The influence on gauge block length calibration attributed to changes in atmospheric pressure, as a result of altitude for example, has been described [1] in equation (1). The estimation established therein considered Young's modulus of elasticity E, which represents normal stress and normal strain per unit length; however, the length correction for pressure on an object in a bath of the atmosphere is more accurately described using the bulk modulus of elasticity K, which represents a volume effect. The relationship between Young's modulus and the bulk modulus is [2]

where K and E are in units of Pa, and σ is Poisson's ratio. The change in length ΔL of a gauge block of nominal length L by a pressure change of ΔP in Pa, is given by [3, 4]

For practical purposes K = 204 GPa and σ = 0.33 for steel gauge blocks.

Acknowledgments
The author thanks Jack Stone (National Institute for Standards and Technology, USA), Andrew Lewis (National Physical Laboratory, UK) Gerhard Bönsch (Physikalisch-Technische Bundesanstalt, Germany) and Jim Pekelsky (National Research Council Canada, Canada) for fruitful discussion.

References

[1] Decker J E 2001 Some important characteristics of gauge block artefacts for international comparison Metrologia 38 269-72
[2] Timoshenko S 1951 Theory of Elasticity 2nd edn (New York: McGraw-Hill) p 10
[3] Bayer-Helms F 1973 Über den Einfluss von Luftdruck und Gewichtskraft auf Endmasse PTB-Mitt. 2/73 97-8
[4] Darnedde H 1992 High-precision calibration of long gauge blocks using the vacuum wavelength comparator Metrologia 29 349-59