Effects produced by the Motion of Electrified Bodies. 245 

 or transforming to polars, 



Jo t-'o Jb. 7 



367TCT 



= T5R' 

 For values of r < R we may, by the same reasoning as before, 

 substitute A ^ (,U) in the integral for ^ J. Now 



making this substitution, the integral becomes 

 ,2, ,2 

 R 



|sJJJ -^-dxdydz 



36r 3 sin 3 cos 2 cos 2 30 d<9 <&• 



367T(T 



T5R* 



Hence, adding this to the part previously obtained for values 



of r>R, we see that the coefficient of vv r from F —- is zero, 



; dt ' 



and, similarly, the coefficient of iuw f from this part of the inte- 

 gral vanishes. jfW j 



Let us now take the terms arising from 1 1 I Gr— dxdydz 



and take, as before, the part arising from the product of that 

 part of G due to e with the part of -j due to e' . The coeffi- 

 cient of uv! in this part will be the same as the coefficient of 

 vv' in the former part, and so will vanish. 

 The coefficient of vv f 



Now for values of r > R we may, as before, substitute -r^> - 



d 2 1 <^ r 



for —k -7: and it becomes 

 dy l r n 



a- \ \\r 2 1— — -j dx dy dz. 



By transforming to polars, as before, this may be shown to be 

 Phil Mag. S. 5. Vol. 11. No. 68. April 1881. T 



