Theory of Surface Forces. 153 



The considerations, which the equations (27) and (28) 

 produced, may be applied also to a cylindrical capillary layer. 

 Quite in the same way as in § 4, we find again : 



2 {_v 2 — vi v 2 — v x J ; 



(48) and (30) give : 



CH.-B;*-*{iHS.-.5±»} + ^(W. (49) 

 On the other hand we have : 



2 v k^ = *W-. v v l±?l 9 . . . (50) 



Pl—p2 V2 — V! V S — Vi J 



where p^v denotes the volume integral of the pressure p N , 



or : 



1 C 2 

 P*—y$\ S'pvdh. 



This relation (50) we prove in the following way : — 



At the formation of the unit of mass of the capillary 



layer the quantities of liquid and vapour which have produced 



the matter of the capillary layer, were : 



Pi^mPi aDd W.-ft (see above § 4). 

 Pi—P* Pi—P* 



The available energy which has disappeared is consequently: 



_ (a-zw* + vp^pi \ = _ fm=& +p A . 



I Pi-pi pi~p2 ^ J lP\-Ps J 



.... (51) 



If p represents the average value of the density of the 

 capillary layer, we have for the last expression : 



the 



If 2 * 



If p T = -^ I $ f p T dh t we may consider — p t v 



available energy which is gained at the formation of a unit 

 of mass of the capillary layer. 



The change of the available energy at the formation of the 

 capillary layer per unit of mass, i.e. the capillary energy 

 HS, consequently becomes : 



