333 



when 1 is the current measured by the aid of the galvanometei 

 G. If we divide both parts by yy — Tf. "e get finally: 



or expressed in words: the total current flowing through Ihe linear 

 part B is obtained by division of the part .1 into those circuits which 

 are the consequence of the presence of a constant electromotive force 

 in the linear part B, by integration of the electric force £ along 

 every circuit, by division every time of these line integrals by the 

 resistance of the circuit, and by taking finally the sum of all these 

 quotients. 



If we now call an element of a circuit in case (2) brietly ds, we 

 can, with the omission of the indices, also write: 



-41 



(£ ils. 



Hence we may assign an imaginary current to every circuit 



p 



p 



i . «' = I l?s ds. 



from which follows; 



On the other hand 



p 

 holds according to the law of Oim for the linear part, when W„ 

 represents the resistance of this. 



By adding the two last relations we get : 



iw ^ 1 W„= i<is ds, 



in which the integration is extended all along the circuit. If we put: 



I (JTs dn z= E, 



we get : 



ƒ 



E 1 W„ 

 i = ', (13) 



w w 



and further by summation over all the circuits and introduction of: 



