﻿for Measurement of Resistances and Capacities. 303 



values of the lead into each one of the three equalities included 

 in (1), and that there exist in each case simple and accurate 

 means of adjusting the commutator to the corresponding 

 positions. This is shown by the following analytical in- 

 vestigation of the current through the galvanometer, and the 

 values of the lead which correspond to each one of the three 

 equalities (1). 



In a Wheatstone's-bridge system the combinations may be 

 arranged either as in fig. 1, or as in fig. 3, which is obtainable 



Tier. 3. 



from fig. 1 by simple interchanges of the battery and gal- 

 vanometer without altering the lettering. In both arrange- 

 ments when the system comprises only the resistances 

 P, Q, R, S, F and f and the capacities H and K, situated as 

 in the figures, the differential equation of the current C 

 through the galvanometer branch due to an E.M.F. E in the 

 battery branch is given by the expression 



(PS'-R'Q)E 



= ^;, 



F/(P + Q + R / + S') + F(P + QXR' + JS')+/(P + R , )(Q + ^) + 



+ PQ(R' + S')+R'S'(P + Q), . (2) 

 where R/ and S' denote differential operators such that 



R' = R4- 



HD 



S' = S + 



KD 



D = 



(3) 



The relations corresponding to incomplete balances which 



