28 Prof, W. H. Bragg on the " Elastic Medium " 



at P must be 



E, (1 + jQ.Q 

 4tt' OP ' 



If there is to be equilibrium, these must be equal at every 

 point of the surface of separation. 



.-. E 1 (1- /A )=E 2 (1+ /A ) 



_ -^i — E 2 



By giving /z, this value, which is independent of the position 

 of the point P, we make the pressures balance each other 

 everywhere. We have therefore found that state of the 

 medium into which it will settle under the given conditions. 



It is easy to write down the energy of the strain. For if 

 d be the distance from the centre of the sphere to the plane 

 of separation of the two media, the pressure at the surface of 

 the charged sphere is approximately 



4tt'U UP 

 r being the radius of the sphere and small compared with d. 



The energy is obtained by multiplying this by ^. 



There is therefore a force urging the sphere towards the 

 plane ; and the magnitude of it 



= E 1 ^ 

 Sir' U L ' 



' E x -E 2 Q 2 



= E X . 



E. + E/lGTr.cF 



12. Let us next take the case of a sphere of one dielectric 

 (elasticity = E 2 ) immersed in another dielectric (elasticity = E : ) 

 in which there is a uniform displacement ; or, as it is often 

 termed, the sphere in the uniform field. 



Here again, I think, by using the present method, the 

 problem is much easier to understand. 



To fix our ideas, suppose the displacement is to the left, and 

 that E 2 is less than E 1# Let the uniform displacement of the 

 field =b, let the radius of the sphere =r. 



It is obvious that since the medium in the sphere is weaker 

 than that outside, the sphere will yield as a whole and be dis- 

 placed further in the direction of the existing distribution of 

 the field. The lines of displacement behind the sphere will 



