MEASUREMENT OF POTENTIAL DIFFERENCE 279 



Ro is the resistance of the galvanometer plus any resistance 

 placed directly in series with the instrument. 

 The mesh equations are: 



IG(RG + ri) - yr, - P.D. = 0; 

 y(ri + r 2 + fife) - I G ri + e = 0. 



PD 



ri + r 2 + 



+ 



+ r 2 + fife 



The standard potentiometer current when it has been adjusted, 



as in the ordinary potentiometer, by bringing the galvanometer 



g 

 to zero with the standard cell in circuit, is ^p -- p there- 



fore , L _, p, is the graduation marked on the slides of the 



instrument. 



If the null method be employed, 



py* > 



' a T 



= P.D. = reading on slides. 



The instrument being in exact balance, suppose that the applied 

 potential difference, P.D., is increased by a small amount 

 6[P.D.], so that it becomes P.D. + 5[P.D.], the slides being 

 kept as they were. A current will now flow through the galva- 

 nometer and its value will be 



_J[P.DJ 



P _, 7*1(72 + fife) (14) 



This shows that in measuring any potential difference, the major 

 portion of it may be read from the slides as usual, and to this 



may be added the voltage I G \RG H ^T) in order to 



V f i -f- r- 2 + Khl 



obtain the total value. 



The quantity (R G + - 7^-) is the total resistance of 



\ T] -p T<> -j- rill' 



the galvanometer circuit, with P.D. and e short-circuited. If 

 this resistance be kept constant for all positions of the slides and 



