= Vernier zero correction
{c}
{title2=$L=r-z$}
A \b[Vernier zero correction] removes an indicated offset observed at a known zero setting of a <Vernier scale>. If the raw indication is $r$ and the indication at true zero is $z$, the additive model gives
$$
L=r-z.
$$
The zero error is $z$; the correction applied to a later reading is its negative. This model addresses an offset, not every possible scale or contact error.
For an original signed example, a raw reading $r=12.35\,\mathrm{mm}$ with closed-jaw indication $z=+0.10\,\mathrm{mm}$ gives $L=12.25\,\mathrm{mm}$. If the zero indication is instead $-0.10\,\mathrm{mm}$, the corrected reading is $12.45\,\mathrm{mm}$. A negative zero indication therefore requires adding its magnitude. It does not imply a negative object length.
The reference setting must represent the intended zero: clean, properly contacting outside faces on a <caliper> are one example. Record the actual signed indication and the scale convention, rather than relying on a memorized rule about which engraved zero lies to the left. The manufacturer guide explains the coincidence reading and identifies jaw tilt, force and viewing geometry as separate error sources.<Quick Guide to Precision Measuring Instruments: Calipers by Mitutoyo>[printed pp. 16–17, scale reading and Sources of Error]{ref}
For standard uncertainties, the additive model gives
$$
u^2(L)=u^2(r)+u^2(z)-2\operatorname{cov}(r,z).
$$
With stipulated independent $u(r)=0.03\,\mathrm{mm}$ and $u(z)=0.02\,\mathrm{mm}$, the combined value is approximately $0.0361\,\mathrm{mm}$. Subtracting a measured offset does not make that offset known exactly. Correlation can matter when both observations share an uncertain reference or drift contribution.<Guide to the expression of uncertainty in measurement by JCGM>[§5.2, correlated input estimates]{ref}
A second reference checks the limitation. Suppose true zero reads $0.10\,\mathrm{mm}$ but a known $50.00\,\mathrm{mm}$ separation reads $50.60\,\mathrm{mm}$. Removing the zero offset leaves $50.50\,\mathrm{mm}$, still $0.50\,\mathrm{mm}$ high. A model $r=aL+z$ would have $a=1.01$ here. <Measurement calibration> across the working interval is needed to distinguish scale error from a zero correction, with the relevant <measurement uncertainty> retained.
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