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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. - -Title: Novum organon renovatum - -Author: William Whewell - -Release Date: January 10, 2023 [eBook #69764] - -Language: English - -Produced by: Ed Brandon from materials kindly provided by the Internet - Archive, and with help gratefully received from various - voluntary sources. - -*** START OF THE PROJECT GUTENBERG EBOOK NOVUM ORGANON RENOVATUM *** - - -NOVUM ORGANON -RENOVATUM. - -BY WILLIAM WHEWELL, D.D., - -MASTER OF TRINITY COLLEGE, CAMBRIDGE, AND -CORRESPONDING MEMBER OF THE INSTITUTE OF FRANCE. - -BEING THE SECOND PART OF THE PHILOSOPHY -OF THE INDUCTIVE SCIENCES. - -_THE THIRD EDITION, WITH LARGE ADDITIONS._ - -ΛΑΜΠΑΔIΑ ΕΧΟΝΤΕΣ ΔIΑΔΩΣΟΥΣIΝ ΑΛΛΗΛΟIΣ - -LONDON: -JOHN W. PARKER AND SON, WEST STRAND. -1858. - - - - -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. - -HERSCHEL, _Discourse on Natural Philosophy_, Art. 96. - - - -CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS. - - - -{{iii}} -PREFACE. - - -EVEN if Bacon's _Novum Organon_ 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 -_Organ_ 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 {iv} 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 _Organ_ which has -something uniform in its working? If we can shew that this is so, we -shall have the _New Organ_, which Bacon aspired to construct, -_renovated_ according to our advanced intellectual position and -office. - -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 _History of the Sciences_, and -the _History of Scientific Ideas_[1\P]; the former containing the -history of the sciences, so far as it depends on {v} observed -_Facts_; the latter containing the history of those _Ideas_ by which -such Facts are bound into Theories. - -[Note 1\P: Published in two former editions as part of the -_Philosophy of the Inductive Sciences_ (b. i--x.).] - -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[2\P]. 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 _the Method of Gradation_ and _the Method of Natural -Classification_, spoken of b. iii. c. viii; and in a narrower sense, -of _the Method of Curves_, _the Method of_ {vi} _Means_, _the Method -of Least Squares_ and _the Method of Residues_, spoken of in chap. -vii. of the same Book. Also the Remarks on the _Use of Hypotheses_ -and on the _Tests of Hypotheses_ (b. ii. c. v.) point out features -which mark the usual course of discovery. - -[Note 2\P: _Nov. Org._ lib. i. aph. 61.] - -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 -_Colligation of Facts_; (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. - -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 b. iii. -c. ii. 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 {vii} place -are treated of in Chapters iii. and iv. of that Book. - -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 _clarification_ 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 _History of Scientific Ideas_. 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 _metaphysical_ 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 _no_ metaphysics in their heads, but by having _good_ -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 _History of Scientific Ideas_ 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 {viii} 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. - -In Chapter vi. of the Second Book, I have spoken of _the Logic of -Induction_. Several writers[3\P] 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 _Philosophy of the Sciences_. 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 {ix} 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 _Logic of Induction_, -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. _That_ 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.). - -[Note 3\P: Apelt _Die Theorie der Induction_: Gratry _Logique_.] - -"There will be good hopes for the Sciences then, and not till then, -when by a true SCALE 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. - -"But in establishing such propositions, we must devise some other -FORM OF INDUCTION than has hitherto been in use; and this must be -one which serves not only to prove and discover _Principles_, (as very -general Propositions are called,) but also the narrower and the -intermediate, and in short, all true Propositions." - -And he elsewhere speaks of successive FLOORS of Induction. - -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 {x} conceive, in the construction of a -_Scheme_ 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[4\P]; 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[5\P]. The Logic of Induction contains other portions, -which may be seen in the following work, b. ii. c. vi. - -[Note 4\P: See the Tables at the end of book ii.] - -[Note 5\P: _Cosmos_, vol. ii. n. 35.] - -I have made large additions to the present edition, especially in -what regards the Application of Science, (b. iii. c. ix.) 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 _social_ machinery for the advancement of science. There can be -no doubt that at certain stages of sciences, {xi} 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. - -I have thrown the substance of my results into Aphorisms, as Bacon -had done in his _Novum Organum_. 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. - -I have only to repeat what I have already said; that this task of -adapting the _Novum Organum_ to the {xii} present state of Physical -Science, and of constructing a _Newer Organ_ 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. - - TRINITY LODGE, - - 1 _November_, 1858. - - - -{{xiii}} -TABLE OF CONTENTS. - - - PAGE -PREFACE **iii - - - -BOOK I. -APHORISMS CONCERNING IDEAS. - -APHORISMS I.--XVIII. Ideas in general 5--7 - XIX.--XLIV. Ideas in the Pure Sciences 8--12 - XLV.--LV. Ideas in the Mechanical Sciences 13--15 - LVI.--LXXI. Ideas in the Secondary Mechanical - Sciences. 15--18 - LXXII.--**LXXIII. Ideas in the Mechanico-chemical - Sciences 18 - LXXIV.--LXXIX. Ideas in Chemistry 18 - LXXX.--LXXXI. Ideas in Morphology 19 - **LXXXII.--C. Ideas in Classificatory Science 20--23 - CI.--CVI. Ideas in Biology 23--24 - CVII.--CXVII. Ideas in Palæontology 24--26 - -BOOK II. -OF KNOWLEDGE. - -CHAP. I. OF TWO PRINCIPAL PROCESSES BY WHICH SCIENCE IS - CONSTRUCTED 27 - -CHAP. II. OF THE EXPLICATION OF CONCEPTIONS 30 - _Sect._ I. _The Historical Progress._ - _Art._ 1. The Explication of Conceptions, - 2. Has taken place historically by discussions. -{xiv} - _Art._ 3. False Doctrines when exposed appear impossible: - 4. But were plausible before - 5. Men's Minds gradually cleared. - _Sect._ II. _Use of definitions._ - _Art._ 6. Controversies about Definitions. - 7. Not arbitrary Definitions. - 8. Attention to Facts requisite. - 9. Definition is not essential. - 10. The omission of Definition not always blameable. - _Sect._ III. _Use of Axioms._ - _Art._ 11. Axioms serve to express Ideas. - _Sect._ IV. _Clear and appropriate Ideas._ - _Art._ 12. We must see the Axioms clearly. - 13. Inappropriate Ideas cannot lead to Truth. - 14. The fault is in the Conceptions. - 15. Rules cannot teach Discovery; - 16. But are not useless. - 17. Discussion as well as Facts needed. - _Sect._ V. _Accidental Discoveries._ - _Art._ 18. No Scientific Discovery is accidental. - 19. Such accidents do not happen to common Men. - 20. Examples. - 21. So far Explication of Conceptions. - -CHAP. III. OF FACTS AS THE MATERIALS OF SCIENCE 50 - _Art._ 1. Facts must be true. - 2. Facts not separable from Ideas. - 3. The Ideas must be distinct. - 4. Conceptions of the Intellect only to be admitted. - 5. Facts are to be observed with reference to - Space and Time: - 6. And also to other Ideas. - 7. The Decomposition of Facts. -{xv} - _Art._ 8. This step is not sufficient. - 9. It introduces Technical Terms, - 10. And Classification. - 11. The materials of Science. - -CHAP. IV. OF THE COLLIGATION OF FACTS 59 - _Art._ 1. Facts are colligated by Conceptions. - 2. Science begins with common Observation. - 3. Facts must be decomposed. - 4. What Ideas first give Sciences. - 5. Facts must be referred to Ideas. - 6. Sagacity needed. - 7. Discovery made by Guesses. - 8. False Hypotheses preluding to true ones. - 9. New Hypotheses not mere modifications of old ones. - 10. Hypotheses may have superfluous parts. - 11. Hypotheses to be compared with Facts. - 12. Secondary Steps. - -CHAP. V. OF CERTAIN CHARACTERISTICS OF SCIENTIFIC INDUCTION 70 - _Sect._ I. _Invention a part of Induction._ - _Art._ 1. Induction the source of Knowledge. - 2. Induction involves a New Element. - 3. Meaning of Induction. - 4. The New Element is soon forgotten. - 5. Induction includes a Definition and a Proposition. - _Sect._ II. _Use of Hypotheses._ - _Art._ 6. Discoveries made by Guesses, - 7. Which must be compared with Facts. - 8. Hypotheses are suspected. - 9. Hypotheses may be useful though inaccurate. - _Sect._ III. _Tests of Hypotheses._ - _Art._ 10. True Hypotheses foretel Phenomena, - 11. Even of different kinds.--Consilience of Inductions. -{xvi} - _Art._ 12. True Theories tend to Simplicity. - 13. Connexion of the last Tests. - -CHAP. VI. OF THE LOGIC OF INDUCTION 97 - _Art._ 1. Steps of Generalization, - 2. May be expressed by _Tables_. - 3. Which exhibit Inductive Steps; - 4. And the Consilience of Inductions; - 5. And the tendency to Simplicity; - 6. And the names of Discoverers; - 7. And the Verifications of Theory; - 8. By means of several easy steps. - 9. This resembles Book-keeping. - 10. The Logic of Induction. - 11. Attention at each step required. - 12. General Truths are not mere additions of - particulars: - 13. But a new view is introduced. - 14. Formula of Inductive Logic: - 15. May refer to Definition. - 16. Formula inadequate. - 17. Deductive Connexion of Steps. - 18. Relation of Deductive and Inductive Reasoning. - 19. The Criterion of Truth. - 20. Theory and Fact. - 21. Higher and Lower Generalizations. - -CHAP. VII. OF LAWS OF PHENOMENA AND OF CAUSES 118 - _Art._ 1. Knowledge of Laws of Phenomena. - 2. _Formal_ and _Physical_ Sciences. - 3. Causes in Astronomy. - 4. Different Mechanical Causes in other Sciences. - 5. Chemical and Vital Forces as Causes. - 6. Difference of these kinds of Force. - 7. Difficulty of conceiving new Causes. - 8. Men willingly take old Causes. - 9. Is the Magnetic Fluid real? - 10. Are Causes to be sought? (Comte's Doctrine.) - 11. Both Laws and Causes to be studied. -{xvii} - -CHAP. VIII. OF ART AND SCIENCE 129 - _Art._ 1. Art precedes Science. - 2. Contrast of Art and Science. - 3. Instinct and Insight. - 4. Difference of Art and Instinct. - 5. Does Art involve Science? - 6. Science unfolds Principles. - 7. Science may improve Art. - 8. Arts not classified with Sciences. - -CHAP. IX. OF THE CLASSIFICATION OF SCIENCES 136 - _Art._ 1. Use and Limits of such Classification. - 2. Classification depends on the Ideas. - 3. This points out Transitions. - 4. The Classification. - -INDUCTIVE TABLE OF ASTRONOMY 140 - -INDUCTIVE TABLE OF OPTICS 140 - -BOOK III. -OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE. - -CHAP. I. INTRODUCTION 141 - _Art._ 1. Object of this Book. - 2. An Art of Discovery not possible. - 3. Use of Methods. - 4. Series of Six Processes. - 5. Methods of Observation and Induction. - -CHAP. II. OF METHODS OF OBSERVATION 145 - _Art._ 1. Referring to Number, Space, and Time. - 2. Observations are never perfect. - 3. (I.) _Number is naturally exact_. - 4. (II.) _Measurement of Space_. - 5. Instruments Invented in Astronomy, - 6. And improved. -{xviii} - _Art._ 7. Goniometer. - 8. Standard of Length. - 10. (III.) _Measurement of Time_. - 11. Unit of Time. - 12. Transit Instrument. - 13. Chronometers. - 14. (IV.) _Conversion of Space and Time_. - 15. Space may Measure Time. - 16. Time may Measure Space. - 17. (V.) _The Method of Repetition_. - 18. The Method of Coincidences. - 19. Applied to Pendulums. - 20. (VI.) _Measurement of Weight_. - 21. Standard of Weight. - 22. (VII.) _Measurement of Secondary Qualities_. - 23. "The Howl" in Harmonics. - 24. (VIII.) _Manipulation_. - 25. Examples in Optics. - 26. (IX.) _The Education of the Senses_, - 27. By the Study of Natural History. - 28. Preparation for Ideas. - -CHAP. III. OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS; - _and first_ OF INTELLECTUAL EDUCATION 164 - _Art._ 1. (I.) _Idea of Space_. - 2. Education by Geometry. - 3. (II.) _Idea of Number_. - 4. Effect of the usual Education. - 5. (III.) _Idea of Force_. - 6. Study of Mechanics needed, - 7. To make Newton intelligible. - 8. No _Popular_ Road. - 9. (IV.) _Chemical Ideas_. - 10. (V.) _Natural History Ideas_. - 11. Natural Classes to be taught. - 12. Mathematical Prejudices, - 13. To be corrected by Natural History. - 14. Method of Natural History, - 15. Resembles common language. -{xix} - _Art._ 16. Its Lessons. - 17. (VI.) _Well-established Ideas alone to be used_. - 18. How are Ideas cleared? - -CHAP. IV. OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS, - _continued_.--OF THE DISCUSSION OF IDEAS 180 - _Art._ 1. Successive Clearness, - 2. Produced by Discussion. - 3. Examples. - 4. Disputes not useless, - 5. Although "metaphysical." - 6. Connected with Facts. - -CHAP. V. ANALYSIS OF THE PROCESS OF INDUCTION 186 - _Sect._ I. _The Three Steps of Induction._ - _Art._ 1. Methods may be useful. - 2. The three Steps. - 3. Examples. - 4. Mathematical names of the Steps. - _Sect._ II. _Of the Selection of the Fundamental Idea._ - _Art._ 5. Examples. - 6. The Idea to be found by trying, - 7. Till the Discovery is made; - 8. Preluded by Guesses. - 9. Idea and Facts homogeneous. - 10. Idea tested by the Facts. - -CHAP. VI. GENERAL RULES FOR THE CONSTRUCTION OF THE CONCEPTION 195 - _Art._ 1. First: for Quantity. - 2. Formula and Coefficients found together. - 3. Example. Law of Cooling. - 4. Determined by Experiment. - 5. Progressive Series of Numbers. - 6. Recurrent Series. - 7. Use of Hypotheses. - 8. Even with this there are difficulties. -{xv} - -CHAP. VII. SPECIAL METHODS OF INDUCTION APPLICABLE TO QUANTITY 202 - _Sect._ I. _The Method of Curves._ - _Art._ 1. Its Process. - 2. Its Use. - 3. With imperfect Observations. - 4. It corrects Observations. - 5. _Obstacles_. (I.) Ignorance of the argument. - 6. (II.) Combination of Laws. - _Sect._ II. _The Method of Means._ - _Art._ 7. Its Relation to the Method of Curves. - 8. Its process. - 9. _Argument_ required to be known. - 10. Use of the Method. - 11. Large masses of Observations used. - 12. Proof of the Use of the Method. - _Sect._ III. _The Method of Least Squares._ - _Art._ 13. Is a Method of Means. - 14. Example. - _Sect._ IV. _The Method of Residues._ - _Art._ 15. Occasion for its Use. - 16. Its Process. - 17. Examples. - 18. Its Relation to the Method of Means. - 19. Example. - 20. "Residual Phenomena." - -CHAP. VIII. METHODS OF INDUCTION DEPENDING ON RESEMBLANCE 220 - _Sect._ I. _The Law of Continuity._ - _Art._ 1. Its Nature and Application, - 2. To Falling Bodies, - 3. To Hard Bodies, - 4. To Gravitation. - 5. The Evidence. -{xxi} - _Sect._ II. _The Method of Gradation._ - _Art._ 6. Occasions of its Use. - 7. Examples. - 8. Not enjoined by Bacon. - 9. Other Examples. - 10. Its Value in Geology. - 11. Limited Results. - _Sect._ III. _The Method of Natural Classification._ - _Art._ 12. Examples of its Use. - 13. Its Process. - 14. Negative Results. - 15. Is opposed to Arbitrary Definitions. - 16. Propositions and Definitions correlative. - 17. Definitions only provisional. - -CHAP. IX. OF THE APPLICATION OF INDUCTIVE TRUTHS 233 - _Art._ 1. This forms the Sequel of Discovery. - 2. Systematic Verification of Discoveries. - 3. Correction of Coefficients. - 4. Astronomy a Model. - 5. Verification by new cases. - 6. Often requires fresh calculation. - 7. Cause of Dew. - 8. Useful Applications. - -CHAP. X. OF THE INDUCTION OF CAUSES 247 - _Art._ 1. Is to be pursued. - 2. Induction of Substance. - 3. Induction of Force. - 4. Induction of Polarity. - 5. Is Gravity Polar? - 6. Induction of Ulterior Causes. - 7. Of the Supreme Cause. -{xxii} - -BOOK IV, -OF THE LANGUAGE OF SCIENCE. - -INTRODUCTION 257 - - APHORISMS CONCERNING THE LANGUAGE OF SCIENCE. - -_Aphorism_ I. Relative to the Ancient Period 258 - _Art._ 1. Common Words. - 2. Descriptive Terms. - 3. Theoretical Terms. -_Aphorism_ II. Relative to the Modern Period 269 - _Art._ 1. Systematic Nomenclature. - 2. Systematic Terminology. - 3. Systematic Modification. -_Aphorisms_ (III. IV. V. VI. VII) relative to the - Application of Common Words 278 -_Aphorisms_ (VIII. IX. X. XI. XII. XIII.) relative to the - Construction of New Terms 285 -_Aphorism_ XIV. Binary Nomenclature 307 - XV. Linnæan Maxims 308 - XVI. Numerical Names 309 - XVII. Names of more than two Steps 310 - XVIII. No arbitrary _Terms_ 311 - XIX. Forms fixed by Convention 314 - XX. _Form_ of Terms 318 - _Art._ 1. Terms derived from Latin and Greek. - 2. German Terms. - 3. Descriptive Terms. - 4. Nomenclature. Zoology. - 5. ------------- Mineralogy. - 6. ------------- Botany. - 7. ------------- Chemistry. - 8. ------------- Crystallography. -{xxiii} -_Aphorism_ XXI. Philological Rules 328 - _Art._ 1. Hybrids. - 2. Terminations of Substantives. - 3. Formations of Substantives (names of things). - 4. Abstract Substantives. - 5. Rules of derivation from Greek and Latin. - 6. Modification of Terminations. -_Aphorism_ XXII. Introduction of Changes 341 - -FURTHER ILLUSTRATIONS OF THE APHORISMS ON SCIENTIFIC - LANGUAGE, FROM THE RECENT COURSE OF SCIENCES. - -1. BOTANY. -_Aphorism_ XXIII. Multiplication of Genera 346 - -2. COMPARATIVE ANATOMY. -_Aphorism_ XXIV. Single Names to be used 353 - XXV. The History of Science is the History - of its Language 355 - XXVI. Algebraical Symbols 357 - XXVII. Algebraical Analogies 364 - XXVIII. Capricious Derivations 365 - XXIX. Inductions are our Definitions 368 - - - -{{1}} -NOVUM ORGANON RENOVATUM. - - - - -DE Scientiis tum demum bene sperandum est, quando per SCALAM 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. - -In constituendo autem Axiomate, Forma INDUCTIONIS 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. - - BACON, _Nov. Org._, Aph. civ. cv. - - - -{{3}} -NOVUM ORGANON RENOVATUM. - - -THE name _Organon_ 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 _Novum -Organon_, 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. - -Inasmuch as we have gone through the _Histories_ of the principal -_Sciences_, from the earliest up to the present time, in a previous -work, and have also traced the _History of Scientific Ideas_ 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 {4} is our task in the present -volume; and to mark the reference of this undertaking to the work of -Bacon, we name our book _Novum Organon Renovatum_. - -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. - - - -{{5}} -NOVUM ORGANON RENOVATUM. - - - -BOOK I. - -APHORISMS CONCERNING IDEAS DERIVED FROM THE HISTORY OF IDEAS. - - -I. - -_MAN is the Interpreter of Nature, Science the right -interpretation._ (_History of Scientific Ideas_: Book I. Chapter 1.) - -II. - -_The_ Senses _place before us the_ Characters _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._ (Ibid. I. 2.) - -III. - -_The_ Alphabet, _by means of which we interpret Phenomena, consists -of the_ Ideas _existing in our own minds; for these give to the -phenomena that coherence and significance which is not an object of -sense._ (I. 2.) - -IV. - -_The antithesis of_ Sense _and_ Ideas _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. 2.) -{6} - -V. - -Fact _and_ Theory _correspond to Sense on the one hand, and to Ideas -on the other, so far as we are_ conscious _of our Ideas: but all facts -involve ideas_ unconsciously; _and thus the distinction of Facts and -Theories is not tenable, as that of Sense and Ideas is._ (I. 2.) - -VI. - -_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. 2.) - -VII. - -_Ideas are not_ trans_formed, but_ in_formed Sensations; for without -ideas, sensations have no form._ (I. 2.) - -VIII. - -_The Sensations are the_ Objective, _the Ideas the_ Subjective _part -of every act of perception or knowledge._ (I. 2.) - -IX. - -_General Terms denote_ Ideal Conceptions, _as a_ circle, _an_ orbit, -_a_ rose. _These are not_ Images _of real things, as was held by the -Realists, but Conceptions: yet they are conceptions, not bound -together by mere_ Name, _as the Nominalists held, but by an Idea._ -(I. 2.) - -X. - -_It has been said by some, that all Conceptions are merely_ states -_or_ feelings of the mind, _but this assertion only tends to -confound what it is our business to distinguish._ (I. 2.) - -XI. - -_Observed Facts are connected so as to produce new truths, by -superinducing upon them an Idea: and such truths are obtained_ by -Induction. (I. 2.) {7} - -XII. - -_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_ Successive Generalizations. (I. 2.) - -XIII. - -_Truths obtained by Induction are made compact and permanent by -being expressed in_ Technical Terms. (I. 3.) - -XIV. - -_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. 5.) - -XV. - -_Necessary truths derive their necessity from the_ Ideas _which they -involve; and the existence of necessary truths proves the existence -of Ideas not generated by experience._ (I. 5.) - -XVI. - -_In Deductive Reasoning, we cannot have any truth in the conclusion -which is not virtually contained in the premises._ (I. 6.) - -XVII. - -_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_ perceiving -_the axiomatic evidence of the_ axioms _belonging to each_ -Fundamental Idea. (I. 6.) - -XVIII. - -_The Fundamental Ideas which it is most important to consider, as -being the Bases of the Material Sciences, are the Ideas of_ Space, -Time (_including Number_), Cause (_including Force and Matter_), -Outness _of Objects, and_ Media _of Perception of Secondary -Qualities,_ Polarity (_Contrariety_), {8} _Chemical_ Composition -_and_ Affinity, Substance, Likeness _and Natural_ Affinity, Means -and Ends (_whence the Notion of Organization_), Symmetry, _and the -Ideas of_ Vital Powers. (I. 8.) - -XIX. - -_The Sciences which depend upon the Ideas of Space and Number are_ -Pure _Sciences, not_ Inductive _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._ (II. 1.) - -XX. - -_The Ideas on which the Pure Sciences depend, are those of_ Space -_and_ Number; _but Number is a modification of the conception of -Repetition, which belongs to the Idea of_ Time. (II. 1.) - -XXI. - -_The_ Idea of Space _is not derived from experience, for experience -of external objects_ pre_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_ form _of our perceptions, -and regulates them, whatever the_ matter _of them may be._ (II. 2.) - -XXII. - -_Space is not a General Notion collected by abstraction from -particular cases; for we do not speak of_ Spaces _in general, but of -universal or absolute_ Space. _Absolute Space is infinite. All -special spaces are_ in _absolute space, and are parts of it._ (II. 3.) - -XXIII. - -_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._ (II. 3.) {9} - -XXIV. - -_We have an_ Intuition _of objects in space; that is, we contemplate -objects as_ made up _of spatial parts, and apprehend their spatial -relations by the same act by which we apprehend the objects -themselves._ (II. 3.) - -XXV. - -Form _or Figure is space limited by boundaries. Space has -necessarily_ three _dimensions, length, breadth, depth; and no -others which cannot be resolved into these._ (II. 3.) - -XXVI. - -_The Idea of Space is exhibited for scientific purposes, by the_ -Definitions _and_ Axioms _of Geometry; such, for instance, as -these:--the_ Definition of a Right Angle, _and_ of a Circle;--_the_ -Definition of Parallel Lines, _and the_ Axiom _concerning -them;--the_ Axiom _that_ two straight lines cannot inclose a space. -_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._ (II. 4.) - -XXVII. - -_The Definitions and Axioms of Elementary Geometry do not_ -completely _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_ a curve line which joins two -points is less than any broken line joining the same points and -including the curve line. (II. 4.) - -XXVIII. - -_The perception of a_ solid object _by sight requires that act of -mind by which, from figure and shade, we infer distance and position -in space. The perception of_ figure _by sight requires that act of -mind by which we give an outline to each object._ (II. 6.) {10} - -XXIX. - -_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_ the muscular sense. (II. 6.) - -XXX. - -_The_ Idea of Time _is not derived from experience, for experience -of changes_ pre_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_ form _of our -perceptions, and regulates them, whatever the_ matter _of them may -be._ (II. 7.) - -XXXI. - -_Time is not a General Notion collected by abstraction from -particular cases. For we do not speak of particular_ Times _as -examples of time in general, but as parts of a single and infinite_ -Time. (II. 8.) - -XXXII. - -_Time, like Space, is a form, not only of perception, but of_ -Intuition. _We consider the whole of any time as_ equal _to the_ sum -_of the parts; and an occurrence as_ coinciding _with the portion of -time which it occupies._ (II. 8.) - -XXXIII. - -_Time is analogous to Space of_ one dimension: _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._ (II. 8.) - -XXXIV. - -_The Repetition of a set of occurrences, as, for example, strong and -weak, or long and short sounds, according to a_ {11} _steadfast order, -produces_ Rhythm, _which is a conception peculiar to Time, as Figure -is to Space._ (II. 8.) - -XXXV. - -_The simplest form of Repetition is that in which there is no -variety, and thus gives rise to the conception of_ Number. (II. 8.) - -XXXVI. - -_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_:--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. (II. 9.) - -XXXVII. - -_The Perception of Time involves a constant and latent kind of -memory, which may be termed a_ Sense of Succession. _The Perception -of Number also involves this Sense of Succession, although in small -numbers we appear to apprehend the units simultaneously and not -successively._ (II. 10.) - -XXXVIII. - -_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._ (II. 10.) - -XXXIX. - -Intuitive _is opposed to_ Discursive _reason. In intuition, we obtain -our conclusions by dwelling upon_ one _aspect of the fundamental -Idea; in discursive reasoning, we combine_ several _aspects of the -Idea,_ (_that is, several axioms,_) _and reason from the -combination._ (II. 11.) - -XL. - -_Geometrical deduction_ (_and deduction in general_) _is called_ -Synthesis, _because we introduce, at successive steps, the_ {12} -_results of new principles. But in reasoning on the relations of -space, we sometimes go on_ separating _truths into their component -truths, and these into other component truths; and so on: and this -is geometrical_ Analysis. (II. 11.) - -XLI. - -_Among the foundations of the Higher Mathematics, is the_ Idea of -Symbols _considered as general_ Signs _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_:--The interpretation of such symbols must be perfectly -general. _This Idea **and Axiom are the bases of Algebra in its most -general form._ (II. 12.) - -XLII. - -_Among the foundations of the Higher Mathematics is also the_ Idea -of a Limit. _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_:--What is true up to the Limit -is true at the Limit. _This Idea and Axiom are the bases of all -Methods of Limits, Fluxions, Differentials, Variations, and the -like._ (II. 12.) - -XLIII. - -_There is a_ pure _Science of Motion, which does not depend upon -observed facts, but upon the Idea of motion. It may also be termed_ -Pure Mechanism, _in opposition to Mechanics Proper, or_ Machinery, -_which involves the mechanical conceptions of force and matter. It -has been proposed to name this Pure Science of Motion,_ Kinematics. -(II. 13.) - -XLIV. - -_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_ {13} _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._ -(II. 14.) - -XLV. - -_The_ Idea of Cause, _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,_ -(_including Statics and Dynamics,_) _Hydrostatics, and Physical -Astronomy._ (III. 1.) - -XLVI. - -_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._ (III. 2.) - -XLVII. - -_The Idea of Cause is expressed for purposes of science by these -three Axioms_:--Every Event must have a Cause:--Causes are measured -by their Effects:--Reaction is equal and opposite to Action. -(III. 4.) - -XLVIII. - -_The Conception of Force involves the Idea of Cause, as applied to -the motion and rest of bodies. The conception of_ force _is suggested -by muscular action exerted: the conception of_ matter _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._ (III. 5.) - -XLIX. - -_Mechanical Science depends on the Conception of Force; and is -divided into_ Statics, _the doctrine of Force preventing_ {14} -_motion, and_ Dynamics, _the doctrine of Force producing motion._ -(III. 6.) - -L. - -_The Science of Statics depends upon the Axiom, that Action and -Reaction are equal, which in Statics assumes this form_:--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. -(III. 6.) - -LI. - -_The Science of Hydrostatics depends upon the Fundamental Principle -that_ fluids press equally in all directions. _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._ (III. 6.) - -LII. - -_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_ a body not -acted upon by a force will move with a uniform velocity in a -straight line. _The Second Axiom,--that Causes are measured by their -Effects,--gives rise to the Second Law of Motion,--that_ when a -force acts upon a body in motion, the effect of the force is -compounded with the previously existing motion. _The Third -Axiom,--that_ Reaction is equal and opposite to Action,--_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._ (III. 7.) {15} - -LIII. - -_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._ (III. 7.) - -LIV. - -_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_ a -perpetual motion is impossible;--_that_ the velocities of bodies -acquired by falling down planes or curves of the same vertical -height are equal;--_that_ the actual descent of the center of -gravity is equal to its potential ascent. _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._ (III. 7.) - -LV. - -_It is a_ Paradox _that Experience should lead us to truths -confessedly universal, and apparently necessary, such as the Laws of -Motion are. The_ Solution _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_ Form, _Experience, the_ Matter, _of these Laws._ -(III. 8.) - -LVI. - -Primary _Qualities of Bodies are those which we can conceive as -directly perceived;_ Secondary _Qualities are those_ {16} _which we -conceive as perceived by means of a Medium._ (IV. 1.) - -LVII. - -_We necessarily perceive bodies as_ without _us; the Idea of_ -Externality _is one of the conditions of perception._ (IV. 1.) - -LVIII. - -_We necessarily assume a_ Medium _for the perceptions of Light, -Colour, Sound, Heat, Odours, Tastes; and this Medium_ must _convey -impressions by means of its mechanical attributes._ (IV. 1.) - -LIX. - -_Secondary Qualities are not_ extended _but_ intensive: _their effects -are not augmented by addition of parts, but by increased operation -of the medium. Hence they are not measured directly, but by_ scales; -_not by_ units, _but by_ degrees. (IV. 4.) - -LX. - -_In the Scales of Secondary Qualities, it is a condition_ (_in order -that the scale may be complete,_) _that every example of the quality -must either_ agree _with one of the degrees of the Scale, or lie -between two_ contiguous _degrees._ (IV. 4.) - -LXI. - -_We perceive_ by means of _a medium and_ by means of _impressions on -the nerves: but we do not_ (_by our senses_) _perceive either the -medium or the impressions on the nerves._ (IV. 1.) - -LXII. - -_The_ Prerogatives of the Sight _are, that by this sense we -necessarily and immediately apprehend the_ position _of its objects: -and that from visible circumstances, we_ infer _the_ distance _of -objects from us, so readily that we seem to perceive and not to -infer._ (IV. 2.) {17} - -LXIII. - -_The_ Prerogatives of the Hearing _are, that by this sense we -perceive relations perfectly precise and definite between two notes, -namely,_ Musical Intervals (_as an_ Octave, _a_ Fifth); _and that -when two notes are perceived together, they are comprehended as -distinct,_ (_a_ Chord,) _and as having a certain relation,_ (Concord -_or_ Discord.) (IV. 2.) - -LXIV. - -_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._ (IV. 2.) - -LXV. - -_The_ First Paradox of Vision _is, that we see objects_ upright, -_though the images on the retina are_ inverted. _The solution is, -that we do not see the image on the retina at all, we only see by -means of it._ (IV. 2.) - -LXVI. - -_The_ Second Paradox of Vision _is, that we see objects_ single, -_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_ (_small or -distant_) _objects single, when their images fall on_ corresponding -points _of the two retinas._ (IV. 2.) - -LXVII. - -_The law of single vision for_ near _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._ (IV. 2.) - -LXVIII. - -_The ultimate object of each of the Secondary Mechanical Sciences -is, to determine the nature and laws of the processes_ {18} _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_ laws _of the phenomena; and for this purpose a_ -Measure _or_ Scale _of each quality is necessary._ (IV. 4.) - -LXIX. - -_Secondary qualities are measured by means of such effects as can be -estimated in number or space._ (IV. 4.) - -LXX. - -_The Measure of Sounds, as high or low, is the_ Musical Scale, _or_ -Harmonic Canon. (IV. 4.) - -LXXI. - -_The Measures of Pure Colours are the_ Prismatic Scale; _the same, -including_ Fraunhofer's Lines; _and_ Newton's Scale _of Colours. The -principal Scales of Impure Colours are_ Werner's Nomenclature _of -Colours, and_ Merimée's Nomenclature _of Colours_. (IV. 4.) - -LXXII. - -_The Idea of_ Polarity _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._ -(V. 1.) - -LXXIII. (Doubtful.) - -_Coexistent polarities are fundamentally identical._ (V. 2.) - -LXXIV. - -_The Idea of Chemical_ Affinity, _as implied in Elementary -Composition, involves peculiar conceptions. It is not properly -expressed by assuming the qualities of bodies to_ resemble _those of -the elements, or to depend on the_ figure _of the elements, or on -their_ attractions. (VI. 1.) {19} - -LXXV. - -_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._ (VI. 2.) - -LXXVI. - -_The governing principles of Chemical Affinity are, that it is_ -elective; _that it is_ definite; _that it_ determines the properties -_of the compound; and that_ analysis is possible. (VI. 2.) - -LXXVII. - -_We have an idea of_ Substance: _and an axiom involved in this Idea -is, that_ the weight of a body is the sum of the weights of all its -elements. (VI. 3.) - -LXXVIII. - -_Hence Imponderable Fluids are not to be admitted as chemical -elements._ (VI. 4.) - -LXXIX. - -_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._ (VI. 5.) - -LXXX. - -_We have an Idea of_ Symmetry; _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._ (VII. 1.) - -LXXXI. - -_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._ (VII. 3.) {20} - -LXXXII. - -_When we consider any object as_ One, _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._ (VIII. 1.) - -LXXXIII. - -_We collect individuals into_ Kinds _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._ (VIII. 1.) - -LXXXIV. - -_The_ Names _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_ fish _in natural history, but it is a_ fish _in commerce -and law._ (VIII. 1.) - -LXXXV. - -_We take for granted that each kind of things has a special_ -character _which may be expressed by a Definition. The ground of our -assumption is this;--that reasoning must be possible._ (VIII. 1.) - -LXXXVI. - -_The "Five Words,"_ Genus, Species, Difference, Property, Accident, -_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._ -(VIII. 1.) - -LXXXVII. - -_The construction of a Classificatory Science includes_ Terminology, -_the formation of a descriptive language;_--Diataxis, _the Plan of -the System of Classification, called_ {21} _also the_ -Systematick;--Diagnosis, _the Scheme of the Characters by which the -different Classes are known, called also the_ Characteristick. -Physiography _is the knowledge which the System is employed to -convey. Diataxis includes_ Nomenclature. (VIII. 2.) - -LXXXVIII. - -Terminology _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,_ directly _according -to the convention, not through the medium of explanation or -comparison._ (VIII. 2.) - -LXXXIX. - -_The_ Diataxis,_ 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._ -(VIII. 2.) - -XC. - -_An_ Artificial System _is one in which the_ smaller _groups_ (_the -Genera_) _are_ natural; _and in which the_ wider _divisions_ -(_Classes, Orders_) _are constructed by the_ peremptory _application -of selected Characters;_ (_selected, however, so as not to break up -the smaller groups._) (VIII. 2.) - -XCI. - -_A_ Natural System _is one which attempts to make_ all _the -divisions_ natural, _the widest as well as the narrowest; and -therefore applies_ no _characters_ peremptorily. (VIII. 2.) - -XCII. - -_Natural Groups are best described, not by any Definition which -marks their boundaries, but by a_ Type _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._ (VIII. 2.) -{22} - -XCIII. - -_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._ (VIII. 2.) - -XCIV. - -_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_ (_Scientific_) _Natural History were introduced into -education, men might become familiar with the fixation of the -signification of words by_ Types; _and this process agrees more -nearly with the common processes by which words acquire their -significations._ (VIII. 2.) - -XCV. - -_The attempts at Natural Classification are of three sorts; -according as they are made by the process of_ blind trial, _of_ -general comparison, _or of_ subordination of characters. _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_ majority. _Neither of these methods can -really be carried into effect. The method of Subordination of -Characters considers some characters as_ more important _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._ -(VIII. 2.) - -XCVI. - -_A_ Species _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_ -definite _difference._ (VIII. 2.) {23} - -XCVII. - -_A_ Genus _is a collection of species which resemble each other more -than they resemble other species: the resemblance being opposed to -a_ definite _difference._ (VIII. 2.) - -XCVIII. - -_The_ Nomenclature _of a Classificatory Science is the collection of -the names of the Species, Genera, and other divisions. The_ binary -_nomenclature, which denotes a species by the_ generic _and_ specific -_name, is now commonly adopted in Natural History._ (VIII. 2.) - -XCIX. - -_The_ Diagnosis, _or Scheme of the Characters, comes, in the order -of philosophy, after the Classification. The characters do not_ make -_the classes, they only enable us to_ recognize _them. The Diagnosis -is an Artificial Key to a Natural System._ (VIII. 2.) - -C. - -_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_ different _sets of -characters, must_ coincide _with each other._ (VIII. 4.) - -CI. - -_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._ -(IX. 2.) - -CII. - -_Life is a System of Vital Forces; and the conception of such Forces -involves a peculiar Fundamental Idea._ (IX. 3.) {24} - -CIII. - -_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._ (_Thus the ingredients -of gunpowder, liberated from their chemical union, exert great -mechanical Force: a galvanic battery acting by chemical process does -the like._) _Vital Forces include in their nature both chemical -Affinities and mechanical Forces: for Vital Powers produce both -chemical changes,_ (_as digestion,_) _and motions which imply -considerable mechanical force,_ (_as the motion of the sap and of -the blood._) (IX. 4.) - -CIV. - -_In_ voluntary _motions, Sensations produce Actions, and the -connexion is made by means of Ideas: in_ reflected _motions, the -connexion neither seems to be nor is made by means of Ideas: in_ -instinctive _motions, the connexion is such as requires Ideas, but -we cannot believe the Ideas to exist._ (IX. 5.) - -CV. - -_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_ in vain, _is as necessarily true as the maxim that -nothing happens_ by chance. (IX. 6.) - -CVI. - -_The Idea of living beings as subject to_ disease _includes a -recognition of a Final Cause in organization; for disease is a state -in which the vital forces do not attain their_ proper ends. (IX. 7.) - -CVII. - -_The Palætiological Sciences depend upon the Idea of Cause: but the -leading conception which they involve is that of_ historical cause, -_not mechanical cause._ (X. 1.) {25} - -CVIII. - -_Each Palætiological Science, when complete, must possess three -members: the_ Phenomenology, _the_ Ætiology, _and the_ Theory. (X. -2.) - -CIX. - -_There are, in the Palætiological Sciences, two antagonist -doctrines:_ Catastrophes _and_ Uniformity. _The doctrine of a_ -uniform course of nature _is tenable only when we extend the nation -of Uniformity so far that it shall include Catastrophes._ (X. 3.) - -CX. - -_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._ (X. 3.) - -CXI. - -_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_ -beginning _of the chain._ (X. 3.) - -CXII. - -_Since the Palætiological sciences deal with the conceptions of -historical cause,_ History, _including_ Tradition, _is an important -source of materials for such sciences._ (X. 4.) - -CXIII. - -_The history and tradition which present to us the providential -course of the world form a_ Sacred Narrative; _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._ (X. 4.) {26} - -CXIV. - -_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._ (X. 4.) - -CXV. - -_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._ (X. 4.) - -CXVI. - -_In contemplating the series of causes and effects which constitutes -the world, we necessarily assume a_ First Cause _of the whole -series._ (X. 5.) - -CXVII. - -_The Palætiological Sciences point backwards with lines which are -broken, but which all converge to the_ same _invisible point: and -this point is the Origin of the Moral and Spiritual, as well as of -the Natural World._ (X. 5.) - - - - -NOVUM ORGANON RENOVATUM. - - -{{27}} -BOOK II. - -OF THE CONSTRUCTION OF SCIENCE. - - - -CHAPTER I. - -OF TWO PRINCIPAL PROCESSES BY WHICH SCIENCE IS CONSTRUCTED. - - -APHORISM I. - -_THE two processes by which Science is constructed are the_ -Explication of Conceptions, _and the_ Colligation of Facts. - - -TO 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 {28} 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 _Science_. 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. - -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 _History of the Inductive Sciences_ and -the _History of Scientific Ideas_,) must acquire its real value and -true place in our design. - -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 {29} 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 _Conceptions_ are _made more clear_ in themselves, or by which -the Conceptions more strictly _bind together the Facts_. 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 _the Explication of Conceptions_ and _the Colligation of Facts_: -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. - - - -{{30}} -CHAPTER II. - -OF THE EXPLICATION OF CONCEPTIONS. - - -APHORISM II. - -_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._ - - -APHORISM III. - -_Conceptions, for purposes of science, must be_ appropriate _as well -as clear: that is, they must be modifications of_ that _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_ no discovery is the work of -accident. - - -SECT. I.--_Historical Progress of the Explication of Conceptions._ - -1. WE have given the appellation of _Ideas_ to certain comprehensive -forms of thought,--as _space_, _number_, _cause_, _composition_, -_resemblance_,--which we apply to the phenomena which we -contemplate. But the special modifications of these ideas which are -{31} exemplified in particular facts, we have termed _Conceptions_; -as _a circle_, _a square number_, _an accelerating force_, _a -neutral combination_ of elements, a _genus_. 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 _unfolded_, -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 _Explication of Conceptions_. - -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. - -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 _Force_ were an important part of the progress of the -science of Mechanics. The struggles by which philosophers attained a -right general conception of _plane_, of _circular_, of _elliptical -Polarization_, were some of the most difficult steps in the modern -discoveries of Optics. A Conception of the _Atomic Constitution_ 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 _Species_ and _Genera_ -have been rendered more exact, have improved the science of Botany: -the imperfection of the science of {32} Mineralogy arises in a great -measure from the circumstance, that in that subject, the Conception -of a _Species_ is not yet fixed. In Physiology, what a vast advance -would that philosopher make, who should establish a precise, -tenable, and consistent Conception of _Life_! - -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. - -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, {33} -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. - -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 {34} 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. - -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. - -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 {35} mechanical conceptions:--as, for example, the -question concerning the measure of the Force of Percussion;--the war -of the _Vis Viva_;--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. - - -SECT. II.--_Use of Definitions._ - -6. The result of such controversies as we have been speaking of, -often appears to be summed up in a _Definition_; 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 _uniform force_ is, -that it generates a velocity proportional to the _space_ from rest, -or to the _time_. The controversy of the _Vis Viva_ was, what was -the {36} proper Definition of the _measure of force_. A principal -question in the classification of minerals is, what is the -Definition of a _mineral species_. Physiologists have endeavoured to -throw light on their subject, by Defining _organization_, or some -similar term. - -7. It is very important for us to observe, that these controversies -have never been questions of insulated and _arbitrary_ 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 _Vis Viva_, 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. - -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 _then_ 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. - -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 {37} -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 _use_ 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. - -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. {38} - -9. But though _Definition_ may be subservient to a right explication -of our conceptions, it is _not essential_ 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 _Moving Force_ -which urges bodies downwards upon an inclined plane, while he still -hesitated whether to call it _Momentum_, _Energy_, _Impetus_, or -_Force_, and did not venture to offer a Definition of the thing -which was the subject of his thoughts. The Conception of -_Polarization_ 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 _Polarization_ had no definite -meaning, and was merely an expression of our ignorance. The -Definition which was offered by Haüy and others of a _Mineralogical -Species_;--'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 _Strata_, and _Formations_, and _Epochs_, -among geologists, has not prevented the discussions which they have -carried on upon such subjects from being highly serviceable {39} 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. - -10. Men are often prone to consider it as a thoughtless _omission_ -of an essential circumstance, and as a _neglect_ 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 _that_ 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 _define_, 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 {40} 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. - - -SECT. III.--_Use of Axioms._ - -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 _other mode_ 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 _History_ 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 _Axioms_, -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 {41} -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 -_History_. 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. - - -SECT. IV.--_Clear and appropriate Ideas._ - -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 _Clearness of -Ideas_ 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 {42} Idea. The Criterion -is, that the person shall _see_ 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. - -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 -_appropriate_. 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 -_Force_;--Chemistry, the Conception of _Elementary -Composition_;--Physiology, the Conception of _Vital Powers_. 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 _History_ 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 -{43} new science by the application of principles which belong to an -old one, will lead to frivolous and barren speculations. - -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 -_inappropriate_ geometrical conceptions of the properties of the -circle:--they speculated to no purpose about the elementary -composition of bodies, because they assumed the _inappropriate_ -conception of _likeness_ between the elements and the compound, -instead of the genuine notion of elements merely _determining_ 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 _inappropriate_ mechanical and -chemical and other ideas which were applied in succession to the -subject failed in bringing into view any genuine physiological -truth. - -14. That the real cause of the failure in the instances above -mentioned lay in the _Conceptions_, 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. - -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 {44} apprehension strictly determined by the -subject of our speculations. - -15. It may, however, be said that this injunction that we are to -employ _appropriate_ Conceptions only in the formation of our -knowledge, cannot be of practical use, because we can only determine -what Ideas _are_ 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. - -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 _History_ 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, {45} 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[1\2]. 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. - -[Note 1\2: This agrees with what M. Necker has well observed in his -_Règne Mineral_, that those who have treated mineralogy as a merely -chemical science, have substituted the analysis of substances for -the classification of individuals. See _History of Ideas_, b. viii. -chap. iii.] - -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 -_discussion_ 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 _Species_ -in Mineralogy would at present be perhaps the most important step -which the science could make. A just conception of the nature of -_Life_, (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. - -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 {46} 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. - - -SECT. V.--_Accidental Discoveries._ - -18. Another consequence follows from the views presented in this -Chapter, and it is the last I shall at present mention. _No -scientific discovery_ can, with any justice, be considered _due to -accident_. 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[2\2] 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 -{47} 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. - -[Note 2\2: B. i. of this vol. Aphorism III.] - -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? - -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 -_Double Refraction_ of light.' But Bartholinus could have seen no -such consequence in the accident if he had not previously had a -clear conception of _single refraction_. A lady, in describing an -optical experiment which had been shown her, said of her teacher, -'He told me to _increase and diminish_ {48} _the angle of -refraction_, 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 _Polarization_ 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 _sides_, 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 {49} 'in all these -fundamental discoveries appropriate ideas had no share,' and that -the discoveries 'might have been made by the most ordinary -observers.' - -21. I have now, I trust, shown in various ways, how the _Explication -of Conceptions_, 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. - - - -{{50}} -CHAPTER III. - -OF FACTS AS THE MATERIALS OF SCIENCE. - - -APHORISM IV. - -_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._ - -APHORISM V. - -_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._ - -APHORISM VI. - -_The resolution of complex Facts into precise and measured partial -Facts, we call the_ Decomposition of Facts. _This process is -requisite for the progress of science, but does not necessarily lead -to progress._ - - -1. WE 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. - -When we inquire what Facts are to be made the materials of Science, -perhaps the answer which we {51} should most commonly receive would -be, that they must be _True Facts_, 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. - -But such maxims are far from being easy to apply, as a little -examination will convince us. - -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 _read_ 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 {52} any otherwise -than as a _Fact_ 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[3\2], 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, _inseparable_ portions of the -process {53} 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. - -[Note 3\2: _History of Ideas_, B. ii. c. vi. s. 6.] - -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. - -3. But still, it cannot be doubted that in selecting the Facts which -are to form the foundation of Science, {54} 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? - -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. - -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. - -4. In the first place. Facts, when used as the materials of physical -Science, must be _referred to Conceptions of the Intellect only_, -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 {55} state -of mind which these descriptions imply can be of no scientific -value. We cannot make the poets our observers. - - Armorum sonitum toto Germania cœlo - Audiit; insolitis tremuerunt motibus Alpes. - Vox quoque per lucos vulgo exaudita silentes - Ingens; et simulacra modis pallentia miris - Visa sub obscurum noctis: pecudesque locutæ. - -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. - -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. - -5. And thus we are led to another Rule:--that in collecting Facts -which are to be made the basis of {56} Science, the Facts are to be -observed, as far as possible, _with reference to place, figure, -number, motion_, 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. - -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 -_with reference to other Conceptions also_: 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 _Concords_ -and _Discords_; the science of Mechanics arose from not only -observing motions as they take place in Time and Space, but further, -referring them to _Force_ as their _Cause_. 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. - -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 _Decomposition of Facts_. It is the {57} 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. - -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. - -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 _Terms_ 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 _Hours_, and _Days_, and _Cycles_, _Altitude_ and -_Declination_, _Phases_ and _Aspects_. In the same manner, in Music, -the concords had names assigned them, as _Diapente_, _Diatessaron_, -_Diapason_; in studying Optics, the _Rays_ of light were spoken of -as {58} having their course altered by _Reflexion_ and _Refraction_; -and when useful observations began to be made in Mechanics, the -observers spoke of _Force_, _Pressure_, _Momentum_, _Inertia_, and -the like. - -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. - -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. - - - -{{59}} -CHAPTER IV. - -OF THE COLLIGATION OF FACTS. - - -APHORISM VII. - -_Science begins with_ common _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_ Observation _and_ Experiment. - -APHORISM VIII. - -_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_ tentative hypotheses _and selecting the right one. -But a supply of appropriate hypotheses cannot be constructed by -rule, nor without inventive talent._ - -APHORISM IX. - -_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._ - - -1. FACTS 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 {60} 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 _squares of numbers_, the _cubes of distances_, and the -_proportionality_ 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 -_central accelerating force_, 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 _Colligation of Facts_: 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. - -2. Science begins with _Common_ 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 _History_) 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 {61} _kinds_ 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. - -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. - -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 {62} 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 _Resemblance_ may be noticed, as coming next to those of -Space and Number in original precision; and the Idea of _Cause_, 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. - -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 _Observation_, or, -when we ourselves occasion the facts, _Experiment_. 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 {63} in the preceding Books[4\2], 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 _polarization_; the phenomena of -mixture, when there is an alteration of qualities as well as -quantities, must be combined by a Conception of _elementary -composition_. 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. - -[Note 4\2: _Hist. of Sci. Id._ Bs. v. vi. vii. viii. ix. x.] - -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 -_pressure_, while Aristotle could not see in them anything more than -the results {64} of the strangeness of the properties of the -circle;--or which impelled Pascal to explain by means of the -Conception of the _weight of air_, 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 _refraction_, 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. - -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 _Guesses_; 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 _Hypotheses_, 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 {65} 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. - -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. - -9. It would, however, be a great mistake to suppose that the -hypotheses, among which our choice thus {66} 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 _geometrical_ combination of lines and circles, -but by referring the properties to genuine _mechanical_ 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 _epicycles_ 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 _neutralizing_ 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 _interference_ of several rays. - -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. - -10. The Conceptions which a true theory requires are very often -clothed in a _Hypothesis_ which connects {67} 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 _Fluid_. 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 _Ether_ 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 -_Atoms_. 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. - -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 {68} 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 _History_ 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 -_Temperament_. 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. - -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. {69} - -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. - - - -{{70}} -CHAPTER V. - -OF CERTAIN CHARACTERISTICS OF SCIENTIFIC INDUCTION. - - -APHORISM X. - -_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._ - -APHORISM XI. - -_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._ - -APHORISM XII. - -_It is a test of true theories not only to account for, but to -predict phenomena._ - -APHORISM XIII. - -Induction _is a term applied to describe the process of a true -Colligation of Facts by means of an exact and appropriate -Conception._ An Induction _is also employed to denote the_ -proposition _which results from this process._ - -APHORISM XIV. - -The Consilience of Inductions _takes place when an Induction, -obtained from one class of facts, coincides with an Induction, -obtained from another different class. This_ {71} _Consilience is a -test of the truth of the Theory in which it occurs._ - -APHORISM XV. - -_An Induction is not the mere_ sum _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_ superinduced; _and a peculiar -constitution and discipline of mind are requisite in order to make -this Induction._ - -APHORISM XVI. - -_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._ - - -SECT. I.--_Invention a part of Induction._ - -1. THE 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 _Induction_; -which is usually and justly spoken of as the genuine source of all -our _real general knowledge_ 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 _real_, because it arises from the combination of Real Facts, but -it is _general_, 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: {72} 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 -_Form_, facts the _Material_, 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. - -2. Induction is familiarly spoken of as the process by which we -collect a _General Proposition_ from a number of _Particular Cases_: -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 {73} 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. - -Thus[5\2] 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 {74} actual -cases are intelligible and explicable by means of the Conception of -_Forces_, 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, -_Momentum_, 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 _Momentum gained and lost_ 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. - -[Note 5\2: I repeat here remarks made at the end of the _Mechanical -Euclid_, p. 178.] - -3. Hence in every inference by Induction, there is some Conception -_superinduced_ upon the Facts: and we may henceforth conceive this -to be the peculiar import of the term _Induction_. 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[6\2], 'is when by means of one extreme term[7\2] 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 _conversely_, 'All {75} 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 _evidence_ of the inference; and overlooks a step which is of -far more importance to our knowledge, namely, the _invention_ of the -second extreme term. In the above instance, the particular -luminaries, Mercury, Venus, Mars, are one logical _Extreme_; the -general designation Planets is the _Middle Term_; but having these -before us, how do we come to think of _description of ellipses_, -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[8\2]; but the _statement_ 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 _Term_, 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 _guess_ at least -that, in this respect, he might _convert_ 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 _discovery_; the Verification of the Proposition was the great -step in the _proof_ 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 {76} _Invention_, which is requisite -in every inductive inference. - -[Note 6\2: _Analyt. Prior._ lib. ii. c. xxiii. Περὶ τῆς ἐπαγωγῆς.] - -[Note 7\2: The syllogism here alluded to would be this:-- - Mercury, Venus, Mars, describe ellipses about the Sun; - All Planets do what Mercury, Venus, Mars, do; - Therefore all Planets describe ellipses about the Sun.] - -[Note 8\2: Εἰ οὖν ἀντιστρέφει τὸ Γ τῷ Β καὶ μὴ ὑπερτείνει τὸ -μέσον.--Aristot. _Ibid._] - -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 _round_, the Earth and the Planets as -_revolving_ about the Sun, and as _drawn_ 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 _own_ our obligation to those discoverers, -but we hardly _feel_ it: for in what other manner (we ask in our -thoughts) could we represent the facts to ourselves? - -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 {77} 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 -_Cycle_ dispels the mystery. The Planets perform a tangled and mazy -dance; but _Epicycles_ reduce the maze to order. The Epicycles -themselves run into confusion; the conception of an _Ellipse_ 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 _answer_ such questions rashly, they take nothing for granted. -They do not recollect how much they assume in _asking_ 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 _what_ we assert, but _how_ 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. - -5. In collecting scientific truths by Induction, we often find (as -has already been observed) a Definition {78} 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. - - -SECT. II.--_Use of Hypotheses._ - -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. - -The tendencies of our speculative nature[9\2], carrying {79} 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. - -[Note 9\2: 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.--_Hist. Ind. Sc._ b. v. c. ii.] - -Hence advances in knowledge[10\2] 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; {80} 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 _rule_ of the -genius of discovery, rather than (as has often been taught in modern -times) to the _exception_. - -[Note 10\2: These observations are made on occasion of Kepler's -speculations, and are illustrated by reference to his -discoveries.--_Hist. Ind. Sc._ b. v. c. iv. sect. 1.] - -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 {81} 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. - -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[11\2] 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[12\2].' - -[Note 11\2: _Hist. Ind. Sc._ b. v. c. iv. sect. 1.] - -[Note 12\2: _Hist. Ind. Sc._ b. vii. c. ii. sect. 3.] - -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 {82} affection -for these, have been prone to overlook, to distort, and to -misinterpret facts. In this manner, _Hypotheses_ 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. - -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 _cautious_ and _rigorous_; 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 _abstaining from_ -such suppositions, but in _not adhering_ 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 {83} 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. - -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 _testing_ 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. - - -SECT. III.--_Tests of Hypotheses._ - -9. A maxim which it may be useful to recollect is this;--that -_hypotheses may often be of service to science, when they involve a -certain portion of incompleteness, and even of errour_. 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 {84} false, but we -shall be able to translate it into the language of truth. - -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 _Doctrine -of epicycles_ 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 _circular_ nature of all the -celestial motions, and in making the heavenly bodies revolve _round -the earth_. 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 _epicyclical hypothesis_. - -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 _Nature's horrour of a vacuum_ (_fuga -vacui_), 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[13\2] appears to wonder that men did not at once -divine the weight of the air, from which the phenomena formerly -ascribed to the _fuga vacui_ really result. 'Loaded, {85} 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 _one_ -principle, there is a strong presumption that the principle is not -altogether baseless. And in reality is it not true that nature _does_ -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. - -[Note 13\2: Deluc, _Modifications de l'Atmosphère_, Partie 1.] - -That imperfect and false hypotheses, though they may thus explain -_some_ phenomena, and may be useful in the progress of science, -cannot explain _all_ 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 _is_ consistent with _all_ the observed -facts;--will of course be understood. We shall afterwards have to -speak of the other steps of such a progress. - -10. Thus the hypotheses which we accept ought to explain phenomena -which we have observed. But they {86} ought to do more than this: -our hypotheses ought to _foretel_ 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. - -The scientific doctrines which have at various periods been -established have been verified in this manner. For example, the -_Epicyclical Theory_ of the heavens was confirmed by its -_predicting_ 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 _Laws of Refraction_ -enabled mathematicians to _predict_, by calculation, what would be -the effect of any new form or combination of transparent lenses. -Newton's hypothesis of _Fits of Easy Transmission and Easy -Reflection_ 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 _predict_ -the forms and colours of thin plates for a wide range of given -cases. The hypothesis that Light operates by _Undulations_ and -_Interferences_, afforded the means of _predicting_ results under a -still larger extent of conditions. In like manner in the {87} -progress of chemical knowledge, the doctrine of _Phlogiston_ -supplied the means of _foreseeing_ the consequence of many -combinations of elements, even before they were tried; but the -_Oxygen Theory_, 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 _foresee_ such -facts in untried cases. And the Theory of _Electromagnetic Forces_, -as soon as it was rightly understood, enabled those who had mastered -it to _predict_ motions such as had not been before observed, which -were accordingly found to take place. - -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. - -11. We have here spoken of the prediction of facts _of the same -kind_ as those from which our rule was collected. But the evidence -in favour of our {88} induction is of a much higher and more -forcible character when it enables us to explain and determine cases -of a _kind different_ 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 _that_ being the point -where truth resides. - -Accordingly the cases in which inductions from classes of facts -altogether different have thus _jumped together_, 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 _Consilience of Inductions_. - -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 _Third Law_, of the proportionality of the -cubes of the distances to the squares of the periodic times of the -planets, explained also his _First_ and _Second Laws_, 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 -_Perturbations_ of the moon and planets by the sun and by each -other, also accounted for the fact, apparently altogether dissimilar -and remote, of the _Precession of the equinoxes_. 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 {89} 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 _Fringes_, -explained also the _Colours of thin plates_ 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 _Double Refraction_ 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 _directions_ of the two -refracted rays, accounted also for the positions of their _Planes of -Polarization_[14\2], a phenomenon which, taken by itself, it had -perplexed previous mathematicians, even to represent. - -[Note 14\2: _Hist. Ind. Sc._ b. ix. c. xi. sect. 4.] - -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 _felicities_[15\2]. 