404 



Physics. "(hl the sjisteni lieMuie-water.'" By Dr. F. E. C. Scheffkr. 



^Coiiiimiijicated by Prof. J. D. van dku Waals). 



1. In the 17^'' contribution ^) to the tlieory of binary mixtures 

 Prof. VAN DEK Waals has demonstrated that the phenomena wliich 

 occur when the concentration of the vapour phase with three-})hase 

 pressure lies between that of the two coexisting liquid phases, may 

 be derived from the course of the plaitpoint curve alreadj^ drawn 

 in fig. 43 of the 14^'' contribution ^). In this T-x projection the 

 plaitpoint line exhibits two minima and one maximum ; the minimum 

 Pa!j and the maximum Prd are heterogeneous double plaitpoints, 

 hence they lie in the covered region, and correspond to cusps in the 

 ]^-T projection. The other minimum indicated in tig. 43 by Q,, is 

 a homogeneous double plaitpoint, and may occur both in the stable 

 and in the covered region. Further two points are found on the 

 plaitpoint curve which indicate the highest, resp. the lowest temperature 

 at ^vhicll three-phase equilibrium can occur. These two points, the 

 critical endpoints, which indicate stable states, must lie on the 

 branches APcd, I'esp. BP„b in fig. 43. 



Whereas the different situation of the lower ci'itical endpoint on 

 tlie branch BPab does not bring about an essential modification in 

 the phenomena, three possibilities present themselves with regard to 

 the situation of the higher critical endpoint, which give rise to the 

 distinction of three different cases; the endpoint of the three-phase 

 pressure can namely either lie on the leftside (Type 1), or on the 

 rightside (Type 3) of the minimum on the plaitpoint line, or it can 

 just coincide with it (Type 2). The last case, to which fig. 43 

 corresponds, may be considered as the transition between the two 

 preceding ones. 



We have an example of type 3 in the system ether-water. 



For the peculiarities which present themselves for this system 1 

 may refer to my publication in these Proceedings ') and to Prof. 

 VAN DER Waals' 21^'' contribution'). 



The chance of the occurrence of type 2 seems naturally very 

 slight; yet it is very well possible that further investigation will 

 make us acquainted with a system for which the distance between 

 the minimum of the plaitpoint line and the endpoint of the three- 



1) These Proc. Vol. XIV p. 655. 



2) These Proc. Vol. XI p. 816. 

 8) These Proc. Vol. XV p. ?80. 

 *) These Proc. Vol. XV p. 602. 



