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 isothermal 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. 1 

 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 liquid 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. (iii)] by a change in colour, as in 



1 Van der Heide, " Doppelsalze von Kalium- und Magnesiumsulfat : Schonit 

 und Kaliumastrakanit," Zs.physik. Chem. 12, 1893, p. 416. 