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 -_Modification of polarization_ to which Fresnel was led by his -general views, accounted for the Rule respecting the _Angle at which -light is polarized_, discovered by Sir D. Brewster[16\2]. The -conceptions of the theory pointed out peculiar _Modifications_ of -the phenomena when _Newton's rings_ were produced by polarised -light, which modifications were {90} ascertained to take place in -fact, by Arago and Airy[17\2]. When the beautiful phenomena of -_Dipolarized light_ were discovered by Arago and Biot, Young was -able to declare that they were reducible to the general laws of -_Interference_ which he had already established[18\2]. And what was no -less striking a confirmation of the truth of the theory, _Measures_ -of the same element deduced from various classes of facts were found -to coincide. Thus the _Length_ of a luminiferous undulation, -calculated by Young from the measurement of _Fringes_ of shadows, -was found to agree very nearly with the previous calculation from -the colours of _Thin plates_[19\2]. - -[Note 15\2: See _Hist. Ind. Sc._ b. ix. c. xii.] - -[Note 16\2: _Ib._ c. xi. sect. 4.] - -[Note 17\2: See _Hist. Ind. Sc._ b. ix. c. xiii. sect. 6.] - -[Note 18\2: _Ib._ c. xi. sect. 5.] - -[Note 19\2: _Ib._ c. xi. sect. 2.] - -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. - -12. In the preceding Article I have spoken of the hypothesis with -which we compare our facts as being framed _all at once_, 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 _added_ 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 {91} -'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. - -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 _tend to simplicity_ 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. - -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 _no_ combination of _equable_ 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 {92} epicycles had -been thus accumulated, they all disappeared and gave way to the -simpler conception of an _elliptical_ 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 _elliptical_ theory. Astronomers could -not but suppose themselves in a wrong path, when the prospect grew -darker and more entangled at every step. - -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. - -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. {93} 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 -_that_, 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 _phlogiston_ 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. - -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, {94} which is already assumed in uniaxal -crystals[20\2], 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. - -[Note 20\2: _Hist. Ind. Sc._ b. ix. c. xi. sect. 5.] - -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 {95} the -machine, but its parts do not fit. They hold together only while he -presses them. This is not the character of truth. - -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[21\2], 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 _one class_ of -facts are found to explain _another class_ 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. - -[Note 21\2: _Hist. Ind. Sc._ b. x. c. iv.] - -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 _Consilience of Inductions_ from different and -separate classes of facts;--and the progressive _Simplification of -the Theory_ 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 {96} 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. - -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 _successive -generalization_. This is a subject of great importance, and -deserving of being well illustrated; it will come under our notice -in the next chapter. - - - -{{97}} -CHAPTER VI. - -OF THE LOGIC OF INDUCTION. - - -APHORISM XVII. - -_The_ Logic of Induction _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._ - -APHORISM XVIII. - -_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_ Formulæ; _and every -train of inductive inference to be sound, must be capable of -resolution into a scheme of such Formulæ, legitimately constructed._ - -APHORISM XIX. - -_The_ inductive act of thought _by which several Facts are -colligated into one Proposition, may be expressed by saying:_ The -several Facts are exactly expressed as one Fact, if, and only if, we -adopt the Conceptions and the Assertion _of the Proposition._ - - -APHORISM XX. - -_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_ {98} _indefinitely repeated: and -these successive processes are the_ Steps _of Induction, or of_ -Generalization, _from the lowest to the highest._ - -APHORISM XXI. - -_The relation of the successive Steps of Induction may be exhibited -by means of an_ Inductive Table, _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._ - -APHORISM XXII. - -_The Logic of Induction is the_ Criterion of Truth _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._ - -APHORISM XXIII. - -_The distinction of_ Fact _and_ Theory _is only relative. Events and -phenomena, considered as Particulars which may be colligated by -Induction, are_ Facts; _considered as Generalities already obtained -by colligation of other Facts, they are_ Theories. _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._ - - -1. THE 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 -_ascending from particular to general_ propositions, and from these -to propositions still more general;--of {99} truths _included_ in -other truths of a higher degree of generality;--of different _stages -of generalization_;--and of the _highest step_ 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. - -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 _included_ 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 _included_ in certain propositions concerning the movements -of those luminaries with respect to the stars. But all these -propositions are really _included_ 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 _included_ 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 _included_ 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. {100} - -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 ⏟ or ⎵,) 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 -_genealogical tree_ 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. - -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 -_Induction_. 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 _union_ 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 _new -conception_, a {101} 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. - -4. The principal features of the progress of science spoken of in -the last chapter are clearly exhibited in these Tables; namely, the -_Consilience of Inductions_ 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 _Consilience_. Accordingly, in the Table of -Astronomy we find that the columns which contain the facts and -theories relative to the _sun_ and _planets_, after exhibiting -several stages of induction within themselves, are at length -suddenly connected with a column till then quite distinct, -containing the _precession of the equinoxes_. In like manner, in the -Table of Optics, the columns which contain the facts and theories -relative to _double refraction_, and those which {102} include -_polarization by crystals_, 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 _Consilience_. - -5. The constant _Tendency to Simplicity_ 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. - -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 _Discoverer_ 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 {103} 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. - -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 _discovery_. -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 -_verification_ 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 {104} of the conjunction, we establish the whole system of -truths, however wide and various it may be. - -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 _if_ 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 _is_ true, may be ascertained, by the -same kind of attention, when this proposition is resolved into _its_ -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. - -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 {105} 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. - -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 _Logic of Induction_. By _Logic_ has generally been meant -a system which teaches us so to arrange our {106} reasonings that -their truth or falsehood shall be evident in their form. In -_deductive_ 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 _Syllogism_; and this _form_, -along with the rules which belong to it, does in fact supply us with -a criterion of deductive or demonstrative reasoning. The _Inductive -Table_, 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 _are_ so included,--that the general truth -_is_ so constituted,--then affords little room for errour, with -moderate attention and clearness of thought. - -11. We may find an example of this _act of attention_ 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. {107} -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 _seen to be consistent_ 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. - -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, _first_, the diurnal revolution just spoken of; -_second_, the motions of the moon among the fixed stars; _third_, -the motions of the planets with reference to the fixed stars and the -sun; _fourth_, the motion of the sun in the ecliptic. And the scheme -being clearly conceived, we _see_ that all the particular facts -_are_ 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. - -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 {108} 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;--_first_, -that the sun's mean force on different planets follows the specified -variation (which is proved from Kepler's third law); _second_, 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); _third_, 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 _seen_ to agree with each of these particular -propositions, and thus is fully established. - -12. But when we say that the more general proposition _includes_ 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 _in a new -light_. 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 _sum_ 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 {109} -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 _seen to be consistent_ 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. - -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. - -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 {110} diurnal motion; and the latter is more simple.' But -these verbal statements are to be understood as mere hints[22\2]: -they cannot supersede the necessity of the student's contemplating -for himself the mechanical principles and the nature of motion thus -referred to. - -[Note 22\2: In the Inductive Tables they are marked by an -asterisk.] - -14. In the common or Syllogistic Logic, a certain _Formula_ 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? - -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 _included_ 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 -_evidence_ when the proposition is once suggested; but the Inductive -step consists in the _suggestion_ 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 _ellipse_ 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 {111} 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. - -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. - -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.' - -This Formula has been adopted in stating the Inductive Propositions -which constitute the basis of the science of Mechanics, in a work -intitled _The Mechanical Euclid_. The fundamental truths of the -subject are expressed in _Inductive Pairs_ of Assertions, consisting -each of a Definition and a Proposition, such as the following: - -DEF.--A _Uniform Force_ is that which acting in the direction of the -body's motion, adds or subtracts equal velocities in equal times. - -PROP.--Gravity is a Uniform Force. - -Again, - -DEF.--Two _Motions_ are _compounded_ when each produces its separate -effect in a direction parallel to itself. - -PROP.--When any Force acts upon a body in motion, the motion which -the Force would produce in the {112} body at rest is compounded with -the previous motion of the body. - -And in like manner in other cases. - -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. - -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 _only_ 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. -{113} - -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 _can_ be true, -_is_ 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, _and only if_, we adopt the -Conception and the Assertion' of the inductive inference. - -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 _one step_ in our inductive -inference, may imply _many steps_ of demonstrative proof. The -connexion is this, that the particular case is included in the -general one, that is, may be _deduced_ 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. {114} - -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 -_beginning_ of the demonstration. In an inductive inference, the -Definitions and Principles are the _final result_ 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 _hypothesis_ -of the deductive reasoning, is the _inference_ 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. - -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 {115} exist: but -then it shows that it _is_ sagacity, by also producing the -demonstration. - -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 _not_ Induction. - -19. Such Tabular arrangements of propositions as we have constructed -may be considered as the _Criterion of Truth_ 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 {116} 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. - -20. At any one of these steps of Induction in the Table, the -inductive proposition is a _Theory_ with regard to the Facts which -it includes, while it is to be looked upon as a _Fact_ with respect -to the higher generalizations in which it is included. In any other -sense, as was formerly shown, the opposition of _Fact_ and _Theory_ -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 _Facts_, 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 -_premiss_ of one syllogism and the _conclusion_ 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. - -21. To obviate mistakes I may remark that the terms _higher_ and -_lower_, when used of generalizations, are unavoidably represented -by their opposites in our Inductive Tables. The highest -generalization is that {117} which includes all others; and this -stands the lowest on our page, because, reading downwards, that is -the place which we last reach. - -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. - - - -{{118}} -CHAPTER VII. - -OF LAWS OF PHENOMENA AND OF CAUSES. - - -APHORISM XXIV. - -_Inductive truths are of two kinds_, Laws of Phenomena, _and_ -Theories of Causes. _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._ - - -1. IN 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 _what_ takes place, not _why_ 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 {119} said of many other sciences. -The discovery of _the Laws of Phenomena_ 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 _Causes_ of the phenomena. - -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. - -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 _History_, -distinguished the two portions of the science by certain terms. I -have thus spoken of _Formal_ Astronomy and _Physical_ Astronomy. The -latter phrase has long been commonly employed to describe that -department of Astronomy which deals with {120} 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 _forms_ of our apprehension of -phenomena. The laws of phenomena may be considered as _formulæ_, -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. - -3. What _kinds of cause_ 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. {121} - -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. - -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 -{122} these powers are not on that account less real, nor a less fit -and worthy subject of scientific inquiry. - -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 _mechanical_ -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. - -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[23\2] is directed, not to {123} 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[24\2], '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. - -[Note 23\2: Eleventh, Twelfth, and Thirteenth Series of Researches, -_Phil. Trans._ 1837 and 8.] - -[Note 24\2: Art. 1318.] - -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 {124} expressing this -conviction[25\2], 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. - -[Note 25\2: Multa me movent, &c.,--Pref. to the _Principia_, already -quoted in the _History_.] - -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[26\2];--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 {125} 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 _real_ only so far as they are -_polar_. 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. - -[Note 26\2: _Hist. Ind. Sc._ b. xi. c. ii.] - -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[27\2].' 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 {126} 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. - -[Note 27\2: Comte, _Philosophie Positive_.] - -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. - -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 {127} 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. - -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. - -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 _laws of phenomena_, and their -_causes_. 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 {128} 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. - -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 **work. 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. - - - -{{129}} -CHAPTER VIII. - -OF ART AND SCIENCE. - - -APHORISM XXV. - -_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._ - -APHORISM XXVI. - -_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._ - - -1. THE 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 _Science_ 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. - -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 {130} -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 _every_ -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 {131} 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. - -2. We here mean by _Science_, 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 -_practical Arts_ of life, the points of difference are sufficiently -manifest. The object of Science is _Knowledge_; the object of Art -are _Works_. 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 _what_ is done, then comes the question _why_ 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 {132} multiplied; complex, and -varied, the results of one or two simple and general laws. - -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 _Instinct_. 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 _Insight_. 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. - -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 _that_ 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, {133} 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. - -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 _knows_ 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. - -6. The real state of the case is, that the principles which Art -_involves_, Science alone _evolves_. 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 _unfolded_ by our speculative powers into -{134} systematic shape, become Science, is true; but it is precisely -this process of _development_ 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. - -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. - -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 {135} 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. - - - -{{136}} -CHAPTER IX. - -OF THE CLASSIFICATION OF SCIENCES. - - -1. THE 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. - -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 _History_ 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 {137} natural and fundamental -element;--namely, the _Ideas_ 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 _Ideas_, 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 _with regard -to it_, 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 _Number_ is a mere modification of the Idea of Time, -and _Force_ 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 _precede_ -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. - -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[28\2] -led us to the consideration {138} 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 _History_ 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. - -[Note 28\2: _Hist. Ind. Sc._ b. xvii. c. v. sect. 2.] - -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. {139} - -The Classification of the Sciences is given over leaf. - -A few remarks upon it offer themselves. - -The _Pure_ Mathematical Sciences can hardly be called _Inductive_ -Sciences. Their principles are not obtained by Induction from Facts, -but are necessarily assumed in reasoning upon the subject matter -which those sciences involve. - -The Astronomy of the Ancients aimed only at explaining the motions -of the heavenly bodies, as a _mechanism_. Modern Astronomy, explains -these motions on the principles of Mechanics. - -The term _Physics_, 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 -_Physical_ applied to any science and opposed to _Formal_, 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. - -The term _Metaphysics_ is applied to subjects in which the Facts -examined are emotions, thoughts and mental conditions; subjects not -included in our present survey. {140} - - Fundamental Ideas or Sciences. Classification. - Conceptions. - -Space Geometry ) -Time ) Pure Mathematical -_Number_ Arithmetic } -Sign Algebra ) Sciences. -Limit Differentials ) -_Motion_ Pure Mechanism } Pure Motional - Formal Astronomy } Sciences. - -Cause -_Force_ Statics ) -_Matter_ Dynamics ) Mechanical -_Inertia _ Hydrostatics } -_Fluid Pressure_ Hydrodynamics ) Sciences. - Physical Astronomy ) - -Outness -Medium _of Sensation_ Acoustics ) -Intensity _of Qualities_ Formal Optics ) Secondary -_Scales of Qualities_ Physical Optics } Mechanical - Thermotics ) Sciences. - Atmology ) (_Physics_.) -Polarity Electricity ) Analytico-Mecha- - Magnetism } nical Sciences. - Galvanism ) (_Physics_.) - -Element (_Composition_) -_Chemical_ Affinity -Substance (_Atoms_) Chemistry Analytical Science. -Symmetry Crystallography } Analytico-Classifi- -Likeness Systematic Mineralogy } catory Sciences. -_Degrees of Likeness_ Systematic Botany ) - Systematic Zoology } Classificatory -_Natural_ Affinity Comparative Anatomy ) Sciences. -(_Vital Powers_) -Assimilation -Irritability -(_Organization_) Biology Organical Sciences. -Final Cause -Instinct -Emotion Psychology (_Metaphysics_.) -Thought -Historical Causation Geology ) - Distribution of ) Palætiological - Plants and Animals } Sciences. - Glossology ) - Ethnography ) -First Cause Natural Theology. - - - - -[*Transcriber's Note: The two following tables were inserted on -separate sheets at this point. They were structured as trees, but -have here been converted into a diagram to be read from left to -right, and an associated key. Arrows have replaced the brackets -Whewell used. In the original, the names of discoverers and comments -about inadequate explanations were printed in red.] - -INDUCTIVE TABLE OF ASTRONOMY - -a r ) { ) - ) { ) -b → j s ) { J ) - ) → z { ) -c → k ) { ) - ) ) -d → l t ) ) - ) -e → m ) ) { b1 → c1 → m1 ) - u ) → A E → H ) → M { N → Q → W ) -f → n ) ) { b1 → d1 → n1 ) ) - ) ) ) - ) { R → X b1 → e1 ) ) ) -g → o v → B F → I K ) { ) ) ) - ) { O S → Y b1 → f1 )→ o1 ) ) - ) { ) ) ) - ) { S → Z b1 → g1 ) ) )→ u1 -h → p w → C G L ) )→ t1 ) - P T b1 → h1 → p1 ) ) - ) ) - q x → D b1 i1 → q1 ) ) - ) ) -i y b1 j1 → r1 ) ) - ) ) - U → a1 b1 k1 → s1 ) ) - ) ) - V b1 → l1 ) ) - - -a = THE EARTH appears to be immovable. -b = THE STARS keep their relative places in the vault of the sky, -and with the Sun and Moon, rise, move, and set. -c = THE MOON'S bright part is of the shape of a ball enlightened by -the Sun. -d = THE MOON'S ECLIPSES occur when she is full. -e = ECLIPSES OF THE SUN AND MOON often occur. -f = THE MOON rises and sets at different times and places. Her -course among the Stars varies. -g = THE PLANETS are morning and evening Stars: are direct, -stationary, and retrograde. -h = THE SUN rises, culminates, and sets in different times and -places at different seasons: different CONSTELLATIONS are visible at -night. -i = THE TIDES ebb and flow. -j = Chald^ns. _The Sphere of the Heavens appears to make a Diurnal -Revolution._ -k = Greeks. The Moon receives her light _from the Sun_. -l = Greeks. The Moon's Eclipses are caused by the _Earth's shadow._ -m = Chald^ns. The Moon's Eclipses follow certain cycles. -n = Greeks. The Moon appears to revolve monthly in an _oblique -orbit_, which has _Nodes_ and an _Apogee_. -o = Chaldeans. The Planets have proper motions and certain _Cycles_. -p = Pythagoras. The Sun appears to move annually in an _Ecliptic_ -oblique to the diurnal motion. -q = The places of Stars are determined by their Longitude measured -from the Equinox. -r = The forms and dist^s of known parts of the earth are such as fit -a convex surface. -s = The visible Pole of the Heavens rises or drops as we travel N. -or S. -t = The boundary of the Earth's shadow is always circular. -u = By observations of Eclipses, the Moon's Nodes and Apogee -revolve, and her motion is unequal according to certain laws. -v = By observations of the Planets, their progressions, stations, -and retrogradations. -w = By observations of the Sun, his motion is unequal according to -certain laws. -x = By observations, Longitudes of Stars increase. -y = By observations, the Tides depend on the Moon and Sun. -z = Aristotle? The Earth is a _Globe_, about which the Sphere of the -Heavens performs a _Diurnal Revolution_. -A = Hipparchus. The Moon appears to move in an _Epicycle_ carried by -a Deferent: the _Velocity of Apogee_ and _Nodes_ determined. -B = Eudoxus. The Planets appear to move in Epicycles carried by -_Deferents_. -C = Hipparchus. The Sun appears to move in an _Eccentric_, his -_Apogee_ being fixed. -D = Hippar. There is a _Precession of the Equinoxes_. -E = By additional observations, the Moon's motion has another -inequality. Evection. -F = By additional observations, the Planets' motions in their -Epicycles are unequal according to certain laws. -G = By additional observations, the Sun's Apogee moves. Albategnius. -H = Ptolemy. The Moon appears to move in an _Epicycle_ carried by an -_Eccentric_. -I = Ptolemy. The Planets appear to move in _Epicycles_ carried by -_Eccentrics_. -J = * _By the nature of motion_, the apparent motion is the same -whether the Heavens or the Earth have a diurnal revolution: the -latter is _simpler_. -K = * _By the nature of motion_, the apparent motion is the same if -the Planets revolve about the Sun: this is _simpler_. -L = * _By the nature of motion_, the apparent motion of the Sun is -the same if the Earth revolve round the Sun: this is _simpler_. -M = * Copernicus. 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 _Heliocentric Theory_ governs -subsequent speculations. -N = Retaining Moon's Eccentric and Epicycle; By additional -observations, the Moon's motion has other inequalities. -O = Retaining but referring to the Sun as center the Planets' -Epicycles and Eccentrics and the annual Orbit; -P = Retaining obs^ns. Earth's Aphelion revolves. -Q = Tycho. Moon's _Variation_; _Unequal Motion of Node_; _Change of -Inclination_. -R = By calc^ns. of the periodic times and distances. -S = By additional observations and calculations. -T = Planets' Aphelia revolve. Jupiter and Saturn's motions have an -inequality dep^g. on their mutual positions. -U = THE WEIGHT of bodies dimin^s in going towards the Equator. -V = THE SATELLITES of Jupiter and Saturn revolve according to -Kepler's Laws. -W = Horrox. Halley. The Moon moves in an _Ellipse_ with variable -_axis_ and _eccentricity_. -X = Kepler. Distances cubed are as times squared. -Y = Kepler. Areas as described by Planets are as times. -Z = Kepler. Curves described by Planets are as ellipses. -a1 = Newton. Earth is oblate. -b1 = * By Mechanics. -c1 = * Newton. Moon is attracted by the Earth. Fall of heavy bodies. -d1 = * Newton. Moon's inequalities produced by attraction of Sun. -e1 = * Newton. Wren. Hooke. Sun's force on different Planets is -invers. as square of distance. -f1 = * Newton. Planets are attracted by the Sun. -g1 = * Newton. Sun attracts Planets invers. as square of distance. -h1 = * Newton. These inequalities are produced by mutual attraction -of the Planets. -i1 = Precession of Equinoxes is produced by attraction of Moon and -Sun on oblate Earth. -j1 = Tides are produced by attraction of Moon and Sun on -Sea. Explanation imperfect. -k1 = Diminution of gravity and oblateness of Earth arise from -attractions of parts. -l1 = * Newton. Jupiter and Saturn attract their Satellites inversely -as the square of the distance, and the Sun attracts Planets and -Satellites alike. -m1 = Newton. Earth attracts Moon invers. as square of distance. -n1 = Newton. Sun attracts Moon. -o1 = Newton. Sun attracts Planets inversely as the square of the -distance. -p1 = Newton. Planets attract each other. -q1 = * Newton. Moon and Sun attract parts of the Earth. -r1 = * Newton. Moon and Sun attract the Ocean. -s1 = * Newton. Parts of the Earth attract each other. -t1 = Newton. All parts of the Earth, Sun, Moon. and Planets -attract _each other_ with Forces inversely as the square of the -distance. -u1 = Newton. THE THEORY OF UNIVERSAL GRAVITATION. (All bodies -attract each other with a Force of _Gravity_ which is inversely as -the squares of the distances.) - - -INDUCTIVE TABLE OF OPTICS - -First Facts. The common and obvious Phænomena of Light and Vision. - -By the _Idea of a Medium_ Light and Vision take place by means of -something intermediate. - -First Law of Phænomena. The effects take place in straight lines -denoted by the Term _Rays_. - -Facts of - -a → m h1 ) ( ) ) - ) ( ) ) -b → n ) ) i1 ) ( ) ) - )→ r ) ) ( C1 ) ) -c o ) )→ K ) ) ( ) → F1 ) - ) ) j1 )→ x1 ( ) ) -d p ) L S ) ) ( ) ) - ) ) ) -e s → M ) T h1 ) D1 ) ) ) → H1 ) - )→ ) ) ) ) -f t ) U k1 ) ( ) → G1 ) ) - ( E1 ) ) ) -g ) ( u → W l1 ) ( ) ) ) - ) ( ) ) ) - ) ( v → X l1 )→ y1 ) ) - )→ q ( ) ) ) - ) ( w → Y j1 ) ) ) - ) ( ) - ) ( x → Z ) ) ) ) - ( ) m1 ) ) ) - ( y → a1 ) ) ) ) - ( ) ) → I1 ) - ( z n1 )→ z1 ) ) - ( ) ) ) → K1 - ( A N b1 o1 ) ) ) - q ←( ) ) ) - ( B O p1 ) ) ) - ( ) - ( C ) c1 q1 ) ) ) - ( ) V ) ) ) - ( D ) d1 q1 ) ) ) - ( ) ) ) - ( E j1 )→ A1 ) ) - ( ) ) ) - ( F P e1 ) ) ) ) - ( ) r1 ) ) ) - ( G f1 ) ) ) ) - ( ) → J1 ) - ( H Q s1 ) - ) -h ( R g1 t1 ) ) - ( ) ) -i ( I u1 ) ) - ( ) ) -j ( v1 )→ B1 ) - ) ) -k ( w1 ) ) - ( J ) ) -l ( w1 ) ) - - -a = Rays falling on water, specula, &c. -b = Rays passing through water, glass, &c. Measures. Ptolemy. -c = Colours seen by prisms, in rainbow, &c. -d = Colours in diff. transp. Substances. Optical instrum^ts. -e = Two Images in Rhomb. of Calcspar. -f = Two Images in other crystals. -g = Two Rhombs of Calcspar make 4 images alternately appear and -disappear. -h = Fringes of shadows. Grimaldi. Hook. Newton. -i = Spectra of gratings. Fraunhofer. -j = Colours of striated surfaces. Coventry's Micromet^r. Barton's -Buttons. Young. -k = Colours of _thick Plates_. Newton. -l = Colours of _thin Plates_. Hook. Newton. -m = Euclid. Ang. Inc. equals Ang. Reflection. -n = Snell. Sin. Refr. to Sin. Inc. in giv. _Ratio_ in same med. -o = By measures of Refraction. -p = Dispersion of colours is same when Refr. is diff. Measures. -Dollond. -q = Huyghens. Rays of light have four Sides with regard to which -their properties alternate. -Newton. Idea of _Polarization_ introduced, which governs subsequent -observations. _Dipolarization_ with Colours. -r = Newt. Refr. R^o. is diff. for diff. colours, but in same med. is -const. for each colour. -s = Measures. Huyghens. -t = Double Refr. in biaxal crystals. Brewster. -u = Rays are polarized by Calcspar, Quartz, &c. -v = Rays are polarized by biaxal crystals. -w = Rays are polarized by Tourmaline, Agate, &c. -x = Rays are polarised by Refl. at glass. -y = Rays are polarized by transmission through glass. -z = Variable q^y. of pol. refl. light paral. plane of Refl. Arago. -A = Variable q^y. of pol. refl. light perp. plane of Refl. -B = Whole light reflected by internal Refl. -C = Pol. Rays through uniaxal crystals give colours. Rings. -Wollaston. -D = Pol. Rays through biaxal crystals give colours. Arago. -E = Pol. Rays. through imperf. crystallized bodies give colours. -(Glass strained, jellies prest.) Brewster. -F = Pol. Rays in axis of Quartz give a peculiar set of colours. -Plane of Pol^n twisted diff^ly. for diff. colours. Biot. Arago. -G = Pol. Rays oblique in Quartz give peculiar rings, &c. -H = Pol. Rays through certain liquids give a peculiar set of colours. -I = The Laws of these Phænomena were never discovered till Theory -had indicated them. -J = _Newton's Scale of Colours._ -_Fits_ of Rays. Newton. -K = Dollond. -L = Prop^n of Ref. R^s is diff. in diff. med. _Achromatism_. -M = Huygh^s. Law of Double Ref. exp. by a spheroid. -N = Change of plane of pol. by Refl. Arago -O = Light is _circularly pol._ by 2 Refl. in _Fresnel's Rhomb._ -Fresnel. -P = + in dir^n of plagihedral faces. J. Herschel. -Q = Plane of Pol^n. twisted. Biot -R = Fringes obliterated by stopping light from one edge or -interposing a glass. Young. Arago. -S = Ratios not reconcilable. _Irrationality_. Blair. -T = Fresnel. -U = Law exp. by surface of 4 dim^s. -V = Optical classification of crystals. Brewster. -W = Newt. Malus. Ray pol. in _principal plane_ of Rhomb.; and perp. -to it. -X = Brews. Biot. Ray pol. in plane bisecting ang. at axis; and perp. -to it. -Y = Brews. Ray pol. paral. to axis. -Z = Malus. Ray pol. in plane of Refl. for _given angle_. -a1 = Malus. Ray partially pol. in plane perp. to plane of -Reflection. -b1 = None Refl^d. if tan. ang. equal Refr. R^o. Brewster. -c1 = Tint is as sq. of sin. Biot. -d1 = Tint is as sin. α sin. β. Brewster. Biot. -Lemniscates. J. Herschel. -e1 = * By interf. of resolved undul^ns. of 2 rays circularly pol^d. -in opp. directions. * Fresnel. -f1 = * By interf. of resolved undul^ns. of 2 rays elliptically -pol^d. in opp. directions. * Airy. -g1 = * By interf. of rays from edges. Young. -h1 = * Refl. produced by spherical undul^ns. -i1 = * Refr. produced by spherical undul^ns. of diff. vel. for diff. -colour. -j1 = † Explanation imperfect. -k1 = * Refr. produced by curved surf. undul^ns. -l1 = * Pol^n. being prod. by resolution of transv^e undul^ns. -m1 = * Polarization being produced by resolution of transverse -undulations. -n1 = * Undul^ns. being com^d. acc. to laws of elastic bodies. -o1 = * Undul^ns. being com^d. acc. to a certain hypothesis. -p1 = * Impossible formulæ being interpreted by analogy. -q1 = * By interf. of resolved parts of transverse undul^ns. -r1 = * Same hypothesis explains separation of rays in axis and -oblique. † Explanation imperfect. * Maccullagh. -s1 = † Explan. wanting. -t1 = * By interf. of rays from all parts. * Young. * Fresnel. -u1 = * By interf. of undul^ns. from all parts. * Fraunhofer. -v1 = * By interf. of rays from striæ. * Young. -w1 = * By interf. of undul^ns. from two surfaces. * Young. -x1 = * Huyghens. Reflection and Refraction are propagation of -undulations. -y1 = * Young. * Fresnel. Polarization in crystals is transverse -undulations. -z1 = * Fresnel. Polarization in Reflection and Refraction is -transverse undulations. -A1 = * Fresnel. * Arago. Dipolarized Colours are produced by -interference of Rays polarized in same plane; length of undulation -being different for different colours. -B1 = * Young. * Fresnel. Colours of Fringes, Gratings, Striæ, thick -Plates, thin Plates &c. are produced by interference of undulations; -length of undulation being different for different colours. -C1 = * Undulations being propagated by the uniform elasticity of -each medium. -D1 = * Undul^ns. prop. by el^y. of medium diff. in 2 diff. dir^ns, -(_axis of crystal._) -E1 = * Undul^ns. being prop. by elasticity of med. diff. in 3 diff. -directions (_axes_). -F1 = Young. Reflection and double Refraction are propagation of -undulations by crystalline elasticity. -G1 = * Fresnel. Double Refr. and Pol. arise from same cause. -H1 = Young. Fresnel. Light is transverse undulations propagated in -media by elasticity dependent on axis, when crystalline. -I1 = Fresnel. Light is transverse undul^ns. transmitted from one -med. to another according to probable hypotheses. -J1 = Young. Fresnel. Colours result from interferences, the lengths -of undulation being different for different colours. -K1 = THE UNDULATORY THEORY OF LIGHT. - - - - -{{141}} -NOVUM ORGANON RENOVATUM. - - -BOOK III. - -OF METHODS EMPLOYED IN THE FORMATION OF SCIENCE. - -CHAPTER I. - -INTRODUCTION. - - -APHORISM XXVII. - -_The Methods by which the construction of Science is promoted are,_ -Methods of Observation, Methods of obtaining clear Ideas, _and_ -Methods of Induction. - - -1. IN 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 {142} contain still more -valuable suggestions, and indicate a more practical acquaintance -with the subject. Among these, I must especially distinguish Sir -John Herschel's _Discourse on the Study of Natural Philosophy_. 