Self-induction of Wires. 203 



which gives rise to five conditions, 



k 4 fe 4 = S 2 S 3 , 



SiS^R^— R 2 R 3 ) = L 2 S 2 + L 3 S3— L^ — L 4 S 4 , k 



1 4 3 2 

 LiL 4 =L 2 L 3 . 



Here it looks as if the resistance-balance were unneces- 

 sary ; and, as there can be no steady current, this seems a 

 sufficient reason for its not being required. But, in fact, the 

 third condition, by union with the others, eliminating 

 S 3 , L 3 , S 4 , and L 4 by means of the other four conditions, 

 becomes 



)= (R R -RE) ^ A (RjSx — R 2 S 2 ) (LjR 2 — RiL 2 ) — (L 2 S 2 — L^)' ,^ 



(R 3 S 4 — R 4 S 2 ) (L X R 2 — R 4 L 2 ) 



So the obvious way of satisfying it is by the true resistance- 

 balance. 



If there are condensers only, without resistance-shunts, 

 we have 



Z=(Sp)-\ (62c) 



so that 



S 1 S 4 =S 2 S 3 (63c) 



as the sole condition of balance. 



If two sides are resistances, R x and R 2 , and two are con- 

 densers, S 3 and S 4 , we obtain 



KjB^ajS, (64c) 



as the sole condition. The multiplication of special kinds 

 of balance is a quite mechanical operation, presenting no 

 difficulties. 



Passing now to balances in which induction between diffe- 

 rent branches is employed, suppose we have, in the first 

 place, a true resistance-balance, R 1 R 4 = R 2 R 3 , but not an 

 induction-balance, so that there is sound produced. Then, 

 by means of small test coils placed in the different branches, 

 we find that we may reduce the sound to a minimum in a 

 great many ways by allowing induction between different 

 branches. If the sound to be destroyed is feeble, we may 

 think that we have got a true induction-balance; but if it is 



P 2 



