162 ELECTRICAL MEASUREMENTS 



Then with the first position of the rocker 



A #(7*5 ~h X) -f- X(r$ -f- Si) 

 B ot(r ~h $1) -f~ $1(7*6 -f- #) 



and with the second position of the rocker 

 B = ^~ 



Equating these two expressions for ^ an equation results of the 



form 



C(X - Si) = 0. 



C is a function of the various resistances; all the algebraic 

 signs entering into it are + so the condition Dj = D n = 

 shows that 



It will be noted that this result is obtained regardless of the 

 values of A and B, that is, without making the galvanometer 

 exactly differential. 



Suppose DI and D// are equal but not zero, that is, that there 

 are deflections of the same amount and toward the same end of 

 the scale for both positions of the rocker. In the case where 

 is = i's and a = a', that is, where there is no alteration of the 

 circuit resistance, the relation between X and S is still 



r Y NS 

 X = Si or A = 



N + S 



If the battery current and a alter slightly, due to the different 

 positions of the rocker, and the adjustments are made so that 

 DI = D/j, the departure from the relation Si = X is so slight 

 that it may be neglected even in precision work. 



The Kohlrausch method of employing the differential galva- 

 nometer is the only one adapted to work of the highest precision. 



The Wheatstone Bridge. This instrument which is so uni- 

 versally used in the determination of electrical resistance 

 was invented by Mr. S. Hunter Christie, of the Royal Military 

 Academy at Woolwich. He published an account of it in the 

 Philosophical Transactions, under date of Feb. 28, 1833, calling 



