THE MEASUREMENT OF RESISTANCE 197 



(10) and (17) that with a Thomson galvanometer the Wheat- 

 stone bridge arrangement will be the more sensitive in the ratio, 



fe--V> 



n 



N + P 



If a critically damped moving-coil instrument is to be used 

 and the resistance of the bridge is so low that the instrument is 

 over-damped, it will be necessary to increase the resistance of 

 the galvanometer circuit. It will be assumed that the resistance 

 a is low compared with m and n. The arrangement then 

 becomes the equivalent of a Wheatstone bridge where the 

 resistance of the galvanometer branch is 



mn 



R being the resistance added in order to obtain critical damping. 

 Let the resistance of the circuit necessary for critical damping 

 be R c , then 



RC = RB ~f~ R G 



where 



~ 



M + N + X + P 

 When the bridge is slightly out of balance 



r x (M + X)SP 



(R c -R B )(M + N + X + P) + (M + X) (N + P) 



D - SJ, - S, /WX (18) 



If the instrument is under-damped, it will be necessary to 

 place a shunt around the bridge between the galvanometer 

 terminals. In this case, if Ro is the resistance of the galva- 

 nometer and R s that of the shunt, 



+ (M + X) (N + P)(R 



