The third chief case which can occur is that no two of the components are completely miscible with one another. In this case, therefore, we shall obtain three paraboloid boundary curves, as shown in Fig. 93. If, now, we imagine these three curves to expand in towards the centre of the triangle, as might happen, for example, by lowering the temperature, a point will {252} be reached at which the curves partly overlap, and we shall get the appearance shown in Fig. 94. The points _a_, _b_, and _c_ represent the points where the three curves cut, and the triangle _abc_ is a region where the curves overlap. From this diagram we can see that any mixture having a composition represented by a point in one of the clear spaces at the corners of the larger triangle, will form a homogeneous solution; if the composition corresponds to any point lying in one of the quadrilateral regions _x__{1}, _x__{2} or _x__{3}, two ternary solutions will be formed; while, if the composition is represented by any point in the inner triangle, separation into three layers will occur. [Illustration: FIG. 94.] Since in the clear regions at the corners of the triangle we have three components in two phases, liquid and vapour, the systems have three degrees of freedom. At constant temperature, therefore, the condition of the system is not defined until the concentrations of two of the components are fixed. A system belonging to one of the quadrilateral spaces has, as we have seen, two degrees of freedom; besides the temperature, one concentration must be fixed. Lastly, a system the composition of which falls within the inner triangle _abc_, will form three layers, and will therefore possess only one degree of freedom. If the temperature is fixed, the composition of the three layers is also determined, viz. that of the points _a_, _b_, and _c_ respectively; and a change in the composition of the original mixture can lead only to a difference in the relative amounts of the three layers, not to a difference in their composition. An example of a system which can form three liquid phases is found in water, ether, and succinic nitrile.[330] * * * * * {253} CHAPTER XV PRESENCE OF SOLID PHASES A. The Ternary Eutectic Point.--In passing to the consideration of those ternary systems in which one or more solid phases can exist together with one liquid phase, we shall first discuss not the solubility curves, as in the case of two-component systems, but the simpler relationships met with at the freezing point. That is, we shall first of all examine the freezing point curves of ternary systems. [Illustration: FIG. 95.]