In statistical work which deals with integral variates, the data frequently appear in the form of ratios, or unreduced proper fractions, e.g. sex- and fecundity-ratios; and to facilitate comparison these are arranged in classes, all the ratios falling within the same class being considered as equivalent. These classes must, as far as possible, contain an equal number of the ratios. Further, in certain fields the different kinds of ratios do not all occur with the same frequency, that is, one denominator will occur more frequently than another, without any reference to the number of fractions having this denominator.