88 



f - T,n +- p,v = ,• - T,r; + p^v' = Mil .... (3') 



Tlie validitj' of tlie relations (2) and (.3) may be established by 

 means of Boltzmann's equation modified by van der Waals 



M \{Xdx^Ydy-\-Zdz) 

 1 1 ___A 



wiiicli M\{Xdx -\- Ydy -\- Zdz) represents the work done on the 



1 



molecular quantity on transition from a layer with density — to a 



V 



1 

 layer with density — ;-. 



V 



When in a point of the capillary layer at h the energy with 

 omission of the constant amounts to 



2 S 4 N 



— ao 



2 dh^ 4:1 dh' 



n\ 



the molecular pressure in this point in the direction of the layer 



c, d-Q c^ d\ 

 2^^ 47^W 



c, d-Q c^ d*Q 

 can 1)6 represented by — Qe = a^' -[- ^Q-^ + TA'^* ' ^ 



1 all - 



in which /> represents the pressure belonging to the homogeneous 

 phase of the density q, we have 



c„ d^Q 



If we substitute /;, from this relation in (3), the latter passes into : 



_ a,y — 0, ^ — MliT log {v — 6) + pv = iiM . 

 "" ' dh" 



This equation, which we have dei'ived by the aid of kinetic con- 

 siderations, is the condition of equilibrium, at which Prof, van der 

 Waals arrives in his "Thermodyjiamical theory of capillarity". 



Following in Prof, van der Waals's steps, Dr. A. van Eldik has 

 aiven a thermodvnamic theory of the capillarity for a mixture of two 



o ■ .Jit 



substances. By applying that the total free energy must be a minimum 

 for all variations of q and .r, which satisfy I (>.?; c/A = constant and 



Q (1 — .u) dh = constant, he found for the variation with respect to 9 



ƒ 



