The Calculation of the Path of a Radio-Ray in a Given Ionosphere

A third degree function is presented giving in a hypothetical way the electronic density in the ionosphere as a function of height or distance to the earthcenter: by inserting appropriate values of the constants, in accordance with measured values from ionospheric sounding stations, it is possible to arrive at any desired or proposed form of distribution (Chapman, Hacke), though there is no physical base for this third degree curve given in this paper. This function allows, after substitution, to calculate exactly, i.e., without any approximation, traveling-time, reached maximum height, and reached distance on the earth's surface of a radio-ray radiated at a given angle. Briefly, the calculation of the ray-path in an ionosphere based on measured values and heights of ionization-maxima at the ionospheric stations and based on arbitrarily selected values of gradients, is shown to be possible.