Arc measurement

Arc measurement,

Arc measurement campaigns in Europe were the precursors to the International Association of Geodesy (IAG).^[4]

History

The first known arc measurement was performed by

(240 BC) between Alexandria and Syene in what is now Egypt, determining the radius of the Earth with remarkable correctness. In the early 8th century, Yi Xing performed a similar survey.^[5]

The French physician

).

Later arc measurements aimed at determining the

et al.).

. Bessel compiled several meridian arcs, to compute the famous Bessel ellipsoid (1841).

Nowadays, the method is replaced by worldwide

.

List of other instances

• 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

Determination

Assume the

of two endpoints, ${\displaystyle \phi _{s}}$ (standpoint) and ${\displaystyle \phi _{f}}$ (forepoint), are precisely at the midpoint of the meridian arc can then be determined as:

${\displaystyle R={\frac {{\mathit {\Delta }}'}{\vert \phi _{s}-\phi _{f}\vert }}}$

where ${\displaystyle {\mathit {\Delta }}'}$ is the

(MSL).

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

${\displaystyle {\mathit {\Delta }}}$ 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 ${\displaystyle {\mathit {\Delta }}}$ is reduced to the corresponding distance at MSL, ${\displaystyle {\mathit {\Delta }}'}$ (see: Geographical distance#Altitude correction).

Two arc measurements at different latitudinal bands serve to determine Earth's flattening.

See also

• Astrogeodesy
• Earth ellipsoid
• Geodesy
• Gradian § Relation to the metre
• History of geodesy
  • Spherical Earth § History
  • Meridian arc § History
  • Earth's circumference § History
• Meridian arc
• Paris Meridian

References