48 THE DIRECT-CURRENT MO'lol; CH. Ill 



We shall in all cases take the positive sign, so as to 

 get the greatest possible value of M and the least possible 

 value of C. 



In Equation 15, n is the speed of the motor in 

 revolutions per second. If the shaft of the motor is 

 geared or belted to a second shaft, so that the speed 

 of the former is v times that of the latter, we can 

 write : 



.]/ = -lA/(l )r 



2vn ( v \ E' 1 I } 



where n is now the speed of the second shaft, which we 

 shall call the main shaft. We shall call v the velocity 

 ratio. 



We should notice here that the expression -v,- is un- 



MJ 



altered by the introduction of gearing, since it is immaterial 

 whether the work is being done directly by the motor or 

 through the medium of gearing. In practice some of the 

 work would be represented by overcoming the friction of 

 the gearing, some by the friction of the shaft of the motor ; 

 the larger part of the work, however, would be done on 

 the main shaft ; the term w includes all of these. 



Example 15.- Work has to be done at the rate of 

 7 kilowatts on a main shaft rotating at 1,200 r.p.in. ; the 

 shaft is to be turned by a motor geared to the main shaft 

 with a velocity ratio 1*3 ; the resistance of the motor is 

 0*06 ohm, and the tension of the line 125 volts; to find 

 the induction factor of the motor. We see at once that 

 M will be less than that in Example 14, in the ratio of 

 1-3 to 1, or M=4'67 ; the speed of the motor will be 

 1,560 r.p.m.; the current will be 58 amperes, the same as 

 in Example 14. 



