( 525 ) 



1 da 



a dx 2 



1 db "~"3~' 



b dx 

 which value ■/, becomes = %, when the independence of b of the 

 volume is relinquished. 



, °> , ö a ir 



lu this case the hue cuts the line -r — =0 still in two 



O.V 0> oV 



points. One point is that above mentioned, the second lies at smaller 

 v and larger v. So nearer the component with the smallest value of b. 

 With increase of temperature the two points of intersection draw 

 nearer to each other, and as second problem we may put : to exa- 

 mine the circumstances under which the two points of intersection 

 of these curves coincide. The three equations from which this cir- 



cu instance is determined, are then: - — == 0, - — — = and a third 



Ou 2 OX Of 



which expresses that these curves touch, viz. : 



ö> V d'tp d 3 if> 



dVd.c J d.v'dv d> 3 

 or 



d'p V d'pd'p 



d.vdv J ö.r 3 or 2 



Above the temperature at which these circumstances are fulfilled, 



d a if> d 2 xp 



- — =0andr-r- = do not intersect any longer, and the comnli- 



dv' 2 dxdv J [ 



cation in the course of the isobars, viz. that there is one that 



intersects itself, has disappeared. 



The third problem is more or less isolated, but yet I should like 



to treat it in this connection: viz. that for which the line - — = 



Or' 1 



dhy d s \p 



has a double point, and so at the same time r-r = and r— - — = 0. 



If there is a minimum 1\ for mixtures taken us homogeneous, such 

 a point is really a double point. If there should be a maximum Tk, 

 it is an isolated point. We find then again u = Vk, T= 1\ and the 

 value of x is that for which Tk has a minimum or maximum value. 

 Let us call the three values of x obtained for those three problems 

 x x , x, and a\ , then : 



*> < ■»] < ■''* 

 r J\ > T, > 1\ . 



