regretted that no distinct theory of the constitution of comets had guided his observations of Halley's cometa; in attempting to verify or refute any good hypothesis, not only would there have been a chance of establishing a true theory, but if confuted, the very confutation would probably have involved a large store of useful observations.

It would be an interesting work, but one which I cannot undertake, to trace out the gradual reaction which has taken place in recent times against the purely empirical, or Baconian, theory of induction. Francis Bacon, seeing the futility of the scholastic logic, which had long been predominant, asserted that the accumulation of facts and the careful and orderly abstraction of axioms, or general laws from them, constituted the true method of induction. This method, as far as we can gather its exact nature from Bacon's writings, would correspond to the process of exhaustive examination and classification to which I have just alluded. The value of this method might be estimated historically by the fact that it has not been followed by any of the great masters of science. Whether we look to Galileo, who preceded Bacon, to Gilbert, his contemporary, or to Newton and Descartes, his successors, we find that discovery was achieved by the exactly posite method to that advocated by Bacon. ThroughNewton's works, as I shall more fully show in sucwing pages, we find deductive reasoning wholly preant, and experiments are employed, as they should confirm or refute hypothetical anticipations of In my Elementary Lessons in Logic' (p. stated belief that there was no kind of my Bacon in Newton's works. I have since : Newton does once or twice employ the

Cometary Theory,' Philosophical Magazine, April, vol. xxxvii. p. 243.

expression experimentum crucis in his Opticks,' but this is the only expression, so far as I am aware, which could indicate on the part of Newton direct or indirect acquaintance with Bacon's writings b.

Other great physicists of the same age were equally prone to the use of hypotheses rather than the blind accumulation of facts in the Baconian manner. Hooke emphatically asserts in his posthumous work on Philosophical Method, that the first requisite of the Natural Philosopher is readiness at guessing the solution of many phenomena and making queries. He ought to be very well skilled in those several kinds of philosophy already known, to understand their several hypotheses, suppositions, collections, observations, &c., their various ways of ratiocinations and proceedings, the several failings and defects, both in their way of raising, and in their way of managing their several theories: for by this means the mind will be somewhat more ready at guessing at the solution of many phenomena almost at first sight, and thereby be much more prompt at making queries, and at tracing the subtlety of Nature, and in discovering and searching into the true reason of things.'

We find Horrocks, again, than whom no one was more filled with the scientific spirit, telling us how he tried theory after theory in order to discover one which was in accordance with the motions of Mars. It might readily be shown again that Huyghens, who possessed one of the most perfect philosophical intellects, followed the deductive process combined with continual appeal to experiment, with a skill closely analogous to that of Newton. As to Descartes and Leibnitz, their investigations were too much opposed to the Baconian rules, since they too often

b See Philosophical Transactions,' abridged by Lowthorp. 4th edit. vol. i. p. 130.

c Horrocks, 'Opera Posthuma' (1673), p. 276.

adopted hypothetical reasoning to the exclusion of experimental verification. Throughout the eighteenth century science was supposed to be advancing by the pursuance of the Baconian method, but in reality hypothetical investigation was the main instrument of progress. It is only in the present century that physicists began to recognise this truth. So much opprobrium had been attached by Bacon to the use of hypotheses, that we find Young speaking of them in an apologetic tone. The practice of advançing general principles and applying them to particular instances is so far from being fatal to truth in all sciences, that when those principles are advanced on sufficient grounds, it constitutes the essence of true philosophy d'; and he quotes cases in which Sir Humphry Davy trusted to his theories rather than his experiments. The late Sir John Herschel, who was both a practical physicist and an abstract logician, always entertained the deepest respect for Bacon, and made the 'Novum Organum'

possible the basis of his admirable Discourse on the Study of Natural Philosophy.' Yet we find him in Chapter VII fully recognising the part which the formation and verification of theories forms in the higher and more general investigations of physical science. The late Mr. J. S. Mill carried on the reaction by recognising as a distinct method the Deductive Method in which Ratiocination, that is, deductive reasoning, is employed for the discovery of new opportunities of testing and verifying hypothesis. His main error consisted in the fact that throughout the other parts of his system he inveighed against the value of the deductive process, and even asserted from time to time that every process of reasoning is inductive. In fact Mill fell into much confusion in the use of the words induction and deduction, because he

d Young's Works, vol. i. p. 593.

failed to observe that the inverse use of deduction constitutes induction.

Even Francis Bacon was not wholly unaware of the value of hypothetical anticipation. In one or two places he incidentally acknowledges it, as when he remarks that the subtlety of nature surpasses that of reason, adding that 'axioms abstracted from particular facts in a careful and orderly manner, readily suggest and mark out new particulars.'

The true course of inductive procedure is that which has yielded all the more lofty and successful results of science. It consists in Anticipating Nature, in the sense of forming hypotheses as to the laws which are probably in operation; and then observing whether the combinations of phenomena are such as would follow from the laws supposed. The investigator begins with facts and ends with them. He uses such facts as are in the first place known to him in suggesting probable hypotheses; deducing other facts which would happen if a particular hypothesis is true, he proceeds to test the truth of his notion by fresh observations or experiments. If any result prove different from what he expects, it leads him either to abandon or to modify his hypothesis; but every new fact may give some new suggestion as to the laws in action. Even if the result in any case agrees with his anticipations, he does not regard it as finally confirmatory of his theory, but proceeds to test the truth of the theory by new deductions and new trials.

The investigator in such a process is assisted by the whole body of science previously accumulated. He may employ analogy, as I shall point out, to guide him in the choice of hypotheses. The manifold connexions between one science and another may give him strong clues to the kind of laws to be expected, and he thus always selects out of the infinite number of possible hypotheses those

which are, as far as can be foreseen at the moment, most probable. Each experiment, therefore, which he performs is that most likely to throw light upon his subject, and even if it frustrate his first views, it probably tends to put him in possession of the correct clue.

Requisites of a Good Hypothesis.

There will be no difficulty in pointing out to what conditions, or rather to what condition an hypothesis must conform in order to be accepted as valid and probable. That condition, as I conceive, is the single one of enabling us to infer the existence of phenomena which occur in our experience. Agreement with fact is the one sole and sufficient test of a true hypothesis.

Hobbes, indeed, has named two conditions which he considers requisite in an hypothesis, namely, (1) That it should be conceivable and not absurd; (2) That it should allow of phenomena being necessarily inferred. Boyle, in noticing Hobbes' views, proposed to add a third condition, to the effect that the hypothesis should not be inconsistent with any other truth or phenomenon of nature. Of these three conditions, I am inclined to think that the first cannot be accepted, unless by inconceivable and absurd we mean self-contradictory or inconsistent with the laws. of thought and nature. I shall have to point out that some of the most sure and satisfactory theories involve suppositions which are wholly inconceivable in a certain sense of the word, because the mind cannot sufficiently extend its ideas to frame a notion of the actions supposed to exist. That the force of gravity should act instantaneously between the most distant parts of the planetary system, or that a ray of violet light should consist of

e Boyle's Physical Examen,' p. 84.