Simple expressions for the field as a function of direction at distances of many wave-lengths from any antenna above a plane earth are obtained. Except near the surface of the earth the field varies as 1/r. In agreement with results of others it is found that on the surface of the earth for values of kr, (k=2π/λ), large compared to unity and yet small compared to the (complex) dielectric constant, the vertical component of the field varies as 1/r while if the distance is large compared to the dielectric constant the field decreases as 1/(kr)2. The various constants etc., depending on antenna form and ground characteristics, are shown to be connected with quantities previously used for the determination of radiation resistance so that the same numerical work used to find the total radiation from an antenna also determines its directional characteristics.
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W. W. Hansen (1936) studied this question.
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