748 



<fW, = A, öa, + A, öa, + (4) 



Further the external electromotive forces will perform work per 

 unity of time equal to : 



dW. 

 dt 





in which <i denotes the electrical current. The work done by the 

 system amounts, therefore, per unitj' of time to : 



dW. 



dt 



For this we may write 



dW„ 



- fide, ^). dr. 



J(d + (^e.^)dT+J{(i,(l)dr, 



dt 

 in which €' denotes the electrical force. Now in the conductors 



From the supposition that in the conductors a will be infinitely 

 large, follows that here (£* -}- '^e must be = 0, whereas outside the 



dW' 

 conductors ^ = 0. Hence the first term in the expression for — — - 



dt 



disappears. When we make use of the expression : 



^ =: c curl S^ ^) 



we get after partial integration 



1 TXT /-• /^ 



' = c I {yp.curl (i) . dri-c I [S?, (ïl.v • de. 



The second term disappears on account of the supposition that 

 no energy leaves the system through radiation. We finally get then 

 by the aid of the relation : 



— c curl ^ = ^— , 

 Ot 



^■=-,r(-?)* 



dt 

 If the variation of 55 in the time dt is d^, we get: 



(fW^=:- f{^,(m).dt (5) 



The total work performed by the system now amounts to the 

 sum of (4) and (5), 



1) Here Lorentz's system of unities is used. 



