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Francis Upchurch wrote:

I've most likely got this completely wrong, but what about doing a kind of "lunar" with a sextant horizontal, measure angle between Polaris and another stars? Would that give us accurate Azimuths for this method? Experts please comment.
Francis

Despite your last sentence, I would comment that a theodolite would be the more natural instrument for azimuth measurements. That would be on land, of course. I see no way to measure azimuths with any accuracy at sea. I do not see how you could use a sextant to measure azimuths except for objects very near the horizon, which would limit such a technique to very low latitudes in the Northern hemisphere using Polaris.

On land, it is (was) fairly routine practice to use azimuth measurements of Polaris or the Sun to reference a survey to true North. This was from a known latitude and longitude, of course. Where you are attempting to find latitude and longitude, it is always far more efficient to use the altitudes of celestial bodies rather than azimuths, even with a theodolite.

Geoffrey Kolbe