CH. IX CONTROL 193 



ing according to Equation 69. This step will commence 

 at 78 seconds from the start. The form of the curves will 

 be the same as those in Case I. The car will be started 

 in 87 seconds, and the energy taken from the line in that 

 time is 605 x 10 4 foot-pounds. These results are shown 

 in Figs. 46 and 47. 



This method is better than either of the former 

 methods. The gain is made on the first step, where the 

 acceleration is high. This step, however, lasts only for 15 

 seconds, as the motors speed up so quickly that the rheostat 

 is soon all out. 



If at the end of the first step we allow the motors to 

 speed up in series they will attain a final speed of 149 

 r.p.m., and this speed will be reached in about 25 seconds, 

 or 40 seconds from the moment of starting. We may 

 connect the motors in parallel at any moment while they are 

 speeding up in series. Thus in Fig. 48 they are shown to 

 have been connected in parallel just at the moment when 

 full speed in series has been reached. They now speed up 

 as in Fig. 46, full speed is reached in 95 seconds, with an 

 expenditure of energy of 497 x 10 4 foot-pounds. It thus 

 appears that there is a saving of energy in allowing the 

 motors to attain full speed in series, but there is a loss of 

 time amounting to 15 seconds. The energy saved is 

 not increased if the throwing over into parallel is delayed 

 for any number of seconds, but the loss of time is pro- 

 portionately increased. 



The motors may be connected in parallel at the 

 moment when the acceleration on Step I. is the same as 

 that on Step II. ; this point can be found in Fig. 48 by 

 drawing a tangent to the rounded portion of Step I., 

 parallel to the acceleration curve on Step II. There would 







