Some Points in the Methodology of Urban Population Distributions

For some operational problems concerned with urban populations, the actual location of population within each city is not of primary importance. For such problems, it may be best to proceed in terms of the function A(D) defined as being the city area over which the population density ≧ D. Knowledge of this function enables a suitable symmetric representation of a city of fairly arbitrary form to be determined, and Weiss' problem of maximizing the population in a given total area chosen from the regions of a sequence of cities to be tackled in reasonably general terms. General equations are given for this problem. Simple cities of nonstandard form may satisfy a generalization of Sherratt's form, to which a number of Sherratt's results are easily extended. When distance from the (unique) city center is important—such as in a single-bomb centrally-directed nuclear attack—Clark's type of representation is appropriate. Equations for the expected number of casualties in such an attack are given for Sherratt's (asymmetric) and Clark's type of city.