Measurements of Inductance. 



529 



x is 



L'-M 



M 



R + R' 



, + R'^ ^~ e )> where g== ~~ iy-M ; that ° £ U is 

 complicated and devoid o£ interest. 



§ 10. The comparison of: two M's by Maxwell's method is. 



the example quoted in Lord Ravleigh's report. The short- 

 circuit equations are : — 



{(L 1 + L 2 )D + R}a7-(M 1 + M 2 )D?/ + M 2 D^-(L 1 fL 2 )/=0, 

 M.D.*- (NJ) + R,)y- (^D + G>-M! f= 0, 

 M 2 D^-(K 2 D + R 2 )?/+{(N 2 +^)D + (G + R 2 )}^-M 2 /=0. 



Initially /<?=/, y = z = 0; the initial values of x, y , z are 



R/" 



found by multiplying -~ respectively by 



N^ + ^JNx + Ns), M.Na+^Mx + Ma), and M^-M^Ni, : 

 where A stands for 



It, ! 



I Lj-f-L., 

 i M 2 



M X +1L 



-9 



As the equation in D is on ^J a cubic, it will suffice for the 

 vanishing of c 1} c 2 , c 3 in z that the initial values o£ z, s, and 



z should vanish, I e. ^ = ^; further, the condition for 



the aggregate balance is ^ = J^ ; tliese tw0 conditioris suffice,. 



then for a continuous balance. The cubic then breaks up 

 into' {(M^Mj^ + MiN^D + CMi + MOG + MjR*, and a 

 quadratic factor free from G and g, but involving the other- 

 constants. 



Phil. Mag. S. 6. Vol. 25. No. 148. April 1913. 2 



