An Auxiliary Latitude which gives a Sphere equal Surface Area relative to an Ellipsoid. The
authalic latitude is defined by

(1) |

(2) |

(3) |

(4) |

The inverse Formula is found from

(5) |

(6) |

(7) |

**References**

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. 16, 1987.

© 1996-9

1999-05-25