The present paper considers sampling from a stream of particulate material, where primary sampling units are increments of a specified volume or mass comprising of individual particles of the material sampled. The concepts and methods employed in this area were first developed systematically by Gy [Gy, P., 1982. Sampling of Particulate Materials-Theory and Practice. Elsevier, Amsterdam] for the case where increments were selected at equidistant mass or time intervals. The existing methodology requires further extension to cases where the increments are selected at irregularly spaced intervals. An extension is given in the present paper for particulate sampling at irregularly spaced mass intervals. The methods developed are general and apply equally to other cases where the concepts of short-term and long-term variation are readily adapted and the structure of a systematic sampling can, in principle, be implemented. Specific contributions made in the paper to the area of sampling particulate materials are: (i) a weighted estimator of the critical content of a lot for dealing with the unequally spaced assays, (ii) a modification of the usual increment variance by introducing corresponding weights in the formula, (iii) an estimator of the long-term variance derived from a modified increment variance, and (iv) a measure of precision of the weighted estimator. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.