Use of Mutual Inductometers. 501 



Thus we see that in an equal arm bridge the simplest con- 

 ditions are got by making sure that the ratio arms have equal 

 self inductances. They can be adjusted by interchanging 

 them and altering until the interchange does not alter the 

 balance of the bridge. 



Case (3). If R and S are unequal, let R/S = c as before. 

 The arrangement is best used as follows. 



Let Q be an auxiliary balancing coil, set to give a balance 

 in the bridge initially when M = and P = P . 



Thus we have for the preliminary conditions 



P S-QR = o> 2 (lA-NZ) (11) 



and SL-RN = QZ-P \ (12) 



Now let a coil to be tested, having resistance T and self 

 inductance X, be introduced into the arm P, and let the 

 balance be restored by reducing P to P x and by setting M. 



Then we have 



(P 1 + T)S-QR=a> 2 [(L + X-M)X-(N + M)Z] 

 and S(L + X)-RN = (S + R)M-(P 1 + T)\ + QZ. 

 Subtracting from these (11) and (12) respectively, 

 (Pi - P + T)S = to 2 [(X - M)\~ Ml] 



= a> 2 [X\-M(A + 0] 

 and SX = (S + R)M-(P 1 -P + T)\. 



In the most useful practical case / and X are small com- 

 pared with X and M, so we may take as a first approximation 



SX=(S + R)M 



or X=(l + <r)M (13) 



Hence 



p.-p^T^vx-riM/s 



or T = P -P 1 + ft ) 2 (<rA-/)M/S. . (U) 



and a closer approximation then is 



X=M[l + <r-ft> 2 (<7\-Z)\/S] . . . (15) 



Thus the unknown T and X are obtained from the change 

 made in P, the reading of M, and the corrections due to X 

 and I. It will be found that the correction is usually almost 

 negligible in the expression for the inductance X. On the 



