( 458 ) 



simultaneously with solid a.-, and he also in internal equilihrium. 



But if that internal condition of equilibrium is not known we can 

 only determine the gross composition of the liquid as a mixture 

 of «2 ^ïif^ ^2 ^^^^ "1 this way we find the point t which is the 

 projection of s. 



Acting in the same manner we should obtain for all temperatures 

 the actual composition of the solutions which at various tempera- 

 tures are in equilibrium with solid a^ and also their gross composition 

 if we look upon them as binary mixtures built up from a^ and /;,. 



The same might be determined in regard to the liquids in equili- 

 brium with solid h^ or solid ah. This shows that the equilibria of 

 binary mixtures in which a dissociating compound may be formed 

 from tiie components, must really be looked upon as ternary mixtures 

 with a limiting ^clause, implied in the dissociation equilibrium in 

 the liquid. 



For this reason the form of the solubility-lines which we obtain 

 in the system, considered as a binary mixture, is totally dependent on 

 the manner in which the dissociation in the liquid phase and the 

 melting-surfaces of the components change with a change of temperature. 



Guided by these ideas, Mr. Aten has worked out diiferent theore- 

 tically-possible cases which can partly explain abnormal solubility- 

 lines and which point, in addition, to phenomena as yet undiscovered. 



Let us first suppose that the conq)Ound ah in the liquid condition 

 is exothermic. 



In such a case the dissociation of the compound at first increases 

 but little as the temperature rises, then very much and afterwards 

 again but little. If we draw, in the triangle, a series of dissociation 

 isotherms for equal temperature intervals, these will at elevated 

 temperatures lie close to the side aj)^ and will differ but little. 

 Afterwards they will diverge greatly and finally come close together 

 and approach the sides o^nb and h^ah. In Fig 2, nine such isotherms 

 are shown. 



Let us now draw for the same series of temperature the solubility- 

 isotherms of a, and assume as the most normal case that they come 

 closer together as the temperature falls (from 9 to 1). 



The locus of the intersections of the dissociation- and solubility- 

 isotherms is the projection of the spacial melting-point-curve for a^. 



By projection on the side aj)^ we get the gross composition expressed 

 in «2 and h^ and by now plotting temperatures as ordinates w^e 

 obtain the solubility line ABCDEF commencing at the melting 

 point A. The line thus drawn exhibits three portions EF, FC and 

 CBA wdiich, particularly in the case of many salts, have been 



