The following equations place the *x*-Axis of the projection on the equator and the
*y*-Axis at Longitude , where is the Longitude and is the
Latitude.

(1) | |||

(2) | |||

(3) | |||

(4) | |||

(5) | |||

(6) |

The inverse Formulas are

(7) | |||

(8) |

where is the Gudermannian Function. Loxodromes are straight lines and Great Circles are curved.

An oblique form of the Mercator projection is illustrated above. It has equations

(9) | |||

(10) |

where

(11) | |||

(12) | |||

(13) |

The inverse Formulas are

(14) | |||

(15) |

There is also a transverse form of the Mercator projection, illustrated above. It is given by the equations

(16) | |||

(17) | |||

(18) | |||

(19) |

where

(20) | |||

(21) |

Finally, the ``universal transverse Mercator projection'' is a Map Projection which maps the Sphere into 60 zones of 6° each, with each zone mapped by a transverse Mercator projection with central Meridian in the center of the zone. The zones extend from 80° S to 84° N (Dana).

**References**

Dana, P. H. ``Map Projections.'' http://www.utexas.edu/depts/grg/gcraft/notes/mapproj/mapproj.html.

Snyder, J. P. *Map Projections--A Working Manual.* U. S. Geological Survey Professional Paper 1395.
Washington, DC: U. S. Government Printing Office, pp. 38-75, 1987.

© 1996-9

1999-05-26