There are excellent web resources on the history and the mathematics of navigation. "The American Practical Navigator," first published by Nathaniel Bowditch in1802, is entirely downloadable from a site at Plymouth University. Norris Weimer at the University of Alberta has a page on The Mercator Conformal Projection with good historical links. Java applets for calculating meridional parts and for solving the Mercator sailing problem have been posted by Jacky Wong, webmaster of the Hong Kong Marine Department.
1. How to get from here to there?
A standard problem in navigation is: given the coordinates of two points on the earth's surface, to calculate how far and in what direction one should travel to get from one to the other.
Suppose we are traveling by air, or that the two points are on the same body of water with no obstacles in the way. This makes it a purely geometric problem.
There are in fact two traditional solutions to this problem. One sets the course along the the rhumb-line, the other along the great circle. "Mercator sailing" and "Great circle sailing" are the names for the two kinds of calculations involved. In this column we will describe the two solutions and explain how they are related.