We shall assume that we are dealing with the aqueous solution of two salts which can give rise to a double salt, in which case we can represent the solubility relations in a system of rectangular co-ordinates. In this case we should obtain, as before (Fig. 120), the isotherm _adcb_, if we express the {302} composition of the solution in gram-molecules of A or of B to 100 gram-molecules of water. [Illustration: FIG. 120.] Let us suppose, now, that the double salt is in equilibrium with the solution at a definite temperature, and that the composition of the solution is represented by the point e. The greater part of the solution is now separated from the solid phase, and the latter, _together with the adhering mother liquor_, is analyzed. The composition (expressed, as before, in gram-molecules of A and B to 100 gram molecules of water) will be represented by a point (_e.g._ _f_) on the line _e_S, where S represents the composition of the double salt. That this is so will be evident when one considers that the composition of the whole mass must lie between the composition of the solution and that of the double salt, no matter what the relative amounts of the solid phase and the mother liquor. If, in a similar manner, we analyze a solution of a different composition in equilibrium with the same double salt (not necessarily at the same temperature as before), and also the mixture of solid phase and solution, we shall obtain two other points, as, for example, _g_ and _h_, and the line joining these must likewise pass through S. The method of finding the {303} composition of an unknown double salt consists, therefore, in finding, in the manner just described, the position of two lines such as _ef_ and _gh_. The point of intersection of these lines then gives the composition of the double salt. If the double salt is anhydrous, the point S lies at infinity, and the lines _ef_ and _gh_ are parallel to each other. The same result is arrived at by means of the triangular method of representation.[377] If we start with the three components in known amounts, and represent the initial composition of the whole by a point in the triangle, and then ascertain the final composition of the solution in equilibrium with the solid phase at a definite temperature, the line joining the points representing the initial and end concentration passes through the point representing the composition of the solid phase. If two determinations are made with solutions having different initial and final concentrations in equilibrium with the same solid phase, then the point of intersection of the two lines so obtained gives the composition of the solid phase. * * * * * {304} CHAPTER XVII ABSENCE OF A LIQUID PHASE