Electromagnetic Theory of Moving Charges. 493. 



/»» dX 



■•• * = ° / /e . x 



= c*l — = 



1 V(a s 



X) 



dX 



where ja is given by 



a 2 + //, 6 2 + /* 



or *' . / , £ _ i 



Determining the value of the constant so that the density 

 at a point shall be , , , we get 



4> 



e_C" d\ 



^X \/(a 2 + X){b 2 + X){c 2 + k 2 X)' 

 Putting 6= a, c=ka, we get 



Showing that, as Mr. Heaviside pointed out, the field of a 

 point charge is given when the conductor is an oblate 

 spheroid whose axes have the ratio 1 : k. 

 For a sphere the integral becomes 



, e , + k'a 



where U = \/\— k~ = xp 



and 6 is given 4>y 



To test the value of <£ let us make k' approach zero, i. e. the 

 motion becomes infinitely slow. 6 is then =r. 



_- , Lt , (r4 &'a) — log(r— k'a) 

 Then *=8^^ lo S^ S^ " 



— e ^ — e 



§ira* r ~ 47rr* 



