-4" href="#note3-4"><span class="fnanchor">3</span></a>. -The vast importance of nomenclature -in natural history was not recognized till the -modern period.</p> -<div class="footnote"><span class="label"><a id="note3-4" href="#fnanchor3-4">3</a></span> -In his <i>History of Animals</i>, (b. i. c. vi.), he says, -that the great classes of animals are Quadrupeds, Birds, -Fishes, Whales (<i>Cetaceans</i>), Oysters (<i>Testaceans</i>), -animals like crabs which have no general name (<i>Crustaceans</i>), -soft animals (<i>Mollusks</i> and <i>Insects</i>). He does, -however, call the Crustaces by a name (<i>Malacostraca</i>, soft-shelled) -which has since been adopted by Naturalists. -</div> -<p class="end">We have, however, hitherto considered only the -formation or appropriation of single terms in science; -except so far as several terms may in some instances -be connected by reference to a common theory. But -when the value of technical terms began to be fully -appreciated, philosophers proceeded to introduce them -into their sciences more copiously and in a more systematic -manner. In this way, the modern history of -technical language has some features of a different -aspect from the ancient; and must give rise to a separate Aphorism.</p> -<p class="center" id="a2"><span class="sc">Aphorism</span> II.</p> -<p><i>In the Modern Period of Science, besides the three processes -anciently employed in the formation of technical -terms, there have been introduced Systematic Nomenclature, -Systematic Terminology, and the Systematic Modification of -Terms to express theoretical relations</i><a id="fnanchor4-4" href="#note4-4"><span class="fnanchor">4</span></a>.</p> -<div class="footnote"><span class="label"><a id="note4-4" href="#fnanchor4-4">4</a></span> -On the subject of Terminology and Nomenclature, -see also Aphorisms <a href="#a88">LXXXVIII</a> and <a href="#a98">XCVIII</a> concerning Ideas, -and b. viii. c. ii. of the <i>History of Scientific Ideas</i>. In those -places I have spoken of the distinction of <i>Terminology</i> -and <i>Nomenclature</i>. -</div> -<p><span class="sc">Writers</span> upon science have gone on up to modern -times forming such technical terms as they had occasion for, -by the three processes above <span class="pagenum" id="page270">270</span> described;—namely, -appropriating and limiting words in common -use;—constructing for themselves words descriptive of -the conception which they wished to convey;—or -framing terms which by their signification imply the -adoption of a theory. Thus among the terms introduced -by the study of the connexion between magnetism and electricity, -the word <i>pole</i> is an example of the -first kind; the name of the subject, <i>electro-magnetism</i>, -of the second; and the term <i>current</i>, involving an -hypothesis of the motion of a fluid, is an instance of the -third class. In chemistry, the term <i>salt</i> was adopted -from common language, and its meaning extended to -denote any compound of a certain kind; the term <i>neutral</i> -salt implied the notion of a balanced opposition in -the two elements of the compound; and such words as -<i>subacid</i> and <i>superacid</i>, invented on purpose, -were introduced to indicate the cases in which this balance -was not attained. Again, when the phlogistic theory -of chemistry was established, the term <i>phlogiston</i> was -introduced to express the theory, and from this such -terms as <i>phlogisticated</i> and <i>dephlogisticated</i> were derived, -exclusively words of science. But in such instances -as have just been given, we approach towards -a systematic modification of terms, which is a peculiar -process of modern times. Of this, modern chemistry -forms a prominent example, which we shall soon consider, -but we shall first notice the other processes mentioned -in the Aphorism.</p> -<p id="b4a2a1">I. In ancient times, no attempt was made to invent -or select a Nomenclature of the objects of Natural -History which should be precise and permanent. The -omission of this step by the ancient naturalists gave -rise to enormous difficulty and loss of time when the -sciences resumed their activity. We have seen in the -history of the sciences of classification, and of botany -in especial<a id="fnanchor5-4" href="#note5-4"><span class="fnanchor">5</span></a>, -that the early cultivators of that study in -modern times endeavoured to identify all the plants -described by Greek and Roman writers with those -which grow in the north of Europe; and were involved <span class="pagenum" id="page271">271</span> -in endless confusion<a id="fnanchor6-4" href="#note6-4"><span class="fnanchor">6</span></a>, -by the multiplication of names -of plants, at the same time superfluous and ambiguous. -The <i>Synonymies</i> which botanists (Bauhin and others) -found it necessary to publish, were the evidences of -these inconveniences. In consequence of the defectiveness -of the ancient botanical nomenclature, we are -even yet uncertain with respect to the identification of -some of the most common trees mentioned by classical -writers<a id="fnanchor7-4" href="#note7-4"><span class="fnanchor">7</span></a>. -The ignorance of botanists respecting the -importance of nomenclature operated in another manner to -impede the progress of science. As a good nomenclature -presupposes a good system of classification, -so, on the other hand, a system of classification cannot -become permanent without a corresponding nomenclature. -Cæsalpinus, in the sixteenth -century<a id="fnanchor8-4" href="#note8-4"><span class="fnanchor">8</span></a>, published -an excellent system of arrangement for plants; but -this, not being connected with any system of names, -was never extensively accepted, and soon fell into oblivion. -The business of framing a scientific botanical -classification was in this way delayed for about a century. -In the same manner, Willoughby’s classification -of fishes, though, as Cuvier says, far better than any -which preceded it, was never extensively adopted, in -consequence of having no nomenclature connected -with it.</p> -<div class="footnote"><span class="label"><a id="note5-4" href="#fnanchor5-4">5</a></span> -<i>Hist. Ind. Sc.</i> b. xvi. c. ii. -</div> -<div class="footnote"><span class="label"><a id="note6-4" href="#fnanchor6-4">6</a></span> -<i>Hist. Ind. Sc.</i> b. xvi. c. iii. sect. 3. -</div> -<div class="footnote"><span class="label"><a id="note7-4" href="#fnanchor7-4">7</a></span> -For instance, whether the <i>fagus</i> of the Latins -be the beech or the chestnut. -</div> -<div class="footnote"><span class="label"><a id="note8-4" href="#fnanchor8-4">8</a></span> -<i>Ib.</i> b. xvi. c. iii. sect. 2. -</div> -<p id="b4a2a2">II. Probably one main cause which so long retarded -the work of fixing at the same time the arrangement -and the names of plants, was the great number of minute -and diversified particulars in the structure of each -plant which such a process implied. The stalks, leaves, -flowers, and fruits of vegetables, with their appendages, -may vary in so many ways, that common language is quite -insufficient to express clearly and precisely their -resemblances and differences. Hence -botany required not only a fixed system of <em>names</em> of -plants, but also an artificial system of phrases fitted to -<em>describe</em> their parts: not only a <i>Nomenclature</i>, -but also <span class="pagenum" id="page272">272</span> -a <i>Terminology</i>. The Terminology was, in fact, an -instrument indispensably requisite in giving fixity to the -Nomenclature. The recognition of the kinds of plants -must depend upon the exact comparison of their resemblances -and differences; and to become a part of -permanent science, this comparison must be recorded -in words.</p> -<p>The formation of an exact descriptive language for -botany was thus the first step in that systematic -construction of the technical language of science, which is -one of the main features in the intellectual history of -modern times. The ancient botanists, as De -Candolle<a id="fnanchor9-4" href="#note9-4"><span class="fnanchor">9</span></a> -says, did not make any attempt to select terms of -which the sense was rigorously determined; and each -of them employed in his descriptions the words, metaphors, -or periphrases which his own genius suggested. -In the History of Botany<a id="fnanchor10-4" href="#note10-4"><span class="fnanchor">10</span></a>, -I have noticed some of the -persons who contributed to this improvement. ‘Clusius,’ -it is there stated, ‘first taught botanists to describe well. -He introduced exactitude, precision, neatness, elegance, method: -he says nothing superfluous; -he omits nothing necessary.’ This task was further -carried on by Jung and Ray<a id="fnanchor11-4" href="#note11-4"><span class="fnanchor">11</span></a>. -In these authors we -see the importance which began to be attached to the -exact definition of descriptive terms; for example, Ray -quotes Jung’s definition of <i>Caulis</i>, a stalk.</p> -<div class="footnote"><span class="label"><a id="note9-4" href="#fnanchor9-4">9</a></span> -<i>Theor. Elem. de Bot.</i> p. 327. -</div> -<div class="footnote"><span class="label"><a id="note10-4" href="#fnanchor10-4">10</a></span> -<i>Hist. Ind. Sc.</i> b. xvi. c. iii. sect. 3. -</div> -<div class="footnote"><span class="label"><a id="note11-4" href="#fnanchor11-4">11</a></span> -<i>Hist. Ind. Sc.</i> b. xvi. c. iii. sect. 3 (about <span class="sc">a.d.</span> 1660). -</div> -<p>The improvement of descriptive language, and the -formation of schemes of classification of plants, went -on gradually for some time, and was much advanced -by Tournefort. But at last Linnæus embodied and -followed out the convictions which had gradually been -accumulating in the breasts of botanists; and by remodelling -throughout both the terminology and the -nomenclature of botany, produced one of the greatest -reforms which ever took place in any science. He -thus supplied a conspicuous example of such a reform, -and a most admirable model of a language, from which <span class="pagenum" id="page273">273</span> -other sciences may gather great instruction. I shall -not here give any account of the terms and words introduced -by Linnæus. They have been exemplified in -the <i>History of -Science</i><a id="fnanchor12-4" href="#note12-4"><span class="fnanchor">12</span></a>; -and the principles which they -involve I shall consider separately hereafter. I will -only remind the reader that the great simplification in -<i>nomenclature</i> which was the result of his labours, consisted -in designating each kind of plant by a <i>binary</i> -term consisting of the name of the <i>genus</i> combined -with that of the <i>species</i>: an artifice seemingly obvious, -but more convenient in its results than could possibly -have been anticipated.</p> -<div class="footnote"><span class="label"><a id="note12-4" href="#fnanchor12-4">12</a></span> -<i>Ib.</i> c. iv. sect. 1–3. -</div> -<p>Since Linnæus, the progress of Botanical Anatomy -and of Descriptive Botany have led to the rejection of -several inexact expressions, and to the adoption of -several new terms, especially in describing the structure -of the fruit and the parts of cryptogamous plants. -Hedwig, Medikus, Necker, Desvaux, Mirbel, and especially -Gærtner, Link, and Richard, have proposed -several useful innovations, in these as in other parts -of the subject; but the general mass of the words -now current consists still, and will probably continue -to consist, of the terms established by the Swedish -Botanist<a id="fnanchor13-4" href="#note13-4"><span class="fnanchor">13</span></a>.</p> -<div class="footnote"><span class="label"><a id="note13-4" href="#fnanchor13-4">13</a></span> -De Candolle, <i>Th. Elem.</i> p. 307. -</div> -<p>When it was seen that botany derived so great advantages -from a systematic improvement of its language, it was -natural that other sciences, and especially -classificatory sciences, should endeavour to follow its -example. This attempt was made in Mineralogy by -Werner, and afterwards further pursued by Mohs. -Werner’s innovations in the descriptive language of -Mineralogy were the result of great acuteness, an intimate -acquaintance with minerals, and a most methodical spirit: -and were in most respects great improvements upon previous -practices. Yet the introduction -of them into Mineralogy was far from regenerating -that science, as Botany had been regenerated by the -Linnæan reform. It would seem that the perpetual <span class="pagenum" id="page274">274</span> -scrupulous attention to most minute differences, (as of -lustre, colour, fracture,) the greater part of which are -not really important, fetters the mind, rather than -disciplines it or arms it for generalization. Cuvier has -remarked<a id="fnanchor14-4" href="#note14-4"><span class="fnanchor">14</span></a> -that Werner, after his first <i>Essay on the -Characters of Minerals</i>, wrote little; as if he had been -afraid of using the system which he had created, and -desirous of escaping from the chains which he had -imposed upon others. And he justly adds, that Werner -dwelt least, in his descriptions, upon that which is -really the most important feature of all, the crystalline -structure. This, which is truly a definite character, -like those of Botany, does, when it can be clearly discerned, -determine the place of the mineral in a system. -This, therefore, is the character which, of all others, -ought to be most carefully expressed by an appropriate -language. This task, hardly begun by Werner, has -since been fully executed by others, especially by Romé -de l’Isle, Haüy, and Mohs. All the forms of crystals -can be described in the most precise manner by the -aid of the labours of these writers and their successors. -But there is one circumstance well worthy our notice -in these descriptions. It is found that the language -in which they can best be conveyed is not that of -words, but of <em>symbols</em>. The relations of space which -are involved in the forms of crystalline bodies, though -perfectly definite, are so complex and numerous, that -they cannot be expressed, except in the language of -mathematics: and thus we have an extensive and -recondite branch of mathematical science, which is, in -fact, only a part of the Terminology of the mineralogist.</p> -<div class="footnote"><span class="label"><a id="note14-4" href="#fnanchor14-4">14</a></span> -<i>Éloges</i>, ii. 134. -</div> -<p>The Terminology of Mineralogy being thus reformed, -an attempt was made to improve its Nomenclature also, -by following the example of Botany. Professor Mohs -was the proposer of this innovation. The names framed -by him were, however, not composed of two but of -three elements, designating respectively the Species, -the Genus, and the Order<a id="fnanchor15-4" href="#note15-4"><span class="fnanchor">15</span></a>: -thus he has such species as <span class="pagenum" id="page275">275</span> -<i>Rhombohedral Lime Haloide</i>, <i>Octahedral Fluor Haloide</i>, -<i>Prismatic Hal Baryte</i>. These names have not been -generally adopted; nor is it likely that any names -constructed on such a scheme will find acceptance -among mineralogists, till the higher divisions of the -system are found to have some definite character. We -see no real mineralogical significance in Mohs’s Genera -and Orders, and hence we do not expect them to retain -a permanent place in the science.</p> -<div class="footnote"><span class="label"><a id="note15-4" href="#fnanchor15-4">15</a></span> -<i>Hist. Ind. Sc.</i> b. xv. c. ix. -</div> -<p>The only systematic names which have hitherto -been generally admitted in Mineralogy, are those -expressing the chemical constitution of the substance; -and these belong to a system of technical terms -different from any we have yet spoken of, namely to -terms formed by systematic modification.</p> -<p id="b4a2a3">III. The language of Chemistry was already, as we -have seen, tending to assume a systematic character, -even under the reign of the phlogiston theory. But -when oxygen succeeded to the throne, it very fortunately -happened that its supporters had the courage -and the foresight to undertake a completely new and -systematic recoinage of the terms belonging to the science. -The new nomenclature was constructed upon a -principle hitherto hardly applied in science, but eminently -commodious and fertile; namely, the principle -of indicating a modification of relations of elements, -by a change in the termination of the word. Thus -the new chemical school spoke of sulph<i>uric</i> and sulph<i>urous</i> -acids; of sulph<i>ates</i> and sulph<i>ites</i> of bases; and -of sulph<i>urets</i> of metals; and in like manner, of phos<i>phoric</i> -and phos<i>phorous</i> acids, of phos<i>phates</i>, phos<i>phites</i>, -phos<i>phurets</i>. In this manner a nomenclature was produced, -in which the very name of a substance indicated -at once its constitution and place in the system.</p> -<p>The introduction of this chemical language can never -cease to be considered one of the most important steps -ever made in the improvement of technical terms; and -as a signal instance of the advantages which may result -from artifices apparently trivial, if employed in a -manner conformable to the laws of phenomena, and -systematically pursued. It was, however, proved that <span class="pagenum" id="page276">276</span> -this language, with all its merits, had some defects. -The relations of elements in composition were discovered -to be more numerous than the modes of -expression which the terminations supplied. Besides -the sulphurous and sulphuric acids, it appeared there -were others; these were called the <i>hyposulphurous</i> and -<i>hyposulphuric</i>: but these names, though convenient, -no longer implied, by their form, any definite relation. -The compounds of Nitrogen and Oxygen are, in order, -the <i>Protoxide</i>, the <i>Deutoxide</i> or <i>Binoxide</i>; -<i>Hyponitrous</i> Acid, <i>Nitrous</i> Acid, and <i>Nitric</i> Acid. The -nomenclature here ceases to be systematic. We have -three oxides of Iron, of which we may call the first the -<i>Protoxide</i>, but we cannot call the others the <i>Deutoxide</i> -and <i>Trioxide</i>, for by doing so we should convey a -perfectly erroneous notion of the proportions of the -elements. They are called the <i>Protoxide</i>, the <i>Black</i> -Oxide, and the <i>Peroxide</i>. We are here thrown back -upon terms quite unconnected with the system.</p> -<p>Other defects in the nomenclature arose from errours -in the theory; as for example the names of the muriatic, -oxymuriatic, and hyperoxymuriatic acids; which, -after the establishment of the new theory of chlorine, -were changed to <i>hydrochloric</i> acid, <i>chlorine</i>, and <i>chloric</i> -acid.</p> -<p>Thus the chemical system of nomenclature, founded -upon the oxygen theory, while it shows how much may -be effected by a good and consistent scheme of terms, -framed according to the real relations of objects, proves -also that such a scheme can hardly be permanent in -its original form, but will almost inevitably become -imperfect and anomalous, in consequence of the accumulation -of new facts, and the introduction of new -generalizations. Still, we may venture to say that -such a scheme does not, on this account, become worthless; -for it not only answers its purpose in the stage of -scientific progress to which it belongs:—so far as it is -not erroneous, or merely conventional, but really systematic -and significant of truth, its terms can be translated at once -into the language of any higher generalization which is -afterwards arrived at. If terms express <span class="pagenum" id="page277">277</span> relations -really ascertained to be true, they can never -lose their value by any change of the received theory. -They are like coins of pure metal, which, even when -carried into a country which does not recognize the -sovereign whose impress they bear, are still gladly -received, and may, by the addition of an explanatory -mark, continue part of the common currency of the -country.</p> -<p>These two great instances of the reform of scientific -language, in Botany and in Chemistry, are much the -most important and instructive events of this kind -which the history of science offers. It is not necessary -to pursue our historical survey further. Our remaining -Aphorisms respecting the Language of Science -will be collected and illustrated indiscriminately, from -the precepts and the examples of preceding philosophers -of all periods<a id="fnanchor16-4" href="#note16-4"><span class="fnanchor">16</span></a>.</p> -<div class="footnote"><span class="label"><a id="note16-4" href="#fnanchor16-4">16</a></span> -See at the <a href="#page346">end</a> of these Aphorisms, further illustrations -of them from the recent history of Comparative Anatomy and Chemistry. -</div> -<p>We may, however, remark that Aphorisms III., IV., -V., VI., VII., respect peculiarly the Formation of -Technical Terms by the Appropriation of Common -Words, while the remaining ones apply to the Formation of New Terms.</p> -<p class="end">It does not appear possible to lay down a system of -rules which may determine and regulate the construction -of all technical terms, on all the occasions on -which the progress of science makes them necessary or -convenient. But if we can collect a few maxims such -as have already offered themselves to the minds of -philosophers, or such as may be justified by the instances -by which we shall illustrate them, these maxims may -avail to guide us in doubtful cases, and to prevent our -aiming at advantages which are unattainable, or being -disturbed by seeming imperfections which are really -no evils. I shall therefore state such maxims of this -kind as seem most sound and useful. <span class="pagenum" id="page278">278</span></p> -<p class="center" id="a3"><span class="sc">Aphorism</span> III.</p> -<p><i>In framing scientific terms, the appropriation of old -words is preferable to the invention of new ones.</i></p> -<p><span class="sc">This</span> maxim is stated by Bacon in his usual striking -manner. After mentioning <i>Metaphysic</i>, as one of the -divisions of Natural Philosophy, he -adds<a id="fnanchor17-4" href="#note17-4"><span class="fnanchor">17</span></a>: ‘Wherein -I desire it may be conceived that I use the word <i>metaphysic</i> -in a different sense from that that is received: -and in like manner I doubt not but it will easily -appear to men of judgment that in this and other particulars, -wheresoever my conception and notion may -differ from the ancient, yet I am studious to keep the -ancient terms. For, hoping well to deliver myself from -mistaking by the order and perspicuous expressing of -that I do propound; I am otherwise zealous and affectionate -to recede as little from antiquity, either in -terms or opinions, as may stand with truth, and the -proficience of knowledge, . . . To me, that do desire, -as much as lieth in my pen, to ground a sociable intercourse -between antiquity and proficience, it seemeth -best to keep a way with antiquity <i>usque ad aras</i>; and -therefore to retain the ancient terms, though I sometimes -alter the uses and definitions; according to the -moderate proceeding in civil governments, when, -although there be some alteration, yet that holdeth -which Tacitus wisely noteth, <i>eadem magistratuum -vocabula</i>.’</p> -<div class="footnote"><span class="label"><a id="note17-4" href="#fnanchor17-4">17</a></span> -<i>De Augm.</i> lib. iii. c. iv. -</div> -<p>We have had before us a sufficient number of examples of -scientific terms thus framed; for they formed -the first of three classes which we described in the -First Aphorism. And we may again remark, that -science, when she thus adopts terms which are in common -use, always limits and fixes their meaning in -a technical manner. We may also repeat here the -warning already given respecting terms of this kind, -that they are peculiarly liable to mislead readers who <span class="pagenum" id="page279">279</span> -do not take care to understand them in their technical -instead of their common signification. <i>Force</i>, <i>momentum</i>, -<i>inertia</i>, <i>impetus</i>, <i>vis viva</i>, are terms which are -very useful, if we rigorously bear in mind the import -which belongs to each of them in the best treatises on -Mechanics; but if the reader content himself with -conjecturing their meaning from the context, his -knowledge will be confused and worthless.</p> -<p class="end">In the application of this Third Aphorism, other -rules are to be attended to, which I add.</p> -<p class="center" id="a4"><span class="sc">Aphorism</span> IV.</p> -<p><i>When common words are appropriated as technical terms, -their meaning and relations in common use should be retained -as far as can conveniently be done.</i></p> -<p><span class="sc">I will</span> state an example in which this rule seems to -be applicable. Mr Davies -Gilbert<a id="fnanchor18-4" href="#note18-4"><span class="fnanchor">18</span></a> -has recently proposed -the term <i>efficiency</i> to designate the work which -a machine, according to the force exerted upon it, is -capable of doing; the work being measured by the -weight raised, and the space through which it is raised, -jointly. The usual term employed among engineers -for the work which a machine actually does, measured -in the way just stated, is <i>duty</i>. But as there appears -to be a little incongruity in calling that work <i>efficiency</i> -which the machine <em>ought</em> to do, when we call that -work <i>duty</i> which it really does, I have proposed to -term these two quantities <i>theoretical efficiency</i> and -<i>practical efficiency</i>, or <i>theoretical duty</i> and <i>practical -duty</i><a id="fnanchor19-4" href="#note19-4"><span class="fnanchor">19</span></a>.</p> -<div class="footnote"><span class="label"><a id="note18-4" href="#fnanchor18-4">18</a></span> -<i>Phil. Trans.</i> 1827, p. 25. -</div> -<div class="footnote"><span class="label"><a id="note19-4" href="#fnanchor19-4">19</a></span> -The term <i>travail</i> is used by French engineers, -to express <i>efficiency</i> or <i>theoretical duty</i>. This term -has been rendered in English by <i>labouring force</i>. -</div> -<p class="end">Since common words are often vague in their meaning, I add as -a necessary accompaniment to the Third -Aphorism the following:— <span class="pagenum" id="page280">280</span></p> -<p class="center" id="a5"><span class="sc">Aphorism</span> V.</p> -<p><i>When common words are appropriated as technical terms, -their meaning may be modified, and must be rigorously fixed.</i></p> -<p><span class="sc">This</span> is stated by Bacon in the above extract: ‘to -retain the ancient terms, though I sometimes <i>alter the -uses and definitions</i>.’ The scientific use of the term is -in all cases much more precise than the common use. -The loose notions of <i>velocity</i> and <i>force</i> for instance, -which are sufficient for the usual purposes of language, -require to be fixed by exact measures when these are -made terms in the science of Mechanics.</p> -<p>This scientific fixation of the meaning of words is to -be looked upon as a matter of convention, although it -is in reality often an inevitable result of the progress -of science. <i>Momentum</i> is conventionally defined to be -the product of the numbers expressing the weight and -the velocity; but then, it could be of no use in expressing -the laws of motion if it were defined otherwise.</p> -<p>Hence it is no valid objection to a scientific term -that the word in common language does not mean -exactly the same as in its common use. It is no -sufficient reason against the use of the term <i>acid</i> for a -class of bodies, that all the substances belonging to -this class are not sour. We have seen that a <i>trapezium</i> -is used in geometry for any four-sided figure, -though originally it meant a figure with two opposite -sides parallel and the two others equal. A certain -stratum which lies below the chalk is termed by -English geologists <i>the green sand</i>. It has sometimes -been objected to this denomination that the stratum -has very frequently no tinge of green, and that it is -often composed of lime with little or no sand. Yet -the term is a good technical term in spite of these -apparent improprieties; so long as it is carefully -applied to that stratum which is geologically equivalent -to the greenish sandy bed to which the appellation was -originally applied.</p> -<p>When it appeared that <i>geometry</i> would have to be -employed as much at least about the heavens as the -earth, Plato exclaimed against the folly of calling the <span class="pagenum" id="page281">281</span> -science by such a name; since the word signifies -‘earth-measuring;’ yet the word <i>geometry</i> has retained -its place and answered its purpose perfectly well up to -the present day.</p> -<p>But though the meaning of the term may be modified or -extended, it must be rigorously fixed when it is -appropriated to science. This process is most abundantly -exemplified by the terminology of Natural History, -and especially of Botany, in which each term has -a most precise meaning assigned to it. Thus Linnæus -established exact distinctions between <i>fasciculus</i>, -<i>capitulum</i>, <i>racemus</i>, <i>thyrsus</i>, <i>paniculus</i>, <i>spica</i>, <i>amentum</i>, -<i>corymbus</i>, <i>umbella</i>, <i>cyma</i>, <i>verticillus</i>; or, in the language -of English Botanists, <i>a tuft</i>, <i>a head</i>, <i>a cluster</i>, <i>a -bunch</i>, <i>a panicle</i>, <i>a spike</i>, <i>a catkin</i>, <i>a corymb</i>, <i>an umbel</i>, -<i>a cyme</i>, <i>a whorl</i>. And it has since been laid down as -a rule<a id="fnanchor20-4" href="#note20-4"><span class="fnanchor">20</span></a>, -that each organ ought to have a separate and -appropriate name; so that the term <i>leaf</i>, for instance, -shall never be applied to <i>a leaflet</i>, <i>a bractea</i>, or <i>a sepal</i> -of the calyx.</p> -<div class="footnote"><span class="label"><a id="note20-4" href="#fnanchor20-4">20</a></span> -De Candolle, <i>Theor. El.</i> 328. -</div> -<p>Botanists have not been content with fixing the -meaning of their terms by verbal definition, but have -also illustrated them by figures, which address the eye. -Of these, as excellent modern examples, may be mentioned -those which occur in the works of -Mirbel<a id="fnanchor21-4" href="#note21-4"><span class="fnanchor">21</span></a>, and -Lindley<a id="fnanchor22-4" href="#note22-4"><span class="fnanchor">22</span></a>.</p> -<div class="footnote"><span class="label"><a id="note21-4" href="#fnanchor21-4">21</a></span> -<i>Élémens de Botanique</i>. -</div> -<div class="footnote end"><span class="label"><a id="note22-4" href="#fnanchor22-4">22</a></span> -<i>Elements of Botany</i>. -</div> -<p class="center"><span class="sc">Aphorism</span> VI.</p> -<p><i>When common words are appropriated as technical terms, -this must be done so that they are not ambiguous in their -application.