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    Re: accuracy of Cook's lunars
    From: Alexandre Eremenko
    Date: 2013 Jan 7, 21:55 -0500

    That's why I am surprised
    with the student's thesis about Cook's accuracy.
    But I suspect that her claims are based on comparing Cook's
    (unknown) positions at sea with positions of some capes
    which Cook could SEE from his position.
    I don't understand how we can determine now Cook's exact
    position at the time of his
    observation at sea.
    > An  interesting bit of trivia:
    > Averaging Bligh's Longitude with that of Cook's first, as noted by Bligh,
    > you get 149-29.275, or thereabouts.
    > Henry
    > On Mon, Jan 7, 2013 at 4:42 PM, Alexandre E Eremenko <
    > eremenko---purdue.edu> wrote:
    >> Let me add that the longitude of Point Venus
    >> (Cooks observatory has a memorial sign) which I determined from
    >> Terraserver is 149d 29'6.
    >> Alex.
    >> On Mon, 7 Jan 2013, Henry Halboth wrote:
    >>> It's rather refreshing to see the subject of Lunars again being
    >>> discussed.
    >>> For those who may be interested, I post, without comment, the following
    >>> excerpt from Captain (later Admiral) Bligh's narrative concerning his
    >>> second voyage to Tahiti, as first published in 1792.
    >>> "The result of the mean of 50 sets of lunar observations taken by me on
    >>> shore, gives for the Longitude of Point Venus                 210 33 57
    >>> E
    >>> Captain Cook, in 1769, places it in    210 27 30
    >>> In 1777, his last voyage                    210 22 28"
    >>> Regards,
    >>> Henry
    >>> On Mon, Jan 7, 2013 at 3:30 PM, Frank Reed wrote:
    >>>  Hanno Ix, you wrote:
    >>>> "I wonder if the ephemeris especially of the moon as used by Cook can
    >>>> still be studied today. Naturally, Cooks errors cannot have been any
    >>>> smaller than the ones of those."
    >>>> Even better. Although we can certainly study the tables (Mayer) that
    >>>> were
    >>>> used to generate the early Nautical Almanacs, we may as well jump
    >>>> straight
    >>>> to the product itself. Very nearly all Nautical Almanac editions from
    >>>> the
    >>>> first in 1767 through the early 20th century are available in full on
    >>>> Google Books. To compare these with correct values (as nearly as can
    >>>> be
    >>>> determined given some continuing small uncertainties in delta-T for
    >>>> that
    >>>> era), we need lunar distance tables given, preferably in degrees,
    >>>> minutes,
    >>>> and seconds, as was normal back then, and we need those tables for the
    >>>> rather unusual argument of GAT, Greenwich Apparent Time, which was
    >>>> standard
    >>>> before the switch to GMT which came in 1834 (and was considered
    >>>> seriously
    >>>> late by commentators at the time). Back in 2004 I made available
    >>>> online
    >>>> software which does just that. I am attaching an image of a portion of
    >>>> the
    >>>> tables for Sun-Moon lunar distances from August 1767 compared against
    >>>> data
    >>>> from my online app for the same dates, lined up to match the tabular
    >>>> format
    >>>> of the old Nautical Almanac. As you can see, there are cases where the
    >>>> difference is as large as 50 seconds of arc, but there are others
    >>>> where
    >>>> the
    >>>> difference is only 1 second of arc. For an "average" lunar this will
    >>>> add
    >>>> an
    >>>> uncertainty equivalent to an error of something like 0.25' in the
    >>>> distance.
    >>>> Whatever the observational error may be, this error would sometimes
    >>>> increase it and other times cancel it out. On average two sources of
    >>>> error
    >>>> add as the square root of the sum of the squares, so if they had,
    >>>> let's
    >>>> say, 0.25' error from observations, then the net error would be
    >>>> sqrt(2)*0.25 or about 0.35' (equivalent to 42 seconds in time or 10'
    >>>> in
    >>>> longitude). By 1805 the errors in the lunar distance tables had been
    >>>> significantly reduced. By 1875, they were nearly perfect for
    >>>> navigational
    >>>> use (though lunars were essentially obsolete at sea by that date,
    >>>> there
    >>>> were still a handful of practitioners, and there were definitely
    >>>> lunarians
    >>>> on land, exploring and mapping Africa, for example).
    >>>> -FER
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    > View and reply to this message: http://fer3.com/arc/m2.aspx?i=121764

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