rhumb line), maintaining a constant latitude and recording regular estimates of the distance sailed until evidence of land was sighted. Generalizations On the Riemann sphere The surface of the Earth can be understood mathematically as a Riemann sphere, that is, as a projection of the sphere to the complex plane. In this case, loxodromes can be understood as certain classes of Möbius transformations. Spheroid The formulation above can be easily extended to a spheroid. The course of the rhumb line is found merely by using the ellipsoidal isometric latitude. In formulas above on this page, substitute the conformal latitude on the ellipsoid for the latitude on the sphere. Similarly, distances are found by multiplying the ellipsoidal meridian arc length by the secant of the azimuth. See also Great circle Geodesics on an ellipsoid Great ellipse Isoazimuthal Rhumbline network Seiffert's spiral Small circle References Note: this article incorporates text from the 1878 edition of The Globe Encyclopaedia of Universal Information, a work in the public domain Further reading External links Constant Headings and Rhumb Lines at MathPages. RhumbSolve(1), a utility for ellipsoidal rhumb line calculations (a component of GeographicLib); supplementary documentation. An online version of RhumbSolve. Navigational Algorithms Paper: The Sailings. Chart Work - Navigational Algorithms Chart Work free software: Rhumb line, Great Circle, Composite sailing, Meridional parts. Lines of position Piloting - currents and coastal fix. Mathworld Loxodrome. Cartography Spirals Spherical curves Navigation Geodesy