Induction-Coil Potentials Page 567

therefore equal to the “mutual inductance” of the coils as usually defined, i.e. the induction through the secondary due to the primary current divided by the value of the latter.

For similar reasons the self-inductance \(L_2\) of the secondary coil is less than the value for steady or for uniformly distributed currents, while \(L_1\) has the usual meaning. The coefficient of coupling, \(k\), of the coils is defined by

\[ k = \sqrt{\frac{L_{12} \cdot L_{21}}{L_1 L_2}}. \]

The value of the secondary capacity, \(C_2\), depends upon the manner in which the charge is distributed in the secondary coil, but it is unnecessary to determine it. For the purpose of calculating the secondary potential \(V_2\) from the expression (1) it is sufficient to know the values of the six quantities \(L_1 C_1\), \(L_2 C_2\), \(L_{21}\), \(k\), \(R_1/L_1\), \(R_2/L_2\). \(R_1\) and \(R_2\) are the effective resistances of the primary and secondary circuits.

These six quantities were determined as described below for an 18-inch-spark coil⁶, with three primary condensers of capacities about 3, 2, and 1 microfarad respectively. These condensers had mica insulation, and for the sake of definiteness were connected directly across the terminals of the primary coil. If the condenser is connected across the interruptor in the usual manner, the primary circuit then includes the battery, amperemeter, and rheostat, and the self-inductance and resistance of the primary circuit will, therefore, be different in different experiments.

The secondary terminals were connected directly to the oscillograph, in parallel with which was a variable spark-gap consisting of two brass spheres, each 2 cm. in diameter, supported on ebonite pillars. The oscillograph has been described in a former paper⁷. The instrument has very small electrostatic capacity, and in its present form it can be used directly for potentials sufficient to give a 24-cm. spark between the ball electrodes.

Determination of \(L_{21}\).

This coefficient, which, as explained above, is equal to the mutual inductance of the primary and secondary coils, was determined by two methods. In the first it was compared with a known mutual inductance by the ballistic galvanometer

⁶ The primary coil was in four sections. Except where otherwise stated these were all in series.
⁷ E. T. Jones, Phil. Mag. xiv. p. 238 (1907). Cf. also l. c. (2), p. 708.