348 TENTH ANNUAL REPORT OP 



E, The electro-motive force of C. 

 E', The electro-motive force of I. 



The current of the element C divides at a and h into two parts; one 



of which passes through the conductor by d, the other through I. 



The resistance to conduction of the one branch is r, that of the other 



I'r 



is V ; hence the resistance of the two branches together is and 



"^ l'-\-r 



the undivided current which C produces is — 



E __ ^(l' -\-r) 



^ , I'r ~" l{l' + r) -{- I' r 

 l'-\-r 



In this we neglect the electro-motive force in I, 



The part of the entire current which ^^asses through I is — ■ 



E^^ . (1) 



The entire current which I produces, and which is divided between 

 the branches a C 6 and a d h, is — 



I' {l-\-r)-\-rl 



The two currents (1) and (2) pass through the multiplier in oppo- 

 site directions. Since the denominators of the values (1) and (2) are 

 exactly equal, the multiplier evidently will stand at the zero point, if 



E r = E' (Z + r). { 



For given values of E E' and I a value of r can always be found 

 which will satisfy equation (3); that is, there is a certain length of the 

 conducting wire a d b with which the multiplier indicates no current, 

 ■when the wire coming from a is brought in contact with one of tha 

 poles of C. 



If the resistance r be too great, the multiplier will indicate a cur- 

 rent in favor of C ; on the contrary, the current of C in the multiplier 

 ■will preponderate if th-e resistance r is too small. 



If the resistance r in the wire a db is precisely such that the multi- 

 plier remains at zero when the circuit is closed at a, or when equation 

 (3) is satisfied, we get from this equation the following : 



E' = E j-^' (4) 



I + r 



We can thus compute the value of E'; that is, the electro-motive force 

 of 1, when E^ the electro-motive force of C, is known, and also the 

 values of resistance I and r. 



Tlie exact length of the wire a d b cannot be attained at the first 

 trial ; in general by closing the circuit at a the needle of the multiplier 

 ■will be deflected to one side or the other, according as the wire" is too 

 long or too short. By a few trials, shortening or lengthening tlio 

 ■wire a d bas may be necessary, it is easy to find such a length thatthe 

 galvanometer will indicate no current, or at most a very feeble one. 



