ALTERNATE EXPLANATIONS OF URBAN RANK-SIZE RELATIONSHIPS1

PICK any large area. It will likely contain many small cities, a lesser number of medium-size cities, and but few large cities. This pattern of city sizes has been observed to be quite regular from one area to another. That is, when the frequency of occurrence of city sizes in any area is compared with the frequency of occurrence of sizes in another area, the two frequencies are very much alike. An example is furnished by a comparison of city sizes and ranks in the Republic of Korea and the state of Washington (Figure 1). Frequencies for the two areas are quite similar. Such empirical regularities of city size have been noted many times and have long posed a challenge to those who would explain or interpret them.2 Several explanatory schemes directly or indirectly related to the problem of repeated regularities of patterns of occurrence of city sizes have been proposed. The present discussion brings these schemes together for comparison, namely, the schemes or theories of G. K. Zipf, W. Christaller, N. Rashevsky, and H. A. Simon.3 In the ensuing discussion it will be noted that city size regularities associated