XXVI.Further note on the propagation of radio waves over a finitely conducting spherical earth

Abstract

In a former article (III.) it was pointed out that in the theory of the propagation of radio waves over a finitely conducting earth two different approximations for the many Bessel functions occurring in the problem can be introduced, viz., (a) the more simple tang, approximation (up till now used by most workers in this field), and (b) the less simple Hankel approximation, but which is required when the wave-length is small compared with the circumference of the earth. In III. the field on the surface of the earth due to an emitter on the ground was calculated with an exclusive use of this better Hankel approximation, whereas in II., the superiority of the approximation not being fully realized yet at the time, curves for the field above the ground were calculated with the aid of both approximations. The results obtained there have now been fully recalculated with the exclusive use of the Hankel approximation resulting in the figs. 5 and 6, which therefore should replace the former figs. 19 and 20 of II. In these new figures the curves could be given ranging from the immediate proximity of the emitter up to well into the shadow region, due to the good fit existing in the transition region between the geometric optical formula (5) and the residue formula (4 b). Here the formerly introduced “divergence factor” was numerically of great importance.