﻿Theory of Surface Forces. 561 



which shows (see (4 a) ) that the absolute value of the potential 

 energy per unit of volume is equal to the cohesion per unit 

 of surface perpendicular to the lines of force. 



§1. The surface-pressure*. — Suppose a liquid in equi- 

 librium with its vapour; if the surface is a plane, the lines of 

 force in the capillary layer and adjacent to it may be considered 

 as straight lines. The surface pressure is nothing but the 

 difference of the thermic pressure f in the direction of the 

 lines of force (normal to the surface) at the limits of 

 the capillary layer. (We always consider the capillary layer 

 as plane and between the liquid and saturated vapour.) 



The hydrostatic pressure being the vapour-pressure and 

 thus the same in the liquid- and vapour-phase, the absolute 

 value of the difference of the thermic pressures d 1 — d 2 is 

 consequently the same as those of the cohesions. As in the 

 interior of the liquid and of the vapour R is nul, the expres- 

 sions (5) for the cohesions become 



8?r/ X 2 ' 



If Vx and V 2 are the respective potentials for the interior of 

 the liquid- and vapour-phase, we have therefore for the 

 surface-pressure 



4?<* , - v *> W 



For every homogenic phase, A 2 V = 0, and the equation (3) 

 shows 



V= f p= — ±irfX 2 p, 



whence, calling p Y and p 2 the densities of the liquid and of the 

 vapour respectively, and substituting in (6), we obtain the 

 expression 



K = -VV(pr~/v) (?) 



For p 2 = we get 



K 1 = 27rf\ 2 p l 2 . 



27T/V is therefore the coefficient a in the expression for the 

 intrinsic pressure of Rayleigh or for the molecular pressure 



* Molecular pressure of Laplace or intrinsic pressure ot Rayleigh, 

 when the surface of the liquid can be considered as free, neglecting the 

 influence of the vapour. 



f Young conceives the hydrostatic pressure as the difference between 

 the power of repulsion and the cohesion. I have called that power of 

 repulsion, " the thermic pressure." 



