30 



Each value of e occurring- twice, i.e. combined with the two 

 values different from e which a can take, we have in addition to (1 J 8) 



'ƒ 



or 



— do, 

 On 



SO that (117) becomes 



' 2xJ on 



As now outside the sphere 



r =r \ o dr 







we have for every closed surface that does not surround the sphere 

 E^:=0, but for every surface that does 



a 



E^ — 2jtc \^dr. . . . . . . (119) 







As to E.^ we remark that substituting (65) in (41) and taking 

 into consideration (64) we find, 



G — Y.T, Q = 7<\/^r (120) 



From this we conclude that E^ is zero if there is no matter 

 inside the surface a. In order to determine E^ in the opposite 

 case, we remember that 6r is independent of the choice of coordinates. 

 To calculate this quantity we may therefore use the value of T 

 indicated in § 56, which is sufficient to calculate E^ as far as the 

 terms of the first order. We have therefore 



G=-Q 



and if, using further on rectangular coordinates, we take for 1^ — g 

 the normal value c, 



ex. 



From this we find by substitution in (114) for the case of the 

 closed surface a surrounding the sphere 



/j = — 2jrc I Qdr , 



E. 







This equation together with (119) shows that in (113) when 

 integrated over the whole space the terms of the first order really 

 cancel each other. In order to calculate those of the second order 



