184 Messrs. J. P. Kuenen and W. G. Robson on 



entirely on the proportion in which the two substances are 

 mixed, between what limits of pressure the phases may exist, 

 and (this is of especial importance) at what temperature the 

 phases become identical. In other words, above the critical 

 point for the upper liquid and the vapour the solubility-curve 

 does not exist, in the same way as the curve does not exist 

 beyond a critical point of the two liquids. 



The character of the solubility-curve cannot therefore be 

 ascertained without taking into account the vapour. Let us 

 consider the nature of the solubility-curve from this point of 

 view. 



The complete solubility-curve consists of three branches, two 

 of which represent the compositions of the liquids, the third 

 that of the vapour. The vapour branch may be either between 

 or outside the liquid branches, according as the three-phase 

 pressure is higher than or between the pressures of the pure 

 substances *. Of these three branches, with rise of tempera- 

 ture two will reach a critical point : either the two liquid 

 branches, as was the case with most of the mixtures examined 

 by Alexejew and Rothmund ; or one of the liquid branches and 

 the vapour branch. Moreover, cases occur (see above) where 

 the liquid branches form a critical point with fall of 

 temperature. We shall call such a point a lower critical point. 

 It will be seen that a number of combinations, some of which 

 are represented in the diagrams 1-4, is possible. 



Figs. 1 and 2 are the solubility-curves for liquids which 

 have an upper critical point. The dotted curve representing 

 the composition of the vapour is outside the liquid curves in 

 fig. 1, between them in fig. 2. In both cases it stops suddenly 

 at the critical temperature of the liquids. The case repre- 

 sented in fig. 2 is in many respects a remarkable one. It has 

 the peculiarity that the composition of the vapour is the same 

 as that of the liquids at their critical point. And it may be 

 proved that, above this critical temperature, there is a 

 maximum vapour-pressure or minimum boiling-point. We 

 have ascertained by some rough measurements that several 

 mixtures belong to this type. Examples of such mixtures 

 are methyl alcohol and carbon disulphide, ethyl alcohol and 

 carbon disulphide, water and phenol f> water and aniline. 

 These mixtures, however, require further investigation, so 

 that we will not discuss them at present. 



* Konowalow, I. c. 



t This combination has since been fully investigated by van der Lee 

 (Dissertation, Amsterdam, November 1898), and also bv Lehfeldt (Phil. 

 Mag. [5] xlvii. p. 284). 



