272 REPORT— 1901. 



which the solutions are saturated with a given substailce. By joining the 

 points in the horizontal plane, areas are obtained which represent in 

 plan the surfaces in space just referred to. 



To plot the horizontal plan some thought is necessary, as there are 

 three salts to be represented on two axes and therefore one of the salts 

 must be eliminated. In the case under consideration, in which Magnesium 

 chloride and Potassium sulphate are the reciprocal salts on the one axis, to 

 plot Magnesium chloride, Potassium sulphate must be eliminated. This 

 is already done in the case in question in calculating out the results given in 

 the table on p. 270 ; therefore it suffices to measure off twenty-one MgCl^ 

 units upwards from the origin. As Potassium chloride and Magnesium 

 sulphate are the reciprocal salts represented on the second axis, to plot 

 Potassium chloride, ]\Iagnesium sulphate must be eliminated, or vice versd. 

 To do this, it is only necessary to bear in mind that 



25KoCl., + llMgS04 + 21MgCL 

 = 25K, + (ll + 21)Mg + llSOi + (25 + 21)Cl,, 



which, assuming the SO^ to be present wholly as KoSO^, in order to elimi- 

 nate MgSO^, gives 



11 K,SO, + 1 4K,CL + 32MgCl,. 



Therefore fourteen units of Potassium chloride are measured off on the 

 K.jCla axis from the origin. In practice the straightforward geometric 

 method needs only to be followed, and the number of molecules of the 

 one salt, less the number of molecules of its reciprocal, may be measured 

 off on the one axis, the value deduced from the corresponding pair being 

 measured off on the other. The five points M, n, p, q, and r, when so 

 plotted, fall inside the framework, and to complete the diagram are joined 

 to one another, or to the appropriate points on the framework — i.e., to those 

 representing solutions saturated in presence of two of the three equilibra- 

 tors present at the particular point inside the diagram. Thus the point 

 M, representing a solution saturated in presence of KCl, K0SO4, and 

 Schonite, is joined to the points E, representing a solution saturated in 

 presence of KCl and K.jSOj, and f, representing a solution saturated in 

 presence of KoSO^ and Schonite, but not to either G or l, as these represent 

 solutions saturated in presence of only one of the three equilibrators. The 

 lines divide the diagram into areas or fields, each field representing a 

 solution saturated with but one salt in presence of varying quantities of 

 other salts. 



To complete the graphic representation, ordinates are erected at each 

 point of equilibrium representing the total number of molecules in solu- 

 tion. The surfaces touching the extremities of these ordinates represent 

 the various saturated fields. 



To complete the model it is necessary to join the origin, o, by triangular 

 surfaces to each of the marginal points, A — l ; the hollow surface so 

 formed is the true base of the model. Fig. 4 is reproduced from a photo- 

 graph of a rough cardboard model so constructed. The model is supported 

 in its true position on the plane diagram by caixlboard sheets which 

 represent the vertical co-ordinates at all points on the outer edges of the 

 diagram. 



In interpreting the model it is to be noted that points within the 

 solid represent the compositions of all possible solutions. Points within 

 the fields on the upper surfaces represent solutions satui'ated with one, 



