Economical Algorithms for Mercator Transversal Projections.

The use of an intermediary sphere between the ellipsoid and the plane makes it possible to obtain algorithms withh finite formulas to replace the conventional calculation in the Gauss-Krueger or Transverse Mercator family of geodetic projections. In 1899 O. Schreiber used Gauss's second solution for the conformal spherical projection of the ellipsoid with the transverse projection of this sphere onto the plane so as to produce the map of Prussia. In this article the authors apply the same principle to three problems, with the advantage of being able to place the reference parallels of Gauss's second solution close to the given points. This proves to be most effective as a practical approximation to the conventional Mercator transverse (Mt) solution. The proposed algorithms are compared to the conventional ones using a programmable calculator. Refs.