The different solubilities are shown in Fig. 128. In this diagram the solubility of the two barium salts has been neglected. A is the solubility of K_{2}CO_{3}.2H_{2}O; addition of BaCO_{3} does not alter this. B is the solubility of K_{2}CO_{3}.2H_{2}O + K_{2}SO_{4} + BaCO_{3}. A and B almost coincide, since the potassium sulphate is very slightly soluble in the concentrated solution of potassium carbonate. D gives the concentration of the solution in equilibrium with K_{2}SO_{4} + BaSO_{4}. The most interesting point is C. This solution is obtained by adding a small quantity of water to BaCO_{3} + K_{2}SO_{4}, whereupon, being in the transition interval, BaSO_{4} separates out and an equivalent amount of K_{2}CO_{3} goes into solution. C is the end point of the curve CO, which is called the Guldberg-Waage curve, because these investigators determined several points on it. In their experiments, Guldberg and Waage found the ratio K_{2}CO_{3} : K_{2}SO_{4} in solution to be constant and equal to 4. This result is, however, not exact, for the curve CO is not a straight line, as it should be if the above ratio were constant; but it is concave to the abscissa axis, and more so at lower than at higher temperatures. The following table refers to the temperature of 25°. The Roman numbers in the first column refer to the points in Fig. 128. The numbers in the column [Sigma]_k__{2} give the amount, {329} in gram-molecules, of K_{2}CO_{3} + K_{2}SO_{4} contained in 1000 gram-molecules of water:-- SOLUBILITY DETERMINATIONS AT 25°.