Variable Mutual Inductances. 163 
M be the reading for balance when N is inserted, then 
N = 2(M-M )*. 
Even if a and b are well matched, it is always well to begin 
by reading their difference if any. 
It will be noticed that the method is really a differential 
one; when N is introduced into the arm AC no alteration has 
to be made in the other arms except to increase the resistance 
of AB by an amount equal to the resistance of the coil N. 
But although it has all the advantages of differential mea- 
surement, the reading can be made to give N diiectly without 
having to take a difference at all. This is due to the use 
of the inductive balancing coil b f. 
The method has the advantage that it does not require the 
knowledge of the absolute value of any resistance. The non- 
inductive bridge arms must be equal ; to check the equality 
they can be interchanged. For the noninductive adjustable 
resistance r I usually employ a special rheostat consisting of 
two slightly flattened thin wires running parallel to one 
another at a few millimetres distance, with a sliding contact 
piece across them to complete the circuit. The inductance 
of such a rheostat can be approximately calculated, and 
may thus be allowed for when measuring very small self 
inductances. The inductance of the part added to com- 
pensate for the introduction of N has merely to be subtracted 
from the result. 
In practice the method proves very convenient ; with the 
variable mutual inductance described above, self inductances 
of any value from 0*1 microhenry up to 2000 microhenries can 
be measured directly without the bridge being altered in any 
way except in the rheostat?'. In a later model shown in the 
accompanying Plate IX. the whole scale of the movable coil 
corresponds to 20 microhenries, and at this value it can be read 
to 1 or 2 in 1000— at 200 microhenries to 1 or 2 in 10,000. 
All the resistances of the coils are very low, and the sensitivity 
can be considerably increased by using M. Wien's method 
of connecting the vibration galvanometer to the bridge by 
means of a transformer of suitable ratio (ftj/^o small). The 
* (Oct. 1st, 1907.) If, instead of the coil N, a condenser K with 
series (absorption) resistance q he added, then 
l//rK=2M, 
and q— change in r. 
t If coil b be made noninductive we revert to Maxwell's method of 
comparing the M of a pair of coils with the L of one of them. 
Equation' (2) then reduces to L/M=-(l + R/S). Maxwell, 'Elect. & 
Mag.' 2nd edit. vol. ii. § 756. 
M2 
