ELECTROMOTORS. 539 



Faraday's disc, for instance), the electromotive force is simply 

 proportional to the number n of turns, or of oscillations of the 

 machine in unit time, and may be represented by E r When the 

 velocity is constant, such a machine acts exactly like an ordinary 

 battery. It can always produce a current in a metallic circuit, 

 since the condition E>/R always holds when the current is very 

 feeble. 



2nd. If the machine is composed of fixed wires and of movable 

 wires, or of two systems of electromagnets (provided that we remain 

 within the limits in which the magnetisation is proportional to the 

 magnetising force), the electromotive force is proportional to the 

 strength of the current, and may be represented by nAI. A 

 machine of this kind can only produce and keep up a current 

 when the velocity is so great that #A>R. For any value of n 



-Tt 



greater than , the strength of the current increases until the 

 A 



resistance of the circuit, owing to the heat disengaged, has reached 

 the value nA. 



Suppose that the current has to overcome an electromotive 

 force E' external to itself. 



The value of the efficiency of the apparatus, as in the case of 

 the battery, is , 



and the work utilised in unit time is 



E'(E-E') 

 R 



In the former case the conditions of efficiency, and of maximum 

 work, are the same as for a battery. 



In the second case, in which E = AI, we have 



The efficiency is constant, and the work utilised is proportional to 

 the square of the current. 



If the external work is nothing more than that of setting in 

 motion a second machine identical with the first, the electromotive 

 forces E and E' are proportional to the number of turns n and n' 

 of the two machines ; on the other hand, these electromotive forces 



