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.