History of longitude instant in time, local solar time at a location varies by one hour for every 15 degrees change of longitude (360 degrees divided by 24 hours), there is a direct relationship between time and longitude. If the navigator knew the time at a fixed reference point when some event occurred at the ship's location, the difference between the reference time and the apparent local time would give the ship's position relative to the fixed location. Finding apparent local time is relatively easy. The problem, ultimately, was how to determine the time at a distant reference point while on a ship.
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