Induction-Coil Potentials Page 569

frequencies used in this experiment the induction coefficients of the coils are not very different from their values for steady currents.

The Coefficient of Coupling.

The coupling coefficient, \(k\), was determined by finding the frequency of the oscillations of the secondary coil (connected only to the oscillograph and ball electrodes), with the primary coil open and with the primary terminals connected by a short piece of wire. The ratio of the squares of these frequencies is \(1 - k^2\). These oscillations were started by sparking to the ball electrodes with two pointed conductors connected to a second induction-coil, and the curve of potential was photographed in the usual way. With the primary closed the oscillation curve only appeared with great difficulty, and many exposures were taken before a photograph sufficiently good for measurement was obtained. The amplitude of the curve was small, but was sufficient to allow the period to be determined with fair accuracy. The frequency was found to be 1246. With the primary open the frequency was 599·4. This was measured near the end of the curve where the amplitude, and consequently the magnetizing current, is small, in order to minimize as far as possible any error arising from the difference in the degree of magnetization of the core in the two experiments due to the shielding action of the induced current in the primary when on closed circuit.

These frequencies give the value ·768 for \(k^2\). The value given in the former paper⁸ for the same two coils was ·8142. This was determined by a similar method, in which, however, a condenser was connected to the terminals of the secondary coil. It appears, therefore, that the coefficient of coupling of the coils (for natural oscillations) is less when the terminals of the secondary coil are free or connected to bodies of very small capacity, than when they are connected to a condenser of considerable capacity, in which case the oscillating current in the secondary is more nearly uniformly distributed.

The matter was further tested by determining the coupling coefficient with the secondary coil connected to various capacities, the largest being a leyden-jar of about ·001 microfarad, and the smallest consisting of two tinfoil sheets, 19·94 square centimetres in area, separated by a glass plate

⁸ L. c. (2), p. 716.