Page:Popular Science Monthly Volume 74.djvu/558

554 variable components, is capable of $$n+2-r$$ degrees of freedom or variations in phase, of which not more than $$n+2$$ can coexist at the same pressure and temperature. Such systems, in Trevor's nomenclature, are spoken of as invariant, monovariant, divariant, etc., according to the number of possible variations of state. Thus water has three independent phases, ice, liquid and steam, and is invariant, the three phases being in equilibrium at only one pressure and temperature, called the triple point, where the steam-line, ice-line and hoar-frost line meet. But when calcium carbonate, calcium oxide and carbon dioxide  are in equilibrium, we have three coexistent phases formed of two components  and the system is monovariant. By this rule the chemist is able to predict the number of modifications of which a chemical substance is capable from observation of its physical properties alone, or the number of substances in a mixture from notation of the number of phases possible, or the strength of a saturated solution from its temperature and pressure. Many different proofs of the phase rule have been given by mathematicians and physicists from varied and independent points of view, and there is every indication that it is a complete and accurate statement of a general chemical law. Its practical significance remained for a long time undiscovered until the Dutch chemist Van der Waals took it up, and when, in 1884-6, his colleague, Bakhuis Roozeboom, found himself unable to explain certain puzzling phenomena connected with the equilibrium of gaseous hydrates and of double ammonium salts, van der Waals was able to direct his attention to Gibbs's theorem and showed him, by working out a special case, how thermodynamic methods might be applied to practical chemistry. From that time on Roozeboom became the devoted champion of the phase rule, which he compares to the ground plan of a gigantic building in which all the collected phenomena of chemical equilibrium can be stored in a convenient and comprehensive manner. "This structure," he adds with pride, "has since been completed, almost exclusively by the work of the laboratories of Leyden and Amsterdam." In fact, the investigations of Roozeboom and van't Hoff upon double salts, solid solutions and metals are among the most brilliant results of modern chemistry. It is in connection with the graphic study of chemicophysical changes by the phase rule that Gibbs's diagrams and surfaces