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    Re: Lunars: Three simultaneous observations
    From: George Huxtable
    Date: 2004 Sep 21, 23:50 +0100

    I agree fully with Frank Reed about there being no necessity for three
    simultaneous observations when taking lunars.
    I imagine that this was done on Navy vessels, with a superfluity of
    deck-officers and middies, and a little ceremony made of the occasion, such
    as Navy vessels so enjoyed.
    No doubt, an extra body would be useful to read the chronometer and make
    notes, and perhaps to take a sextant to the lantern to note its reading, so
    preserving the navigator's night-vision.
    He added-
    >You should take a
    >look at some of the positions generated during Cook's first Pacific voyage
    >during which lunars were used extensively (they brought an astronomer). The
    >longitudes are exceptionally good. Navigators using lunars and later
    >had no problem finding islands charted by Cook.
    My comment here is rather tangential to the point that Frank was making.
    Even though he had a chronometer on his second and third voyages, Cook
    generated about as many lunar positions as on his first.
    First, because he had been ordered to test out his new chronometers, and in
    unknown seas there was nothing to compare them with except lunars (and
    Jupiter satellites).
    Second, because it was asking too much to expect a chronometer to continue
    keeping good time over such long voyages, lasting for years. In fact, Cook,
    using lunars, was able to allow for the accumulating error of his
    chronometers, and without that, his chronometer longitudes would have been
    of little use.
    Third, because Cook's chronometers had their share of failings, stoppings,
    and breakdowns: the final failure of the Kendall watch occurring remarkably
    close to the time of Cook's own death. It was then necessary to rely on
    lunars in order to get home.
    It's all in "Background to Discovery", ed. Derek Howse (1990), in Howse's
    chapter V, "Navigation and astronomy in the voyages".
    Now to Frank's statement- "The longitudes are exceptionally good.
    Navigators using lunars and later chronometers had no problem finding
    islands charted by Cook."
    That's true, though it depends what is meant by "exceptionally good". No
    matter how precise the observations and calculations were, Cook was
    dependent on the accuracy of the lunar distance tables, as we have been
    discussing in another thread.
    How good were those tables? Well, even twenty-odd years later, an analysis
    of Vancouver's longitudes around Juan de Fuca Strait in 1792 shows that
    predictions of the Moon's celestial longitude were often out by up to 50
    arc-seconds. This followed a cyclic pattern over a lunation. Lunar
    distances would show cyclic errors of a similar order. Such errors could
    put a calculated longitude out by 25 arc-minutes, maybe more. With this,
    any observationl error would have to be combined. Presumably the Moon
    predictions were no better in Cook's time. For a lunar, accuracy to 25
    minutes would be considered quite good going.
    When Cook's longitudes happen to coincide rather precisely with modern
    values (and indeed, many do) we have to put at least some of that down to
    luck. Either Cook had, without knowing it, happened to make his
    observations during that part of the lunation when the Moon prediction
    error was small. Or else, some of the inevitable random error in his
    observation had happened to work to cancel out some of the error in the
    Moon prediction.
    Even when a later navigator had a Cook position to guide him to an island,
    I presume that he would still approach it along an East-West line, using
    latitude sailing. To do otherwise would risk combining any error in Cook's
    mapping of longitude, with any error in determining his own longitude at
    sea. The island being sought could be put right below the horizon, by the
    combined effect of those longitude errors.
    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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