The illustration which has been given relates to physical equilibrium, but the rule is applicable to cases involving chemical changes as well. In comparing the phase-rule with the law of mass action, it will be noticed that both have to do with equilibrium. The great advantage of the former is that it is entirely independent of the molecular condition of the substances in the different phases. For instance, it makes no difference so far as the application of the rule is concerned, whether a substance in solution is dissociated, undissociated or combined with the solvent. In any case, the solution constitutes one phase. On the other hand, the rule is purely qualitative, giving information only as to whether a given change in conditions is possible. The law of mass action is a quantitative expression so that when the value of the constant is once known, the change can be calculated which takes place in the entire system if the concentration of one substance is varied. The law, however, requires a knowledge of the molecular condition of the reacting substances, which may be uncertain or unknown, and chiefly on this account it has, like the phase-rule, often only a qualitative significance. The phase rule has served as a most valuable means of classifying systems in equilibrium and as a guide in determining the possible conditions under which such systems can exist. As illustrations of its practical application, van’t Hoff used it as an underlying principle in his investigations on the conditions under which salt deposits have been formed in nature, and Rooseboom was able by its means to explain the very complicated relations existing in the alloys of iron and carbon which form the various grades of wrought iron, steel and cast iron. _Thermochemistry._—This branch of chemistry has to do with heat evolved or absorbed in chemical reactions. It is important chiefly because in many cases it furnishes the only measure we have of the energy changes involved in reactions. To a great extent, it dates from the discovery by Hess in 1840 of a fundamental law which states that the heat evolved in a reaction is the same whether it takes place in one or in several stages. This law has made it possible to calculate the heat values of a large number of reactions which cannot be determined by direct experiment.