226 GENERAL DIAGRAMS FOR SYNCHRONOUS MOTORS 



coil is in turn the geometrical sum of the E.M.F.'s of its two sides, 

 which E.M.F.'s may or may not be in phase according to whether or 

 not the coil pitch is equal to the pole pitch. The fundamental 

 E.M.F.'s of the two sides of each coil will differ in phase by the 

 deficiency in coil pitch measured in electrical degrees, and the funda- 

 mental E.M.F.'s of the coil sides in two adjacent slots will differ in 

 phase by the electrical angular pitch of the slots. In each case the 

 phase difference between the mih harmonics is m times that between 

 the fundamentals. 



In calculating the tap E.M.F. the author introduces the " differ- 

 ential factor," the ratio of the resultant or geometrical sum to the 

 arithmetrical sum of the various E.M.F,'s. 



Let Nsp= slots per pole, and p' the number of belt spans per 

 electrical circumference (p' = 2 for diametral connection and 3 for 



TC 



three-phase delta or six-phase double delta); then =the phase 



J\ sp 



difference between the fundamental E.M.F.'s of two adjacent slots, 

 = the phase difference between the corresponding mih harmonics 



J\ sp 



and 7^ = slots per belt. The total phase rotation (or combined 



P 

 phase displacement) of the mih harmonic in all the slots of the belt 



will be 



WX 2./Vsp_2W7C 

 " ' 



sp 



and the resultant of the mih harmonics is proportional to 



P 



2 sin f-. By the same constant a single mih harmonic is proportional 

 to 2 sin - , and the arithmetical sum of the 7- mih harmonics is 



21\sp 



. 



p 2JM sp 



The differential factor for the mih harmonic of the belt E.M.F. ; 

 or the belt-differential factor for the wth harmonic is then 



wx 



p' sm T 7 " 



kdm = ^N~ P ~ ~^T> ...... (4) 



sin TT 



