A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Paul Bedel
Date: 2019 Jan 13, 02:43 -0800
Thank you very much, Lars. I think you have the good answer for the "arcs". Logs are still mysterious and I'm going to continue the search; I'll tell you my results later (if there is one ...).
As said in the Bowditch 1977, page 564, the Goodwin's tables "alpha beta gamma navigation tables" were first built to calculate vers(AH) = [cos(Lat - Dec) - cos(90° - H)]/cos(Lat).cos(Dec) with the trick described by the American Mathematical Society reviewer. Martelli used the same formula, involving hav(AH) and other tricks.
It's true, sights taken in moon shine are very rough, but if you have nothing else they can be used to have an idea of the fix with uncertainty (maybe 10 to 15').