470 PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
conductor. When M is positive, the induced current due to increase of the primary 
current is negative. 
Induction by Motion of Conductor. 
(30) Case 2nd. Let x remain constant, and let M change from M to M', then 
so that if M is increased, which it will he by the primary and secondary circuits 
approaching each other, there will be a negative induced current, the total quantity of 
electricity passed through B being Y. 
This is induction by the relative motion of the primary and secondary conductors. 
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 
e®+ w =B^+Sy>+*^(L i c+My)+y|(M*+%). (8) 
Here %x is the work done in unit of time by the electromotive force £ acting on the 
current x and maintaining it, and v\y is the work done by the electromotive force ri. 
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, 
R# 2 +S/=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 
i^(I^+2Mqr+N,f) + i 
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 
iLr 2 +M^+i% 2 =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. 
