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A sensitivity mass is a small calibrated mass added to a loaded weighing instrument to determine its response to a known mass increment. NIST's double-substitution procedure calls this a sensitivity weight and uses it to establish sensitivity under the conditions of the comparison.^[ref] It supplies a local input step rather than a new determination of the entire load from zero.

Let an original comparator give indications $r_0$ before and $r_1$ after adding mass $m_{\mathrm{sw}}$. For a stable linear response over that increment,where $\Delta r$ is another indication difference near that working load. A constant additive zero cancels from each difference; instrumental drift or load-dependent response need not cancel.

For original indications $r_0=860$, $r_1=885$ and assigned sensitivity mass $10.020\mathrm{mg}$, the local response is about $2.495$ indication increments per milligram. A difference $\Delta r=7.5$ increments gives $\Delta m=3.006\mathrm{mg}$. Using only a nominal $10\mathrm{mg}$ label instead would give $3.000\mathrm{mg}$. The assigned mass and its measurement uncertainty, rather than the nominal label alone, enter the comparison.

The added step must be large enough to resolve reliably but remain within the response region relevant to the unknown/reference comparison. NIST specifies selection criteria and regularly spaced observations; it also requires the standards to have valid calibration information.^[ref] Keep handling, settling and environmental conditions consistent. A sensitivity mass does not by itself cancel buoyancy, temperature effects or uncertainty in the main measurement standard. Those contributions remain in the full double substitution weighing model.

A substitution measurement method compares an unknown with a reference by placing them successively in the same relevant position of a measuring system. The comparison seeks a match or measures a difference while retaining as much of the system response as possible. The VIM lists substitution among measurement methods; the detailed sequence belongs to the measurement procedure.^[ref]

For a physical application, NIST's double substitution weighing procedure compares a standard and an unknown of the same nominal mass twice, using a weighing instrument as a comparator. It also determines response with a known sensitivity mass and includes measurement-assurance checks.^[ref] The measurement standard supplies the reference value; the comparator need not establish the whole mass independently from its own zero.

An original simplified drift model shows why sequence matters. Let a comparator indication at equally spaced time index $t$ bewith fixed response coefficient $a$, additive offset $b$ and linear instrumental drift $d$. Observe standard S at $t=0$, unknown X at $t=1,2$, and S again at $t=3$. The mean X indication and mean S indication have the same mean time $3/2$, givingBoth the constant offset and the stipulated linear drift cancel. For $m_S=m_0=100\mathrm{g}$, $a=500{\mathrm{g}}^{-1}$, $b=10$ and $d=2$, an unknown $m_X=100.004\mathrm{g}$ gives indications $10,14,16,16$. Their paired means differ by two, recovering $0.004\mathrm{g}$.

This teaching sequence isolates one cancellation mechanism; it is not the full NIST procedure. Nonlinear drift, unequal timing, changing response or different positioning can defeat it. NIST's procedure separately addresses buoyancy and uncertainty contributions.^[ref] A close match does not remove the reference's measurement uncertainty or establish that the substitution left every relevant condition unchanged.