According to the periodic law, all the properties of the elements are periodic functions of their atomic weights, varying from substance to substance in a perfectly regular manner. The elements thus fall into periods, or octaves, as Newlands called them, of a very striking character. If, for example, we start with univalent lithium, the next higher element has a valence of two, the next of three, and then comes carbon, whose atom is quadrivalent. Following carbon, the combining power of successive elements decreases until we reach sodium, in which something like the properties of lithium recur. Above sodium the same rise goes on to the fourth element higher, silicon, which resembles carbon, and then follows the regular step-by-step falling away, to end with chlorine, the last member of the second period. This periodic rising and falling is characteristic of all the elements, and they were so tabulated by Mendelejeff as to be perfectly clear, with a clearness which is not to be given by words. In Mendelejeff’s table certain gaps appeared, which he ascribed to the existence of undiscovered metals. For three of these he predicted the properties, starting out from the properties of their neighbors. This was a rash thing to do, but the venture has been fully vindicated. In 1875 Lecoq de Boisbandram discovered gallium, which filled one of the gaps; scandium and germanium filled the other two later. The predictions of Mendelejeff were fulfilled; atomic weight, specific gravity, fusibility, the character of the compounds to be formed, were all foreseen for each of the three new elements; and, so far as experiment has yet gone, his anticipations have been perfectly realized. Every good theory is prophetic; but few generalizations have been so strikingly verified in this respect as has the periodic law. In spite of some outstanding difficulties, yet to be explained, the law has served to great advantage in the classification of the elements, and it has had much to do with the late revival of inorganic chemistry. The latter branch of science, long comparatively neglected, has now gained new interest, and for it, in the near future, a great growth can be prophesied. The immediate effect of the periodic law was to prove that the elements are connected with one another by general relations, and so to stimulate the belief in their possibly common origin. This view has many upholders, although it is also strongly opposed, but the weight of argument seems to be in its favor. On philosophic grounds it is at least more probable than the opposite opinion, which can not account in any way for the regularities which have been observed. From another source, partly physical and partly chemical, the theory of the unity of matter has received strong support, and this statement brings us to another of the greatest discoveries made during the nineteenth century--that of the spectroscope and spectrum analysis.