﻿Theory of Surface Forces. 569 



V designating the potential for the point considered and 

 being given by (19). From this formula (19) we derive : 



dV dp _rg_ <i'V _ <h d s p 



dh ~ die 1.2dh* 



Moreover for the potential function — / — — , we have 



c« 



1.2 1.2.3.4 _ 1.2.3.4.5.6 _ _ 1 _ 2 

 a 6^ t' 4 Y" 



1.2 1.2.3.4 



whence 



7— = 2a — - + 2aV -y£ + 2aX 4 - ■ . + . .. 



dti dk dh 3 T c/A ^ 



Hence integration with respect to A gives : 



or 



The value o£ H, on changing the sign, is nothing but the 

 second member of the formula (21). Finally one sees that 



H = -3W-2B (22) 



This relation may he established without necessarily having 



dV 

 recourse to the square of the expression for ~j- f. 



Hence : dh 



The value of the surface-tension is three times the work to he 

 done in conveying the parts of the capillary layer (per unit of 

 surface) to an infinite distance from each other, or, which is 

 practically the same thing, beyond the sphere of sensible 

 activity, decreased by twice the virial of the forces of cohesion. 



* 1 fdVV _ n2 (dpV . n4 (dW ^ ..JdSpV . 9n , v2 dpd^p 



^y=iiy+^ + ^W w 



dh dh A 



+ dh dh 5 + \ dh dlv + dh' dh 5 \ T ' 



t G. Bakker, Zeitschr . fur phys. Chem. xxxiii. p. 498 (1900). See 

 above, § 5, and Eayleijrli " On the Theory of Surface Forces, II." Phil. 

 Mag. Feb. 1892, formula (22). 



