now consider the case of an infinitely small change of the function 

 which indicates the relation between 33 and C*, in some parts of the 

 held, as result of an infinitely small change of a general coordinate o. 

 In general (15) will be valid both before and after the change 

 of a, so that analogous to (8) we get from tfiis: 



If the resistances remain unchanged we get analogous to (8'): 

 d de, d de„ 



which relation is also open to analogous interpretation. 



In the special case of a linear relation between S3 and 'p we 

 shall get in the same way analogous to (9) : 



^(W>,) = ^("^«.)' (18) 



o« Oct 



which becomes for invariable resistances: 



^'^^=^^^^ ^^^ > 



oa o« 



Here t'j and e^ have the same signification as above in (16). 



6. We now inquire into the work of the ponderomotive forces, 

 being accompanied with a modification in the magnetic field, which 

 is the consequence of the infinitely small change da. We assume 

 that at the change da the external electromotive forces remain un- 

 changed, and likewise the coefficients o, which in the most general 

 case determine the relation between the electrical force and the 

 current. 



If I»; represents the electric force, and i^ the external electromotive 

 force, then the quantity of energy 



K® + €0 • 3! • dS . dt. 



will be consumed as Joule heat in the volume element dS in the 

 time dt. 



On the other hand the energy supplied by the current generators 

 in the time dt is : 



(^^.^:s).dS.dt. 

 The difference of these two expressions: 

 — {'i.^).dS.dt 

 passes into other modes of energy. Integrated with respect to all 

 the conductors this becomes : 



