542 Mr. E. Cunningham on the 



Hence dw ■',*/( IV < . 



and therefore 



so that the longitudinal mass is equal to 

 1 dW 1 C ,_,' , 



It is the second term in this expression that is neglected 

 by Abraham, and which he has to account for by assuming 

 the energy of the electron to be made up of W together with 

 a term not electromagnetic in origin. 



We proceed to evaluate this expression in the two cases 

 (i.) of a sphere with uniform volume density; (ii.) of a sphere 

 with uniform surface charge. 



(i.) Volume Distribution. 

 U ~5ac 2 /T 



Hence 



VV 5a£V 1+ 3c 2 /- 



dG_i^(l v 2 /c 2 \ 

 dv o ~5ac 2 L0 + /3 3 J 



" 5ac 2 /3 3 ' 



ldW_Zj^f 2 / V\ 1 \ 

 v dv ~ 5 a/3 1 3c 2 ^ \ ~*~ '6c 2 ) <?J3 2 J 



1 e 2 r, tfi 



~ 5 ac 2 /3 3 



i a /"ff /J. 



f>o^(Fi)o^T = po | I f cos 6 . - 7rr/3 cos e?27rr 2 sin 6 d6 dr 



Oc/0 



8ttV 



a 5 



2 



3 



' 5"* 



3 



1 £ 2 







~ 5 a ' 







