329 



_ 1 <L1/, __ 1 oil/ 



In the same way for an infuiitesinial eliange of 4 the integral 



current in the first conductor will amount to 



_ 1 ^M, 



c . i«j di. 



If (U^ = (li^, it follows from this by the aid of (2) 



«ijtfej :z= iv,de.^ (3') 



de. de„ 



If by ^-- resp. r— we denote the quotient ot tlie integral current 



in tiie first resp. second conductor and the change of current in 

 the second resp. first conductor, we may also write: 



de, d,', 

 '"' .V" =^ "'' A^ ^^^ 



In case the permeability is independent of the intensity of the 

 field, so that S in general is a linear vector function of .p, both 

 .ip and 5B are linear functions of i, and /,, hence M, and M, too. 

 Then we may write: 



From (2) then follows the known thesis: 



A, = ^.. (5) 



i.e. with equal currents in the two circuits tiie first sends as many 

 induction lines through the second as the second through the first. 

 For this case the magnetic field energy becomes according to (J): 



r=^A,',^ + -A,v, + ^^.'7 .... ((5) 



2c c 2c 



If the current in the first circuit increases by (//j, then the integral 

 current in the second amounts to: 



c . w, c . w„ 



On increase of the current in the second conductor by <//, the 

 integral current: 



de — — hii^ii 



C . ?(.'i 



flows through the first. 



Both expressions can be integrated. If e, resp. <?, represent the 

 integral currents, which pass through the first resp. second circuit 



