Available recommendations on the methodology of determining the weight of samples for sieve analysis are not always justified and controversial.In theoretical studies on this issue, some methodological provisions are not convincing enough. In particular, the fundamental principle of determining the weight of the sample, which states: “It is required to determine the weight of the sample, the sieve analysis of which with a probability, however close to one, will give a result dcv, lying within (1 ± 0.02) Dcv. Since the sample is intended to determine in bulk material quantitative ratios of grains of different sizes, it is necessary that the number of grains in each class of sample material corresponds to their actual numerical proportion in the sample mass, which should be the basis for calculating the weight of the sample.

The weight of a sample taken from mined minerals and their products is usually determined by empirical formulas of the form Q = kda number of researchers have developed and offer theoretical formulas for this purpose, the conclusion of which is based on the regularities of mass phenomena studied by the methods of mathematical statistics, in particular, on the regularities of Gauss, Poisson, binomial frequency distributions, as well as the theory of errors.

Reduction by successive division into two more or less equal parts is a common operation in mineral sampling. The weight limit to which a particular material can be reduced depends on the particle size distribution, the content of the component to be determined (useful), the magnitude and degree of irregularity of the phenocrysts of that component in the host rock, the specified accuracy of reduction, and the degree of confidence in obtaining a sample with the specified accuracy. However, until recently, the mathematical dependence of the reduction weight limit on these parameters has not yet been established, although this iss. has been occupying the attention of specialists for many years. In the present work the results of experimental and theoretical researches are stated, which allowed to establish the regularity of distribution of mineral grains in the parts allocated by reduction and to find the mathematical dependence of the limiting weight of reduction (sample weight) on the main features of the sampled mineral.