capacity and self induction uniformly distributed along the axis of symmetry of wave propagation and transmitting slow electrical oscillations without sensible distortion and attenuation.
Besides the above three requirements seem to be essential to the establishment of the resonating condition.
First. The earth’s diameter passing through the pole should be an odd multiple of the quarter wave length – that is, of the ratio between the velocity of light – and four times the frequency of the currents.
Second. It is necessary to employ oscillations in which the rate of radiation of energy into space in the form of hertzian or electromagnetic waves is very small. To given an idea, I would say that the frequency should be smaller then twenty thousand per second, through shorter waves might be practicable. The lowest frequency would appear to be six per second, in which case there will be but one node, at or near the ground-plate, and, paradoxical as it may seem, the effect will increase with the distance and will be greatest in a region diametrically opposite the transmitter. With oscillations still slower the earth, strictly speaking, will not resonate, but simply act as a capacity, and the variation of potential will be more or less uniform over its entire surface.
Third. The most essential requirement is, however, that irrespective of frequency the wave or wave-train should continue for a certain interval of time, which I have estimated to be not less then one-twelfth or probably 0.08484 of a second and which is taken in passing to and returning from the region diametrically opposite the pole over the earth’s surface with a mean velocity of about four hundred and seventy-one thousand two hundred and forty kilometers per second.
