The Sampling Fundamental Error: Why sample mass and size matter.

Pierre Gy’s Theory of Sampling (TOS) provides the mathematical framework for understanding why sample mass directly affects analytical error. The Fundamental Sampling Error (FSE) is the minimum error introduced when extracting a small portion from a larger heterogeneous lot.
FSE is governed by:
– Fragment size (d): coarser particles → higher heterogeneity → larger FSE.
– Liberation factor (l): the degree to which the mineral of interest is freed from the host matrix.
– Sample mass (M): FSE decreases as mass increases.
– Constitution heterogeneity (CH): intrinsic variability within the lot.
This is why crushing and pulverisation are not merely mechanical steps — they are variance reduction procedures. Reducing fragment size from d95=2mm to d95=75µm can reduce FSE by two orders of magnitude on the same analytical portion mass.
In practice, a 50g analytical pulp subsample from a coarsely crushed rock will carry higher FSE than the same 50g taken after fine pulverisation. Grade variability observed between field duplicates and preparation duplicates often traces back to insufficient size reduction rather than instrument performance.
For nugget-effect elements like gold, platinum, or coarse native copper, the FSE problem is compounded. Screen fire assay methods and large-mass leach digestions exist precisely to address this.