500 



Mr. A. Campbell on the 



In fig. 2 let the resistances of the four arms be P, Q, R, 

 and S, and their self inductances L, N, I, and \ respectively. 



Fte. 2. 



Let M be the mutual inductance as shown. By procedure 

 similar to that in §2 it is easy to show that 



and 



PS-QR=a) 2 [(L-M)A-(N + M)r] 

 SL-RN=(S + R)M-PA, + QZ . , 



Several cases are important. 



Case (1). When M = we have 



and 



PS-QR = a> 2 (lA-NZ) 

 SL-RN = QZ-P\. . 



(5) 

 (6) 



(7) 

 (8) 



These are Giebe's equations for the ordinary self-inductance 

 bridge. 



Case (2). IfK = S, 



then (P-Q)R=o) 2 [(L-M)X-(N + M)/] 



and (L-N-2M)K=QZ-P\. 



If also \ = l, 

 then (P-Q)R=ft> 2 Z(L-N-2M) 



and (Q-P)Z = R(L-N-2M). 



Hence either R 2 = — co 2 l 2 , which is impossible, 



P = Q 



or 



and 



L-N = 2M. 



(9) 

 (10) 



