160 THE DIRECT-CURRENT MOTOR CH. VII 



limiting the transmitted torque to that at which slipping 

 takes place. 



In establishing Equations 82 to 87 we assumed that 

 the whole mass to be moved was situated so that its centre 

 of gravity rotated in a circle of d inches diameter. In the 

 case of a lift it is easy to see that the weight of the car is 

 acting at a point on the rim of the rope drum, so that the 

 mass that has to be moved may be considered as being 

 virtually situated at a point d inches from the centre of the 

 drum. Also, the mass of the drum or other rotating part 

 may without difficulty be conceived as acting at the rim of 

 the drum, the mass thus acting being, of course, such as 

 will give the same moment of inertia as the drum itself. 



When, however, we come to the case of a motor driving 

 a railway car it is not so obvious that the mass that has to 

 be accelerated is now that of the car, and that the weight 

 W in Equation 81, for instance, is the weight of the car. 

 A reference to Figs. 13 and 14 may make this clearer. 

 We have already shown that the dynamical conditions of 

 the two cases here illustrated are identical, and that while 

 in Fig. 13 the force T acts vertically through the rope, 

 in Fig. 14 the same force acts horizontally on the car 

 axle. Hence in the first case the mass that has to be 

 accelerated is that hanging at the end of the rope, while 

 in the second it is that of the car itself. 



We shall now give a graphic solution of the 

 acceleration problem, by which we shall be able to 

 take account of any variations that may exist in the value 

 of the induction factor. 



We shall take as an example the motors used on the 

 City and South London Railway. There are two motors 

 on each locomotive, the armatures being placed directly on 



