ƒ 



((f . :o . ds . dt. 



If we introduce 



3 = curl .P), 

 and if we make use of the known thesis of tlio vector calculus liiat 

 the following equation holds generally : 



dw [31 SB] = SS curl 9J -51 curl i5 

 then we get for the above expression : 



— c { {curl If-, .p) dS.dt + c ( dir [(£, .fp] dS . dt. 



Introducing further ; 



/cr. 1 '^■^ 



c d« 

 and making use of Gauss's theorem, we get: 



( [ — , .fp \lS .dt~\--cl ['$, .P)]. da . dt. 



The second term vanishes, as on the surfaces of the current con- 

 ductors the normal component of 'i^', Sp'j is continuous, and the 

 integral amounts to zero over the plane in infinity. Accordingly the 

 first term only remains. This will have to be equal to the increase of 

 the energy of the magnetic tield ami the work of the ponderomotive 

 forces. Hence we get : 



dT 4- <U — / [ - , .ip j dS . dt. 



Per volume and time nnity : 



dT + (fA = i — , .? I dt. 



For the energy of the magnetic field per volume unity the expression : 



7' = ƒ (.0. d^)- 



holds generally. 



With tiie change da we shall get: 



i^ + 'l-'Q ^ 



dr = I (.p, d'b') — . I (.ip, <i'S), 







in which do represents the change of tiie final value of -C», and 

 'iV the value of '1^ corresponding to .(> in the changed state. Now 

 we get : 



