Scattering of electromagnetic waves in beyond-the-horizon radio transmission

A formula is developed for the cross section in electromagnetic wave propagation beyond the horizon. The theory assumes that the propagation is the result of scattering by ellipsoidal shaped inhomogeneities in the atmosphere causing variations in the dielectric constant. The method of derivation is straightforward and gives a clear physical picture of the nature of the process. Simplifications concerning the geometric shape, size, and distribution of these inhomogeneities yield 1) the semi-empirical formula of Norton and 2) the formula derived by Gordon for large sized inhomogeneities. Thus, the physical implications contained in these formulas are clearly demonstrated.