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I haven't gone into that Reaper log page in the same detail as has Antoine, 
but perhaps I can answer his question.

Lunar distance is observed the same worldwide, as long as the Moon can be 
seen, which is why it works. It doesn't depend on latitude or longitude, 
except for two corrections, for parallax and refraction. These are both 
dependent on altitude of the Moon, which is why the observer's position 
needs to be (at least roughly)known, if the whole business is to be done by 
calculation.

But, in a real observation at sea, that could be bypassed. The necessary 
altitudes, of Moon and other-body, could instead be measured, above the 
horizon, with a sextant, close to the moment of the lunar. No great 
precision was necessary. Then the parallax and refraction could be applied, 
using lookup tables, and used to clear the lunar distance. That, indeed, 
was the normal way in which the job was done, at sea. However, one of the 
problems with a star lunar was that if it was taken away from twilight, 
even a rough estimate of altitudes was hard to obtain, without a clear 
horizon.

Right from the first Nautical Almanac, in 1767, Maskelyne pointed out how, 
in that situation, the altitudes, and corrections, could be calculated 
instead, using estimated lat and long. A sufficiently good estimate of 
latitude, for that purpose, was usually available to a navigator. As for 
the longitude, if the initial guess turned out to be wrong, the 
lunar-distance process would improve it, and a bit of reiteration would 
give a better one.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message ----- 
From: "Antoine Couette" 
To: 
Sent: Saturday, March 20, 2010 8:49 AM
Subject: [NavList] Re: David Thomson and his lunar tables


Dear Frank,


In [NavList 12359], you published a very interesting "real world" example 
of a Sep 1809 Lunar on-board Brig-Reaper of Boston.

*******

I replied with the following results in [NavList 12366] + a clarification 
on the date in [NavList 12371]:

...///...

and with to-day computing tools, we get an observation date of Sep 15, 1809 
...///... as we would reckon it to-day, and ...///...  a UT time of 
09h41m32.9s with an observed position as follows:

S 27°47'6 and E 048°34'8 for an account longitude equal to 48°40' (he found 
longitude equal to E048°45'). So this sharp Observer was definitely within 
5 minutes in Longitude from his DR.... Whaooo !!!

Some more examples ? :-)) ....

...///...

*******

Meanwhile, I crossed checked my results with your On-Line Computer just to 
find a 0.0' difference in Longitude for the given time and full 
coordinates. Once again, we are on-board the very same ship .  :-))

By curiosity, I looked up your enclosed Log-book Tabular clearing 
computation to try guessing where the Navigator did take his (DR) Latitude 
in account.

His DR Latitude was not far from S27°47'6. So, let us do a bit of numbers 
guessing :

Lat = - 27°47'6 = - 27.7933 , Lat * 2 = - 55.58667 , Lat / 2 = - 13.896667

I fail to see any such number on the Log report.

Logaritms then ? But since they are not defined for negative numbers,

- Did they use the Lat Cosine  (= 0.8846352) , with has 9.9467642 for 10Log 
? But in such case "some" information is lost, namely the North or South 
Hemisphere information since (Cos -A = Cos +A ), or

- Did they use some kind of special function for angles such as 
versine/haversine to avoid all problems with Logaritms ???

I am just curious here because - just from looking up at this clearing 
computation method - I fail to see where and how he managed to take their 
(DR) Latitude in account in their Moon Clearing process.

I would think that some knowledge of the Observer's Latitude is an 
information absolutely required in any Lunar Clearing process, whatever the 
method actually used, would it not ?

And by the way, which Lunar reduction method is he using ? You said that it 
is not the one recommended by Bowditch.

Just a "ribbit" question from a Curious ...

Kermit


Antoine M. "Kermit" Couëtte
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