Before that time, certainly, attempts had been made to bring the different known cases of equilibria--chemical and physical--under general laws. From the very first, both Wenzel[6] and Berthollet[7] recognized the influence exercised by the _mass_ of the substances on the equilibrium of the system. It was reserved, however, for Guldberg and Waage, by their more general statement and mathematical treatment of the Law of Mass Action,[8] to inaugurate the period of quantitative study of equilibria. The law which these investigators enunciated {8} served satisfactorily to summarize the conditions of equilibrium in many cases both of homogeneous and, with the help of certain assumptions and additions, of heterogeneous equilibrium. By reason, however, of the fact that it was developed on the basis of the kinetic and molecular theories, and involved, therefore, certain hypothetical assumptions as to the nature and condition of the substances taking part in the equilibrium, the law of mass action failed, as it necessarily must, when applied to those systems in which neither the number of different molecular aggregates nor the degree of their molecular complexity was known. Ten years after the law of mass action was propounded by Guldberg and Waage, Willard Gibbs,[9] Professor of Physics in Yale University, showed how, in a perfectly general manner, free from all hypothetical assumptions as to the molecular condition of the participating substances, all cases of equilibrium could be surveyed and grouped into classes, and how similarities in the behaviour of apparently different kinds of systems, and differences in apparently similar systems, could be explained. As the basis of his theory of equilibria, Gibbs adopted the laws of thermodynamics,[10] a method of treatment which had first been employed by Horstmann.[11] In deducing the law of equilibrium, Gibbs regarded a system as possessing only three independently variable factors[12]--temperature, pressure, and the concentration of the components of the system--and he enunciated the general theorem now usually known as the _Phase Rule_, by which he defined the conditions of equilibrium as a relationship between the number of what are called the phases and the components of the system.