188 ELECTRICAL MEASUREMENTS 



the deflection which would be obtained if some particular gal- 

 vanometer were used. 



Suppose that the maximum allowable bridge current, /' B , is 

 fixed by the heating in the arm X and that l' x is the greatest 

 current which can be employed in that arm. 



If a Kelvin galvanometer of the best resistance is employed 

 and the bridge is out of balance by a small amount, 6P, then 

 using equations (1), (3), (4) and the approximate relation 



M 



the deflection of the galvanometer is given by 



D=KI G ^R G = K( d ~}(I^) 7 -- i *V --. (10) 



The sensitiveness which can be obtained is seen to be pro- 

 portional to the square root of the allowable power loss in the 

 arm which limits the bridge current. 



Now suppose that a critically damped moving-coil galva- 

 nometer is to be used. 



In this case let R' be the total resistance of the galvanometer 

 branch of the circuit. R' will he made up of the resistance of 

 the galvanometer itself plus any resistance which it is necessary to 

 add in order to bring about critical damping. Let R c be the total 

 resistance of the galvanometer circuit which is required for critical 

 damping, then as the bridge is nearly balanced, 



= RC, a definite resistance, 



o M , N , x . C, 



also 



M 



and 



M _ X 

 N = ~ P,' 



Suppose that the resistance of the arm P is increased from 

 the value necessary for a perfect balance by a small amount, 

 5P, then the galvanometer current becomes 



