Both Jed and Steve Lawrence responded to my comments about Chinese navigation and longitude measurement. Rather than annotate each post, I will comment on both, based on Menzies' book.
Longitude is based on measurement of time from some reference point. In the contest between Harrison and the British astronomers which I have read about, reference was made to a complex mathematical method using lunar observation. I don't know details. Menzies notes, and many agree, that the Chinese were master astronomers who knew the sky very, very well. They made precision 'sundials' and water clocks which were calibrated with the sundials. At a landfall on a distant shore, an observatory could be built which would accurately define the zenith and the local meridian. An eclipse of the moon gave precise moments which could be related to the position against the fixed stars. This event was simultaneously observable from the Chinese reference observatory. When sailors returned it was possible to accurately determine the angular relationship on the surface of the earth, and thereby the longitude. The Polynesians also navigated across long stretches of ocean, based on the night sky and the rhythm of the waves as refracted from distant islands, and other factors. Lunar eclipses aren't often convenient. The transit of Jupiter by one of its moons is a much more frequent event, simultaneously observable at two points, and the relative longitude established back home. Mike Carrell
