the range that we expect a nearest-neighbour town of the 'same population' to have. The general form may be written as — xet < ps < Pant (4.15) where p, is the population of the sample town, pj is the population of the nearest neighbour, e, is the standard error of the distribution of city sizes, and x is the abscissa of the standard normal curve associated with the desired confidence level (Thomas, 1961, p. 405). See Appendix Table Al. To translate this into practical terms: If the sample town has a population of 105 persons, we can define the 'same population' for the nearest neighbour as lying between 72 and 159 inhabitants. Any difference in population within these limits may be regarded as due to chance and disregarded. The fact that the limits are asymmetric about 105 is due to the characteristic log-log curve of the population of Iowa towns. (b) Spacing and cluster size. Using this definition, Thomas (1961) investigated the relationships between population and spacing between settlements 'of the same size' for 89 sample towns in Iowa (Figure 4.18). Statistical investigation showed, as expected, a positive association between the logarithms of distance and population size, although the proportion of distance variation 'explained' by size was only about one third ye 0.35). In a follow-up study, Thomas (1962) was able to test his findings on the 1950 population against the five earlier census records for this century. He found a surprising degree of stability in the distance-size relationship. Only for the 1900 census did the degree of