During the formative period of the new doctrines, between 1840 and 1858, many discoveries were made which helped toward the final consummation. Even earlier than this the researches of Graham upon the phosphoric acids had familiarized chemists with the idea that different substances might have very different combining powers, and other polybasic acids were found to exist among organic compounds. The discovery by Wurtz, in 1849, that the hydrogen of ammonia was replaceable by organic radicles, forming the compound ammonias or amines, was a logical extension of the theory of substitutions; and the recognition at about the same time, by Hofmann, of ammonia as a distinct type upon which many other substances could be modeled, was another long step forward. In 1851 Williamson argued that nearly all inorganic and many organic molecules could be represented as analogous in structure to water, and a year later, as a result of his researches upon the organo-metallic bodies--zinc ethyl, tin ethyl, etc.--Frankland expressed the belief that every elementary atom has a definite combining power which limits the number of other atoms capable of direct union with it. This was the theory of valence in its first and simplest form, undeveloped to its consequences, but unmistakably clear. To carbon compounds in general it was yet to be applied. In 1858 the work of Cannizzaro appeared, and a general revision of chemical formulæ became necessary. The advanced views which a few chemists had held began to find a more general acceptance, and the significance of the change was gradually realized. In the same year Kekulé showed that the atom of carbon had a combining capacity of four, and furthermore that in many organic compounds the carbon atoms were in part united with each other, and even linked, as it were, into chains. Still later, studying benzene, he found that its six carbon atoms were best regarded as joined together in the form of a closed ring, and with this conception the idea of chemical structure received at last a definite form. These linkages of atoms, these rings and their derivatives, could all be represented graphically to the eye, in accordance with the combining power of the several elements, and so the structural formulæ of modern chemistry came into vogue. Types, substitutions, compound radicles, were all covered by and included in the new generalization, and each of the older theories was seen to be but an expression of special cases, rather than of any general law. No truth was set aside, but all were co-ordinated. To the non-chemical reader the foregoing passages may seem vague and abstruse, but in an essay of this scope greater elaboration is inadmissible. It is clear, however, that each forward step has been a logical development of the atomic theory, which, as we shall see later, does not end even here.