On Mathematics of Navigational Calculations for Meridian Sailing

Meridian sailing is actually a special case of sailing uniquely determined by relative coordinates ',. In this note we discuss explicit finding of certain navigational parameters. These include loxodrome distance, rhumb line and geographic and geocentric latitude of a position on the globe surface. The latter is expressed in terms of the inverse incomplete elliptic integral of the third kind ; we discuss and survey certain traditional and recent methods of computation of this function.