154 THE DIRECT-CURRENT MOTOR CH. VII 



I 



The speed at any instant is given by n = n.j(l ae T ). 

 If the speed is constant for a short interval dt seconds, the 

 number of revolutions made in this time is ndt, hence 1 1n- 

 total revolutions made between o and f seconds is given 





N=n, f (l ae T )dt ............... (73). 



Jo 



Integrating this between the given limits, we have 



__ 



N=n f \t-ar(l -e" T )| ............... (74). 



If t is large compared with T we may neglect the expres- 

 < 



sion are T , Hence 



N=n f - ( t ar] ..................... (75). 



If D is the total distance travelled in feet, as in the case 

 of a railway motor, and sy the final speed in feet per second, 

 we can write 



D=S f {taT\....: ............. ..(76). 



If 6 is the circular measure of the angle turned through 

 in t seconds, and if o> is the final angular velocity, we 



have 



= o>{t-aT\ ..................... (77). 



This case is illustrated by the motion of a crane-stage 



or turret. Care must be taken to see that the term 

 _t^ 



are T can be safely neglected. In Equation 7571/is found 

 from n f = ~~-^- -, where !'4>lc f M is the torque in inch- 



pounds required to overcome the frictional and other re- 

 sistances to motion which are supposed to remain constant. 



