Chemistry has already one great generalization, which, though relating to one of the subordinate aspects of chemical phenomena, possesses within its limited sphere this comprehensive character; the principle of Dalton, called the atomic theory, or the doctrine of chemical equivalents: which by enabling us to a certain extent to foresee the proportions in which two substances will combine, before the experiment has been tried, constitutes undoubtedly a source of new chemical truths obtainable by deduction, as well as a connecting principle for all truths of the same description previously obtained by experiment. § 7. The discoveries which change the method of a science from experimental to deductive, mostly consist in establishing, either by deduction or by direct experiment, that the varieties of a particular phenomenon uniformly accompany the varieties of some other phenomenon better known. Thus the science of sound, which previously stood in the lowest rank of merely experimental science, became deductive when it was proved by experiment that every variety of sound was consequent on, and therefore a mark of, a distinct and definable variety of oscillatory motion among the particles of the transmitting medium. When this was ascertained, it followed that every relation of succession or coexistence which obtained between phenomena of the more known class, obtained also between the phenomena which corresponded to them in the other class. Every sound, being a mark of a particular oscillatory motion, became a mark of everything which, by the laws of dynamics, was known to be inferrible from that motion; and everything which by those same laws was a mark of any oscillatory motion among the particles of an elastic medium, became a mark of the corresponding sound. And thus many truths, not before suspected, concerning sound, become deducible from the known laws of the propagation of motion through an elastic medium; while facts already empirically known respecting sound, become an indication of corresponding properties of vibrating bodies, previously undiscovered. But the grand agent for transforming experimental into deductive sciences, is the science of number. The properties of numbers, alone among all known phenomena, are, in the most rigorous sense, properties of all things whatever. All things are not coloured, or ponderable, or even extended; but all things are numerable. And if we consider this science in its whole extent, from common arithmetic up to the calculus of variations, the truths already ascertained seem all but infinite, and admit of indefinite extension.