Editing Arc measurement (section)

==Determination==
Assume the [[astronomic latitude]]s of two endpoints, <math>\phi_s</math> (standpoint) and <math>\phi_f</math> (forepoint) are known; these can be [[latitude determination|determined]] by [[astrogeodesy]], observing the [[zenith distance]]s of sufficient numbers of [[star]]s ([[meridian altitude]] method). 

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:
:<math>R = \frac{\mathit{\Delta}'}{\vert\phi_s - \phi_f\vert}</math>
where the latitudes are in radians and <math>\mathit{\Delta}'</math> is the [[arc length]] on [[mean sea level]] (MSL).

Historically, the distance between two places has been determined at low precision by [[Pacing (surveying)|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 (surveying)|baseline]] and a [[triangulation network]] linking [[Benchmark (surveying)|fixed points]]. The [[meridian distance]] <math>\mathit{\Delta}</math> 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 <math>\mathit{\Delta}</math> is reduced to the corresponding distance at MSL, <math>\mathit{\Delta}'</math> (see: [[Geographical distance#Altitude correction]]).