of nature, makes an hypothesis what the cause is and how it acts, deduces from this what the effect of a cause so acting must be, and then verifies the hypothesis by ascertaining whether the effects actually observed are those deduced.

The same method is used in discovering an anagram; as if one were required to find an anagram of Terrible Poser and discovers it to be Sir Robert Peel. It is noticeable that the one who is quick in discovering an anagram, is the one who sees it in the given letters; that is, he creates an hypothesis. On verifying the hypothesis he may find that it lacks a letter, or has one too many, and tries again. But the one who takes each letter in succession as the initial and tries to find all the possible combinations, proceeds slowly and, oftener than not, fails.

The same method is used in deciphering an inscription in an unknown character. The study of natural science is a deciphering of the book of

nature.

3. The hypothesis is a creation of the imagination, and, in great discoveries and inventions, it is this creation which reveals the "vision and faculty divine of genius." If the marks of the camel had been confusedly intermingled with those of other animals along the same path, the Arab's problem would have been more difficult. But in nature the effects of many undetermined causes are thus intermingled. The observer must create in imagination a definite system in which a part of these heterogeneous facts shall be conceived as effects of a determinate complex of causes acting in accordance with a determinate law.

4. In creating a correct hypothesis the student is aided by knowledge already attained; as the Arab's knowledge of the camel's foot gave him a clew to the true hypothesis; as the trilingual inscription on the Rosetta stone gave to Champollion the clew for interpreting other hieroglyphics. It is only they who have been close observers of nature who are likely to make hypotheses worthy of examination. And they are aided to do it not merely by their knowledge, but by their trained habits of observation. They are aided also by analogy. Things which resemble each other in some particulars are conjectured to be alike in others. Thus Newton conjectured that the diamond would be found to be a combustible from its resemblance to known combustibles in its high power of refracting light. And Franklin conjectured, from the resemblance of thunder and lightning to the phenomena of the discharge of a Leyden jar, that they were effects of the same cause.

Hence scientific discovery and mechanical invention are not due merely to "the vision and faculty divine of genius," but also to painstaking observation, intellectual discipline and large acquisitions of knowledge. Says Tyndall: "It is by a kind of inspiration that we rise from the wise and sedulous contemplation of nature to the principles on which the

facts depend. The mind is, as it were, a photographic plate, which is gradually cleansed by the effort to think rightly, and which when cleansed, and not before, receives impressions from the light of truth. This passage from facts to principles is called induction, which in its highest form is inspiration; but to make it sure the inward light must be shown to be in accord with the outward fact. To prove or disprove the induction we must resort to deduction and experiment."*

5. For the verification of an hypothesis there are two requisites. Af ter deducing from the hypothesis all the results implied in its truth, all the facts must be found by observation to correspond. Also, there must be no other hypothesis with the deduced results of which the facts equally correspond. There were formerly two hypotheses as to electricity, Franklin's and Dufay's. Neither of them sufficiently accounted for the facts; both are displaced by the present hypothesis. There were two hypotheses of combustion, that of phlogiston and that of oxygen. After long and sharp controversy among scientists, the latter has displaced the former. When an hypothesis is verified in both of the ways indicated it is considered to be scientifically established.

Verification is sometimes possible in a third way, by bringing the hitherto unknown agent under actual observation. So the existence of a planet beyond Uranus was inferred by the hypothetical method and the planet was afterwards discovered. In most cases the object sought cannot be brought under direct observation by any means which man can command. Nor is this necessary to the scientific verification and establishment of the hypothesis. The law that gravitation acts with a force directly as the mass and inversely as the square of the distance is suggested by mathematical principles and verified by the accordance with it of the movements of the heavenly bodies, and is thus scientifically established beyond all doubt. But it is forever impossible by any weighing or mechanical testing of forces to establish it by direct observation. It is equally impossible to establish the law of the conservation and correlation of force by direct observation of the molecular action into which the motion of masses is transformed, or of the transformations of molecular action, as from electricity into heat. In like manner the hypothesis of the æther can never be verified by direct observation of the æther. There is no ground for the assertion that inference by the method of hypothesis is not established until the agent and sequence sought are brought under direct observation; and the demand for verification in this third way is no more imperative in philosophy and theology than in empirical science. And yet it is continually being demanded as essential in the former by those who in physical science freely

Fragments of Science, p. 60.

accept hypotheses as established which do not admit of verification in this third way. The value of the method is in carrying our knowledge beyond the range of observation.

6. The hypothetical method rests on the intuitive principle that effect must have a cause adequate to produce it.

every

7. The hypothetical method is of fundamental importance in all scientific investigation. It has been used in scientific discovery in all ages; and with success corresponding not merely to the genius of the discoverer, but to the degree and exactness of knowledge and the habits of accurate observation guiding him in creating his hypothesis. Thus Archimedes hypothetically referred the conditions of equilibrium on the lever to the conception of pressure, while Aristotle could see in them only the strange results of the properties of the circle; Pascal adopted correctly the hypothesis of the weight of the air which his predecessors had referred to nature's horror of a vacuum; Vitellio and Roger Bacon referred the magnifying power of a convex lens to the refraction of the rays towards the perpendicular, while others conceived it to result from the matter of the lens irrespective of its form. In view of such facts Whewell says: "Facts cannot be observed as facts except in virtue of the conceptions which the observer 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." To the same purport are the words of Comte: "No real observation of any kind of phenomena is possible, except in so far as it is first directed and finally interpreted by some theory. Scientifically speaking all isolated empirical observation is idle and even radically uncertain; science can use only those observations which are connected at least hypothetically with some law.

