Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/387

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��MUTUAL INDUCTION OF TWO COILS.

��355

��position of the circuits can be easily performed. In order to attain a sufficient degree of accuracy, it is necessary that the distance between the circuits should be capable of exact measurement. But when the distance between the circuits is sufficient to prevent errors of measurement from introducing large errors into the result, the coefficient of induction itself is necessarily very much reduced in magnitude. Now for many experiments it is necessary to make the coefficient of induction large, and we can only do so by bringing the circuits close together, so that the method of direct measure ment becomes impossible, and, in order to determine the coefficient of induction, we must compare it with that of a pair of coils ar ranged so that their coefficient may be obtained by direct measure ment and calculation.

This may be done as follows :

Let A and a be the standard pair of coils, B and b the coils to be compared with them. Con nect A and B in one circuit, and place the electrodes of the gal vanometer, G, at P and Q, so that the resistance of PAQ is R, and that of QBP is S, K being the resistance of the gal vanometer. Connect a and b in one circuit with the battery. Fi g . <ji.

Let the current in A be #,

that in J3,y, and that in the galvanometer, xy, that in the battery circuit being y.

Then, if 3/j is the coefficient of induction between A and a, and 3/2 that between B and b, the integral induction current through the galvanometer at breaking the battery circuit is

���R

��K K

��(8)

��By adjusting the resistances R and S till there is no current through the galvanometer at making or breaking the galvanometer circuit, the ratio of M 2 to 3/j may be determined by measuring that of S to R.

��A a 2

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