  The auxiliary latitudes are essential tools in cartography. This paper
summarizes methods for converting between them with an emphasis on providing
full double-precision accuracy. This includes series expansions in the third
flattening, where the truncation error is precisely measured and where
estimates of the radii of convergence are given. Also new formulas are given
for computing the rectifying and authalic latitudes with minimal roundoff
error.

Geophysics