Facts which must form the basis of a positive theory could not be collected to any purpose without some preliminary theory which should guide the collection. Our understanding cannot act without some doctrine, false or true, vague or precise, which may concentrate and stimulate its efforts and afford ground enough for speculative continuity to sustain our mental action."†

8. The Newtonian method is now commonly called induction. The simple induction recognized by Bacon is the only induction which, as peculiar and distinct from all other processes of reasoning or of

*Philosophy of Inductive Sciences, Vol. ii. pp. 189, 206.

Cours de Philosophie Positive, Tom. iv. pp. 418, 665, 667. Léçons 48, 51. Martineau's Translation, pp. 475 and 525.

thought, is entitled to the name. It is this which until recently has

been called induction.

The application of this name to the Newtonian method increases the confusion of thought which has existed on the subject, and misleads by pushing the real induction into the background and giving its name to a complex process each of whose three subordinate processes is already known by its appropriate name, hypothesis, deduction, verification. The first is a creative act of imagination, the second is deduction and cannot at the same time be induction, and the third is observation and a comparison of what we observe with what we have deduced. Prof. Jevons regarding this process as induction, is driven to the conclusion, "If I have taken a correct view of logical method, there is really no such thing as a distinct process of induction."*

The reaction against the Baconian induction in recent scientific thought is worthy of attention. It is remarkable that it is against the induction of Lord Bacon, so long glorified as the epoch-making thought which rescued the human mind from the hypotheses and deductions of scholasticism and metaphysics, and turned it in the direction of discovery and of useful knowledge. It is remarkable that the reaction is to the methods of hypothesis and deduction, once so much under opprobrium as the methods of metaphysics that the appellation " inductive," with the Baconian meaning, was given to the physical sciences as marking their distinctive preeminence. Newton himself, with singular unconsciousness, felt obliged to utter the disclaimer, "hypotheses non fingo;" and later discoverers by the hypothetical method have apologized for its use. Since the physical sciences have claimed and do claim preeminent and even exclusive certainty and value as being founded on observation, it is remarkable that this reaction is away from this recognition of the preeminence of observation and to a depreciation of it as "idle and even radically uncertain," and of no scientific "use," except as "directed and interpreted by some theory." And it is remarkable that after all this reactionary change, scientists insist on applying the old name induction to the method of hypothesis, deduction and verification, as if fearing that the physical sciences would lose prestige if they were known to be preeminently sciences of hypothesis, deduction and verification called by their proper names. "Wide is the range of words this way and that."†

9. Neither induction nor the hypothetical method is peculiar to investigations in physical science. Each is a method spontaneously used by the human mind in investigations in sciences of every kind and in

Princ. of Science, p. 579.

† Επέων δὲ πολὺς νομὸς ἔνθα καὶ ἔνθα. Iliad xx. 249.

the common affairs of life. Lord Bacon did not invent nor discover the method of induction. It had always been in use. He guarded the minds of men against false reasoning, turned them to the study of persons and things rather than of notions and words, and to the study of reality in its bearings on the conduct of life and the welfare of man. Newton did not discover nor first use the hypothetical method. Descartes distinctly recognizes it in his "Dissertatio de Methodo;" and it was used in discoveries both by Lord Bacon's predecessors and successors. Lange, after noticing these facts, makes the extraordinary mistake of saying that "Newton reverted to Bacon."* The truth is that, independently of all logical theories, this method and the simple induction of Lord Bacon are the methods spontaneously used by the human mind in investigating facts, whether in science or in the practical affairs of life.

10. Correct hypotheses and the discoveries involved in them have often been suggested by genius, long before the hypotheses have been verified and the discoveries made. Very striking is Lord Bacon's anticipation of the modern discovery that heat is motion. In explaining his suggestion of this fact, he says emphatically; "it must not be thought that heat generates motion or motion heat (though in some respects this be true) but that the very essence of heat, or the substantial self (quid ipsum) of heat is motion and nothing else." Descartes anticipated the vortex rings of Sir Wm. Thompson. Aristotle anticipated Columbus. He says that the earth must be spherical, and proves it from the tendency of things in all places downwards and from the spherical form of the earth shown in eclipses of the moon; and he argues that it is comparatively small, because in traveling north or south the position of the stars changes, and stars are seen in Greece or Cyprus, which are not seen in countries further north; and then says; "Wherefore we may judge that those persons who connect the region in the neighborhood of the pillars of Hercules with that towards India and who assert that in this way the sea is one, do not assert things very improbable."§ Anticipations of scientific discovery sometimes come from speculative philosophy. Schelling suggested the identity of the forces of magnetism, electricity, and chemical affinity; || Kant in his Naturgeschichte des Himmels anticipated the nebular theory of Laplace. Sometimes these anticipations

Geschichte des Materialismus, i. 239, 240.

† Novum Organum, B. II. 20, Basil Montagu's Edition.

Wurtz, Atomic Theory; Cleminshaw's Trans. p. 329.

? Aristotle de Coelo, Lib. 14, Ed. Casaub. p. 290, 291, quoted Whewell Hist. of Inductive Sciences, Vol. I. p. 133.

Whewell's Philosophy of the Inductive Sciences, B. V. Chap. II. 12.