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], a phenomenon which, taken by itself, it had perplexed previous mathematicians, even to represent.
[14] 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]. 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]. 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]. 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]. 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].
[15] See Hist. Ind. Sc. b. ix. c. xii.
[16] Ib. c. xi. sect. 4.
[17] See Hist. Ind. Sc. b. ix. c. xiii. sect. 6.
[18] Ib. c. xi. sect. 5.