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    Re: Old style lunar
    From: George Huxtable
    Date: 2004 Dec 10, 15:41 +0000

    Alex wrote-
    >Is it his almanach that is responsible for this
    >scattering of measurements,
    >as Frank suggested? A 1800 almanac probably was not
    >very good in its Moon part.
    >But this is probably easy to check. If anyone has a 1800
    >(or around) almanach. Just compare it with Frank's online
    >lunar dist predictor. As I understand it gives accurate results
    >for the XIX century.
    This has been done for a limited period, around the time of George
    Vancouver's arrival from across the Pacific in 1792: I have mentioned the
    paper before, on Nav-l.
    "Captain Vancouver's longitudes 1792", by Nicholas A Doe, appeared in The
    Journal of Navigation (of London, not the American journal with a similar
    name), vol 48 No 3 (September 1995), pages 374 to 388.
    Maskelyne's lunar distances, given at 3-hour intervals in the Almanac, were
    derived by second-order interpolation (so allowing for curvature) from the
    distance between the ecliptic lat / long of the Moon, and that of the other
    body, predicted at 12-hour intervals.
    Of the many steps in this calculation process, the most error-prone was
    obtaining the ecliptic longitude of the Moon, because of defects in the
    prediction theory. Doe, comparing almanac predictions with the modern JPL
    ephemeris, and also comparing with actual Moon observations made at the
    same period from Greenwich, shows that from mid-March to early May 1782
    there was a strong cyclic monthly error in the predicted Moon's longitude.
    The average error was about 25 arc-seconds, and the variation was about
    23.5 arc-seconds either side of that average, with a period of 29 days. So,
    in that period, there was no time when the error was zero, the error was
    always in the range 2 to 50 arc-seconds, always in the sense that made
    Vancouver's calculated Westerly longitudes less than they should have been.
    There's a useful project waiting out there for someone prepared to put a
    bit of effort into it. From 1767 on, when mariners started to work lunar
    distances from the Nautical Almanac, whatever errors occurred in the lunar
    predictions would put the longitudes of all mariners using lunars, anywhere
    in the World, out by the same amount on the same day.
    If we knew what those almanac errors were, a present historian, following a
    journal account of any lunar navigator from Cook's day on, would be able to
    correct for almanac errors, retrospectively, any recorded positions based
    on those lunars.
    To do that needs some dedicated soul to first extract the appropriate Moon
    ecliptic-longitudes, noted at noon and midnight, from the Almanacs, and
    compare them with modern predictions, for (say) the century following 1767.
    Perhaps less-frequent comparisons than two per day would be acceptable. The
    comparison with modern predictions could readily be automated, no doubt,
    once the extraction from the early almanacs had been done. As almanacs have
    been digitised from 1804 by the Mystic museum, someone that's handy with
    OCR (optical character recognition) software might be able to automate much
    of the data-extraction process from that date onward. For the years from
    1767 to 1803, there seems no alternative but to scan through old library
    volumes, transcribing lots of numbers into a laptop.
    If someone were to create such a useful tool, we would now know the
    longitudes of those mariners, better than they knew then themselves.. Of
    course, their own measurement errors and inaccuracies would remain.
    Eric Forbes' monograph, "The birth of navigationl science", states (ref. 63)-
    "Dr Thomas Young's "Report on the progressive improvents of the lunar
    tables",  preserved among the Board of Longitude Confirmed Minutes for 2
    November 1820, , contains a synopsis of more than 4000 observations of the
    moon's celestial position over a period of 36 years (RGO MSS, PRO Ref 535,
    p 317). This summary indicates which sets of lunar tables had been used in
    comparing the lunar computations throughout that time, as well as the
    respective errors thought to have been inherent in each...."
    I haven't seen Young's report, but it looks as if it might provide a good
    starting point for any such modern study-project as I am advocating here.
    contact George Huxtable by email at george---.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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