THE MEASUREMENT OF RESISTANCE 189 



(M + X)I X 5P XI X 5P 



~ Rc(M + tf + X+P) ~ Rc(X + P) 



I l \ i dP \ / 



= y (?) 



and the deflection is 



(ID 



S v is the volt sensitivity of the galvanometer when it is critically 

 damped. 



As in the previous case, the sensitiveness of the bridge is 

 proportional to the square root of the allowable power loss in 

 the arm which limits the bridge current. 



If the resistance of the bridge (R B ) is so great that the gal- 

 vanometer is under-damped, a resistance must be put in parallel 

 with the bridge between the galvanometer terminals. Let 

 the value of this resistance be R s and let R K be the resistance 

 which it is necessary, in any case, to put in series with the gal- 

 vanometer in order to attain critical damping. That is, let 



RC = RG ~h RK- 



In this particular case R K is the parallel resistance of the 

 bridge and the resistance with which it is shunted, or 



/,' Rn 

 '' Rs + Rn 



also 



(M + X)(N + P) 

 = M + N + X -f 'P 



The galvanometer current when the bridge is slightly out of 

 balance is 



" 



R a ) + R B Rs](M + N + X + 1') 



D 



The sensitivity is seen to be diminished in the ratio 



RB 



