454 Intelligence and Miscellaneous Articles. 



Such a generalization can be justified in each particular case when 

 it is admitted that the effect produced by a change in the magnets 

 and currents is equivalent to that which would be obtained by 

 bringing from an infinite distance a magnet or current equal to the 

 given variation. The consideration of the streams of force only 

 will appear especially legitimate if it be conceived that electric and 

 magnetic actions are not really exerted at a distance, but are due 

 to a modification of the intervening medium, characterized at every 

 point by the direction and magnitude of the force. 



Let us first consider the effect of a current upon itself. The 

 stream of force which traverses the circuit, supposed invariable, is 

 proportional to the intensity of the current, and can be represented 

 by TJI, the factor U designating the stream of force corresponding 

 to the unit of current. If the variation of the current be dl, the 

 variation of the stream of force is JJdl, and the energy derived 

 from the pile 



mdi^df^). 



As long as the current has not become constant a part of the 



TJI 2 



energy of the pile is therefore employed to augment the term -~-, 



called the 'potential energy of the current. Suppose that there is in 

 the vicinity a second current, of intensity I', in a circuit of con- 

 stant form. The stream of force from the second current which 

 traverses the circuit of the first is proportional to the intensity ; it 

 may be represented by VI'. The factor V denotes the stream of 

 force that emanates from either of the two circuits and traverses 

 the other when the two currents have the same intensity equal to 

 unity. The product II'V is called the relative potential energy of 

 the two currents. 



When the product I'V, in consequence of a change of intensity 

 or a displacement, varies by d(TY), the energy derived from the 

 pile of the first current is Id(L'Y). Therefore, if the two modifica- 

 tions are simultaneous and are produced during the time dt, we 

 have for the first circuit 



Mdt=mdt+d(^^ + ld(l'Y); (4) 



and, in like manner, for the second, 



m'dt=I'Wdt+d(j?^+Td(IV) (5) 



By addition we get 



(Ei+ET)*=(PR+r 2 EV«+d(^ + 55! +irv)+nw. (6) 



This equation expresses that the energy furnished by the two 

 piles during the time dt is employed in heating the conductors, in- 

 creasing the potential energy of each of the currents as well as their 

 relative potential energy? and, lastly, in furnishing the electro- 

 dynamic work corresponding to the relative displacement. If the 



