A theory and results of its application for a topographic analysis of a mountain catchment in the Appalachian Mountains, U.S.A. is provided. The catchment was divided into triangular segments (average area .simeq. 0.6 acre; 1 acre = 0.405 ha) that were analyzed in the 3-dimensional coordinate system; topographic parameters of each triangle were computed and their distribution was represented by isolines. Areas included in specified ranges of inclination and azimuth are given in a tabular form in hectares, and they can be located on maps with isolines of azimuth and inclination. The average gradient of slope inclination is greater on northeast- and north-facing slopes (0.32.degree./m) than on southwest- and south-facing slopes (0.17.degree./m). The method has potential for application in land ecological, hydrological and meteorological studies where a mathematical description of land-surface configuration is needed. The development of a system for automatically reading the coordinates from maps and storing them for computer processing would bring nearer the possibility of using this method for detailed biogeophysical analyses of large mountain regions.