﻿Theory of Surface Forces. 567 



I purpose demonstrating that the expression — (2B + 3W), 

 which is null for the liquid or vapour, is nothing hut the super- 

 ficial tension in the case of the capillary layer. 



Admitting the function of force to be — /- at which I 



arrived above, the force which is exercised between two 

 elements of mass becomes : 



j,mm' , mm' 



f ^-e-r+fg—erv. 



Now the virial B of the forces of cohesion is expressed by 



.~ . /1<0 mm'e-v . , ^ , 



B = i/S — +tfq2mm'e-V' 9 



further, 



w i/x mm ' r e ~ ,r , 



whence 



2B=— W + i/ySfiwnV-*' (18) 



The last term of (18) may be considered as the potential 

 energy of a homogenic agent of which the function of force is 



fqe-*. 



Let us calculate, on this hypothesis, the potential energy of 

 a system of plane parallel layers, such as the capillary layer 

 is. According to Rayleigh *, one has for the potential V at 

 a point of the capillary layer : 



v=-% P - i*-*e, ?t il >- (m 



p 1.2rfA- 1.2.3.4tf/i 4 '••' ' ^ iJ) 



= l u»yjr(u)du, and -ty(ii) = 2ir 1 u(p(u)du, 

 Jo J« 



<j>(u) being the potential function. 



The potential energy of our system of layers per unit of 

 surface is thus : 



where 



Cn- 



W= JJ V- -a |>B+ «-£ •( jy* 



f//i being the element normal to the surfaces of the system of 

 layers, the indices 1 and 2 relating respectively to the liquid 

 and to the saturated vapour. 



* Phil. Mag-. Feb. 1892, p ; 210. 

 2 P2 



