Arc measurement, sometimes degree measurement (German: Gradmessung, after the gradian), is the astro-geodetic determination of the local radius of curvature of the figure of the Earth by determining the difference in astronomical latitude and longitude between two locations, the arc length between which is known. The most common instantes, meridian arc measurements, involved only astronomical latitude and the meridian arc length, although longitude (parallel) and oblique arc measurements are also possible.
The first known arc measurement was performed by Eratosthenes (240 BC) between Alexandria and Syene in what is now Egypt, determining the radius of the Earth with remarkable correctness. The Dutch geodesist Snellius (~1620) repeated the experiment between Alkmaar and Bergen op Zoom using more modern geodetic instrumentation (Snellius' triangulation).
Later arc measurements aimed at determining the flattening of the Earth ellipsoid by measuring at different geographic latitudes. The first of these was the French Geodesic Mission, commissioned by the French Academy of Sciences in 1735–1738, involving measurement expeditions to Lapland (Maupertuis et al.) and Peru (Pierre Bouguer et al.).
Struve measured a geodetic control network via triangulation between the Arctic Sea and the Black Sea, the Struve Geodetic Arc. Bessel compiled several meridian arcs, to compute the famous Bessel ellipsoid (1841).
- Al-Ma'mun's arc measurement
- Posidonius' arc measurement
- Swedish–Russian Arc-of-Meridian Expedition
- Picard's arc measurement
- Dunkirk-Collioure arc measurement (Cassini, Cassini, and de La Hire)
- Dunkirk-Collioure arc measurement (Cassini de Thury and de Lacaille)
- Meridian arc of Delambre and Méchain
- West Europe-Africa Meridian-arc
- De Lacaille's arc measurement
- Fernel's arc measurement
- Norwood's arc measurement
- Boscovich and Maire's arc measurement
- Maclear's arc measurement
- Hopfner's arc measurement
- Earth ellipsoid
- History of geodesy
- Meridian arc
- Paris Meridian
- Torge, W.; Müller, J. (2012). Geodesy. De Gruyter Textbook. De Gruyter. p. 5. ISBN 978-3-11-025000-8. Retrieved 2021-05-02.
- Jordan, W., & Eggert, O. (1962). Jordan's Handbook of Geodesy, Vol. 1. Zenodo. http://doi.org/10.5281/zenodo.35314
- Torge, W. (2008). Geodäsie. De Gruyter Lehrbuch (in German). De Gruyter. p. 5. ISBN 978-3-11-019817-1. Retrieved 2021-05-02.