Theory of Surface Forces. 149 



V2 



The members with * 2 are again neglected. 



To find an expression for/> T ', we multiply the equation (2 a) 

 with h and integrate with respect to A. In this way we find 



or as : R 1 = R — \%, 



^^=Rr(i+/ R ) ft -Kr(i-4>.,. 



By substitution in (32) the expression for the work done 

 by p<x becomes : 



^^+f 1 K?(i*A>»-f 1 M 1_ 2B>- 



Further we have : s 5^ = l-"~sb« Neglecting the terms 

 with -tw 2 ? we nave f° r the work done by p T : 



and the total work becomes : 



pS^+p 2 rdS-(l-|)n^-^)^S. . (33) 



If we had written the equation (2 a) in the form : 



(R 2 — h) dpx = 2(p N —p T ) dh, 



and had taken dh in the opposite sense to that adopted above, 

 we should have found (by substitution of the expression for p T ' 

 in (32)) for the work done by p T : 



The total work may be expressed thus by : 



f ^+p^d&-(l+^(p,-p T )dS, . (34) 



or if we take half the sum of (33) and (34) the work is 

 expressed by : 



p(8d£ + Sd8)-S(p*-pd<lS*, ■ ■ • ( 35 > 



* For the plane capillary layer we have: v = s£ and H = ( p s — -p T )C 

 The expression (35) becomes, therefore, for the plane capillary layer : 

 pdv— HrfS. 



