220 PROFESSOR A. E. H. LOVE ON THE 



Since the pressure vanishes at this surface, the expression 



Ivyp* {a 3 - (a + U ) a } + XA ( 1 -iV) e~^a (ujr) 

 vanishes, or we have, neglecting U a 2 , 



so that U a contains the same surface harmonic as a,. The form of Fj is determined 

 by the condition that W is the potential of a distribution of density p through the 

 volume of the sphere r = a, together with a distribution of density p U n on its 

 surface. Just as in 14, this condition leads to the equation 



F, = tVAs-V^V 



48. Now let the bounding surface in the strained state be 



r = a + b cos 0, 



which represents a sphere with its centre at a small distance b from the origin in the 

 direction of the axis of the harmonic. We find 



r cos , 



W = - 



S ft *~ 



br cos 6. 



If s 2 a 2 > 5, the condensation is greatest near the centre, and it is positive on the 

 side remote from that towards which the surface is displaced, so that the centre of 

 gravity is displaced in the opposite sense to the surface. The distance of the centre 

 of gravity from the origin is easily proved to be 5b/(s 2 a 2 5). 



Fig. 1. 



Fig. 2. 



