254 Dr. J. A. Fleming on the Distribution of 



(«+y)N 1 +iM 1 + ^+~yU=E, (i.) 



yN a +sM 2 +yS=-E, (ii) 



(^ + ^ / )M 1 4yiM 2 -2(L 1 + L 2 + r) + 2Q=0; . (iii.) 



add equations (i.) and (ii.) and arrange, putting n for ^, 

 (JV + E> + (Njn + N 2 n + R + S> + (M x + M s )n*=0, 

 M^ + (M 1 n + M 2 n)?/+{(L 1 + L 2 + r)n+Q}0=O. 



Eliminating y, we have 



{n(N x n + R) (Mi + M s ) -M^OV + N 2 n + R + S) \x 

 + ((M 1 + M 2 )V-{(L 1 + L g + r)n + Q}'{N 1 n + N s n + B+S})«=0. 



Hence we get 



\ n 2 (M 2 "N"! - MxN s ) -n(M a S - M 2 R) } x 

 a denominator which does not concern us 



If matters are so arranged that 2 = 0, or the galvanometer 

 shows no current, 



(M^-MiN,) J =(M 1 S-M 2 R); 



hence if there is no " kick " on the galvanometer on making 

 the current, then 



M 2 ~S* 



§ 20. Theorem. — To determine the capacity of a condenser 

 by means of a Wheatstone's bridge (fig. 19). 



Let a, /?, 7, S be the four points of a Wheatstone's bridge; 

 and let the branch between a and /3 be interrupted at a b, and 

 a Leyden jar or condenser inserted provided with some rapid 

 commutator, such as a tuning-fork, so that whilst the outside 

 of the jar is kept permanently attached to /3, the inside is 

 alternately joined to a and b. 



If a tuning-fork is used and its prongs have small metal 

 styles which just come down to the surface of the mercury in 

 two little cups, when the fork vibrates, as the prongs come 

 together, the upper point dips in; and as they separate, the 

 lower one dips in ; hence the shank of the fork is alternately 

 connected with one and the other cup. The interval between 

 the time of connection being exactly half the time of a com- 

 plete oscillation of the fork. 



Now let the meshes of the network be called $ + z, z } andy; 