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. - -2. But, in truth, we must acknowledge, before we proceed with this -subject, that, speaking with strictness, an _Art of Discovery_ 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. - -3. In Book II. 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 {143} 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 _Methods_, of which in the present -Book we must give a brief view. In this more technical form, the -observation of facts involves the _Measurement of Phenomena_; 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 _Methods of Observation_, and _Methods of Induction_, 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. - -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 _Laws of Phenomena_. A higher and ulterior -step remains behind, and follows in natural order the discovery of -Laws of Phenomena; namely, the _Discovery of Causes_; 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 _Applications_ of our Discoveries; -including in the phrase, _Verifications_ 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. - (1.) Decomposition of Facts; - (2.) Measurement of Phenomena; - (3.) Explication of Conceptions; - (4.) Induction of Laws of Phenomena; - (5.) Induction of Causes; - (6.) Application of Inductive Discoveries. - -5. Of these six processes, the methods by which the second and -fourth may be assisted are here our {144} 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. - -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 _Methods_ by which this work, in -its widest sense, is executed, and these I shall term Methods of -Observation. - - - -{{145}} -CHAPTER II. - -OF METHODS OF OBSERVATION. - - -APHORISM XXVIII. - -_The Methods of Observation of Quantity in general are_, Numeration, -_which is precise by the nature of Number; the_ Measurement of Space -_and_ of Time, _which are easily made precise; the_ Conversion of -Space and Time, _by which each aids the measurement of the other; -the_ Method of Repetition; _the_ Method of Coincidences _or_ -Interferences. _The measurement of Weight is made precise by the_ -Method of Double-weighing. _Secondary Qualities are measured by -means of_ Scales of Degrees; _but in order to apply these Scales, -the student requires the_ Education of the Senses. _The Education of -the Senses is forwarded by the practical study of_ Descriptive -Natural History, Chemical Manipulation, _and_ Astronomical -Observation. - - -1. I 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. - -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. _Observations are never perfect._ For we -{146} 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 _limb_ 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. - -Still, in many cases, good Methods can remove very much of this -inaccuracy, and to these we now proceed. - -3. (I.) _Number_.--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 {147} 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 _unit_ 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[1\3], 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. - -[Note 1\3: _Hist. Ind. Sc._ b. xvi. c. vii.] - -4. (II.) _Measurement of Space._--Of quantities admitting of -_continuous_ 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 _unit_ 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 _fraction_. But -besides this measurement of linear space, {148} 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 -_arbitrary_ unit, for there is a _natural unit_, the total -circumference, to which all arcs may be referred. For the sake of -convenience, the whole circumference is divided into 360 parts or -_degrees_; and by means of these degrees and their parts, all arcs -are expressed. The _arcs_ are the measures of the _angles at the -center_, and the degrees may be considered indifferently as -measuring the one or the other of these quantities. - -5. In the History of Astronomy[2\3], 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 -_quadrants_,) and accuracy to the divisions of the _limb_[3\3]. But -the application of the _telescope_ to the astronomical quadrant and -the fixation of the center of the field by a _cross_ 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 {149} by applying to the -telescope a _micrometer_ which might subdivide the smaller divisions -of the arc. - -[Note 2\3: _Hist. Ind. Sc._ b. iii. c. iv. sect. 3.] - -[Note 3\3: _Ib._ b. vii. c. vi. sect. 1.] - -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 _stepping_ round the circle, the partial -arcs were made to bear their exact relation to the whole -circumference. - -7. Astronomy is not the only science which depends on the -measurement of angles. Crystallography also requires exact measures -of this kind; and the _goniometer_, 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. - -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 _foot_, a _cubit_, a -_fathom_; 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 {150} 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 _metres_. 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. - -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[4\3]. - -[Note 4\3: On the precautions employed in astronomical instruments -for the measure of space, see Sir J. Herschel's _Astronomy_ (in the -_Cabinet Cyclopædia_,) Arts. 103-110.] - -10. (III.) _Measurement of Time_.--The methods of measuring Time are -not so obvious as the methods of {151} 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. - -11. What is the _natural unit_ 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 _his_ motions. Accordingly the solar day (the -_mean_ solar day) is divided into 24 hours, {152} 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 _standard_ of time (and the -standard of space in like manner) equally answers its purpose, -whether or not it coincides with any _whole number_ of units. - -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 _transit instrument_ with which this -is done being adjusted with all imaginable regard to accuracy[5\3]. - -[Note 5\3: On the precautions employed in the measure of time by -astronomers, see Herschel's _Astronomy_, Art. 115-127.] - -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. - -14. (IV.) _Conversion of Space and Time._--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 _space_ which any point -describes, is _proportional_ to the _time_ 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 {153} space, we may often obtain more convenient and -precise measures, than we can by measuring directly the element with -which we are concerned. - -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[6\3] 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 _times_ of the transits -of successive stars across some visible mark in our own meridian, -determine the _angular distances_ of the meridian circles of all the -stars from one another. - -[Note 6\3: A _meridian_ is a circle passing through the poles about -which the celestial sphere revolves. The meridian _of any place_ on -the earth is that meridian which is exactly over the place.] - -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. - -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 -{154} 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. - -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 {155} 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. - -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 -_not proportional_ 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. - -17. (V.) _The Method of Repetition in Measurement._--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 -{156} 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. - -In the latter of these instances, we have the principle of -repetition truly exemplified, because (as has been justly observed -by Sir J. Herschel[7\3],) 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 -_clamp_) 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 _nine_ times be found to go twice round the -circle, it must be _exactly_ 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. - -[Note 7\3: _Disc. Nat. Phil._ art. 121.] - -18. Connected with the principle of repetition, is the _Method of -coincidences_ or _interferences_. 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 {157} 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 _coincides_ with a certain division of the -first, (the 5th,) it is certain that 2 and _three-tenths_ is the -_exact_ 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 -_zero_ 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 -_Vernier_, from the name of its inventor. - -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 150/151 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 {158} 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. - -We have hitherto spoken of methods of measuring time and space, but -other elements also may be very precisely measured by various means. - -20. (VI.) _Measurement of Weight._--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. - -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 _Method -of double weighing_; according to which the standard weights, and -the body which is to be weighed, are successively put in the _same_ -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[8\3]. - -[Note 8\3: For other methods of measuring weights accurately, see -Faraday's _Chemical Manipulation_, p. 25.] - -21. There is no natural _Standard_ of weight. The conventional -weight taken as the standard, is the weight of a given bulk of some -known substance; for instance, a _cubic foot of water_. 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 -_distilled_ water. - -22. (VII.) _Measurement of Secondary Qualities._--We have already -seen[9\3] that secondary qualities are estimated by means of -conventional Scales, which refer {159} 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 _in unison_ 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 _matches_. 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. - -[Note 9\3: B. iii. c. ii. Of the Measure of Secondary Qualities.] - -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 _howl_; and the exactness of the unison is known by this -howl vanishing. - -24. (VIII.) _Manipulation._--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 {160} -essentially dependent for success on mere manipulation[10\3].' 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 _Chemical Manipulation_, may be seen by -reference to Dr. Faraday's work on that subject. - -[Note 10\3: Faraday's _Chemical Manipulation_, p. 3.] - -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 -_Treatise on New Philosophical Instruments_, published in 1813, is -an excellent model of the kind of resource {161} 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 _irregular_ 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, _when_ 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. - -26. (IX.) _The Education of the Senses._--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[11\3], when we find such terms as _tin-white_ or -_pinchbeck-brown_, 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 _glassy lustre_, _fatty lustre_, _adamantine -lustre_, denote certain kinds of {162} 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. - -[Note 11\3: B. viii. c. iii. Terminology.] - -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 _terminology_: -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. - -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[12\3]. 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 {163} 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. - -[Note 12\3: _Hist. Ind. Sc_. b. xvi. c. iv. sect. 2.] - -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. - -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. - - - -{{164}} -CHAPTER III. - -OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS; _and first_ OF -INTELLECTUAL EDUCATION. - - -APHORISM XXIX. - -_The Methods by which the acquisition of clear Scientific Ideas is -promoted, are mainly two_; Intellectual Education _and_ Discussion -of Ideas. - -APHORISM XXX. - -_The Idea of Space becomes more clear by studying_ Geometry; _the -Idea of Force, by studying_ Mechanics; _the Ideas of Likeness, -of Kind, of Subordination of Classes, by studying_ Natural History. - -APHORISM XXXI. - -Elementary Mechanics _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._ - -APHORISM XXXII. - -Natural History _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._ {165} - - -THE 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 _Methods_ of acquiring clear Ideas. These two ways are -Education and Discussion. - -1. (I.) _Idea of Space._--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 _similar triangles_ 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 _the sphere with its circles_ -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 _pure_[13\3] _doctrine of -motion_, were required as an introduction to the theory of -Epicycles: the properties of _conic sections_ were needed, as a -preparation for the discoveries of Kepler. And not only was it -necessary that men should possess a _knowledge_ of certain figures -and their properties; but it was equally necessary that they should -have the _habit of reasoning_ 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 {166} 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 _discoursing_ -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. - -[Note 13\3: See _Hist. Sc. Ideas_, b. ii. c. xiii.] - -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 {167} applications of symbols in the highest -problems of physical astronomy appear to have made some teachers of -mathematics imagine that it is best to _begin_ 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. - -3. (II.) _Idea of Number, &c._--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, _Mechanism_, requires either great -natural aptitude in the student, or a mind properly disciplined by -suitable branches of mathematical study. - -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 {168} may be pursued by single -philosophers dispersed here and there in the community. - -5. (III.) _Idea of Force._--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. - -6. As habitually distinct conceptions of _space_ and {169} _motion_ -were requisite for the reception of the doctrines of formal -astronomy, (the Ptolemaic and Copernican system,) so a clear and -steady conception of _force_ 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[14\3]; 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. - -[Note 14\3: _Hist. Sc. Ideas_, b. iii. c. x.] - -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 {170} 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 _good_, 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[15\3]. - -[Note 15\3: The University of Cambridge has, by a recent law, made -an examination in Elementary Mechanics requisite for the Degree of -B.A.] - -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 _elementary_; 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 {171} 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 _Royal Road_. 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 _Popular Road_ 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. - -9. (IV.) _Chemical Ideas._--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. {172} 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 _polarity_, mechanical -and chemical, of which we spoke in a former part of this work. - -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 -_chemical_ 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 {173} cannot with any advantage, -form a portion of the general intellectual education[16\3]. - -[Note 16\3: 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.] - -10. (V.) _Natural-History Ideas._--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 {174} 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 _genus_, _species_, and of _higher_ and _lower steps_ -of classification, we communicate precision, clearness, and method -to the intellect, through a great range of its operations. - -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 _natural_ not the artificial _classifications_; 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 _assumed_ character, but natural, -recognized by some _discovered_ 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 _natural classes_, -can teach. - -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 _circle_, or a -_square_, its definition comes along with it: and this definition is -supposed to supply all that the reasoner needs to know, respecting -the term. {175} 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. - -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 _kinds_ 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[17\3] 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[18\3], 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. - -[Note 17\3: Lindley's _Nat. Syst. Bot._ p. 81.] - -[Note 18\3: _Hist. Sc. Ideas,_ b. viii. c. ii. sect. 3.] - -14. But it may be asked, if we cannot define a {176} 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? - -The answer to this question involves the general principle of a -natural method of classification, which has already been -stated[19\3] and need not here be again dwelt on. It has been shown -that names of _kinds_ of things (_genera_) associate them according -to total resemblances, not partial characters. The principle which -connects a group of objects in natural history is not a -_definition_, but a _type_. Thus we take as the type of the Rose -family, it may be, the common _wild rose_; all species which -resemble this flower more than they resemble any other group of -species are also _roses_, and form one _genus_. All genera which -resemble Roses more than they resemble any other group of genera are -of the same _family_. And thus the Rose family is collected about -some one species, which is the type or central point of the group. - -[Note 19\3: _Hist. Sc. Ideas,_ b. viii. c. ii. sect. 3.] - -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. - -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 _Method -of_ {177} _Type_ 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. - -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 _objects_ -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[20\3]. So {178} long as a plant, in its most -essential parts, is more _like_ a rose than any thing else, it _is_ -a rose. He knows no other definition. - -[Note 20\3: 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 _defined_: 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.] - -17. (VI.) _Well-established Ideas alone to be used._--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. - -18. But it may be asked, How is it that time {179} 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. - -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 _Discussion_, which we have -already mentioned as the second of the two ways by which scientific -views are developed into full maturity. - - - -{{180}} -CHAPTER IV. - -OF METHODS OF ACQUIRING CLEAR SCIENTIFIC IDEAS, _continued._--OF THE -DISCUSSION OF IDEAS. - - -APHORISM XXXIII. - -_The conception involved in scientific truths have attained the -requisite degree of clearness by means of the_ Discussions -_respecting ideas which have taken place among discoverers and their -followers. Such discussions are very far from being unprofitable to -science. They are_ metaphysical, _and must be so: the difference -between discoverers and barren reasoners is, that the former employ -good, and the latter bad metaphysics._ - - -1. IT 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 {181} forwards, we at last bring it into focus, and -perceive every feature of the prospect sharp and bright. - -2. We have in the last Book[21\3] 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. - -[Note 21\3: B. **ii. c. ii. Of the Explication of Conceptions.] - -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 -_method_) by which the Explication of Conceptions is carried to the -requisite point among philosophers. - -3. In the _History_ of the Fundamental Ideas of the Sciences which -forms the Prelude to this work, and in the _History of the Inductive -Sciences_, 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 {182} 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 _refracted rays_ of light, obscure and confused in Seneca, -growing clearer in Roger Bacon, more definite in Descartes, -perfectly distinct in Newton. The _polarity_ of light, at first -contemplated with some perplexity, became very distinct to Malus, -Young, and Fresnel; yet the phenomena of _circular polarization_, -and still more, the _circular polarization of fluids_, leave us, -even at present, some difficulty in fully mastering this conception. -The _related polarities_ 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[22\3], 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 -_chemical polarity_, 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 _classificatory_ 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 _physiological_ -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 _History of Scientific Ideas_, a review {183} 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 -_discussion_ of its Fundamental Ideas has hitherto had. - -[Note 22\3: _Hist. Ind. Sc._ b. xiii. c. 6.] - -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! - -Yet some writers are accustomed to talk with contempt of all past -controversies, and to wonder at the blindness of those who did not -_at first_ take the view which was established _at last_. 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. -{184} - -5. Again, some persons condemn all that we have here spoken of as -the discussion of ideas, terming it _metaphysical_: and in this -spirit, one writer[23\3] 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 _metaphysics_ 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 _facts_, must be -consistent with _itself_: 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 _à priori_ reasoners. - -[Note 23\3: M. Auguste Comte, _Cours de Philosophie Positive_.] - -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 {185} real -scheme of nature. With his ideas unfolded by education, sharpened by -controversy, rectified by metaphysics, he may _understand_ the -natural world, but he cannot _invent_ 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. - -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. - - - -{{186}} -CHAPTER V. - -ANALYSIS OF THE PROCESS OF INDUCTION. - - -APHORISM XXXIV. - -_The Process of Induction may be resolved into three steps; the_ -Selection of the Idea, _the_ Construction of the Conception, _and -the_ Determination of the Magnitudes. - -APHORISM XXXV. - -_These three steps correspond to the determination of the_ -Independent Variable, _the_ Formula, _and the_ Coefficients, _in -mathematical investigations; or to the_ Argument, _the_ Law, _and -the_ Numerical Data, _in a Table of an astronomical or other_ -Inequality. - -APHORISM XXXVI. - -_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._ - -APHORISM XXXVII. - -_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_ -homogeneous; _and the Rule must be_ tested by the Facts. - - -SECT. I.--_The Three Steps of Induction._ - -1. WHEN facts have been decomposed and phenomena measured, the -philosopher endeavours to combine them into general laws, by the aid -of {187} 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[24\3], 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. - -[Note 24\3: B. ii. c. vi.] - -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 _Selection of the Idea_, _the -Construction of the Conception_, and _the Determination of the -Magnitudes_. It will be recollected that by the word _Idea_, (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 _Conception_ I denote more special -modifications of these ideas, as a _circle_, a _square number_, a -_uniform force_, a _like form_ of flower. Now in order to establish -any law by reference to facts, we must select the _true Idea_ and the -_true Conception_. For example; when Hipparchus found[25\3] 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 _idea_ on which it depended;--whether it was regulated for -instance, by _space_, or by _time_; 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 -_time_ as the regulative _idea_ 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 _conception_, or the rule of the -progression, was to be {188} rightly constructed. Finally, it being -ascertained that the change did go on uniformly, the question then -occurred what was its _amount_:--whether exactly a degree in a -century, or more, or less, and how much: and thus the determination -of the _magnitude_ completed the discovery of the law of phenomena -respecting this star. - -[Note 25\3: _Hist. Ind. Sc._ b. iii. c. iv. sect. 3.] - -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 _Argument_. 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 _Law_ of the Inequality, and its _Amount_. 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. - -4. In a great body of cases, _mathematical_ language and calculation -are used to express the connexion {189} 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 _Independent -Variable_, the Construction of the _Formula_, and the Determination -of the _Coefficients_. 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 _time_, -(which we may denote by the symbol _t_,) for the _independent -variable_. But though the star changes its place _with_ the time, -the change is not _proportional_ 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 _formula at + btt_. The question then occurs, what -are the values of the _coefficients_ _a_ and _b_; and a little -examination of the case shows us that _a_ must be 2, and _b_, 1: so -that the formula is 2_t_ + _tt_. 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. - -We now proceed to offer some suggestions of methods by which each of -these steps may be in some degree promoted. {190} - - -SECT. II.--_Of the Selection of the Fundamental Idea._ - -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. - -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 _time_, 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 {191} 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 _try_ these and -other modes of obtaining a science of the weather: that is, we may -refer the phenomena to the idea of _time_, introducing the -conception of a cycle;--or to the idea of external _force_, by the -conception of the moon's action;--or to the idea of _mutual action_, -introducing the conceptions of thermotical and atmological agencies, -operating between different regions of earth, water, and air. - -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 _trying_ 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 _verified_ 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 _likeness_; 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 {192} of confusion and -darkness till the right idea was introduced. - -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 -_angle of refraction_, 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, (_the -course of a single ray_,) instead of applying the truer idea, of the -_interference of two rays_. Newton gave a wrong rule for the double -refraction of Iceland spar, by making the refraction depend on the -_edges_ of the rhombohedron: Huyghens, more happy, introduced the -idea of the _axis of symmetry_ of the solid, and thus was able to -give the true law of the phenomena. - -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. - -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 {193} 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 _History -of the Sciences_, we have termed the _Prelude_ of a Discovery. The -two steps of _proposing_ a philosophical problem, and of _solving_ -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 _Argument_, and then the _Law_ 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. - -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:--_The idea and the facts must be homogeneous_: 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 _velocities_, not the _changes of velocity_, -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 _relations_ of the particles in _space_; -and yet they have neglected the only facts in the constitution of -bodies which have a reference to space--namely, _crystalline form_, -and _optical properties_. No progress can be made in the theory of -the elementary structure of bodies, {194} without making these -classes of facts the main basis of our speculations. - -10. The only other Rule which I have to offer on this subject, is -that which I have already given:--_the Idea must be tested by the -facts_. 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 _true law_ by employing any conceptions, the idea -from which these conceptions are derived is the _right_ 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. - -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. - -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. - - - -{{195}} -CHAPTER VI. - -GENERAL RULES FOR THE CONSTRUCTION OF THE CONCEPTION. - - -APHORISM XXXVIII. - -_The Construction of the Conception very often includes, in a great -measure, the Determination of the Magnitudes._ - -APHORISM XXXIX. - -_When a series of_ progressive _numbers is given as the result of -observation, it may generally be reduced to law by combinations of -arithmetical and geometrical progressions._ - -APHORISM XL. - -_A true formula for a progressive series of numbers cannot commonly -be obtained from a_ narrow range _of observations._ - -APHORISM XLI. - -Recurrent _series of numbers must, in most cases, be expressed by -circular formulæ._ - -APHORISM XLII. - -_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. IN speaking of the discovery of laws of nature, those which -depend upon _quantity_, 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 {196} the cases in which quantities numerically -measurable are concerned, leaving it for a subsequent task to extend -our principles to ideas of other kinds. - -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. - -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. - -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 next 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. - -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 {197} cooling of the -thermometer was noted for many temperatures. It was found that - - For the temperature 240 the rapidity of cooling was 10·69 - 220 " 8·81 - 200 " 7·40 - 180 " 6·10 - 160 " 4·89 - 140 " 3·88 - -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-- - - 1·88, 1·41, 1·30, 1·21, 1·01, &c. - -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, - - 1·33, 1·09, 1·07, 1·20, 1·27, - -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[26\3] is obtained, giving results {198} which very -nearly coincide with the observed facts, as may be seen in the -margin. - -[Note 26\3: The formula is _v_ = 2·037(_a^t_ - 1) where _v_ is the -velocity of cooling, _t_ the temperature of the thermometer -expressed in degrees, and _a_ is the quantity, 1·0077. - -The degree of coincidence is as follows:-- - - Excess of temperature of Observed Calculated - the thermometer, or values values - values of _t_. of _v_. of _v_. - - 240 10·69 10·68 - 220 8·81 8·89 - 200 7·40 7·34 - 180 6·10 6·03 - 160 4·89 4·87 - 140 3·88 3·89 - 120 3·02 3·05 - 100 2·30 2·33 - 80 1·74 1·72 ] - -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. - -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 _excess_ 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[27\3]. - -[Note 27\3: For if _θ_ be the temperature of the inclosure, and _t_ -the excess of temperature of the hot body, it appears, by this law, -that the radiation of heat is as _a^θ_. And hence the quickness of -cooling, which is as the excess of radiation, is as _a^θ+t_ - _a^θ_; -that is, as _a^θ_(_a^t_ - 1) which agrees with the formula given in -the last note. - -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.] - -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 {199} probable hypothesis as means of -suggestion for our formulæ. - -5. In a _progressive_ 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. - -6. In Astronomy, the series of observations which we have to study -are, for the most part, not progressive, but _recurrent_. 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 _cycles_. In cases in which the observed numbers are -of this kind, the formula which expresses them must be a _circular -function_, 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 {200} -increasing. The main business of formal astronomy consists in -resolving the celestial phenomena into a series of _terms_ of this -kind, in detecting their _arguments_, and in determining their -_coefficients_. - -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 _Hypothesis_ 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[28\3], '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 _Law of the -Sines_, 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. - -[Note 28\3: _De Rev._ l. i. c. iv.] - -8. But with all the aid that Hypotheses and Calculation can afford, -the construction of true formulæ, in {201} 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 _History of Science_, we have seen -how long and how hard Kepler laboured, before he converted the -formula for the planetary motions, from an _epicyclical_ -combination, to a simple _ellipse_. 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[29\3], with a -happy sagacity, discovered the formula to be simply this, that the -_index_ of refraction is the _tangent_ of the angle of polarization. - -[Note 29\3: _Hist. Ind. Sc._ b. ix. c. vi.] - -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. - - - -{{202}} -CHAPTER VII. - -SPECIAL METHODS OF INDUCTION APPLICABLE TO QUANTITY. - - -APHORISM XLIII. - -_There are special Methods of Induction applicable to Quantity; of -which the principal are, the_ Method of Curves, _the_ Method of -Means, _the_ Method of Least Squares, _and the_ Method of Residues. - -APHORISM XLIV. - -The Method of Curves _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._ - -APHORISM XLV. - -The Method of Means _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_ above _and defects_ -below _the quantities which the law in question would produce, will, -in a collection of_ many _observations_, balance _each other._ {203} - -APHORISM XLVI. - -The Method of Least Squares _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_ most probable _mean._ - -APHORISM XLVII. - -The Method of Residues _consists in subtracting, from the quantities -given by Observation, the quantity given by any Law already -discovered; and then examining the remainder, or_ Residue, _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_ Second Residue, _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_ prominent _in the -observations._ - -APHORISM XLVIII. - -_The Method of Means and the Method of Least Squares cannot be -applied without our_ knowing the Arguments _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._ - - -IN 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:--{204} - I. The Method of Curves. - II. The Method of Means. -III. The Method of Least Squares. - IV. The Method of Residues. - - -SECT. I.