</i></p> -<p><span class="sc">An</span> example will explain this maxim. The conditions -of a body, as a solid, a liquid, and an air, have -been distinguished as different <i>forms</i> of the body. But -the word <i>form</i>, as applied to bodies, has other -meanings; so that if we were to inquire in <i>what form</i> -water exists in a snow-cloud, it might be doubted -whether the forms of crystallization were meant, or <span class="pagenum" id="page282">282</span> -the different forms of ice, water, and vapour. Hence -I have proposed<a id="fnanchor23-4" href="#note23-4"><span class="fnanchor">23</span></a> -to reject the term <i>form</i> in such cases, -and to speak of the different <i>consistence</i> of a body in -these conditions. The term <i>consistence</i> is usually -applied to conditions between solid and fluid; and may -without effort be extended to those limiting conditions. -And though it may appear more harsh to extend the -term <i>consistence</i> to the state of air, it may be justified -by what has been said in speaking of Aphorism V.</p> -<div class="footnote"><span class="label"><a id="note23-4" href="#fnanchor23-4">23</a></span> -<i>Hist. Ind. Sc.</i> b. x. c. ii. sect. 2. -</div> -<p>I may notice another example of the necessity of -avoiding ambiguous words. A philosopher who makes -method his study, would naturally be termed a <i>methodist</i>; -but unluckily this word is already appropriated -to a religious sect: and hence we could hardly venture -to speak of Cæsalpinus, Ray, Morison, Rivinus, -Tournefort, Linnæus, and their successors, as <i>botanical -methodists</i>. Again, by this maxim, we are almost -debarred from using the term <i>physician</i> for a cultivator of -the science of physics, because it already signifies a -practiser of physic. We might, perhaps, still use <i>physician</i> -as the equivalent of the French <i>physicien</i>, in -virtue of Aphorism V.; but probably it would be better -to form a new word. Thus we may say, that while -the Naturalist employs principally the ideas of resemblance -and life, the <i>Physicist</i> proceeds upon the ideas -of force, matter, and the properties of matter.</p> -<p class="end">Whatever may be thought of this proposal, the -maxim which it implies is frequently useful. It is -this.</p> -<p class="center"><span class="sc">Aphorism</span> VII.</p> -<p><i>It is better to form new words as technical terms, than to -employ old ones in which the last three Aphorisms cannot be -complied with.</i></p> -<p><span class="sc">The</span> principal inconvenience attending the -employment of new words constructed expressly for the use -of science, is the difficulty of effectually introducing -them. Readers will not readily take the trouble to -learn the meaning of a word, in which the memory is <span class="pagenum" id="page283">283</span> -not assisted by some obvious suggestion connected with -the common use of language. When this difficulty is -overcome, the new word is better than one merely appropriated; -since it is more secure from vagueness and -confusion. And in cases where the inconveniences -belonging to a scientific use of common words become -great and inevitable, a new word must be framed and -introduced.</p> -<p>The Maxims which belong to the construction of -such words will be stated hereafter; but I may notice -an instance or two tending to show the necessity of -the Maxim now before us.</p> -<p>The word <i>Force</i> has been appropriated in the science -of Mechanics in two senses: as indicating the cause of -motion; and again, as expressing certain measures of -the effects of this cause, in the phrases <i>accelerating -force</i> and <i>moving force</i>. Hence we might have occasion -to speak of the accelerating or moving force <i>of</i> a -certain <i>force</i>; for instance, if we were to say that the -force which governs the motions of the planets resides -in the sun; and that the accelerating force <i>of</i> this <i>force</i> -varies only with the distance, but its moving force -varies as the product of the mass of the sun and the -planet. This is a harsh and incongruous mode of expression; -and might have been avoided, if, instead of -<i>accelerating force</i> and <i>moving force</i>, single abstract -terms had been introduced by Newton: if, for instance, -he had said that the velocity generated in a -second measures the <i>accelerativity</i> of the force which -produces it, and the momentum produced in a second -measures the <i>motivity</i> of the force.</p> -<p>The science which treats of heat has hitherto had no -special designation: treatises upon it have generally -been termed treatises <i>On Heat</i>. But this practice of -employing the same term to denote the property and -the science which treats of it, is awkward, and often -ambiguous. And it is further attended with this -inconvenience, that we have no adjective derived from -the name of the science, as we have in other cases, -when we speak of <i>acoustical</i> experiments and <i>optical</i> -theories. This inconvenience has led various persons -to suggest names for the Science of Heat. M. Comte <span class="pagenum" id="page284">284</span> -terms it <i>Thermology</i>. In the <i>History of the Sciences</i>, -I have named it <i>Thermotics</i>, which appears to me to -agree better with the analogy of the names of other -corresponding sciences, <i>Acoustics</i> and <i>Optics</i>. -<i>Electricity</i> is in the same condition as Heat; having -only one word to express the property and the science. -M. Le Comte proposes <i>Electrology</i>: for the same reason -as before, I should conceive <i>Electrics</i> more agreeable to -analogy. The coincidence of the word with the plural -of Electric would not give rise to ambiguity; for <i>Electrics</i>, -taken as the name of a science, would be singular, -like <i>Optics</i> and <i>Mechanics</i>. But a term offers itself to -express <i>common</i> or <i>machine Electrics</i>, which appears -worthy of admission, though involving a theoretical -view. The received doctrine of the difference between -Voltaic and Common Electricity is, that in the former -case the fluid must be considered as in motion, in the -latter as at rest. The science which treats of the former -class of subjects is commonly termed <i>Electrodynamics</i>, -which obviously suggests the name <i>Electrostatics</i> for the latter.</p> -<p>The subject of the Tides is, in like manner, destitute -of any name which designates the science concerned -about it. I have ventured to employ the term <i>Tidology</i>, -having been much engaged in tidological researches.</p> -<p>Many persons possess a peculiarity of vision, which -disables them from distinguishing certain colours. On -examining many such cases, we find that in all such -persons the peculiarities are the same; all of them -confounding scarlet with green, and pink with blue. -Hence they form a class, which, for the convenience of -physiologists and others, ought to have a fixed designation. -Instead of calling them, as has usually been -done, ‘persons having a peculiarity of vision,’ we might -take a Greek term implying this meaning, and term -them <i>Idiopts</i>.</p> -<p class="end">But my business at present is not to speak of the -selection of new terms when they are introduced, but -to illustrate the maxim that the necessity for their -introduction often arises. The construction of new terms -will be treated of subsequently. <span class="pagenum" id="page285">285</span></p> -<p class="center" id="a8"><span class="sc">Aphorism</span> VIII.</p> -<p><i>Terms must be constructed and appropriated so as to be -fitted to enunciate simply and clearly true general propositions.</i></p> -<p><span class="sc">This</span> Aphorism may be considered as the fundamental -principle and supreme rule of all scientific terminology. -It is asserted by Cuvier, speaking of a particular case. -Thus he says<a id="fnanchor24-4" href="#note24-4"><span class="fnanchor">24</span></a> -of Gmelin, that by placing -the lamantin in the genus of morses, and the siren in -the genus of eels, he had rendered every general proposition -respecting the organization of those genera -impossible.</p> -<div class="footnote"><span class="label"><a id="note24-4" href="#fnanchor24-4">24</a></span> -<i>Règne Animal</i>, Introd. viii. -</div> -<p>The maxim is true of words appropriated as well -as invented, and applies equally to the mathematical, -chemical, and classificatory sciences. With regard to -most of these, and especially the two former classes, it -has been abundantly exemplified already, in what has -previously been said, and in the <i>History of the Sciences</i>. -For we have there had to notice many technical terms, -with the occasions of their introduction; and all these -occasions have involved the intention of expressing in -a convenient manner some truth or supposed truth. -The terms of Astronomy were adopted for the purpose -of stating and reasoning upon the relations of the -celestial motions, according to the doctrine of the sphere, -and the other laws which were discovered by astronomers. -The few technical terms which belong to Mechanics, -<i>force</i>, <i>velocity</i>, <i>momentum</i>, <i>inertia</i>, &c., were -employed from the first with a view to the expression -of the laws of motion and of rest; and were, in the -end, limited so as truly and simply to express those -laws when they were fully ascertained. In Chemistry, -the term <i>phlogiston</i> was useful, as has been shown in -the <i>History</i>, in classing together processes which really -are of the same nature; and the nomenclature of the -<i>oxygen</i> theory was still preferable, because it enabled -the chemist to express a still greater number of general truths. <span class="pagenum" id="page286">286</span></p> -<p>To the connexion here asserted, of theory and nomenclature, -we have the testimony of the author of -the oxygen theory. In the Preface to his <i>Chemistry</i>, -Lavoisier says:—‘Thus while I thought myself employed -only in forming a Nomenclature, and while I -proposed to myself nothing more than to improve the -chemical language, my work transformed itself by degrees, -without my being able to prevent it, into a -Treatise on the Elements of Chemistry.’ And he then -proceeds to show how this happened.</p> -<p>It is, however, mainly through the progress of Natural -History in modern times, that philosophers have -been led to see the importance and necessity of new -terms in expressing new truths. Thus Harvey, in the -Preface to his work on Generation, says:—‘Be not -offended if in setting out the History of the Egg I -make use of a new method, and sometimes of unusual -terms. For as they which find out a new plantation -and new shores call them by names of their own coining, -which posterity afterwards accepts and receives, -so those that find out new secrets have good title to -their compellation. And here, methinks, I hear Galen -advising: If we consent in the things, contend not -about the words.’</p> -<p>The Nomenclature which answers the purposes of -Natural History is a Systematic Nomenclature, and -will be further considered under the next Aphorism. -But we may remark, that the Aphorism now before -us governs the use of words, not in science only, but -in common language also. Are we to apply the name -<i>fish</i> to animals of the whale kind? The answer is -determined by our present rule: we are to do so, or not, -accordingly as we can best express true propositions. -If we are speaking of the internal structure and physiology -of the animal, we must not call them <i>fish</i>; for -in these respects they deviate widely from fishes: they -have warm blood, and produce and suckle their young -as land quadrupeds do. But this would not prevent -our speaking of the <i>whale-fishery</i>, and calling such -animals <i>fish</i> on all occasions connected with this employment; -for the relations thus arising depend upon the -animal’s living in the water, and being caught in a <span class="pagenum" id="page287">287</span> -manner similar to other fishes. A plea that human -laws which mention fish do not apply to whales, would -be rejected at once by an intelligent judge.</p> -<p>[A bituminiferous deposit which occurs amongst the -coal measures in the neighbourhood of Edinburgh was -used as coal, and called ‘Boghead Cannel Coal.’ But -a lawsuit arose upon the question whether this, which -geologically was not <i>the coal</i>, should be regarded in -law as <i>coal</i>. The opinions of chemists and geologists, -as well as of lawyers, were discrepant, and a direct -decision of the case was evaded.<a id="fnanchor25-4" href="#note25-4"><span class="fnanchor">25</span></a>]</p> -<div class="footnote end"><span class="label"><a id="note25-4" href="#fnanchor25-4">25</a></span> -Miller’s <i>Chemistry</i>, iii. 98. -</div> -<p class="center" id="a9"><span class="sc">Aphorism</span> IX.</p> -<p><i>In the Classificatory Sciences, a Systematic Nomenclature -is necessary; and the System and the Nomenclature are -each essential to the utility of the other.</i></p> -<p><span class="sc">The</span> inconveniences arising from the want of a good -Nomenclature were long felt in Botany, and are still -felt in Mineralogy. The attempts to remedy them by -<i>Synonymies</i> are very ineffective, for such comparisons of -synonyms do not supply a systematic nomenclature; -and such a one alone can enable us to state general -truths respecting the objects of which the classificatory -sciences treat. The <i>System</i> and the <i>Names</i> ought to -be introduced together; for the former is a collection -of asserted analogies and resemblances, for which -the latter provide simple and permanent expressions. -Hence it has repeatedly occurred in the progress of -Natural History, that good Systems did not take root, -or produce any lasting effect among naturalists, because -they were not accompanied by a corresponding Nomenclature. -In this way, as we have already noticed, -the excellent botanical System of Cæsalpinus was -without immediate effect upon the science. The work -of Willoughby, as Cuvier -says<a id="fnanchor26-4" href="#note26-4"><span class="fnanchor">26</span></a>, -forms an epoch, and <span class="pagenum" id="page288">288</span> -a happy epoch in Ichthyology; yet because Willoughby -had no Nomenclature of his own, and no fixed names -for his genera, his immediate influence was not great. -Again, in speaking of Schlotheim’s work containing -representations of fossil vegetables, M. Adolphe Brongniart -observes<a id="fnanchor27-4" href="#note27-4"><span class="fnanchor">27</span></a> -that the figures and descriptions are -so good, that if the author had established a -nomenclature for the objects he describes, his work would -have become the basis of all succeeding labours on -the subject.</p> -<div class="footnote"><span class="label"><a id="note26-4" href="#fnanchor26-4">26</a></span> -<i>Hist. des Poissons</i>, Pref. -</div> -<div class="footnote"><span class="label"><a id="note27-4" href="#fnanchor27-4">27</a></span> -<i>Prodrom. Veg. Foss.</i> p. 3. -</div> -<p>As additional examples of cases in which the improvement -of classification, in recent times, has led -philosophers to propose new names, I may mention -the term <i>Pœcilite</i>, proposed by Mr. Conybeare -to designate the group of strata which lies below the oolites -and lias, including the new red or variegated sandstone, -with the keuper above, and the magnesian limestone below it. -Again, the transition districts of our -island have recently been reduced to system by Professor -Sedgwick and Mr. Murchison; and this step has -been marked by the terms <i>Cambrian</i> system, and -<i>Silurian</i> system, applied to the two great groups of -formations which they have respectively examined, -and by several other names of the subordinate members of these formations.</p> -<p>Thus System and Nomenclature are each essential -to the other. Without Nomenclature, the system is -not permanently incorporated into the general body of -knowledge, and made an instrument of future progress. -Without System, the names cannot express general -truths, and contain no reason why they should be -employed in preference to any other names.</p> -<p>This has been generally acknowledged by the most -philosophical naturalists of modern times. Thus -Linnæus begins that part of his Botanical Philosophy in -which names are treated of, by stating that the -foundation of botany is twofold, <i>Disposition</i> and -<i>Denomination</i>; and he adds this Latin line,</p> -<p class="eq center"><span class="medium">Nomina si nescis perit et cognitio rerum.</span> -<span class="pagenum" id="page289">289</span></p> -<p class="eq noind">And Cuvier, in the Preface to his <i>Animal Kingdom</i>, -explains, in a very striking manner, how the attempt -to connect zoology with anatomy led him, at the same -time, to reform the classifications, and to correct the -nomenclature of preceding zoologists.</p> -<p>I have stated that in Mineralogy we are still destitute -of a good nomenclature generally current. From -what has now been said, it will be seen that it may -be very far from easy to supply this defect, since we -have, as yet, no generally received system of mineralogical -classification. Till we know what are really -different species of minerals, and in what larger -groups these species can be arranged, so as to have -common properties, we shall never obtain a permanent -mineralogical nomenclature. Thus <i>Leucocyclite</i> and -<i>Tesselite</i> are minerals previously confounded with -Apophyllite, which Sir John Herschel and Sir David -Brewster distinguished by those names, in consequence -of certain optical properties which they exhibit. But -are these properties definite distinctions? and are -there any external differences corresponding to them? -If not, can we consider them as separate species? and -if not separate species, ought they to have separate -names? In like manner, we might ask if <i>Augite</i> and -<i>Hornblende</i> are really the same species, as Gustavus -Rose has maintained? if <i>Diallage</i> and <i>Hypersthene</i> are -not definitely distinguished, which has been asserted -by Kobell? Till such questions are settled, we cannot -have a fixed nomenclature in mineralogy. What -appears the best course to follow in the present state -of the science, I shall consider when we come to speak -of the form of technical terms.</p> -<p class="end">I may, however, notice here that the main Forms -of systematic nomenclature are two:—terms which -are produced by combining words of higher and lower -generality, as the binary names, consisting of the name -of the genus and the species, generally employed by -natural historians since the time of Linnæus;—and -terms in which some relation of things is indicated by -a change in the form of the word, for example, an -alteration of its termination, of which kind of <span class="pagenum" id="page290">290</span> -nomenclature we have a conspicuous example in the modern -chemistry.</p> -<p class="center" id="a10"><span class="sc">Aphorism</span> X.</p> -<p><i>New terms and changes of terms, which are not needed in -order to express truth, are to be avoided.</i></p> -<p><span class="sc">As</span> the Seventh Aphorism asserted that novelties -in language may be and ought to be introduced, when -they aid the enunciation of truths, we now declare -that they are not admissible in any other case. New -terms and new systems of terms are not to be introduced, -for example, in virtue of their own neatness or -symmetry, or other merits, if there is no occasion for -their use.</p> -<p>I may mention, as an old example of a superfluous -attempt of this kind, an occurrence in the history of -Astronomy. In 1628 John Bayer and Julius Schiller -devised a <i>Cœlum Christianum</i>, in which the common -names of the planets, &c., were replaced by those of -Adam, Moses, and the Patriarchs. The twelve Signs -became the twelve Apostles, and the constellations -became sacred places and things. Peireskius, who had -to pronounce upon the value of this proposal, praised -the piety of the inventors, but did not approve, he -said<a id="fnanchor28-4" href="#note28-4"><span class="fnanchor">28</span></a>, -the design of perverting and confounding -whatever of celestial information from the period of the -earliest memory is found in books.</p> -<div class="footnote"><span class="label"><a id="note28-4" href="#fnanchor28-4">28</a></span> -Gassendi, <i>Vita Peireskii</i>, 300. -</div> -<p>Nor are slight anomalies in the existing language of -science sufficient ground for a change, if they do not -seriously interfere with the expression of our knowledge. -Thus Linnæus says<a id="fnanchor29-4" href="#note29-4"><span class="fnanchor">29</span></a> -that a fair generic name -is not to be exchanged for another though apter one: -and<a id="fnanchor30-4" href="#note30-4"><span class="fnanchor">30</span></a> -if we separate an old genus into several, we -must try to find names for them among the synonyms -which describe the old genus. This maxim excludes -the restoration of ancient names long disused, no less -than the needless invention of new ones. Linnæus <span class="pagenum" id="page291">291</span> -lays down this rule<a id="fnanchor31-4" href="#note31-4"><span class="fnanchor">31</span></a>; -and adds, that the botanists of -the sixteenth century well nigh ruined botany by their -anxiety to recover the ancient names of plants. In -like manner Cuvier<a id="fnanchor32-4" href="#note32-4"><span class="fnanchor">32</span></a> -laments it as a misfortune, that -he has had to introduce many new names; and declares -earnestly that he has taken great pains to preserve -those of his predecessors.</p> -<div class="footnote"><span class="label"><a id="note29-4" href="#fnanchor29-4">29</a></span> -<i>Phil. Bot.</i> 246. -</div> -<div class="footnote"><span class="label"><a id="note30-4" href="#fnanchor30-4">30</a></span> -<i>Ib.</i> 247. -</div> -<div class="footnote"><span class="label"><a id="note31-4" href="#fnanchor31-4">31</a></span> -<i>Phil. Bot.</i> 248. -</div> -<div class="footnote"><span class="label"><a id="note32-4" href="#fnanchor32-4">32</a></span> -<i>Règne Anim.</i> Pref. xvi. -</div> -<p>The great bulk which the Synonymy of botany and -of mineralogy have attained, shows us that this maxim -has not been universally attended to. In these cases, -however, the multiplication of different names for the -same kind of object has arisen in general from ignorance -of the identity of it under different circumstances, -or from the want of a system which might assign to -it its proper place. But there are other instances, in -which the multiplication of names has arisen not from -defect, but from excess, of the spirit of system. The -love which speculative men bear towards symmetry -and completeness is constantly at work, to make them -create systems of classification more regular and more -perfect than can be verified by the facts: and as good -systems are closely connected with a good nomenclature, -systems thus erroneous and superfluous lead to -a nomenclature which is prejudicial to science. For -although such a nomenclature is finally expelled, when -it is found not to aid us in expressing the true laws -of nature, it may obtain some temporary sway, during -which, and even afterwards, it may be a source of -much confusion.</p> -<p>We have a conspicuous example of such a result in -the geological nomenclature of Werner and his school. -Thus it was assumed, in Werner’s system, that his -<i>First</i>, <i>Second</i>, and <i>Third Flötz Limestone</i>, his <i>Old</i> and -<i>New Red Sandstone</i>, were universal formations; and -geologists looked upon it as their business to detect -these strata in other countries. Names were thus -assigned to the rocks of various parts of Europe, which -created immense perplexity before they were again -ejected. The geological terms which now prevail, for <span class="pagenum" id="page292">292</span> -instance, those of Smith, are for the most part not -systematic, but are borrowed from accidents, as localities, -or popular names; as <i>Oxford Clay</i> and <i>Cornbrash</i>; -and hence they are not liable to be thrust out -on a change of system. On the other hand we do not -find sufficient reason to accept the system of names of -strata proposed by Mr. Conybeare in the <i>Introduction -to the Geology of England and Wales</i>, according to -which the <i>Carboniferous Rocks</i> are the <i>Medial Order</i>,—having -above them the <i>Supermedial Order</i> (<i>New Red -Sand</i>, <i>Oolites</i> and <i>Chalk</i>), and above these the -<i>Superior Order</i> (<i>Tertiary Rocks</i>); and again,—having -below, the <i>Submedial Order</i> (the <i>Transition Rocks</i>), -and the <i>Inferior Order</i> (<i>Mica Slate</i>, <i>Gneiss</i>, <i>Granite</i>). -For though these names have long been proposed, it -does not appear that they are useful in enunciating -geological truths. We may, it would seem, pronounce -the same judgment respecting the system of geological -names proposed by M. Alexander Brongniart, in his -<i>Tableau des Terrains qui composent l’écorce du Globe</i>. -He divides these strata into nine classes, which he -terms <i>Terrains Alluviens</i>, <i>Lysiens</i>, <i>Pyrogenes</i>, <i>Clysmiens</i>, -<i>Yzemiens</i>, <i>Hemilysiens</i>, <i>Agalysiens</i>, <i>Plutoniques</i>, -<i>Vulcaniques</i>. These classes are again variously subdivided: -thus the Terrains Yzemiens are <i>Thalassiques</i>, -<i>Pelagiques</i>, and <i>Abyssiques</i>; and the Abyssiques are -subdivided into <i>Lias</i>, <i>Keuper</i>, <i>Conchiliens</i>, <i>Pœciliens</i>, -<i>Peneens</i>, <i>Rudimentaires</i>, <i>Entritiques</i>, <i>Houillers</i>, -<i>Carbonifers</i> and <i>Gres Rouge Ancien</i>. Scarcely any amount -of new truths would induce geologists to burthen -themselves at once with this enormous system of new -names: but in fact, it is evident that any portion of -truth, which any author can have brought to light, -may be conveyed by means of a much simpler apparatus. -Such a nomenclature carries its condemnation -on its own face.</p> -<p>Nearly the same may be said of the systematic nomenclature -proposed for mineralogy by Professor Mohs. -Even if all his Genera be really natural groups, -(a doctrine which we can have no confidence in till they are -confirmed by the evidence of chemistry,) there is no <span class="pagenum" id="page293">293</span> -necessity to make so great a change in the received -names of minerals. His proceeding in this respect, so -different from the temperance of Linnæus and Cuvier, -has probably ensured a speedy oblivion to this part of -his system. In crystallography, on the other hand, in -which Mohs’s improvements have been very valuable, -there are several terms introduced by him, as <i>rhombohedron</i>, -<i>scalenohedron</i>, <i>hemihedral</i>, <i>systems</i> of -crystallization, which will probably be a permanent portion of -the language of science.</p> -<p>I may remark, in general, that the only persons who -succeed in making great alterations in the language of -science, are not those who make names arbitrarily and -as an exercise of ingenuity, but those who have much -new knowledge to communicate; so that the vehicle is -commended to general reception by the value of what -it contains. It is only eminent discoverers to whom -the authority is conceded of introducing a new system -of names; just as it is only the highest authority in the -state which has the power of putting a new coinage in -circulation.</p> -<p>I will here quote some judicious remarks of Mr. -Howard, which fall partly under this Aphorism, and -partly under some which follow. He had proposed, as -names for the kinds of clouds, the following: <i>Cirrus</i>, -<i>Cirrocumulus</i>, <i>Cirrostratus</i>, <i>Cumulostratus</i>, <i>Cumulus</i>, -<i>Nimbus</i>, <i>Stratus</i>. In an abridgment of his views, given -in the Supplement to the <i>Encyclopædia Britannica</i>, -English names were proposed as the equivalents of these; -<i>Curlcloud</i>, <i>Sondercloud</i>, <i>Wanecloud</i>, <i>Twaincloud</i>, -<i>Stackencloud</i>, <i>Raincloud</i>, <i>Fallcloud</i>. -Upon these Mr. Howard observes: ‘I mention these, in order -to have the opportunity of saying that I do not adopt them. -The names for the clouds which I deduced from the Latin, -are but seven in number, and very easy to remember. -They were intended as <em>arbitrary terms</em> for the <em>structure</em> -of clouds, and the meaning of them was carefully fixed -by a definition. The observer having once made himself -master of this, was able to apply the term with -correctness, after a little experience, to the subject -under all its varieties of form, colour, or position. The <span class="pagenum" id="page294">294</span> -new names, if meant to be another set of arbitrary -terms, are superfluous; if intended to convey in themselves -an explanation in English, they fail in this, by -applying to some part or circumstance only of the definition; -the <em>whole</em> of which must be kept in view to -study the subject with success. To take for an example -the first of the modifications. The term <i>cirrus</i> -very readily takes an abstract meaning, equally applicable -to the rectilinear as to the flexuous forms of the -subject. But the name of <i>curl-cloud</i> will not, without -some violence to its <em>obvious sense</em>, acquire this more -extensive one: and will therefore be apt to mislead the -reader rather than further his progress. Others of -these names are as devoid of a meaning obvious to the -English reader, as the Latin terms themselves. But -the principal objection to English or any other local -terms, remains to be stated. They take away from -the nomenclature its general advantage of constituting, -as far as it goes, an universal language, by means -of which the intelligent of every country may convey -to each other their ideas without the necessity of -translation.’</p> -<p class="end">I here adduce these as examples of the arguments -against changing an established nomenclature. As -grounds of selecting a new one, they may be taken -into account hereafter.</p> -<p class="center" id="a11"><span class="sc">Aphorism</span> XI.</p> -<p><i>Terms which imply theoretical views are admissible, as -far as the theory is proved.</i></p> -<p><span class="sc">It</span> is not unfrequently stated that the circumstances -from which the names employed in science borrow their -meaning, ought to be facts and not theories. But such -a recommendation implies a belief that facts are rigorously -distinguished from theories and directly opposed -to them; which belief, we have repeatedly seen, is unfounded. -When theories are firmly established, they -become facts; and names founded on such theoretical -views are unexceptionable. If we speak of the <i>minor</i> <span class="pagenum" id="page295">295</span> -<i>axis</i> of Jupiter’s <i>orbit</i>, or of his <i>density</i>, or of <i>the angle -of refraction</i>, or <i>the length of an undulation</i> of red -light, we assume certain theories; but inasmuch as the -theories are now the inevitable interpretation of ascertained -facts, we can have no better terms to designate -the conceptions thus referred to. And hence the rule -which we must follow is, not that our terms must -involve no theory, but that they imply the theory only -in that sense in which it is the interpretation of the -facts.