DOUBLE SALTS 145 
devoted to the investigation of solubility relations. The 
temperature-concentration curves (Table IV.) for the three 
condensed 3-phase systems, viz.: (1) solution + simple salt 
MA + simple salt M’A, (2) solution + double salt + simple salt 
MA, (3) solution + double salt + simple salt M’A, are perfectly 
analogous to the corresponding temperature-pressure curves 
(Table III.), in that their intersection marks the transition point, 
7.e. the temperature at which the concentration of the different 
solutions is the same and at which the three solid phases, 
double salt and its two constituent simple salts, can co-exist. 
The graphic representation of these solubility relations has to 
take account of three variables, (1) the temperature and (ii and 
iii) the amount present in the saturated solution of each of the 
components MA and M’A. The most satisfactory manner of 
doing this is by means of space models with three rectangular 
axes,! though much may be accomplished by means of figures 
in a plane, such as those reproduced in Table IV. In the 
projection there adopted * the temperature axis is placed verti- 
cally, and the values found at different temperatures for the 
concentration of the two components MA and M’A (expressed 
as the number of molecules present in one hundred molecules 
of water) are represented by ordinates on both sides of the 
temperature axis. Hence two corresponding points such as 
G and G’, M and M,, etc., always belong together and refer to 
the same solution, whose concentration with respect to MA and 
M’A they represent for a special temperature. 
The determination over a certain temperature range of such 
solubility curves, together with an extensive use of graphic 
methods for their representation, have made it possible to get 
complete knowledge of the equilibrium condition of the system 
makers, “Gleichgewicht des Doppelsalzes von Jodblei und Jodkalium mit 
wassriger Lésung,” zbzd. 9, 1892, p. 57; and Io, 1892, p. 467; “ Graphische 
Ableitungen aus den Loésungsisothermen eines Doppelsalzes und seiner Kom- 
ponenten und mdgliche Formen der Umwandlungscurve,” zd7d., 11, 1893, pp. 55-110; 
“ Theoretische und experimentelle Untersuchung tiber kryohydratische Tempera- 
turen bei Systemen von zwei Salzen mit oder ohne Doppelsalzbildung,” zdzd., 
12, 1893, p. 73. 
1 Of such representations in space, that best known is the carnallite model, 
Van’t Hoff and Meyerhoffer, Zs. Dhyszh. Chet. 30, 1899, pp. 86 e¢ seg. See also 
Finlay, Zhe Phase Rule, pp. 275 e¢ seq. 
* Koppel, “ Die Bildungs- und Léslichkeitsverhaltnisse analoger Doppelsalze,” 
Zs. phystk. Chem. 52, 1905, p. 385. 
IO 
