40 BELL SYSTEM TECHNICAL JOURNAL 



Collecting reals and imaginaries, 



Ra = lOOOr 



and 



Rb = IOOOZb. 



If measurements Ri, Vi and i?2, ^2 are made on the bad and good 

 wires respectively, 



i?iai = lOOOz-i 

 and 



i?2a2 = lOOOro; 

 also 



RA = IOOOXb 

 and 



R.h2 = IOOOXb, 



R,h = RA, 

 or 



^ = h 

 R2 ~ h ' 



Yet the design of a suitable bridge is not concerned alone with 

 balanced condition, but rather with the sensitivity and ease of balance 

 with slight unbalances present. An indication of the probable sensi- 

 tivity is afforded by a solution of this bridge network to determine 

 the phase and magnitude of the galvanometer unbalance current with 

 respect to the impressed voltage. These have been obtained from 

 the equation 



£(22^4 — 2123) ,-.. 



*3 = : 7- — r^T : (3) 



in which the denominator is a determinate, and the symbols are those 

 used in Fig. 9. 



Since the condition for balance is 



S1S3 = S2S4 



we have, using the notation of Fig. 8, 



1000(r - jXb) = R{a - jb) 



and, equating reals and imaginaries, 



lOOOr = aR, (4) 



lOOOXi, ^ bR. (5) 



