Theory of Surface Forces. 219 



if 



T=,r J o sxrK- (p 2 -ft) 2 , • • • (25) 



where (25) agrees with the value of the tension found for this 

 case by Laplace. 



In the application to a sphere of liquid surrounded by an 

 atmosphere of vapour, equations (9), (11), (12) remain un- 

 changed, in spite of the curvature of the surface. If tff" denote 

 the external pressure acting upon the vapour, 



Pl = v" + K Pl *, (26) 



p 2 = v" + Kp 2 2 + 2T/R. . . . (27) 



The symbol w is still regarded as denned algebraically by 

 (6), so that 



»,=«", w 2 = w" + 2T/R (28) 



Integrating (12) by parts, we find 



P2 Pi J(.) P 



or by (28), 



i;;y*4- <» 



In this equation «r is a known function of p. If we com- 

 pare it with (13), where w' represents the external pressure 

 of the vapour in contact with a plane surface of liquid, we 

 shall be able to estimate the effect of the curvature. It is to 

 be observed that the limits of integration are not the same in 

 the two cases. If we retain pi, p 2 for the plane surface, and 

 for the curved surface write p L + 8p ls p 2 + Sp 2 , we have from (29) 



UX 2 — TtT 



"77 



Pi J P1 P ft(p 2 + fy 2 ) 



or by (28), 



£=?** *&-*.'• •;■•*> 



The limits of integration are now the same as in (13), so 

 that by subtraction 



, . m/1 1\ ^T 



(w — «r )( )= Tr -, 



V2 Pi/ R P2 



or 



sr" = *r' + l 1 -?'- (31) 



P2-P1 

 Q2 



