Studies in mathematical theory of human relations. II

In continuation of previous studies, relations are studied between two classes of population, of which one is characterized by a much greater ability to organize and supervise the productive activities of the other. Under some special and rather simple assumptions, it is shown that this kind of interreaction results first in an increase of the ratio of the cumulative results of productive activities for the two classes in favor of the first. With time, however, this ratio reaches a maximum and declines. An expression for the life span of such organized classes is obtained.In the second section, a study is made of possible non-uniformities of spatial distribution of the population. Some possible applications are made to the theory of the variation of the ratio of urban to rural population, showing how that ratio may increase with increasing total population.