THE INDUCTION MOTOR. 



345 



Z r = number of lines forming the resultant 



field. 



The values of the fields due to the several coils may be 

 written in the form Z sin 6, since they vary harmonically 

 in the same manner as the current, and attain a maximum 

 value Z. 



Hence, at the instant under consideration, they will 

 have values as follows, where 6 can be chosen to have any 

 value from to 360. 



z l Z sin 9 in the direction Z^ in Fig. 173. 

 z 2 = Z sin (9 120) in a direction Z 2 . 

 z 3 Z sin (9 + 120) in a direction Z 3 . 



FKI. 173. THREE MAGNETIC FLUXES DUE TO S-PHASE CURRENT. 



Resolve each of these fields in two directions respec- 

 tively parallel and perpendicular to the direction of the 

 field of coil I. 



From Fig. 173 it is clear that the components are 



Horizontal. Vertical. 



for 2 1} . . Z l and zero 

 z,, . . OP PZ, 

 z 3 , . . OP PZ 3 



Let us first evaluate the horizontal components : 

 for z,, Z l = Z sin 6. 



z 2 , OP = OZ, (- cos 60) 



= Z sin (B - 120) ( -cos 60) = - i Z 



sin (6 - 120). 

 ,, OP = OZ 3 (- cos 60) 



= Z sin (8 + 120) (- J) = - 4 Z 



sin(0 + 120). 



