= Sensitivity mass
= Sensitivity weight
{synonym}
A \b[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.<Weighing by Double Substitution by National Institute of Standards and Technology>[SOP4–2019, p3, Summary and apparatus; pp6–7, selection and use of sensitivity weight]{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 $m_{\rm sw}$. For a stable linear response over that increment,
$$
K=\frac{r_1-r_0}{m_{\rm sw}},\qquad
\Delta m=\frac{\Delta r}{K}
=m_{\rm sw}\frac{\Delta r}{r_1-r_0},
$$
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.<Weighing by Double Substitution by National Institute of Standards and Technology>[p1, prerequisites; p3, Summary; pp6–8, sensitivity selection and observations]{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.
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