By the continued addition of acetic acid, the composition of the successive conjugate solutions in equilibrium with one another becomes, as the table shows, more nearly the same, and a point is at length reached at which the two solutions become identical. This will therefore be a _critical point_ (p. 98). Increased addition of acetic acid beyond this point will lead to a single homogeneous solution. These relationships are represented graphically by the curve _a_K_b_, Fig. 84. The points on the branch _a_K represent the composition of the solutions relatively rich in chloroform (heavier layer), those on the curve _b_K the composition of solutions relatively rich in water (lighter layer); and the points on these two branches representing conjugate solutions are joined together by "tie-lines." Thus, the points _a'b'_ represent conjugate solutions, and the line _a'b'_ is a tie-line. [Illustration: FIG. 84.] Since, now, acetic acid when added to a heterogeneous mixture of chloroform and water does not enter in equal amounts into the two layers, but in amounts depending on its coefficient of distribution between chloroform and water,[321] the {243} tie-lines will not be parallel to AB, but will be inclined at an angle. As the solutions become more nearly the same, the tie-lines diminish in length, and at last, when the conjugate solutions become identical, shrink to a point. For the reason that the tie-lines are, in general, not parallel to the side of the triangle, the critical point at which the tie-line vanishes will not be at the summit of the curve, but somewhere below this, as represented by the point K. The curve _a_K_b_, further, forms the boundary between the heterogeneous and homogeneous systems. A mixture of chloroform, water, and acetic acid represented by any point outside the curve _a_K_b_, will form only one homogeneous phase; while any mixture represented by a point within the curve, will separate into two layers having the composition represented by the ends of the tie-line passing through that point. Thus, a mixture of the total composition _x_, will separate into two layers having the composition _a'_ and _b'_ respectively.