216 TIIK l)li;K<T-<Vi;i;KNT MOTOH CJI. X 



the weight of a train without reducing the acceleration, 

 when the resistance to motion has been diminished in the 

 ratio of /* to 1. It appears that for any given reduction 

 of the frictional resistances, the possible increase in the 

 weight diminishes with the acceleration. 



Example 50. The trains on the Liverpool Over- 

 head Railway were made up of two cars, each weighing 

 19 tons, giving 38 tons as the weight of the train. Each 

 train was driven by two motors taking 1GO amperes at 

 the start when in parallel, or 80 amperes per motor. The 

 resistance to motion appeared to be 410 pounds per motor, 

 from the record of the current taken by the motors when 

 running at a uniform speed. The question arose as to 

 whether an additional car could be put on each train if the 

 resistance to motion were reduced by the use of roller bear- 

 ings, the acceleration and the maximum current from the 

 line remaining unaltered. Tests were made showing that a 

 train fitted with roller bearings offered only one-fifth of the 

 resistance to motion at the moment of starting, of that of a 

 train with ordinary bearings. This gave yu,=5. Experi- 

 ment showed that the tractive effort per motor for 80 amperes 

 was 1,100 pounds. Using these values in Equation 97, we 

 find that the weight of the train may be increased to 56 tons 

 with unaltered acceleration. At the moment of starting 

 the motors are connected in series, and then switched over 

 into parallel ; this affects the result slightly in favour of 

 the roller bearings, the time of covering the first 400 yards 

 being, by calculation, 57 seconds with ordinary, and ~>'2 

 seconds with roller bearings. If no other alteration is 

 made, the final speed will be increased by the introduction 

 of the new bearings from 26 to 48 miles an hour. 



We have now to consider the case where the final 



