331 



2, with this difference, iiowever, that the current in the first con- 

 ductor is ii -\- di. 



Now according to (8') the difference of [de.,)i^j^ and {de^\^i^j^di, 

 mnhiplied by the resistance of tiie first conductor must be equal to 

 the difference of (f/e,),, ,,-, and (c/cj),-, +(/,•,,„, multiplied by tlie resistance 

 of the second conductor. 



If the relation between $ and .p is linear, then on change of « 

 the relation (7) will hold, both before and after the change, so that 

 we have qtiife generally 



d Ö 



^ ('".«.) = g^ 0", O (ï^) 



If the resistances are not dependent on « we have 



i.e. when in the first circuit there runs a current t, the second being 

 without current, and the change dn is accompanied with an integral 

 current de^ in the second conductor, then flie product of de^ with 

 the resistance of the second circuit will be equal to the product of 

 the resistance of the first circuit with the integral current (/c,, which 

 flows through the first circuit in consequence of the change da, 

 when the current i now exists in the second conductor, the first 

 being currentless. 



3. Up to now we only considered linear conductors. In order 

 to be able to apply the above derived relations to three-dimensional 

 conductors, we shall first prove a general thesis. 



We imagine an arbitrary conductor in which certain electrical 

 forces are active. Let the conductor be an anisotropic body, of 

 such a symmetry, however, that there are three main directions 

 which are vertical with respect to each other, in which the current 

 coincides with the electrical force. In this case: 



3:, = <Tn ^1- + <T„ C",/ + O,, ^, \ 



3y = <T„ €•,: + «T„ ^f-y + ff„ IE- J (10) 



in which 



Now let a system of electrical forces S(i) give rise to a current 

 j>'), the system ^>-' giving rise to a current j'"^*- Then the follow- 

 ing equation will hold for every volume element, as is easy to 

 see by the aid of (10) : 



