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 the 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 connection 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 49'

It is undeniable that a theory which thus appears to afford an explanation of different classes of facts strikes the imagination with considerable force, and that its very simplicity furnishes prima facie evidence of its truth. But what is required before a hypothesis can be placed beyond suspicion is formal proof, and that, it appears to me, is furnished by Mr. Mill's 'methods,' and not by Dr. Whewell's requisitions of explanation, prediction, and consilience of inductions. For the questions at issue between Mr. Mill and Dr. Whewell, see Whewell's Novum Organon Renovatum (where his views are stated in their latest and most matured form), Bk. II. ch. v. $ 3, and Mill's Logic, Bk. III. ch. xiv. § 6.

Note 2.-In attempting to determine the conditions to which a legitimate hypothesis must conform, I have avoided the employment of the expressions vera causa and adæquata causa. In the first place, a hypothesis may simply attempt to find a general expression for a number of isolated facts without referring them to any cause, as was the case with the various hypotheses respecting the shape of the planetary orbits, and hence to speak as if a hypothesis always assigned a cause is an undue limitation of the meaning of the word. But to the expression vera causa there is a more special exception. Its meaning

49 Novum Organon Renovatum, Bk. II. ch. v. art. II.

is ambiguous. Is it the actual cause which produces a phenomenon, or a cause which we know to be actually existent, or a cause analogous to an existent cause? The student will find a criticism of this expression (first employed by Newton) in Dr. Whewell's Philosophy of Discovery, ch. xviii. § 5, &c. The expression cannot have been used in the first, which is its most obvious, sense, for, as Dr. Whewell says, although it is the philosopher's aim to discover such causes, he would be little aided in his search of truth, by being told that it is truth which he is to seek.' But in the second of the two remaining senses, the requirement, as would now be generally acknowledged, is too stringent, and, if it had been invariably observed, would have prevented us from reaping some of the greatest discoveries in science, while in the last it is so vague as to be of no practical service. It has been attempted to affix other meanings to the phrase; but there can be little doubt that Newton, having in mind the Vortices of Descartes, intended to protest against the introduction of causes of whose existence we have no direct knowledge, and consequently laid down a rule, which the subsequent history of science has shown to be needlessly stringent.

Note 3.-We sometimes find the expression a 'gratuitous hypothesis.' By this is meant the assumption of an unknown cause, when the phenomenon is capable of being explained by the operation of known causes, or the introduction of an extraneous (though it may be

known) cause, when the phenomenon is capable of being accounted for by the causes already known to be in operation. Of the latter case we should have instances, where a man is supposed to have acted at the suggestion of another, though his own motives would supply a sufficient explanation of his conduct, or where a man is supposed to have been poisoned, though he was already known to have been suffering from a fatal disease. Of the former case we should have instances in the crystalline spheres of the ancient astronomers and in the masses of crystal which were supposed by Lodovico delle Colombe to fill up the cavities of the moon (there being no instances known to us of the existence of crystal in these huge masses, and the phenomena being capable of explanation without making the supposition); in the caloric (which was supposed to be a distinct substance) of the early writers on heat, and in the 'electrical fluid' of the early electricians. In all these instances, under whichever of the two cases they may fall, the objection to the hypothesis is that it seems 'not to be needed.'

I have said nothing of 'gratuitous hypotheses' in the text, as a hypothesis, though it may appear to be gratuitous, may still be legitimate, and may even ultimately turn out to be true.

CHAPTER III.

On the Inductive Methods.

INDUCTION has been defined to be a legitimate inference from the known to the unknown. But the unknown must not be entirely unknown. It must be known to agree in certain circumstances with the known, and it is in virtue of this agreement that the inference is made. Now, how are we to ascertain what are the common circumstances which justify the inductive inference? X and Y may both agree in exhibiting the circumstances a, b, c, but it will not follow because X exhibits the quality m, that therefore this quality will also necessarily be found in Y. Nor even, if twenty, thirty, a hundred, or a thousand cases could be adduced in which the circumstances a, b, c were found to be accompanied by the circumstance m, would it follow necessarily (it might not even follow probably) that the next case in which we detected the circumstances a, b, would also exhibit the quality m. We might pass through a field containing thousands of blue hyacinths, but this would. not justify us in expecting that the next time we saw