CH. VII ACCELERATION 155 



In Equation 76 the speed S can be shown to be 



262 - of the revolutions per second of the motor, where 



v . 



d is the diameter of the car wheel. 



Equation 76 may be conveniently written 



t= D -+ar (78). 



8 f 



From these equations we can see the influence of the 

 time factor, Equation 76 showing the reduction in the 

 distance travelled when the time is given, and Equation 

 78 the increase in the time when the distance is given. 

 A reference to Fig. 38 will make this clearer. The area 

 between the acceleration curve and the time base measured 

 from the origin to any given point oa, represents the 

 distance travelled in that time. If the time factor were 

 nothing the distance would be given by n f t, that is, by the 

 area oadf. The area obdf represents the amount that has 

 to be deducted to give the true distance travelled in a given 



time t, and is equal to nr, where n is the speed at i seconds. 



_t 



If the term re T is neglected, the amount deducted is 

 n f r. 



We now have to find the value of the constant 



1\ in the expression for the time factor r = , From Eq ua- 



kM 



tion 63 we see that k is a constant which multiplied 

 into the accelerating current gives the acceleration in 

 r.p.s. per second. If c a is the accelerating current we 

 can write : 



-* < 80 >- 



