Fig. 113 is a diagrammatic sketch of the model for carnallite looked at sideways from above. Along the X-axis is measured the concentration of magnesium chloride in the {285} solution; along the Y-axis, the concentration of potassium chloride; while along the T-axis is measured the temperature. The three axes are at right angles to one another. The XT-plane, therefore, contains the solubility curve of magnesium chloride; the YT-plane, the solubility curve of potassium chloride, and in the space between the two planes, there are represented the composition of solutions containing both magnesium and potassium chlorides. Any _surface_ between the two planes will represent the various solutions in equilibrium with only one solid phase, and will therefore indicate the area or field of existence of bivariant ternary systems. A _line_ or _curve_ formed by the intersection of two surfaces will represent solutions in equilibrium with two solid phases (viz. those belonging to the intersecting surfaces), and will show the conditions for the existence of univariant systems. Lastly, _points_ formed by the intersection of three surfaces will represent invariant systems, in which a solution can exist in equilibrium with three solid phases (viz. those belonging to the three surfaces). We shall first consider the solubility relations of the single salts. The complete equilibrium curve for magnesium chloride and water is represented in Fig. 113 by the series of curves ABF_{1} G_{1} H_{1} J_{1} L_{1} N_{1}. AB is the freezing-point curve of ice in contact with solutions containing magnesium chloride, and B is the cryohydric point at which the solid phases ice and MgCl_{2},12H_{2}O can co-exist with solution. BFG is the solubility curve of magnesium chloride dodecahydrate. This curve shows a point of maximum temperature at F_{1}, and a retroflex portion F_{1}G_{1}. The curve is therefore of the form exhibited by calcium chloride hexahydrate, or the hydrates of ferric chloride (Chapter VIII.). G_{1} is a transition point at which the solid phase changes from dodecahydrate to octahydrate, the solubility of which is represented by the curve G_{1}H_{1}. At H_{1} the octahydrate gives place to the hexahydrate, which is the solid phase in equilibrium with the solutions represented by the curve H_{1}J_{1}. J_{1} and L_{1} are also transition points at which the solid phase undergoes change, in the former case from hexahydrate to tetrahydrate; and in the latter case, {286} from tetrahydrate to dihydrate. The complete curve of equilibrium for magnesium chloride and water is, therefore, somewhat complicated, and is a good example of the solubility curves obtained with salts capable of forming several hydrates. The solubility curve of potassium chloride is of the simplest form, consisting only of the two branches AC, the freezing-point curve of ice, and CO, the solubility curve of the salt. C is the cryohydric point. This point and the two curves lie in the YT-plane.