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Dear Kermit,
Thanks for pointing that Cook's Lunars were discussed 2 years ago
(when I did not follow the list). Could you indicate more
preciesly the dates of the title of the topic?

I use this opportinuty to bring to your attention that I also
worked some Cook's Lunars, and posted the results on the list in 2007.
Most of these messages have the words Point Venus in the title.
But recently I put these messages together in one article:
http://www.math.purdue.edu/~eremenko/Navigation/Accuracy/pointvenus.pdf

To understand what is wrong with the observation you mention,
I have to go through all details of your calculation,
but here is my first guess:
Do you assume that the "time by chronometer" is the GMT?
Do they mention their chronopmeter correction?
And more importantly: their clock used in Point Venus observations
was NOT showing GMT. It was not showing Mean Solar time at any place.
It showed the Sideral time (SHA). Such a specially regulated chronometer.
I was also very puzzled before I figured this out!

But this is just my first guess.

Alex.

On Thu, 19 Jul 2012, utf-8?Q?Antoine Cou=C3=ABtte?= wrote:

>
> Hello to all,
>
>
> Some 2 years ago, and further to our dear George's suggestion, we covered 
some of the Cook's Lunars which were published for the year 1773.
>
> Let me get back to the one published for Sep 07th, 1773
>
> *******
>
> Here are the published data :
>
>> From "Ohamaneno Harbourg in Ulietea", Sep, 07th, 1773
>
> Time by Chronometer # 1 : 02h08m43s.0
> Sun to Moon limb to limb distance 105�47'04" (as a result of 10 averaged observations)
> Altitude of the Sun (LL observation) : 12�38'24"
> Altitude of the Moon (UL observation) : 43�29'00"
> Longitude : 208�35'48" East of Greenwich, which equates to W 151�24"12"
> Latitude : S 16�45'30"
> Temperature : 77.5 (Farenheit)
> There is also a specific note stating the following : " it must here be 
obferved, that all altitudes are put down as they were obferved with Hadley's 
Sextant, from the fhip's deck, and consequently are to be corrected for the 
femi-diameter of the object, the refraction, and dip of the horizon, which , 
on the Adventure, was about 3' 50" ...///...
>> From this note here-above and from further indications exchanged on this 
Forum, we have concluded that it is reasonable to use a Height of Eye equal 
to 15'5 (4m70)
> And, last but not least, a "historical" nautical chart of the "Ohamaneno 
Harbourg in Ulietea"  was also published by one NavList Member. This chart 
enables us to ascertain that Adventure's mooring point was on the Western 
part of the Island.
>
> *******
>
> So, as a starting point, I first identified Cook's mooring point with Google 
Earth (WGS 84). By comparison with the published "historical" chart, they is 
little doubt that Cook's actual anchorage point was (very) close to the 
following position : S 16�45'33" W151�29'48" on RAIATEA Island.
>
> Here we can observe that Cook's Latitude was already extremely accurate (to 
within 100 yards) while his believed Longitude was (probably) 5 miles off. 
The position believed by Cook (S 16�45'30" W 151�24"12") might still be 
considered as a "valid" anchorage point for our research to-day. In fact 
Google Earth shows that it is lying in the vicinity of the reef which a 
passage through them. However, such believed position of S 16�45'30" W 
151�24"12" - in the eastern coast of RAIETEA - is NOT consistent with the 
data  published on the historical chart which - again - clearly show that 
"Ohamaneno Harbourg in Ulietea" definitely lies on the western side of this 
same island.
>
> *******
>
> All the above to indicate that - with modern computing tools and using TT-UT 
= +16.4s - I have reworked this Lunar using the "Ohamaneno Harbourg in 
Ulietea" coordinates as given by Google Earth, i.e. S 16�45'33" W151�29'48"
>
> With all the data as indicated here-above, I find that UT of Cook's observation was 17h07m18s5.
>
> When feeding these data into your Computer, Frank, I get the following grade 
" Error in Lunar 0'1, error in Longitude 2'0 "
>
> So there is little doubt that the results here-above constitute (close to) 
the Best modern reconstruction of this Lunar performed some 240 years ago.
>
> *******
>
> THINGS START BEING INTERESTING RIGHT HERE !
>
>> From Frank's computer, we can also get the following data :
>
> Moon Apparent Altitude at DR 42�28'2 and Moon Altitude Correction -0�39'0 
(which yields a Moon Center geocentric altitude of 43�07'2) , and
> Sun Apparent Altitude at DR 13�30'3 and Sun Altitude correction +3'7 (which 
yields a Sun Center geocentric altitude of 13�26'3), and
> Cleared Distance (i.e. geocentric Moon center to Sun center distance) 105�57'4
>
> All your values Frank, are exactly the same ones which I am deriving, as 
long as you published topocentric heights are published for Body centers 
affected by refraction and with Height of Eye equal to 0ft, which I believe 
is the actual case  , no ?
>
> The intriguing remark here is that I CAN NOT find any way to reconcile the 
published height values given by Cook, i.e.
>
> Altitude of the Sun (LL observation) : 12�38'24"
> Altitude of the Moon (UL observation) : 43�29'00"
>
> with any of the heights values computed nowadays as showing on your Computer, Frank, ...
>
> If indeed, we are to understand that the Cook's published values are exactly 
as stated, i.e. U/L limb with the effect of both Dip and Refraction included, 
I am therefore computing such data as follows : Sun LL height = 13�17'9 with 
Sun Az = 079�6, and Moon UL height = 42�47'1 with Moon Az = 311�9 .
>
> Still no way to reconcile these values with the ones published by Cook.
>
> Even if considering that SUN/MOON heights determinations are not so critical 
for accurate Lunars determination (see Frank's lectures on this subject), and 
even if considering that from (our) currently used position, the horizon was 
definitely obscured by the close land in the Sun's Direction (and probably 
not in  the Moon's direction since there seems to be a gap between 2 distant 
islands exactly in the Moon's Azimuth at this time of Observation) it looks 
DEFINITELY STRANGE that the heights published by Cook might be in error by 
over three quarters of a degree in this specific example.
>
> Any cue here ? Am I missing something ?
>
> Thanks for your Kind understanding and reply(ies)
>
> Kermit
>
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