A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Paul Bedel
Date: 2019 Jan 11, 06:35 -0800
Hi Lars and thank you very much for your very interesting posts. Here are other developments about Gerbault's calculations.
The formula used in "Johnson's Tables" maybe something like: hav(HA) = [hav(90°- Alt) - hav(colat - PD)] / [hav(colat + PD) - hav(colat - PD)] = A/B where PD is the polar distance 90° - dec. This formula was found by H. B. Goodwin in 1910 and discussed in the "Nautical Magazine". Logs of A and B can be found directly in a double entry table correctly arranged with direct and complementary arguments. Following your idea, a constant (about 0.7276) is added to the logs.
Gerbault made his observations at about 22h 10 civil local time. How did he see the horizon line ?... the moon first quarter was on 1st of april!
I think so the tables used are not from A. C. Johnson (1828-1909) who was Naval Instructor in the Royal Navy and not sub-lieutenant, so I'll try to have more informations on Gerbault and his methods of navigation. First, I'll re-read his books about his Atlantic crossing and first circumnavigation: "Seul à travers l'Atlantique" (1924), "A la poursuite du Soleil" (1929) and "Sur la route du retour"(1929).
Paul, 48° 40' N, 1° 59' W.