SMALL towns and villages in agricultural areas of Anglo-America exist mainly because of their function as central places for the exchange of goods and services, each for its local farm trade area. In any given area small centers are closely spaced and more numerous; large centers, offering greater services, are more widely spaced and less numerous. Theoretical consideration must be given to these commonplace facts in view of the need for developing an analytical framework for settlement geography, comparable to the principles of location in industrial geography. If generalizations can be found true of the functions and spacing of trade centers, the significance of regional differences in the hierarchy of these centers can be assessed. The theoretical principles for analyzing trade centers dernve from two main sources: European geographers and American rural sociologists. Christaller' in Germany has presented the most comprehensive theoretical system of analysis, covering centers from the smallest market towns to the largest cities. He was preceded almost 20 years by Galpin,2 who studied rural communities in New York and Wisconsin. Galpin and the sociologists who have followed him are concerned primarily with the social relatioiAships of farmers with other farmers and with the inhabitants of the trade centers. Christaller and the European geographers influenced by him give their attention to functional attributes and spatial arrangement of the centers. Two basic principles derive from the work in Europe and America: (i) trade centers are graded according to population and functional attributes (though the categories recognized are widely divergent and there is no agreement on criteria); and (2) the locational pattern of trade centers is controlled mainly by the radial movement of traffic, which creates circular trade areas and causes centers with equivalent functions to be spaced at approximately equal distances from one another over any uniformly productive and populated territory. But because there is no such thing as a perfectly uniform territory, many