Alternate Current Transformer. 7t 



We thus have four leakage coefficients and it will be noticed 

 that they are connected with the two coefficients x^ and x.^ 

 hitherto used by the equations 



X., = x.2.2 - .r,2 (see ^ 43). 



61. The equations of motion are 



El = rfi, + nij^^i = nCi + wn/'^^ Nj (I- ) 



E.,= - r.Co-fio :i,No = - r..C.,-wn./^ K, (H-) 

 -- ■' at " "^ 



where Ej, E.^, are the terminal e.m.f's, and r^, r^, the internal 

 resistances of the coils. 



If R be the external resistance or its equivalent in the 

 secondary circuit, and Cos^ the power-factor of the load, 



E.,Cos<^ = r/'^C, (III.) 



Eliminating E.^ between equations (II.) and (III.) and putting 



= Ti -— = T.i, 



R 



-Coscfi=e 



[Note that the 6 here is the same as the ^Cos^ in the early 

 part of this papei\] 



we get 



{l+x,jS;fi, = -(l + xjKle-<h^Ky'^r^~'^^)n,C. 



(IV.) 

 from which by § 59, 6, we find that 



where 



A' = eil+2x,JJoBS + 2^+x,f+ \) 



+ 2^/ Sin (8 + <^) + X,, Sin</> + 9^\ + ] , 

 X,^'= 1 + 2.r,,Cos8 + x,i ; 

 and that 



