378 BELL SYSTEM TECHNICAL JOURNAL 



and 



r2 — To — Re 



C, 



= p%{R - R') + i>Vi(/4 - U) - p'rsiL + h- W), (2) 



where h' , r^ , W , and R' are the values of U, r^, h, and R at balance 

 with L short circuited, and p Is 2t times the frequency. These are 

 practically identical with Owen's equations (10) and (12). 



In equation (1), each of the third and fourth terms contains two 

 factors of second order, namely r-i and (r^ -]- Re — r^'), and h and 

 {h — U) respectively. 



We may therefore write 



CMR - R') = L -\- (/, - /./). (3) 



In equation (2), let 



TT^ = - A^3, pl\ = Xu ph = Xi, 

 pL = X, pl'i = xo, and pi-/ = x-/. 



Then we may write 



(4) 



- (r/ - r.- Re)pX, = pxAR - R') + pr^ix^ - x,') 



- pn{X + Xi - Xo'). 



But from (3) 



p p, L + h- /■/ - {X -i-xo- x,')X, 



K — K = p; = • 



Substituting in (4), 



To' - To - Re = h (.V4 - Xi ) ]^ - Ji' 



rajX + ^2 - x->') 



X, 



v. V, — v/ r., 



= {X + Xo ~ x./ 



and 



/-i i? - R''^ Xi 



Re = r,' - r, - (X + X, - Xo') ((/, + 54 + ^J . (5) 



where qi = ratio of reactance to resistance of arm BC, 



qi = ratio of reactance to resistance of change in arm AD, 

 Qi = ratio of reactance to resistance in arm AB. 



From equation (3) we see that, if we take a zero reading first, the 

 inductance is given by the expression 



