TRANSACTIONS OF SECTION A. 445 
M,, M,, are the induction coefficients to be compared; RS, the resistances of 
the two secondaries (with associated resistance coils); N,, N., their coefficients 
of self-induction. Thus— 
(M, +M,) E=(,N, —M,N,) +(M,R—M,8) y. 
Since y begins from 0 and ends at 0, the integral electro-motive force vanishes: 
if 
M,R-M,S=0. 
If this condition is satisfied, there is no integral current through the galvanometer,. 
and then the ratio of induction coefficients is known by the ratio of resistances. 
In general, however, the evanescence of the integral current is obtained by the | 
opposition of consecutive positive and negative parts, and even although the whole- 
duration of the effect be but a small fraction of the time of vibration, the needle of 
the galvanometer will be disturbed in such a manner as to make it difficult to say 
whether or not the whole impulse acting upon it be zero. To obtain a satisfactory 
Measurement it is necessary to secure at least an approximate fulfilment of the 
second condition required in order that the current may be zero throughout, viz.— 
M,N, —M,N, =0. 
In this there is no difficulty, as we can easily increase the defective self-induction 
by the addition of other coils, placed at a sufficient distance. The most convenient 
plan is to include two coils by the variation of the relative situation of which the 
self-induction can be adjusted. With moderate care the initial impulsive electro- 
motive force, caused by a sudden variation of the primary current, and dependent 
only upon the induction coefficients, may be made so small that the needle shows 
no uneasiness when the other adjustment relative to the resistances is complete. 
In March 1881 I attempted, in conjunction with Messrs. Glazebrook and 
Dodds, to carry out the plan above suggested for the comparison of two co- 
efficients of mutual induction. No satisfactory result could be obtained in the 
ordinary method of working, the needle showing uneasiness whatever resistances 
were employed, so that it was impossible to fix upon any particular value as 
corresponding to a zero integral current. The addition of other coils to increase 
the self-induction of one of the secondaries was so far successful that the needle 
could be reduced to quietness, but calculation showed that the additional self- 
induction found to be necessary in experiment was much in excess of what the 
above theory would indicate. The explanation which afterwards suggested itself 
to me was that the anomalous effect was due to the conducting rings upon which 
some of the coils were wound, and whose presence complicates the otherwise simple 
theory. We verified this view by bringing a coil of wire into the neighbourhood 
of one of the principal coils, the behaviour of the galvanometer needle heing very 
sensibly different according as the auxiliary coil was open or closed. 
The kind of embarrassment to which measurements of this kind are subject is 
well illustrated by placing the galvanometer in a tertiary circuit, not directly 
influenced at all by the battery current in the primary. A pair of coils with 
double wires, such as are often used for large electro-magnets, is suitable for the 
experiment. One wire of the first coil is connected with the battery, and forms 
the primary circuit. The second wire of the first coil and the first wire of the 
second coil are connected, and constitute together the secondary circuit. The 
second wire of the second coil and the galvanometer form the tertiary circuit. The 
apparatus must be so adjusted that no effect is perceived at the galyanometer when 
the secondary is broken, whatever may happen in the primary. When this ad- 
justment is complete the secondary is closed, and the effect is observed of opening 
or closing the primary. If the contacts are properly made, the integral current 
through the galvanometer at each operation is rigorously zero, but in the experi- 
ments that I have made no one could infer the fact from the behaviour of the 
galvanometer needle. The effect may be exaggerated by the insertion of a few iro. 
wires into the induction coils, 
