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    Re: Captain Cook's Sep 07th, 1773 Lunar revisited
    From: Antoine Couëtte
    Date: 2012 Jul 19, 23:08 -0700

    Dear Brad and Alex,

    Thanking you and reading you five on all your most recent contributions.

    *******

    I say again the same things a bit differently.

    If we assume that in this published Cook's Lunar the MOST RELIABLE DATA as they can be estimated to-day are the following :

    1 - the Observer's Position : "Ohamaneno Harbourg in Ulietea", as depicted on the "historical" charts (which you now have at hand) and which is nowadays very easily recognizable on Google Earth, hence the following Coordinates : S 16°45'33" W151°29'48", and

    2 - the Sextant Distance : Sun to Moon limb to limb distance of 105°47'04" , (as a result of 10 averaged observations), and

    3 - the following environmental constraints : Temperature : 77.5°F, Height of Eye : 15.5 ft , and Sea Level Pressure being set (by default) to 29.92 Inches of Mercury, WHILE DISCARDING THE SUN AND MOON HEIGHTS, and

    4 - A date close to Sep 07th, 1773,

    THEN there is UNIQUELY and ONLY ONE specific UT Time and date at which all (non discarded) data will (extremely well) fit, namely the date of Sep 07th, 1773 at UT=17h07m18s5 in our "modern and current" understanding of this exact time. I am ruling out any computation blunder based on such "starting data" since - with the very same starting data and end result (i.e. Date and UT) Frank's Computer independently rates this Lunar as [QUOTE] Error in Lunar 0'1 with (consequential and potential) Error in Longitude Equal to 2'0 [UNQUOTE].

    With all assumptions 1 to 4 hereabove, the quoted SUN LL and MOON UL altitudes simply do not "match" satisfactorily.

    THERE SEEMS TO BE NO WAY AROUND :

    IF we use altitudes and discard known position (see here-under) to find a "best match" for the quoted SUN and MOON altitudes,

    THEN there is no way we can and will ever come even close to "Ohamaneno Harbourg in Ulietea".

    *******

    Now and according to your both suggestions - and more especially coming from you Alex - if I now discard our quite well ascertained position, but use the quoted heights instead - as being U/L Limb which [QUOTE] consequently are to be corrected for the femi-diameter of the object, the refraction, and dip of the horizon, which , on board the Adventure, was about 3' 50" [UNQUOTE] , then - through modern computation tools which did not exist at the time of Cook - I am getting the following results :

    First Solution :

    Sep 07th at UT = 17h06m01s3 at the following position N54°22'6W153°07'7 . These results are rated by Frank's Computer as [QUOTE] Error in Lunar 0.1' , Error in Longitude 2'1 [UNQUOTE]. From this independent check, I can rule out a computation blunder.
    Obviously we can discard this position in the North Pacific Ocean, not far away from Alaska.

    Second Solution :

    Sep 07th at UT = 17h06m04s9 at the following position S16°22'4W151°53'8 . These results are rated by Frank's Computer as [QUOTE] Error in Lunar 0.1' , Error in Longitude 2'1 [UNQUOTE]. From this independent check, I can rule out a computation blunder here too.

    We are now between TUPAI, MAUPITI and BORA-BORA Islands some 30 NM away from "Ohamaneno Harbourg in Ulietea".

    Therefore, if the quoted heights are correct, then I see no way to reconcile the observed position hereabove with a vessel being anchored at "Ohamaneno Harbourg in Ulietea" .

    *******

    There now remains the point of checking whether the horizon was land blocked or not.

    You can refer to the chart I earlier enclosed on which I had written that, from "Ohamaneno Harbourg in Ulietea" the "free/not land blocked" Azimuts are [175°-312°] and [326°-338°] .

    From "Ohamaneno Harbourg in Ulietea" definitely the Sun (in Azimuth 079°6) was obscured by the shore and the hills quite close from the Adventure mooring point, and

    From this same anchorage place, in the Moon's Azimut direction 311.9°, the shore is much farther away. As I had earlier mentioned, and as seen from RAIATEA, the Moon had just "crossed" the south western tip of BORA-BORA and was transiting in the gap between BORA-BORA and TUPAI. This seems why they probably had to wait to observe their Moon Height. However, and as regards the Moon, from HOE = 15.5 ft, the horizon was certainly rather well defined even in the exact direction of BORA-BORA which is 16 NM away. The visible horizon must have been closer for them that the BORA-BORA shoreline. In other words, from "Ohamaneno Harbourg in Ulietea" and at a height of 15.5 ft very likely the visible Horizon was not blocked at all by BORA-BORA which far too far away (16NM). But, since the Moon was just starting crossing the gap between BORA-BORA and TUPAI, all chances are that they most probably had a quite reliable horizon for their Moon Height observation.

    *******

    (Provisional) Conclusion : Whatever the assumptions we make, there apparently looks like there is NO WAY to reconcile all Published data :

    * If on one hand we accept the position of the Adventure in "Ohamaneno Harbourg in Ulietea" as being a truly and firmly established one and no longer subject to discussion, then the quoted heights do not satisfactorily fit, especially the one for the Moon which was no longer land-blocked in azimuth 311.9° and which is definitely expected to be much more in agreement with modern determination. As you indicated Brad, suspecting an index error of some 3/4 of a degree seems totally unrealistic, even for a "lower quality" sextant. By the way, Brad, I think that George had made reference to a different source than yours when he had stated that the Sextant used for Moon and Sun heights was not as accurate as the one for Limb to Limb distance. It is therefore an excellent independent information and confirmation that you give us here and thank you very much for it.

    * If on the other hand we accept that the quoted Sun and Moon heights are correct, then the position which best matches the height data altogether with the sextant limb to limb distance is a position 30 NM off "Ohamaneno Harbourg in Ulietea" ...


    SO ... am I missing something ???


    Please, to all our dear Number Crunchers (Paul, Dave, Frank ...), be so kind as to give your thoughts on this one ...

    Best Regards to all

    Kermit

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