NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Peter Blaskett
Date: 2024 Apr 12, 17:56 -0700
Jim Wyse, and others.
As to the longitude of the Oxford observations:
Thomas Hornsby was a fellow of Corpus Cristi College, and in 1763 was appointed Savilian Chair of Astronomy. Presumably he was observing in Corpus Cristi in 1766 as it is recorded he used his personal telescope from the window of his room. Also he did not move his quadrant to a new house in New College Lane because he could not get it up the stairs. This was well before the Radcliffe Observatory was conceived.
The longitude of Corpus Cristi College seems a likely site, and this is about 1° 15' 15" West. Thus the deduced longitude of Eclipse Island then would have been 57° 36' 15".
As to how the computations were done, there is a large article in Chauvenet Vol 1, chapter ten (X), 20 pages or more, which if you can wade through then 'you're a better man than I, Gunga Din'. Basically the time of equal Right Ascension of Sun & Moon are computed, and then go from that to correct for parallax in latitude and longitude.