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Arc measurement, sometimes called degree measurementJordan, W., & Eggert, O. (1962). Jordan's Handbook of Geodesy, Vol. 1. Zenodo. http://doi.org/10.5281/zenodo.35314 (), is the astrogeodetic technique of determining the radius of Earth and, by extension, its circumference. More specifically, it seeks to determine the local Earth radius of curvature of the figure of the Earth, by relating the latitude difference (sometimes also the longitude difference) and the geographic distance (arc length) Surveying between two locations on Earth's surface. The most common variant involves only astronomical latitudes and the meridian arc length and is called meridian arc measurement; other variants may involve only astronomical longitude ( parallel arc measurement) or both geographic coordinates ( oblique arc measurement). Arc measurement campaigns in Europe were the precursors to the International Association of Geodesy (IAG). Nowadays, the method is replaced by worldwide and by satellite geodesy.
The French physician Jean Fernel measured the arc in 1528. 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.).
Friedrich Struve measured a geodetic control network via triangulation between the Arctic Sea and the Black Sea, the Struve Geodetic Arc.
Then, the empirical Earth's meridional radius of curvature at the midpoint of the meridian arc can then be determined inverting the great-circle distance (or circular arc length) formula:
Historically, the distance between two places has been determined at low precision by pacing or odometry.
High precision land surveys can be used to determine the distance between two places at nearly the same longitude by measuring a baseline and a triangulation network linking fixed points. The meridian distance from one end point to a fictitious point at the same latitude as the second end point is then calculated by trigonometry. The surface distance is reduced to the corresponding distance at MSL, (see: Geographical distance#Altitude correction).
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