160 TREATISE ON ALTERNATING CURRENTS. 



an initial velocity given to it, a torque is produced, and the rotor 

 will continue to rotate with a speed which increases till a speed 

 almost corresponding to synchronism with the stator current is 

 attained. 



To see this more clearly, we may suppose the alternating 

 magnetic field replaced by two rotary fields of equal strength, and 

 revolving with the same angular velocity in opposite directions. 

 We leave the reader to prove that this is a legitimate supposition. 



If the rotor is started by some means in either direction, the 

 induced rotor currents may be regarded as the algebraic sum of the 

 currents due to cutting these two rotary fields. 



Let the slips relative to the two rotary fields be KI and K 2 

 respectively, and suppose that the rotor is started in the direction 

 of K 2 diminishing. Then KI is less than, and K 2 greater than, unity, 

 and KI -f- K2 = 2. 



Let the corresponding torques be T\ and T 2 , which act in 

 opposite directions, so that the resultant torque is T\ T% ; then 

 by (14)- 



and 



therefore the resultant torque is given by 



rr T -WeS \ KI K 2 1 



"^\r?"+~nW " rf -f K3 VJ 



JV 2 2 eV 2 (K 2 - K 2 )(KlK 2 S 2 2 - fa 2 ) , 9 ., 



By supposition, K 2 KI is positive; therefore T\ T 2 is 

 positive, if 



r 2 2 is positive 



Now, KiK 2 is never greater than unity ; therefore a monophase 

 induction motor cannot run at all unless the reactance is numeri- 

 cally greater than the resistance. So long, however, as KiK 2 s 2 2 r 2 2 

 remains positive, the resultant torque will remain in the same 

 direction, and the motor will continue to run. 



It appears, however, that a monophase induction motor cannot 



