552 PROPERTIES OF THE ELECTROMAGNETIC FIELD. 



The potential energy of currents may therefore be expressed by 

 an integral (5) which contains the currents themselves, or by an 

 integral in respect of all parts of the space in which are magnetic 

 forces. In the former case, the reciprocal action of the currents is 

 considered as being directly exerted at a distance ; in the second 

 case, this action results from the elasticity of the intervening medium. 

 If we adopt this point of view, we see that the potential energy of the 

 medium at each point, for unit volume, is expressed by 



571. RELATIVE DISPLACEMENT OF CIRCUITS. The formulae (3) 

 correspond to the case in which, the circuit being fixed, induction is 

 due to the mean variation in the field ; the quantities F, G, and H 

 are at each point mere functions of the time. But if, while the field 

 is variable, we displace or alter the configuration of the circuit, 

 the co-ordinates x, y, z should themselves be considered as functions 

 of the time. Equation (i) should then be written 



The electromotive force utilised in the time dt is - </Q, so that 

 the electromotive force of induction e at a given moment is expressed 

 by 



*=-^=- ^T-+^^+T-^- 77* 



, 



" ds ~b ^s ^s J 



+ 



s s s 



