OPERATION OF SYNCHRONOUS MOTORS, HUNTING 129 



Consequently, if p equals the resistance, and ^.the inductance of 

 the damping circuit, the induced current i is due to the superposition 

 of two currents of two different frequencies: * 



r 



The energy consumed is represented by the integral 



W= [ eidt, 

 Jo 



which contains products of terms having different frequencies. If the 

 integration is supposed to extend over a sufficiently long period, these 

 terms can be neglected in comparison with the others, which alone 

 increase indefinitely. In that case, the value of the mean power 

 expended per second can be written as follows: 



The first term is substantially constant, since T' remains near T. 

 On the contrary, the second term, which vanishes when T'= T, increases 

 rapidly with the difference of frequencies. It represents the correlative 

 increase of energy consumed, which produces the damping. 



Supposing the difference ^ to be very small, the inductance 



may be neglected, in comparison with the resistance, in the second 

 term. In the first term, on the contrary, the inductance is always very 

 large, in comparison with the resistance, and, consequently, the latter 



