332 



IntegTated witli i esperf to aii arbili'uiy volume of tlie concliictor 

 tliis yields: 



/'m-(o . ^c-')) . ds =z [(^(.-i) . yx)) . ds (11) 



Tills we apply to a (.'ondiiotoi' consistiiifj;- of two parts, one of 

 wliioli, A, is a tliree-dimeiisional body, whereas tlie other, B, which 

 is to be considered as linear, is in contact with the three-dimensional 

 |)art in its initial point /-* and its tinal point Q. Let us suppose 

 in the linear part a galvanometer (r, which we use to measure the 

 cnrrent / in the linear part. The case that arbitrary electrical forces 

 are active in this system, e.g. originating from indnction actions 

 which can vary tVoni moment to moment, we shall denote by (1). 

 In case (2) on the other hand we imagine a constant electromotive 

 force to act in the linear part. Then there will exist a potential 

 difference tfQ — ffp between the points Q and P. 



In both cases we divide the three-dimensional part A into the 

 circnits that comjtose the cnrrent. Let us call the current in each 

 circuit i and let us denote an element of the circuit by (h, then 

 the relation (11) gives: 



2 /g f '^ . iCi) dsCi) = ^ [a ^f,\ . i (1) . rfsc ). 



In this the integration takes place along the circuits, the summa- 

 tion extending over all the circuits. In the lefthand member we 



1 

 may write /'-')=:-(</ y — (f p), when //'"--' denotes the resistance of 



a circuit in case (2). For every circuit this current is multiplied by 

 the linear integral of the electrical force in case (1) along the circuit. 

 In the righthand member we shall have to distingnish between 

 circuits which are closed in themselves inside the part A, and 

 circuits which start in 0. and terminate in P. For the tirst kind: 



' (2) 



seeing that 



^j; 0-iJ = — V '/■ 

 For the second kind : 



J 



ƒ 



(2) 



further holding for this: 



