402 ELECTRICAL MEASUREMENTS 



inductance of constant resistance is used at L x and the balance 

 is obtained by varying L x and R P . 

 From 32 and 33, 



LX = C x r x (Rp Rx) 

 RP = Rx + r x - 

 From these equations, 



r x P - x X 



C * '- " (R, - R x )* + MA aml r * = fi, - fix ' 



A 



Obviously the frequency must be constant and of known value. 



The Impedance Bridge with Four Inductive Arms. 20 It is de- 

 sirable to inquire as to the conditions necessary for a balance 

 if all four arms of the impedance bridge contain inductances. 

 This arises from the fact that if very small inductances are to be 

 compared, using currents of high frequency, the residual induct- 

 ances existing in the ordinary double-wound resistance coils 

 become of great moment. The reactances of the bridge coils 

 may be positive or negative according as the inductance or ca- 

 pacity component preponderates, and at times may be of the 

 same order of magnitude as the reactance under measurement. 

 In a bridge with four inductive arms, 



Z N = R N 

 Z P = R P 



Z x = R x 

 and at balance, 



Z M Z P = Z N Z X . 

 Substituting, 



= R X R N 



x L N L x co 2 



The horizontal component gives as one condition for balance, 



[L N L X - L M L P ] u 2 + R P R M - RxR N = (35) 



The vertical component gives as the other necessary condition, 



RpL M R N L X R X L N -f- RiuLp = (36) 



