THERE has been, to some extent, a divergence of purpose between the work of mathematical statisticians and mathematical economists. The former have studied variation, such as the form and measurement of frequency groups, and the correlation between two or more variables; the latter have studied equations of equilibrium, in which the data represent totals, margins, the representative, the average-single quantities in general-where heterogeneity does not enter into the argument. Econometricians have, indeed, worked on variation and covariation, but most attention has been given to examples where time is one of the variables, that is to time series; and the relationships obtained have been in the form of a demand curve in one group of studies, to periodic curves in time in another, and to correlation between quantities which are paired in time, but not variable at a given instant of time. I wish to direct attention to a field which has not been thoroughly explored, and in which, so far as I know, little work is being done. What are the forces which produce the variation found in common phenomena, how far are they economic, what changes in frequency distributions are produced by economic forces, how can they best be described or measured? To name one example, which has already been studied: Incomes in certain circumstances are distributed in accordance with Pareto's equation. What has produced this particular form; is the form modified by economic change, or rather by changes in the sociological or legal spheres; how can the effects of these best be measured? Variation has been studied in many fields and it may be well to mark off those which are not primarily economic from those which are. We will exclude anthropometry and biometry, and statistics of mortality and morbidity. Demographic statistics generally would enter only in their economic aspects, such as age distribution in occupations, and concentration of population. Within the economic sphere proper, there are many distributions which have been the subject of careful work: price changes in time, local variations in price, prices of securities, size of industrial firms, rates of profit and dividends, ratio of
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