WHAT IS THE POINT OF MINIMUM AGGREGATE TRAVEL?1

THE January, 1954 issue of Economic Geography carried an article by John Fraser Hart in which he described the properties of certain kinds of statistical centers and the available means of determining these centers.2 In discussing the center known as the "point of minimum aggregate travel," he remarked, with a certain note of despair, that it could only be found by trial and error, using a polar-coordinate annule. This method gave a reasonably close approximation of the true point, although it had the disadvantage of being quite time-consuming. Again in 1959, in a note in the Geographical Review, John Q. Stewart and William Warntz stated that "the only known practical way of finding it is to compute aggregate travel distances for a number of points and to approximate, by trial and error, the point of minimum."3 The present article offers a solution to this vexed problem and seizes the opportunity to include a short historical comment on centrographic techniques. For the past several years geographers and social scientists in related fields have shown a renewed interest in a "spatial methodology for areal distributions."4 The idea, at least in