Inside SOP 4: double substitution, the workhorse of mass calibration

Ask a mass laboratory how it actually compares an unknown weight to a standard and the answer, most of the time, is double substitution — the procedure NIST documents as SOP 4 in the library here.

The idea is to make the balance a comparator rather than a scale. The standard and the unknown are weighed in an S–X–X–S sequence on the same balance within a few minutes, so the result depends on the small observed differences, not on the balance's absolute calibration. Drift that is linear in time largely cancels; a sensitivity weight converts the difference readings into mass units. The companion single-substitution procedure (SOP 7) trades a little uncertainty for speed by halving the observations.

The practical judgment is choosing when each design is enough: echelon of the weights, the tolerance being defended, and whether air buoyancy corrections are applied all feed that choice. The full procedure — including the data reduction and the uncertainty treatment — is in the library, page-searchable, with OIML R 111 defining the weight classes the results are judged against.