330 



oil increase of' llie ciineiil in llie f^econd res[i. first circuit lo tiie same 

 amount /, the relation 



«i»'i =*'2"'s (^) 



exists l>et\veen tliese quantities. 



2. We shall now consider tiie case that the function wliich 

 represents the relation between '2i and -Ó is variable in some parts 

 of the field. This variability is meant in very general sense : we may 

 e. g. imagine it as a dependence of volume, pressure, temperature 

 etc. or as variations in consequence of elastic deformations, while also 

 motions of the particles of the medium may be understood by it. 

 We except, however, such changes which are attended with motions 

 of the current conductors or parts of them. Let the variability be 

 expressed by means of liie general coordinate «. Then the induction 

 flux through the circuits will in general depend on <t. With a varia- 

 tion of <( the relation (2) holds l)oth before and after the change, 

 so that we get: 



d bM, _ d dM^ 

 drt d?', d« dij 

 for which we may write, seeing that 



1 1 



— dM, z=. — n\de, — dM, = — u\de. 



öaV'^dTj^VaV'^dTj (') 



when we attach analogous signification to tlie partial differential 



quotients and ^- as above tor (3). It the resistances are not 



0/„ Of, 



dependent on «, we get: 



01, 0(( Of, Oa 



We may express this relation in the following words: Successively 

 we measure four quantities of electricity : i. the integral current 

 (r/f, );,,,-, in the first conductor, which is the result of the change fZtf, 

 whilst the currents i^ and /, run tiirough the two conductors; 

 2. tlie integral cuirent {de,);^j„, which flows in the second conductor 

 under the same circumstances; 3. the integral current ((/(?i)/,_,\j^rf/ in 

 the first conductor, which is the result of the same ciiange as under 

 J, wiiii this difference however, that the current in the second 

 conductor is /j-|-'//; 4. tiie integral current ((/Cj);^ -|- ,/,•,,„ in tiie second 

 conductor, which is the consequence of the same change as under 



