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THE ‘characteristic’ defined by Yule1and the ‘index of diversity’ defined by Fisher2are two measures of the degree of concentration or diversity achieved when the individuals of a population are classified into groups. Both are defined as statistics to be calculated from sample data and not in terms of population constants. The index of diversity has so far been used chiefly with the logarithmic distribution. It cannot be used everywhere, as it does not always give values which are independent of sample size; it cannot do so, for example, when applied to an infinite population of individuals classified into a finite number of groups. Williams3has pointed out a relationship between the characteristic and the index of diversity when both are applied to a logarithmic distribution. The present purpose is to define and examine a measure of concentration in terms of population constants.