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Parametric Latitude

An Auxiliary Latitude also called the Reduced Latitude and denoted $\eta$ or $\theta$. It gives the Latitude on a Sphere of Radius $a$ for which the parallel has the same radius as the parallel of geodetic latitude $\phi$ and the Ellipsoid through a given point. It is given by


In series form,

\eta=\phi-e_1\sin(2\phi)+{\textstyle{1\over 2}}{e_1}^2\sin(4\phi)-{\textstyle{1\over 3}}{e_1}^3\sin(6\phi)+\ldots,


e_1\equiv{1-\sqrt{1-e^2}\over 1+\sqrt{1-e^2}}.

See also Auxiliary Latitude, Ellipsoid, Latitude, Sphere


Adams, O. S. ``Latitude Developments Connected with Geodesy and Cartography with Tables, Including a Table for Lambert Equal-Area Meridional Projections.'' Spec. Pub. No. 67. U. S. Coast and Geodetic Survey, 1921.

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, p. 18, 1987.

© 1996-9 Eric W. Weisstein