﻿r I lieory of Surface Force*. 559 



in which g, A, and B are arbitrary positive and negative 

 constants. C is a constant that can be omitted. 



2nd > jl( \ Aj sin ( yr + a ) 

 <p{r) = 



in which A } , r/, and a are constants. 



If we restrict ourselves to functions which relate to forces 

 as they occur in nature, the second potential function must 

 be excluded. If we further restrict ourselves to the forces 

 which cause the cohesion of Young in the capillary theory, 

 the constant B of the first potential function must be nul and 

 we get : — 



#w = - or -/ ,. • 



§ 2. Potential enemy per unit of volume. — The analogy of 

 the equations 



A 2 V = 4tt/> and A 2 V = y 2 V + 47r//?, 



and that of the functions 



— •- and — t - 

 r r 



have led to my seeking in the case of capillary forces (of 

 cohesion) expressions analogous to those which Maxwell 

 discovered for the energy and tensions in the case of electrical 

 phenomena. The potential energy is always expressed by 



if one substitutes for p the value derived from relation (3) 



we see 



W=i$Vpdxdydz; 



! or p the value derive 



w = 4^f YA * yd * d y d: ~ &f^ idx d 'J d: > 



dV 

 and as at an infinite distance V and ~j— &c. annul, the 



ax 



integration by parts shows : — 



or, if R represents the force acting on unit of mass, 



