An explicit expression of the attenuation for a radio wave is obtained for a class of terrains consisting, along the wave path, of several sections of different heights and different electrical properties, taking into account the earth's curvature for every section. Here the boundaries of two sections are assumed to be discontinuous, in both height and electromagnetic property, and each boundary may have a thin ridge of arbitrary height. This mathematical model well represents terrains containing ridges, bluffs, coastlines with cliffs, etc., with great varieties of combination along the wave path, and furthermore enables us to systematically obtain an explicit expression of the radio wave intensity over them. The latter expression is obtained in terms of the multiple residue series, in accordance with the number of the terrain sections involved, and, when the class of terrains is reduced to a homogeneous spherical earth, either by letting all the heights and electrical properties of the section be equal or, with one particular section fixed, by letting all the other section lengths equal zero, then the series are uniformly reduced to the well-known Bremmer series for a homogeneous spherical earth. When the lengths of the internal sections are sufficiently large, the effects of the terminal sections (over which the transmitter and receiver are located) become isolated, and this enables us to evaluate those terminal effects, or ‘terminal gain,’ in detail, independently of those of the other internal sections, to use the terminal gain in just the same way as the ordinary antenna height gain function has been used for the ground wave propagation over a homogeneous spherical earth.