Method of treating Electrostatic Theorems. 



27 



Let the sphere bearing a charge Q be immersed in a 

 dielectric of elasticity E l7 the elasticity of the other medium 



Fig. 6. 



being E 2 and E : being > E 2 . 



Consider the displacement at any point P. If E 3 were 

 equal to E 1? the displacement across the surface would be 



7 7Tp2 • jyp • If E 2 were zero, then, by the last section, 



the displacement would be 2 . — rrp 2 . ^p. 



Since E 2 lies between and E t it is natural to guess that 

 the actual displacement is (1 +fi) . j — -4 p 



TYp , where fi lies 



between and 1 : and it is easy to show that this condition 

 of things produces equilibrium everywhere. 



Under this condition of things the medium to the left of 

 the plane of separation is strained as it would be if E 2 were 

 equal to E„ and there were placed a charge — jjlQ, at O' (the 

 image of 0) in addition to that at 0. The medium to the 

 right is strained as if E 2 were equal to E x and there were 

 placed at a charge (1+aO Q. 



Considering the strain of the first medium, the pressure at 

 P must be 



Ei /_Q__Mi\ 

 4ttA0P op/ 



Considering the strain of the second medium, the pressure 



