The periodic law, in the words of its author, is the “direct outcome of the stock of generalisations of established facts which had been accumulated by the end of the decade 1860–1870.” It is founded wholly on experiment, and is as much the embodiment of fact as are the laws of chemical combination. It was based upon the adoption of the definite numerical values of the atomic weights, as indicated by Cannizzaro, as a consequence of the hypothesis of Avogadro, and upon the assumption that the relations between the atomic weights of analogous elements must be governed by a general law. The application of the periodic law immediately led to the re-determination of certain atomic weights and to the correction of their assumed atomic values. At the time of its enunciation the determination of the valency of an element was purely empirical, with no apparent necessary relation to that of other elements. We find now that the valency is a matter of _a priori_ knowledge, just as much as any other property of the element. The amended values for the atomic weight and valency of a number of elements thus demanded by the law have been confirmed by all the experimental criteria employed by chemists. The generalisation further indicated the existence of new elements; it pointed out their probable sources, and foretold their properties. Instances of this power of divination in the law are to be seen, as already mentioned, in the discovery of _gallium_ by Lecoq de Boisbaudran, of _scandium_ by Nilson, and of _germanium_ by Winkler, the existence and main properties of which were severally foretold by Mendeléeff in 1871. The promulgation of the law was heralded as a proof of the validity of the conception of a primordial matter. It was held that it can find a rational explanation only in the idea of unity in the formative material. But its author would not admit that his generalisation had any relation to the Pythagorean hypothesis: The periodic law, based as it is on the solid and wholesome ground of experimental research, has been evolved independently of any conception as to the nature of the elements. It does not in the least originate in the idea of an unique matter, and it has no historical connection with that relic of the torments of classical thought; and therefore it affords no more indication of the unity of matter or of the compound nature of the elements than do the laws of Avogadro, and Gerhardt, or the law of specific heats, or even the conclusions of spectrum analysis. None of the advocates of a unique matter has ever tried to explain the law from the standpoint of ideas taken from a remote antiquity, when it was found convenient to admit the existence of many gods—and of a unique matter.