</p> -<p>For example, the term <i>polarization</i> of light was -objected to, as involving a theory. Perhaps the term -was at first suggested by conceiving light to consist of -particles having poles turned in a particular manner. -But among intelligent speculators, the notion of -polarization soon reduced itself to the simple conception of -opposite properties in opposite positions, which is a bare -statement of the fact: and the term being understood -to have this meaning, is a perfectly good term, and -indeed the best which we can imagine for designating -what is intended.</p> -<p>I need hardly add the caution, that names involving -theoretical views not in accordance with facts are to be -rejected. The following instances exemplify both the -positive and the negative application of this maxim.</p> -<p>The distinction of <i>primary</i> and <i>secondary</i> rocks in -geology was founded upon a theory; namely, that those -which do not contain any organic remains were first -deposited, and afterwards, those which contain plants -and animals. But this theory was insecure from the -first. The difficulty of making the separation which -it implied, led to the introduction of a class of <i>transition</i> -rocks. And the recent researches of geologists lead -them to the conclusion, that those rocks which are -termed <i>primary</i>, may be the newest, not the oldest, -productions of nature.</p> -<p>In order to avoid this incongruity, other terms have -been proposed as substitutes for these. Sir C. Lyell -remarks<a id="fnanchor33-4" href="#note33-4"><span class="fnanchor">33</span></a>, -that granite, gneiss, and the like, form a class <span class="pagenum" id="page296">296</span> -which should be designated by a common name; which -name should not be of chronological import. He proposes -<i>hypogene</i>, signifying ‘nether-formed;’ and thus -he adopts the theory that they have not assumed their -present form and structure at the surface, but determines -nothing of the period when they were produced.</p> -<div class="footnote"><span class="label"><a id="note33-4" href="#fnanchor33-4">33</a></span> -<i>Princ. Geol.</i> iv. 386. -</div> -<p>These hypogene rocks, again, he divides into unstratified -or <i>plutonic</i>, and altered stratified, or <i>metamorphic</i>; -the latter term implying the hypothesis that the stratified -rocks to which it is applied have been altered, by -the effect of fire or otherwise, since they were deposited. -That fossiliferous strata, in some cases at least, have -undergone such a change, is demonstrable from -facts<a id="fnanchor34-4" href="#note34-4"><span class="fnanchor">34</span></a>.</p> -<div class="footnote"><span class="label"><a id="note34-4" href="#fnanchor34-4">34</a></span> -<i>Elem. Geol.</i> p. 17. -</div> -<p>The modern nomenclature of chemistry implies the -oxygen theory of chemistry. Hence it has sometimes -been objected to. Thus Davy, in speaking of the -Lavoisierian nomenclature, makes the following remarks, -which, however plausible they may sound, will -be found to be utterly -erroneous<a id="fnanchor35-4" href="#note35-4"><span class="fnanchor">35</span></a>. -‘Simplicity and -precision ought to be the characteristics of a scientific -nomenclature: words should signify <em>things</em>, or the <em>analogies</em> of -things, and not <em>opinions</em>.... A substance in one age -supposed to be simple, in another is proved to be compound, -and <i>vice versâ</i>. A theoretical nomenclature is liable -to continual alterations: <i>oxygenated muriatic acid</i> is -as improper a term as <i>dephlogisticated marine acid</i>. -Every school believes itself to be in the right: and if -every school assumes to itself the liberty of altering -the names of chemical substances in consequence of -<em>new ideas</em> of their composition, there can be no permanency -in the language of the science; it must always -be confused and uncertain. Bodies which are <em>similar</em> -to each other should always be classed together; and -there is a presumption that their composition is <em>analogous</em>. -<i>Metals</i>, <i>earths</i>, <i>alkalis</i>, are appropriate names -for the bodies they represent, and independent of all -speculation: whereas <i>oxides</i>, <i>sulphurets</i>, and <i>muriates</i> -are terms founded upon opinions of the composition of -bodies, some of which have been already found erroneous. <span class="pagenum" id="page297">297</span> -The least dangerous mode of giving a systematic form -to a language seems to be to signify the analogies of -substances by some common sign affixed to the beginning -or the termination of the word. Thus as the -metals have been distinguished by a termination in -<i>um</i>, as <i>aurum</i>, so their calciform or oxidated state -might have been denoted by a termination in <i>a</i>, as -<i>aura</i>: and no progress, however great, in the science -could render it necessary that such a mode of appellation should be changed.’</p> -<div class="footnote"><span class="label"><a id="note35-4" href="#fnanchor35-4">35</a></span> -<i>Elements of Chem. Phil.</i> p. 46. -</div> -<p>These remarks are founded upon distinctions which -have no real existence. We cannot separate <em>things</em> -from their <em>properties</em>, nor can we consider their properties -and analogies in any other way than by having -<em>opinions</em> about them. By contrasting <em>analogies</em> with -<em>opinions</em>, it might appear as if the author maintained -that there were certain analogies about which there -was no room for erroneous opinions. Yet the analogies -of chemical compounds, are, in fact, those points -which have been most the subject of difference of opinion, -and on which the revolutions of theories have -most changed men’s views. As an example of analogies which -are still recognized under alterations of -theory, the writer gives the relation of a metal to its -oxide or calciform state. But this analogy of metallic -oxides, as Red Copper or Iron Ore, to Calx, or burnt -lime, is very far from being self-evident;—so far indeed, -that the recognition of the analogy was a great -step in chemical <em>theory</em>. The terms which he quotes, -<i>oxygenated muriatic acid</i> (and the same may be said of -<i>dephlogisticated marine acid</i>,) if improper, are so not -because they involve theory, but because they involve -false theory;—not because those who framed them did -not endeavour to express analogies, but because they -expressed analogies about which they were mistaken. -Unconnected names, as <i>metals</i>, <i>earths</i>, <i>alkalis</i>, are good -as the <em>basis</em> of a systematic nomenclature, but they -are not substitutes for such a nomenclature. A systematic -nomenclature is an instrument of great utility -and power, as the modern history of chemistry has -shown. It would be highly unphilosophical to reject <span class="pagenum" id="page298">298</span> -the use of such an instrument, because, in the course -of the revolutions of science, we may have to modify, -or even to remodel it altogether. Its utility is not by -that means destroyed. It has retained, transmitted, -and enabled us to reason upon, the doctrines of the -earlier theory, so far as they are true; and when this -theory is absorbed into a more comprehensive one, (for -this, and not its refutation, is the end of a theory <i>so -far as</i> it is true,) the nomenclature is easily translated -into that which the new theory introduces. We have -seen, in the history of astronomy, how valuable the -theory of <i>epicycles</i> was, in its time: the nomenclature -of the relations of a planet’s orbit, which that theory -introduced, was one of Kepler’s resources in discovering -the <i>elliptical</i> theory; and, though now superseded, -is still readily intelligible to astronomers.</p> -<p>This is not the place to discuss the reasons for the -<em>form</em> of scientific terms; otherwise we might ask, in -reference to the objections to the Lavoisierian nomenclature, -if such forms as <i>aurum</i> and <i>aura</i> are good to -represent the absence or presence of oxygen, why such -forms as <i>sulphite</i> and <i>sulphate</i> are not equally good to -represent the presence of what we may call a smaller -or larger dose of oxygen, so long as the oxygen theory -is admitted in its present form; and to indicate still -the difference of the same substances, if under any -change of theory it should come to be interpreted in a -new manner.</p> -<p>But I do not now dwell upon such arguments, my -object in this place being to show that terms involving -theory are not only allowable, if understood so far as -the theory is proved, but of great value, and indeed of -indispensable use, in science. The objection to them is -inconsistent with the objects of science. If, after all -that has been done in chemistry or any other science, -we have arrived at no solid knowledge, no permanent -truth;—if all that we believe now may be proved to -be false to-morrow;—then indeed our opinions and -theories are corruptible elements, on which it would -be unwise to rest any thing important, and which we -might wish to exclude, even from our names. But if <span class="pagenum" id="page299">299</span> -our knowledge has no more security than this, we can -find no reason why we should wish at all to have names -of things, since the names are needed mainly that we -may reason upon and increase our knowledge such as -it is. If we are condemned to endless alternations of -varying opinions, then, no doubt, our theoretical terms -may be a source of confusion; but then, where would -be the advantage of their being otherwise? what would -be the value of words which should express in a more -precise manner opinions equally fleeting? It will perhaps -be said, our terms must express facts, not theories: -but of this distinction so applied we have repeatedly -shown the futility. Theories firmly established -are facts. Is it not a fact that the rusting of iron -arises from the metal combining with the oxygen of -the atmosphere? Is it not a fact that a combination -of oxygen and hydrogen produces water? That our -terms should express <em>such</em> facts, is precisely what we -are here inculcating.</p> -<p>Our examination of the history of science has led us -to a view very different from that which represents it -as consisting in the succession of hostile opinions. It -is, on the contrary, a progress, in which each step is -recognized and employed in the succeeding one. Every -theory, so far as it is true, (and all that have prevailed -extensively and long, contain a large portion of truth,) -is taken up into the theory which succeeds and seems -to expel it. All the narrower inductions of the first -are included in the more comprehensive generalizations -of the second. And this is performed mainly by means -of such terms as we are now considering;—terms involving -the previous theory. It is by means of such -terms, that the truths at first ascertained become so -familiar and manageable, that they can be employed as -elementary facts in the formation of higher inductions.</p> -<p>These principles must be applied also, though with -great caution, and in a temperate manner, even to -descriptive language. Thus the mode of describing the -forms of crystals adopted by Werner and Romé de l’Isle -was to consider an original form, from which other -forms are derived by <i>truncations</i> of the edges and the <span class="pagenum" id="page300">300</span> -angles. Haüy’s method of describing the same forms, -was to consider them as built up of rows of small -solids, the angles being determined by the <i>decrements</i> -of these rows. Both these methods of description involve -hypothetical views; and the last was intended to -rest on a true physical theory of the constitution of -crystals. Both hypotheses are doubtful or false: yet -both these methods are good as modes of description: -nor is Haüy’s terminology vitiated, if we suppose (as -in fact we must suppose in many instances,) that crystalline -bodies are not really made up of such small -solids. The mode of describing an octahedron of fluor -spar, as derived from the cube, by decrements of one -row on all the edges, would still be proper and useful -as a description, whatever judgment we should form of -the material structure of the body. But then, we must -consider the solids which are thus introduced into the -description as merely hypothetical geometrical forms, -serving to determine the angles of the faces. It is in -this way alone that Haüy’s nomenclature can now be -retained.</p> -<p>In like manner we may admit theoretical views into -the descriptive phraseology of other parts of Natural -History: and the theoretical terms will replace the -obvious images, in proportion as the theory is generally -accepted and familiarly applied. For example, in -speaking of the Honeysuckle, we may say that the -upper leaves are <i>perfoliate</i>, meaning that a single -round leaf is perforated by the stalk, or threaded upon -it. Here is an image which sufficiently conveys the -notion of the form. But it is now generally recognized -that this apparent single leaf is, in fact, two opposite -leaves joined together at their bases. If this were doubted, -it may be proved by comparing the upper leaves -with the lower, which are really separate and opposite. -Hence the term <i>connate</i> is applied to these conjoined -opposite leaves, implying that they grow together; or -they are called <i>connato-perfoliate</i>. Again; formerly -the corolla was called <i>monopetalous</i> or <i>polypetalous</i>, as -it consisted of one part or of several: but it is now -agreed among botanists that those corollas which <span class="pagenum" id="page301">301</span> appear -to consist of a single part, are, in fact, composed -of several soldered together; hence the term <i>gamopetalous</i> -is now employed (by De Candolle and his followers) instead -of monopetalous<a id="fnanchor36-4" href="#note36-4"><span class="fnanchor">36</span></a>.</p> -<div class="footnote"><span class="label"><a id="note36-4" href="#fnanchor36-4">36</a></span> -On this subject, see Illiger, <i>Versuch einer Systematischen Vollständigen -Terminologie für das Thierreich und Pflanzenreich</i> (1810). De Candolle, <i>Théorie -Élémentaire de la Botanique</i>. -</div> -<p class="end">In this way the language of Natural History not -only expresses, but inevitably implies, general laws of -nature; and words are thus fitted to aid the progress -of knowledge in this, as in other provinces of science.</p> -<p class="center" id="a12"><span class="sc">Aphorism</span> XII.</p> -<p><i>If terms are systematically good, they are not to be rejected -because they are etymologically inaccurate.</i></p> -<p><span class="sc">Terms</span> belonging to a system are defined, not by the -meaning of their radical words, but by their place in -the system. That they should be appropriate in their -signification, aids the processes of introducing and -remembering them, and should therefore be carefully -attended to by those who invent and establish them; -but this once done, no objections founded upon their -etymological import are of any material weight. We -find no inconvenience in the circumstance that <i>geometry</i> -means the measuring of the earth, that the name -<i>porphyry</i> is applied to many rocks which have no fiery -spots, as the word implies, and <i>oolite</i> to strata which -have no roelike structure. In like manner, if the term -<i>pœcilite</i> were already generally received, as the name -of a certain group of strata, it would be no valid -ground for quarrelling with it, that this group was not -always variegated in colour, or that other groups were -equally variegated: although undoubtedly in <em>introducing</em> -such a term, care should be taken to make it -as distinctive as possible. It often happens, as we have -seen, that by the natural progress of changes in language, -a word is steadily confirmed in a sense quite -different from its etymological import. But though <span class="pagenum" id="page302">302</span> -we may accept such instances, we must not wantonly -attempt to imitate them. I say, not wantonly: for if -the progress of scientific identification compel us to -follow any class of objects into circumstances where -the derivation of the term is inapplicable, we may still -consider the term as an unmeaning sound, or rather -an historical symbol, expressing a certain member of -our system. Thus if, in following the course of the -<i>mountain</i> or <i>carboniferous</i> limestone, we find that in -Ireland it does not form mountains nor contain coal, -we should act unwisely in breaking down the nomenclature -in which our systematic relations are already -expressed, in order to gain, in a particular case, -a propriety of language which has no scientific value.</p> -<p>All attempts to act upon the maxim opposite to -this, and to make our scientific names properly descriptive -of the objects, have failed and must fail. For -the marks which really distinguish the natural classes -of objects, are by no means obvious. The discovery of -them is one of the most important steps in science; -and when they are discovered, they are constantly -liable to exceptions, because they do not contain the -essential differences of the classes. The natural order -<i>Umbellatæ</i>, in order to be a natural order, -must contain some plants which have not umbels, as -<i>Eryngium</i><a id="fnanchor37-4" href="#note37-4"><span class="fnanchor">37</span></a>. -‘In such cases,’ said Linnæus, ‘it is of small import -what you call the order, if you take a proper series -of plants, and give it some name which is clearly understood -to apply to the plants you have associated.’ -‘I have,’ he adds, ‘followed the rule of borrowing the -name <i>à fortiori</i>, from the principal feature.’</p> -<div class="footnote"><span class="label"><a id="note37-4" href="#fnanchor37-4">37</a></span> -See <i>Hist. Ind. Sc.</i> b. xvi. c. iv. sect. 5. -</div> -<p>The distinction of crystals into systems according to -the degree of symmetry which obtains in them, has -been explained elsewhere. Two of these systems, of -which the relation as to symmetry might be expressed -by saying that one is <i>square pyramidal</i> and the other -<i>oblong pyramidal</i>, or the first <i>square prismatic</i> and the -second <i>oblong prismatic</i>, are termed by Mohs, the first, -<i>Pyramidal</i>, and the second <i>Prismatic</i>. And it may <span class="pagenum" id="page303">303</span> -be doubted whether it is worth while to invent other -terms, though these are thus defective in characteristic -significance. As an example of a needless rejection of -old terms in virtue of a supposed impropriety in their -meaning, I may mention the attempt made in the last -edition of Haüy’s <i>Mineralogy</i>, to substitute <i>autopside</i> -and <i>heteropside</i> for <i>metallic</i> and <i>unmetallic</i>. It was -supposed to be proved that all bodies have a metal for -their basis; and hence it was wished to avoid the term -<i>unmetallic</i>. But the words <i>metallic</i> and <i>unmetallic</i> -may mean that minerals <em>seem</em> metallic and unmetallic, -just as well as if they contained the element <i>opside</i> to -imply this seeming. The old names express all that -the new express, and with more simplicity, and therefore -should not be disturbed.</p> -<p>The maxim on which we are now insisting, that we -are not to be too scrupulous about the etymology of -scientific terms, may, at first sight, appear to be at -variance with our <a href="#a4">Fourth</a> Aphorism, that words used -technically are to retain their common meaning as far -as possible. But it must be recollected, that in the -Fourth Aphorism we spoke of <i>common</i> words <i>appropriated</i> -as technical terms; we here speak of words -<i>constructed</i> for scientific purposes. And although it is, -perhaps, impossible to draw a broad line between these -two classes of terms, still the rule of propriety may be -stated thus: In technical terms, deviations from the -usual meaning of words are bad in proportion as the -words are more familiar in our own language. Thus -we may apply the term <i>Cirrus</i> to a cloud composed of -filaments, even if these filaments are straight; but to -call such a cloud a <i>Curl cloud</i> would be much more -harsh.</p> -<p class="end">Since the names of things, and of classes of things, -when constructed so as to involve a description, are -constantly liable to become bad, the natural classes -shifting away from the descriptive marks thus prematurely -and casually adopted, I venture to lay down -the following maxim. <span class="pagenum" id="page304">304</span></p> -<p class="center" id="a13"><span class="sc">Aphorism</span> XIII.</p> -<p><i>The fundamental terms of a system of Nomenclature may -be conveniently borrowed from casual or arbitrary circumstances.</i></p> -<p><span class="sc">For</span> instance, the names of plants, of minerals, and -of geological strata, may be taken from the places -where they occur conspicuously or in a distinct form; -as <i>Parietaria</i>, <i>Parnassia</i>, <i>Chalcedony</i>, -<i>Arragonite</i>, <i>Silurian</i> system, <i>Purbeck</i> limestone. These names may -be considered as at first supplying standards of reference; -for in order to ascertain whether any rock be -<i>Purbeck</i> limestone, we might compare it with the -rocks in the Isle of Purbeck. But this reference to a -local standard is of authority only till the place of the -object in the system, and its distinctive marks, are ascertained. -It would not vitiate the above names, if it -were found that the <i>Parnassia</i> does not grow on Parnassus; -that <i>Chalcedony</i> is not found in Chalcedon; or -even that <i>Arragonite</i> no longer occurs in Arragon; for -it is now firmly established as a mineral species. Even -in geology such a reference is arbitrary, and may be -superseded, or at least modified, by a more systematic -determination. <i>Alpine</i> limestone is no longer accepted -as a satisfactory designation of a rock, now that we -know the limestone of the Alps to be of various ages.</p> -<p>Again, names of persons, either casually connected -with the object, or arbitrarily applied to it, may be -employed as designations. This has been done most -copiously in botany, as for example, <i>Nicotiana</i>, <i>Dahlia</i>, -<i>Fuchsia</i>, <i>Jungermannia</i>, <i>Lonicera</i>. And Linnæus has -laid down rules for restricting this mode of perpetuating -the memory of men, in the names of plants. -Those generic names, he -says<a id="fnanchor38-4" href="#note38-4"><span class="fnanchor">38</span></a>, -which have been constructed -to preserve the memory of persons who have -deserved well of botany, are to be religiously retained. -This, he adds, is the sole and supreme reward of the -botanist’s labours, and must be carefully guarded and <span class="pagenum" id="page305">305</span> -scrupulously bestowed, as an encouragement and an -honour. Still more arbitrary are the terms borrowed -from the names of the gods and goddesses, heroes and -heroines of antiquity, to designate new genera in those -departments of natural history in which so many have -been discovered in recent times as to weary out all -attempts at descriptive nomenclature. Cuvier has -countenanced this method. ‘I have had to frame many -new names of genera and sub-genera,’ he -says<a id="fnanchor39-4" href="#note39-4"><span class="fnanchor">39</span></a>, ‘for -the sub-genera which I have established were so -numerous and various, that the memory is not satisfied -with numerical indications. These I have chosen -either so as to indicate some character, or among the -usual denominations, which I have latinized, or finally, -after the example of Linnæus, among the names of -mythology, which are in general agreeable to the ear, -and which are far from being exhausted.’</p> -<div class="footnote"><span class="label"><a id="note38-4" href="#fnanchor38-4">38</a></span> -<i>Phil. Bot.</i> 241. -</div> -<div class="footnote"><span class="label"><a id="note39-4" href="#fnanchor39-4">39</a></span> -<i>Règne An.</i> p. 16. -</div> -<p>This mode of framing names from the names of persons -to whom it was intended to do honour, has been -employed also in the mathematical and chemical sciences; -but such names have rarely obtained any permanence, -except when they recorded an inventor or -discoverer. Some of the constellations, indeed, have -retained such appellations, as <i>Berenice’s Hair</i>; and the -new star which shone out in the time of Cæsar, would -probably have retained the name given to it, of the -<i>Julian Star</i>, if it had not disappeared again soon after. -In the map of the Moon, almost all the parts have -had such names imposed upon them by those who -have constructed such maps, and these names have -very properly been retained. But the names of new -planets and satellites thus suggested have not been -generally accepted; as the <i>Medicean</i> stars, the name -employed by Galileo for the satellites of Jupiter; the -<i>Georgium Sidus</i>, the appellation proposed by Herschel -for Uranus when first -discovered<a id="fnanchor40-4" href="#note40-4"><span class="fnanchor">40</span></a>; -Ceres <i>Ferdinandea</i>, <span class="pagenum" id="page306">306</span> -the name which Piazzi wished to impose on the small -planet Ceres. The names given to astronomical Tables -by the astronomers who constructed them have been -most steadily adhered to, being indeed names of books, -and not of natural objects. Thus there were the -<i>Ilchanic</i>, the <i>Alphonsine</i>, the <i>Rudolphine</i>, -the <i>Carolinian</i> Tables. Comets which have been ascertained -to be periodical, have very properly had assigned to -them the name of the person who established this -point; and of these we have thus, <i>Halley’s</i>, <i>Encke’s -Comet</i>, and <i>Biela’s</i> or <i>Gambart’s Comet</i>.</p> -<div class="footnote"><span class="label"><a id="note40-4" href="#fnanchor40-4">40</a></span> -In this case, the name <i>Uranus</i>, selected with -a view to symmetry according to the mythological order of descent -of the persons (<i>Uranus</i>, <i>Saturn</i>, <i>Jupiter</i>, <i>Mars</i>) -was adopted by astronomers in general, though not proposed or -sanctioned by the discoverer of the new planet. In the cases of -the smaller planets, <i>Ceres</i>, <i>Pallas</i>, <i>Juno</i>, and <i>Vesta</i>, -the names were given either by the discoverer, or with his sanction. -Following this rule, Bessel gave the name of <i>Astræa</i> to a new -planet discovered in the same region by Mr. Hencke, as mentioned in -the additions to book vii. of the <i>History</i> (2nd Ed.). Following the -same rule, and adhering as much as possible to mythological connexion, -the astronomers of Europe have with the sanction of M. Le Verrier, -given the name of <i>Neptune</i> to the planet revolving beyond Uranus, -and discovered in consequence of his announcement of its probable existence, -which had been inferred by Mr. Adams and him (calculating in ignorance -of each other’s purpose) from the perturbations of Uranus; as I -have stated in the Additions to the Third Edition of the <i>History</i>. -</div> -<p>In the case of discoveries in science or inventions of -apparatus, the name of the inventor is very properly -employed as the designation. Thus we have the <i>Torricellian</i> -Vacuum, the <i>Voltaic</i> Pile, <i>Fahrenheit’s</i> Thermometer. -And in the same manner with regard to -laws of nature, we have <i>Kepler’s</i> Laws, <i>Boyle</i> or <i>Mariotte’s</i> -law of the elasticity of air, <i>Huyghens’s</i> law of -double refraction, <i>Newton’s</i> scale of colours. <i>Descartes’</i> -law of refraction is an unjust appellation; for the discovery -of the law of sines was made by Snell. In deductive mathematics, -where the invention of a theorem -is generally a more definite step than an induction, -this mode of designation is more common, as <i>Demoivre’s</i> -Theorem, <i>Maclaurin’s</i> Theorem, <i>Lagrange’s</i> Theorem, -<i>Eulerian</i> Integrals.</p> -<p>In the <i>History of Science</i><a id="fnanchor41-4" href="#note41-4"><span class="fnanchor">41</span></a> I have remarked that in -the discovery of what is termed galvanism, Volta’s <span class="pagenum" id="page307">307</span> -office was of a higher and more philosophical kind -than that of Galvani; and I have, on this account, -urged the propriety of employing the term <i>voltaic</i>, -rather than <i>galvanic</i> electricity. I may add that the -electricity of the common machine is often placed in -contrast with this, and appears to require an express -name. Mr. Faraday calls it <i>common</i> or <i>machine</i> electricity; -but I think that <i>franklinic</i> electricity would -form a more natural correspondence with <i>voltaic</i>, and -would be well justified by Franklin’s place in the history -of that part of the subject.</p> -<div class="footnote end"><span class="label"><a id="note41-4" href="#fnanchor41-4">41</a></span> -b. xiii. c. 1. -</div> -<p class="center"><span class="sc">Aphorism</span> XIV.</p> -<p><i>The Binary Method of Nomenclature</i> (<i>Names by Genus -and Species</i>) <i>is the most convenient hitherto employed in -Classification.</i></p> -<p><span class="sc">The</span> number of species in every province of Natural -History is so vast that we cannot distinguish them -and record the distinctions without some artifice. The -known species of plants, for instance, were 10,000 in the -time of Linnæus, and are now probably 60,000. It -would be useless to endeavour to frame and employ -separate names for each of these species.</p> -<p>The division of the objects into a subordinated system -of classification enables us to introduce a Nomenclature -which does not require this enormous number -of names. The artifice employed is, to name a specimen -by means of two (or it might be more) steps of the -successive division. Thus in Botany, each of the Genera -has its name, and the species are marked by the addition -of some epithet to the name of the genus. In this -manner about 1,700 Generic Names, with a moderate -number of Specific Names, were found by Linnæus -sufficient to designate with precision all the species of -vegetables known at his time. And this <i>Binary Method</i> of -Nomenclature has been found so convenient, -that it has been universally adopted in every other -department of the Natural History of organized beings. <span class="pagenum" id="page308">308</span></p> -<p class="end">Many other modes of Nomenclature have been tried, -but no other has at all taken root. Linnæus himself -appears at first to have intended marking each species -by the Generic Name, accompanied by a characteristic -Descriptive Phrase; and to have proposed the employment -of a <i>Trivial</i> Specific Name, as he termed it, only -as a method of occasional convenience. The use of -these trivial names, however, has become universal, as -we have said; and is by many persons considered the -greatest improvement introduced at the Linnæan reform.</p> -<p class="center" id="a15"><span class="sc">Aphorism</span> XV.