In 1599 the first published table of meridional parts which provided the basis for the most accurate of rhumb lines sailings,Mercator sailing. Mercator sailing provides a mathematical solution of the plot as made on a Mercator chart. It is similar to plane sailing , but uses meridional difference and difference of longitude in place of difference of latitude and departure.
Mercator sailing problems are solved graphically when measurement is made on a mercator chart, they can also be solved mathematical. Table 5 in Bowditch (1981 green edition) gives the Meridional parts, in this table the meridional parts aretabulated to one decimal place for each minute of latitude from the equator to the poles. For mathematical solution the formulas
For course angle
tan C = DLo
m DLo = m tan C
Solution for distance
D = l sec C
Solution can also be made by compution by traverse Table 3 in Bowditch, you enter Table 3 with your course and distance to find D. Lat.
