= Gauge block wringing
\b[Gauge block wringing] joins suitably finished measuring faces by bringing them into intimate contact with a controlled sliding or twisting motion. The resulting adhesion lets <gauge blocks> form a composite <length standard> or contact an auxiliary plane for <interferometry>. The contact layer is part of the length convention: a calibrated block length includes one wringing-layer contribution.<The Gauge Block Handbook by Ted Doiron and John S. Beers>[§2.2.2, Nomenclature and Definitions; Appendix B, Gauge Block Wringing]{ref}
Adhesion is not explained adequately by saying that air was removed and atmospheric pressure alone holds the blocks together. NIST's handbook describes multiple surface- and fluid-dependent contributions, including <surface tension>, and warns that film thickness varies with surface condition and time. It does not supply a universal predictive film model.<The Gauge Block Handbook by Ted Doiron and John S. Beers>[Appendix B, Physics of Wringing Films, printed pp. 138–139]{ref}
An original bookkeeping model explains the length convention. Let $g_i$ be a block's geometric face separation and let $w_i$ be the effective layer contribution in its calibration, so its defined length is $l_i=g_i+w_i$. If a stack of $n$ blocks is wrung to an auxiliary plane, it has $n-1$ internal contacts and one base contact. Its top height can be written
$$
H=\sum_{i=1}^{n}g_i+\sum_{j=0}^{n-1}w'_j,
\qquad
H-\sum_{i=1}^{n}l_i=\sum_{j=0}^{n-1}w'_j-\sum_{i=1}^{n}w_i.
$$
Thus compatible contacts can make defined lengths additive without treating every interface as an additional correction beyond the certificates. Differences between calibration and use remain a <wringing-film uncertainty>.
For three stipulated blocks each carrying an effective $10\,\mathrm{nm}$ calibration contribution, three equivalent contacts contribute the same $30\,\mathrm{nm}$ already counted in their defined lengths. If one actual contact contributes $25\,\mathrm{nm}$ instead, the height in this simplified model differs by $15\,\mathrm{nm}$. These chosen values illustrate the convention; they are not a measured stack or a universal film specification.
Experimentally, NIST describes viewing a block wrung to a transparent optical flat: a uniform contact appearance supports a satisfactory wring, while coloured or bright regions indicate poor contact. Rewringing and checking the optical result tests an interface contribution that merely adding nominal lengths would miss.<The Gauge Block Handbook by Ted Doiron and John S. Beers>[§3.2.1, Flatness Measurements]{ref} Cleanliness, surface damage and <thermal expansion> during handling still affect the comparison. A visibly adhering stack is not, by itself, proof of the required dimensional accuracy.
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