--_The Method of Curves._ - -1. THE 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 _curve_. In the language -of mathematicians, the variable quantity, whose changes we would -consider, is made the _ordinate_ of the curve, and the quantity on -which the changes depend is made the _abscissa_. 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. - -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 {205} 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 _Lines_, 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. - -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. {206} - -3. But the Method of Curves not only enables us to obtain laws of -nature from _good_ Observations, but also, in a great degree, from -observations which are very _imperfect_. 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 _through_ the points given by our observations, but -_among_ them: drawing it, as has been said by one of the -philosophers[30\3] who first systematically used this method, 'with -a bold but careful hand.' {207} 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. - -[Note 30\3: Sir J. Herschel, _Ast. Soc. Trans._ vol. v. p. 1.] - -4. By this method, thus getting rid at once, in a great measure, of -errours of observation, we obtain data which are _more true than -the_ individual _facts themselves_. 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 _whole mass of the facts_, and -remove the errours of actual observation[31\3], 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. - -[Note 31\3: _Ib._ vol. v. p. 4.] - -One of the most admirable examples of the use of this Method of -Curves is found in Sir John Herschel's _Investigation of the Orbits -of Double Stars_[32\3]. 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 _raw_ 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 {208} -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 _through_, at least -_among_ the points, so as to approach tolerably near them all; and -thus approaching to the orbit which is the subject of -investigation.' - -[Note 32\3: _Ib._] - -5. The _Obstacles_ which principally impede the application of the -Method of Curves are (I.) our _ignorance of the arguments_ of the -changes, and (II.) the _complication of several laws_ with one -another. - -(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 _argument_ of the change should, in fact, be made the -_abscissa_ of the curve. If we were to express, by a series of -ordinates, the _hour_ 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 _solar -hour_, but the _hour_ at which the _moon_ passes the meridian. But -if we are supposed to be aware that _this_ is the _argument_, (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. - -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 _parallax_ and the _declination_ 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 {209} 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. - -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 _diurnal_ change of small amount, we -know; but when we have abstracted this Inequality, (of which the -Argument is the _time of day_,) 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. - -6. (II.) In the next place, I remark that a difficulty is thrown in -the way of the Method of Curves by _the Combination of several laws_ -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 _vice versa_; and all these Arguments of change, the -Distance from Syzygy, the Parallax, the Declination, complete their -circuit and {210} 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 _all_ 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. - -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 _Equation of the Center_, the _Evection_, the -_Variation_, and the _Annual Equation_. 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. {211} - - -SECT. II.--_The Method of Means._ - -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 _Mean_ of the unequal -quantities. Hence the correction of our observations by the method -of curves consists in taking the Mean of the observations. - -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 _Mean_ 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. {212} - -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. - -9. The Method of Means requires a knowledge of the _Argument_ 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 _day of the moon's age_; and we then take the mean -of all those which thus happen at the _same period_ 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. - -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 _many_ 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 {213} 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[33\3]. 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. - -[Note 33\3: Provided the argument of the law which we neglect have -no coincidence with the argument of the law which we would -determine.] - -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 {214} 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. - -But there are other instances hardly less remarkable. Mr. Lubbock's -first investigations of the laws of the tides of London[34\3], -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[35\3]. 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. - -[Note 34\3: _Phil. Trans._ 1831.] - -[Note 35\3: This period of nineteen years was also selected for a -reason which is alluded to in a former note. 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 (_Phil. Tr._ 1838. -_On the Determination of the Laws of the Tides from Short Series of -Observations_), that with regard to Parallax at least, the Means of -one year give sufficient accuracy.] - -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 {215} same -manner, is to annihilate itself, and to disappear altogether from -the result. - - -SECT. III.--_The Method of Least Squares._ - -13. The Method of Least Squares is in fact a method of means, but -with some peculiar characters. Its object is to determine the _best -Mean_ of a number of observed quantities; or the _most probable Law_ -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 _equally_ 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 _Errours_ themselves, but the _Sum of -their Squares_, of the _smallest_ possible amount. - -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 _most probably_ 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. - - Sums of Sums of Squares -Observation 4, 12, 14 Errours Errours. of Errours. -Series (1) 4, 9, 14 0, 3, 0 3 9 - " (2) 6, 10, 14 2, 2, 0 4 8 - " (3) 5, 10, 15 1, 2, 1 4 6 - -Here, although the first series gives the sum of the {216} 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 _most probable_ series of the three. - -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. - - -SECT. IV.--_The Method of Residues._ - -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, _several_ 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. - -16. When we have, in a series of changes of a variable quantity, -discovered _one_ 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 _Residue_, 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 _it_ 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 {217} -this being done, the difference of our Rule and of the Residue -itself, forms a _Second Residue_. This Second Residue we may again -bring under our consideration; and may perhaps in _it_ 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 -_Third Residue_; and so on. - -17. This course has really been followed in various inquiries, -especially in those of Astronomy and Tidology. The _Equation of the -Center_, for the Moon, was obtained out of the _Residue_ of the -Longitude, which remained when the _Mean Anomaly_ was taken away. -This Equation being applied and disposed of, the _Second Residue_ -thus obtained, gave to Ptolemy the _Evection_. The _Third Residue_, -left by the Equation of the Center and the Evection, supplied to -Tycho the _Variation_ and the _Annual Equation_. 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 _Semimensual Inequality_; the _Residue_ of this supplied the -corrections due to the Moon's _Parallax_ and _Declination_; and when -these were determined, the _remaining Residue_ was explored for the -law of the Solar Correction. - -18. In a certain degree, the Method of Residues and the Method of -Means are _opposite_ to each other. For the Method of Residues -extricates Laws from their combination, _bringing them into view in -succession_; while the Method of Means discovers each Law, not by -bringing the others into view, but by _destroying their effect_ -through an accumulation of observations. By the Method of Residues -we should _first_ extract the Law of the Parallax Correction of the -Tides, and _then_, from the Residue left by this, obtain the -Declination Correction. But we might at once employ the Method {218} -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. - -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 -_unexplained Residue_ 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. - -20. Sir John Herschel, in his _Discourse on the Study of Natural -Philosophy_ (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 {219} -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. - -We likewise shall proceed to offer a few remarks on Methods of -Induction applicable to other relations than those of quantity. - - - -{{220}} -CHAPTER VIII. - -METHODS OF INDUCTION DEPENDING ON RESEMBLANCE. - - -APHORISM XLIX. - -The Law of Continuity _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._ - -APHORISM L. - -The Method of Gradation _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._ - -APHORISM LI. - -_The Method of Gradation, applied to decide the question, whether the -existing_ geological _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_ recorded _limits of -intensity._ - -APHORISM LII. - -The Method of Natural Classification _consists in classing cases, -not according to any_ assumed _Definition, but according to the -connexion of the facts themselves, so as to make them the means of -asserting general truths._ {221} - - -SECT. I.--_The Law of Continuity._ - -1. THE 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. - -The _Law of Continuity_ 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. - -2. The Law of Continuity is asserted by Galileo in a particular -application; and the assertion which it {222} suggests is by him -referred to Plato;--namely[36\3] 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[37\3]: 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[38\3]: 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 -_equal_ momentums: but in this case, by the first part of the law the -body would _retain all_ its motion; and by the second part of the law -it would _lose_ a portion of it: hence the Cartesian Law is false. - -[Note 36\3: _Dialog._ iii. 150. iv. 32.] - -[Note 37\3: _Opera_, i. 366.] - -[Note 38\3: Cartes, _Prin._ p. 35.] - -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[39\3]. '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 _continuous_ 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 {223} 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 _never_ violated in actual fact. There are not -really any such bodies as have been termed _perfectly hard_: 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. - -[Note 39\3: In the _Encyc. Brit._ p. 537.] - -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[40\3]? Again: if -any one says that there is a material ether which does not -gravitate[41\3], 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. - -[Note 40\3: _Principia_, lib. iii. prop. 6.] - -[Note 41\3: _Ib._ cor. 2.] - -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, {224} than in the invention of new truths. It is -a test of truth, rather than an instrument of discovery. - -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. - - -SECT. II.--_The Method of Gradation._ - -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 _Method of Gradation_ 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. - -7. Thus for instance, one of the early _Divisions_ established by -electrical philosophers was that of _Electrics_ and _Conductors_. -But this division Dr. Faraday has overturned as an essential -opposition. He takes[42\3] a _Gradation_ 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 {225} -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[43\3]] why should we refuse the same relation to the same -exhibitions of force in the metals?" - -[Note 42\3: _Researches_, 12th series, art. 1328.] - -[Note 43\3: These words refer to another proposition, also -established by the Method of Gradation.] - -The process employed by the same sagacious philosopher to show the -_identity_ of Voltaic and Franklinic electricity, is another example -of the same kind[44\3]. 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. - -[Note 44\3: _Hist. Ind. Sc._ b. xiv. c. ix. sect. 2.] - -Again; to show that the decomposition of bodies in the Voltaic -circuit was not due to the _Attraction_ of the Poles[45\3], Mr. -Faraday devised a beautiful series of experiments, in which these -supposed _Poles_ 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. - -[Note 45\3: _Ibid. Researches_, art. 497.] - -8. The reader of the _Novum Organon_ may perhaps, in looking at such -examples of the Rule, be reminded of some of Bacon's Classes of -Instances, as his _instantiæ absentiæ in proximo_, and his -_instantiæ migrantes_. 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 {226} processes are vitiated by his -proposing to himself the _form_ or _cause_ of the property before -him, as the object of his inquiry; instead of being content to -obtain, in the first place, the _law of phenomena_. Thus his -example[46\3] of a Migrating Instance is thus given. "Let the -_Nature inquired into_ 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 _Form of Whiteness_ 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. - -[Note 46\3: _Nov. Org._ lib. ii. Aph. 28.] - -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. - -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 {227} the rocks called _trap rocks_ must -be classed with those to which a _sedimentary_ origin is ascribed. -For it was shown that a gradual _transition_ 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. - -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 _gradation_ which leads, with -no wide chasm or violent leap, to the state of things of which -geological researches have supplied the evidence. - -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 _gradation_; 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 _same kind_. Those who, dwelling in a city, see, from time to -time, one house built and another pulled down, may say that such -_existing causes_, operating through past time, sufficiently explain -the existing condition of the city. Yet we arrive at important -political and historical truths, by considering the _origin_ of a -city as an event of a _different order_ 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 {228} 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. - -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 -_uniformitarians_ and _catastrophists_: 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. - -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. - - -SECT. III. _The Method of Natural Classification._ - -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 {229} 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[47\3]: which, ever since its -general adoption, has been a leading principle in the speculations -of geologists. - -[Note 47\3: _Hist. Ind. Sc._ b. xviii. c. ii. sect. 3.] - -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, {230} 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 -_Geological Equivalents_[48\3] has been applied to a great part of -Europe. - -[Note 48\3: _Hist. Ind. Sc._ b. xviii. c. iii. sect. 4.] - -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 _to -that particular case_, 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. - -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 _Method of Type_, and was put in opposition to the -_Method of Definition_. - -The Method of Natural Classification is directly opposed to the -process in which we assume and apply _arbitrary_ 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 {231} 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 _define_ 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 _Natural Classes_, -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. - -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. - -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 _Definitions_ 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 _Rose_ family, that they have _alternate -stipulate leaves_, we do not, therefore, exclude from the family the -genus _Lowæa_, which has _no stipulæ_. 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 _Eocene_, _Miocene_, and _Pliocene_, he took -a numerical criterion {232} (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 _Pliocene_ and _Miocene_ 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 -_oolite_ or _porphyry_, when it has no roelike structure and no -fiery spots. - -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 _Laws of Phenomena_ 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. - - - -{{233}} -CHAPTER IX. - -OF THE APPLICATION OF INDUCTIVE TRUTHS. - - -APHORISM LIII. - -_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_ verification _of the theory._ - -APHORISM LIV. - -_Such observations and experiments, when numerous and accurate, -supply also_ corrections _of the_ constants _involved in the theory; -and sometimes_, (_by the Method of Residues_,) additions _to the -theory._ - -APHORISM LV. - -_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._ - -APHORISM LVI. - -_An_ extension _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._ - -APHORISM LVII. - -_The practical inventions which are most important in Art may be -either unimportant parts of Science, or results not explained by -Science._ {234} - -APHORISM LVIII. - -_In modern times, in many departments. Art is constantly guided, -governed and advanced by Science._ - -APHORISM LIX. - -_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._ - - -1. BY 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 _verification_ of the discovery by -additional experiments and reasonings, and its _extension_ 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 _Sequel_ of the epoch; as the collection of -facts, and the elucidation of conceptions, form its Prelude. - -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 _Laboratory_; 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 _Observatories_, in which the consequences of -the theory were habitually compared with the results of observation. -And to facilitate this comparison, _Tables_ of great extent have -been calculated, with immense labour, from each theory, showing the -place which the {235} 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[49\3]. 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. - -[Note 49\3: _Hist. Ind. Sc._ b. vii. c. vi. sect. 6.] - -3. In these last expressions, we suppose the theory, not only to be -tested, but also to be _corrected_ 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 _Constants_ or _Coefficients_ -of these Inequalities of which the _Argument_ is already known. This -he is enabled to do by the methods explained in the fifth chapter of -this book; the Method of Means, and especially the Method of Least -Squares. In other cases, he finds, by the Method of Residues, 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. - -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, -_a continued and corrected system, of observation and calculation_, -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. {236} - -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:--_extensions_ 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[50\3]. 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. - -[Note 50\3: _Hist. Ind. Sc._ b. vii. c. iv. sect. 3.] - -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 {237} forget, -however, that there is a great and essential difference between -inductive and deductive processes of the mind. The discovery of a -_new_ theory, which is true, is a step widely distinct from any mere -development of the consequences of a theory already invented and -established. - -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 {238} 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 _felicities_ 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. - -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. - -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 _Inquiry into the Cause of -Dew_, 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[51\3] -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 {239} necessary to -constitute vapour, and is hence called the _constituent -temperature_. But these principles were not generally familiar in -England till Dr. Wells introduced them into his _Essay on Dew_, -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. - -[Note 51\3:_Hist. Ind. Sc._ b. x. c. iii. sect. 5.] - -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. - -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[52\3], from the conversion of its -materials into gases. In Mineralogy also we have to apply the {240} -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. - -[Note 52\3: 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.] - -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. - -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 _Novum -Organon_ 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 {241} 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 {242} 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. - -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. - -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 _do_ -as well {243} as to _see_. 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 {244} clocks and watches, flying machines -and printing presses involved no new mechanical principle. - -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. - -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 -{245} 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. - -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 _Eriometer_, 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 _Dextrin_, from its -impressing a right-handed rotation on the plane of polarization. - -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. - -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 {246} 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. - -We must now conclude our task by a few words on the subject of -inductions involving Ideas ulterior to those already considered. - - - -{{247}} -CHAPTER X. - -OF THE INDUCTION OF CAUSES. - - -APHORISM LX. - -_In the_ Induction of Causes _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._ - -APHORISM LXI. - -_The Induction of Substance, of Force, of Polarity, go beyond mere -laws of phenomena, and may be considered as the Induction of -Causes._ - -APHORISM LXII. - -_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._ - -APHORISM LXIII. - -_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._ - - -1. WE formerly[53\3] 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 -{248} 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. - -[Note 53\3: B. ii. c. vii.] - -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. - -We may illustrate this in a few cases. - -2. _Induction of Substance._--The Idea of Substance[54\3] 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 _Method of the Balance_. -We have seen[55\3] 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[56\3] that the same Idea leads us to this Maxim;--that -_Imponderable Fluids_ are not to be admitted as _chemical_ elements -of bodies. - -[Note 54\3: _Hist. Sc. Ideas_, Book vi. c. iii.] - -[Note 55\3: _Ibid._ b. vi. c. iv.] - -[Note 56\3: _Ibid._] - -Whether those which have been termed _Imponderable Fluids_,--the -supposed fluids which produce the phenomena of Light, Heat, -Electricity, Galvanism, Magnetism,--really exist or no, is a -question, not merely of the _Laws_, but of the _Causes_ 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 {249} electrical _phenomena_ with those chemical doctrines to -which the Idea of Substance is necessarily applied. - -3. _Induction of Force._--The inference of _Mechanical Forces_ 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. - -4. _Induction of Polarity._--The forces to which Dr. Faraday -ascribes the action in these cases are _Polar Forces_[57\3]. We have -already endeavoured to explain the Idea of Polar Forces; which -implies[58\3] 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 {250} formerly -spoke[59\3]. 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. - -[Note 57\3: _Researches_, 12th series.] - -[Note 58\3: B. v. c. i.] - -[Note 59\3: Book v. c. i.] - -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. - -6. _Induction of Ulterior Causes._--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 {251} 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? - -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. - -_Of the Supreme Cause._--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 _whence_, -and _why_, and _by what power_, 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? - -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 {252} 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. - -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. - -We have seen how different are the kinds of cause to which we are -led by scientific researches. _Mechanical Forces_ are insufficient -without _Chemical Affinities_; Chemical Agencies fail us, and we are -compelled to have recourse to _Vital Powers_; Vital Powers cannot be -merely physical, and we must believe in something hyperphysical, -something of the nature of a _Soul_. Not only do biological -inquiries lead us to assume an animal soul, but they drive us much -further; they bring before us _Perception_, and _Will_ evoked by -Perception. Still more, these inquiries disclose to us _Ideas_ 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 _us_, and thus we -pass from _things_ to _persons_; we have the idea of _Personality_ -awakened. And the idea of Design and _Purpose_, 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. - -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 {253} 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. - -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. - -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 {254} 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. - -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 -{255} 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? - -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.' - -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 {256} 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: - - ΕΝ AΡΧΗ ΗΝ Ὁ ΛΟΓΟΣ, ΚΑI Ὁ ΛΟΓΟΣ ΗΝ ΠΡΟΣ ΤΟΝ ΘΕΟΝ, ΚΑI ΘΕΟΣ ΗΝ Ὁ - ΛΟΓΟΣ. - - - -{{257}} -NOVUM ORGANON RENOVATUM. - - -BOOK IV. - -OF THE LANGUAGE OF SCIENCE. - - -INTRODUCTION. - -IT has been shown in the _History of the Sciences_, and has further -appeared in the course of the _History of Ideas_, 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 -{258} the first place take a rapid survey of the manner in which -Technical Terms have been employed from the earliest periods of -scientific history. - -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 _Ancient_ and the -latter the _Modern_ Period. In illustrating the two following -Aphorisms, I will give examples of the course followed in each of -these periods. - - -APHORISM 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._ - - -THE 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. - -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 _sphere_, a _cone_, a -_cylinder_, had among the Greeks, at first, {259} meanings less -precise than those which geometers gave to these words, and besides -the mere designation of form, implied some use or application. A -_sphere_ (σφαῖρα) was a hand-ball used in games; a _cone_ (κῶνος) -was a boy's spinning-top, or the crest of a helmet; a _cylinder_ -(κύλινδρος) was a roller; a _cube_ (κύβος) was a die: till these -words were adopted by the geometers, and made to signify among them -pure modifications of space. So an _angle_ (γωνία) was only a -corner; a _point_ (σημεῖον) was a signal; a _line_ (γραμμὴ) was a -mark; a _straight_ line (εὐθεῖα) was marked by an adjective which at -first meant only _direct_. A _plane_ (ἐπίπεδον) is the neuter form -of an adjective, which by its derivation means _on the ground_, and -hence _flat_. 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 _rhombus_ (ῥόμβος) by its -derivation, might mean any figure which is _twisted_ 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 -_trapezium_ (τραπέζιον) originally signifies a _table_, 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 -_trapezium_. 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. - -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[1\4], a -_day_, a _month_, a _year_, 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, {260} that we may consider the -terms which involve this conception as parts of common language; as -the _pole_ (πόλος); the _arctic circle_, which includes the stars -that never set[2\4]; the _horizon_ (ὁρίζων) a boundary, applied -technically to the circle bounding the visible earth and sky. The -_turnings of the sun_ (τροπαὶ ἠελίοιο), which are mentioned by -Hesiod, gave occasion to the term _tropics_, the circles at which -the sun in his annual motion turns back from his northward or -southward advance. The _zones_ of the earth, (the _torrid_, -_temperate_, and _frigid_;) the _gnomon_ of a dial; the _limb_ (or -border) of the moon, or of a circular instrument, are terms of the -same class. An _eclipse_ (ἔκλειψις) is originally a deficiency or -disappearance, and joined with the name of the luminary, an _eclipse -of the sun_ or _of the moon_, described the phenomenon; but when the -term became technical, it sufficed, without addition, to designate -the phenomenon. - -[Note 1\4: _Hist. Ind. Sci._ b. iii. c. i.] - -[Note 2\4: _Hist. Ast._ b. iii. c. i. sect. 8.] - -In Mechanics, the Greeks gave a scientific precision to very few -words: we may mention _weights_ (βάρεα), the _arms of a lever_ -(μήχεα), its _fulcrum_ (ὑπομόχλιον), and the verb _to balance_ -(ἰσσοῤῥοπεῖν). Other terms which they used, as _momentum_ (ῥοπὴ) and -_force_ (δύναμις), 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, _vis_, -seems to be connected with a Greek word, ἲς, or ϝὶς, which often has -nearly the same meaning; but originally, as it would seem, signified -a sinew or muscle, the obvious seat of animal strength. - -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 _variation_ is made to mean, in -astronomy, the second inequality of the moon's motion; in magnetism, -the _variation_ signifies the angular deviation of the {261} -compass-needle from the north; in pure mathematics, the _variation_ -of a quantity is the formula which expresses the result of any small -change of the most general kind. In like manner, _parallax_ -(παράλλαξις) denotes a _change_ 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. _Alkali_ at first denoted the ashes of a particular plant, -but afterwards, all bodies having a certain class of chemical -properties; and, in like manner, _acid_, the class opposed to -alkali, was modified in signification by chemists, so as to refer no -longer to the taste. - -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 _force_, _momentum_, -_action and reaction_, and the like, often afford examples of the -inaccuracy thus arising from the scientific appropriation of common -terms. - -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 _parallelogram_ -(παραλληλόγραμμον), which denotes a plane figure bounded by two -pairs of parallel lines; a _parallelopiped_ {262} -(παραλληλοπίπεδον), which signifies a solid figure bounded by three -pairs of parallel planes. A _triangle_ (τρίγωνος, _trigon_) and a -_quadrangle_ (τετράγωνος, _tetragon_) were perhaps words invented -independently of the mathematicians: but such words extended to -other cases, _pentagon_, _decagon_, _heccædecagon_, _polygon_, are -inventions of scientific men. Such also are _tetrahedron_, -_hexahedron_, _dodecahedron_, _tesseracontaoctohedron_, -_polyhedron_, and the like. These words being constructed by -speculative writers, explain themselves, or at least require only -some conventional limitation, easily adopted. Thus _parallelogram_, -might mean a figure bounded by any number of sets of parallel lines, -but it is conventionally restricted to a figure of _four_ sides. So -a _great circle_ in a sphere means one which passes through the -center of the sphere; and a _small circle_ is any other. So in -trigonometry, we have the hypotenuse (ὑποτενοῦσα), or _subtending_ -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 _complement_, _supplement_, _cosine_, -_cotangent_, a _spherical angle_, the _pole of a circle_, or of a -sphere. The word _sine_ itself appears to belong to the class of -terms already described as scientific appropriations of common -terms, although its origin is somewhat obscure. - -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 _ecliptic_. The circle -which the sun describes in his diurnal motion, when the days and -nights are equal, the Greeks called the _equidiurnal_ (ἰσημερινὸς,) -the Latin astronomers the _equinoctial_, and the corresponding -circle on the earth was the _equator_. The ecliptic intersected the -equinoctial in the _equinoctial points_. The _solstices_ (in Greek, -τροπαὶ) were the times when the sun arrested his motion northwards -or {263} southwards; and the _solstitial points_ (τὰ τροπικὰ σημεῖα) -were the places, in the ecliptic where he then was. The name of -_meridians_ was given to circles passing through the poles of the -equator; the _solstitial colure_ (κόλουρος, curtailed), was one of -these circles, which passes through the solstitial points, and is -intercepted by the horizon. - -We have borrowed from the Arabians various astronomical terms, as -_Zenith_, _Nadir_, _Azimuth_, _Almacantar_. 