The interest and importance of investigations into the conditions of equilibrium between two substances, lie in the determination not only of the conditions for the stable existence of the participating substances, but also of whether or not chemical action takes place between these two components; and if combination occurs, in the determination of the nature of the compounds formed and the range of their existence. In all such investigations, the Phase Rule becomes of conspicuous value on account of the fact that its principles afford, as it were, a touchstone by which the character of the system can be determined, and that from the form of the equilibrium curves obtained, conclusions can be drawn as to the nature of the interaction between the two substances. In order to exemplify the application of the principles of the Phase Rule more fully than has already been done, illustrations will be drawn from investigations on the interaction of organic compounds; on the equilibria between optically active compounds; and on alloys. {208} Summary of the Different Systems of Two Components.--Before passing to the consideration of the application of the Phase Rule to the investigation of particular problems, it will be well to collect together the different types of equilibrium curves with which we are already acquainted; to compare them with one another, in order that we may then employ these characteristic curves for the interpretation of the curves obtained as the result of experiment. In investigating the equilibria between two components, three chief classes of curves will be obtained according as-- I. No combination takes place between the two components. II. The components can form definite compounds. III. The components separate out in the form of mixed crystals. The different types of curves which are obtained in these three cases are represented in Figs. 63, 64, 65. These different diagrams represent the whole series of equilibria, from the melting point of the one component (A) to that of the other component (B). The curves represent, in all cases, the composition of the solution, or phase of variable composition; the temperature being measured along one axis, and the composition along the other. We shall now recapitulate very briefly the characteristics of the different curves. [Illustration: FIG. 63.]