Energetics of the Induction Balance. 59 



to the balancing conditions, 



h=h; k—H (10) 



vi=v 2 ; v s =Vi (11) 



In the generalized bridge it conditions a first order balance, 

 while in practical cases it uniquely determines a true 

 balance, and, as the following examples show, the appropriate 

 formula to be applied to any bridge method of comparison 

 can be derived from inspection. 



§ 4. I. Comparison of Inductances. 



Maxwell's method*: — 



(1) U,=U 2 =U 3 =U 4 =0; T,=T t =0. 

 r ^2 T 4 . L 2 _ R 2 



-TAj K3 L4 R 



(2) U!=U 2 =U 3 =U4=0; T 3 =T 4 =0. 



Ti = T2_ . Li __ Kj 

 R 2 1^! L 2 K 2 



II. Comparison of Capacities. 



Bridoe method :- 



(1) Condensers open : 



=T 4 = 



=0; 





u 1= u 3 = 



=0. 



u 4 



B3' 



•'• 



C 2 



_R 3 





H?- 



Ri 



(2) Condensers in parallel with two adjacent arms of 

 balanced bridge ; same conditions as (1). 



(3) Condensers across parts (r 2 and r 4 ) only of the arms: 



Tl =T 2 =T 8 =:T4=0; U^Us^O. 



IJs^U* . C 2 _ B, x n 2 



Ki Ii 3 C4 K 3 r 2 2 



* Clerk Maxwell, ' Electricity and Magnetism ' (3rd ed.) ii. § 757, 

 p. 398. 



