DLo = p sec Lm
p = DLo cos Lm
The mean latitude (Lm) is half the arithmetical sum of the latitudes of two places on the same side of the equator. The mean latitude is labeled N or S to indicate whether it is north or south of the equator. If a course line crosses the equator, that part on each side (the north latitude and south latitude portions) should be solved separately. This sailing, like most elements of navigation, contains certain approximations which produce answers somewhat less accurate than those by more rigorous solutions. For ordinary purposes, the results are more accurate than the navigation of the vessel using them. From time to time suggestions have been made that a correction be applied to eliminate the error introduced by assuming that the meridians of the point of departure and of the destination converge uniformly (as the two sides of a plane angle), rather than as the sine of the latitude (approximately). The proposed correction usually takes the form of some quantity to be added to or subtracted from the middle latitude to obtain a "corrected middle latitude" for use in the solution. Tables giving such a correction have been published for both spherical and spheroidal earths. The actual correction is not a simple function of the middle latitude and the difference of longitude, because the basic formulas of the sailing are themselves based upon a sphere, rather than a spheroid. The use of such a correction is misleading, and may introduce more error than it eliminates.
Example - A vessel steams 1,253.0 miles 0n course 070 from Lat. 15-17.0 N, Long. 151-37.0 E.
Required - (1) Latitude and (2) Longitude of the point of arrival.
Solution - By computation: (1) l = D cos C; p = D sin C (2) DLo = p sec Lm.
To see solution go to "CLICK HERE TO VIEW FORM" for MID - LATITUDE FORM