A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Jouan
Date: 2017 Jul 3, 04:18 -0700
Let me send again to Navlist members a slide that I presented** in Marine Museum of Paris on May 2014 (last time was a year ago, I guess). From pages 22-26 of his book, you can see how Antoine Yvon-Villarceau was visionary.
Here is a short translation of the text in the slide:
"x, y, z represent rectangular coordinates of the location, according to a linear scale, with the Earth radius taken as unity (=1). So the 2 first equations generates 2 planes, and the last equation the Earth sphere itself. Therefore, the problem is reduced to compute the intersection of 2 planes with a sphere. But, for practical use, we don't recommend to use the given formulas, because of the associated computing difficulties [on 1877!] We propose a method which is less direct, but quicker to be applied."
The proposed method was Marcq Saint-Hilaire's one, using chronometers at sea, with a lot of justifications (noticeably in part II, by AVED de MAGNAC). Notice that cartesian equations were coming back only one century later, to be solved by matrix algebra (first time on 1976).
** The title of my contribution was "Navigation aux astres, aux satellites, et hybridation : de Villarceau à nos jours"
Navigating with stars, with satellites and hybridizing: from Villarceau to nowadays.