Graphs to Prof. Sommerfeld's Attenuation Formula for Radio Waves

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Abstract
The importance of close confrontation of Prof. Sommerfeld's attenuation formula with field-strength measurements is stressed. The fallacy of Prof. Zenneck's formula in most practical cases is pointed out, and a short summary given of Prof. Sommerfeld's conclusions, with approximate expressions for the "numerical distance" and the angle determining various shapes of theoretical attenuation curves. At very great distances, the signals over flat ground are shown always to decrease as the inverse square of distance, while at short distances short waves die away approximately as the inverse square root of distance. At intermediate distances, curious phenomena are shown to occur; in some cases, as illustrated by examples, the field vanishes altogether at a finite distance, to reappear farther away. An abac is included and instructions given for its use to obtain the inductivity and conductivity of the ground over which a series of field-strength measurements have been made. Results of such computations in Sweden and England are given. By using a graph reproduced in the paper an easy method of predicting field strengths for all wavelengths over soil, whose electrical constants are known, is devised. A simple semi-empirical formula to account for the curvature of the Earth at moderate distances is presented, and lines for better antenna construction touched upon, minimizing jamming from down-coming rays, and saving power as well.