NavList:

Dear Frank, Dear All,

" Find whatever use you like in these scenarios " 

Hence, I am to run wild unclassical here.

Classical Lunars require 3 angles : 1 Lunar Distance, 1 Moon Height and 1 "other body" (here M. Sun) height to deliver only ... 1  (!!!) angle : Local true solar time from which we can easily derive Greenwich True Solar Time and Greenwich Mean Solar Time as well, which after a +12h addition has eventually become our current Time entry variable in Nautical Almanacs.

With current computation power, we can now make full use of these 3 initial angles to deliver 2 more angles : the Observer's Latitude and Longitude.

This is what I have undertaken with your 2 vertical Lunar examples.

Following results with own Ephemeris accurate to +/- 4" for the Moon and +/- 0.5" for the Sun.

Lunar I  : UT = 16:32:47.5 , with Lat = N00°11.5' , Lon = W089°55.7' , Azimuths difference 180° +/- 0.083°, computed position falling 12 NM from true position

Lunar II : UT = 15:14:58.5 , with Lat = N10°17.2' , Lon = W089°51.1' , Azimuths difference 180° +/- 0.014°, computed position falling 18 NM from true position

It should be noted also that : (1) if we were both using exactly the same Ephemeris and : (2) if there were no errors in the published data, chronometer determination errors would be under 1 s  and position error would be under 5 NM for both cases.

Still, both cases are extremely unfavorable here because of the opposite Azimuths (huge GDOP's).

Let's then work another case earlier published on NavList :

"From Cape Agulhas running for Madagascar" on Sep 15th, 1809 : LD = 71°56' , Moon UL = 38°35' , Sun LL = 55°36'

Following results :

09h41m36s / N17°02' / E065°15' / Azimuths difference 61.4° . And:

09h41m29s / S27°48' / E048°35' / azimuths difference 61.4 °.

Obviously this last position is the right one since it put us just south of Madagascar on the intended track.

The Navigator's Longitude was computed as E48°45' , which is only 10' off what we can derive to day. Quite a good result !

So, from this totally unclassical prospective, it is a bit unfortunate - if not regrettable - that the Navigators then might have been taught and trained to accept lower standards for their heights determinations.

Had they always been as strict for their heights measurements and recordings than for their LD's, we would even better know their positions then.

But ... through reworking their own historical observations from Navigators Logbooks, we can not only "grade" their Lunars with excellent and very accurate computation tools, but we can at the same time recover their full positions, i.e. Lon and Lat, which they did not and could not perform at all through only their Lunar Observations. They had to use meridian observations to get their Latitudes then.

Best Lunarian Regards to all,

Antoine M. "Kermit" Couëtte