72O INDUSTRIAL APPLICATIONS. 



The field of the inducing current is proportional to I'L', or 



to V , ; that is to say, to its mean density , and the field pro- 



/I'\ 

 duced is a function < ( of this density. As the electromotive 



force is proportional to the field, to the velocity, and to the length 



V 



L or of the induced wire, we may write 



S'/ K \ K' 



The quantities K and K' are constants if the thickness of the 

 insulator is proportional to the diameter of the wire ; the factor C 

 depends on the volumes V and V and on the quality of the iron, 

 especially as regards the inductor. 



The useful work is 



and the efficiency 



< 



u= i 



El 

 When the inductor receives the whole of the current, we have 



u=i- 



and this efficiency is a maximum for the current, which makes 

 the fraction 



C^IIH 



a maximum. 



If the electromotive force were simply proportional to the 

 current of the inductors, it would be sufficient to make the 



ratio - 7-7 = ~ a maximum, which is the case when the 



'b 



two resistances a and b are equal to each other. 



