The sampling of a run-of-mine (ROM) ore with the objective of controlling the fundamental variance associated with the sampling step is a poorly understood subject. Finding the effective sampling constant by repetitive sampling to establish the variance between nominally identical subsamples of a given mass of the ore is a laborious, time-consuming and very expensive exercise._x000D_
In this paper, the run-of-mine ore is modelled using three components: ore, waste, and relatively fine material which shows significant liberation of the mineral phase(s) carrying the target analyte. The expression for the sampling constant of the mixture is developed from first principles. The form of the equation provides insight into the factors that are important in controlling the magnitude of the sampling constant and hence the fundamental uncertainty associated with a given mass of sample._x000D_
The controlling factors are shown to be the size distribution of the ore/waste mixture, the proportion of waste mixed with the ore and the extent of liberation and the size distribution of the liberated material in the finer fractions.