A quarter of a century later (1867), Guldberg and Waage gave a precise mathematical expression of the law, but still it attracted very little attention from investigators. A tremendous impetus was given to the subject by the electrolytic dissociation theory of Arrhenius (1887), and the extension of the additive laws of gases to dilute solutions, by Van’t Hoff (1885). This was but a comparatively small field in the subject, but it stimulated activity along the whole line, the wonderful increase of our knowledge concerning the velocity or rates of reaction, the heat changes involved, and the marvelous development of electrolytic chemistry being pertinent instances. The generalization of Gibbs, known as the phase rule (1876), which accurately states the condition for equilibrium in the system, and the Theorem of Le Chatelier (1884), that any change in the factors of equilibrium from outside is followed by a reverse change within the system, together with the mass law, now give us a consistent theoretical foundation for the subject. In general terms, it may be said that all chemistry, at least all theoretical chemistry, properly belongs to the province of physical chemistry, and the title, while in many ways convenient, is misleading. III. ORGANIC CHEMISTRY. Compounds containing carbon enter into all the products of a living cell. For this reason the chemistry of carbon compounds came to be known as organic chemistry. This should not be taken as a definition, however, without limitations. Many of the compounds containing carbon are not known to enter into living tissue in any way, and their connection with it is very remote and not essential. On the other hand, it should be remembered that many organic compounds, and those even of most importance, contain some other element,—nitrogen, for example,—as the significant one. While nearly all the known elements can enter into organic compounds, the vast majority of such substances are composed of but very few. For instance, those classes of which sugar, starch, the fats, etc., are examples, contain only carbon, oxygen, and hydrogen. With nitrogen, sulphur, and phosphorus added to these elements, almost the entire range of organic chemistry is covered. Organic chemistry, therefore, differs from inorganic chemistry in that, while the number of compounds is much larger, the number of elements involved is very limited. [Illustration: MICHAEL FARADAY.] Berzelius may be regarded as having founded organic chemistry in the beginning of this century. As a result of his analyses of the salts of organic acids, he clearly demonstrated that the laws of definite and multiple proportions hold equally for organic compounds and for inorganic ones. The work of this master was ably furthered by Liebig (1803–1873), who devised most elegant methods for the analytical investigation of organic compounds, methods which are in use to-day without any essential change.