Variable Mutual Inductances. 
165 
necessary a coil c of sufficient self inductance to make N 
considerably greater than L. Let a balance be obtained 
(by Maxwell's Method) and hence 
and 
PS=RQ, 
NS = LR. 
(9) 
(10) 
Fisr. 9- 
Fit?. 10. 
Now, without altering any other branches, let the secondary 
coils be introduced (in opposition) into the galvanometer 
circuit as shown in fig. 10. 
If a balance be now obtained by adjusting the variable M, 
then it is easy to show that 
(P+R)M 2 =(Q + S)M„ .... (11) 
and PS-p 2 M 2 (L-M 1 )=QR- i 9 2 M 1 (ISr-M 2 ). . (12) 
Since (9) and (10) still hold, these equations both reduce 
EMa-SMi (13) 
to 
which gives M 3 immediately in terms of the reading M. 1 and 
the resistances R and S (neither of which include copper 
coils) . The self inductance of the added coil c need not be 
known, but if R and S have not a slide wire between them, 
c ought to be slightly adjustable, which is easily arranged by 
having part of it a small coil of a few turns that can be 
shifted about over the remainder. 