</p> -<p><i>The Maxims of Linnæus concerning the Names to be used -in Botany</i>, (Philosophia Botanica, Nomina. Sections 210 -to 255) <i>are good examples of Aphorisms on this subject.</i></p> -<p><span class="sc">Both</span> Linnæus and other writers (as Adanson) have -given many maxims with a view of regulating the -selection of generic and specific names. The maxims -of Linnæus were intended as much as possible to exclude -barbarism and confusion, and have, upon the -whole, been generally adopted.</p> -<p>These canons, and the sagacious modesty of great -botanists, like Robert Brown, in conforming to them, -have kept the majority of good botanists within salutary -limits; though many of these canons were objected to by -the contemporaries of Linnæus (Adanson -and others<a id="fnanchor42-4" href="#note42-4"><span class="fnanchor">42</span></a>) -as capricious and unnecessary restrictions.</p> -<div class="footnote"><span class="label"><a id="note42-4" href="#fnanchor42-4">42</a></span> -Pref. cxxix. clxxii. -</div> -<p>Many of the names introduced by Linnæus certainly -appear fanciful enough. Thus he gives the name <i>Bauhinia</i> -to a plant which has leaves in pairs, because the -Bauhins were a pair of brothers. <i>Banisteria</i> is the -name of a climbing plant in honour of Banister, who -travelled among mountains. But such names once -established by adequate authority lose all their -inconvenience and easily become permanent, and hence the -reasonableness of one of the Linnæan -rules<a id="fnanchor43-4" href="#note43-4"><span class="fnanchor">43</span></a>:—<br /> - That as such a perpetuation of the names of persons <span class="pagenum" id="page309">309</span> -by the names of plants is the only honour that botanists -have to bestow, it ought to be used with care and -caution, and religiously respected.</p> -<div class="footnote"><span class="label"><a id="note43-4" href="#fnanchor43-4">43</a></span> -<i>Phil. Bot.</i> s. 239. -</div> -<p>[3rd ed. It may serve to show how sensitive botanists -are to the allusions contained in such names, -that it has been charged against Linnæus, as a proof -of malignity towards Buffon, that he changed the name -of the genus <i>Buffonia</i>, established by Sauvages, into -<i>Bufonia</i>, which suggested a derivation from <i>Bufo</i>, a -toad. It appears to be proved that the spelling was not -Linnæus’s doing.]</p> -<p>Another Linnæan maxim is (Art. 219), that the generic -name must be fixed before we attempt to form a -specific name; ‘the latter without the former is like -the clapper without the bell.’</p> -<p>The name of the genus being fixed, the species may -be marked (Art. 257) by adding to it ‘a single word -taken at will from any quarter;’ that is, it need not -involve a description or any essential property of the -plant, but may be a casual or arbitrary appellation. -Thus the various species of -<i>Hieracium</i><a id="fnanchor44-4" href="#note44-4"><span class="fnanchor">44</span></a> -are <i>Hieracium -Alpinum</i>, <i>H. Halleri</i>, <i>H. Pilosella</i>, <i>H. dubium</i>, <i>H. -murorum</i>, &c., where we see how different may be the -kind of origin of the words.</p> -<div class="footnote"><span class="label"><a id="note44-4" href="#fnanchor44-4">44</a></span> -Hooker, <i>Fl. Scot.</i> 228. -</div> -<p class="end">Attempts have been made at various times to form -the names of species from those of genera in some more -symmetrical manner. But these have not been successful, -nor are they likely to be so; and we shall venture -to propound an axiom in condemnation of such names.</p> -<p class="center" id="a16"><span class="sc">Aphorism</span> XVI.</p> -<p><i>Numerical names in Classification are bad; and the same -may be said of other names of kinds, depending upon any -fixed series of notes of order.</i></p> -<p><span class="sc">With</span> regard to numerical names of kinds, of species -for instance, the objections are of this nature. Besides -that such names offer nothing for the imagination to -take hold of, new discoveries will probably alter the <span class="pagenum" id="page310">310</span> -numeration, and make the names erroneous. Thus, if -we call the species of a genus 1, 2, 3, a new species -intermediate between 1 and 2, 2 and 3, &c. cannot be -put in its place without damaging the numbers.</p> -<p>The geological term <i>Trias</i>, lately introduced to designate -the group consisting of the <em>three</em> members -(Bunter Sandstein, Muschelkalk, and Keuper) becomes -improper if, as some geologists hold, two of these -members cannot be separated.</p> -<p>Objections resembling those which apply to numerical -designations of species, apply to other cases of fixed -series: for instance, when it has been proposed to mark -the species by altering the termination of the genus. -Thus Adanson<a id="fnanchor45-4" href="#note45-4"><span class="fnanchor">45</span></a>, -denoting a genus by the name <i>Fonna</i> -(<i>Lychnidea</i>), conceived he might mark five of its species -by altering the last syllable, <i>Fonna</i>, <i>Fonna-e</i>, <i>Fonna-i</i>, -<i>Fonna-o</i>, <i>Fonna-u</i>; then others by <i>Fonna-ba</i>, <i>Fonna-ka</i>, -and so on. This would be liable to the same evils -which have been noticed as belonging to the numerical -method<a id="fnanchor46-4" href="#note46-4"><span class="fnanchor">46</span></a>.</p> -<div class="footnote"><span class="label"><a id="note45-4" href="#fnanchor45-4">45</a></span> -Pref. clxxvi. -</div> -<div class="footnote end"><span class="label"><a id="note46-4" href="#fnanchor46-4">46</a></span> -In like manner the names assigned by Mr. Rickman -to the successive of styles of Gothic architecture in England,—<i>Early -English</i>, <i>Decorated</i>, and <i>Perpendicular</i>,—cannot -be replaced by numerical designations, <i>First Pointed</i>, -<i>Second Pointed</i>, <i>Third Pointed</i>. For—besides that -he who first distinctly establishes classes has the right of -naming them, and that Mr. Rickman’s names are really appropriate -and significant—these new names would confound all meaning -of language. We should not be able to divide Early English, or Decorated, -or Perpendicular into sub-styles;—for who could talk of <i>First -Second Pointed</i> and <i>Second Second Pointed</i>; and what -should we call that pointed style—the <i>Transition</i> -from the Norman—which precedes the <i>First Pointed</i>? -</div> -<p class="center"><span class="sc">Aphorism</span> XVII.</p> -<p><i>In any classificatory science names including more than -two steps of the classification may be employed if it be found -convenient.</i></p> -<p><span class="sc">Linnæus</span>, in his canons for botanical nomenclature -(Art. 212), says that the names of the class and the -order are to be <em>mute</em>, while the names of the Genus -and Species are <em>sonorous</em>. And accordingly the names <span class="pagenum" id="page311">311</span> -of plants (and the same is true of animals) have in common -practice been binary only, consisting of a generic -and a specific name. The class and the order have not -been admitted to form part of the appellation of the -species. Indeed it is easy to see that a name, which -must be identical in so many instances as that of an -Order would be, would be felt as superfluous and burthensome. -Accordingly, Linnæus makes it one of his -maxims<a id="fnanchor47-4" href="#note47-4"><span class="fnanchor">47</span></a>, -that the name of the Class and Order must not -be expressed but understood, and hence, he says, Royen, -who took <i>Lilium</i> for the name of a Class, rightly -rejected this word as a generic name, and substituted -<i>Lirium</i> with the Greek termination.</p> -<div class="footnote"><span class="label"><a id="note47-4" href="#fnanchor47-4">47</a></span> -<i>Phil. Bot.</i> s. 215. -</div> -<p>Yet we must not too peremptorily assume such -maxims as these to be universal for all classificatory -sciences. It is very possible that it may be found advisable -to use <em>three</em> terms, that of Order, Genus, and -Species in designating minerals, as is done in Mohs’s -nomenclature, for example, <i>Rhombohedral Calc Haloide</i>, -<i>Paratomous Hal Baryte</i>.</p> -<p class="end">It is possible also that it may be found useful in the -same science (Mineralogy) to mark some of the steps of -classification by the termination. Thus it has been proposed -to confine the termination <i>ite</i> to the Order <i>Silicides</i> -of Naumann, as Apophyll<i>ite</i>, Stilb<i>ite</i>, Leuc<i>ite</i>, &c., -and to use names of different form in other orders, as -Talc <i>Spar</i> for Brennerite, Pyramidal Titanium <i>Oxide</i> -for Octahedrite. Some such method appears to be the -most likely to give us a tolerable mineralogical nomenclature.</p> -<p class="center"><span class="sc">Aphorism</span> XVIII.</p> -<p><i>In forming a Terminology, words may be invented when -necessary, but they cannot be conveniently borrowed from -casual or arbitrary -circumstances</i><a id="fnanchor48-4" href="#note48-4"><span class="fnanchor">48</span></a>.</p> -<div class="footnote"><span class="label"><a id="note48-4" href="#fnanchor48-4">48</a></span> -I may also refer to <i>Hist. Sc. Id.</i> b. viii. -c. ii. sec. 2, for some remarks on Terminology. -</div> -<p><span class="sc">It</span> will be recollected that Terminology is a language -employed for describing objects, Nomenclature, a body <span class="pagenum" id="page312">312</span> -of names of the objects themselves. The <i>names</i>, as -was stated in the last maxim, may be arbitrary; but -the <i>descriptive</i> terms must be borrowed from words of -suitable meaning in the modern or the classical languages. -Thus the whole terminology which Linnæus -introduced into botany, is founded upon the received -use of Latin words, although he defined their meaning -so as to make it precise when it was not so, according -to Aphorism <a href="#a5">V.</a> But many of the terms were invented by him -and other botanists, as <i>Perianth</i>, <i>Nectary</i>, -<i>Pericarp</i>; so many, indeed, as to form, along with the -others, a considerable language. Many of the terms -which are now become familiar were originally invented -by writers on botany. Thus the word <i>Petal</i>, -for one division of the corolla, was introduced by -Fabius Columna. The term <i>Sepal</i> was devised by -Necker to express each of the divisions of the calyx. -And up to the most recent times, new denominations -of parts and conditions of parts have been devised by -botanists, when they found them necessary, in order to -mark important differences or resemblances. Thus the -general <i>Receptacle</i> of the flower, as it is termed by -Linnæus, or <i>Torus</i> by Salisbury, is continued into -organs which carry the stamina and pistil, or the pistil -alone, or the whole flower; this organ has hence been -termed<a id="fnanchor49-4" href="#note49-4"><span class="fnanchor">49</span></a> -<i>Gonophore</i>, <i>Carpophore</i>, and <i>Anthophore</i>, in -these cases.</p> -<div class="footnote"><span class="label"><a id="note49-4" href="#fnanchor49-4">49</a></span> -De Candolle’s <i>Th. El.</i> 405. -</div> -<p>In like manner when Cuvier had ascertained that -the lower jaws of Saurians consisted always of six -pieces having definite relations of form and position, -he gave names to them, and termed them respectively -the <i>Dental</i>, the <i>Angular</i>, the <i>Coronoid</i>, the <i>Articular</i>, -the <i>Complementary</i>, and the <i>Opercular</i> Bones.</p> -<p>In all these cases, the descriptive terms thus introduced -have been significant in their derivation. An -attempt to circulate a perfectly arbitrary word as a -means of description would probably be unsuccessful. -We have, indeed, some examples approaching to arbitrary -designations, in the Wernerian names of colours, <span class="pagenum" id="page313">313</span> -which are a part of the terminology of Natural History. -Many of these names are borrowed from natural -resemblances, as <i>Auricula purple</i>, <i>Apple green</i>, <i>Straw -yellow</i>; but the names of others are taken from casual -occurrences, mostly, however, such as were already -recognized in common language, as <i>Prussian blue</i>, -<i>Dutch orange</i>, <i>King’s yellow</i>.</p> -<p class="end">The extension of arbitrary names in scientific terminology -is by no means to be encouraged. I may mention a case -in which it was very properly avoided. -When Mr. Faraday’s researches on Voltaic electricity -had led him to perceive the great impropriety of the -term <i>poles</i>, as applied to the apparatus, since -the processes have not reference to any opposed points, but to -two opposite directions of a path, he very suitably -wished to substitute for the phrases <i>positive pole</i> and -<i>negative pole</i>, two words ending in <i>ode</i>, from <span class="greek">ὅδος</span>, a -way. A person who did not see the value of our present maxim, -that descriptive terms should be descriptive in their origin, -might have proposed words perfectly arbitrary, as <i>Alphode</i>, -and <i>Betode</i>: or, if he -wished to pay a tribute of respect to the discoverers -in this department of science, <i>Galvanode</i> and <i>Voltaode</i>, -But such words would very justly have been rejected -by Mr. Faraday, and would hardly have obtained any -general currency among men of science. <i>Zincode</i> and -<i>Platinode</i>, terms derived from the metal which, in one -modification of the apparatus, forms what was previously -termed the pole, are to be avoided, because in -their origin too much is casual; and they are not a -good basis for derivative terms. The pole at which -the zinc is, is the Anode or Cathode, according as it is -associated with different metals. Either the <i>Zincode</i> -must sometimes mean the pole at which the Zinc is, -and at other times that at which the Zinc is not, or -else we must have as many names for poles as there -are metals. <i>Anode</i> and <i>Cathode</i>, the terms which Mr. -Faraday adopted, were free from these objections; for -they refer to a natural standard of the direction of the -voltaic current, in a manner which, though perhaps -not obvious at first sight, is easily understood and <span class="pagenum" id="page314">314</span> -retained. <i>An</i>ode and <i>Cath</i>ode, the <i>rising</i> and the <i>setting</i> -way, are the directions which correspond to east and -west in that voltaic current to which we must ascribe -terrestrial magnetism. And with these words it was -easy to connect <i>Anïon</i> and <i>Cathïon</i>, to designate the -opposite elements which are separated and liberated at -the two <i>Electrodes</i>.</p> -<p class="center" id="a19"><span class="sc">Aphorism</span> XIX.</p> -<p><i>The meaning of Technical Terms must be fixed by convention, -not by casual reference to the ordinary meaning of -words.</i></p> -<p><span class="sc">In</span> fixing the meaning of the Technical Terms which -form the Terminology of any science, at least of the -descriptive Terms, we necessarily fix, at the same time, -the perceptions and notions which the Terms are to -convey to a hearer. What do we mean by <i>apple-green</i> or -<i>French grey</i>? It might, perhaps, be supposed that, in -the first example, the term <i>apple</i>, referring to so familiar -an object, sufficiently suggests the colour intended. -But it may easily be seen that this is not true; for -apples are of many different hues of green, and it is -only by a conventional selection that we can appropriate -the term to one special shade. When this appropriation -is once made, the term refers to the sensation, -and not to the parts of this term; for these enter into -the compound merely as a help to the memory, whether -the suggestion be a natural connexion as in ‘apple-green,’ -or a casual one as in ‘French grey.’ In order -to derive due advantage from technical terms of this -kind, they must be associated <em>immediately</em> with -the perception to which they belong; and not connected with -it through the vague usages of common language. The -memory must retain the sensation; and the technical -word must be understood as directly as the most familiar word, -and more distinctly. When we find such -terms as <i>tin-white</i> or <i>pinchbeck-brown</i>, the metallic -colour so denoted ought to start up in our memory -without delay or search. <span class="pagenum" id="page315">315</span></p> -<p>This, which it is most important to recollect with -respect to the simpler properties of bodies, as colour -and form, is no less true with respect to more compound -notions. In all cases the term is fixed to a peculiar -meaning by convention; and the student, in order to -use the word, must be completely familiar with the convention, -so that he has no need to frame conjectures -from the word itself. Such conjectures would always -be insecure, and often erroneous. Thus the term <i>papilionaceous</i>, -applied to a flower, is employed to indicate, -not only a resemblance to a butterfly, but a resemblance -arising from five petals of a certain peculiar shape and -arrangement; and even if the resemblance to a butterfly -were much stronger than it is in such cases, yet if it -were produced in a different way, as, for example, by -one petal, or two only, instead of a ‘standard,’ two -‘wings,’ and a ‘keel’ consisting of two parts more or -less united into one, we should no longer be justified in -speaking of it as a ‘papilionaceous’ flower.</p> -<p>The formation of an exact and extensive descriptive -language for botany has been executed with a degree of -skill and felicity, which, before it was attained, could -hardly have been dreamt of as attainable. Every part -of a plant has been named; and the form of every part, -even the most minute, has had a large assemblage of -descriptive terms appropriated to it, by means of which -the botanist can convey and receive knowledge of form -and structure, as exactly as if each minute part were -presented to him vastly magnified. This acquisition -was part of the Linnæan Reform, of which we have -spoken in the <i>History</i>. ‘Tournefort,’ says De Candolle<a id="fnanchor50-4" href="#note50-4"><span class="fnanchor">50</span></a>, -‘appears to have been the first who really perceived the -utility of fixing the sense of terms in such a way as -always to employ the same word in the same sense, and -always to express the same idea by the same word; but -it was Linnæus who really created and fixed this botanical -language, and this is his fairest claim to glory, for -by this fixation of language he has shed clearness and -precision over all parts of the science.’</p> -<div class="footnote"><span class="label"><a id="note50-4" href="#fnanchor50-4">50</a></span> -<i>Théor. Élém.</i> p. 327. <span class="pagenum" id="page316" style="font-size: large">316</span> -</div> -<p>It is -not necessary here to give any detailed account -of the terms of botany. The fundamental ones have -been gradually introduced, as the parts of plants were -more carefully and minutely examined. Thus the -flower was successively distinguished into the <i>calyx</i>, the -<i>corolla</i>, the <i>stamens</i>, and the <i>pistils</i>: the sections of -the corolla were termed <i>petals</i> by Columna; those of -the calyx were called <i>sepals</i> by -Necker<a id="fnanchor51-4" href="#note51-4"><span class="fnanchor">51</span></a>. Sometimes -terms of greater generality were devised; as <i>perianth</i> -to include the calyx and corolla, whether one or both of -these were present<a id="fnanchor52-4" href="#note52-4"><span class="fnanchor">52</span></a>; -<i>pericarp</i> for the part inclosing the -grain, of whatever kind it be, fruit, nut, pod, &c. And -it may easily be imagined that descriptive terms may, -by definition and combination, become very numerous -and distinct. Thus leaves may be called -<i>pinnatifid</i><a id="fnanchor53-4" href="#note53-4"><span class="fnanchor">53</span></a>, -<i>pinnnatipartite</i>, -<i>pinnatisect</i>, <i>pinnatilobate</i>, <i>palmatifid</i>, <i>palmatipartite</i>, -&c., and each of these words designates -different combinations of the modes and extent of the -divisions of the leaf with the divisions of its outline. In -some cases arbitrary numerical relations are introduced -into the definition: thus a leaf is called -<i>bilobate</i><a id="fnanchor54-4" href="#note54-4"><span class="fnanchor">54</span></a> -when -it is divided into two parts by a notch; but if the notch -go to the middle of its length, it is <i>bifid</i>; if it go near -the base of the leaf, it is <i>bipartite</i>; if to the base, it is -<i>bisect</i>. Thus, too, a pod of a cruciferous plant is -a <i>silica</i><a id="fnanchor55-4" href="#note55-4"><span class="fnanchor">55</span></a> -if it be four times as long as it is broad, but if it be -shorter than this it is a <i>silicula</i>. Such terms being -established, the form of the very complex leaf or frond -of a fern is exactly conveyed, for example, by the following phrase: -‘fronds rigid pinnate, pinnæ recurved -subunilateral pinnatifid, the segments linear undivided -or bifid spinuloso-serrate<a id="fnanchor56-4" href="#note56-4"><span class="fnanchor">56</span></a>.’</p> -<div class="footnote"><span class="label"><a id="note51-4" href="#fnanchor51-4">51</a></span> -De Candolle, 329. -</div> -<div class="footnote"><span class="label"><a id="note52-4" href="#fnanchor52-4">52</a></span> -For this Erhart and De Candolle use <i>Perigone</i>. -</div> -<div class="footnote"><span class="label"><a id="note53-4" href="#fnanchor53-4">53</a></span> -De Candolle, 318. -</div> -<div class="footnote"><span class="label"><a id="note54-4" href="#fnanchor54-4">54</a></span> -<i>Ibid.</i> 493. -</div> -<div class="footnote"><span class="label"><a id="note55-4" href="#fnanchor55-4">55</a></span> -<i>Ibid.</i> 422. -</div> -<div class="footnote"><span class="label"><a id="note56-4" href="#fnanchor56-4">56</a></span> -Hooker, <i>Brit. Flo.</i> p. 450. <i>Hymenophyllum Wilsoni</i>, Scottish filmy -fern, abundant in the highlands of Scotland and about Killarney. -</div> -<p>Other characters, as well as form, are conveyed with -the like precision: Colour by means of a classified scale -of colours, as we have seen in speaking of the -<a href="#b3c2a22">Measures</a> <span class="pagenum" id="page317">317</span> -of Secondary Qualities; to which, however, we must -add, that the naturalist employs arbitrary names, (such -as we have already quoted,) and not mere numerical -exponents, to indicate a certain number of selected -colours. This was done with most precision by Werner, -and his scale of colours is still the most usual standard -of naturalists. Werner also introduced a more exact -terminology with regard to other characters which are -important in mineralogy, as lustre, hardness. But -Mohs improved upon this step by giving a numerical -scale of hardness, in which <i>talc</i> is 1, <i>gypsum</i>, 2, <i>calc spar</i> -3, and so on, as we have already explained in the History -of Mineralogy. Some properties, as specific gravity, -by their definition give at once a numerical -measure; and others, as crystalline form, require a -very considerable array of mathematical calculation -and reasoning, to point out their relations and gradations. -In all cases the features of likeness in the objects -must be rightly apprehended, in order to their -being expressed by a distinct terminology. Thus no -terms could describe crystals for any purpose of natural -history, till it was discovered that in a class of minerals -the proportion of the faces might vary, while the angle -remained the same. Nor could crystals be described so -as to distinguish species, till it was found that the -derived and primitive forms are connected by very simple -relations of space and number. The discovery of the -mode in which characters must be apprehended so that -they may be considered as <em>fixed</em> for a class, -is an important step in the progress of each branch of Natural -History; and hence we have had, in the History of -Mineralogy and Botany, to distinguish as important -and eminent persons those who made such discoveries, -Romé de Lisle and Haüy, Cæsalpinus and Gesner.</p> -<p>By the continued progress of that knowledge of minerals, -plants, and other natural objects, in which such -persons made the most distinct and marked steps, but -which has been constantly advancing in a more gradual -and imperceptible manner, the most important and essential -features of similarity and dissimilarity in such -objects have been selected, arranged, and fitted with <span class="pagenum" id="page318">318</span> -names; and we have thus in such departments, systems -of Terminology which fix our attention upon the -resemblances which it is proper to consider, and enable us to -convey them in words.</p> -<p>The following Aphorisms respect the Form of Technical Terms.</p> -<p class="end">By the <i>Form</i> of terms, I mean their philological -conditions; as, for example, from what languages they -may be borrowed, by what modes of inflexion they -must be compounded, how their derivatives are to be -formed, and the like. In this, as in other parts of the -subject, I shall not lay down a system of rules, but -shall propose a few maxims.</p> -<p class="center" id="a20"><span class="sc">Aphorism</span> XX.</p> -<p><i>The two main conditions of the Form of technical terms -are, that they must be generally intelligible, and susceptible -of such grammatical relations as their scientific use requires.</i></p> -<p><span class="sc">These</span> conditions may at first appear somewhat -vague, but it will be found that they are as definite as -we could make them, without injuriously restricting -ourselves. It will appear, moreover, that they have -an important bearing upon most of the questions respecting -the form of the words which come before us; -and that if we can succeed in any case in reconciling -the two conditions, we obtain terms which are practically good, -whatever objections may be urged against -them from other considerations.</p> -<p id="b4a20a1">1. The former condition, for instance, bears upon -the question whether scientific terms are to be taken -from the learned languages, Greek and Latin, or from -our own. And the latter condition very materially -affects the same question, since in English we have -scarcely any power of inflecting our words; and therefore -must have recourse to Greek or Latin in order to -obtain terms which admit of grammatical modification. -If we were content with the term <i>Heat</i>, to express the -<em>science</em> of heat, still it would be a bad technical term, -for we cannot derive from it an adjective like <span class="pagenum" id="page319">319</span> -<i>thermotical</i>. -If <i>bed</i> or <i>layer</i> were an equally good term with -<i>stratum</i>, we must still retain the latter, in order that -we may use the derivative <i>Stratification</i>, for which the -English words cannot produce an equivalent substitute. -We may retain the words <i>lime</i> and <i>flint</i>, but -their adjectives for scientific purposes are not <i>limy</i> -and <i>flinty</i>, but <i>calcareous</i> and <i>siliceous</i>; and hence we -are able to form a compound, as <i>calcareo-siliceous</i>, -which we could not do with indigenous words. We -might fix the phrases <i>bent back</i> and <i>broken</i> to mean (of -optical rays) that they are reflected and refracted; but -then we should have no means of speaking of the -angles of <i>Reflection</i> and <i>Refraction</i>, of the <i>Refractive</i> -Indices, and the like.</p> -<p>In like manner, so long as anatomists described certain -parts of a vertebra as <i>vertebral laminæ</i>, or <i>vertebral -plates</i>, they had no adjective whereby to signify -the properties of these parts; the term <i>Neurapophysis</i>, -given to them by Mr. Owen, supplies the corresponding -expression <i>neurapophysial</i>. So again, the term -<i>Basisphenoid</i>, employed by the same anatomist, is -better than <i>basilar</i> or <i>basial process of the sphenoid</i>, -because it gives us the adjective <i>basisphenoidal</i>. And -the like remark applies to other changes recently -proposed in the names of portions of the skeleton.</p> -<p>Thus one of the advantages of going to the Greek -and Latin languages for the origin of our scientific -terms is, that in this way we obtain words which -admit of the formation of adjectives and abstract -terms, and of composition, and of other inflexions. -Another advantage of such an origin is, that such terms, -if well selected, are readily understood over the whole -lettered world. For this reason, the descriptive language -of science, of botany for instance, has been, for -the most part, taken from the Latin; many of the -terms of the mathematical and chemical sciences have -been derived from the Greek; and when occasion -occurs to construct a new term, it is generally to that -language that recourse is had. The advantage of such -terms is, as has already been intimated, that they -constitute an universal language, by means of which <span class="pagenum" id="page320">320</span> -cultivated persons in every country may convey to -each other their ideas without the need of translation.</p> -<p>On the other hand, the advantage of indigenous -terms is, that so far as the language extends, they are -intelligible much more clearly and vividly than those -borrowed from any other source, as well as more easily -manageable in the construction of sentences. In the -descriptive language of botany, for example, in an -English work, the terms <i>drooping</i>, <i>nodding</i>, <i>one-sided</i>, -<i>twining</i>, <i>straggling</i>, appear better than -<i>cernuous</i>, <i>nutant</i>, <i>secund</i>, <i>volubile</i>, -<i>divaricate</i>. For though the -latter terms may by habit become as intelligible as the -former, they cannot become more so to any readers; -and to most English readers they will give a far less -distinct impression.</p> -<p id="b4a20a2">2. Since the advantage of indigenous over learned -terms, or the contrary, depends upon the balance of -the capacity of inflexion and composition on the one -hand, against a ready and clear significance on the -other, it is evident that the employment of scientific -terms of the one class or of the other may very properly -be extremely different in different languages. -The German possesses in a very eminent degree that -power of composition and derivation, which in English -can hardly be exercised at all, in a formal manner. -Hence German scientific writers use native terms to -a far greater extent than do our own authors. The -descriptive terminology of botany, and even the systematic -nomenclature of chemistry, are represented -by the Germans by means of German roots and inflexions. -Thus the description of <i>Potentilla anserina</i>, -in English botanists, is that it has <i>Leaves interruptedly -pinnate</i>, <i>serrate</i>, <i>silky</i>, <i>stem creeping</i>, <i>stalks axilllar</i>, -<i>one-flowered</i>. Here we have words of Saxon and -Latin origin mingled pretty equally. But the German -description is entirely Teutonic. <i>Die Blume in Achsel</i>; -<i>die Blätter unterbrochen gefiedert</i>, <i>die Blättchen scharf -gesagt</i>, <i>die Stämme kriechend</i>, <i>die Bluthenstiele -einblumig</i>. We could imitate this in our own language, by -saying <i>brokenly-feathered</i>, <i>sharp-sawed</i>; by using <i>threed</i> -for <i>ternate</i>, as the Germans employ <i>gedreit</i>; by saying <span class="pagenum" id="page321">321</span> -<i>fingered-feathered</i> for <i>digitato-pinnate</i>, and the like. -But the habit which we have, in common as well as -scientific language, of borrowing words from the Latin -for new cases, would make such usages seem very -harsh and pedantic.