and at the surface 



[ 456 ] 



LII. On the Theory of Surface Forces. 

 By Lord Rayleigh, Sec. ' E.S. 



[Continued from p. 298.] 



WE may apply the same formulae to compare the pressures 

 at the centre and upon the surface of a spherical mass 

 of fluid, surrounded by vacuum. If the radius be r, we have 

 at the centre 



v=4^f>n(/)rf/, 



Jo 

 so that the excess of pressure at the centre is 



4 w J>n(/)^/-2^>n(/)rf/+^|>n(/)rf/. . (34) 



If r exceed the range of the forces, (34) becomes 



2^j>n(/)^+^j>n(/)rf/=K+^, . . (35) 



as was to be expected. As the curvature increases from zero* 

 there is at first a rise of pressure. A maximum occurs when r 

 has a particular value, of the order of the range. Afterwards 

 a diminution sets in, and the pressure approaches zero, as r 

 decreases without limit. 



If the surface of fluid, not acted on by external force, 

 be of variable curvature, it cannot remain in equilibrium. 

 For example, at the pole of an oblate ellipsoid of revolution 

 the potential will be greater than at the equator, so that in 

 order to maintain equilibrium an external polar pressure 

 would be needed. An extreme case is presented by a rectan- 

 gular mass, in which the potential at an edge is only one 

 half, and at a corner only one eighth, of that general over a 

 face. 



When the surface is other than spherical, we cannot obtain 

 so simple a general expression as (34) to represent the excess 

 of internal over superficial pressure ; but an approximate 

 expression analogous to (35) is readily found. 



The potential at a point upon the surface of a convex mass 

 differs from that proper to a plane surface by the potential of 

 the meniscus included between the surface and its tangent 



