152 THE DIRECT-CI I;I;K\T MOTOR en. vn 



when / = o, is the final speed divided by the time factor. 

 If the initial speed is not xero we have from Equation 69 



''''= a V' OT ^ZV* ...(72). 



dt r T 



Thus when anything occurs to change the speed from 

 ?(, to %, the initial rate of change of speed is ' "' . This 



T 



measures the sensitiveness of the motor to changes of load, 

 and will guide us when the specification precludes more 

 than a definite change of speed for certain brief and sudden 

 changes in the running conditions. 



In the cases considered hitherto in which the speed is 

 caused to vary, the change has been made suddenly. If 

 part of the resistance in the circuit be in the form of a 

 rheostat, R may be reduced gradually as the motor speeds 

 up, so that the current remains constant. This may be 

 done by hand or automatically. The induction factor being 

 constant, the acceleration is also constant. If the motor 



starts from rest, the current at the moment of starting is 

 -pi 



given by c, = , and if r, f is the frictional current we get 

 R 



at once the acceleration from Equation 63. The current 

 will remain constant until the rheostat is all out; the 



speed at which this will occur is given by n= 



where c l is the starting current and R the resistance of the 

 motor only. The motor will now speed up in accordance 

 with the law of Equation 70. 



The following graphical construction will enable 

 us to obtain the form of the acceleration curve. 



In Fig. 36 take oa equal to the number of seconds in 



