Induction-Coil Potentials Page 566

theoretical and experimental curves for the coils with air-core and with the core of iron-filings, fair agreement in the case of the iron-wire core.

In the present paper further tests are described of the applicability of the theory to the case of an induction-coil. In these, smaller primary capacities were used, and the constants of the circuits were determined in actual working conditions. The effect of varying the primary capacity is specially considered, and a view is put forward which differs from that usually held as to the function and the most effective value of this capacity.

There are two things which should be borne in mind in determining the constants of the primary and secondary circuits of an induction-coil. The first is that, owing to the variable permeability of the core, it is necessary to use mean values of the induction-coefficients, which can only be expected to give correct values for the secondary potential over a limited range of values of the primary current.

The other is that the induction-coil as generally used has the terminals of its secondary coil connected to bodies of very small capacity, e.g. spark-gap terminals, the electrodes of an exhausted tube, or an electrometer or electrostatic oscillograph of very small capacity. In these circumstances, the capacity of the secondary circuit is mainly distributed along the secondary coil, and when the oscillations are taking place and no discharge is passing, the current is not uniform throughout the length of this coil, but is greatest at the central winding and very nearly zero at the terminals⁴. The system is in fact similar to that of the oscillation transformer, or Tesla coil, the theory of which was given by Drude⁵.

The expression “mutual inductance” is not appropriate to such a system, but if (in Drude’s notation) \(L_{12}\) is the coefficient of induction of the secondary on the primary, and \(L_{21}\) that of the primary on the secondary, then \(L_{12}\) is less than \(L_{21}\). \(L_{12}\) is defined as the magnetic induction through the primary coil due to the secondary current divided by the value of the latter in the central winding. On the other hand, the terminals of the primary coil are connected to a condenser of considerable capacity, so that the current in this coil is uniformly distributed. The coefficient \(L_{21}\) is

⁴ As the current varies (in its fundamental oscillation) as the cosine of an angle proportional to the distance from the central winding, this distribution of current will be referred to as a cosine distribution.
⁵ Drude, Ann. d. Physik, xiii. p. 512 (1904).