494 INDUCTION. 



This equation expresses that during the time *#, the energy due 

 to the chemical actions is equal to the thermal energy expended in 

 the circuit on Joule's law. 



Suppose now that instead of being stationary, the magnetic 

 system moves in accordance with electromagnetic actions. The 

 external work resulting from this displacement, can only be borrowed 

 from the sole source of energy in the system (that is, the chemical 

 action), and the preceding equation must be in default. On the 

 other hand, there is no reason for supposing that the laws of Faraday 

 and Joule cease to hold ; in other words, the weights of the bodies 

 combined in the different couples must still be proportional to the 

 strength of the current, and the thermal energy disengaged in the 

 circuit is equal to the product of the resistance into the square of 

 the strength. Hence, the strength of the current could not retain 

 its original value. 



514. Suppose now that the magnet is displaced in such a way 

 that the new value of the strength remains constant. So long as 

 this condition is fulfilled, the excess of chemical work over the 

 thermal energy expended in the circuit in the time dt, serves to 

 produce the external work dT corresponding to the electromagnetic 

 forces. Hence, if I is the strength of the current, 



(3) EL#=I 2 R<// + arr. 



If Q is the flow of force due to the magnetic system which 

 traverses the circuit, entering by its negative face, we have 



Replacing dT by this value in the equation (3), and dividing 

 by \dt, we get 



(4) E = IR + f- 



In order that the strength of the current shall be constant, the 



dQ 

 displacement must take place so that the differential is itself 



constant. 



Putting I -! = /', equations (i) and (4) give 



(5) 



