CONNECTION BETWEEN THE ARC TO CHORD CORRECTIONS AND THE SPHERICAL (ELLIPSOIDAL) EXCESS

On the basis of the simple relation between spherical excess and arc to chord correction, formulas to compute the arc to chord correction for different map projections can be derived. If we know the arc to chord correction, however, the spherical/ellipsoidal excess and thus the area of figures on the surface of the sphere or ellipsoid, which are bounded by orthodromes, can be computed simply. Therefore we do not need to know the datum surface coordinates of a figure determined by its corner points' coordinates on a conformal map projection