</p> -<p>We may add that, in consequence of these different -practices in the two languages, it is a common habit -of the German reader to impose a scientific definiteness -upon a common word, such as our <a href="#a5">Fifth</a> Aphorism -requires; whereas the English reader expects rather -that a word which is to have a technical sense shall be -derived from the learned languages. <i>Die Kelch</i> and -<i>die Blume</i> (the cup and the flower) easily assume the -technical meaning of <i>calyx</i> and <i>corolla</i>; <i>die Griffel</i> -(the pencil) becomes <i>the pistil</i>; and a name is easily -found for the <i>pollen</i>, the <i>anthers</i>, and the <i>stamens</i>, by -calling them the dust, the dust-cases, and the dust-threads -(<i>der Staub</i>, <i>die Staub-beutel</i>, or <i>Staub-fächer</i>, -and <i>die Staub-fäden</i>), This was formerly done in -English to a greater extent than is now possible without -confusion and pedantry. Thus, in Grew’s book on -the <i>Anatomy of Plants</i>, the calyx is called the -<i>impalement</i>, and the sepals the <i>impalers</i>; the petals are called -the <i>leaves of the flower</i>; the stamens with their anthers -are the <i>seminiform attire</i>. But the English language, -as to such matters, is now less flexible than it was; -partly in consequence of its having adopted the Linnæan -terminology almost entire, without any endeavour to -naturalize it. Any attempt at idiomatic description -would interfere with the scientific language -now generally received in this country. In Germany, -on the other hand, those who first wrote upon science -in their own language imitated the Latin words which -they found in foreign writers, instead of transferring -new roots into their own language. Thus the <i>Numerator</i> -and <i>Denominator</i> of a fraction they call the -<i>Namer</i> and the <i>Counter</i> (<i>Nenner</i> and <i>Zähler</i>). This -course they pursued even where the expression was -erroneous. Thus that portion of the intestines which -ancient anatomists called <i>Duodenum</i>, because they -falsely estimated its length at twelve inches, the <span class="pagenum" id="page322">322</span> -Germans also term <i>Zwölffingerdarm</i> (twelve-inch-gut), -though this intestine in a whale is twenty feet long, -and in a frog not above twenty lines. As another -example of this process in German, we may take the -word <i>Muttersackbauchblatte</i>, the <i>uterine peritonæum</i>.</p> -<p>It is a remarkable evidence of this formative power -of the German language, that it should have been -able to produce an imitation of the systematic chemical -nomenclature of the French school, so complete, -that it is used in Germany as familiarly as the original -system is in France and England. Thus Oxygen -and Hydrogen are <i>Sauerstoff</i> and -<span class="correction" title="emended from Wafferstoff"><i>Wasserstoff</i></span>; Azote is -<i>Stickstoff</i> (suffocating matter); Sulphuric and Sulphurous -Acid are <i>Schwefel-säure</i> and <i>Schwefelichte-säure</i>. -The Sulphate and Sulphite of Baryta, and Sulphuret -of Baryum, are <i>Schwefel-säure Baryterde</i>, <i>Schwefelichte-säure -Baryterde</i>, and <i>Schwefel-baryum</i>. Carbonate of -Iron is <i>Kohlen-säures Eisenoxydul</i>; and we may observe -that, in such cases, the German name is much -more agreeable to analogy than the English one; for -the Protoxide of Iron, (<i>Eisenoxydul</i>,) and not the -Iron itself, is the base of the salt. And the German -language has not only thus imitated the established -nomenclature of chemistry, but has shown itself capable -of supplying new forms to meet the demands -which the progress of theory occasions. Thus the -Hydracids are <i>Wasserstoff-säuren</i>; and of these, the -Hydriodic Acid is <i>Iodwasserstoff-säure</i>, and so of the -rest. In like manner, the translator of Berzelius has -found German names for the sulpho-salts of that -chemist; thus he has <i>Wasserstoffschwefliges Schewefellithium</i>, -which would be (if we were to adopt his -theoretical view) hydro-sulphuret of sulphuret of -lithium: and a like nomenclature for all other similar -cases.</p> -<p id="b4a20a3">3. In English we have no power of imitating this -process, and must take our technical phrases from -some more flexible language, and generally from the -Latin or Greek. We are indeed so much accustomed -to do this, that except a word has its origin in one of -these languages, it hardly seems to us a technical <span class="pagenum" id="page323">323</span> -term; and thus by employing indigenous terms, even -descriptive ones, we may, perhaps, lose in precision -more than we gain in the vividness of the impression. -Perhaps it may be better to say <i>cuneate</i>, <i>lunate</i>, <i>hastate</i>, -<i>sagittate</i>, <i>reniform</i>, than <i>wedge-shaped</i>, <i>crescent-shaped</i>, -<i>halbert-headed</i>, <i>arrow-headed</i>, <i>kidney-shaped</i>. -<i>Ringent</i> and <i>personate</i> are better than any English -words which we could substitute for them; <i>labiate</i> is -more precise than <i>lipped</i> would readily become. -<i>Urceolate</i>, <i>trochlear</i>, are more compact than <i>pitcher-shaped</i>, -<i>pulley-shaped</i>; and <i>infundibuliform</i>, <i>hypocrateriform</i>, -though long words, are not more inconvenient than -<i>funnel-shaped</i> and <i>salver-shaped</i>. In the same way it -is better to speak (with Dr. -Prichard<a id="fnanchor57-4" href="#note57-4"><span class="fnanchor">57</span></a>,) -of <i>repent</i> and -<i>progressive</i> animals, than of <i>creeping</i> and progressive: -the two Latin terms make a better pair of correlatives.</p> -<div class="footnote"><span class="label"><a id="note57-4" href="#fnanchor57-4">57</a></span> -<i>Researches</i>, p. 69. -</div> -<p id="b4a20a4">4. But wherever we may draw the line between -the proper use of English and Latin terms in descriptive -phraseology, we shall find it advisable to borrow -almost all other technical terms from the learned languages. -We have seen this in considering the new -terms introduced into various sciences in virtue of our -<a href="#a9">Ninth</a> Maxim. We may add, as further examples, -the names of the various animals of which a knowledge -has been acquired from the remains of them -which exist in various strata, and which have been -reconstructed by Cuvier and his successors. Such are -the <i>Palæotherium</i>, the <i>Anoplotherium</i>, the <i>Megatherium</i>, -the <i>Dinotherium</i>, the <i>Chirotherium</i>, the <i>Megalichthys</i>, -the <i>Mastodon</i>, the <i>Ichthyosaurus</i>, the <i>Plesiosaurus</i>, -the <i>Pterodactylus</i>. To these others are every -year added; as, for instance, very recently, the -<i>Toxodon</i>, <i>Zeuglodon</i>, and <i>Phascolotherium</i> of Mr. Owen, -and the <i>Thylacotherium</i> of M. Valenciennes. Still -more recently the terms <i>Glyptodon</i>, <i>Mylodon</i>, <i>Dicynodon</i>, -<i>Paloplotherium</i>, <i>Rhynchosaurus</i>, have been added -by Mr. Owen to designate fossil animals newly determined by him. <span class="pagenum" id="page324">324</span></p> -<p>The names of species, as well as of genera, are thus -formed from the Greek: as the Plesiosaurus <i>dolichodeirus</i> -(long-necked), Ichthyosaurus <i>platyodon</i> (broad-toothed), -the Irish elk, termed Cervus <i>megaceros</i> -(large-horned). But the descriptive specific names are -also taken from the Latin, as Plesiosaurus <i>brevirostris</i>, -<i>longirostris</i>, <i>crassirostris</i>; besides which there are -arbitrary specific names, which we do not here consider.</p> -<p>These names being all constructed at a period when -naturalists were familiar with an artificial system, the -standard language of which is Latin, have not been -taken from modern language. But the names of living -animals, and even of their classes, long ago formed in -the common language of men, have been in part adopted -in the systems of naturalists, agreeably to Aphorism -<a href="#a3">Third</a>. Hence the language of systems in natural -history is mixed of ancient and modern languages. -Thus Cuvier’s divisions of the vertebrated animals are -<i>Mammifères</i> (Latin), <i>Oiseaux</i>, <i>Reptiles</i>, -<i>Poissons</i>; <i>Bimanes</i>, <i>Quadrumanes</i>, <i>Carnassières</i>, -<i>Rongeurs</i>, <i>Pachydermes</i> (Greek), <i>Ruminans</i> (Latin), -<i>Cétacés</i> (Latin). In -the subordinate divisions the distribution being more -novel, the names are less idiomatic: thus the kinds of -Reptiles are <i>Cheloniens</i>, <i>Sauriens</i>, <i>Ophidiens</i>, <i>Batraciens</i>, -all which are of Greek origin. In like manner. -Fish are divided into <i>Chondropterygiens</i>, <i>Malacopterygiens</i>, -<i>Acanthopterygiens</i>. The unvertebrated animals -are <i>Mollusques</i>, <i>Animaux articulés</i>, and <i>Animaux -rayonnés</i>; and the Mollusques are divided into six classes, -chiefly according to the position or form of their foot; -namely, <i>Cephalopodes</i>, <i>Pteropodes</i>, <i>Gasteropodes</i>, -<i>Acephales</i>, <i>Brachiopodes</i>, <i>Cirrhopodes</i>.</p> -<p>In transferring these terms into English, when the -term is new in French as well as English, we have -little difficulty; for we may take nearly the same -liberties in English which are taken in French; and -hence we may say <i>mammifers</i> (rather <i>mammals</i>), <i>cetaceans</i> -or <i>cetaces</i>, <i>batracians</i> (rather <i>batrachians</i>), using -the words as substantives. But in other cases we -must go back to the Latin: thus we say <i>radiate</i> <span class="pagenum" id="page325">325</span> animals, -or <i>radiata</i> (rather <i>radials</i>), for <i>rayonnés</i>. These -changes, however, rather refer to another Aphorism.</p> -<p>(Mr. Kirby has proposed <i>radiary</i>, <i>radiaries</i>, for -<i>radiata</i>.)</p> -<p id="b4a20a5">5. When new Mineral Species have been established -in recent times, they have generally had arbitrary -names assigned to them, derived from some person or -places. In some instances, however, descriptive names -have been selected; and then these have been generally -taken from the Greek, as <i>Augite</i>, <i>Stilbite</i>, <i>Diaspore</i>, -<i>Dichroite</i>, <i>Dioptase</i>. Several of these Greek names -imposed by Haüy, refer to some circumstances, often -fancifully selected, in his view of the crystallization of -the substance, as <i>Epidote</i>, <i>Peridote</i>, <i>Pleonast</i>. Similar -terms of Greek origin have been introduced by others, -as <i>Orthite</i>, <i>Anorthite</i>, <i>Periklin</i>. Greek names founded -on casual circumstances are less to be commended. -Berzelius has termed a mineral <i>Eschynite</i> from -<span class="greek">αἰσχυνὴ</span>, <i>shame</i>, because it is, he conceives, a shame for -chemists not to have separated its elements more distinctly -than they did at first.</p> -<p id="b4a20a6">6. In Botany, the old names of genera of Greek origin -are very numerous, and many of them are descriptive, -as <i>Glycyrhiza</i> (<span class="greek">γλυκὺς</span> -and <span class="greek">ῥιζα</span>, sweet root) liquorice, -<i>Rhododendron</i> (rose-tree), <i>Hæmatoxylon</i> (bloody -wood), <i>Chrysocoma</i> (golden hair), <i>Alopecurus</i> (fox-tail), -and many more. In like manner there are names -which derive a descriptive significance from the Latin, -either adjectives, as <i>Impatiens</i>, <i>Gloriosa</i>, <i>Sagittaria</i>, -or substantives irregularly formed, as <i>Tussilago</i> (à -tussis domatione), <i>Urtica</i> (ab urendo tactu), <i>Salsola</i> -(à salsedine). But these, though good names when they -are established by tradition, are hardly to be imitated -in naming new plants. In most instances, when this -is to be done, arbitrary or local names have been -selected, as <i>Strelitzia</i>.</p> -<p id="b4a20a7">7. In Chemistry, new substances have of late had -names assigned them from Greek roots, as <i>Iodine</i>, from -its violet colour, <i>Chlorine</i> from its green colour. In -like manner fluorine has by the French chemists been -called <i>Phthor</i>, from its destructive properties. So the <span class="pagenum" id="page326">326</span> -new metals, <i>Chrome</i>, <i>Rhodium</i>, <i>Iridium</i>, <i>Osmium</i>, had -names of Greek derivation descriptive of their properties. -Some such terms, however, were borrowed from -localities, as <i>Strontia</i>, <i>Yttria</i>, the names of new earths. -Others have a mixed origin, as <i>Pyrogallic</i>, <i>Pyroacetic</i>, -and <i>Pyroligneous</i> Spirit. In some cases the derivation -has been extravagantly capricious. Thus in the process for -making Pyrogallic Acid, a certain substance is -left behind, from which M. Braconnot extracted an -acid which he called <i>Ellagic</i> Acid, framing the root of -the name by reading the word <i>Galle</i> backwards.</p> -<p>The new laws which the study of Electro-chemistry -brought into view, required a new terminology to express -their conditions: and in this case, as we have -observed in speaking of the <a href="#a12">Twelfth</a> Maxim, arbitrary -words are less suitable. Mr. Faraday very properly -borrowed from the Greek his terms <i>Electrolyte</i>, <i>Electrode</i>, -<i>Anode</i>, <i>Cathode</i>, <i>Anïon</i>, <i>Cathïon</i>, <i>Dielectric</i>. In -the mechanico-chemical and mechanical sciences, however, -new terms are less copiously required than in the -sciences of classification, and when they are needed, -they are generally determined by analogy from existing -terms. <i>Thermo-electricity</i> and <i>Electro-dynamics</i> were -terms which very naturally offered themselves; Nobili’s -<i>thermo-multiplier</i>, Snow Harris’s <i>unit-jar</i>, were -almost equally obvious names. In such cases, it is -generally possible to construct terms both compendious -and descriptive, without introducing any new radical -words.</p> -<p id="b4a20a8">8. The subject of Crystallography has inevitably -given rise to many new terms, since it brings under -our notice a great number of new relations of a very -definite but very complex form. Haüy attempted -to find names for all the leading varieties of crystals, -and for this purpose introduced a great number of -new terms, founded on various analogies and allusions. -Thus the forms of calc-spar are termed by him <i>primitive</i>, -<i>equiaxe</i>, <i>inverse</i>, <i>metastatique</i>, <i>contrastante</i>, <i>imitable</i>, -<i>birhomboidale</i>, <i>prismatique</i>, <i>apophane</i>, <i>uniternaire</i>, -<i>bisunitaire</i>, <i>dodécaèdre</i>, <i>contractée</i>, <i>dilatée</i>, <i>sexduodecimale</i>, -<i>bisalterne</i>, <i>binoternaire</i>, and many others. -The <span class="pagenum" id="page327">327</span> -want of uniformity in the origin and scheme of these -denominations would be no valid objection to them, if -any general truth could be expressed by means of -them: but the fact is, that there is no definite -distinction of these forms. They pass into each other -by insensible gradations, and the optical and physical -properties which they possess are common to all of -them. And as a mere enunciation of laws of form, -this terminology is insufficient. Thus it does not at -all convey the relation between the <i>bisalterne</i> and the -<i>binoternaire</i>, the former being a combination of the -<i>metastatique</i> with the <i>prismatique</i>, the latter, of the -<i>metastatique</i> with the <i>contrastante</i>: again, -the <i>contrastante</i>, the <i>mixte</i>, the <i>cuboide</i>, -the <i>contractée</i>, the <i>dilatée</i>, all contain -faces generated by a common law, the -index being respectively altered so as to be in these -cases, 3, <span style="font-size: 80%"><sup>3</sup>⁄<sub>2</sub></span>, -<span style="font-size: 80%"><sup>4</sup>⁄<sub>5</sub></span>, -<span style="font-size: 80%"><sup>9</sup>⁄<sub>4</sub></span>, -<span style="font-size: 80%"><sup>5</sup>⁄<sub>9</sub></span>; -and this, which is the most -important geometrical relation of these forms, is not at -all recorded or indicated by the nomenclature. The -fact is, that it is probably impossible, the subject of -crystallography having become so complex as it now is, -to devise a system of names which shall express the -relations of form. Numerical symbols, such as those -of Weiss or Naumann, or Professor Miller, are the -proper ways of expressing these relations, and are the -only good crystallographic terminology for cases in -detail.</p> -<p>The terms used in expressing crystallographic laws -have been for the most part taken from the Greek by -all writers except some of the Germans. These, we -have already stated, have constructed terms in their -own language, as <i>zwei-und-ein gliedrig</i>, and the like.</p> -<p>In Optics we have some new terms connected with -crystalline laws, as <i>uniaxal</i> and <i>biaxal</i> crystals, <i>optical -axes</i>, which offered themselves without any effort on -the part of the discoverers. In the whole history of -the undulatory theory, very few innovations in language -were found necessary, except to fix the sense of -a few phrases, as <i>plane-polarized</i> light in opposition to -<i>circularly-polarized</i>, and the like.</p> -<p>This is still more the case in Mechanics, Astronomy, <span class="pagenum" id="page328">328</span> -and pure mathematics. In these sciences, several of -the primary stages of generalization being already -passed over, when any new steps are made, we have -before us some analogy by which we may frame our -new terms. Thus when the <i>plane of maximum areas</i> -was discovered, it had not some new arbitrary denomination -assigned it, but the name which obviously described -it was fixed as a technical name.</p> -<p>The result of this survey of the scientific terms of -recent formation seems to be this;—that indigenous -terms may be employed in the descriptions of facts -and phenomena as they at first present themselves; -and in the first induction from these; but that when -we come to generalize and theorize, terms borrowed -from the learned languages are more readily fixed and -made definite, and are also more easily connected with -derivatives. Our native terms are more impressive, -and at first more intelligible; but they may wander -from their scientific meaning, and are capable of little -inflexion. Words of classical origin are precise to the -careful student, and capable of expressing, by their -inflexions, the relations of general ideas; but they are -unintelligible, even to the learned man, without express -definition, and convey instruction only through -an artificial and rare habit of thought.</p> -<p class="end">Since in the balance between words of domestic and -of foreign origin so much depends upon the possibility -of inflexion and derivation, I shall consider a little -more closely what are the limits and considerations -which we have to take into account in reference to -that subject.</p> -<p class="center" id="a21"><span class="sc">Aphorism</span> XXI.</p> -<p><i>In the composition and inflexion of technical terms, philological -analogies are to be preserved if possible, but modified -according to scientific convenience.</i></p> -<p><span class="sc">In</span> the language employed or proposed by writers -upon subjects of science, many combinations and forms -of derivation occur, which would be rejected and condemned -by those who are careful of the purity and <span class="pagenum" id="page329">329</span> -correctness of language. Such anomalies are to be -avoided as much as possible; but it is impossible to -escape them altogether, if we are to have a scientific -language which has any chance of being received into -general use. It is better to admit compounds which -are not philologically correct, than to invent many -new words, all strange to the readers for whom they -are intended: and in writing on science in our own -language, it is not possible to avoid making additions -to the vocabulary of common life; since science requires -exact names for many things which common -language has not named. And although these new -names should, as much as possible, be constructed in -conformity with the analogies of the language, such -extensions of analogy can hardly sound, to the grammarian’s -ear, otherwise than as solecisms. But, as our -maxim indicates, the analogy of science is of more -weight with us than the analogy of language: and although -anomalies in our phraseology should be avoided -as much as possible, innovations must be permitted -wherever a scientific language, easy to acquire, and -convenient to use, is unattainable without them.</p> -<p>I shall proceed to mention some of the transgressions -of strict philological rules, and some of the -extensions of grammatical forms, which the above -conditions appear to render necessary.</p> -<p id="b4a21a1">1. The combination of different languages in the -derivation of words, though to be avoided in general, -is in some cases admissible.</p> -<p>Such words are condemned by Quintilian and other -grammarians, under the name of hybrids, or things of a -mixed race; as <i>biclinium</i> from <i>bis</i> and <span class="greek">κλίνη</span>; <i>epitogium</i>, -from <span class="greek">ἐπὶ</span> and <i>toga</i>. Nor are such terms to be -unnecessarily introduced in science. Whenever a homogeneous -word can be formed and adopted with the -same ease and convenience as a hybrid, it is to be preferred. -Hence we must have <i>ichthyology</i>, not <i>piscology</i>, -<i>entomology</i>, not <i>insectology</i>, <i>insectivorous</i>, -not <i>insectophagous</i>. In like manner, it would be better to say -<i>unoculus</i> than <i>monoculus</i>, though the latter has the -sanction of Linnæus, who was a purist in such matters. <span class="pagenum" id="page330">330</span> -Dr. Turner, in his <i>Chemistry</i>, speaks of <i>protoxides</i> and -<i>binoxides</i>, which combination violates the rule for -making the materials of our terms as homogeneous as -possible; <i>protoxide</i> and <i>deutoxide</i> would be preferable, -both on this and on other accounts.</p> -<p>Yet this rule admits of exceptions. <i>Mineralogy</i>, -with its Greek termination, has for its root <i>minera</i>, a -medieval Latin word of Teutonic origin, and is preferable -to <i>Oryctology</i>. <i>Terminology</i> appears to be better -than <i>Glossology</i>: which according to its derivation -would be rather the science of language in general -than of technical terms; and <i>Horology</i>, from <span class="greek">ὅρος</span>, a -term, would not be immediately intelligible, even to -Greek scholars; and is already employed to indicate -the science which treats of horologes, or time-pieces.</p> -<p>Indeed, the English reader is become quite familiar -with the termination <i>ology</i>, the names of a large -number of branches of science and learning having that -form. This termination is at present rather apprehended -as a formative affix in our own language, indicating a science, -than as an element borrowed from -foreign language. Hence, when it is difficult or impossible -to find a Greek term which clearly designates -the subject of a science, it is allowable to employ some -other, as in <i>Tidology</i>, the doctrine of the Tides.</p> -<p>The same remark applies to some other Greek elements of -scientific words: they are so familiar to us -that in composition they are almost used as part of -our own language. This naturalization has taken -place very decidedly in the element <i>arch</i>, (<span class="greek">ἀρχὸς</span> a -leader,) as we see in <i>archbishop</i>, <i>archduke</i>. It is -effected in a great degree for the preposition <i>anti</i>: thus -we speak of <i>anti-slavery</i> societies, <i>anti-reformers</i>, -<i>anti-bilious</i>, or <i>anti-acid</i> medicines, without being conscious -of any anomaly. The same is the case with the Latin -preposition <i>præ</i> or <i>pre</i>, as appears from such words as -<i>pre-engage</i>, <i>pre-arrange</i>, <i>pre-judge</i>, <i>pre-paid</i>; and in -some measure with <i>pro</i>, for in colloquial language we -speak of <i>pro-catholics</i> and <i>anti-catholics</i>. Also the -preposition <i>ante</i> is similarly used, as <i>ante-nicene</i> fathers. -The preposition <i>co</i>, abbreviated from <i>con</i>, and <span class="pagenum" id="page331">331</span> implying -things to be simultaneous or connected, is firmly -established as part of the language, as we see in <i>coexist</i>, -<i>coheir</i>, <i>coordinate</i>; hence I have called those lines -<i>cotidal</i> lines which pass through places where the high -water of the tide occurs simultaneously.</p> -<p id="b4a21a2">2. As in the course of the mixture by which our -language has been formed, we have thus lost all -habitual consciousness of the difference of its ingredients, -(Greek, Latin, Norman-French, and Anglo-Saxon): we -have also ceased to confine to each ingredient the mode -of grammatical inflexion which originally belonged to -it. Thus the termination <i>ive</i> belongs peculiarly to -Latin adjectives, yet we say <i>sportive</i>, <i>talkative</i>. In -like manner, <i>able</i> is added to words which are not -Latin, as <i>eatable</i>, <i>drinkable</i>, <i>pitiable</i>, <i>enviable</i>. Also -the termination <i>al</i> and <i>ical</i> are used with various roots, -as <i>loyal</i>, <i>royal</i>, <i>farcical</i>, <i>whimsical</i>; hence we may -make the adjective <i>tidal</i> from <i>tide</i>. This ending, <i>al</i>, -is also added to abstract terms in <i>ion</i>, as <i>occasional</i>, -<i>provisional</i>, <i>intentional</i>, <i>national</i>; hence we may, if -necessary, use such words as <i>educational</i>, <i>terminational</i>. -The ending <i>ic</i> appears to be suited to proper -names, as <i>Pindaric</i>, <i>Socratic</i>, <i>Platonic</i>; hence it may -be used when scientific words are derived from proper -names, as <i>Voltaic</i> or <i>Galvanic</i> electricity: to which I -have proposed to add <i>Franklinic</i>.</p> -<p>In adopting scientific adjectives from the Latin, we -have not much room for hesitation; for, in such cases, -the habits of derivation from that language into our -own are very constant; <i>ivus</i> becomes <i>ive</i>, as <i>decursive</i>; -<i>inus</i> becomes <i>ine</i>, as in <i>ferine</i>; <i>atus</i> becomes <i>ate</i>, as -<i>hastate</i>; and <i>us</i> often becomes <i>ous</i>, as <i>rufous</i>; <i>aris</i> -becomes <i>ary</i>, as <i>axillary</i>; <i>ens</i> becomes <i>ent</i>, as <i>ringent</i>. -And in adopting into our language, as scientific terms, -words which in another language, the French for instance, -have a Latin origin familiar to us, we cannot -do better than form them as if they were derived -directly from the Latin. Hence the French adjectives -<i>cétacé</i>, <i>crustacé</i>, <i>testacé</i>, may become either <i>cetaceous</i>, -<i>crustaceous</i>, <i>testaceous</i>, according to the analogy of -<i>farinaceous</i>, <i>predaceous</i>, or else <i>cetacean</i>, -<i>crustacean</i>, <span class="pagenum" id="page332">332</span> -<i>testacean</i>, imitating the form of <i>patrician</i>. Since, as -I shall soon have to notice, we require substantives as -well as adjectives from these words, we must, at least -for that use, take the forms last suggested.</p> -<p>In pursuance of the same remark, <i>rongeur</i> becomes -<i>rodent</i>; and <i>edenté</i> would become <i>edentate</i>, but that -this word is rejected on another account: the adjectives -<i>bimane</i> and <i>quadrumane</i> are <i>bimanous</i> and -<i>quadrumanous</i>.</p> -<p id="b4a21a3">3. There is not much difficulty in thus forming -adjectives: but the purposes of Natural History require -that we should have substantives corresponding -to these adjectives; and these cannot be obtained without -some extension of the analogies of our language. -We cannot in general use adjectives or participles as -singular substantives. <i>The happy</i> or <i>the doomed</i> would, -according to good English usage, signify those who are -happy and those who are doomed in the plural. Hence -we could not speak of a particular scaled animal as <i>the -squamate</i>, and still less could we call any such animal -<i>a squamate</i>, or speak of <i>squamates</i> in the plural. Some -of the forms of our adjectives, however, do admit of -this substantive use. Thus we talk of <i>Europeans</i>, <i>plebeians</i>, -<i>republicans</i>; of <i>divines</i> and <i>masculines</i>; of the -<i>ultramontanes</i>; of <i>mordants</i> and <i>brilliants</i>; -of <i>abstergents</i> and <i>emollients</i>; -of <i>mercenaries</i> and <i>tributaries</i>; -of <i>animals</i>, <i>mammals</i>, and <i>officials</i>; of <i>dissuasives</i> and -<i>motives</i>. We cannot generally use in this way adjectives -in <i>ous</i>, nor in <i>ate</i> (though <i>reprobates</i> is an exception), -nor English participles, nor adjectives in which there -is no termination imitating the Latin, as <i>happy</i>, <i>good</i>. -Hence, if we have, for purposes of science, to convert -adjectives into substantives, we ought to follow the -form of examples like these, in which it has already -appeared in fact, that such usage, though an innovation -at first, may ultimately become a received part of -the language.</p> -<p>By attention to this rule we may judge what expressions -to select in cases where substantives are -needed. I will take as an example the division of -the mammalian animals into Orders. These Orders, <span class="pagenum" id="page333">333</span> -according to Cuvier, are <i>Bimanes</i>, <i>Quadrumanes</i>, <i>Carnassiers</i>, -<i>Rongeurs</i>, <i>Edentés</i>, <i>Ruminants</i>, <i>Pachydermes</i>, -<i>Cétacés</i>; and of these, <i>Bimanes</i>, <i>Quadrumanes</i>, <i>Rodents</i>, -<i>Ruminants</i>, <i>Pachyderms</i> are admissible as English substantives -on the grounds just stated. <i>Cetaceous</i> -could not be used substantively; but <i>Cetacean</i> in such -a usage is sufficiently countenanced by such cases as -we have mentioned, <i>patrician</i>, &c.; hence we adopt -this form. We have no English word equivalent to -the French <i>Carnassiers</i>: the English translator of -Cuvier has not provided English words for his technical -terms; but has formed a Latin word, <i>Carnaria</i>, -to represent the French terms. From this we might -readily form <i>Carnaries</i>; but it appears much better to -take the Linnæan name <i>Feræ</i> as our root, from which -we may take <i>Ferine</i>, substantive as well as adjective; -and hence we call this order <i>Ferines</i>. The word for -which it is most difficult to provide a proper representation -is <i>Edenté</i>, <i>Edentata</i>: for, as we have said, it -would be very harsh to speak of the order as the -<i>Edentates</i>; and if we were to abbreviate the word -into <i>edent</i>, we should suggest a false analogy with -<i>rodent</i>, for as <i>rodent</i> is <i>quod rodit</i>, that which gnaws, -<i>edent</i> would be <i>quod edit</i>, that which eats. And even -if we were to take <i>edent</i> as a substantive, we could -hardly use it as an adjective: we should still have to -say, for example, the <i>edentate</i> form of head. For these -reasons it appears best to alter the form of the word, -and to call the Order the <i>Edentals</i>, which is quite -allowable, both as adjective and substantive.