Geographic Area and Map Projections

BASIC truism of geography is that the incidence of phenomena differs from place to place on the surface of the earth. Theoretical treatises that assume a uniformly fertile plain or an even distribution of population are to this extent deficient. As Edgar Kant' has put it: "The theoretical conceptions, based on hypotheses of homogeneous distribution must be adapted to geographical reality. This implies, in practice, the introduction of corrections with regard to the existence of blank districts, deserts of a phenomenon, massives or special points. That is to say that in practice we have to take into especial consideration the anisotropical qualities of the area geographica." The ceteris paribus assumptions that are repugnant to a geographer are those which conflict seriously with the fundamental fact that the distribution of phenomena on the surface of the earth is highly variable. Von Thiinen,2 for example, postulates a uniform distribution of agricultural productivity; his economic postulates are no less arbitrary, but they disturb the geographer somewhat less. Christaller's central-place theory is in a similar category; for the necessary simplifying assumptions, among them a uniform distribution of purchasing power, are unsatisfactory from a geographic point of view.3 In order to test the theory empirically, one must find rather large regions in which the assumptions obtain to a fairly close approximation. The theory can, of course, be made more realistic by relaxing the assumptions, but this generally entails an increase in complexity. An alternate approach, hopefully simpler but equivalent, is to remove the differences in geographic distribution by a modification of the geometry or of the geographic background. This has been attempted by other geographers with some success, but without clear statement of the problem.