196 ELECTRICAL MEASUREMENTS 



a perfect balance by a small amount, 5P, the galvanometer 

 deflection is 



D = KI 



D is to be made a maximum by adjusting R G . On differentiating 

 and equating the result to zero it will be found that the maximum 

 value of D will be obtained when 



mn (M+X)(N + P) 

 H - + 



That is, the galvanometer resistance should be equal to that of 

 the remainder of the circuit in which it is placed. 



Sensitiveness Attainable in Measurements With the Thomson 

 Bridge. The sensitiveness of the bridge increases propor- 

 tionally to I B) the limit being reached when one of the arms 

 begins to heat unduly. As the bridge is usually employed, the 

 limit will be set by either X or P. 



When the bridge is nearly balanced and the resistance a is 

 small compared with m and n, 



M + X a I rM + 



If a Thomson galvanometer of the best resistance is employed, 

 the value for R reduces to 



P(M + X + m) 

 ~ 



X+P 



and 



I B M8P 



2(N - 



Substituting these values in the expression for D and reducing 

 gives 



(17) 



X)[X(N + P) + mP] 



If m = this reduces to equation (10) which applies to the 

 Wheatstone bridge. 



If the same conductors M, N, X, P are arranged as a Wheat- 

 stone bridge and then as a Thomson bridge it will be found from 





