258 THE DIRECT-CURRENT MOTOR CH. XI 



A the ratio of 4-78 to 3-18. The expenditure of energy 

 will then be the same as for the motors with induction 

 curve A. 



The economy of working may be expressed in 

 terms of the energy required to move the given weight 

 through the given distance. This may be stated in terms 

 of watt-hours per ton mile. Thus in the previous 

 example, the trains can be worked at the required speed 

 with an expenditure of 60-5 watt -hours per ton mile ; the 

 distance, of course, includes that in which the brakes are 

 on. The actual energy expenditure is 85'5 watt-hours 

 per ton mile. 



The results of our investigation may be summed up as 

 follows : There are three forms of expenditure of energy 

 involved in carrying a train of given weight through a 

 given distance in a given time. (1) The work done in 

 overcoming train resistance. This depends on the 

 distance, and can only be reduced by increasing the 

 mechanical efficiency of the motors. (2) The work done 

 in producing kinetic energy. This increases as the 

 square of the final speed. Equation 103 gives us the 

 least possible final speed for the given conditions, and 

 thus the least possible expenditure of energy in accelerat- 

 ing. (3) The energy expended in heat. Equation 111 



shows that this increases as the square of =-^. Equation 



Mv 



103 gives us the least possible value of ^^, if M is to be 



Mv 



constant. If, however, series winding is used, the heat 

 loss may be reduced to any desired extent by increasing 

 M , but at the expense of an increase in the weight of the 

 motor. 



