OH. X TIME CURVES 217 



speed is not given, but may be made anything we 

 please. 



Suppose that the distance D in feet that has to be 

 covered and the accelerating current per motor are given. 

 The problem then before us is to determine the values of 

 M, v, and d, so that the distance may be covered in the 

 shortest time. 



We may divide the whole period of motion into two 

 parts, that of acceleration and that of uniform speed. We 

 shall assume for the present that the parallel method of 

 control is used, and that the motor or motors speed up 

 with uniform acceleration until full speed is reached. 



In Fig. 55 let Jib represent the time occupied in ac- 

 celerating, ba the final speed, and bg the time occupied in 

 completing the given distance ; the area hafg will then 

 represent the whole distance travelled. 



We know from Equation 93 that the acceleration 



varies inversely as . We may express this by the 

 equation 



K (98)> 



where 7r, is a constant and 8= ---- . 



Mv 



The na. peed is given by the equation 



s,= 2Q2 x 10- 3 x d x -^~ C/E f.p.s. ,..(99), 

 v M 



where E is the tension of the line and c f R the internal 

 drop at full speed. If c f R is specified, the final speed 

 will be independent of variations of c /5 which will, as we 

 have seen, decrease slightly when d is decreased. In other 

 words, if we are at liberty to fix the drop by adjusting the 



