Spheroidal Sailing and the Middle Latitude

The standard formulae, assuming a spherical Earth, for converting distance on a rhumb-line track into differences of latitude and longitude are: where C is the course and α is known as the middle latitude. It is approximately the mean latitude when both points are on the same side of the equator; tables of the correction to be applied to the mean latitude to give the middle latitude are given in most collections of nautical tables.