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.]