334 



w W, 



if H', is the resistance of tlie part A, 



U' E \\\ E 



i =r ' — :s ^ = —^ ^' - , 



W^ -f W^ w W w 



if W is the resistance of tiie whole system. 



11 now by in we represent a resistance which is ^ limes as 



]\\ 



great as that of the circuit between Q and P, we get : 



E 



1=2- (14) 



w 



The resistance to introduced here is practically the resistance of 

 a circuit closed in itself, to which the circuits of case (2) discussed 

 above can be supplemented by contin nation into the linear part of 

 the conductor. The summation is extended here over all the circuits 

 of the case indicated above by (2). 



5. We shall now consider the case of two current conductors of 

 the kind considered just now, so each consisting of a three-dimensional 

 and a linear part. When currents pass throngh these conductors, 

 either in one of them or in both, and we want to examine the 

 induction action which is the conseqnence of a change, either of 

 the current in these condnetors or of the properties of the surrounding 

 tield, then we may, therefore, according to what was derived just 

 now, divide these conductors into the circuits which are the conse- 

 quence of the presence of a constant electromotive force in the 

 linear part of these conductors, examine the induction action in each 

 of these circuits and take the sum of these. 



Let the resistances of the conductors bo IF, and IF,, the currents, 

 measured in the linear part, /j and 1.,. We shall examine the 

 influence of a change of these currents. We can now divide the 

 lirst conductor into in circuits, each with a current i'l, the second 

 into // circuits, each with a current i^, so that we shall have: 



ƒ J = ;«/, ƒ 2 = ni.,. 



The resistance of each circuit of the first conductor amounts to 

 m.W^, of the second conductor to u.W^, as the electromotive 

 force must be taken the same for all of them on division into circuits. 

 If we increase the current in every circuit of the second conductor 

 by tU^, then the total induction flux through the p"' circuit of the 

 first conductor will be increased by : 



