INDUCTANCE AND CAPACITY 411 



v-j [ Z P Z M - Z N Z X jma> (Z M + Z N ) J. 



B [Z (Z M + Z N + Z X + Z P ) + (Z M + Z^)(Z X + Z P ) J 

 For a balance, 



Z P Z M - Z N Z X jraco (Z M + *) = 0. 





The balance arms of the bridge, M and N, are non-inductive. 

 On substituting the values 



Z M = RM 



Z N =RN 



Z x = Rx 



Z P = R P 



and separating the quadrature components , the horizontal com- 

 ponent gives 



R M R P = R N R X . (44) 



The vertical component gives 



R M [L P + m] = R N [L x - m]. (45) 



If Z M = Z N (that is, if a bridge with equal ratio arms is used), 



Rp = Rx 



and 



L x L P = 2m. 



This arrangement is useful in measuring small inductances, for 

 as suggested by A. Campbell, 24 a method of -differences can 

 be used thus eliminating the effects of residual inductances in the 

 bridge arms. 



Referring to Fig. 239, the inductance to be measured is inserted 

 in the gap n. m is a variable mutual inductance which can be 

 adjusted without changing the inductance or the resistance of the 

 secondary circuit. The inductance of either the arm X or the 

 arm P and the resistance of P must be adjustable. 



Let L x , L P and R x , Rp be the values of the inductances and 

 resistances when the bridge is balanced with n short-circuited 

 and the mutual inductance set at zero. Then 



L x L P = 

 Rx - RP = 0. 