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 _parallax_, _horizon_, -_eclipse_, though appropriated technical terms among the Greeks, are -to us invented technical terms. - -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 -_zwei-und-zwei-gliedrig_, _ein-und-zwei-gliedrig_, -_drey-und-drey-gliedrig,_ _&c._, (two-and-two-membered, -one-and-two-membered, &c.) And Hessel, also a writer on -crystallography, speaks of _doubly-one-membered edges_, -_four-and-three spaced rays_, and the like. - -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 {264} 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 _Fourth_, a _Fifth_, an _Octave_, -(_Diatessaron_, _Diapente_, _Diapason_,) a _Comma_, which is the -difference of a _Major_ and _Minor Tone_; we have the various -_Moods_ or _Keys_, and the notes of various lengths, as _Minims_, -_Breves_, _Semibreves_, _Quavers_. In chemistry, _Gas_ 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. - -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 _latitude_ and _longitude_, 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 _length_ 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 -_Precession_ 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 _Right Ascension_ 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 _right_ -sphere; that is, a sphere which supposes the spectator to be at the -equator. The _Oblique Ascension_ (a term now little used), is -derived in like manner from an oblique sphere. The motion of a -planet is _direct_ or _retrograde_, _in_ {265} _consequentia_ -(_signa_), or _in antecedentia_, 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 _equation of time_ 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 _equation of the center_ 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 _equations_, by the application -of which her motion is brought nearer and nearer to perfect -uniformity. The second of these equations is called the _evection_, -the third the _variation_, the fourth the _annual equation_, The -motion of the sun as affected by its inequalities is called his -_anomaly_, 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 _deferent_, -_epicycle_, _eccentric_. In like manner, the theories which have -more recently taken the place of the theory of epicycles have -introduced other technical terms, as the _elliptical orbit_, the -_radius vector_, and the _equable description of areas_ by this -radius, which phrases express the true laws of the planetary -motions. - -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 {266} we have -seen in the examination of the foundations of mechanics, the terms -_force_ and _inertia_ derive their precise meaning from a -recognition of the first law of motion; _accelerating force_ and -_composition of motion_ involve the second law; _moving force_, -_momentum_, _action_ and _reaction_, are expressions which imply the -third law. The term _vis viva_ was introduced to express a general -property of moving bodies; and other terms have been introduced for -like purposes, as _impetus_ by Smeaton, and _work done_, by other -engineers. In the recent writings of several French engineers, the -term _travail_ is much employed, to express the work done and the -force which does it: this term has been rendered by _labouring -force_. The proposition which was termed the _hydrostatic paradox_ -had this name in reference to its violating a supposed law of the -action of forces. The verb to _gravitate_, and the abstract term -_gravitation_, sealed the establishment of Newton's theory of the -solar system. - -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 _regulus_, 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 _caput mortuum_. Quick silver, -that is, live silver (_argentum vivum_), was killed by certain -admixtures, and was _revived_ when restored to its pure state. - -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 _hysterics_, _hypochondriac_, -_melancholy_, _cholera_, _colic_, _quinsey_ {267} (_squinantia_, -συνάγχη, a suffocation), _megrim_, _migrane_ (_hemicranium_, the -middle of the skull), _rickets_, (_rachitis_, from ῥάχις, the -backbone), _palsy_, (_paralysis_, παράλυσις,) _apoplexy_ (ἀποπληξία, -a stroke), _emrods_, (αἱμοῤῥοΐδες, _hemorrhoids_, a flux of blood), -_imposthume_, (corrupted from _aposteme_, ἀπόστημα, an abscess), -_phthisis_ (φθίσις, consumption), _tympanum_ (τυμπανία, swelling), -_dropsy_ (_hydropsy_, ὕδρωψ,) _sciatica_, isciatica (ἰσκιαδικὴ, -from ἰσκίον, the hip), _catarrh_ (κατάῤῥους, a flowing down), -_diarrhœa_ (διαῤῥοία, a flowing through), _diabetes_ (διαβήτης, a -passing through), _dysentery_ (δυσεντερία, a disorder of the -entrails), _arthritic_ pains (from ἄρθρα, 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 (ὑστέρα, the last place,) signifies the womb, according to -its order in a certain systematic enumeration of parts. The second -word, _hypochondriac_, means something affecting the viscera below -the cartilage of the breastbone, which cartilage is called χόνδρος; -_melancholy_ and _cholera_ derive their names from supposed -affections of χολὴ, the bile. _Colic_ is that which affects the -_colon_ (κῶλον), the largest member of the bowels. A disorder of the -eye is called _gutta serena_ (the 'drop serene' of Milton), in -contradistinction to _gutta turbida_, in which the impediment to -vision is perceptibly opake. Other terms also record the opinions of -the ancient anatomists, as _duodenum_, a certain portion of the -intestines, which they estimated as twelve inches long. We might add -other allusions, as the _tendon of Achilles_. - -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 _mercurial_, -_martial_, _jovial_, or _saturnine_, accordingly as their characters -were supposed to be determined by the influence of the planets, -Mercury, Mars, Jupiter, or Saturn. Other expressions, such as -_disastrous_, _ill-starred_, _exorbitant_, _lord of the ascendant_, -and hence _ascendancy_, _influence_, {268} a _sphere of action_, and -the like, may serve to show how extensively astrological opinions -have affected language, though the doctrine is no longer a -recognized science. - -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. - -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. - -Various plants derive their names from their supposed virtues, as -_herniaria_, _rupture-wort_; or from legends, as _herba Sancti -Johannis_, _St. John's wort_. The same is the case with minerals: -thus the _topaz_ was asserted to come from an island so shrouded in -mists that navigators could only _conjecture_ (τοπάζειν) where it -was. In these latter cases, however, the legend is often not the -true origin of the name, but is suggested by it. - -The privilege of constructing names where they are wanted, belongs -to natural historians no less than to {269} 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[3\4]. The vast -importance of nomenclature in natural history was not recognized -till the modern period. - -[Note 3\4: In his _History of Animals_, (b. i. c. vi.), he says, -that the great classes of animals are Quadrupeds, Birds, Fishes, -Whales (_Cetaceans_), Oysters (_Testaceans_), animals like crabs -which have no general name (_Crustaceans_), soft animals (_Mollusks_ -and _Insects_). He does, however, call the Crustaces by a name -(_Malacostraca_, soft-shelled) which has since been adopted by -Naturalists.] - -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. - - -APHORISM II. - -_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_[4\4]. - -[Note 4\4: On the subject of Terminology and Nomenclature, see also -Aphorisms LXXXVIII and XCVIII concerning Ideas, and b. viii. c. ii. -of the _History of Scientific Ideas_. In those places I have spoken -of the distinction of _Terminology_ and _Nomenclature_.] - - -WRITERS upon science have gone on up to modern times forming such -technical terms as they had occasion for, by the three processes -above {270} 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 _pole_ is an example of the first kind; the -name of the subject, _electro-magnetism_, of the second; and the -term _current_, involving an hypothesis of the motion of a fluid, is -an instance of the third class. In chemistry, the term _salt_ was -adopted from common language, and its meaning extended to denote any -compound of a certain kind; the term _neutral_ salt implied the -notion of a balanced opposition in the two elements of the compound; -and such words as _subacid_ and _superacid_, 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 _phlogiston_ was introduced to express the -theory, and from this such terms as _phlogisticated_ and -_dephlogisticated_ 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. - -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[5\4], 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 {271} in -endless confusion[6\4], by the multiplication of names of plants, at -the same time superfluous and ambiguous. The _Synonymies_ 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[7\4]. 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[8\4], 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. - -[Note 5\4: _Hist. Ind. Sc._ b. xvi. c. ii.] - -[Note 6\4: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 3.] - -[Note 7\4: For instance, whether the _fagus_ of the Latins be the -beech or the chestnut.] - -[Note 8\4: _Ib._ b. xvi. c. iii. sect. 2.] - -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 _names_ of plants, -but also an artificial system of phrases fitted to _describe_ their -parts: not only a _Nomenclature_, but also {272} a _Terminology_. -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. - -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[9\4] 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[10\4], 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[11\4]. 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 -_Caulis_, a stalk. - -[Note 9\4: _Theor. Elem. de Bot._ p. 327.] - -[Note 10\4: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 3.] - -[Note 11\4: _Hist. Ind. Sc._ b. xvi. c. iii. sect. 3 (about A.D. -1660).] - -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 {273} 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 _History of Science_[12\4]; and the principles -which they involve I shall consider separately hereafter. I will -only remind the reader that the great simplification in -_nomenclature_ which was the result of his labours, consisted in -designating each kind of plant by a _binary_ term consisting of the -name of the _genus_ combined with that of the _species_: an artifice -seemingly obvious, but more convenient in its results than could -possibly have been anticipated. - -[Note 12\4: _Ib._ c. iv. sect. 1-3.] - -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[13\4]. - -[Note 13\4: De Candolle, _Th. Elem._ p. 307.] - -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 {274} -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[14\4] that Werner, after his -first _Essay on the Characters of Minerals_, 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 _symbols_. 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. - -[Note 14\4: _Éloges_, ii. 134.] - -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[15\4]: thus he has such species as {275} _Rhombohedral Lime -Haloide_, _Octahedral Fluor Haloide_, _Prismatic Hal Baryte_. 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. - -[Note 15\4: _Hist. Ind. Sc._ b. xv. c. ix.] - -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. - -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_uric_ and sulph_urous_ acids; of sulph_ates_ and sulph_ites_ -of bases; and of sulph_urets_ of metals; and in like manner, of -phos_phoric_ and phos_phorous_ acids, of phos_phates_, phos_phites_, -phos_phurets_. 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. - -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 {276} 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 _hyposulphurous_ and _hyposulphuric_: but these -names, though convenient, no longer implied, by their form, any -definite relation. The compounds of Nitrogen and Oxygen are, in -order, the _Protoxide_, the _Deutoxide_ or _Binoxide_; _Hyponitrous_ -Acid, _Nitrous_ Acid, and _Nitric_ Acid. The nomenclature here -ceases to be systematic. We have three oxides of Iron, of which we -may call the first the _Protoxide_, but we cannot call the others -the _Deutoxide_ and _Trioxide_, for by doing so we should convey a -perfectly erroneous notion of the proportions of the elements. They -are called the _Protoxide_, the _Black_ Oxide, and the _Peroxide_. -We are here thrown back upon terms quite unconnected with the -system. - -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 _hydrochloric_ acid, _chlorine_, -and _chloric_ acid. - -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 -{277} 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. - -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[16\4]. - -[Note 16\4: See at the end of these Aphorisms, further illustrations -of them from the recent history of Comparative Anatomy and -Chemistry.] - -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. - -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. {278} - - -APHORISM III. - -_In framing scientific terms, the appropriation of old words is -preferable to the invention of new ones._ - - -THIS maxim is stated by Bacon in his usual striking manner. After -mentioning _Metaphysic_, as one of the divisions of Natural -Philosophy, he adds[17\4]: 'Wherein I desire it may be conceived -that I use the word _metaphysic_ 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 _usque ad aras_; 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, _eadem magistratuum vocabula_.' - -[Note 17\4: _De Augm._ lib. iii. c. iv.] - -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 {279} do not -take care to understand them in their technical instead of their -common signification. _Force_, _momentum_, _inertia_, _impetus_, -_vis viva_, 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. - -In the application of this Third Aphorism, other rules are to be -attended to, which I add. - - -APHORISM IV. - -_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 WILL state an example in which this rule seems to be applicable. -Mr Davies Gilbert[18\4] has recently proposed the term _efficiency_ -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 _duty_. But as -there appears to be a little incongruity in calling that work -_efficiency_ which the machine _ought_ to do, when we call that work -_duty_ which it really does, I have proposed to term these two -quantities _theoretical efficiency_ and _practical efficiency_, or -_theoretical duty_ and _practical duty_[19\4]. - -[Note 18\4: _Phil. Trans._ 1827, p. 25.] - -[Note 19\4: The term _travail_ is used by French engineers, to -express _efficiency_ or _theoretical duty_. This term has been -rendered in English by _labouring force_.] - -Since common words are often vague in their meaning, I add as a -necessary accompaniment to the Third Aphorism the following:-- {280} - - -APHORISM V. - -_When common words are appropriated as technical terms, their -meaning may be modified, and must be rigorously fixed._ - - -THIS is stated by Bacon in the above extract: 'to retain the ancient -terms, though I sometimes _alter the uses and definitions_.' The -scientific use of the term is in all cases much more precise than -the common use. The loose notions of _velocity_ and _force_ 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. - -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. _Momentum_ 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. - -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 _acid_ for a -class of bodies, that all the substances belonging to this class are -not sour. We have seen that a _trapezium_ 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 _the -green sand_. 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. - -When it appeared that _geometry_ would have to be employed as much -at least about the heavens as the earth, Plato exclaimed against the -folly of calling the {281} science by such a name; since the word -signifies 'earth-measuring;' yet the word _geometry_ has retained -its place and answered its purpose perfectly well up to the present -day. - -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 _fasciculus_, _capitulum_, _racemus_, -_thyrsus_, _paniculus_, _spica_, _amentum_, _corymbus_, _umbella_, -_cyma_, _verticillus_; or, in the language of English Botanists, _a -tuft_, _a head_, _a cluster_, _a bunch_, _a panicle_, _a spike_, _a -catkin_, _a corymb_, _an umbel_, _a cyme_, _a whorl_. And it has -since been laid down as a rule[20\4], that each organ ought to have -a separate and appropriate name; so that the term _leaf_, for -instance, shall never be applied to _a leaflet_, _a bractea_, or _a -sepal_ of the calyx. - -[Note 20\4: De Candolle, _Theor. El._ 328.] - -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[21\4], and Lindley[22\4]. - -[Note 21\4: _Élémens de Botanique_.] - -[Note 22\4: _Elements of Botany_.] - - -APHORISM VI. - -_When common words are appropriated as technical terms, this must be -done so that they are not ambiguous in their application._ - - -AN example will explain this maxim. The conditions of a body, as a -solid, a liquid, and an air, have been distinguished as different -_forms_ of the body. But the word _form_, as applied to bodies, has -other meanings; so that if we were to inquire in _what form_ water -exists in a snow-cloud, it might be doubted whether the forms of -crystallization were meant, or {282} the different forms of ice, -water, and vapour. Hence I have proposed[23\4] to reject the term -_form_ in such cases, and to speak of the different _consistence_ of -a body in these conditions. The term _consistence_ 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 _consistence_ to the state of -air, it may be justified by what has been said in speaking of -Aphorism V. - -[Note 23\4: _Hist. Ind. Sc._ b. x. c. ii. sect. 2.] - -I may notice another example of the necessity of avoiding ambiguous -words. A philosopher who makes method his study, would naturally be -termed a _methodist_; 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 _botanical methodists_. Again, by this -maxim, we are almost debarred from using the term _physician_ for a -cultivator of the science of physics, because it already signifies a -practiser of physic. We might, perhaps, still use _physician_ as the -equivalent of the French _physicien_, 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 _Physicist_ proceeds upon the ideas of -force, matter, and the properties of matter. - -Whatever may be thought of this proposal, the maxim which it implies -is frequently useful. It is this. - - -APHORISM VII. - -_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._ - - -THE 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 {283} -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. - -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. - -The word _Force_ 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 _accelerating force_ and _moving force_. Hence we might have -occasion to speak of the accelerating or moving force _of_ a certain -_force_; 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 _of_ this _force_ 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 _accelerating force_ and -_moving force_, single abstract terms had been introduced by Newton: -if, for instance, he had said that the velocity generated in a -second measures the _accelerativity_ of the force which produces it, -and the momentum produced in a second measures the _motivity_ of the -force. - -The science which treats of heat has hitherto had no special -designation: treatises upon it have generally been termed treatises -_On Heat_. 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 _acoustical_ experiments -and _optical_ theories. This inconvenience has led various persons -to suggest names for the Science of Heat. M. Comte {284} terms it -_Thermology_. In the _History of the Sciences_, I have named it -_Thermotics_, which appears to me to agree better with the analogy -of the names of other corresponding sciences, _Acoustics_ and -_Optics_. - -_Electricity_ is in the same condition as Heat; having only one word -to express the property and the science. M. Le Comte proposes -_Electrology_: for the same reason as before, I should conceive -_Electrics_ more agreeable to analogy. The coincidence of the word -with the plural of Electric would not give rise to ambiguity; for -_Electrics_, taken as the name of a science, would be singular, like -_Optics_ and _Mechanics_. But a term offers itself to express -_common_ or _machine Electrics_, 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 _Electrodynamics_, which obviously suggests the -name _Electrostatics_ for the latter. - -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 _Tidology_, having been much engaged in tidological -researches. - -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 -_Idiopts_. - -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. {285} - - -APHORISM VIII. - -_Terms must be constructed and appropriated so as to be fitted to -enunciate simply and clearly true general propositions._ - - -THIS 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[24\4] 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. - -[Note 24\4: _Règne Animal_, Introd. viii.] - -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 _History of the Sciences_. 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, _force_, _velocity_, _momentum_, _inertia_, -&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 _phlogiston_ was useful, as has -been shown in the _History_, in classing together processes which -really are of the same nature; and the nomenclature of the _oxygen_ -theory was still preferable, because it enabled the chemist to -express a still greater number of general truths. {286} - -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 _Chemistry_, 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. - -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.' - -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 _fish_ 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 _fish_; 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 _whale-fishery_, and calling such animals _fish_ -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 {287} 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. - -[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 _the coal_, should be regarded in law as -_coal_. The opinions of chemists and geologists, as well as of -lawyers, were discrepant, and a direct decision of the case was -evaded.[25\4]] - -[Note 25\4: Miller's _Chemistry_, iii. 98.] - - -APHORISM IX. - -_In the Classificatory Sciences, a Systematic Nomenclature is -necessary; and the System and the Nomenclature are each essential to -the utility of the other._ - - -THE 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 _Synonymies_ 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 _System_ -and the _Names_ 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[26\4], forms an -epoch, and {288} 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[27\4] 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. - -[Note 26\4: _Hist. des Poissons_, Pref.] - -[Note 27\4: _Prodrom. Veg. Foss._ p. 3.] - -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 _Pœcilite_, 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 _Cambrian_ system, and _Silurian_ 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. - -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. - -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, _Disposition_ and -_Denomination_; and he adds this Latin line, - Nomina si nescis perit et cognitio rerum. {289} -And Cuvier, in the Preface to his _Animal -Kingdom_, 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. - -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 _Leucocyclite_ and _Tesselite_ 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 _Augite_ and -_Hornblende_ are really the same species, as Gustavus Rose has -maintained? if _Diallage_ and _Hypersthene_ 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. - -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 -{290} nomenclature we have a conspicuous example in the modern -chemistry. - - -APHORISM X. - -_New terms and changes of terms, which are not needed in order to -express truth, are to be avoided._ - - -AS 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. - -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 _Cœlum Christianum_, 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[28\4], the design of perverting and confounding whatever of -celestial information from the period of the earliest memory is -found in books. - -[Note 28\4: Gassendi, _Vita Peireskii_, 300.] - -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[29\4] that a -fair generic name is not to be exchanged for another though apter -one: and[30\4] 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 -{291} lays down this rule[31\4]; 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[32\4] -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. - -[Note 29\4: _Phil. Bot._ 246.] - -[Note 30\4: _Ib._ 247.] - -[Note 31\4: _Phil. Bot._ 248.] - -[Note 32\4: _Règne Anim._ Pref. xvi.] - -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. - -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 _First_, _Second_, and _Third Flötz -Limestone_, his _Old_ and _New Red Sandstone_, 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 {292} instance, those of Smith, are for the -most part not systematic, but are borrowed from accidents, as -localities, or popular names; as _Oxford Clay_ and _Cornbrash_; 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 _Introduction to -the Geology of England and Wales_, according to which the -_Carboniferous Rocks_ are the _Medial Order_,--having above them the -_Supermedial Order_ (_New Red Sand_, _Oolites_ and _Chalk_), and -above these the _Superior Order_ (_Tertiary Rocks_); and -again,--having below, the _Submedial Order_ (the _Transition -Rocks_), and the _Inferior Order_ (_Mica Slate_, _Gneiss_, -_Granite_). 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 _Tableau des Terrains qui composent l'écorce du Globe_. He -divides these strata into nine classes, which he terms _Terrains -Alluviens_, _Lysiens_, _Pyrogenes_, _Clysmiens_, _Yzemiens_, -_Hemilysiens_, _Agalysiens_, _Plutoniques_, _Vulcaniques_. These -classes are again variously subdivided: thus the Terrains Yzemiens -are _Thalassiques_, _Pelagiques_, and _Abyssiques_; and the -Abyssiques are subdivided into _Lias_, _Keuper_, _Conchiliens_, -_Pœciliens_, _Peneens_, _Rudimentaires_, _Entritiques_, _Houillers_, -_Carbonifers_ and _Gres Rouge Ancien_. 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. - -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 {293} -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 _rhombohedron_, -_scalenohedron_, _hemihedral_, _systems_ of crystallization, which -will probably be a permanent portion of the language of science. - -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. - -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: -_Cirrus_, _Cirrocumulus_, _Cirrostratus_, _Cumulostratus_, -_Cumulus_, _Nimbus_, _Stratus_. In an abridgment of his views, given -in the Supplement to the _Encyclopædia Britannica_, English names -were proposed as the equivalents of these; _Curlcloud_, -_Sondercloud_, _Wanecloud_, _Twaincloud_, _Stackencloud_, -_Raincloud_, _Fallcloud_. 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 _arbitrary terms_ for the _structure_ 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 {294} 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 _whole_ 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 _cirrus_ very readily takes an abstract -meaning, equally applicable to the rectilinear as to the flexuous -forms of the subject. But the name of _curl-cloud_ will not, without -some violence to its _obvious sense_, 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.' - -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. - - -APHORISM XI. - -_Terms which imply theoretical views are admissible, as far as the -theory is proved._ - - -IT 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 _minor_ {295} _axis_ of Jupiter's _orbit_, or of his -_density_, or of _the angle of refraction_, or _the length of an -undulation_ 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. - -For example, the term _polarization_ 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. - -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. - -The distinction of _primary_ and _secondary_ 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 _transition_ rocks. And the recent -researches of geologists lead them to the conclusion, that those -rocks which are termed _primary_, may be the newest, not the oldest, -productions of nature. - -In order to avoid this incongruity, other terms have been proposed -as substitutes for these. Sir C. Lyell remarks[33\4], that granite, -gneiss, and the like, form a class {296} which should be designated -by a common name; which name should not be of chronological import. -He proposes _hypogene_, 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. - -[Note 33\4: _Princ. Geol._ iv. 386.] - -These hypogene rocks, again, he divides into unstratified or -_plutonic_, and altered stratified, or _metamorphic_; 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[34\4]. - -[Note 34\4: _Elem. Geol._ p. 17.] - -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[35\4]. 'Simplicity and precision ought to be -the characteristics of a scientific nomenclature: words should -signify _things_, or the _analogies_ of things, and not _opinions_. -. . . A substance in one age supposed to be simple, in another is -proved to be compound, and _vice versâ_. A theoretical nomenclature -is liable to continual alterations: _oxygenated muriatic acid_ is as -improper a term as _dephlogisticated marine acid_. 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 _new ideas_ of their composition, there can be no -permanency in the language of the science; it must always be -confused and uncertain. Bodies which are _similar_ to each other -should always be classed together; and there is a presumption that -their composition is _analogous_. _Metals_, _earths_, _alkalis_, are -appropriate names for the bodies they represent, and independent of -all speculation: whereas _oxides_, _sulphurets_, and _muriates_ are -terms founded upon opinions of the composition of bodies, some of -which have been already found erroneous. {297} 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 _um_, as _aurum_, so -their calciform or oxidated state might have been denoted by a -termination in _a_, as _aura_: and no progress, however great, in -the science could render it necessary that such a mode of -appellation should be changed.' - -[Note 35\4: _Elements of Chem. Phil._ p. 46.] - -These remarks are founded upon distinctions which have no real -existence. We cannot separate _things_ from their _properties_, nor -can we consider their properties and analogies in any other way than -by having _opinions_ about them. By contrasting _analogies_ with -_opinions_, 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 _theory_. The terms which -he quotes, _oxygenated muriatic acid_ (and the same may be said of -_dephlogisticated marine acid_,) 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 _metals_, _earths_, _alkalis_, -are good as the _basis_ 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 -{298} 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 _so far as_ 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 _epicycles_ 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 _elliptical_ theory; and, -though now superseded, is still readily intelligible to astronomers. - -This is not the place to discuss the reasons for the _form_ of -scientific terms; otherwise we might ask, in reference to the -objections to the Lavoisierian nomenclature, if such forms as -_aurum_ and _aura_ are good to represent the absence or presence of -oxygen, why such forms as _sulphite_ and _sulphate_ 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. - -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 {299} 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 _such_ facts, is precisely what we are here -inculcating. - -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. - -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 _truncations_ of the edges and the {300} 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 -_decrements_ 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. - -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 -_perfoliate_, 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 _connate_ is applied to -these conjoined opposite leaves, implying that they grow together; -or they are called _connato-perfoliate_. Again; formerly the corolla -was called _monopetalous_ or _polypetalous_, as it consisted of one -part or of several: but it is now agreed among botanists that those -corollas which {301} appear to consist of a single part, are, in -fact, composed of several soldered together; hence the term -_gamopetalous_ is now employed (by De Candolle and his followers) -instead of monopetalous[36\4]. - -[Note 36\4: On this subject, see Illiger, _Versuch einer -Systematischen Vollständigen Terminologie für das Thierreich und -Pflanzenreich_ (1810). De Candolle, _Théorie Élémentaire de la -Botanique_.] - -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. - - -APHORISM XII. - -_If terms are systematically good, they are not to be rejected -because they are etymologically inaccurate._ - - -TERMS 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 _geometry_ means the measuring of the earth, that the name -_porphyry_ is applied to many rocks which have no fiery spots, as -the word implies, and _oolite_ to strata which have no roelike -structure. In like manner, if the term _pœcilite_ 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 _introducing_ 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 {302} 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 _mountain_ or _carboniferous_ -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. - -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 _Umbellatæ_, in order to be a natural order, must contain some -plants which have not umbels, as _Eryngium_[37\4]. '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 _à -fortiori_, from the principal feature.' - -[Note 37\4: See _Hist. Ind. Sc._ b. xvi. c. iv. sect. 5.] - -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 _square pyramidal_ and the other -_oblong pyramidal_, or the first _square prismatic_ and the second -_oblong prismatic_, are termed by Mohs, the first, _Pyramidal_, and -the second _Prismatic_. And it may {303} 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 _Mineralogy_, to substitute _autopside_ and _heteropside_ for -_metallic_ and _unmetallic_. It was supposed to be proved that all -bodies have a metal for their basis; and hence it was wished to -avoid the term _unmetallic_. But the words _metallic_ and -_unmetallic_ may mean that minerals _seem_ metallic and unmetallic, -just as well as if they contained the element _opside_ to imply this -seeming. The old names express all that the new express, and with -more simplicity, and therefore should not be disturbed. - -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 Fourth 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 _common_ words _appropriated_ as technical terms; we here -speak of words _constructed_ 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 _Cirrus_ to a cloud composed of -filaments, even if these filaments are straight; but to call such a -cloud a _Curl cloud_ would be much more harsh. - -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. {304} - - -APHORISM XIII. - -_The fundamental terms of a system of Nomenclature may be -conveniently borrowed from casual or arbitrary circumstances._ - - -FOR 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 _Parietaria_, _Parnassia_, _Chalcedony_, -_Arragonite_, _Silurian_ system, _Purbeck_ limestone. These names -may be considered as at first supplying standards of reference; for -in order to ascertain whether any rock be _Purbeck_ 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 _Parnassia_ does not grow on Parnassus; that _Chalcedony_ -is not found in Chalcedon; or even that _Arragonite_ 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. _Alpine_ 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. - -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, _Nicotiana_, -_Dahlia_, _Fuchsia_, _Jungermannia_, _Lonicera_. 