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    Lunar-distance almanac errors [was; The Online Nautical Almanac- beware!]
    From: George Huxtable
    Date: 2004 Jul 7, 17:45 +0100

    Frank Reed wrote, under threadname "The Online Nautical Almanac- beware!"
    >For what it's worth, the lunar distances in the 1804 Nautical Almanac are
    >wrong by up to one minute of arc by my calculations. So if you're trying to
    >figure out where he "really was" based on the observations or if you're
    >trying to
    >determine how good his observations were, you may want to get modern ephemeris
    >data, too.
    It will be really useful to have such data available.
    Others have noticed similar problems with the Nautical Almanac predictions
    for that period.
    I recommend a really interesting paper by Nicholas A Doe in the (British
    RIN) Journal of Navigation, vol 49 No 3, September 1995, on "Captain
    Vancouver's Longitudes 1792". I haven't found a way, yet, to contact
    Nicholas Doe (as opposed to his presumed siblings John and Jane Doe), but
    am aware that 12 years ago he was resident in the White Rock area of
    Vancouver. If anyone can help me to track him down, I would be most
    grateful. I know that he has published in "Lighthouse", journal of the
    Canadian Hydrographic Association, so perhaps he is, or was, a
    hydrographer. His Vancouver paper shows him to be right on top of the
    Doe says that the Spanish naval officer Dionisio Alcala Galiano discussed
    the existence of such errors with Vancouver when they met in Nootka in
    1792, and that the geographer Humboldt had, in the early 1800s, surmised
    that the early lunar tables were inaccurate.
    Doe states that the lunar distance errors resulted primarily from
    deficiencies in predicting the Moon's ecliptic longitude (which would be no
    surprise), and he plots differences in that quantity from modern JPL
    predictions over about 45 days in 1792. These show a marked cyclic
    difference varying between 5 and 50 arc-seconds, with a period of about a
    month. That corresponds reasonably well with Frank Reed's assessment of
    errors "up to 1 minute of arc" in the 1804 almanac.
    I seem to remember that somewhere, in Beaglehole's great 4-vol edition of
    Cook's journals, there's a reference to later revisions to some of Cook's
    longitudes as a result of errors, discovered later, in the almanacs he
    used, but in all those pages I can't locate it now.
    Doe refers to a paper by the "Lord Commissioners of the Admiralty" in 1848,
    "Reduction of Observations of the Moon made at Greenwich from 1750 to
    1830", now in the Royal Greenwich Observatory archives at Cambridge
    University, in which some of these discrepancies were studied with
    hindsight. I haven't (yet) looked at that paper, but it might make
    interesting reading.
    It's a surprise, to me, and something of a disappointment, that in the
    thirty-odd years that elapsed after the first almanac, for 1767, the lunar
    predictions hadn't got significantly more accurate (if it's true that they
    hadn't). Mayer had died, but Maskelyne remained in charge for many years.
    Did anyone continue working on the detailed theory of the Moon's motion, or
    had the Commissioners of Longitude just got complacent once the first
    almanac had appeared?
    Did Greenwich wait until 1848, I wonder, before instituting a comparison
    between their own observed Moon positions and their own predictions?
    For those of us who follow up old voyages, for one reason or another, it
    would be useful to have a publication or website available which showed the
    amounts by which the predicted almanac Moon positions were in error over
    those lunar-era years from 1767. It's easy enough, now,  to calculate the
    precise positions, then, using modern data and technology; but a comparison
    with the published data of that era would involve a lot of dreary
    transcribing from old almanacs, so would have to be something of a
    labour-of-love. It's a pity that Maskelyne didn't publish in
    machine-readable form. Perhaps it's an application for OCR technology, but
    would requires access to some rare volumes, closely guarded by jealous
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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