Theory of Surface Forces. 151 



As for a cylindrical capillary layer the curvature is ^ and 



only the half of the curvature of a spherical capillary layer 

 with the same R, we have instead of the equation (2aj(§ 2): 



c?Pn(Ri + ^)=— (pK—p^dh. . . . (41) 

 By integration with respect to h : 



p y dh= — \ p v dh + \ p T dh, 



or: Pl -p 2 =Wj^M (37) 



In order to deduce the equation of energy we calculate 

 firstly the work done by the pressure pi, p v , and pi. 



The capillary layer (per unit of mass) is determined by 

 two parameters, and we consider the temperature to be 

 variable while R = constant. 



The work done by p 2 and p x becomes : 



i$ 2 p2dt;+iS 1 pidt, 



or, whereas S 2 =" S ( 1 -f ^k j and Si = S 1 1— —^ \ 



The work done by the pressure p T parallel to the capillary 

 layer becomes further : 



ZdSi PT dh (i+ |-) = dbfy + §M 2 



The total work becomes consequently : 



P 8^r- L Srfr {Pl - P2 ) +ds(i- X) & + g^r 5 - (4 2) 



By multiplication of (41) by h and integration, we find 

 easily : 



where 



1 C* 

 * Ji 

 * For dS' = 2TrR'dz, consequently ~2 t 2TrR'dhp T dz = $ dS' p? d/t. 



