The Followers of Maxwell. 355 



will be of the same kind as in the electric case ; so that the 

 induced magnetic force H' is given by an equation of the form 



where c denotes some constant, and bi, which is analogous to 

 the vector-potential in the electric case, is a circuital vector 

 whose curl is the electric force E! of the variable magnetic 

 system. The value of bi is therefore (l/47r) curl Pot E t : so 

 we have 



H' = - J-. |, curl Pot a, 



47TC" (jt~ 



This must be added to Hi. Writing H 2 for the sum, Hi + H', we 

 see that H 2 is the curl of a 2 , where 



and the electric force E 2 will then be - a 2 . 



This system is not, however, final ; for we must now perform 

 the process again with these improved values of the electric 

 and magnetic forces and the vector-potential ; and so we obtain 

 for the magnetic force the value curl a 3 , and for the electric 

 force the value - a 3 , where 



1 r) z 1 ^* 



= a x - - Pot ax + -- Pot Pot 



4rrc 2 fit* 



This process must again be repeated indefinitely ; so finally we 

 obtain for the magnetic force H the value curl a, and for the 

 electric force E the value - a, where 



1 }*> 



- Pot Pot Pot a! + 



(47TC 2 ) 3 

 2A2 