</p> -<p>[An objection might be made to this term, both in -its Latin, French and English form: namely, that the -natural group to which it is applied includes many -species, both existing and extinct, well provided with -teeth. Thus the armadillo is remarkable for the number -of its teeth; the megatherium, for their complex -structure. But the analogy of scientific language -readily permits us to fix, upon the word <i>edentata</i>, a -special meaning, implying the absence of one particular -kind of teeth, namely, incisive teeth. Linnæus -called the equivalent order <i>Bruta</i>. We could not <span class="pagenum" id="page334">334</span> -apply in this case the term <i>Brutes</i>; for common -language has already attached to the word a wider meaning, -too fixedly for scientific use to trifle with it.]</p> -<p>There are several other words in <i>ate</i> about which -there is the same difficulty in providing substantive -forms. Are we to speak of <i>Vertebrates</i>? or would it -not be better, in agreement with what has been said -above, to call these <i>Vertebrals</i>, and the opposite class -<i>Invertebrals</i>?</p> -<p>There are similar difficulties with regard to the -names of subordinate portions of zoological classification; -thus the Ferines are divided by Cuvier into -<i>Cheiroptéres</i>, <i>Insectivores</i>, <i>Carnivores</i>; and these latter -into <i>Plantigrades</i>, <i>Digitigrades</i>, <i>Amphibies</i>, <i>Marsupiaux</i>. -There is not any great harshness in naturalizing -these substantives as <i>Chiropters</i>, <i>Insectivores</i>, <i>Carnivores</i>, -<i>Plantigrades</i>, <i>Digitigrades</i>, <i>Amphibians</i>, and -<i>Marsupials</i>. These words <i>Carnivores</i> and <i>Insectivores</i> -are better, because of more familiar origin, than Greek -terms; otherwise we might, if necessary, speak of -<i>Zoophagans</i> and <i>Entomophagans</i>.</p> -<p>It is only with certain familiar adjectival terminations, -as <i>ous</i> and <i>ate</i>, that there is a difficulty in using -the word as substantive. When this can be avoided, -we readily accept the new word, as <i>Pachyderms</i>, and -in like manner <i>Mollusks</i>.</p> -<p>If we examine the names of the Orders of Birds, we -find that they are in Latin, <i>Predatores</i> or <i>Accipitres</i>, -<i>Passeres</i>, <i>Scansores</i>, <i>Rasores</i> or <i>Gallinæ</i>, <i>Grallatores</i>, -<i>Palmipedes</i> and <i>Anseres</i>: Cuvier’s Orders are, <i>Oiseaux -de Proie</i>, <i>Passereaux</i>, <i>Grimpeurs</i>, <i>Gallinacés</i>, <i>Échassiers</i>, -<i>Palmipedes</i>. These may be englished conveniently as <i>Predators</i>, -<i>Passerines</i>, <i>Scansors</i>, <i>Gallinaceans</i>, -(rather than <i>Rasors</i>,) <i>Grallators</i>, <i>Palmipedans</i>, [or -rather <i>Palmipeds</i>, like <i>Bipeds</i>]. <i>Scansors</i>, <i>Grallators</i>, -and <i>Rasors</i>, are better, as technical terms, than <i>Climbers</i>, -<i>Waders,</i> and <i>Scratchers</i>. We might venture to -anglicize the terminations of the names which Cuvier -gives to the divisions of these Orders: thus the Predators -are the <i>Diurnals</i> and the <i>Nocturnals</i>; the -Passerines are the <i>Dentirostres</i>, the -<i>Fissirostres</i>, the <span class="pagenum" id="page335">335</span> -<i>Conirostres</i>, the <i>Tenuirostres</i>, and the <i>Syndactyls</i>: the -word <i>lustre</i> showing that the former termination is -allowable. The Scansors are not sub-divided, nor are -the Gallinaceans. The Grallators are <i>Pressirostres</i>, -<i>Cultrirostres</i>, <i>Macrodactyls</i>. The Palmipeds are the -<i>Plungers</i>, the <i>Longipens</i>, the <i>Totipalmes</i> and the -<i>Lamellirostres</i>.</p> -<p>The next class of Vertebrals is the <i>Reptiles</i>, and -these are either <i>Chelonians</i>, <i>Saurians</i>, <i>Ophidians</i>, or -<i>Batrachians</i>. Cuvier writes <i>Batraciens</i>, but we prefer -the spelling to which the Greek word directs us.</p> -<p>The last or lowest class is the <i>Fishes</i>, in which province -Cuvier has himself been the great systematist, -and has therefore had to devise many new terms. -Many of these are of Greek or Latin origin, and can -be anglicized by the analogies already pointed out, as -<i>Chondropterygians</i>, <i>Malacopterygians</i>, <i>Lophobranchs</i>, -<i>Plectognaths</i>, <i>Gymnodonts</i>, <i>Scleroderms</i>. <i>Discoboles</i> and -<i>Apodes</i> may be English as well as French. There are -other cases in which the author has formed the names -of Families, either by forming a word in <i>ides</i> from the -name of a genus, as <i>Gadoides</i>, <i>Gobiöides</i>, or by -gallicizing the Latin name of the genus, as <i>Salmones</i> from -<i>Salmo</i>, <i>Clupes</i> from <i>Clupea</i>, <i>Ésoces</i> from <i>Esox</i>, <i>Cyprins</i> -from <i>Cyprinus</i>. In these cases Agassiz’s favourite form -of names for families of fishes has led English writers -to use the words <i>Gadoids</i>, <i>Gobioids</i>, <i>Salmonoids</i>, -<i>Clupeoids</i>, <i>Lucioids</i> (for <i>Ésoces</i>), <i>Cyprinoids</i>, &c. There is -a taint of hybridism in this termination, but it is attended -with this advantage, that it has begun to be -characteristic of the nomenclature of family groups in -the class <i>Pisces</i>. One of the orders of fishes, -co-ordinate with the Chondropterygians and the Lophobranchs, -is termed <i>Osseux</i> by Cuvier. It appears -hardly worth while to invent a substantive word for -this, when <i>Bony Fishes</i> is so simple a phrase, and may -readily be understood as a technical name of a systematic order.</p> -<p>The Mollusks are the next Class; and these are -divided into <i>Cephallopods</i>, <i>Gasteropods</i>, and the like. -The Gasteropods are <i>Nudibranchs</i>, <i>Inferobranchs</i>, -<span class="pagenum" id="page336">336</span> <i>Tectibranchs,</i> -<i>Pectinibranchs</i>, <i>Scutibranchs</i>, and <i>Cyclobranchs</i>. -In framing most of these terms Cuvier has made hybrids -by a combination of a Latin word with <i>branchiæ</i> -which is the Greek name for the gills of a fish; and has -thus avoided loading the memory with words of an -origin not obvious to most naturalists, as terms derived -from the Greek would have been. Another division -of the Gasteropods is <i>Pulmonés</i>, which we must make -<i>Pulmonians</i>. In like manner the subdivisions of the -Pectinibranchs are the <i>Trochoidans</i> and <i>Buccinoidans</i>, -(<i>Trochoïdes</i>, <i>Buccinoïdes)</i>. The <i>Acéphales</i>, another order -of Mollusks, may be <i>Acephals</i> in English.</p> -<p>After these comes the third grand division, <i>Articulated -Animals</i>, and these are <i>Annelidans</i>, <i>Crustaceans,</i> -<i>Arachnidans</i>, and <i>Insects</i>. I shall not dwell upon the -names of these, as the form of English words which is -to be selected must be sufficiently obvious from the -preceding examples.</p> -<p>Finally, we have the fourth grand division of animals, -the <i>Rayonnés</i>, or <i>Radiata</i>; which, for reasons already -given, we may call <i>Radials</i>, or <i>Radiaries</i>. These are -<i>Echinoderms</i>, <i>Intestinals</i>, (or rather <i>Entozoans</i>,) <i>Acalephes</i>, -and <i>Polyps</i>. The Polyps, which are composite -animals in which many gelatinous individuals are connected -so as to have a common life, have, in many cases, -a more solid framework belonging to the common part -of the animal. This framework, of which coral is a -special example, is termed in French <i>Polypier</i>; the -word has been anglicized by the word <i>polypary</i>, after -the analogy of <i>aviary</i> and <i>apiary</i>. Thus Polyps are -either <i>Polyps with Polyparies</i> or <i>Naked Polyps</i>.</p> -<p>Any common kind of Polyps has usually in the -English language been called <i>Polypus</i>, the Greek termination -being retained. This termination in <i>us</i>, -however, whether Latin or Greek, is to be excluded -from the English as much as possible, on account of -the embarrassment which it occasions in the formation -of the plural. For if we say <i>Polypi</i> the word ceases to -be English, while <i>Polypuses</i> is harsh: and there is the -additional inconvenience, that both these forms would -indicate the plural of individuals rather than of classes. <span class="pagenum" id="page337">337</span> -If we were to say, ‘The Corallines are a Family of the -<i>Polypuses with Polyparies</i>,’ it would not at once occur -to the reader that the last three words formed a technical phrase.</p> -<p>This termination <i>us</i> which must thus be excluded -from the names of families, may be admitted in the -designation of genera; of animals, as <i>Nautilus</i>, <i>Echinus</i>, -<i>Hippopotamus</i>; and of plants, as <i>Crocus</i>, <i>Asparagus</i>, -<i>Narcissus</i>, <i>Acanthus</i>, <i>Ranunculus</i>, <i>Fungus</i>. The same -form occurs in other technical words, as <i>Fucus</i>, <i>Mucus</i>, -<i>Œsophagus</i>, <i>Hydrocephalus</i>, <i>Callus</i>, <i>Calculus</i>, <i>Uterus</i>, -<i>Fœtus</i>, <i>Radius</i>, <i>Focus</i>, <i>Apparatus</i>. It is, however, -advisable to retain this form only in cases where it is -already firmly established in the language; for a more -genuine English form is preferable. Hence we say, -with Mr. Lyell, <i>Ichthyosaur</i>, <i>Plesiosaur</i>, <i>Pterodactyl</i>. In -like manner Mr. Owen anglicizes the termination <i>erium</i>, -and speaks of the <i>Anoplothere</i> and <i>Paleothere</i>.</p> -<p>Since the wants of science thus demand adjectives -which can be used also as substantive names of classes, -this consideration may sometimes serve to determine -our selection of new terms. Thus Mr. Lyell’s names -for the subdivisions of the tertiary strata, <i>Miocene</i>, <i>Pliocene,</i> -can be used as substantives; but if such words as -<i>Mioneous</i>, <i>Plioneous</i>, had suggested themselves, they -must have been rejected, though of equivalent signification, -as not fulfilling this condition.</p> -<p id="b4a21a4">4. (<i>a.</i>) Abstract substantives can easily be formed -from adjectives: from electric we have <i>electricity</i>; from -galvanic, <i>galvanism</i>; from organic, <i>organization</i>; -<i>velocity</i>, <i>levity</i>, <i>gravity</i>, are borrowed from Latin adjectives. -<i>Caloric</i> is familiarly used for the matter of heat, though -the form of the word is not supported by any obvious -analogy.</p> -<p>(<i>b.</i>) It is intolerable to have words regularly -formed, in opposition to the analogy which their meaning -offers; as when bodies are said to have conduct<i>ibility</i> -or conduc<i>ibility</i> with regard to heat. The bodies -are conduct<i>ive</i>, and their property is conduct<i>ivity</i>.</p> -<p>(<i>c.</i>) The terminations <i>ize</i> (rather than <i>ise</i>), <i>ism</i>, and -<i>ist</i>, are applied to words of all origins: -thus we have to <span class="pagenum" id="page338">338</span> -<i>pulverize</i>, to <i>colonize</i>, <i>Witticism</i>, <i>Heathenism</i>, <i>Journalist</i>, -<i>Tobacconist</i>. Hence we may make such words when -they are wanted. As we cannot use <i>physician</i> for a -cultivator of physics, I have called him a <i>Physicist</i>. -We need very much a name to describe a cultivator of -science in general. I should incline to call him a -<i>Scientist</i>. Thus we might say, that as an Artist is a -Musician, Painter, or Poet, a Scientist is a Mathematician, -Physicist, or Naturalist.</p> -<p>(<i>d.</i>) Connected with verbs in <i>ize</i>, we have abstract -nouns in <i>ization</i>, as <i>polarization</i>, <i>crystallization</i>. These -it appears proper to spell in English with <i>z</i> rather than -<i>s</i>; governing our practice by the Greek verbal termination -<span class="greek">ίζω</span> which we imitate. But we must observe -that verbs and substantives in <i>yse</i>, (<i>analyse</i>), belong -to a different analogy, giving an abstract noun in <i>ysis</i> -and an adjective <i>ytic</i> or <i>ytical</i>; (<i>analysis</i>, <i>analytic</i>, -<i>analytical</i>). Hence <i>electrolyse</i> is more proper than -<i>electrolyze</i>.</p> -<p>(<i>e.</i>) The names of many sciences end in <i>ics</i> after -the analogy of <i>Mathematics</i>, <i>Metaphysics</i>; as <i>Optics</i>, -<i>Mechanics</i>. But these, in most other languages, as in -our own formerly, have the singular form <i>Optice</i>, <i>l’Optique</i>, -<i>Optik</i>, <i>Optick</i>: and though we now write <i>Optics</i>, -we make such words of the singular number: ‘Newton’s Opticks -is an example.’ As, however, this connexion in new words -is startling, as when we say -‘Thermo-electrics is now much cultivated,’ it appears -better to employ the singular form, after the analogy -of <i>Logic</i> and <i>Rhetoric</i>, when we have words -to construct. Hence we may call the science of languages -<i>Linguistic</i>, as it is called by the best German writers, -for instance, William Von Humboldt.</p> -<p id="b4a21a5">5. In the derivation of English from Latin or Greek -words, the changes of letters are to be governed by the -rules which have generally prevailed in such cases. -The Greek <span class="greek">οι</span> and <span class="greek">αι</span>, -the Latin <i>oe</i> and <i>ae</i>, -are all converted into a simple <i>e</i>, as in <i>E</i>conomy, Geod<i>e</i>sy, p<i>e</i>nal, -C<i>e</i>sar. Hence, according to common usage, we should -write ph<i>e</i>nomena, not ph<i>æ</i>nomena, pal<i>e</i>ontology, not -pal<i>æ</i>ontology, mioc<i>e</i>ne not mioc<i>æ</i>ne, p<i>e</i>kilite not -<span class="pagenum" id="page339">339</span> p<i>œ</i>kilite. -But in order to keep more clearly in view the -origin of our terms, it may be allowable to deviate from -these rules of change, especially so long as the words -are new and unfamiliar. Dr. Buckland speaks of the -<i>poikilitic</i>, not <i>pecilitic</i>, group of strata: <i>palæontology</i> -is the spelling commonly adopted; and in imitation of -this I have written <i>palætiology</i>. The diphthong <span class="greek">ει</span> was -by the Latins changed into <i>i</i>, as in Arist<i>i</i>des; and -hence this has been the usual form in English. Some -recent authors indeed (Mr. Mitford for instance) write -Arist<i>eid</i>es; but the former appears to be the more -legitimate. Hence we write m<i>i</i>ocene, pl<i>i</i>ocene, not -m<i>ei</i>ocene, pl<i>ei</i>ocene. The Greek <span class="greek">υ</span> -becomes <i>y</i>, and <span class="greek">ου</span> -becomes <i>u</i>, in English as in Latin, as cr<i>y</i>stal, col<i>u</i>re. -The consonants <span class="greek">κ</span> and <span class="greek">χ</span> -become <i>c</i> and <i>ch</i> according -to common usage. Hence we write <i>crystal</i>, -not <i>chrystal</i>, batra<i>ch</i>ian, not batra<i>c</i>ian, <i>c</i>ryolite, not -<i>ch</i>ryolite. As, however, the letter <i>c</i> before <i>e</i> and <i>i</i> -differs from <i>k</i>, which is the sound we assign to the -Greek <span class="greek">κ</span>, it may be allowable to use <i>k</i> in order to avoid -this confusion. Thus, as we have seen, poi<i>k</i>ilite has -been used, as well as pe<i>c</i>ilite. Even in common language -some authors write s<i>k</i>eptic, which appears to be -better than s<i>c</i>eptic with our pronunciation, and is -preferred by Dr. Johnson. For the same reason, namely, -to avoid confusion in the pronunciation, and also, in -order to keep in view the connexion with <i>cathode</i>, the -elements of an electrolyte which go to the anode and -cathode respectively may be termed the anion and -cat<i>h</i>ion; although the Greek would suggest catïon, -(<span class="greek">κατίον</span>).</p> -<p id="b4a21a6">6. The example of chemistry has shown that we -have in the terminations of words a resource of which -great use may be made in indicating the relations of -certain classes of objects: as sulphur<i>ous</i> and sulphur<i>ic</i> -acids; sulph<i>ates</i>, sulph<i>ites</i>, and sulph<i>urets</i>. Since the -introduction of the artifice by the Lavoisierian school, -it has been extended to some new cases. The Chlor<i>ine</i>, -Fluor<i>ine</i>, Brom<i>ine</i>, Iod<i>ine</i>, had their names put into -that shape in consequence of their supposed analogy: -and for the same reason have been termed Chlore, <span class="pagenum" id="page340">340</span> -Phlore, Brome, Iode, by French chemists. In like -manner, the names of metals in their Latin form have -been made to end in <i>um</i>, as Osmium, Palladium; -and hence it is better to say Platin<i>um</i>, Molybden<i>um</i>, -than Platin<i>a</i>, Molybden<i>a</i>. It has been proposed -to term the basis of Boracic acid Bor<i>on</i>; and those who -conceive that the basis of Silica has an analogy with -Boron have proposed to term it Silic<i>on</i>, while those -who look upon it as a metal would name it Silic<i>ium</i>. -Seleni<i>um</i> was so named when it was supposed to be a -metal: as its analogies are now acknowledged to be of -another kind, it would be desirable, if the change were -not too startling, to term it Sel<i>en</i>, as it is in German. -Phosph<i>orus</i> in like manner might be Phosph<i>ur</i>, which -would indicate its analogy with Sulph<i>ur</i>.</p> -<p>The resource which terminations offer has been applied -in other cases. The names of many species of -minerals end in <i>lite</i>, or <i>ite</i>, as Stauro<i>lite</i>, Aug<i>ite</i>. -Hence Adolphe Brongniart, in order to form a name -for a genus of fossil plants, has given this termination -to the name of the recent genus which they nearly -resemble, as Zam<i>ites</i>, from Zamia, Lycopod<i>ites</i> from -Lycopodium.</p> -<p>Names of different genera which differ in termination only -are properly condemned by -Linnæus<a id="fnanchor58-4" href="#note58-4"><span class="fnanchor">58</span></a>; as -<i>Alsine</i>, <i>Alsinoides</i>, <i>Alsinella</i>, <i>Alsinastrum</i>; for there -is no definite relation marked by those terminations. -Linnæus gives to such genera distinct names, <i>Alsine</i>, -<i>Bufonia</i>, <i>Sagina</i>, <i>Elatine</i>.</p> -<div class="footnote"><span class="label"><a id="note58-4" href="#fnanchor58-4">58</a></span> -<i>Phil. Bot.</i> 231. -</div> -<p>Terminations are well adapted to express definite -systematic relations, such as those of chemistry, but -they must be employed with a due regard to all the -bearings of the system. Davy proposed to denote the -combinations of other substances with chlorine by -peculiar terminations; using <i>ane</i> for the smallest -proportion of Chlorine, and <i>anea</i> for the larger, -as Cupr<i>ane</i>, Cupr<i>anea</i>. In this nomenclature, common salt -would be <i>Sodane</i>, and Chloride of Nitrogen would be -<i>Azotane</i>. This suggestion never found favour. It was <span class="pagenum" id="page341">341</span> -objected that it was contrary to the Linnæan precept, -that a specific name must not be united to a -generic termination. But this was not putting the -matter exactly on its right ground; for the rules of -nomenclature of natural history do not apply to -chemistry; and the Linnæan rule might with equal -propriety have been adduced as a condemnation of -such terms as Sulphur<i>ous</i>, Sulphur<i>ic</i>. But Davy’s -terms were bad; for it does not appear that Chlorine -enters, as Oxygen does, into so large a portion of -chemical compounds, that its relations afford a key to -their nature, and may properly be made an element -in their names.</p> -<p class="end">This resource, of terminations, has been abused, -wherever it has been used wantonly, or without -a definite significance in the variety. This is the case in -M. Beudant’s Mineralogy. Among the names which -he has given to new species, we find the following -(besides many in <i>ite</i>), Scolexer<i>ose</i>, Opsim<i>ose</i>, -Exanthel<i>ose</i>, &c.; Diacr<i>ase</i>, Panab<i>ase</i>, Neopl<i>ase</i>; -Neocl<i>ese</i>; Rhodo<i>ise</i>, Stibicon<i>ise</i>, &c.; -Marcel<i>ine</i>, Wilhelm<i>ine</i>, &c.; -Exit<i>ele</i>, and many others. In addition to other objections -which might be made to these names, their -variety is a material defect: for to make this variety -depend on caprice alone, as in those cases it does, is to -throw away a resource of which chemical nomenclature -may teach us the value.</p> -<p class="center" id="a22"><span class="sc">Aphorism</span> XXII.</p> -<p><i>When alterations in technical terms become necessary, it -is desirable that the new term should contain in its form -some memorial of the old one.</i></p> -<p><span class="sc">We</span> have excellent examples of the advantageous -use of this maxim in Linnæus’s reform of botanical -nomenclature. His innovations were very extensive, -but they were still moderated as much as possible, and -connected in many ways with the names of plants then -in use. He has himself given several rules of nomenclature, -which tend to establish this connexion of the <span class="pagenum" id="page342">342</span> -old and new in a reform. Thus he says, ‘Generic -names which are current, and are not accompanied -with harm to botany, should be -tolerated<a id="fnanchor59-4" href="#note59-4"><span class="fnanchor">59</span></a>.’ ‘A -passable generic name is not to be changed for another, -though more apt<a id="fnanchor60-4" href="#note60-4"><span class="fnanchor">60</span></a>’. -‘New generic names are not to -be framed so long as passable synonyms are at -hand<a id="fnanchor61-4" href="#note61-4"><span class="fnanchor">61</span></a>.’ -‘A generic name of one genus, except it be superfluous, -is not to be transferred to another genus, though -it suit the other -better<a id="fnanchor62-4" href="#note62-4"><span class="fnanchor">62</span></a>.’ -‘If a received genus -requires to be divided into several, the name which -before included the whole, shall be applied to the most -common and familiar kind<a id="fnanchor63-4" href="#note63-4"><span class="fnanchor">63</span></a>.’ -And though he rejects -all <em>generic</em> names which have not a Greek or Latin -root<a id="fnanchor64-4" href="#note64-4"><span class="fnanchor">64</span></a>, -he is willing to make an exception in favour of -those which from their form might be supposed to -have such a root, though they are really borrowed from -other languages, as <i>Thea</i>, which is the Greek for goddess; -<i>Coffea</i>, which might seem to come from a Greek -word denoting silence (<span class="greek">κωφός</span>); <i>Cheiranthus</i>, -which appears to mean hand-flower, but is really derived from -the Arabic <i>Keiri</i>: and many others.</p> -<div class="footnote"><span class="label"><a id="note59-4" href="#fnanchor59-4">59</a></span> -<i>Philosophia Botanica</i>, Art. 242. -</div> -<div class="footnote"><span class="label"><a id="note60-4" href="#fnanchor60-4">60</a></span> -Art. 246. -</div> -<div class="footnote"><span class="label"><a id="note61-4" href="#fnanchor61-4">61</a></span> -Art. 247. -</div> -<div class="footnote"><span class="label"><a id="note62-4" href="#fnanchor62-4">62</a></span> -Art. 249. -</div> -<div class="footnote"><span class="label"><a id="note63-4" href="#fnanchor63-4">63</a></span> -Art. 249. -</div> -<div class="footnote"><span class="label"><a id="note64-4" href="#fnanchor64-4">64</a></span> -Art. 232. -</div> -<p>As we have already said, the attempt at a reformation -of the nomenclature of Mineralogy made by Professor Mohs -will probably not produce any permanent -effect, on this account amongst others, that it has not -been conducted in this temperate mode; the innovations -bear too large a proportion to the whole of the -names, and contain too little to remind us of the -known appellations. Yet in some respects Professor -Mohs has acted upon this maxim. Thus he has called -one of his classes <i>Spar</i>, because <i>Felspar</i> belongs to it. -I shall venture to offer a few suggestions on this -subject of Mineralogical Nomenclature.</p> -<p>It has already been remarked that the confusion -and complexity which prevail in this subject render a -reform very desirable. But it will be seen, from the -reasons assigned under the <a href="#a9">Ninth</a> Aphorism, that no -permanent system of names can be looked for, till a <span class="pagenum" id="page343">343</span> -sound system of classification be established. The best -mineralogical systems recently published, however, appear -to converge to a common point; and certain -classes have been formed which have both a natural-historical -and a chemical significance. These Classes, -according to Naumann, whose arrangement appears -the best, are Hydrolytes, Haloids, Silicides, Oxides of -Metals, Metals, Sulphurides (Pyrites, Glances, and -Blendes), and Anthracides. Now we find;—that the -Hydrolytes are all compounds, such as are commonly -termed <i>Salts</i>;—that the Haloids are, many of them, -already called <i>Spars</i>, as <i>Calc Spar</i>, <i>Heavy Spar</i>, <i>Iron -Spar</i>, <i>Zinc Spar</i>;—that the <i>Silicides</i>, the most -numerous and difficult class, are denoted for the most part, -by single words, many of which end in <i>ite</i>;—that the -other classes, or subclasses, <i>Oxides</i>, <i>Pyrites</i>, <i>Glances</i>, -and <i>Blendes</i>, have commonly been so termed; as <i>Red -Iron Oxide</i>, <i>Iron Pyrites</i>, <i>Zinc Blende</i>;—while pure -metals have usually had the adjective <i>native</i> prefixed, -as <i>Native Gold</i>, <i>Native Copper</i>. These obvious features -of the current names appear to afford us a basis -for a systematic nomenclature. The Salts and Spars -might all have the word <i>salt</i> or <i>spar</i> included in their -name, as <i>Natron Salt</i>, <i>Glauber Salt</i>, <i>Mock Salt</i>; <i>Calc -Spar</i>, <i>Bitter Spar</i>, (Carbonate of Lime and Magnesia), -<i>Fluor Spar</i>, <i>Phosphor Spar</i> (Phosphate of Lime), -<i>Heavy Spar</i>, <i>Celestine Spar</i> (Sulphate of Strontian), -<i>Chromic Lead Spar</i> (Chromate of Lead); the <i>Silicides</i> -might all have the name constructed so as to be a -single word ending in <i>ite</i>, as <i>Chabasite</i> (Chabasie), -<i>Natrolite</i> (Mesotype), <i>Sommite</i> (Nepheline), <i>Pistacite</i> -(Epidote); from this rule might be excepted the <i>Gems</i>, -as <i>Topaz</i>, <i>Emerald</i>, <i>Corundum</i>, which might retain -their old names. The Oxides, Pyrites, Glances, and -Blendes, might be so termed; thus we should have -<i>Tungstic Iron Oxide</i> (usually called Tungstate of Iron), -<i>Arsenical Iron Pyrites</i> (Mispickel), <i>Tetrahedral Copper -Glance</i> (Fahlerz), <i>Quicksilver Blende</i> (Cinnabar), -and the metals might be termed <i>native</i>, as -<i>Native Copper</i>, <i>Native Silver</i>.</p> -<p>Such a nomenclature would take in a very large <span class="pagenum" id="page344">344</span> -proportion of commonly received appellations, especially -if we were to select among the synonyms, as is -proposed above in the case of <i>Glauber Salt</i>, <i>Bitter Spar</i>, -<i>Sommite</i>, <i>Pistacite</i>, <i>Natrolite</i>. Hence it might be -adopted without serious inconvenience. It would make -the name convey information respecting the place of -the mineral in the system; and by imposing this condition, -would limit the extreme caprice, both as to -origin and form, which has hitherto been indulged in -imposing mineralogical names.</p> -<p>The principle of a mineralogical nomenclature determined -by the place of the species in the system, has -been recognized by Mr. Beudant as well as Mr. Mohs. -The former writer has proposed that we should say -<i>Carbonate Calcaire</i>, <i>Carbonate Witherite</i>, <i>Sulphate -Couperose</i>, <i>Silicate Stilbite</i>, <i>Silicate Chabasie</i>, and so on. -But these are names in which the part added for the -sake of the system, is not incorporated with the common name, -and would hardly make its way into common use.</p> -<p>We have already noticed Mr. Mohs’s designations -for two of the Systems of Crystallization, the -<i>Pyramidal</i> and the <i>Prismatic</i>, as not characteristic. If it -were thought advisable to reform such a defect, this -might be done by calling them the <i>Square Pyramidal</i> -and the <i>Oblong Prismatic</i>, which terms, while they -expressed the real distinction of the systems, would be -intelligible at once to those acquainted with the Mohsian terminology.</p> -<p>I will mention another suggestion respecting the -introduction of an improvement in scientific language. -The term <i>Depolarization</i> was introduced, because it -was believed that the effect of certain crystals, when -polarized light was incident upon them in certain positions, -was to destroy the peculiarity which polarization -had produced. But it is now well known, that the -effect of the second crystal in general is to divide the -polarized ray of light into two rays, polarized in -different planes. Still this effect is often spoken of as -<i>Depolarization</i>, no better term having been yet devised. -I have proposed and used the term <i>Dipolarization</i>, <span class="pagenum" id="page345">345</span> -which well expresses what takes place, and so nearly -resembles the elder word, that it must sound familiar -to those already acquainted with writings on this -subject.</p> -<p class="end">I may mention one term in another department of -literature which it appears desirable to reform in the -same manner. The theory of the Fine Arts, or the -philosophy which speculates concerning what is beautiful -in painting, sculpture or architecture, and other -arts, often requires to be spoken of in a single word. -Baumgarten and other German writers have termed -this province of speculation <i>Æsthetics</i>; <span class="greek">αἰσθάνεσθαι</span>, <i>to -perceive</i>, being a word which appeared to them fit to -designate the perception of beauty in particular. Since, -however, <i>æsthetics</i> would naturally denote the Doctrine -of Perception in general; since this Doctrine requires -a name; since the term <i>æsthetics</i> has actually been -applied to it by other German writers (as Kant); and -since the essential point in the philosophy now spoken -of is that it attends to Beauty;—it appears desirable -to change this name. In pursuance of the maxim now -before us, I should propose the term <i>Callæsthetics</i>, or -rather (in agreement with what was said in <a href="#page338">page</a> 338) -<i>Callæsthetic</i>, the science of the perception of beauty.</p> -<div class="chapter"> -<p class="end"><span class="pagenum" id="page346"></span></p> -<h3 class="nobreak">FURTHER ILLUSTRATIONS OF THE APHORISMS<br /> -ON SCIENTIFIC LANGUAGE, FROM THE<br /> -RECENT COURSE OF SCIENCES.</h3> -</div> -<hr class="two" /> -<p>1. <span class="sc">Botany</span>.</p> -<p><span class="sc">The</span> nomenclature of Botany as rescued from confusion -by Linnæus, has in modern times been in some -danger of relapsing into disorder or becoming intolerably -extensive, in consequence of the multiplication of -genera by the separation of one old genus into several -new ones, and the like subdivisions of the higher groups, -as subclasses and classes. This inconvenience, and the -origin of it, have been so well pointed out by Mr. G. -Bentham<a id="fnanchor65-4" href="#note65-4"><span class="fnanchor">65</span></a>, -that I shall venture to adopt his judgment -as an Aphorism, and give his reasons for it.