496 Mr. A. Campbell on the Measurement of Mutual 

 Then 



1= — It— U 



md 



0=;, + L§ + Mg 



=?> + L §_ M J-Mf. . . . (1) 

 Also r = ? 2 R, 



^4-K(i-S|); 





So 

 therefore 



,R-r = const, -f- -^^-f SK^ ; 



eft K d£ 



Substituting in (1) we have 



Now, as will be shown below, we may assume all the 

 currents to be sinusoidal, i. e., /i = I 1 sin^ ? 

 .and hence 



r-M/RK = and L-M~ ^ =0. 



Thus for a balance we must have the following two conditions 

 satisfied, viz. : 



M = 10- 6 KRr, ..... (2) 

 and 



L = M^; (3) 



where K is in microfarads. When S = 0, L = M; and this is 

 therefore the minimum permissible value for L. When L 

 is less than M in the pair of coils under test, a third inductive 

 coil must be inserted in the branch OrO to bring the value of 

 L up to at least M, otherwise no balance can be obtained. 

 It will be noticed (a) that if R be kept constant the con- 

 ditions (2) and (3) can be satisfied by independent adjustments 



