542 A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 



represent the work done in unit of time arising from the variations of L, M, 

 and N, or, what is the same thing, alterations in the form and position of the 

 conducting circuits A and JB. 



Now if work is done when a body is moved, it must arise from ordinary 

 mechanical force acting on the body while it is moved. Hence this part of 

 the expression shews that there is a mechanical force urging every part of the 

 conductors themselves in that direction in which L, M, and N will be most 

 increased. 



The existence of the electromagnetic force between conductors carrying 

 currents is therefore a direct consequence of the joint and independent action 

 of each current on the electromagnetic field. If A and B are allowed to approach 

 a distance ds, so as to increase M from M to M' while the currents are x 

 and y, then the work done will be 



(M'-M)xy, 



and the force in the direction of ds will be 



<"> 



and this will be an attraction if x and y are of the same sign, and if M is 

 increased as A and B approach. 



It appears, therefore, that if we admit that the unresisted part of electro- 

 motive force goes on as long as it acts, generating a self-persistent state of 

 the current, which we may call (from mechanical analogy) its electromagnetic 

 momentum, and that this momentum depends on circumstances external to the 

 conductor, then both induction of currents and electromagnetic attractions may 

 be proved by mechanical reasoning. 



What I have called electromagnetic momentum is the same quantity which 

 is called by Faraday * the electrotonic state of the circuit, every change of which 

 involves the action of an electromotive force, just as change of momentum 

 involves the action of mechanical force. 



If, therefore, the phenomena described by Faraday in the Ninth Series of 

 his Experimental Rescarclics were the only known facts about electric currents, 

 the laws of Ampere relating to the attraction of conductors carrying currents, 



* Experimental Researches, Series i. 60, <fec. 