</p> -<div class="footnote end"><span class="label"><a id="note65-4" href="#fnanchor65-4">65</a></span> <i>Linnæan Society’s Proceedings</i>, vol. ii. p. 30 (June, 1857). -</div> -<p class="center"><span class="sc">Aphorism</span> XXIII.</p> -<p><i>It is of the greatest importance that the Groups which -give their substantive names to every included species should -remain large.</i></p> -<p><span class="sc">It</span> will be recollected that according to the Linnæan -nomenclature, the genus is marked by a substantive, (as -<i>Rosa</i>), and the species designated by an adjective added -to this substantive, (as <i>Rosa Alpina</i>); while the natural -orders are described by adjectives taken substantively, -(as <i>Rosaceæ</i>), But this rule, though it has been -universally assented to in theory, has often been deviated -from in practice. The number of known species -having much increased, and the language of Linnæus -and the principles of Jussieu having much augmented -the facilities for the study of affinities, botanists have -become aware that the species of a genus and the genera -of an order can be collected into intermediate groups <span class="pagenum" id="page347">347</span> -as natural and as well defined as the genera and orders -themselves, and names are required for these subordinate -groups as much as for the genera and orders.</p> -<p>Now two courses have been followed in providing -names for these subordinate groups.</p> -<p>1. The original genera (considering the case of genera -in the first place) have been preserved, (if well founded); -and the lower groups have been called <i>subgenera</i>, <i>sections</i>, -<i>subsections</i>, <i>divisions</i>, &c.: and the original names -of the genera have been maintained for the purpose of -nomenclature, in order to retain a convenient and stable -language. But when these subordinate groups are so -well defined and so natural, that except for the convenience -of language, they might be made good genera, -there are given also to these subordinate groups, -substantive or substantively-taken adjective names. When -these subordinate groups are less defined or less natural, -either no names at all are given, and they are distinguished -by figures or signs such as *, **, or § 1, § 2, -&c. or there are given them mere adjective names.</p> -<p>Or, 2, To regard these intermediate groups between -species and the original genera, as so many independent -genera; and to give them substantive names, to be used -in ordinary botanical nomenclature.</p> -<p>Now the second course is that which has produced -the intolerable multiplication of genera in modern -times; and the first course is the only one which can -save botanical nomenclature from replunging into the -chaos in which Linnæus found it. It was strongly -advocated by the elder De Candolle; although in the -latter years of his life, seeing how general was the -disposition to convert his subgenera and sections into -genera, he himself more or less gave in to the general -practice. The same principle was adopted by Endlichen, -but he again was disposed to go far in giving -substantive names to purely technical or ill-defined -subsections of genera.</p> -<p>The multiplication of genera has been much too -common. Botanists have a natural pride in establishing -new genera (or orders); and besides this, it is felt -how useful it is, in the study of affinities, to define and <span class="pagenum" id="page348">348</span> -name all natural groups in every grade, however numerous -they may be: and in the immense variety of language -it is found easy to coin names indefinitely.</p> -<p>But the arguments on the other side much preponderate. -In attempting to introduce all these new -names into ordinary botanical language, the memory is -taxed beyond the capabilities of any mind, and the original -and legitimate object of the Linnæan nomenclature is -wholly lost sight of. In a purely scientific view -it matters little if the Orders are converted into Classes -or Alliances, the Genera into Orders, and the Sections -or Subsections into Genera: their relative importance -does not depend on the names given to them, but on -their height in the scale of comprehensiveness. But -for language, the great implement without which science -cannot work, it is of the greatest importance, as our -Aphorism declares, That the groups which give their -substantive names to every species which they include, -should remain large. If, independently of the inevitable -increase of Genera by new discoveries, such old -ones as <i>Ficus</i>, <i>Begonia</i>, <i>Arum</i>, <i>Erica</i>, &c. are divided -into 10, 20, 30, or 40 independent Genera, with names -and characters which are to be recollected before any -one species can be spoken of;—if Genera are to be -reckoned by tens of thousands instead of by thousands;—the -range of any individual botanist will be limited -to a small portion of the whole field of the sciences.</p> -<p>And in like manner with regard to Orders, so long -as the number of Orders can be kept within, or not -much beyond a couple of hundred, it may reasonably -be expected that a botanist of ordinary capacity shall -obtain a sufficient general idea of their nature and -characters to call them at any time individually to his mind -for the purpose of comparison: but if we double the -number of Orders, all is confusion.</p> -<p>The inevitable confusion and the necessity of maintaining -in some way the larger groups, have been perceived -by those even who have gone the furthest in -lowering the scale of Orders and Genera. As a remedy -for this confusion, they propose to erect the old genera -into independent orders, and the old orders into classes <span class="pagenum" id="page349">349</span> -or divisions. But this is but an incomplete resumption -of the old principles, without the advantage of the old -nomenclature.</p> -<p>And it will not be asserted, with regard to these new -genera, formed by cutting up the old ones, that the new -group is better defined than the group above it: on the -contrary, it is frequently less so. It is not pretended -that <i>Urostigma</i> or <i>Phannacosyce</i>, new genera formed -out of the old genus <i>Ficus</i>, are better defined than the -genus <i>Ficus</i>: or that the new genera which have lately -been cut out of the old genus <i>Begonia</i>, form more natural -groups than <i>Begonia</i> itself does. The principle -which seems to be adopted in such subdivisions of old -genera is this: that the lowest definable group above a -species is a genus. If we were to go a step further, -every species becomes a genus with a substantive name.</p> -<p>It ought always to be recollected that though the -analytical process carried to the uttermost, and -separating groups by observation of differences, is necessary for -the purpose of ascertaining the facts upon which botany -or any other classificatory science is based, it is -a judicious synthesis alone, associating individuals by the ties -of language, which can enable the human mind to take -a comprehensive view of these facts, to deduce from -them the principles of the science, or to communicate -to others either facts or principles.</p> -<p>2. <span class="sc">Comparative Anatomy</span>.</p> -<p>The Language of Botany, as framed by Linnæus, and -regulated by his Canons, is still the most notable and -successful example of scientific terminology which has -obtained general reception among naturalists. But the -Language of Anatomy, and especially of the Comparative -Anatomy of the skeleton, has of late been an object -of great attention to physiologists; and especially to -Mr. Owen; and the collection of terms which he has -proposed are selected with so much thought and care, -that they may minister valuable lessons to us in this -part of our subject.</p> -<p>There is, at first sight, this broad difference between -the descriptive language of Botany and of Comparative <span class="pagenum" id="page350">350</span> -Anatomy; that in the former science, we have comparatively -few parts to describe, (<i>calyx</i>, <i>corolla</i>, <i>stamen</i>, -<i>pistil</i>, <i>pericarp</i>, <i>seed</i>, &c.): while each of these parts is -susceptible of many forms, for describing which with -precision many terms must be provided: in Comparative -Anatomy, on the other hand, the skeletons of many animals -are to be regarded as modifications of a common -type, and the terms by which their parts are described -are to mark this community of type. The terminology -of Botany has for its object <em>description</em>; the language -of Comparative Anatomy must have for its basis <em>morphology</em>. -Accordingly, Mr. Owen’s terms are selected -so as to express the analogies, or, as he calls them, the -<i>homologies</i> of the skeleton; those parts of the skeleton -being termed <i>homologues</i>, which have the same place in -the general type, and therefore ought to have the same -name.</p> -<p>Yet this distinction of the basis of botanical and -anatomical terminology is not to be pushed too far. -The primary definitions in botany, as given by Linnæus, -are founded on morphological views; and imply -a general type of the structure of plants. These are his -definitions (<i>Phil. Bot.</i> Art. 86).<br /> - <span class="sc">Calyx</span>, <i>Cortex</i> plantæ in Fructificatione præsens.<br /> - <span class="sc">Corolla</span>, <i>Liber</i> plantæ in Flora præsens.<br /> - <span class="sc">Stamen</span>, Viscus pro Pollinis præparatione.<br /> - <span class="sc">Pistillum</span>, Viscus fructui adherens pro Pollinis receptione.<br /> - <span class="sc">Pericarpium</span>, Viscus gravidum seminibus, quæ matura dimittit.</p> -<p>But in what follows these leading definitions, the -terms are descriptive merely. Now in Comparative -Anatomy, an important object of terms is, to express -what part of the type each bone represents—to answer -the question, <i>what</i> is it? before we proceed, assuming -that we know what it is, to describe its shape. The -difficulty of this previous question is very great when -we come to the bones of the head; and when we assume, -as morphology leads us to do, that the heads of all -vertebrated animals, including even fishes, are -composed of homologous bones. And, as I have already <span class="pagenum" id="page351">351</span> -said in the History (b. xvii. c. 7), speaking of Animal -Morphology, the best physiologists are now agreed that -the heads of vertebrates may be resolved into a series -of vertebræ, homologically repeated and modified in -different animals. This doctrine has been gradually -making its way among anatomists, through a great -variety of views respecting details; and hence, with -great discrepancies in the language by which it has -been expressed. Mr. Owen has proposed a complete -series of terms for the bones of the head of all vertebrates; -and these names are supported by reasons which -are full of interest and instruction to the physiologist, -on account of the comprehensive and precise knowledge -of comparative osteology which they involve; but they -are also, as I have said, interesting and instructive to -us, as exemplifying the reasons which may be given for -the adoption of words in scientific language. The reasons -thus given agree with several of the aphorisms -which I have laid down, and may perhaps suggest a -few others. Mr. Owen has done me the great honour -to quote with approval some of these aphorisms. The -terms which he has proposed belong, as I have already -said, to the <i>Terminology</i>, not to the <i>Nomenclature</i> of -Zoology. In the latter subject, the Nomenclature (the -names of species) the binary nomenclature established -by Linnæus remains, in its principle, unshaken, simple -and sufficient.</p> -<p>I shall best derive from Mr. Owen’s labours and reflexions -some of the instruction which they supply with -reference to the Language of Science, by making -remarks on his terminology with reference to such -aphorisms as I have propounded on the subject, and others -of a like kind.</p> -<p>Mr. Owen, in his <i>Homologies of the Vertebrate -Skeleton</i>, has given in a Tabular Form his views of -the homology of the bones of the head of vertebrates, -and the names which he consequently proposes for each -bone, with the synonyms as they occur in the writings -of some of the most celebrated anatomical philosophers, -Cuvier, Geoffroy, Hallmann, Meckel and Wagner, -Agassiz and Soemmering. And he has added to this -Table his reasons for dissenting from his predecessors <span class="pagenum" id="page352">352</span> -to the extent to which he has done so. He has done -this, he says, only where nature seemed clearly to refuse -her sanction to them; acting upon the maxim (our -<a href="#a10">Aphorism X</a>.) that new terms and changes of terms -which are not needed in order to express truth, are to -be avoided. The illustrations which I have there given, -however, of this maxim, apply rather to the changes in -nomenclature than in terminology; and though many -considerations apply equally to these two subjects, there -are some points in which the reasons differ in the two -cases: especially in this point:—the names, both of -genera and of species, in a system of nomenclature, may -be derived from casual or arbitrary circumstances, as I -have said in <a href="#a13">Aphorism XIII</a>. But the terms of a scientific -terminology ought to cohere as a system, and therefore -should not commonly be derived from anything -casual or arbitrary, but from some analogy or connexion. -Hence it seems unadvisable to apply to bones -terms derived from the names of persons, as <i>ossa -wormiana</i>; or even from an accident in anatomical -history, as <i>os innominatum</i>.</p> -<p class="end">It is further desirable that in establishing such a -terminology, each bone should be designated by a single -word, and not by a descriptive phrase, consisting of -substantive and adjective. On this ground Mr. Owen -proposes <i>presphenoid</i> for <i>sphenöide anterieur</i>. So also -<i>prefrontal</i> is preferred to <i>anterior frontal</i>, -and <i>postfrontal</i> to <i>posterior frontal</i>. -And the reason which he -gives for this is worthy of being stated as an Aphorism, -among those which should regulate this subject. -I shall therefore state it thus:</p> -<p class="center"><span class="sc">Aphorism</span> XXIV.</p> -<p><i>It is advisable to substitute definite single names -for descriptive phrases as better instruments of thought.</i></p> -<p><span class="sc">It</span> will be recollected by the reader that in the case of -the Linnæan reform of the botanical nomenclature of -species, this was one of the great improvements which -was introduced.</p> -<p>Again: some of the first of the terms which Mr. Owen -proposes illustrate, and confirm by their manifest claim <span class="pagenum" id="page353">353</span> -to acceptance, a maxim which we stated as <a href="#a22">Aphorism -XXII.</a>: namely, -When alterations in technical terms become necessary, -it is desirable that the new term should contain -in its form some memorial of the old one.</p> -<p>Thus for ‘basilaire,’ which Cuvier exclusively applies -to the ‘pars basilaris’ of the occiput, and which -Geoffroy as exclusively applies (in birds) to the -‘pars basilaris’ of the sphenoid, Mr. Owen substitutes the term -<i>basioccipital</i>.</p> -<p>Again: for the term ‘suroccipital’ of Geoffroy, Mr. -Owen proposes <i>paroccipital</i>, to avoid confusion and false -suggestion: and with reference to this word, he makes -a remark in agreement with what we have said in the -discussion of <a href="#a21">Aphorism XXI.</a>: namely, that the combination -of different languages in the derivation of words, -though to be avoided in general, is in some cases admissible. -He says, ‘If the purists who are distressed by -such harmless hybrids as “mineralogy,” “terminology,” -and “mammalogy,” should protest against the combination -of the Greek prefix to the Latin noun, I can -only plead that servility to a particular source of the -fluctuating sounds of vocal language is a matter of taste: -and that it seems no unreasonable privilege to use such -elements as the servants of thought; and in the interests -of science to combine them, even though they come -from different countries, when the required duty is best -and most expeditiously performed by their combination.’</p> -<p>So again we have illustrations of our <a href="#a12">Aphorism XII.</a>, -that if terms are systematically good they are not to be -rejected because they are etymologically inaccurate. In -reference to that bone of the skull which has commonly -been called <i>vomer</i>, the ploughshare: a term which -Geoffroy rejected, but which Mr. Owen retains, he says, -‘When Geoffrey was induced to reject the term <i>vomer</i> -as being applicable only to the peculiar form of the bone -in a small portion of the vertebrata, he appears not to -have considered that the old term, in its wider application, -would be used without reference to its primary -allusion to the ploughshare, and that becoming, as it <span class="pagenum" id="page354">354</span> -has, a purely arbitrary term, it is superior and preferable -to any partially descriptive one.’</p> -<p>Another condition which I have mentioned in <a href="#a20">Aphorism XX.</a>, -as valuable in technical terms is, that they -should be susceptible of such grammatical relations as -their scientific use requires.</p> -<p>This is, in fact, one of the grounds of the Aphorism -which we have already borrowed from Mr. Owen, that -we are to prefer single substantives to descriptive -phrases. For from such substantives we can derive -adjectives, and other forms; and thus the term becomes, -as Mr. Owen says, <em>a better instrument of thought</em>. -Hence, he most consistently mentions it as a recommendation -of his system of names, that by them the -results of a long series of investigations into the special -homologies of the bones of the head are expressed -in simple and definite terms, <em>capable of every requisite -inflection</em> to express the proportion of the parts.</p> -<p>I may also, in reference to this same passage in Mr. -Owen’s appeal in behalf of his terminology, repeat what -I have said under <a href="#a10">Aphorism X.</a>: that the persons who -may most properly propose new scientific terms, are those -who have much new knowledge to communicate: so -that the vehicle is commended to general reception by -the value of what it contains. It is only to eminent -discoverers and profound philosophers that the authority -is conceded of introducing a new system of terms; just -as it is only the highest authority in the state which has -the power of putting a new coinage into circulation. -The long series of investigations of which the results are -contained in Mr. Owen’s table of synonyms, and the -philosophical spirit of his generalizations, entitles him to a -most respectful hearing when he appeals to the Professors -and Demonstrators of Human Anatomy for an unbiassed -consideration of the advantages of the terms -proposed by him, as likely to remedy the conflicting -and unsettled synonymy which has hitherto pervaded -the subject.</p> -<p class="end">There is another remark which is suggested by the -works on Comparative Anatomy, which I am now considering. -I have said in various places that Technical <span class="pagenum" id="page355">355</span> -Terms are a necessary condition of the progress of a science. -But we may say much more than this: and the -remark is so important, that it deserves to be stated as -one of our Aphorisms, as follows:</p> -<p class="center" id="a25"><span class="sc">Aphorism</span> XXV.</p> -<p><i>In an advanced Science, the history of the Language of -the Science is the history of the Science itself.</i></p> -<p><span class="sc">I have</span> already stated in previous Aphorisms (<a href="#a8">VIII.</a> -and <a href="#a11">XI.</a>) that Terms must be constructed so as to -be fitted to enunciate general propositions, and that -Terms which imply theoretical views are admissible for -this purpose. And hence it happens that the history of -Terms in any science which has gone through several -speculative stages, is really the history of the -generalizations and theories which have had currency -among the cultivators of the science.</p> -<p>This appears in Comparative Anatomy from what we -have been saying. The recent progress of that science -is involved in the rise and currency of the Terms which -have been used by the anatomists whose synonyms Mr. -Owen has to discuss; and the reasons for selecting among -these, or inventing others, include those truths and -generalizations which are the important recent steps of the -science. The terms which are given by Mr. Owen in his -table to denote the bones of the head are good terms, <em>if</em> -they <em>are</em> good terms, because their adoption and use is -the only complete way of expressing the truths of homology: -namely, of that Special Homology, according to -which all vertebrate skeletons are referred to the human -skeleton as their type, and have their parts designated -accordingly.</p> -<p>But further: there is another kind of homology which -Mr. Owen calls <i>General</i> Homology, according to which -the primary type of a vertebrate animal is merely a series -of vertebræ; and all limbs and other appendages are -only developements of the parts of one or another of the -vertebræ. And in order to express this view, and in -proportion as the doctrine has become current amongst <span class="pagenum" id="page356">356</span> -anatomists, the parts of vertebræ have been described by -terms of a degree of generality which admit of such an -interpretation. And here, also, Mr. Owen has proposed -a terminology for the parts of the vertebræ, which -seems to convey more systematically and comprehensively -than those of preceding writers the truths to -which they have been tending. Each vertebra is composed -of a <i>centrum</i>, <i>neurapophysis</i>, <i>parapophysis</i>, -<i>pleurapophysis</i>, <i>hæmaphysis</i>, <i>neural spine</i> and -<i>hæmal spine</i>, with certain exogenous parts.</p> -<p>The opinion that the head, as well as the other parts -of the frame of vertebrates, is composed of vertebræ, is -now generally accepted among philosophical anatomists. -In the <i>History</i> (<i>Hist. I. S.</i> b. xvii. c. 7, sect. 1), I have -mentioned this opinion as proposed by some writers; -and I have stated that Oken, in 1807 published a ‘Program’ -<i>On the signification of the bones of the Skull</i>, in -which he maintained, that these bones are equivalent to -four vertebræ: while Meckel, Spix, and Geoffroy took -views somewhat different. Cuvier and Agassiz opposed -this doctrine, but Mr. Owen has in his <i>Archetype and -Homologies of the Vertebrate Skeleton</i> (1848), accepted -the views of Oken, and argued at length against the -objections of Cuvier, and also those of Mr. Agassiz. -As I have noted in the last edition of the <i>History of -the Inductive Sciences</i> (b. xvii. c. 7), he gives a Table in -which the Bones of the Head are resolved into four vertebræ, -which he terms the Occipital, Parietal, Frontal -and Nasal Vertebræ respectively: the neural arches of -which agree with what Oken called the Ear-vertebra, the -Jaw-vertebra, the Eye-vertebra, and the Nose-vertebra.</p> -<p>Besides these doctrines of <i>Special Homology</i> by which -the bones of all vertebrates are referred to their -corresponding bones in the human skeleton, and of <i>General -Homology</i>, by which the bones are referred to the parts -of vertebræ which they represent, Mr. Owen treats of -<i>Serial Homology</i>, the recognition of the same elements -throughout the series of segments of the same skeleton; -as when we shew in what manner the arms correspond -to the legs. And thus, he says, in the head also, the -<i>basioccipital</i>, <i>basisphenoid</i>, -<i>presphenoid</i> and <i>vomer</i> are <span class="pagenum" id="page357">357</span> -homotypes with the <i>centrums</i> of all succeeding vertebræ. -The <i>excoccipitals</i>,<i> alisphenoids</i>, <i>orbitosphenoids</i>, -and <i>prefrontals</i>, are homotypes with the <i>neurapophyses</i> -of all the succeeding vertebræ. The <i>paroccipitals</i>, -<i>mactoids</i> and <i>postfrontals</i>, with the <i>transverse processes</i> -of all the succeeding vertebræ: and so on. Perhaps -these examples may exemplify sufficiently for the general -reader both Mr. Owen’s terminology, and the intimate -manner in which it is connected with the widest -generalizations to which anatomical philosophy has yet been -led.</p> -<p class="end">The same doctrine, that the history of the Language -of a Science is the history of the Science, appears also -in the recent progress of Chemistry; but we shall be -better able to illustrate our Aphorism in this case by -putting forward previously one or two other Aphorisms -bearing upon the history of that Science.</p> -<p class="center"><span class="sc">Aphorism</span> XXVI.</p> -<p><i>In the Terminology of Science it may be necessary to -employ letters, numbers, and algebraical symbols.</i></p> -<p>1. <span class="sc">Mineralogy.</span></p> -<p><span class="sc">I have</span> already said, in <a href="#a15">Aphorism XV.</a>, that -symbols have been found requisite as a part of the -terminology of Mineralogy. The <i>names</i> proposed by -Haüy, borrowed from the crystalline laws, were so -inadequate and unsystematic that they could not be -retained. He himself proposed a <i>notation</i> for crystalline forms, -founded upon his principle of the derivation of such forms -from a <i>primitive</i> form, by <i>decrements</i>, on its <i>edges</i> -or its <i>angles</i>. To denote this derivation he took -the first letters of the three syllables to -mark the faces of the <i>PriMiTive</i> form, <i>P</i>, <i>M</i>, <i>T</i>; the -vowels <i>A</i>, <i>E</i>, <i>I</i>, <i>O</i> to mark the angles; the consonants -<i>B</i>, <i>C</i>, <i>D</i>, &c. to mark the edges; and numerical -exponents, annexed in various positions to these letters, -represented the law and manner of derivation. Thus -when the primitive form was a cube, <sup>1</sup><sub><i>B</i></sub> -represented the result of a derivation by a -decrement of one row <span class="pagenum" id="page358">358</span> -on an edge; that is, a rhombic octahedron; -and <sup>1</sup><sub><i>B</i></sub><i>P</i> represented -the combination of this octahedron with -the primitive cube. In this way the pentagonal -dodecahedron, produced by decrements of 2 to 1 -on half the edges of the cube, was represented by -<i>B</i>² <sup>½</sup><sub><i>C</i></sub> <i>G</i>² ²<i>G</i></p> -<p>Not only, however, was the hypothesis of primitive -forms and decrements untenable, but this notation -was too unsystematic to stand long. And when Weiss -and Mohs established the distinction of Systems of -Crystallography<a id="fnanchor66-4" href="#note66-4"><span class="fnanchor">66</span></a>, -they naturally founded upon that -distinction a notation for crystalline forms. Mohs had -several followers; but his algebraical notation so -barbarously violated all algebraical meaning, that it was -not likely to last. Thus, from a primitive rhombohedron -which he designated by <i>R</i>, he derived, by a -certain process, a series of other rhombohedrons, which -he denoted by <span style="white-space: nowrap;"><i>R</i> + 1,</span> -<span style="white-space: nowrap;"><i>R</i> + 2,</span> -<span style="white-space: nowrap;"><i>R</i> − 1,</span> &c.; and then, by -another mode of derivation from them, he obtained -forms which he marked as <span style="white-space: nowrap;">(<i>R</i> + 2)²,</span> -<span style="white-space: nowrap;">(<i>R</i> + 2)³,</span> &c. In -doing this he used the algebraical marks of addition -and involution without the smallest ground; besides -many other proposals no less transgressing mathematical -analogy and simplicity.</p> -<div class="footnote"><span class="label"><a id="note66-4" href="#fnanchor66-4">66</a></span> -<i>Hist. Ind. Sc.</i> b. xv. c. 4. -</div> -<p>But this notation might easily suggest a better. If -we take a primitive form, we can generally, by two -steps of derivation, each capable of numerical measure, -obtain any possible face; and therefore any crystalline -form bounded by such faces. Hence all that we need -indicate in our crystalline laws is the primitive form, -and two numerical exponents; and rejecting all -superfluity in our symbols, instead of <span style="white-space: nowrap;">(<i>R</i> + 2)³</span> -we might write 2 <i>R</i> 3. Nearly of this kind is the notation of -Naumann. The systems of crystallization, the octahedral -or tessular, the rhombic, and the prismatic, are -marked by the letters <i>O</i>, <i>R</i>, <i>P</i>; and from these are -derived, by certain laws, such symbols as</p> -<p class="center eq"> 3 <i>O</i> ½, ∞ <i>R</i> 2, ½ <i>P</i> 2, <span class="pagenum" id="page359">359</span></p> -<p class="noind eq">which have their definite signification flowing from -the rules of the notation.</p> -<p>But Professor Miller, who has treated the subject -of Crystallography in the most general and symmetrical -manner, adopts the plan of marking each crystalline -plane by <i>three</i> numerical indices. Thus in the -Octahedral System, the cube is {100}; the octahedron -is {111}; the rhombic dodecahedron is {011}; the -pentagonal dodecahedron is π {012}; where π indicates -that the form is not <i>holohedral</i> but <i>hemihedral</i>, -only half the number of faces being taken which the -law of derivation would give. This system is the -most mathematically consistent, and affords the best -means of calculation, as Professor Miller has shown; -but there appears to be in it this defect, that though -an essential part of the scheme is the division of -crystalline forms into Systems,—the Octahedral, -Pyramidal, Rhombohedral and Prismatic,—this division -does not at all appear in the notation.</p> -<p>But whatever be the notation which the crystallographer -adopts, it is evident that he must employ -some notation; and that, without it, he will be unable -to express the forms and relations of forms with which -he has to deal.</p> -<p>2. <span class="sc">Chemistry</span>.</p> -<p>The same has long been the case in Chemistry. -As I have stated elsewhere<a id="fnanchor67-4" href="#note67-4"><span class="fnanchor">67</span></a>, -the chemical nomenclature -of the oxygen theory was for a time very useful -and effective. But yet it had defects which could not -be overlooked, as I have already stated under <a href="#a2">Aphorism II.