## Rectifying Latitude

An Auxiliary Latitude which gives a sphere having correct distances along the meridians. It is denoted (or ) and is given by

 (1)

is evaluated for at the north pole (), and is given by
 (2)

A series for is
 (3)

and a series for is
 (4)

where
 (5)

The inverse formula is
 (6)

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, pp. 125-128, 1921.