A DYNAMICAL THEORY OF THE ELECTROMAGNETIC FIELD. 541 



Equation of Work and Energy. 



(31) To form the equation between work done and energy produced, 

 multiply (1) by x and (2) by y, and add 



-r (Mx + Ny) .......... (8). 



-r 



Here x is the work done in unit of time by the electromotive force acting 

 on the current x and maintaining it, and r}y is the work done by the elec- 

 tromotive force r). Hence the left-hand side of the equation represents the work 

 done by the electromotive forces in unit of time. 



Heat produced by the Current. 



(32) On the other side of the equation we have, first, 



Ry? + Sy* = H ................................. (9), 



which represents the work done in overcoming the resistance of the circuits in 

 unit of time. This is converted into heat. The remaining terms represent 

 work not converted into heat. They may be written 



Intrinsic Energy of the Currents. 



(33) If L, M, N are constant, the whole work of the electromotive forces 

 which is not spent against resistance will be devoted to the development of 

 the currents. The whole intrinsic energy of the currents is therefore 



$Lx i + Mxy + $Ny' = E ........................... (10). 



This energy exists in a form imperceptible to our senses, probably as actual 

 motion, the seat of this motion being not merely the conducting circuits, but 

 the space surrounding them. 



Mechanical Action between Conductors. 



(34) The remaining terms, 



dL . dM dN . , 



