GENERAL LAW OF INDUCTION. 497 



518. GENERAL LAW OF INDUCTION. The preceding reasoning 

 would apply in the same way, and in almost identical terms, to the 

 other cases of induction. 



It is seen to be evident for electromagnetic induction that is to 

 say, that which is produced by the displacement of a system of 

 constant currents, substituted for the magnetic system for we 

 have demonstrated the complete equivalence of the magnetic fields 

 produced by currents and by magnets. 



In the case of currents induced by a variation in the strength of a 

 magnet, or of an adjacent current, the result may be considered as 

 equivalent to that which would be obtained by bringing a magnet or 

 a current, identical with the variation in question, from an infinite 

 distance to superpose it on the former. 



Experiment shows that extra-currents, produced by deformations 

 of the circuit itself, or by changes in the strength of the principal 

 current, are also connected, and in the same manner, with the corres- 

 ponding variations of the flow of magnetic force. 



It may therefore be considered as a general rule thajt any 

 variation in the flow of force in a circuit, whatever be its origin, 

 corresponds to a variation of potential energy, and gives rise to the 

 same electromotive force of induction as if it were produced by the 

 displacement of an external magnetic system. 



This conclusion appears necessary if, abandoning the idea of 

 actions at a distance, we regard the transmission of electrical and 

 magnetic forces as due to a modification' of the elastic properties 

 of the medium ; we can understand then that the only proximate 

 cause of currents induced in a conductor may be the state of the 

 medium in which is the conductor, whatever may be the origin of 

 the forces which are at work in this medium. We may, therefore, 

 formulate the general law of induction phenomena in the following 

 terms : 



The total electromotive force developed in a circuit at a given time is 

 equal to the differential \ in regard to time, of the flow of magnetic force 

 across it. 



Or again : The total quantity of electricity induced in a circuit, is 

 equal to the product of the inverse of its resistance by the total variation 

 of the flow of force across it. 



The flow of force across a circuit at a given time consists of the 

 flow Q, arising from external bodies, magnets or currents, and of the 

 flow produced by the current which traverses the circuit itself. Let 

 L be the value of this latter flow when the intensity of the current 

 is equal to unity ; it will be equal to LI for strength I, and if E are 



K K 



