INDUCTION ELECTROMOTORS. 699 



As the useful work is a maximum, and the efficiency equal to 

 0-50, when 2l = I , the corresponding velocity of the motor is 



If the machine is left to itself, assuming that all sources of 

 friction are suppressed, the velocity increases until the current is 

 zero ; the electromotive force of the machine is then equal to 

 that of the source, and the efficiency equal to unity. 



The maximum number of turns per second is given by the 

 condition N<(0) = E , which corresponds to a finite or infinite 

 velocity according to the form of the function </>(!). 



1255. When the machine is used as electromotor the current 

 can only be kept up provided the energy expended El is higher 

 than, or at lea^t equal to, the energy which the heating of the 

 circuit consumes, that is if we have 



<(!) >IR. 



In order that the machine shall charge itself by being put in 

 motion, we must suppose the circuit traversed by a very small 

 current i\ we have 



<(/') >/R. 



If the external work is reduced to the "heat disengaged in the 

 circuit, equilibrium holds for a current I defined by the equation 



which generally gives a finite value for I . As the intensity of 

 the current diminishes as the resistance increases for a given 



velocity, we see that the ratio - increases generally with the in- 



< H 1 ) 

 tensity. 



1256. Just as with batteries, the available work U of an elec- 

 tromotor is only the excess of the energy expended over that 



