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Jim Wyse, et al

I have located a method of finding the longitude using a solar
eclipse described by "Kerigan" in 'The Complete Mathematical
and General Navigation Tables'. Available here:


https://www.google.com.au/books/edition/The_Complete_Mathematical
_and_General_Na/l5IAAAAAMAAJ?hl=en&gbpv=1&dq=kerigan+longitude
+by+solar+eclipse&pg=PA531&printsec=frontcover

A fully worked example is given, beginning page 557, Problem XVI.

Using "EclipseWise.com" by Fred Espenak, the modern values of the
example are shown in file1.


Using Stellarium at 16:32:04, a Local Apparent Time of 4:23:18
is found.

EOT is 3m 57s So Local Mean Time is 4:19:21

Assumed diff long of 3d 11’ = 0:12:44 of time

Applied to LMT gives a UT of observation 16:32:05
Note: they still reckoned time from noon

This looks well with the modern value of 16:32:15

Kerigan’s calculation is laid out in file2 :

I have not yet begun to try and replicate this computation.

Also, I doubt that this is a method which would have been used by
Witchell to compute Cook's data. I'm confident he used something
other, but I haven't found it yet.

It's all a hunt in progress.

File:

File: