IV. The transmission of electric waves over the surface of the Earth

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Abstract
1. Ever since the time, about 1902, when Marconi first succeeded in sending wireless signals across the Atlantic the question of explaining the mechanism of such transmission has attracted attention among mathematicians. The question may be put in the following form:—The electric waves generated by the sending apparatus differ from waves of light only by having a longer wave-length, which is, nevertheless small compared with the radius of the earth; and the curved surface of the earth may therefore be expected to form a sort of shadow, effectively screening the receiving apparatus at a distance. How, then, does it happen that in practice the waves penetrate into the region of the shadow ? Unfortunately, the question has been investigated by different methods without adequate co-ordination, and the results that have been obtained are somewhat discordant. In these circumstances it appears to be desirable to undertake a critical survey of the question. The various theoretical investigations may be classified as developments of three suggestions: (l) The imperfectly conducting quality, or resistance, of the material, generally sea-water, over which the transmission takes place, may cause the effect observable at a distance to be greater than it would be if the material were perfectly conducting. (2) Owing to the numerical relations connecting the actual wave-lengths used in practice, the size of the earth, and the distances involved, the amount of diffraction, even in the case of perfect conduction, may be greater than would, at first sight, be expected. (3) Transmission through the atmosphere may be notably different from transmission through a homogeneous dielectric. We may refer to these suggestions briefly as the “resistance theory,” the “diffraction theory,” and the “atmospheric theory.” It may be said at once that the atmospheric theory has arisen from the alleged failure of the other two, and that it has not yet been formulated in such a way as to admit of being tested in the same precise analytical fashion as they can. It is still rather speculative and indefinite. In what follows I propose to attend chiefly to the first two suggestions, and to investigate the result that can be obtained by combining them.

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