(10) 



If we start from the difïerential equation in p,;v and T derived 

 by VAN DER Waals (Cont. II, 112). 



Vsrdp = {,v,-,vf)l^] clvf+--dT . . . (1) 



we get from this for constant x that 



T 

 Vsfdp — dT (2) 



or 



T ('^ — — ^ (3) 



If we now multiply numerator and denominator by r — as will 

 prove necessary for simplifying the discussion, we get : 





(4) 



In order to derive the course of the P, T-lines from this equation, 

 the loci must be indicated of the points for which the numerator, 

 resp. the denominator = zero, and at the same time the sign of 

 these quantities within and outside these loci must be ascertained. 



In the V, .ï-üg. 1 the lines ah and cd denote the two connodal 

 lines at a definite temperature. The line PsQs whose x = .r^ the 

 concentration of the solid compound AB cuts these connodal lines 

 and separates the v,.x'-figure into two parts, which call for a separate 

 discussion. 



If Ps denotes the concentration and the volume of the solid com- 

 pound at a definite temperature, then the isobav MQIWB'U'Q'N 

 of the pressure of Ps will cut the connodal lines in two points Q 

 and Q', which points indicate the fluid phases coexisting with the 

 solid substance AB, and therefore will represent a pair of nodes. 



The points for which -— = or — -^ = are situated where 



the isobar has a vertical tangent, so in the points D and JJ as 

 VAN DER Waals ') showed already before. In B the isobar passes 

 through the minimum pressure of the mixture whose x^^^xj), and 

 so it has there an element in common with the isotherm of this 

 concentration. In B' however, the isobar passes through the maxi- 



1) These Proc. IV p. 455. 



