1110 Mr. V. A. Bailey on a Development 



Similarly, when C touches B, a charge q 2 passes through A2, 



;iven by 



-| 2 =^(A 2 ,-A 26 -A U +A W ). 



Hence, in one second the total charge passing through 12 is 



The absence of X from this expression shows that the charge 

 passing through 12 is independent of the point in the network 

 to which the condenser is permanently attached. 



The galvanometer in 12 will give no deflexion when 



i. e., by (2), (3), and (4), when 

 K 12 ?iC 



A 



(Ai a -Al/,-A 2 a+^2&) 



x ^^ (A ma - A mb - A na 4- A, l6 ) = 0. 



This condition for balance reduces to 



__ n Q = A (A w i — A, m2 — A w i + An2) 



(Ala — Aift— A2a + A2j)(A, Ma — A W 6— A^j + Anj). 



. . . (5) 



For the more general case of sources of e.m.f. in every 

 branch of the network, the condition for no deflexion in the 

 galvanometer can be shown in a similar way to be 



-nC = 



A X [E wn K OTW ( A ffl i — A W 2 — A n i 4- A w2 )] 



(Aia— Aij — A 2 « + A26)'2[E^Ki^(A flI «-A m 5-A l(a + A )(6 )] ' 



It is noticeable that the junction X does not appear either 

 implicitly or explicitly in these last two equations, and hence 

 we may draw the following interesting conclusion : — 



In a general network like that shown in fig. 3 (but also having 

 several sources of e.m.f) for which the variables have been 

 adjusted so as to give no galvanometer deflexion, the per- 

 manently-connected plates of the condenser may then be 

 connected to ANY point in the network without disturbing the 

 galvanometer s state of no deflexion. 



