Paradigm Lost: Nikola Tesla's True Wireless Page 8

and excites the [receiving] circuit in the same way as if it is attached to an energized wire.” No radio propagation engineer would have accepted such an argument in 1919. Indeed, the receiver might well detect the transmitted signal, but not for the reasons stated by Tesla. No model of wave propagation asserts that the signal goes under the mountain.¹⁶

Following the work of Hertz, it was apparent that laws of optics could be applied to electrically generated waves. There would have been no problem in explaining the reception of waves by a detector lying on the shaded side of the mountain — it would be described as Fresnel diffraction, a theory put forth by the eponymous French physicist in the period 1815–1818.¹⁷ The theory asserts, in part, that the greater the wavelength used, the stronger the signal that makes its way into the optical “dark side,” provided the distance from the diffracting edge (here, the mountain top) is small measured in wavelengths.¹⁸ Given the long wavelengths employed by Tesla (10 kHz => 30 km. => 18 miles), a number taken from Fig. 1 in his article, there is no trouble in explaining wireless reception on the far side of the mountain. By the time Tesla published this piece, the subject of diffraction of electromagnetic waves had become sophisticated and had engaged the attention of a number of distinguished mathematicians.

If the mountain is modeled as a hemispherical impediment to the wave, and if the earth is a good conductor, then the problem of scattering by the mountain can be attacked using the method of images. The problem becomes that of a plane wave incident upon a sphere. This problem had been solved in the period 1908–9 by Debye and Mie and would also show a signal in the optical shadow cast by the hemispherical mountain.¹⁹

In the period beginning in 1889 and ending in the era of Tesla’s writing, the Scottish mathematician H. M. Macdonald had treated waves from a Hertzian dipole diffracted from the earth, which he modeled as a perfectly conducting sphere.²⁰ His work was improved by the great French scientist and philosopher, Henri Poincaré, who in the period 1909–1912 converted Macdonald’s series of Bessel functions into a definite integral that could be better evaluated. The German mathematical physicist Arnold Sommerfeld, unlike his predecessors, treated the earth as an imperfectly conducting surface, although he simplified matters by making the earth flat. He placed a vertical, electrically short dipole above the earth and derived an expression for the resulting electric and magnetic fields. His results of 1909 were expressed in terms of an integral that he evaluated asymptotically for an observer far from the antenna. He found that a surface wave had been generated, and his theory nicely supported that of another German, Jonathan Zenneck, whose less rigorous work had led to what became known as the Zenneck wave, which existed on the ground at some distance from the antenna. The latter turned out to be the asymptotic solution