282 ELECTRICAL MEASUREMENTS 



necessary for an exact balance, the slides remaining fixed, the 

 galvanometer current will be 



S + RG + pi, 



TI -J- TZ ~r f^'i 



or 



*rn<? r-/*4-ji . r i( r + ^) \ . 



6[/J*S = /c (O + /CG + :~j~ , pi) 



ri + r 2 + / 



The expression in parenthesis is the resistance of the galva- 

 nometer circuit with e short-circuited and the main current cir- 

 cuit open beyond the shunt. The quantity to be added to the* 

 reading of the slides before dividing by S is seen to be the 

 galvanometer reading reduced to volts, provided the switches 

 and coils are so arranged that 



ri(r 2 + Rh) \ 



~T t\,Q I _ i i PL / 



T\ -\- TI -\- tin/ 

 has a fixed value. 



To obtain the greatest speed of working, the resistance of the 

 galvanometer circuit should be such that the galvanometer is 

 critically damped. The free period of the instrument should be 

 about 1 or 2 sec. The arrangement of the potentiometer is 

 shown diagrammatically in Fig. 162. 



To assist in attaining the necessary constant resistance in the 

 galvanometer circuit, the rheostat for controlling the potenti- 

 ometer current is arranged in two parts, r 3 and r 6 , the potenti- 

 ometer wire being connected to the slider which joins the two 

 sections; the coils are so chosen that the parallel resistance of 

 the active portions of r 3 and r 6 is fixed, thus keeping the rheostat 

 resistance between A and B (with e short-circuited) constant. 

 The rheostat marked 0.5 fl is for the fine adjustment of the potenti- 

 ometer current; the corresponding ballast coils in the galva- 

 nometer circuit are marked 0.3 fl. To correct for changes in resist- 

 ance due to displacing the contact point along the potentiometer 

 wire, the ballast resistance r 4 is added, the coils in it being given 

 the proper values. As some of the coils at the upper and lower 

 ends of the series have the same values, the number of .coils re- 

 quired is reduced by cross-connecting, as shown in the lower 

 figure. The volt box employed, shown in Fig. 163, has ballast 



