406 ELECTRICAL MEASUREMENTS 



ZiuZcZp ~h ZMZ r Zp-\- ZitZftZp ~\~ ZMZffZ r ZcZ^Zx 0. (38) 



In the ideal case where the coils of the bridge proper are en- 

 tirely free from inductance and capacity, 



Z M =. R M 



Z x = Rx + j. 

 Zp = R P 



ZN = RN 



1 



Z r = r. 

 Substituting in (38), 



r> r> E> 



h RM^RP + R\tRNRp H- RI^RN^ = ~^~~i (^x -\- juL x ) (39) 



>-, 



Separating the quadrature components, the horizontal com- 

 ponent gives 



L x = R M C r l + + #p. (40) 



The vertical component gives 



R M R P = R N R X . (41) 



Thus a perfect balance of the vibration galvanometer implies 

 that both (40) and (41) are satisfied. 



To expedite matters, it is usual to make a preliminary balance 

 with direct currents, using an ordinary galvanometer, thus satis- 

 fying the condition (41), and then to balance with alternating 

 currents by adjusting r, the vibration galvanometer being em- 

 ployed. This method of procedure assumes that all the resist- 

 ances involved have the same values for both direct and 

 alternating currents. 



Effect of Dissipation of Energy in the Condenser. In the 

 demonstration a perfect condenser has been assumed. As an 

 energy loss occurs in most condensers, it is important to see how 

 this loss will influence the results. As previously shown, an 

 energy loss is equivalent to an increase of the conductance of 

 the condenser. Suppose that the condenser has been measured 



