150 TIIK DIKECT-crKKENT MOTOR c||. VII 



and 1 = o, we see that K=n l n f . Hence Equation 67 

 ran be written thus : 



.(68). 



If we write a for ' - / -' and T for - ~ this becomes 

 n f KM 



w =wXlae T ) .............. ....(69). 



If w, is nothing so that the motor starts from rest, a = 1 , 

 and we get 



(70). 



This equation tells us that if we switch on a motor of 

 constant resistance R and induction factor M, the speed n 

 any time t seconds after connection is less than the final 

 speed n f by a quantity which is itself a fraction of that 

 final speed, the value of the fraction depending on the time 

 and on a certain constant r. 



The act of switching on the motor really amounts to 

 changing the tension on the motor terminals from nothing 

 to E. If the tension on the motor is E } to begin with, it 

 will already be running at a speed which we have called 

 n r Hence if the tension of the line be changed so as to 

 make the motor speed up towards a final speed n f , the 

 speed at any time t seconds after the moment of making 

 the change will be given by the law expressed by 

 Equation 69. 



This equation will hold equally true if the tension of 

 the line instead of being increased is diminished ; in that 

 case a is negative, and the speed at any moment is greater 



