Coefficients of Self-induction and Mutual Induction. 229 



The condition 7=0 implies that L = CB 2 . If this should 

 involve the use of inconveniently high resistances for B, we 

 may diminish the effect of L by shunting B 1? the coil itself, 

 by a resistance S. The expressions for T, F will be changed 

 into 



T=iL.i?-£, 



—2 



F=J{B I .i-{ +$.%-u +W-X-U +...}, 



where B] is the resistance of the coil, R the whole resistance 

 between A and P, R' = R — R 1 . 



The expression for 7 will be the same as before, except the 

 first factor, which now becomes 



This remarkable proposition, that the effect of a shunt on the 

 self-induction of a coil is to diminish it in the ratio 



S 2 : (Rx + S) 2 , 



is of great use in comparing two coils with each other. 

 If we write 7=E(CB 2 -L)/A, 



A = (B. a + c + c.a + b)(a + c.b + a + b. Gt)/ab. 



The value of A indicates the most suitable magnitudes t< 

 choose for the other resistances in the bridge. 

 (1) If a = 6, 



A=(B C + B + 2^.a)(l+^^). 

 This expression is a minimum when 



2 Bc(c + 2G) 

 a = -BW-' 



A = Qy/Bi + v / B + 2c.c + 2G) 2 . 



