498 Mr. A. Campbell on the 



Let N be the self inductance of the coil to be measured, 

 r a constant inductance rheostat, L x L 2 self inductances, 



Fig. 1. 



while the current i acts inductively on both sides of the bridge 

 as shown, the mutual inductances being M and m. The 

 coils L x L 2 may be the upper and lower fixed coils in the 

 inductometer which I have before described (loc. cit.), the 

 inducing coils carrying the current i. Thus L x and L 2 will 

 usually have mutual inductance (call it y) between themselves. 

 Let ij and i 2 be the instantaneous values of the currents (of 

 sine wave form) in the arms L x and L 2 respectively, the 

 resistances of these arms being P and Q. Let a = (o\S — 1, 

 where <o = 27rn, n being the frequency, and let B/S = cr. 



Then, when there is no current through the galvanometer, 

 we have 



Bi 1 = Si 2 or ai 1 -=i % 



and (P + Jjict)ii + Mai + yai 2 



= (Q + L 2 a + Na)i 2 — mai + ycd\. 

 Since i = i x + i 2 we have 



Pi x + Ljoaj + Ma(ij + i 2 ) +yai 2 

 — Qi 2 + L 2 ai 2 + Naz 2 — ma (t 2 + i 2 ) +ycti l . 

 Separating the real and imaginary parts, we obtain 

 P = <rQ 

 and ff(L 8 + N)-L 1 = (w + M)(o-+l)-t/Co— 1) . . (1) 



