71 the Theory of Surface Forces. 457 



plane. The equation of the surface referred to the normal 

 and principal tangents is approximately 



R 1? R 2 being the radii of curvature. The potential, at the 

 origin, of the meniscus is thus 



v=$$n(f)zfd/dd, 



where f 2 = x 2 + y' 2 ; and 



C 2v ,m C/f 2 cos 2 $ f sin 2 9\ JA irf 2 (\ 1 \ 



J. •*-J( / -iir +i iBr) - * = rU + is> 



Accordingly 



v =f(i + i)p n ^ rf /=| + 



1. 

 R 2 



The excess of internal pressure above that at the superficial 

 point in question is thus 



K+ hi> < 36 > 



in agreement with (35). 



For a cylindrical surface of radius r, we have simply 



K+^ (37) 



Returning to the case of a plane surface, we know that 

 upon it V = K, and that in the interior V = 2K. At a point P 

 (fig. 2) just within the surface, the value of V cannot be 



Fiff.2. 



ft 



expressed in terms of the principal quantities K and T, but 

 will depend further upon the precise form of the function II. 

 We can, however, express the value of \V dz, where z is 

 measured inwards along the normal, and the integration 

 extends over the whole of the superficial layer where V differs 

 from 2K. 



Phil Mag. S. 5. Vol. 30. No. 187. Dec. 1890. 2 K 