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[38\4], -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 {305} 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[39\4], '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.' - -[Note 38\4: _Phil. Bot._ 241.] - -[Note 39\4: _Règne An._ p. 16.] - -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 _Berenice's Hair_; and the new star which shone out in the time -of Cæsar, would probably have retained the name given to it, of the -_Julian Star_, 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 -_Medicean_ stars, the name employed by Galileo for the satellites of -Jupiter; the _Georgium Sidus_, the appellation proposed by Herschel -for Uranus when first discovered[40\4]; Ceres _Ferdinandea_, {306} -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 -_Ilchanic_, the _Alphonsine_, the _Rudolphine_, the _Carolinian_ -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, _Halley's_, -_Encke's Comet_, and _Biela's_ or _Gambart's Comet_. - -[Note 40\4: In this case, the name _Uranus_, selected with a view to -symmetry according to the mythological order of descent of the -persons (_Uranus_, _Saturn_, _Jupiter_, _Mars_) 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, -_Ceres_, _Pallas_, _Juno_, and _Vesta_, the names were given either -by the discoverer, or with his sanction. Following this rule, Bessel -gave the name of _Astræa_ to a new planet discovered in the same -region by Mr. Hencke, as mentioned in the additions to book vii. of -the _History_ (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 -_Neptune_ 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 _History_.] - -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 _Torricellian_ Vacuum, the _Voltaic_ -Pile, _Fahrenheit's_ Thermometer. And in the same manner with regard -to laws of nature, we have _Kepler's_ Laws, _Boyle_ or _Mariotte's_ -law of the elasticity of air, _Huyghens's_ law of double refraction, -_Newton's_ scale of colours. _Descartes'_ 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 _Demoivre's_ Theorem, _Maclaurin's_ -Theorem, _Lagrange's_ Theorem, _Eulerian_ Integrals. - -In the _History of Science_[41\4] I have remarked that in the -discovery of what is termed galvanism, Volta's {307} 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 -_voltaic_, rather than _galvanic_ 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 -_common_ or _machine_ electricity; but I think that _franklinic_ -electricity would form a more natural correspondence with _voltaic_, -and would be well justified by Franklin's place in the history of -that part of the subject. - -[Note 41\4: b. xiii. c. 1.] - - -APHORISM XIV. - -_The Binary Method of Nomenclature_ (_Names by Genus and Species_) _is -the most convenient hitherto employed in Classification._ - - -THE 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. - -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 _Binary Method_ of Nomenclature has been -found so convenient, that it has been universally adopted in every -other department of the Natural History of organized beings. {308} - -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 _Trivial_ 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. - - -APHORISM XV. - -_The Maxims of Linnæus concerning the Names to be used in Botany_, -(Philosophia Botanica, Nomina. Sections 210 to 255) _are good -examples of Aphorisms on this subject._ - - -BOTH 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. - -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[42\4]) as capricious and unnecessary restrictions. - -[Note 42\4: Pref. cxxix. clxxii.] - -Many of the names introduced by Linnæus certainly appear fanciful -enough. Thus he gives the name _Bauhinia_ to a plant which has -leaves in pairs, because the Bauhins were a pair of brothers. -_Banisteria_ 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[43\4]:-- -That as such a perpetuation of the names of persons -{309} 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. - -[Note 43\4: _Phil. Bot._ s. 239.] - -[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 _Buffonia_, established by Sauvages, into -_Bufonia_, which suggested a derivation from _Bufo_, a toad. It -appears to be proved that the spelling was not Linnæus's doing.] - -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.' - -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 _Hieracium_[44\4] are _Hieracium Alpinum_, _H. -Halleri_, _H. Pilosella_, _H. dubium_, _H. murorum_, &c., where we -see how different may be the kind of origin of the words. - -[Note 44\4: Hooker, _Fl. Scot._ 228.] - -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. - - -APHORISM XVI. - -_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._ - - -WITH 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 {310} 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. - -The geological term _Trias_, lately introduced to designate the -group consisting of the _three_ members (Bunter Sandstein, -Muschelkalk, and Keuper) becomes improper if, as some geologists -hold, two of these members cannot be separated. - -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[45\4], denoting a genus by the name _Fonna_ -(_Lychnidea_), conceived he might mark five of its species by -altering the last syllable, _Fonna_, _Fonna-e_, _Fonna-i_, -_Fonna-o_, _Fonna-u_; then others by _Fonna-ba_, _Fonna-ka_, and so -on. This would be liable to the same evils which have been noticed -as belonging to the numerical method[46\4]. - -[Note 45\4: Pref. clxxvi.] - -[Note 46\4: In like manner the names assigned by Mr. Rickman to the -successive of styles of Gothic architecture in England,--_Early -English_, _Decorated_, and _Perpendicular_,--cannot be replaced by -numerical designations, _First Pointed_, _Second Pointed_, _Third -Pointed_. 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 _First Second Pointed_ and _Second Second -Pointed_; and what should we call that pointed style--the -_Transition_ from the Norman--which precedes the _First Pointed_?] - - -APHORISM XVII. - -_In any classificatory science names including more than two steps -of the classification may be employed if it be found convenient._ - - -LINNÆUS, in his canons for botanical nomenclature (Art. 212), says -that the names of the class and the order are to be _mute_, while -the names of the Genus and Species are _sonorous_. And accordingly -the names {311} 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[47\4], -that the name of the Class and Order must not be expressed but -understood, and hence, he says, Royen, who took _Lilium_ for the -name of a Class, rightly rejected this word as a generic name, and -substituted _Lirium_ with the Greek termination. - -[Note 47\4: _Phil. Bot._ s. 215.] - -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 _three_ terms, that of Order, -Genus, and Species in designating minerals, as is done in Mohs's -nomenclature, for example, _Rhombohedral Calc Haloide_, _Paratomous -Hal Baryte_. - -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 -_ite_ to the Order _Silicides_ of Naumann, as Apophyll_ite_, -Stilb_ite_, Leuc_ite_, &c., and to use names of different form in -other orders, as Talc _Spar_ for Brennerite, Pyramidal Titanium -_Oxide_ for Octahedrite. Some such method appears to be the most -likely to give us a tolerable mineralogical nomenclature. - - -APHORISM XVIII. - -_In forming a Terminology, words may be invented when necessary, but -they cannot be conveniently borrowed from casual or arbitrary -circumstances_[48\4]. - -[Note 48\4: I may also refer to _Hist. Sc. Id._ b. viii. c. ii. sec. -2, for some remarks on Terminology.] - -IT will be recollected that Terminology is a language employed for -describing objects, Nomenclature, a body {312} of names of the -objects themselves. The _names_, as was stated in the last maxim, -may be arbitrary; but the _descriptive_ 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 V. But many of the terms were invented by him and other -botanists, as _Perianth_, _Nectary_, _Pericarp_; 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 _Petal_, for one division of the -corolla, was introduced by Fabius Columna. The term _Sepal_ 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 _Receptacle_ of the flower, as it is -termed by Linnæus, or _Torus_ 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[49\4] _Gonophore_, -_Carpophore_, and _Anthophore_, in these cases. - -[Note 49\4: De Candolle's _Th. El._ 405.] - -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 _Dental_, the _Angular_, the _Coronoid_, the -_Articular_, the _Complementary_, and the _Opercular_ Bones. - -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, {313} -which are a part of the terminology of Natural History. Many of -these names are borrowed from natural resemblances, as _Auricula -purple_, _Apple green_, _Straw yellow_; but the names of others are -taken from casual occurrences, mostly, however, such as were already -recognized in common language, as _Prussian blue_, _Dutch orange_, -_King's yellow_. - -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 _poles_, 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 -_positive pole_ and _negative pole_, two words ending in _ode_, from -ὅδος, 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 _Alphode_, and -_Betode_: or, if he wished to pay a tribute of respect to the -discoverers in this department of science, _Galvanode_ and -_Voltaode_, But such words would very justly have been rejected by -Mr. Faraday, and would hardly have obtained any general currency -among men of science. _Zincode_ and _Platinode_, 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 _Zincode_ 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. _Anode_ and _Cathode_, -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 {314} retained. _An_ode and -_Cath_ode, the _rising_ and the _setting_ 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 _Anïon_ and _Cathïon_, to designate the opposite -elements which are separated and liberated at the two _Electrodes_. - - -APHORISM XIX. - -_The meaning of Technical Terms must be fixed by convention, not by -casual reference to the ordinary meaning of words._ - - -IN 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 -_apple-green_ or _French grey_? It might, perhaps, be supposed that, -in the first example, the term _apple_, 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 _immediately_ 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 _tin-white_ or -_pinchbeck-brown_, the metallic colour so denoted ought to start up -in our memory without delay or search. {315} - -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 _papilionaceous_, 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. - -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 _History_. 'Tournefort,' says De Candolle[50\4], '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.' - -[Note 50\4: _Théor. Élém._ p. 327.] - -{316} 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 -_calyx_, the _corolla_, the _stamens_, and the _pistils_: the -sections of the corolla were termed _petals_ by Columna; those of -the calyx were called _sepals_ by Necker[51\4]. Sometimes terms of -greater generality were devised; as _perianth_ to include the calyx -and corolla, whether one or both of these were present[52\4]; -_pericarp_ 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 _pinnatifid_[53\4], -_pinnnatipartite_, _pinnatisect_, _pinnatilobate_, _palmatifid_, -_palmatipartite_, &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 -_bilobate_[54\4] when it is divided into two parts by a notch; but -if the notch go to the middle of its length, it is _bifid_; if it go -near the base of the leaf, it is _bipartite_; if to the base, it is -_bisect_. Thus, too, a pod of a cruciferous plant is a -_silica_[55\4] if it be four times as long as it is broad, but if it -be shorter than this it is a _silicula_. 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[56\4].' - -[Note 51\4: De Candolle, 329.] - -[Note 52\4: For this Erhart and De Candolle use _Perigone_.] - -[Note 53\4: De Candolle, 318.] - -[Note 54\4: _Ibid._ 493.] - -[Note 55\4: _Ibid._ 422.] - -[Note 56\4: Hooker, _Brit. Flo._ p. 450. _Hymenophyllum Wilsoni_, -Scottish filmy fern, abundant in the highlands of Scotland and about -Killarney.] - -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 Measures {317} 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 _talc_ is 1, _gypsum_, 2, _calc spar_ 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 _fixed_ 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. - -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 {318} 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. - -The following Aphorisms respect the Form of Technical Terms. - -By the _Form_ 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. - - -APHORISM XX. - -_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._ - - -THESE 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. - -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 _Heat_, -to express the _science_ of heat, still it would be a bad technical -term, for we cannot derive from it an adjective like {319} -_thermotical_. If _bed_ or _layer_ were an equally good term with -_stratum_, we must still retain the latter, in order that we may use -the derivative _Stratification_, for which the English words cannot -produce an equivalent substitute. We may retain the words _lime_ and -_flint_, but their adjectives for scientific purposes are not _limy_ -and _flinty_, but _calcareous_ and _siliceous_; and hence we are -able to form a compound, as _calcareo-siliceous_, which we could not -do with indigenous words. We might fix the phrases _bent back_ and -_broken_ to mean (of optical rays) that they are reflected and -refracted; but then we should have no means of speaking of the -angles of _Reflection_ and _Refraction_, of the _Refractive_ -Indices, and the like. - -In like manner, so long as anatomists described certain parts of a -vertebra as _vertebral laminæ_, or _vertebral plates_, they had no -adjective whereby to signify the properties of these parts; the term -_Neurapophysis_, given to them by Mr. Owen, supplies the -corresponding expression _neurapophysial_. So again, the term -_Basisphenoid_, employed by the same anatomist, is better than -_basilar_ or _basial process of the sphenoid_, because it gives us -the adjective _basisphenoidal_. And the like remark applies to other -changes recently proposed in the names of portions of the skeleton. - -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 {320} cultivated persons in -every country may convey to each other their ideas without the need -of translation. - -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 _drooping_, _nodding_, _one-sided_, _twining_, _straggling_, -appear better than _cernuous_, _nutant_, _secund_, _volubile_, -_divaricate_. 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. - -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 _Potentilla anserina_, in English botanists, is that -it has _Leaves interruptedly pinnate_, _serrate_, _silky_, _stem -creeping_, _stalks axilllar_, _one-flowered_. Here we have words of -Saxon and Latin origin mingled pretty equally. But the German -description is entirely Teutonic. _Die Blume in Achsel_; _die -Blätter unterbrochen gefiedert_, _die Blättchen scharf gesagt_, _die -Stämme kriechend_, _die Bluthenstiele einblumig_. We could imitate -this in our own language, by saying _brokenly-feathered_, -_sharp-sawed_; by using _threed_ for _ternate_, as the Germans -employ _gedreit_; by saying {321} _fingered-feathered_ for -_digitato-pinnate_, 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. - -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 Fifth -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. _Die Kelch_ and _die Blume_ (the cup and the -flower) easily assume the technical meaning of _calyx_ and -_corolla_; _die Griffel_ (the pencil) becomes _the pistil_; and a -name is easily found for the _pollen_, the _anthers_, and the -_stamens_, by calling them the dust, the dust-cases, and the -dust-threads (_der Staub_, _die Staub-beutel_, or _Staub-fächer_, -and _die Staub-fäden_), 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 _Anatomy of Plants_, the calyx is called -the _impalement_, and the sepals the _impalers_; the petals are -called the _leaves of the flower_; the stamens with their anthers -are the _seminiform attire_. 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 _Numerator_ and -_Denominator_ of a fraction they call the _Namer_ and the _Counter_ -(_Nenner_ and _Zähler_). This course they pursued even where the -expression was erroneous. Thus that portion of the intestines which -ancient anatomists called _Duodenum_, because they falsely estimated -its length at twelve inches, the {322} Germans also term -_Zwölffingerdarm_ (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 -_Muttersackbauchblatte_, the _uterine peritonæum_. - -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 -_Sauerstoff_ and _**Wasserstoff_; Azote is _Stickstoff_ (suffocating -matter); Sulphuric and Sulphurous Acid are _Schwefel-säure_ and -_Schwefelichte-säure_. The Sulphate and Sulphite of Baryta, and -Sulphuret of Baryum, are _Schwefel-säure Baryterde_, -_Schwefelichte-säure Baryterde_, and _Schwefel-baryum_. Carbonate of -Iron is _Kohlen-säures Eisenoxydul_; 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, (_Eisenoxydul_,) 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 _Wasserstoff-säuren_; and of these, the Hydriodic Acid -is _Iodwasserstoff-säure_, 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 _Wasserstoffschwefliges -Schewefellithium_, 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. - -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 {323} 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 _cuneate_, _lunate_, -_hastate_, _sagittate_, _reniform_, than _wedge-shaped_, -_crescent-shaped_, _halbert-headed_, _arrow-headed_, -_kidney-shaped_. _Ringent_ and _personate_ are better than any -English words which we could substitute for them; _labiate_ is more -precise than _lipped_ would readily become. _Urceolate_, -_trochlear_, are more compact than _pitcher-shaped_, -_pulley-shaped_; and _infundibuliform_, _hypocrateriform_, though -long words, are not more inconvenient than _funnel-shaped_ and -_salver-shaped_. In the same way it is better to speak (with Dr. -Prichard[57\4],) of _repent_ and _progressive_ animals, than of -_creeping_ and progressive: the two Latin terms make a better pair -of correlatives. - -[Note 57\4: _Researches_, p. 69.] - -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 Ninth 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 _Palæotherium_, the -_Anoplotherium_, the _Megatherium_, the _Dinotherium_, the -_Chirotherium_, the _Megalichthys_, the _Mastodon_, the -_Ichthyosaurus_, the _Plesiosaurus_, the _Pterodactylus_. To these -others are every year added; as, for instance, very recently, the -_Toxodon_, _Zeuglodon_, and _Phascolotherium_ of Mr. Owen, and the -_Thylacotherium_ of M. Valenciennes. Still more recently the terms -_Glyptodon_, _Mylodon_, _Dicynodon_, _Paloplotherium_, -_Rhynchosaurus_, have been added by Mr. Owen to designate fossil -animals newly determined by him. {324} - -The names of species, as well as of genera, are thus formed from the -Greek: as the Plesiosaurus _dolichodeirus_ (long-necked), -Ichthyosaurus _platyodon_ (broad-toothed), the Irish elk, termed -Cervus _megaceros_ (large-horned). But the descriptive specific -names are also taken from the Latin, as Plesiosaurus _brevirostris_, -_longirostris_, _crassirostris_; besides which there are arbitrary -specific names, which we do not here consider. - -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 Third. Hence the language of -systems in natural history is mixed of ancient and modern languages. -Thus Cuvier's divisions of the vertebrated animals are _Mammifères_ -(Latin), _Oiseaux_, _Reptiles_, _Poissons_; _Bimanes_, -_Quadrumanes_, _Carnassières_, _Rongeurs_, _Pachydermes_ (Greek), -_Ruminans_ (Latin), _Cétacés_ (Latin). In the subordinate divisions -the distribution being more novel, the names are less idiomatic: -thus the kinds of Reptiles are _Cheloniens_, _Sauriens_, -_Ophidiens_, _Batraciens_, all which are of Greek origin. In like -manner. Fish are divided into _Chondropterygiens_, -_Malacopterygiens_, _Acanthopterygiens_. The unvertebrated animals -are _Mollusques_, _Animaux articulés_, and _Animaux rayonnés_; and -the Mollusques are divided into six classes, chiefly according to -the position or form of their foot; namely, _Cephalopodes_, -_Pteropodes_, _Gasteropodes_, _Acephales_, _Brachiopodes_, -_Cirrhopodes_. - -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 _mammifers_ (rather _mammals_), _cetaceans_ or -_cetaces_, _batracians_ (rather _batrachians_), using the words as -substantives. But in other cases we must go back to the Latin: thus -we say _radiate_ {325} animals, or _radiata_ (rather _radials_), for -_rayonnés_. These changes, however, rather refer to another -Aphorism. - -(Mr. Kirby has proposed _radiary_, _radiaries_, for _radiata_.) - -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 _Augite_, _Stilbite_, _Diaspore_, _Dichroite_, -_Dioptase_. 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 _Epidote_, _Peridote_, -_Pleonast_. Similar terms of Greek origin have been introduced by -others, as _Orthite_, _Anorthite_, _Periklin_. Greek names founded -on casual circumstances are less to be commended. Berzelius has -termed a mineral _Eschynite_ from αἰσχυνὴ, _shame_, because it is, -he conceives, a shame for chemists not to have separated its -elements more distinctly than they did at first. - -6. In Botany, the old names of genera of Greek origin are very -numerous, and many of them are descriptive, as _Glycyrhiza_ (γλυκὺς -and ῥιζα, sweet root) liquorice, _Rhododendron_ (rose-tree), -_Hæmatoxylon_ (bloody wood), _Chrysocoma_ (golden hair), -_Alopecurus_ (fox-tail), and many more. In like manner there are -names which derive a descriptive significance from the Latin, either -adjectives, as _Impatiens_, _Gloriosa_, _Sagittaria_, or -substantives irregularly formed, as _Tussilago_ (à tussis -domatione), _Urtica_ (ab urendo tactu), _Salsola_ (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 -_Strelitzia_. - -7. In Chemistry, new substances have of late had names assigned them -from Greek roots, as _Iodine_, from its violet colour, _Chlorine_ -from its green colour. In like manner fluorine has by the French -chemists been called _Phthor_, from its destructive properties. So -the {326} new metals, _Chrome_, _Rhodium_, _Iridium_, _Osmium_, had -names of Greek derivation descriptive of their properties. Some such -terms, however, were borrowed from localities, as _Strontia_, -_Yttria_, the names of new earths. Others have a mixed origin, as -_Pyrogallic_, _Pyroacetic_, and _Pyroligneous_ 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 -_Ellagic_ Acid, framing the root of the name by reading the word -_Galle_ backwards. - -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 Twelfth Maxim, -arbitrary words are less suitable. Mr. Faraday very properly -borrowed from the Greek his terms _Electrolyte_, _Electrode_, -_Anode_, _Cathode_, _Anïon_, _Cathïon_, _Dielectric_. 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. _Thermo-electricity_ and _Electro-dynamics_ were -terms which very naturally offered themselves; Nobili's -_thermo-multiplier_, Snow Harris's _unit-jar_, 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. - -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 _primitive_, _equiaxe_, _inverse_, _metastatique_, -_contrastante_, _imitable_, _birhomboidale_, _prismatique_, -_apophane_, _uniternaire_, _bisunitaire_, _dodécaèdre_, -_contractée_, _dilatée_, _sexduodecimale_, _bisalterne_, -_binoternaire_, and many others. The {327} 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 _bisalterne_ and the _binoternaire_, the former being a -combination of the _metastatique_ with the _prismatique_, the -latter, of the _metastatique_ with the _contrastante_: again, the -_contrastante_, the _mixte_, the _cuboide_, the _contractée_, the -_dilatée_, all contain faces generated by a common law, the index -being respectively altered so as to be in these cases, 3, 3/2, 4/5, -9/4, 5/9; 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. - -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 _zwei-und-ein gliedrig_, and the like. - -In Optics we have some new terms connected with crystalline laws, as -_uniaxal_ and _biaxal_ crystals, _optical axes_, 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 _plane-polarized_ light in opposition to -_circularly-polarized_, and the like. - -This is still more the case in Mechanics, Astronomy, {328} 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 _plane of maximum areas_ was discovered, it had -not some new arbitrary denomination assigned it, but the name which -obviously described it was fixed as a technical name. - -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. - -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. - - -APHORISM XXI. - -_In the composition and inflexion of technical terms, philological -analogies are to be preserved if possible, but modified according to -scientific convenience._ - - -IN 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 {329} 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. - -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. - -1. The combination of different languages in the derivation of -words, though to be avoided in general, is in some cases admissible. - -Such words are condemned by Quintilian and other grammarians, under -the name of hybrids, or things of a mixed race; as _biclinium_ from -_bis_ and κλίνη; _epitogium_, from ἐπὶ and _toga_. 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 -_ichthyology_, not _piscology_, _entomology_, not _insectology_, -_insectivorous_, not _insectophagous_. In like manner, it would be -better to say _unoculus_ than _monoculus_, though the latter has the -sanction of Linnæus, who was a purist in such matters. {330} Dr. -Turner, in his _Chemistry_, speaks of _protoxides_ and _binoxides_, -which combination violates the rule for making the materials of our -terms as homogeneous as possible; _protoxide_ and _deutoxide_ would -be preferable, both on this and on other accounts. - -Yet this rule admits of exceptions. _Mineralogy_, with its Greek -termination, has for its root _minera_, a medieval Latin word of -Teutonic origin, and is preferable to _Oryctology_. _Terminology_ -appears to be better than _Glossology_: which according to its -derivation would be rather the science of language in general than -of technical terms; and _Horology_, from ὅρος, 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. - -Indeed, the English reader is become quite familiar with the -termination _ology_, 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 _Tidology_, the doctrine of -the Tides. - -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 _arch_, (ἀρχὸς a leader,) -as we see in _archbishop_, _archduke_. It is effected in a great -degree for the preposition _anti_: thus we speak of _anti-slavery_ -societies, _anti-reformers_, _anti-bilious_, or _anti-acid_ -medicines, without being conscious of any anomaly. The same is the -case with the Latin preposition _præ_ or _pre_, as appears from such -words as _pre-engage_, _pre-arrange_, _pre-judge_, _pre-paid_; and -in some measure with _pro_, for in colloquial language we speak of -_pro-catholics_ and _anti-catholics_. Also the preposition _ante_ is -similarly used, as _ante-nicene_ fathers. The preposition _co_, -abbreviated from _con_, and {331} implying things to be simultaneous -or connected, is firmly established as part of the language, as we -see in _coexist_, _coheir_, _coordinate_; hence I have called those -lines _cotidal_ lines which pass through places where the high water -of the tide occurs simultaneously. - -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 _ive_ belongs peculiarly to Latin adjectives, yet we -say _sportive_, _talkative_. In like manner, _able_ is added to -words which are not Latin, as _eatable_, _drinkable_, _pitiable_, -_enviable_. Also the termination _al_ and _ical_ are used with -various roots, as _loyal_, _royal_, _farcical_, _whimsical_; hence -we may make the adjective _tidal_ from _tide_. This ending, _al_, is -also added to abstract terms in _ion_, as _occasional_, -_provisional_, _intentional_, _national_; hence we may, if -necessary, use such words as _educational_, _terminational_. The -ending _ic_ appears to be suited to proper names, as _Pindaric_, -_Socratic_, _Platonic_; hence it may be used when scientific words -are derived from proper names, as _Voltaic_ or _Galvanic_ -electricity: to which I have proposed to add _Franklinic_. - -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; _ivus_ becomes -_ive_, as _decursive_; _inus_ becomes _ine_, as in _ferine_; _atus_ -becomes _ate_, as _hastate_; and _us_ often becomes _ous_, as -_rufous_; _aris_ becomes _ary_, as _axillary_; _ens_ becomes _ent_, -as _ringent_. 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 _cétacé_, _crustacé_, _testacé_, may become either -_cetaceous_, _crustaceous_, _testaceous_, according to the analogy -of _farinaceous_, _predaceous_, or else _cetacean_, _crustacean_, -{332} _testacean_, imitating the form of _patrician_. 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. - -In pursuance of the same remark, _rongeur_ becomes _rodent_; and -_edenté_ would become _edentate_, but that this word is rejected on -another account: the adjectives _bimane_ and _quadrumane_ are -_bimanous_ and _quadrumanous_. - -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. -_The happy_ or _the doomed_ 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 _the -squamate_, and still less could we call any such animal _a -squamate_, or speak of _squamates_ in the plural. Some of the forms -of our adjectives, however, do admit of this substantive use. Thus -we talk of _Europeans_, _plebeians_, _republicans_; of _divines_ and -_masculines_; of the _ultramontanes_; of _mordants_ and -_brilliants_; of _abstergents_ and _emollients_; of _mercenaries_ -and _tributaries_; of _animals_, _mammals_, and _officials_; of -_dissuasives_ and _motives_. We cannot generally use in this way -adjectives in _ous_, nor in _ate_ (though _reprobates_ is an -exception), nor English participles, nor adjectives in which there -is no termination imitating the Latin, as _happy_, _good_. 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. - -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, {333} -according to Cuvier, are _Bimanes_, _Quadrumanes_, _Carnassiers_, -_Rongeurs_, _Edentés_, _Ruminants_, _Pachydermes_, _Cétacés_; and of -these, _Bimanes_, _Quadrumanes_, _Rodents_, _Ruminants_, -_Pachyderms_ are admissible as English substantives on the grounds -just stated. _Cetaceous_ could not be used substantively; but -_Cetacean_ in such a usage is sufficiently countenanced by such -cases as we have mentioned, _patrician_, &c.; hence we adopt this -form. We have no English word equivalent to the French -_Carnassiers_: the English translator of Cuvier has not provided -English words for his technical terms; but has formed a Latin word, -_Carnaria_, to represent the French terms. From this we might -readily form _Carnaries_; but it appears much better to take the -Linnæan name _Feræ_ as our root, from which we may take _Ferine_, -substantive as well as adjective; and hence we call this order -_Ferines_. The word for which it is most difficult to provide a -proper representation is _Edenté_, _Edentata_: for, as we have said, -it would be very harsh to speak of the order as the _Edentates_; and -if we were to abbreviate the word into _edent_, we should suggest a -false analogy with _rodent_, for as _rodent_ is _quod rodit_, that -which gnaws, _edent_ would be _quod edit_, that which eats. And even -if we were to take _edent_ as a substantive, we could hardly use it -as an adjective: we should still have to say, for example, the -_edentate_ form of head. For these reasons it appears best to alter -the form of the word, and to call the Order the _Edentals_, which is -quite allowable, both as adjective and substantive. - -[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 _edentata_, a special meaning, implying the absence of one -particular kind of teeth, namely, incisive teeth. Linnæus called the -equivalent order _Bruta_. We could not {334} apply in this case the -term _Brutes_; for common language has already attached to the word -a wider meaning, too fixedly for scientific use to trifle with it.] - -There are several other words in _ate_ about which there is the same -difficulty in providing substantive forms. Are we to speak of -_Vertebrates_? or would it not be better, in agreement with what has -been said above, to call these _Vertebrals_, and the opposite class -_Invertebrals_? - -There are similar difficulties with regard to the names of -subordinate portions of zoological classification; thus the Ferines -are divided by Cuvier into _Cheiroptéres_, _Insectivores_, -_Carnivores_; and these latter into _Plantigrades_, _Digitigrades_, -_Amphibies_, _Marsupiaux_. There is not any great harshness in -naturalizing these substantives as _Chiropters_, _Insectivores_, -_Carnivores_, _Plantigrades_, _Digitigrades_, _Amphibians_, and -_Marsupials_. These words _Carnivores_ and _Insectivores_ are -better, because of more familiar origin, than Greek terms; otherwise -we might, if necessary, speak of _Zoophagans_ and _Entomophagans_. - -It is only with certain familiar adjectival terminations, as _ous_ -and _ate_, that there is a difficulty in using the word as -substantive. When this can be avoided, we readily accept the new -word, as _Pachyderms_, and in like manner _Mollusks_. - -If we examine the names of the Orders of Birds, we find that they -are in Latin, _Predatores_ or _Accipitres_, _Passeres_, _Scansores_, -_Rasores_ or _Gallinæ_, _Grallatores_, _Palmipedes_ and _Anseres_: -Cuvier's Orders are, _Oiseaux de Proie_, _Passereaux_, _Grimpeurs_, -_Gallinacés_, _Échassiers_, _Palmipedes_. These may be englished -conveniently as _Predators_, _Passerines_, _Scansors_, -_Gallinaceans_, (rather than _Rasors_,) _Grallators_, _Palmipedans_, -[or rather _Palmipeds_, like _Bipeds_]. _Scansors_, _Grallators_, -and _Rasors_, are better, as technical terms, than _Climbers_, -_Waders,_ and _Scratchers_. We might venture to anglicize the -terminations of the names which Cuvier gives to the divisions of -these Orders: thus the Predators are the _Diurnals_ and the -_Nocturnals_; the Passerines are the _Dentirostres_, the -_Fissirostres_, the {335} _Conirostres_, the _Tenuirostres_, and the -_Syndactyls_: the word _lustre_ showing that the former termination -is allowable. The Scansors are not sub-divided, nor are the -Gallinaceans. The Grallators are _Pressirostres_, _Cultrirostres_, -_Macrodactyls_. The Palmipeds are the _Plungers_, the _Longipens_, -the _Totipalmes_ and the _Lamellirostres_. - -The next class of Vertebrals is the _Reptiles_, and these are either -_Chelonians_, _Saurians_, _Ophidians_, or _Batrachians_. Cuvier -writes _Batraciens_, but we prefer the spelling to which the Greek -word directs us. - -The last or lowest class is the _Fishes_, 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 -_Chondropterygians_, _Malacopterygians_, _Lophobranchs_, -_Plectognaths_, _Gymnodonts_, _Scleroderms_. _Discoboles_ and -_Apodes_ 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 _ides_ from the name of a genus, as _Gadoides_, -_Gobiöides_, or by gallicizing the Latin name of the genus, as -_Salmones_ from _Salmo_, _Clupes_ from _Clupea_, _Ésoces_ from -_Esox_, _Cyprins_ from _Cyprinus_. In these cases Agassiz's -favourite form of names for families of fishes has led English -writers to use the words _Gadoids_, _Gobioids_, _Salmonoids_, -_Clupeoids_, _Lucioids_ (for _Ésoces_), _Cyprinoids_, &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 _Pisces_. One of the -orders of fishes, co-ordinate with the Chondropterygians and the -Lophobranchs, is termed _Osseux_ by Cuvier. It appears hardly worth -while to invent a substantive word for this, when _Bony Fishes_ is -so simple a phrase, and may readily be understood as a technical -name of a systematic order. - -The Mollusks are the next Class; and these are divided into -_Cephallopods_, _Gasteropods_, and the like. The Gasteropods are -_Nudibranchs_, _Inferobranchs_, {336} _Tectibranchs,_ -_Pectinibranchs_, _Scutibranchs_, and _Cyclobranchs_. In framing -most of these terms Cuvier has made hybrids by a combination of a -Latin word with _branchiæ_ 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 -_Pulmonés_, which we must make _Pulmonians_. In like manner the -subdivisions of the Pectinibranchs are the _Trochoidans_ and -_Buccinoidans_, (_Trochoïdes_, _Buccinoïdes)_. The _Acéphales_, -another order of Mollusks, may be _Acephals_ in English. - -After these comes the third grand division, _Articulated Animals_, -and these are _Annelidans_, _Crustaceans,_ _Arachnidans_, and -_Insects_. 