NavList:

Hanno, you wrote:
"One should be able, in theory, to determine longitude by the difference in time of the culminations of the moon and the sun, say."

Yes. Moon culminations were a popular, standard, and apparently accurate method of determining longitude at astronomical observatories for a few decades in the early nineteenth century. Then the telegraph arrived... 

By the way, back to longitude by lunar altitudes, yes, you can greatly improve this technique with an artificial horizon on land, but if you're on land, then lunar distances are that much easier. So why bother? Also longitude by lunar altitudes is only competitive if the Moon's "horns" are nearly horizontal so that its motion along its orbit leads to a significant variation in the altitude.

At sea, if anyone does ever lose GMT (in this century??! Hard to imagine...), the technique of longitude by lunar altitudes is nice and simple, and at least it's something interesting to experiment with. All you really have to do is work a three-body (or more) fix where one of the bodies is the Moon using two different GMTs separated by, let's say, eight minutes (which should amount to two degrees in longitude). If the GMT is nearly right, then all LOPs including the Moon will fall together in a nice little "cocked hat" fix, but if the GMT is considerably in error, the Moon LOP will not align. With most celestial bodies, changing the GMT simply shifts all of the LOPs east or west at the usual rate of four minutes per degree of longitude, but the Moon's position in its orbit changes rapidly enough that its LOP will not shift at the same rate. That's what this method aims to detect. It does work. The accuracy is reduced somewhat compared to ordinary "lunars" due to uncertainties in the horizon, and it is also only useful, as noted above, when the horns of the Moon are more or less horizontal (not a rare thing but of course on the day you need it, that's when this condition won't be met!). In fact, it's not even necessary to get a complete fix. Suppose I have the Moon near due east and a bright star or planet on almost the same azimuth. If I have the right GMT, the LOPs from both objects will fall on top of each other. Or if there's a slight angle between them, they will cross at my best estimated latitude (in nineteenth century terms, I could calculate local time from both objects and they should match). If this condition can be met, finding a star at nearly the same azimuth, then much of the uncertainty in the horizon is eliminated since we're using nearly the same horizon.

Frank Reed