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    Re: Captain Cook's Sep 07th, 1773 Lunar revisited
    From: Don Seltzer
    Date: 2012 Jul 23, 12:42 -0700

    Regarding the ship's journal of the Adventure,
    The relevant pages can be viewed here -
    http://badc.nerc.ac.uk/browse/badc/corral/images/adm55/log001/adm55_log001_page062.jpg
    http://badc.nerc.ac.uk/browse/badc/corral/images/adm55/log001/adm55_log001_page063.jpg

    The convention of this log is that the nautical day starts at noon of the previous civilian calendar day.
    Thus the entry for Tuesday Sept 7 actually covers Monday afternoon through Tuesday morning.
    The entry for Wednesday Sept 8 covers Tuesday afternoon through Wednesday morning.
    The entry for Thursday Sept 9 covers Wednesday afternoon through Thursday morning.

    Local time for 151W is about 14 hours ahead of Greenwich time, so the lunar observation at 17h Greenwich time on Sept 7 would correspond to about 7 am on Sept 8 in Polynesia.

    According to the Adventure log for Sept 8, the previous night the ship had
    'Stood off and on all night about 4 or 5 miles off the entrance of Ohamanino harbor. At noon [Sept 8] anchored with the small bower at the entrance to the reefs in 20 fathoms.'
    It must have been this morning, while approaching the reefs from 4 or 5 miles off, that the lunar observation was made at 7 am.

    With the passing of noon, the log continues with the entries for the next nautical day, Sept 9, detailing the warping into the harbor and the eventual anchoring about a mile from shore at 6 pm of the nautical day Sept 9, calendar day of Sept 8.

    Don Seltzer

    Dear Don, Dear Paul and Dear Alex,


    Thank you for your last contributions which I will cover here-under.

    *******

    First of all, thanks to you Paul for pointing out an error I had made while using HOE=0FT vs HOE = 15.5 ft in a previous post.

    Therefore, here is this such previous post now corrected with adequate values.

    From Ulietea Harbour (S 16°45'33" W151°29'48") the Moon Upper Limb Height was 43°29'00" at time UT = 17h03m17s5 (Paul, you found 17h03m18s : again an excellent agreement between us ... as long as we depart from the very same premises ..) and the Moon was in Azimuth 312°8. I am computing this way with the Moon first since most likely the Moon Height is the most reliable one for refraction correction and also for the reasons given in my previous post on this subject.

    At that same time, the Sun Azimuth was 079°9 ans its Lower Limb Height was 12°12'25", still over one third of a degree off its quoted value of 12°38'24" . However we do achieve narrowing our Sun "initial error" by almost 1/3. Would that be sufficient, given the fact that the Sun horizon was land/hill-blocked ?

    Now, from Position S 16°45'33" W151°29'48" at time UT=17h02m55s5, Cook should have observed a sextant distance of 105°47'55"9 (same independent confirmation by Frank's Online Computer which rates my results as earlier : [QUOTE] Error in Lunar 0.1' , Error in Longitude 2'1 [UNQUOTE]) .

    Cook did observe a reported Sextant Distance of 105°47'04" while he should have observed an actual Distance of 105°47'55"9 .

    Some 50" in the Sextant Distance as a result of 10 observations, ... by Cook ??? Is this an (un)acceptable hypothesis ? Printing blunder ? ... just on this specific Lunar, unfortunately one of the very few for which we nowadays can ascertain the Observer's position with a (super) great Confidence level ????

    When starting up with the same data, there is an excellent agreement between Paul's, Frank's and my values : angular values always match to better than 4", while we know that the best achievable accuracy on Lunar Distances is no better than 6". Therefore, we can safely rule out (now, and thanks to you Paul) any computation blunder here.

    *******

    Now I come to your remarks, Don, regarding your last contribution :

    [QUOTE] How sure are you that Adventure was in Ohamaneno Harbour in Ulietea when the observations were made?

    Looking at the ship's journal, it appears that Adventure was weighing anchor at 6:30 am in Owarre Harbor, Huaheina on Sept 7. At noon, it was 5 or 6 leagues from that harbor. At 3 pm, it rounded the 3 pm rounded south end of Ulietia

    On Sept 8 at Noon, the ship anchored 4 or 5 miles off the entrance to Ohamanino Harbor, with 'Bola-Bola' bearing NWb1/2N

    12:30 pm they began warping into Ohamanino Harbor. At 6 pm, anchored 1 mile offshore.

    I expect that there is a calendar correction to be made, to equate with Greenwich time, but if it corresponds to one day, then the observations were likely made on the morning of Sept 8, ship reckoning, when it was more than 4 or 5 miles off the harbor entrance.[UNQUOTE]

    Very interesting remark from yours. I only have a partial reply to it. In our current dates reckoning, definitely this Lunar was observed at a time and date very close from Sep 07th, 1773 UT=17h03m +/- a few minutes of time. This date is the very same as quoted on Cook's report namely as follows : [QUOTE] "In Ohamaneno harbor in Ulietea. Lat 16 45 1/2 S [UNQUOTE] In other words, during the Local Morning when this Lunar was observed their own date was then reckoned as Sep 07th, 1773 . Did they change date numbering at/after (local) Noon ? I am not sure. George could have told this immediately. Do any of you folks remember anything about this point.

    It might appear that the Adventure's Logbook does not seem consistent with the date given on page 174 (the one I republished). Again, for us to-day, there can no longer be any doubt on the GMT Date and time, as reckoned nowadays. Had this Lunar been observed 24 hours earlier or later, then the Distance would be different by about +/- 14 °.

    For the time being I cannot reconcile the statements of one part of the Logbook which might imply - in your own analysis, Don - that this Lunar was observed on the 06th of September, with one statement found on another part of this same logbook (namely the mention on the harbor location), which definitely implies that this Lunar was observed on Sep 07th, 1773 , a date being both THEIR date and OUR date.

    *******

    Back to you now, Alex, and to you Don. 2 year ago, I attempted in vain to get an electronic copy of this Full 1773 Voyage report by Cook. Any better chance now, and any possible help from you side ? (antoine.m.couetteATclub-internet.fr).

    This still seems an open question on this specific Lunar, one of the very few for which - if Cook was really anchored in "In Ohamaneno harbor in Ulietea. Lat 16 45 1/2 S on that local morning of Sep 07th 1773" - we can nowadays ascertain his actual position by modern means with almost absolute confidence.

    Thanks again to you all.

    Any new input from anybody here ???

    Kermit
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