24 Prof. W. H. Bragg on the " Elastic Medium " 



The pressure at the surface of the first sphere is made up of two 



parts: j- -—due to its own charge, and — • j- due to the 



charge of the other sphere. This is only an approximation to 

 the truth, and the closeness of the approximation depends on 



the smallness of j. Thus we take the pressure at the surface 



of the first sphere to be 



e/Qi , Q 2 y 



4ttVi d)' 



that at the surface of the second, 



JVQi . QA 



47r\ d r 2 /' 

 The energy of the system is therefore 



1 E fQ,» | 2.Q& t Ob 2 ) 



2 ' 47T (. ?'i d ?' 2 J 



If we differentiate with respect to cZ, we see that there is a 

 force of repulsion between the spheres equal to 



E_ Q1Q2 

 4tt' d 2 ' 



This is, of course, the " law of the immerse square." The 



E 1 



factor -j— corresponds to ^, K being the specific inductive 



capacity. In the ordinary statement of the law the K is often 

 omitted, being arbitrarily taken as equal to unity. 



8. So far the correspondence between the results deduced 

 from the ordinary hypothesis and the hypothesis of the elastic 

 medium has been obvious. It is not perhaps quite so plain 

 what in this language corresponds to the " force at any point 

 due to the attractions of an electrical system/'' and in par- 

 ticular to the law that "just outside a conductor this force 

 (F) =47r/9, or, more strictly, K F = 47rp." 



But it must be remembered that the " force at any point 

 due to the attractions of an electrical system " is only a 

 mathematical conception and not an actual physical quantity. 



It is the attraction on a unit of electricity, supposing the 

 presence of that unit not to disturb the pre-existing distribu- 

 tions of the system. This condition is impossible. 



However, on the strain theory we have the law that just 

 outside a conductor, where the medium is pushed back a dis- 

 tance x, there is a force of restitution per unit volume equal 



