Equations of coarseness characterization are increasingly widely used in solving practical problems related to the sampling and beneficiation of ores. Of the considerable number of mathematical expressions proposed, the equation of Prof. S. E. Andreev (see article) and the Rosin-Rammler exponential equation (see article) are the most widely used. Equations (1) and (2) are convenient for practical calculations, but they show good agreement with experience only for small size classes of grinding products. When it is necessary to estimate the particle size distribution of the largest fractions of the product, these equations are of comparatively little use. Equations (1) and (2) are so simple and coincide so well with experience for small values of x that it seemed natural to make an attempt to improve them in such a way that the area of application of these equations was expanded and their positive qualities were preserved. A possible solution of this problem is given below.