Latitude in Snyder (page 15): For the "normal" Mercator projection (on the ellipsoid) this function defines the spacing of the parallels: if the length of the equator on the projection is (units of length or pixels) then the distance, , of a parallel of latitude from the equator is The isometric latitude is closely related to the conformal latitude : The formulae in the previous sections give the auxiliary latitude in terms of the geodetic latitude. The expressions for the geocentric and parametric latitudes may be inverted directly but this is impossible in the four remaining cases: the rectifying, authalic, conformal,
Latitude point on the surrounding sphere (of radius ) which is the projection parallel to the Earth's axis of a point on the ellipsoid at latitude . It was introduced by Legendre and Bessel who solved problems for geodesics on the ellipsoid by transforming them to an equivalent problem for spherical geodesics by using this smaller latitude. Bessel's notation, , is also used in the current literature. The parametric latitude is related to the geodetic latitude by: The alternative name arises from the parameterization of the equation of the ellipse describing a meridian section. In terms of Cartesian coordinates , the