</a> -The relations of elements were too numerous, and their -numerical properties too important, to -be expressed by terminations and other modifications -of words. Thus the compounds of Nitrogen and -Oxygen are the Protoxide, the Deutoxide, Nitrous -Acid, Peroxide of Nitrogen, Nitric Acid. The systematic -nomenclature here, even thus loosely extended, -does not express our knowledge. And the Atomic -Theory, when established, brought to view numerical <span class="pagenum" id="page360">360</span> -relations which it was very important to keep in -sight. If <i>N</i> represents Nitrogen and <i>O</i> Oxygen, the -compounds of the two elements just mentioned might -be denoted by <i>N</i> + <i>O</i>, <i>N</i> + 2<i>O</i>, -<i>N</i> + 3<i>O</i>, <i>N</i> + 4<i>O</i>, <i>N</i> + 5<i>O</i>. -And by adopting a letter for each of the elementary -substances, all the combinations of them might be expressed in this manner.</p> -<div class="footnote"><span class="label"><a id="note67-4" href="#fnanchor67-4">67</a></span> -<i>Hist. Ind. Sc.</i> b. xiv. c. 6. -</div> -<p>But in chemistry there are different orders of combination. -A salt, for instance, is a compound of a -base and an acid, each of which is already compound. -If <i>Fe</i> be iron and <i>C</i> be carbon, <i>Fe</i> + <i>O</i> -will be the protoxide of iron, and <i>C</i> + 2<i>O</i> will be carbonic acid; and -the carbonate of iron (more properly carbonate of -protoxide of iron), may be represented by</p> -<p class="center eq"> (<i>Fe</i> + <i>O</i>) + (<i>C</i> + 2<i>O</i>)</p> -<p class="noind eq">where the brackets indicate the first stage of composition.</p> -<p>But these brackets and signs of addition, in complex -cases, would cumber the page in an inconvenient degree; -and oxygen is of such very wide occurrence, that -it seems desirable to abridge the notation so far as it -is concerned. Hence Berzelius -proposed<a id="fnanchor68-4" href="#note68-4"><span class="fnanchor">68</span></a> -that in the first stage of composition the oxygen should be expressed -by dots over the letter; and thus the carbonate of iron -would be <i>Ḟe</i> + <i>C̈</i>. But Berzelius -further introduced into his notation indexes such as -in algebra denote involution to the square, cube, &c. -Thus <i>Cu</i> being copper, the sulphate of copper is represented -by <i>S⃛</i>²<i>C̈u</i>. This notation, when first proposed, -was strongly condemned by English chemists, and -Berzelius’s reply to them may be taken as stating the -reasons in favour of such notation. He -says<a id="fnanchor69-4" href="#note69-4"><span class="fnanchor">69</span></a>, ‘We -answer to the opponents, that undoubtedly the matter -may be looked at in various lights. The use -of Formulæ has always, for a person who has not -accustomed himself to them, something repulsive; but -this is easy to overcome. I agree with my opponent, <span class="pagenum" id="page361">361</span> -who says that nothing can be understood in a Formula -which cannot be expressed in words; and that if the -words express it as easily as the Formula, the use of -the latter would be a folly. But there are cases in -which this is not so; in which the Formula says in a -glance what it would take many lines to express in -words; and in which the expression of the Formula is -clearer and more easily apprehended by the reader -than the longer description in words. Let us examine -such a Formula, and compare it with the equivalent -description in words. Take, for example, crystallized -sulphate of copper, of which the Formula is</p> -<p class="center eq"> <i>C̈u</i><i>S⃛</i>² + 10<i>H</i>² <i>O</i>.</p> -<p class="noind eq">Now this Formula expresses the following propositions:<br /> - ‘That the salt consists of one atom of copper-oxide -combined with 2 atoms of sulphuric acid and with 10 -atoms of water; that the copper-oxide contains two -atoms of oxygen; and that the sulphuric acid contains -3 atoms of oxygen for one atom of sulphur; that its -oxygen is three times as much as that of the oxide; -and that the number of atoms of oxygen in the acid is -6; and that the number of atoms of oxygen in the -water is 10; that is, 5 times the number in the oxide; -and that finally the salt contains, of simple atoms, 1 -copper, 2 sulphur, 20 hydrogen, and 18 oxygen.</p> -<div class="footnote"><span class="label"><a id="note68-4" href="#fnanchor68-4">68</a></span> -<i>System of Mineralogy</i>, 1816. -</div> -<div class="footnote"><span class="label"><a id="note69-4" href="#fnanchor69-4">69</a></span> -<i>Jahresbericht</i>, 1824, p. 119. -</div> -<p>‘Since so much is expressed in this brief Formula, -how very long would the explanation be for a more -composite body, for example, Alum; for which the -Formula is</p> -<p class="center eq"> <i>K̈</i> <i>S⃛</i>² + 2<i>A⃛l S⃛</i>³ -+ 48<i>H</i>² <i>O</i>.</p> -<p class="noind eq">It would take half a page to express all which this -Formula contains.</p> -<p>‘Perhaps it may be objected that it is seldom that -any one wants to know all this at once. But it might -reasonably be said in reply, that the peculiar value of -the Formula consists in this, that it contains answers -to all the questions which can be asked with regard -to the composition of the body. <span class="pagenum" id="page362">362</span></p> -<p>‘But these Formulæ have also another application, -of which I have sometimes had occasion to make use. -Experiments sometimes bring before us combinations -which cannot be foreseen from the nomenclature, and -for which it is not always easy to find a consistent -and appropriate name. In writing, the Formula may -be applied instead of a Name: and the reader understands -it better than if one made a new name. In -my treatise upon the sulphuretted alkalies I found -Degrees of Sulphur-combination, for which Nomenclature -has no name. I expressed them, for example, -by <i>KS</i><sup>6</sup>, <i>KS</i><sup>8</sup>, <i>KS</i><sup>10</sup> and I believed -that every one understood what was thereby meant. Moreover, I found -another class of bodies in which an electro-negative -sulphuretted metal played the part of an Acid with -respect to an electro-positive sulphuretted metal, for -which a whole new nomenclature was needed; while -yet it were not prudent to construct such a nomenclature, -till more is known on the subject. Instead of -new names I used formulas; for example,</p> -<p class="center eq"> <i>KS</i>² + 2<i>As S</i>³,</p> -<p class="noind eq">instead of saying the combination of 2 atoms of Sulphuret -of Arsenic containing 3 atoms of Sulphur, -with one atom of Sulphuret of Potassium (Kali) with -the least dose of sulphur.’</p> -<p>Berzelius goes on to say that the English chemists -had found themselves unable to find any substitutes -for his formulæ when they translated his papers.</p> -<p>Our English chemists have not generally adopted -the notation of oxygen by dots; but have employed -commas or full stops and symbols (, or . and +), to -denote various degrees of union, and numerical indices. -Thus the double sulphate of copper and potash -is <i>Cu O</i>, <i>SO</i><sub>3</sub> + <i>KO</i>, <i>SO</i><sub>3</sub>.</p> -<p>What has been said is applicable mainly to inorganic -bodies (as salts and -minerals)<a id="fnanchor70-4" href="#note70-4"><span class="fnanchor">70</span></a>. -In these bodies there -is (at least according to the views of many intelligent -chemists) a <em>binary</em> plan of combination, union taking <span class="pagenum" id="page363">363</span> -place between <em>pairs</em> of elements, and the compounds -so produced again uniting themselves to other compound -bodies in the same manner. Thus, in the above -example, copper and oxygen combine into oxide of -copper, potassium and oxygen into potash, sulphur -and oxygen into sulphuric acid; sulphuric acid in its -turn combines both with oxide of copper and oxide -of potassium, generating a pair of salts which are -capable of uniting to form the double compound -<i>Cu O</i>, <i>SO</i><sub>3</sub> + <i>KO</i>, <i>SO</i><sub>3</sub>.</p> -<div class="footnote"><span class="label"><a id="note70-4" href="#fnanchor70-4">70</a></span> -Fownes’s <i>Chemistry</i>. Part iii. -</div> -<p>The most complicated products of inorganic chemistry -may be thus shown to be built up by this -repeated <em>pairing</em> on the part of their constituents. -But with organic bodies the case is remarkably different; -no such arrangement can here be traced. In -sugar, which is <span style="white-space: nowrap;"><i>C</i><sub>12</sub> <i>H</i><sub>11</sub> <i>O</i><sub>11</sub>,</span> -or morphia<a id="fnanchor71-4" href="#note71-4"><span class="fnanchor">71</span></a>, which is -<span style="white-space: nowrap;"><i>C</i><sub>35</sub> <i>H</i><sub>20</sub> <i>NO</i><sub>6</sub>,</span> the elements are -as it were bound together into a single whole, which can enter -into combination with other substances, and be thence discharged -with properties unaltered; the elements not being -obviously arranged in any subordinate groups. Hence -the symbols for those substances are such as I have -given above, no marks of combination being used.</p> -<div class="footnote"><span class="label"><a id="note71-4" href="#fnanchor71-4">71</a></span> -Fownes’s <i>Chemistry</i>, p. 354. -</div> -<p>It is perhaps a consequence of this peculiarity that -organic compounds are <em>unstable</em> in comparison with -inorganic. In unorganic substances generally the elements -are combined in such a way that the most -powerful affinities are -satisfied<a id="fnanchor72-4" href="#note72-4"><span class="fnanchor">72</span></a>, -and hence arises a -state of very considerable permanence and durability. -But in an organic substance containing three -or four elements, there are often opposing affinities -nearly balanced, and when one of these tendencies by -some accident obtains a preponderance and the equilibrium -is destroyed, then the organic body breaks up -into two or more new bodies of simpler and more permanent constitution.</p> -<div class="footnote"><span class="label"><a id="note72-4" href="#fnanchor72-4">72</a></span> -See <i>Hist. Ind. Sc.</i> b. xiv. c. 3. -</div> -<p>There is another property of many organic substances which -is called the <i>Law of Substitution</i>. The <span class="pagenum" id="page364">364</span> -Hydrogen of the organic substance may often be replaced -by Chlorine, Bromine, Iodine, or some other -elements, without the destruction of the primitive -type or constitution of the compound so modified. -And this substitution may take place by several successive -steps, giving rise to a series of substitution-compounds, -which depart more and more in properties -from the original substance. This Law also gives rise -to a special notation. Thus a certain compound called -<i>Dutch liquid</i> has the elements -<span style="white-space: nowrap;"><i>C</i><sub>4</sub> <i>H</i><sub>4</sub> <i>Cl</i><sub>2</sub>:</span> -but this substance is affected by chlorine (<i>Cl</i>) in obedience to the -law of substitution; one and two equivalents of hydrogen being -successively removed by the prolonged -action of chlorine gas aided by sunshine. The successive -products may be thus written</p> -<p class="center eq"> <i>C</i><sub>4</sub> <i>H</i><sub>4</sub> <i>Cl</i><sub>2</sub>; -<i>C</i><sub>4</sub> { <sup><i>H</i><sub>3</sub></sup><sub><i>Cl</i></sub> } <i>Cl</i><sub>2</sub>; -<i>C</i><sub>4</sub> { <sup><i>H</i><sub>2</sub></sup><sub><i>Cl</i><sub>2</sub></sub> } <i>Cl</i><sub>2</sub>. -</p> -<p class="end">Perhaps at a future period, chemical symbols, and -especially those of organic bodies, may be made more -systematic and more significant than they at present -are.</p> -<p class="center"><span class="sc">Aphorism</span> XXVII.</p> -<p><i>In using algebraical symbols as a part of scientific -language, violations of algebraical analogy are to be avoided, -but may be admitted when necessary.</i></p> -<p class="end"><span class="sc">As</span> we must in scientific language conform to etymology, -so must we to algebra; and as we are not to -make ourselves the slaves of the former, so also, not to -the latter. Hence we reject such crystallographical -notation as that of Mohs; and in chemistry we use -<i>C</i><sub>2</sub>, <i>O</i><sub>3</sub> rather -than <i>C</i><sup>2</sup>, <i>O</i><sup>3</sup>, which -signify the square -of <i>C</i> and the cube of <i>O</i>. But we may use, as we have -said, both the comma and the sign of addition, for -chemical combination, for the sake of brevity, though -both steps of combination are really addition. <span class="pagenum" id="page365">365</span></p> -<p class="center"><span class="sc">Aphorism</span> XXVIII.</p> -<p><i>In a complex science, which is in a state of transition, -capricious and detached derivations of terms are common; -but are not satisfactory.</i></p> -<p><span class="sc">In</span> this remark I have especial reference to Chemistry; -in which the discoveries made, especially in organic -chemistry, and the difficulty of reducing them to a -system, have broken up in several instances the old -nomenclature, without its being possible at present to -construct a new set of terms systematically connected. -Hence it has come to pass that chemists have constructed -words in a capricious and detached way: as -by taking fragments of words, and the like. I shall -give some examples of such derivations, and also of -some attempts which have more of a systematic character.</p> -<p>I have mentioned (Aph. <span class="correction" title="emended from XV.">XX.</span> -<a href="#b4a20a7">sect. 7</a>) the word <i>Ellagic</i> -(acid), made by inverting the word <i>Galle</i>. Several -words have recently been formed by chemists by -taking syllables from two or more different words. -Thus Chevreul discovered a substance to which he gave -the name <span class="correction" title="emended from Ethol"><i>Ethal</i></span>, from the first syllables of the words -<i>ether</i> and <i>alcohol</i>, because of its analogy to those liquids -in point of composition<a id="fnanchor73-4" href="#note73-4"><span class="fnanchor">73</span></a>. -So Liebig has the word -<i>chloral</i><a id="fnanchor74-4" href="#note74-4"><span class="fnanchor">74</span></a>.</p> -<div class="footnote"><span class="label"><a id="note73-4" href="#fnanchor73-4">73</a></span> -Turner’s <i>Chemistry</i>, 1834, p. 955 -</div> -<div class="footnote"><span class="label"><a id="note74-4" href="#fnanchor74-4">74</a></span> -Berzelius’ <i>Jahresbericht</i>, xv. p. 372. -</div> -<p>Liebig, examining the product of distillation of alcohol, -sulphuric acid and amber, found a substance which -he termed <i>Aldehyd</i>, from the words <i>Al</i>cohol -<i>dehyd</i>rogenated<a id="fnanchor75-4" href="#note75-4"><span class="fnanchor">75</span></a>. -This mode of making Words has been -strongly objected to by Mr. -Dumas<a id="fnanchor76-4" href="#note76-4"><span class="fnanchor">76</span></a>. -Still more has -he objected to the word <i>Mercaptan</i> (of Zeise), which <span class="pagenum" id="page366">366</span> -he says rests upon a mere play of words; for it means -both <i>mercurium captans</i> and <i>mercurio aptum</i>.</p> -<div class="footnote"><span class="label"><a id="note75-4" href="#fnanchor75-4">75</a></span> -<i>Ibid.</i> xvi. p. 308. -</div> -<div class="footnote"><span class="label"><a id="note76-4" href="#fnanchor76-4">76</a></span> -<i>Leçons de Chimie</i>, p. 354. -</div> -<p>Dumas and Peligot, working on pyroligneous acids, -found reason to believe the existence of a -substance<a id="fnanchor77-4" href="#note77-4"><span class="fnanchor">77</span></a> -which they called <i>methylene</i>, deriving the name from -<i>methy</i>, a spirituous fluid, and <i>hyle</i>, wood. Berzelius -remarks that the name should rather be <i>methyl</i>, and -that <span class="greek">ὕλη</span> may be taken in its signification of matter, to -imply the Radical of Wine: and he proposes that the -older Æther-Radical, -<span style="white-space: nowrap;"><i>C</i><sub>4</sub> <i>H</i><sub>10</sub></span> -shall be called <i>Æthyl</i>, -the newer, <span style="white-space: nowrap;"><i>C</i><sub>2</sub> <i>H</i><sub>6</sub>,</span> <i>Methyl</i>.</p> -<div class="footnote"><span class="label"><a id="note77-4" href="#fnanchor77-4">77</a></span> -Berzelius’ <i>Jahresbericht</i>, xv. (1836). -</div> -<p>This notion of marking by the termination <i>yl</i> the -hypothetical compound radical of a series of chemical -compounds has been generally adopted; and, as we see -from the above reference, it must be regarded as representing -the Greek word <span class="greek">ὕλη</span>: and such hypothetical -radicals of bases have been termed in general <i>basyls</i>.</p> -<p>Bunsen obtained from Cadet’s fuming liquid a substance -which he called <i>Alkarsin</i> (<i>alk</i>ali-<i>ars</i>enic?): and -the substance produced from this by oxidation he -called <i>Alkargen</i><a id="fnanchor78-4" href="#note78-4"><span class="fnanchor">78</span></a>. -Berzelius was of opinion, that the -true view of its composition was that it contained a -compound ternary radical = -<span style="white-space: nowrap;"><i>C</i><sup>6</sup> <i>H</i><sup>12</sup> -<i>As</i><sup>2</sup>,</span> after the manner -of organic bodies; and he proposed for this the -name<a id="fnanchor79-4" href="#note79-4"><span class="fnanchor">79</span></a> <i>Kakodyl</i>. -Alkarsin is Kakodyl-oxyd, K̇d, -Alkargen is Kakodyl-acid, K̈̇d.</p> -<div class="footnote"><span class="label"><a id="note78-4" href="#fnanchor78-4">78</a></span> -<i>Ibid.</i> xviii. p. 497. -</div> -<div class="footnote"><span class="label"><a id="note79-4" href="#fnanchor79-4">79</a></span> -<i>Ibid.</i> xx. p. 527. -</div> -<p>The discovery of Kakodyl was the first instance of -the insulation of an organic metallic -<i>basyl</i><a id="fnanchor80-4" href="#note80-4"><span class="fnanchor">80</span></a>.</p> -<div class="footnote"><span class="label"><a id="note80-4" href="#fnanchor80-4">80</a></span> -Miller’s <i>Chemistry</i>, iii. 220. -</div> -<p>The first of the Hydrocarbon Radicals of the Alcohols was -the radical of Tetrylic alcohol obtained by -Kolbe from Valerate of Potash, and hence called <i>Valyl</i> -<span style="white-space: nowrap;"><i>C</i><sub>16</sub> <i>H</i><sub>18</sub>.</span> -<i>Chloroform</i> is per<i>chloride</i> of <i>formyl</i>, -the hypothetical radical of formic -acid<a id="fnanchor81-4" href="#note81-4"><span class="fnanchor">81</span></a>.</p> -<div class="footnote"><span class="label"><a id="note81-4" href="#fnanchor81-4">81</a></span> -Dumas, <i>Leçons sur la Phil. Chim.</i> p. 356. -<span class="pagenum" id="page367" style="font-size: large">367</span> -</div> -<p>The discovery of such bases goes back to 1815. -The substance formerly called <i>Prussiate of Mercury</i>, -being treated in a particular manner, was resolved into -metallic mercury and <i>Cyanogen</i>. This substance, <i>Cyanogen</i>, -is, according to the older nomenclature, <i>Bicarburet -of Nitrogen</i>; but chemists are agreed that its -most convenient name is <i>Cyanogen</i>, proposed by its -discoverer, Gay-Lussac, in -1815<a id="fnanchor82-4" href="#note82-4"><span class="fnanchor">82</span></a>. -The importance -of the discovery consists in this; that this substance -was the first compound body which was distinctly -proved to enter into combination with elementary substances -in a manner similar to that in which they -combine with each other.</p> -<div class="footnote"><span class="label"><a id="note82-4" href="#fnanchor82-4">82</a></span> -Turner’s <i>Chemistry</i> (1834), p. 420. Miller’s <i>Chemistry</i>, ii. 66. -</div> -<p>The truth of our Aphorism (<a href="#a25">XXV.</a>) that in such a -science as chemistry, the history of the scientific nomenclature -is the history of the science, appears from this; -that the controversies with respect to chemical theories -and their application take the form of objections to the -common systematic names and proposals of new names -instead. Thus a certain compound of potassa, sulphur, -hydrogen, and oxygen, may be regarded either as <i>Hydrosulphate -of Potassa</i>, or as <i>Sulphide of Potassium in -solution</i>, according to different -views<a id="fnanchor83-4" href="#note83-4"><span class="fnanchor">83</span></a>. In some cases -indeed, changes are made merely for the sake of clearness. -Instead of <i>Hydrochloric</i> and <i>Hydrocyanic</i> acid, -many French writers, following Thenard, transpose the -elements of these terms; they speak of <i>Chlorhydric</i> and -<i>Cyanhydric</i> acid; by this means they avoid any ambiguity -which might arise from the use of the prefix -<i>Hydro</i>, which has sometimes been applied to compounds -which contain water<a id="fnanchor84-4" href="#note84-4"><span class="fnanchor">84</span></a>.</p> -<div class="footnote"><span class="label"><a id="note83-4" href="#fnanchor83-4">83</a></span> -Miller’s <i>Chemistry</i>, vol. ii. p. 583. -</div> -<div class="footnote"><span class="label"><a id="note84-4" href="#fnanchor84-4">84</a></span> -<i>Ibid.</i> ii. 433. -</div> -<p>An incompleteness in chemical nomenclature was -further felt, when it appeared, from the properties of -various substances, that mere identity in chemical -composition is not sufficient to produce identity of -chemical character or -properties<a id="fnanchor85-4" href="#note85-4"><span class="fnanchor">85</span></a>. -The doctrine of <span class="pagenum" id="page368">368</span> -the existence of compounds identical in ultimate composition, -but different in chemical properties, was -termed <i>Isomerism</i>. Thus chemists enumerate the following -compounds, all of which contain carbon and -hydrogen in the proportion of single equivalents of -each<a id="fnanchor86-4" href="#note86-4"><span class="fnanchor">86</span></a>;—<i>Methylene</i>, -<i>Olefiant gas</i>, <i>Propylene</i>, <i>Oil gas</i>, -<i>Amylene</i>, <i>Caproylene</i>, <i>Naphthene</i>, <i>Eleene</i>, <i>Peramylene</i>, -<i>Cetylene</i>, <i>Cerotylene</i>, <i>Melissine</i>.</p> -<div class="footnote"><span class="label"><a id="note85-4" href="#fnanchor85-4">85</a></span> -<i>Ibid.</i> ii. 653. -</div> -<div class="footnote"><span class="label"><a id="note86-4" href="#fnanchor86-4">86</a></span> -Miller’s <i>Chemistry</i>, ii. p. 654. -</div> -<p>I will, in the last place, propound an Aphorism -which has already offered itself in considering the -history of Chemistry<a id="fnanchor87-4" href="#note87-4"><span class="fnanchor">87</span></a> -as having a special bearing upon -that Science, but which may be regarded as the supreme -and ultimate rule with regard to the language -of Science.</p> -<div class="footnote end"><span class="label"><a id="note87-4" href="#fnanchor87-4">87</a></span> -<i>Hist. Ind. Sc.</i> b. xiv. c. 1. -</div> -<p class="center"><span class="sc">Aphorism</span> XXIX.</p> -<p><i>In learning the meaning of Scientific Terms, the history of -science is our Dictionary: the steps of scientific induction are -our Definitions.</i></p> -<p><span class="sc">It</span> is usual for unscientific readers to complain that -the technical terms which they meet with in books of -science are not accompanied by plain definitions such as -they can understand. But such definitions cannot be -given. For definitions must consist of words; and, in -the case of scientific terms, must consist of words which -require again to be defined: and so on, without limit. -<i>Elementary substances</i> in chemistry, for instance, what -are they? The substances into which bodies can be -<i>analysed</i>, and by the junction of which they are <i>composed</i>. -But what is <i>analysis</i>? what is <i>composition</i>? We -have seen that it required long and laborious courses of -experiment to answer these questions; and that finally -the balance decided among rival answers. And so it -is in other cases. In entering upon each science, we -come upon a new set of words. And how are we to learn <span class="pagenum" id="page369">369</span> -the meaning of this collection of words? In what other -language shall it be explained? In what terms shall we -define these new expressions? To this we are compelled -to reply, that we cannot translate these terms into any -ordinary or familiar language. Here, as in all other -branches of knowledge, the meaning of words is to be -sought in the progress of thought. It is only by going -back through the successful researches of men respecting -the <i>composition</i> and <i>elements</i> of bodies, that we can -learn in what sense such terms can be understood, so as -to convey real knowledge. In order that they may have -a meaning for us, we must inquire what meaning they -had in the minds of the authors of our discoveries. And -the same is the case in other subjects. To take the instance -of Morphology. When the beginner is told that -every group of animals may be reduced to an <i>Archetype</i>, -he will seek for a definition of Archetype. Such a definition -has been offered, to this effect: the Archetype of -a group of animals is a diagram embodying all the organs -and parts which are found in the group in such a relative -position as they would have had if none had attained -an excessive development. But, then, we are led -further to ask, How are we in each case to become -acquainted with the diagram; to know of what parts it -consists, and how they are related; and further; -What is the standard of <i>excess</i>? It is by a wide -examination of particular species, and by several successive -generalizations of observed facts, that we are led -to a diagram of an animal form of a certain kind, (for -example, a vertebrate;) and of the various ways, -excessive and defective, in which the parts may be developed.</p> -<p>This craving for definitions, as we have already said, -arises in a great degree from the acquaintance with geometry -which most persons acquire at an early age. -The definitions of geometry are easily intelligible by a -beginner, because the idea of space, of which they are -modifications, is clearly possessed without any special -culture. But this is not and cannot be the case in other -sciences founded upon a wide and exact observation of -facts. <span class="pagenum" id="page370">370</span></p> -<p class="end">It was formerly said that there was no Royal Road -to Geometry: in modern times we have occasion often -to repeat that there is no Popular Road—no road easy, -pleasant, offering no difficulty and demanding no toil,—to -Comparative Anatomy, Chemistry or any other of -the Inductive Sciences.</p> -<p class="center medium end">THE END.</p> -<hr class="four" /> -<p class="center small end">CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS.</p> -<div id="tnote"> -<p class="center">Transcriber’s Notes</p> -<p>Whewell published the -first edition of the <i>Philosophy of the Inductive Sciences</i> in -1840 in two volumes, as a companion to the 1837 <i>History of the -Inductive Sciences</i>. Revised second editions of both works -appeared in 1847. The third editions saw a major reshaping of the -<i>Philosophy</i>: a two volume <i>History of Scientific Ideas</i> -(1858 – in Project Gutenberg as #69093), <i>Novum Organon -Renovatum</i> (1858 – the present text, relying upon resources -kindly provided by the Internet Archive), and <i>On the Philosophy -of Discovery: chapters historical and critical</i> (1860 – -long since in Project Gutenberg’s collection: #5155). (The third -edition of the <i>History of the Inductive Sciences</i> is available in PG as #68693.)</p> -<p class="noind">Adaptations in this text</p> -<p>In the present text footnotes are numbered by Book and are placed -after the paragraph to which they attach; in the original, notes -were numbered by chapter. Page numbers appear in colour; where a -word was hyphenated across pages the number has been placed before -the word. Fractions have been transcribed as numerator ⁄ denominator; -the original usually has numerator over a line with denominator -below.</p> -<p>Some unusual symbols occur. On pages <a href="#page357">357</a> and 358, there are -italic letters with a number written above them. On two occasions -<i>B</i> has a 1 above it, and once <i>C</i> has ½ above it. On page <a href="#page364">364</a> -a formula is written with two entries containing <i>H</i> on a line above -<i>Cl</i>. These superpositions have all been transcribed by superscripting the first -and subscripting the second item (with the result that the letters are printed -smaller than in the original). The other oddities have been captured in Unicode.</p> -<p>On pages <a href="#page152">152</a> and <a href="#page197">197</a> Whewell uses -a raised dot as a decimal point and in -footnote <a href="#note26-3">26</a> of Book III. a comma. These have been replaced by a mid -dot.</p> -<p class="noind">Inductive Charts</p> -<p>At the end of Book II. (<a href="#page140a">p. 140</a>), Whewell included two very large inserts, -described in some detail in the Book itself. They were not captured by the scans -available in the Internet Archive. I was kindly provided with photographs of them. -Those charts were four times as wide as the normal page and a quarter as long. -In the html version they have been fairly accurately represented via tables; -but with up to 25 columns these tables will be very difficult to decipher on -small screens. In the text version, coded structure diagrams have been used, -which again utilise the full 70 spaces Project Gutenberg allows.</p> -<p class="noind">Corrections</p> -<p>Corrections are comparatively few. Apart from the silent ones, -they have been marked by dotted red underline, on mouse-over -revealing the nature of the change. Given the various editions, some -of the internal cross-references turn out to be obsolete or -erroneous:<br />  <a href="#note11-3">note 11</a> in Book III. -The text reads B. viii. c. iii. but it refers actually to Book viii. -c. ii. article 3 in earlier editions and in the <i>History of Scientific Ideas</i>, cf. <a href="#a88">Aphorism -88</a> in Book I. of the present volume. Compare also <a -href="#a19">Aphorism 19</a> in this volume’s Book IV.<br />  <a -href="#note58-3">notes 58 and 59</a> in Book III. refer to Book v. -c. i. For the present third edition they should have been aimed at -that chapter of the <i>History of Scientific Ideas</i>.<br /> - On page <a href="#page252">252</a> we are told that the Work is about to conclude, as -the first edition did in a way (all the aphorisms were gathered -after Book XIII. [= our Book III.], followed by various appendices). -But we have Book IV. yet to come, plus some extra illustrations -regarding language and symbols in science.</p> -<p>(I might add that I have not checked the many references to Whewell’s -other related works. The errors here suggest one might need to take -them with a pinch of salt, and help from the browser’s search function.)</p> -<p class="end"> There -are some inconsistencies, notably in spelling, which have in -general not been adjusted; nor have Whewell’s unbalanced quotation -marks and positioning of footnote anchors been modernized. </p> -</div> -</div> -<div style='display:block; margin-top:4em'>*** END OF THE PROJECT GUTENBERG EBOOK NOVUM ORGANON RENOVATUM ***</div> -<div style='text-align:left'> - -<div style='display:block; margin:1em 0'> -Updated editions will replace the previous one—the old editions will -be renamed. -</div> - -<div style='display:block; margin:1em 0'> -Creating the works from print editions not protected by U.S. copyright -law 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. 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