526 Dr. G. Bakker on the 



Now d0=—pdV; 



or d V = - vdO = - UTvd — M . 



v — b 



Integrating, 



where the index corresponds to the liquid state. Further, 



(Gauss and van der Waals)*. 

 By substitution in (27), 



£i+gg = Jg : l{BTlog^-+BTO / v ~ Vl m --V- (28) 



Since the hydrostatic pressure p 1 is nothing but the vapour- 

 pressure and thus at a definite temperature a constant, the 

 equation (28) may be considered as the relation between 

 p 2 and v. For the point H in fig. 4, v = Vi and p x =p 2 ; the 

 equation (28) properly becomes therefore for the point H : 



KT _1 ^ _ RT _« 



^ Vi — b 4<2 U] 2 l^ — 6 Vi' 



By the aid of the well-known relation 



RTlogf£|=«(i-i)+^K-^ 



we find easily that for the point K in fig. 4 the equation (28) 

 properly becomes 



UT a 



Pi = 



b 



T 



As, however, the equation (28) is not easily to be discussed, 

 we start immediately from equation (24) 



fi-fii 



dp 2 =r-J^d~V. . . (24) 

 a 



Now, dO=—pdV or dV= — vd0, and, still ever adopting 



* Hence it has often been wrongly concluded that the potential energy 

 of the forces between the molecules should be — ap. 



