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    Re: accuracy of Cook's lunars
    From: Alexandre Eremenko
    Date: 2013 Jan 7, 16:42 -0500

    Let me add that the longitude of Point Venus
    (Cooks observatory has a memorial sign) which I determined from
    Terraserver is 149d 29'6.
    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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