of Maxwell's Capacity Bridge. 



1109 



Let K denote the reciprocal of! the resistance of a con- 

 ductor {i.e., its "conductance"), and let A vq denote the 



minor of K^ in the determinant 



K 21 



K r _i,i 



K 12 

 K 



22 



K,. 



1,2 



Pi 



Ki.,-i 



K 2 ,,-! 



taking K pp as representing — (K^i + K_^2 + Kj?3 + • ■ ■)• 



Let Vp, V q , . . . etc. denote the potentials at the points 



P, Q, ... etc., of any network, i pq the current in PQ (from 



P to Q), and I p , I q , ... etc., the currents flowing into the net- 



ivork from outside. 



In the particular case of E and all the Fs vanishing 



except I p and I q (for which, of course, Ip= — 1 2 ), it can be 



shown * that 



'12 





(Afc-^-A 



lp + ^lq- 



(1) 



Similarly, if all the Fs vanish, the effect of an internal e.m.f . 

 E is given by relations of the form 



v„-v*= 



K E 



and 



12 



(A — A , — A + A 7 ) 



\ ma mo na ' no) 



A 

 K,„K„„E 



(2) 



(3) 



These last two equations apply directly to the network of 

 fig. 3, if the condenser is assumed to be out of action. To 

 obtain the total effect in conductor 12 with G in action, we 

 may calculate the total discharge per second through 12 due 

 to C acting alone, and then superpose this on i 12 . 



When C touches A, the P.D. across it changes from 

 V 6 — Y x to V a — Y z , i.e., by an amount V fl -V & . 



This causes a discharge q = C(Y a — Vj) to pass through the 

 network, in at X and out at A. Of this, q : say, will pass 



through 12. The ratio — is plainly equal to the ratio of a 



current in 12 to the current I (in at X and out at A) which 

 produces it. Hence, by equation (1), 



2i 



K 1 



^ =^(A 2X -A 2a -A lx + A ]a ). 



* Cf. Maxwell's ' Electricity and Magnetism/ 3rd edition, vol. i. 

 chap, vi., or Jeans's ' Electricity and Magnetism/ chap. ix. 



