Effects 'produced by the Motion of Electrified Bodies. 233 

 for points outside the sphere, 



"F_ ^Pf^ 2 __ a2 \ d 2 1 2,aejj 



*-~~v\6~ yJovs + w 



p_/xgp/5E 2 a 2 \ d 2 1 , / 9 \ 



/^p /5R 2 _ o*\ _^_ 1 

 5 V 6 2Jdxdz R 



Now, by ' Electricity and Magnetism/ § 634, T the kinetic 

 energy 



in our case, 



Now 



= i \ ] | (F« + G-u + Rw)dx dy dz, 



df , n dg 



*i +H S)^ 



dz. 



substituting for F and y ? 



dx dy dz, 



V 



i prp 

 2 20tt 



since the term 



¥^)))roW-r dxd y dz 



jie 

 12 



evidently vanishes. 



Transforming to polars and taking the axis of x as the 

 initial line, the above integral 



fjbe 2 p 2 

 40tt 



Jo II VlT-l) ? m ^^* 



75« 



^0 



By transforming to polars, as before, Ave may show that this 



Similarly, 



# 



= 25a * 



TT ^ / 7 7 



25a 



