Geodesy the ellipsoid varies with latitude, being the longest at the pole and the shortest at the equator as is the nautical mile. A metre was originally defined as the 10-millionth part of the length from equator to North Pole along the meridian through Paris (the target was not quite reached in actual implementation, so that is off by 200 ppm in the current definitions). This means that one kilometre is roughly equal to (1/40,000) * 360 * 60 meridional minutes of arc, which equals 0.54 nautical mile, though this is not exact because the two units are defined on different
Mercator 1569 world map 12 by using compass roses on the equator and it is only in Legend 10 that he introduces the Organum Directorium and also addresses the inverse problems: given the initial point and the direction and distance of the second find the latitude and longitude of the second. Mercator's construction is simply an evaluation of the rhumb line distance in terms of the latitude difference and the azimuth as If the latitude difference is expressed in arc minutes then the distance is in nautical miles. In later life Mercator commented that the principles of his map had not been understood by