THE INDUCTION MOTOR. 



145. The position of the semi-circle can now easily be determined, 

 either by the use of complex imaginary numbers, or graphically, as 

 I prefer. 



The ratio O D' : A' D' can be found at once. We have: 



O& 7 = -^ ATiy 



A' D' = X^ . v 2 , hence 



i 

 OD' ~^'~ v * 



A'D' -v^ v * v * 



146. This constant ratio we call the leakage factor of the trans- 

 former, and denote it by <?. 



I 



(4). 



In Heyland's notation we should have : 



= (i + ^i) (i + - 2 ) i'= T i + T 2 + r i TI 



147. To recapitulate : In a constant-current transformer whose sec- 

 ondary resistance is varied from naught to open-circuit, the terminal 

 voltage varies in such a manner that the vector of the field to which 

 it is proportional and with which it is in quadrature, has for its locus 

 the semi-circle, determined by O t as centre. The position of this 

 circle is perfectly defined if the primary resistance and the leakage 

 factor are known. 



THE CONSTANT-POTENTIAL TRANSFORMER. 



148. If, in Fig. 41, we wanted to know what current would flow 

 through the transformer at a certain difference in phase between O M 

 and O A, if O M were n-times as large as in the diagram, we should 



simply reason that, the counter e. m. f. being n-times as large, only 



times as much current could flow through the transformer. Hence, 

 if we kept O M constant, varying only its phase relative to O A, the 



78 



