Alternate Current Transfor^ner. 51 



m=j-l 



=1 



„_32Br_l_vi_A, 

 ^"^1- o- L 8 8 2y^ 



^l 2z>- "^4/j ^°^2A,+«(1+V2)-1 



j«=j— 1 



^ ( /;/(! w vi + XQ , / hmv, + Xi ^ '^-^ ^ 2X^ + w(l+Vi) + l -| 



+ ^i "2/>- +(" y )3^°g2A, + ;.(l+.0-lJ- 



7n = l 



where, in each of the above expressions, the values to be given to 

 n are all the even numbers from 2 to I'—l, and to m all the odd 

 numbers from 1 toy — 1 inclusive. 



It will be easily seen, by considering the case of a winding 

 with three sections, that by spreading out the free ends of the 

 sections as is done for cooling purposes the values of the coeffi- 

 cients x'l and x".^ will be slightly increased. 



49. If the i-esults in § 48 be written 



o- " ■i:7riJij3(S' 



' a- ' iirn^^' ' ' 



it is easily seen that Xj and X.^ depend only on the shape of the 

 window, the numbers of sections of the two coils, and the ratio 

 of their space-factors. In the following table are given the 

 values of X.2 and Xj for some different values of / and J, for 

 square windows and for oblong ones whose height, measured 

 parallel to the iron tongue, is twice their breadth {2/>'^=4-b), and 

 for some different ratios of space-factors. 



It will be noticed in the following table that tlie coefficient of 

 the coil to which the extreme sections belong is negative, and 

 that the sum of Xj and X.^ is (q.p.) inversely proportional to the 

 product of the numbers of sections: also that the change of the 

 space-factor ratio from 4/3 to 3/4 does not cause much change in 

 X] and X.2, unless in the three-section winding. Hence, by 

 aid of this table we can obtain very approximate values of 



4 a 



