Induction-Coil Potentials Page 571

diminution of the intensity of magnetization of the core with increasing frequency is not sufficient to account for the large falling off in the value of k² shown in Table II.; and we may conclude that the drop in k² is due to the change in the distribution of the current in the secondary coil, i.e. that as the current changes from the uniform to the cosine distribution, the coefficient L₁₂ diminishes more rapidly than L₂. It would be interesting to make similar measurements of k² for coils of different dimensions and forms, especially coils with nonmagnetic cores.

In the above method for measuring k² the oscillations were all started by sparking to the terminals of the secondary coil. There is, however, another way of setting up the oscillations with the primary coil closed, which may be referred to here. If the interruptor of an induction-coil is connected in a shunt across the primary coil, instead of being in the main circuit as usual, when contact is made the primary coil becomes short-circuited and its current begins to decay exponentially. At the same moment oscillations of small amplitude are set up in the secondary, and these are the natural oscillations of the secondary with the primary closed. The potential at the terminals of the secondary coil may be represented by the expression ae^-kt + b sin nt, and the electrometer (being connected idiostatically) shows a deflexion which is proportional to the square of this quantity. This includes a term proportional to sin nt, and another proportional to cos 2nt. The curve should therefore show an oscillation of frequency n/2!$ \pi !$ and another of twice this frequency. As a rule the slower oscillation is much the more prominent, though traces of the octave appeared in some of the photographs.

The most prominent feature of the curves obtained was, therefore, an oscillation of frequency n/2!$ \pi !$, i. e. the frequency of the oscillations of the secondary with primary closed, and not twice this frequency as is the case in the sparking method.

This "short-circuiting" method was tried with various capacities in the secondary circuit. Owing to the smallness of the amplitude of the oscillations, the most sensitive form of electrometer had to be used. The potential at the secondary terminals was in fact not sufficient to produce a 1 mm. spark between the ball electrodes.

The frequencies obtained by both methods are given for comparison in Table III., and one of the curves obtained by the short-circuiting method (no condenser) is shown in Plate VIII. fig. 6.