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. - -Finally, we have the fourth grand division of animals, the -_Rayonnés_, or _Radiata_; which, for reasons already given, we may -call _Radials_, or _Radiaries_. These are _Echinoderms_, -_Intestinals_, (or rather _Entozoans_,) _Acalephes_, and _Polyps_. -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 _Polypier_; the word has been anglicized by the -word _polypary_, after the analogy of _aviary_ and _apiary_. Thus -Polyps are either _Polyps with Polyparies_ or _Naked Polyps_. - -Any common kind of Polyps has usually in the English language been -called _Polypus_, the Greek termination being retained. This -termination in _us_, 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 _Polypi_ the word ceases to be English, while _Polypuses_ -is harsh: and there is the additional inconvenience, that both these -forms would indicate the plural of individuals rather than of -classes. {337} If we were to say, 'The Corallines are a Family of -the _Polypuses with Polyparies_,' it would not at once occur to the -reader that the last three words formed a technical phrase. - -This termination _us_ which must thus be excluded from the names of -families, may be admitted in the designation of genera; of animals, -as _Nautilus_, _Echinus_, _Hippopotamus_; and of plants, as -_Crocus_, _Asparagus_, _Narcissus_, _Acanthus_, _Ranunculus_, -_Fungus_. The same form occurs in other technical words, as _Fucus_, -_Mucus_, _Œsophagus_, _Hydrocephalus_, _Callus_, _Calculus_, -_Uterus_, _Fœtus_, _Radius_, _Focus_, _Apparatus_. 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, _Ichthyosaur_, -_Plesiosaur_, _Pterodactyl_. In like manner Mr. Owen anglicizes the -termination _erium_, and speaks of the _Anoplothere_ and -_Paleothere_. - -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, -_Miocene_, _Pliocene,_ can be used as substantives; but if such -words as _Mioneous_, _Plioneous_, had suggested themselves, they -must have been rejected, though of equivalent signification, as not -fulfilling this condition. - -4. (_a._) Abstract substantives can easily be formed from -adjectives: from electric we have _electricity_; from galvanic, -_galvanism_; from organic, _organization_; _velocity_, _levity_, -_gravity_, are borrowed from Latin adjectives. _Caloric_ is -familiarly used for the matter of heat, though the form of the word -is not supported by any obvious analogy. - -(_b._) 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_ibility_ or conduc_ibility_ with regard to -heat. The bodies are conduct_ive_, and their property is -conduct_ivity_. - -(_c._) The terminations _ize_ (rather than _ise_), _ism_, and _ist_, -are applied to words of all origins: thus we have to {338} -_pulverize_, to _colonize_, _Witticism_, _Heathenism_, _Journalist_, -_Tobacconist_. Hence we may make such words when they are wanted. As -we cannot use _physician_ for a cultivator of physics, I have called -him a _Physicist_. We need very much a name to describe a cultivator -of science in general. I should incline to call him a _Scientist_. -Thus we might say, that as an Artist is a Musician, Painter, or -Poet, a Scientist is a Mathematician, Physicist, or Naturalist. - -(_d._) Connected with verbs in _ize_, we have abstract nouns in -_ization_, as _polarization_, _crystallization_. These it appears -proper to spell in English with _z_ rather than _s_; governing our -practice by the Greek verbal termination ίζω which we imitate. But -we must observe that verbs and substantives in _yse_, (_analyse_), -belong to a different analogy, giving an abstract noun in _ysis_ and -an adjective _ytic_ or _ytical_; (_analysis_, _analytic_, -_analytical_). Hence _electrolyse_ is more proper than -_electrolyze_. - -(_e._) The names of many sciences end in _ics_ after the analogy of -_Mathematics_, _Metaphysics_; as _Optics_, _Mechanics_. But these, -in most other languages, as in our own formerly, have the singular -form _Optice_, _l'Optique_, _Optik_, _Optick_: and though we now write -_Optics_, 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 -_Logic_ and _Rhetoric_, when we have words to construct. Hence we -may call the science of languages _Linguistic_, as it is called by -the best German writers, for instance, William Von Humboldt. - -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 οι and αι, the Latin -_oe_ and _ae_, are all converted into a simple _e_, as in _E_conomy, -Geod_e_sy, p_e_nal, C_e_sar. Hence, according to common usage, we -should write ph_e_nomena, not ph_æ_nomena, pal_e_ontology, not -pal_æ_ontology, mioc_e_ne not mioc_æ_ne, p_e_kilite not {339} -p_œ_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 _poikilitic_, not _pecilitic_, group of -strata: _palæontology_ is the spelling commonly adopted; and in -imitation of this I have written _palætiology_. The diphthong ει was -by the Latins changed into _i_, as in Arist_i_des; and hence this -has been the usual form in English. Some recent authors indeed (Mr. -Mitford for instance) write Arist_eid_es; but the former appears to -be the more legitimate. Hence we write m_i_ocene, pl_i_ocene, not -m_ei_ocene, pl_ei_ocene. The Greek υ becomes _y_, and ου becomes -_u_, in English as in Latin, as cr_y_stal, col_u_re. The consonants -κ and χ become _c_ and _ch_ according to common usage. Hence we -write _crystal_, not _chrystal_, batra_ch_ian, not batra_c_ian, -_c_ryolite, not _ch_ryolite. As, however, the letter _c_ before _e_ -and _i_ differs from _k_, which is the sound we assign to the Greek -κ, it may be allowable to use _k_ in order to avoid this confusion. -Thus, as we have seen, poi_k_ilite has been used, as well as -pe_c_ilite. Even in common language some authors write s_k_eptic, -which appears to be better than s_c_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 _cathode_, the elements of an electrolyte -which go to the anode and cathode respectively may be termed the -anion and cat_h_ion; although the Greek would suggest catïon, -(κατίον). - -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_ous_ and sulphur_ic_ acids; sulph_ates_, sulph_ites_, and -sulph_urets_. Since the introduction of the artifice by the -Lavoisierian school, it has been extended to some new cases. The -Chlor_ine_, Fluor_ine_, Brom_ine_, Iod_ine_, had their names put -into that shape in consequence of their supposed analogy: and for -the same reason have been termed Chlore, {340} Phlore, Brome, Iode, -by French chemists. In like manner, the names of metals in their -Latin form have been made to end in _um_, as Osmium, Palladium; and -hence it is better to say Platin_um_, Molybden_um_, than Platin_a_, -Molybden_a_. It has been proposed to term the basis of Boracic acid -Bor_on_; and those who conceive that the basis of Silica has an -analogy with Boron have proposed to term it Silic_on_, while those -who look upon it as a metal would name it Silic_ium_. Seleni_um_ 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_en_, as it is in -German. Phosph_orus_ in like manner might be Phosph_ur_, which would -indicate its analogy with Sulph_ur_. - -The resource which terminations offer has been applied in other -cases. The names of many species of minerals end in _lite_, or -_ite_, as Stauro_lite_, Aug_ite_. 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_ites_, from Zamia, Lycopod_ites_ from Lycopodium. - -Names of different genera which differ in termination only are -properly condemned by Linnæus[58\4]; as _Alsine_, _Alsinoides_, -_Alsinella_, _Alsinastrum_; for there is no definite relation marked -by those terminations. Linnæus gives to such genera distinct names, -_Alsine_, _Bufonia_, _Sagina_, _Elatine_. - -[Note 58\4: _Phil. Bot._ 231.] - -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 _ane_ for the smallest proportion of -Chlorine, and _anea_ for the larger, as Cupr_ane_, Cupr_anea_. In -this nomenclature, common salt would be _Sodane_, and Chloride of -Nitrogen would be _Azotane_. This suggestion never found favour. It -was {341} 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_ous_, Sulphur_ic_. 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. - -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 _ite_), Scolexer_ose_, Opsim_ose_, Exanthel_ose_, -&c.; Diacr_ase_, Panab_ase_, Neopl_ase_; Neocl_ese_; Rhodo_ise_, -Stibicon_ise_, &c.; Marcel_ine_, Wilhelm_ine_, &c.; Exit_ele_, 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. - - -APHORISM XXII. - -_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._ - - -WE 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 {342} 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[59\4].' 'A passable generic -name is not to be changed for another, though more apt[60\4]'. 'New -generic names are not to be framed so long as passable synonyms are -at hand[61\4].' 'A generic name of one genus, except it be -superfluous, is not to be transferred to another genus, though it -suit the other better[62\4].' '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[63\4].' And -though he rejects all _generic_ names which have not a Greek or -Latin root[64\4], 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 _Thea_, -which is the Greek for goddess; _Coffea_, which might seem to come -from a Greek word denoting silence (κωφός); _Cheiranthus_, which -appears to mean hand-flower, but is really derived from the Arabic -_Keiri_: and many others. - -[Note 59\4: _Philosophia Botanica_, Art. 242.] - -[Note 60\4: Art. 246.] - -[Note 61\4: Art. 247.] - -[Note 62\4: Art. 249.] - -[Note 63\4: Art. 249.] - -[Note 64\4: Art. 232.] - -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 _Spar_, because _Felspar_ belongs to it. I -shall venture to offer a few suggestions on this subject of -Mineralogical Nomenclature. - -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 Ninth Aphorism, that no -permanent system of names can be looked for, till a {343} 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 _Salts_;--that the Haloids are, many of them, already called -_Spars_, as _Calc Spar_, _Heavy Spar_, _Iron Spar_, _Zinc -Spar_;--that the _Silicides_, the most numerous and difficult class, -are denoted for the most part, by single words, many of which end in -_ite_;--that the other classes, or subclasses, _Oxides_, _Pyrites_, -_Glances_, and _Blendes_, have commonly been so termed; as _Red Iron -Oxide_, _Iron Pyrites_, _Zinc Blende_;--while pure metals have -usually had the adjective _native_ prefixed, as _Native Gold_, -_Native Copper_. 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 _salt_ or _spar_ included in their -name, as _Natron Salt_, _Glauber Salt_, _Mock Salt_; _Calc Spar_, -_Bitter Spar_, (Carbonate of Lime and Magnesia), _Fluor Spar_, -_Phosphor Spar_ (Phosphate of Lime), _Heavy Spar_, _Celestine Spar_ -(Sulphate of Strontian), _Chromic Lead Spar_ (Chromate of Lead); the -_Silicides_ might all have the name constructed so as to be a single -word ending in _ite_, as _Chabasite_ (Chabasie), _Natrolite_ -(Mesotype), _Sommite_ (Nepheline), _Pistacite_ (Epidote); from this -rule might be excepted the _Gems_, as _Topaz_, _Emerald_, -_Corundum_, which might retain their old names. The Oxides, Pyrites, -Glances, and Blendes, might be so termed; thus we should have -_Tungstic Iron Oxide_ (usually called Tungstate of Iron), _Arsenical -Iron Pyrites_ (Mispickel), _Tetrahedral Copper Glance_ (Fahlerz), -_Quicksilver Blende_ (Cinnabar), and the metals might be termed -_native_, as _Native Copper_, _Native Silver_. - -Such a nomenclature would take in a very large {344} proportion of -commonly received appellations, especially if we were to select -among the synonyms, as is proposed above in the case of _Glauber -Salt_, _Bitter Spar_, _Sommite_, _Pistacite_, _Natrolite_. 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. - -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 _Carbonate Calcaire_, _Carbonate Witherite_, _Sulphate -Couperose_, _Silicate Stilbite_, _Silicate Chabasie_, 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. - -We have already noticed Mr. Mohs's designations for two of the -Systems of Crystallization, the _Pyramidal_ and the _Prismatic_, as -not characteristic. If it were thought advisable to reform such a -defect, this might be done by calling them the _Square Pyramidal_ -and the _Oblong Prismatic_, which terms, while they expressed the -real distinction of the systems, would be intelligible at once to -those acquainted with the Mohsian terminology. - -I will mention another suggestion respecting the introduction of an -improvement in scientific language. The term _Depolarization_ 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 _Depolarization_, no better term having been yet -devised. I have proposed and used the term _Dipolarization_, {345} -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. - -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 -_Æsthetics_; αἰσθάνεσθαι, _to perceive_, being a word which appeared -to them fit to designate the perception of beauty in particular. -Since, however, _æsthetics_ would naturally denote the Doctrine of -Perception in general; since this Doctrine requires a name; since -the term _æsthetics_ 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 _Callæsthetics_, or rather (in agreement with what -was said in page 338) _Callæsthetic_, the science of the perception -of beauty. - - - -{{346}} -FURTHER ILLUSTRATIONS OF THE APHORISMS - ON SCIENTIFIC LANGUAGE, FROM THE - RECENT COURSE OF SCIENCES. - - -1. BOTANY. - -THE 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[65\4], that I shall venture to adopt -his judgment as an Aphorism, and give his reasons for it. - -[Note 65\4: _Linnæan Society's Proceedings_, vol. ii. p. 30 (June, -1857).] - - -APHORISM XXIII. - -_It is of the greatest importance that the Groups which give their -substantive names to every included species should remain large._ - - -IT will be recollected that according to the Linnæan nomenclature, -the genus is marked by a substantive, (as _Rosa_), and the species -designated by an adjective added to this substantive, (as _Rosa -Alpina_); while the natural orders are described by adjectives taken -substantively, (as _Rosaceæ_), 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 {347} 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. - -Now two courses have been followed in providing names for these -subordinate groups. - -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 _subgenera_, _sections_, _subsections_, -_divisions_, &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. - -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. - -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. - -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 {348} 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. - -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 _Ficus_, _Begonia_, -_Arum_, _Erica_, &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. - -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. - -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 {349} or -divisions. But this is but an incomplete resumption of the old -principles, without the advantage of the old nomenclature. - -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 _Urostigma_ or _Phannacosyce_, new genera -formed out of the old genus _Ficus_, are better defined than the -genus _Ficus_: or that the new genera which have lately been cut out -of the old genus _Begonia_, form more natural groups than _Begonia_ -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. - -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. - - -2. COMPARATIVE ANATOMY. - -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. - -There is, at first sight, this broad difference between the -descriptive language of Botany and of Comparative {350} Anatomy; -that in the former science, we have comparatively few parts to -describe, (_calyx_, _corolla_, _stamen_, _pistil_, _pericarp_, -_seed_, &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 -_description_; the language of Comparative Anatomy must have for its -basis _morphology_. Accordingly, Mr. Owen's terms are selected so as -to express the analogies, or, as he calls them, the _homologies_ of -the skeleton; those parts of the skeleton being termed _homologues_, -which have the same place in the general type, and therefore ought -to have the same name. - -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 (_Phil. Bot._ Art. 86). -CALYX, _Cortex_ plantæ in Fructificatione præsens. -COROLLA, _Liber_ plantæ in Flora præsens. -STAMEN, Viscus pro Pollinis præparatione. -PISTILLUM, Viscus fructui adherens pro Pollinis receptione. -PERICARPIUM, Viscus gravidum seminibus, quæ matura dimittit. - -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, _what_ 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 -{351} 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 -_Terminology_, not to the _Nomenclature_ 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. - -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. - -Mr. Owen, in his _Homologies of the Vertebrate Skeleton_, 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 -{352} 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 Aphorism X.) 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 Aphorism XIII. -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 _ossa wormiana_; or even from an accident in anatomical -history, as _os innominatum_. - -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 _presphenoid_ for _sphenöide anterieur_. So -also _prefrontal_ is preferred to _anterior frontal_, and -_postfrontal_ to _posterior frontal_. 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: - - -APHORISM XXIV. - -_It is advisable to substitute definite single names for descriptive -phrases as better instruments of thought._ - - -IT 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. - -Again: some of the first of the terms which Mr. Owen proposes -illustrate, and confirm by their manifest claim {353} to acceptance, -a maxim which we stated as Aphorism XXII.: 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. - -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 _basioccipital_. - -Again: for the term 'suroccipital' of Geoffroy, Mr. Owen proposes -_paroccipital_, 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 Aphorism XXI.: 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.' - -So again we have illustrations of our Aphorism XII., 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 _vomer_, the ploughshare: a term -which Geoffroy rejected, but which Mr. Owen retains, he says, 'When -Geoffrey was induced to reject the term _vomer_ 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 {354} -has, a purely arbitrary term, it is superior and preferable to any -partially descriptive one.' - -Another condition which I have mentioned in Aphorism XX., as -valuable in technical terms is, that they should be susceptible of -such grammatical relations as their scientific use requires. - -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, _a better instrument of thought_. 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, _capable of every requisite inflection_ to -express the proportion of the parts. - -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 Aphorism -X.: 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. - -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 {355} 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: - - -APHORISM XXV. - -_In an advanced Science, the history of the Language of the Science -is the history of the Science itself._ - - -I HAVE already stated in previous Aphorisms (VIII. and XI.) 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. - -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, _if_ they _are_ 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. - -But further: there is another kind of homology which Mr. Owen calls -_General_ 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 {356} -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 _centrum_, -_neurapophysis_, _parapophysis_, _pleurapophysis_, _hæmaphysis_, -_neural spine_ and _hæmal spine_, with certain exogenous parts. - -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 _History_ (_Hist. I. S._ 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' _On the signification of the bones of the Skull_, 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 -_Archetype and Homologies of the Vertebrate Skeleton_ (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 _History of the Inductive Sciences_ (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. - -Besides these doctrines of _Special Homology_ by which the bones of -all vertebrates are referred to their corresponding bones in the -human skeleton, and of _General Homology_, by which the bones are -referred to the parts of vertebræ which they represent, Mr. Owen -treats of _Serial Homology_, 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 _basioccipital_, _basisphenoid_, -_presphenoid_ and _vomer_ are {357} homotypes with the _centrums_ of -all succeeding vertebræ. The _excoccipitals_,_ alisphenoids_, -_orbitosphenoids_, and _prefrontals_, are homotypes with the -_neurapophyses_ of all the succeeding vertebræ. The _paroccipitals_, -_mactoids_ and _postfrontals_, with the _transverse processes_ 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. - -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. - - -APHORISM XXVI. - -_In the Terminology of Science it may be necessary to employ -letters, numbers, and algebraical symbols._ - - -1. MINERALOGY. - -I HAVE already said, in Aphorism XV., that symbols have been found -requisite as a part of the terminology of Mineralogy. The _names_ -proposed by Haüy, borrowed from the crystalline laws, were so -inadequate and unsystematic that they could not be retained. He -himself proposed a _notation_ for crystalline forms, founded upon -his principle of the derivation of such forms from a _primitive_ -form, by _decrements_, on its _edges_ or its _angles_. To denote -this derivation he took the first letters of the three syllables to -mark the faces of the _PriMiTive_ form, _P_, _M_, _T_; the vowels -_A_, _E_, _I_, _O_ to mark the angles; the consonants _B_, _C_, _D_, -&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, - 1 - _B_ -represented the result of a derivation by a decrement of one row -{358} on an edge; that is, a rhombic octahedron; and - 1 -_BP_ 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 - ½ -_B_² _C G_² ²_G_. - -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[66\4], 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 _R_, he derived, by a -certain process, a series of other rhombohedrons, which he denoted -by _R_ + 1, _R_ + 2, _R_ − 1, &c.; and then, by another mode of -derivation from them, he obtained forms which he marked as -(_R_ + 2)², (_R_ + 2)³, &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. - -[Note 66\4: _Hist. Ind. Sc._ b. xv. c. 4.] - -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 (_R_ + 2)³ we might write 2 _R_ 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 _O_, _R_, _P_; and from these -are derived, by certain laws, such symbols as - 3 _O_ ½, ∞ _R_ 2, ½ _P_ 2, {359} -which have their definite signification flowing from the rules of -the notation. - -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 _three_ 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 _holohedral_ but -_hemihedral_, 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. - -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. - -2. CHEMISTRY. - -The same has long been the case in Chemistry. As I have stated -elsewhere[67\4], 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 Aphorism II. -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 {360} relations -which it was very important to keep in sight. If _N_ represents -Nitrogen and _O_ Oxygen, the compounds of the two elements just -mentioned might be denoted by _N_ + _O_, _N_ + 2_O_, _N_ + 3_O_, -_N_ + 4_O_, _N_ + 5_O_. And by adopting a letter for each of the -elementary substances, all the combinations of them might be -expressed in this manner. - -[Note 67\4: _Hist. Ind. Sc._ b. xiv. c. 6.] - -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 _Fe_ be iron and _C_ be carbon, _Fe_ + _O_ will -be the protoxide of iron, and _C_ + 2_O_ will be carbonic acid; and -the carbonate of iron (more properly carbonate of protoxide of -iron), may be represented by - (_Fe_ + _O_) + (_C_ + 2_O_) -where the brackets indicate the first stage of composition. - -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[68\4] -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 [.]_Fe_ + [..]_C_. But Berzelius further introduced into -his notation indexes such as in algebra denote involution to the -square, cube, &c. Thus _Cu_ being copper, the sulphate of copper is -represented by [...]_S_²[..]_Cu_. 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[69\4], '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, {361} 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 - [..]_Cu_[...]_S_² + 10_H_²_O_. -Now this Formula expresses the following propositions: -'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. - -[Note 68\4: _System of Mineralogy_, 1816.] - -[Note 69\4: _Jahresbericht_, 1824, p. 119.] - -'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 - [..]_K_[...]_S_² + 2[...]_Al_[...]_S_³ + 48_H_²_O_. -It would take half a page to express all which this Formula contains. - -'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. {362} - -'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 _KS_^6, -_KS_^8, _KS_^10 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, - _KS_² + 2_As S_³, -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.' - -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. - -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 -_Cu O_, _SO__3 + _KO_, _SO__3. - -What has been said is applicable mainly to inorganic bodies (as -salts and minerals)[70\4]. In these bodies there is (at least -according to the views of many intelligent chemists) a _binary_ plan -of combination, union taking {363} place between _pairs_ 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 _Cu O_, _SO__3 + _KO_, _SO__3. - -[Note 70\4: Fownes's _Chemistry_. Part iii.] - -The most complicated products of inorganic chemistry may be thus -shown to be built up by this repeated _pairing_ 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 _C__12 _H__11 _O__11, or morphia[71\4], which is -_C__35 _H__20 _NO__6, 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. - -[Note 71\4: Fownes's _Chemistry_, p. 354.] - -It is perhaps a consequence of this peculiarity that organic -compounds are _unstable_ in comparison with inorganic. In unorganic -substances generally the elements are combined in such a way that -the most powerful affinities are satisfied[72\4], 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. - -[Note 72\4: See _Hist. Ind. Sc._ b. xiv. c. 3.] - -There is another property of many organic substances which is called -the _Law of Substitution_. The {364} 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 _Dutch liquid_ has the -elements _C__4 _H__4 _Cl__2: but this substance is affected by -chlorine (_Cl_) 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 - _H__3 _H__2 - _C__4 _H__4 _Cl__2; _C__4 { } _Cl__2; _C_4 { } _Cl__2. - _Cl_ _Cl_2 - -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. - - -APHORISM XXVII. - -_In using algebraical symbols as a part of scientific language, -violations of algebraical analogy are to be avoided, but may be -admitted when necessary._ - - -AS 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 -_C__2, _O__3 rather than _C_², _O_³, which signify the square of _C_ -and the cube of _O_. 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. {365} - - -APHORISM XXVIII. - -_In a complex science, which is in a state of transition, capricious -and detached derivations of terms are common; but are not -satisfactory._ - - -IN 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. - -I have mentioned (Aph. **XX. sect. 7) the word _Ellagic_ (acid), made -by inverting the word _Galle_. 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 **_Ethal_, from the first syllables of the words _ether_ and -_alcohol_, because of its analogy to those liquids in point of -composition[73\4]. So Liebig has the word _chloral_[74\4]. - -[Note: 73\4: Turner's _Chemistry_, 1834, p. 955] - -[Note: 74\4: Berzelius' _Jahresbericht_, xv. p. 372.] - -Liebig, examining the product of distillation of alcohol, sulphuric -acid and amber, found a substance which he termed _Aldehyd_, from -the words _Al_cohol _dehyd_rogenated[75\4]. This mode of making -Words has been strongly objected to by Mr. Dumas[76\4]. Still more -has he objected to the word _Mercaptan_ (of Zeise), which {366} he -says rests upon a mere play of words; for it means both _mercurium -captans_ and _mercurio aptum_. - -[Note 75\4: _Ibid._ xvi. p. 308.] - -[Note 76\4: _Leçons de Chimie_, p. 354.] - -Dumas and Peligot, working on pyroligneous acids, found reason to -believe the existence of a substance[77\4] which they called -_methylene_, deriving the name from _methy_, a spirituous fluid, and -_hyle_, wood. Berzelius remarks that the name should rather be -_methyl_, and that ὕλη may be taken in its signification of matter, -to imply the Radical of Wine: and he proposes that the older -Æther-Radical, _C__4 _H__10 shall be called _Æthyl_, the newer, -_C__2 _H__6, _Methyl_. - -[Note 77\4: Berzelius' _Jahresbericht_, xv. (1836).] - -This notion of marking by the termination _yl_ 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 ὕλη: and such -hypothetical radicals of bases have been termed in general _basyls_. - -Bunsen obtained from Cadet's fuming liquid a substance which he -called _Alkarsin_ (_alk_ali-_ars_enic?): and the substance produced -from this by oxidation he called _Alkargen_[78\4]. Berzelius was of -opinion, that the true view of its composition was that it contained -a compound ternary radical = _C_^6 _H_^12 _As_^2, after the manner of -organic bodies; and he proposed for this the name[79\4] _Kakodyl_. -Alkarsin is Kakodyl-oxyd, [.]Kd, Alkargen is Kakodyl-acid, [∴]Kd. - -[Note 78\4: _Ibid._ xviii. p. 497.] - -[Note 79\4: _Ibid._ xx. p. 527.] - -The discovery of Kakodyl was the first instance of the insulation of -an organic metallic _basyl_[80\4]. - -[Note 80\4: Miller's _Chemistry_, iii. 220.] - -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 _Valyl_ _C__16 _H__18. - -_Chloroform_ is per_chloride_ of _formyl_, the hypothetical radical -of formic acid[81\4]. - -[Note 81\4: Dumas, _Leçons sur la Phil. Chim._ p. 356.] - -{367} The discovery of such bases goes back to 1815. The substance -formerly called _Prussiate of Mercury_, being treated in a -particular manner, was resolved into metallic mercury and -_Cyanogen_. This substance, _Cyanogen_, is, according to the older -nomenclature, _Bicarburet of Nitrogen_; but chemists are agreed that -its most convenient name is _Cyanogen_, proposed by its discoverer, -Gay-Lussac, in 1815[82\4]. 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. - -[Note 82\4: Turner's _Chemistry_ (1834), p. 420. Miller's -_Chemistry_, ii. 66.] - -The truth of our Aphorism (XXV.) 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 _Hydrosulphate of Potassa_, or as -_Sulphide of Potassium in solution_, according to different -views[83\4]. In some cases indeed, changes are made merely for the -sake of clearness. Instead of _Hydrochloric_ and _Hydrocyanic_ acid, -many French writers, following Thenard, transpose the elements of -these terms; they speak of _Chlorhydric_ and _Cyanhydric_ acid; by -this means they avoid any ambiguity which might arise from the use -of the prefix _Hydro_, which has sometimes been applied to compounds -which contain water[84\4]. - -[Note 83\4: Miller's _Chemistry_, vol. ii. p. 583.] - -[Note 84\4: _Ibid._ ii. 433.] - -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[85\4]. The doctrine of -{368} the existence of compounds identical in ultimate composition, -but different in chemical properties, was termed _Isomerism_. Thus -chemists enumerate the following compounds, all of which contain -carbon and hydrogen in the proportion of single equivalents of -each[86\4];--_Methylene_, _Olefiant gas_, _Propylene_, _Oil gas_, -_Amylene_, _Caproylene_, _Naphthene_, _Eleene_, _Peramylene_, -_Cetylene_, _Cerotylene_, _Melissine_. - -[Note 85\4: _Ibid._ ii. 653.] - -[Note 86\4: Miller's _Chemistry_, ii. p. 654.] - -I will, in the last place, propound an Aphorism which has already -offered itself in considering the history of Chemistry[87\4] 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. - -[Note 87\4: _Hist. Ind. Sc._ b. xiv. c. 1.] - - -APHORISM XXIX. - -_In learning the meaning of Scientific Terms, the history of science -is our Dictionary: the steps of scientific induction are our -Definitions._ - - -IT 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. _Elementary -substances_ in chemistry, for instance, what are they? The -substances into which bodies can be _analysed_, and by the junction -of which they are _composed_. But what is _analysis_? what is -_composition_? 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 {369} 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 _composition_ and _elements_ 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 _Archetype_, 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 _excess_? 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. - -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. {370} - -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. - - - -THE END. - - - - - - -CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AT THE UNIVERSITY PRESS. - - - -Transcriber's Notes - -Whewell published the first edition of the _Philosophy of the -Inductive Sciences_ in 1840 in two volumes, as a companion to the -1837 _History of the Inductive Sciences_. Revised second editions of -both works appeared in 1847. The third editions saw a major -reshaping of the _Philosophy_: a two volume _History of Scientific -Ideas_ (1858; in Project Gutenberg as #69093), _Novum Organon -Renovatum_ (1858; the present text, relying upon resources kindly -provided by the Internet Archive), and _On the Philosophy of -Discovery: chapters historical and critical_ (1860; long since in -Project Gutenberg's collection as #5155). (The third edition of the -_History of the Inductive Sciences_ is available in PG as #68693.) - -Adaptations in this text - -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 { }, or {{ }} when -the number is not printed. 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. - -Some unusual symbols occur. On pages 357 and 358, there are italic -letters with a number written above them. On two occasions B has a -1 above it, and once C has ½ above it. On page 364 a formula is -written with two entries containing H on a line above Cl. These -superpositions have been preserved at the cost of some short lines. -The other oddities have been captured by using [ ] to indicate items -above the following character. (They should not be confused with the -use of [ ] for footnote anchors.) For superscripts ^ has been used -except for expressions using only the superscripted numbers -available in Unicode. Subscripts are indicated by a _ preceding the -character. (This unfortunately results in double __ when the -preceding characters are in italics.) - -On pages 152 and 197 Whewell uses a raised dot as a decimal point -and in footnote 26\3 a comma. These have been replaced by a mid dot. - -Inductive Charts - -At the end of Book II., 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. Rather than the tree shape Whewell used, the diagrams have -been made to flow from left to right. - -Corrections - -Corrections are comparatively few. Apart from the silent ones, they -have been marked by ** and are listed below. - - Page Printed text Corrected text -{{xiii}} v iii - LXX. LXXIII. - LXXXV. LXXXII. -p. 12 of and -p. 128 word work -note 21\3 i. ii. -p. 322 Wafferstoff Wasserstoff -p. 365 XV. XX. - Ethol Ethal - -Given the various editions, some of the internal cross-references -turn out to be obsolete or erroneous: -note 11\3 reads B. viii. c. iii. but it refers actually to Book viii. -c. ii. article 3 in earlier editions and in the _History of Scientific -Ideas_, cf. Aphorism 88 in Book I. of the present volume. Compare also -Aphorism 19 in this volume's Book IV. -notes 58\3 and 59\3 refer to Book v. c. i. For the present third -edition they should have been aimed at that chapter of the _History -of Scientific Ideas_. - -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. - - -*** END OF THE PROJECT GUTENBERG EBOOK NOVUM ORGANON RENOVATUM *** - -Updated editions will replace the previous one--the old editions will -be renamed. - -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. Special rules, set forth in the General Terms of Use part -of this license, apply to copying and distributing Project -Gutenberg™ electronic works to protect the PROJECT GUTENBERG™ -concept and trademark. 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