146 SCIENCE PROGRESS 
as dependent on the temperature and the concentration of the 
liquid phase, and also of the effect on the equilibrium condition 
of changes in temperature and concentration, the latter process 
being that termed ‘sothermal evaporation. Thus the theoretical 
foundation was within a comparatively short time made so 
extensive and so firm, that in 1893 the relatively complex 
relations exhibited by the double potassium-magnesium sulphate 
could be elucidated with completeness and comparative ease.} 
It is impossible to give even in this paper a short exposition 
in due order and correct proportion of the theory of double-salt 
formation, as based on the phase rule. Hence, although 
recognising the unsatisfactory nature of the undertaking, all 
it is proposed to do is to say something about such special 
points or such special aspects as seem to present the greatest 
interest. 
1. The Experimental Determination of the Transition Point.— 
The importance, theoretical and practical, attaching to knowledge 
of the exact temperature at which the double salt is formed or 
split, is such as to have led to the working out of a consider- 
able number of experimental methods which it is possible to 
summarise and to classify into direct and indirect, as shown in 
Table V. The results obtained by the various methods exhibit 
not inconsiderable divergence (see values for astrakanite), and 
the suitability of the application of each of these varies with the 
special case under investigation. Short of saying a good deal 
about the technique of the different methods, it is not possible 
to give an adequate account of this aspect of the subject, and 
a brief mention of the principle on which they are based is all 
that can be attempted. 
I. In those methods called direct, the transition point is found 
by actually ascertaining the temperature at which occur any of 
the changes—of volume, energy, appearance—which accompany 
the formation or the splitting of the double salt. Just as the 
change at o° of the solid ice to the quid water is accompanied 
by contraction in volume and absorption of heat, so the trans- 
formation of a double salt into the constituent simple salts is 
accompanied by contraction or expansion in volume (dilatometric 
method), absorption or evolution of heat (thermometric method), 
and sometimes also [method I. (ii1)] by a change in colour, as in 
1 Van der Heide, “ Doppelsalze von Kalium- und Magnesiumsulfat: Schénit 
und Kaliumastrakanit,” Zs. physik. Chem. 12, 1893, p. 416. 
