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    Re: Real accuracy of the method of lunar distances
    From: George Huxtable
    Date: 2003 Dec 31, 12:56 +0000

    Jan Kalivoda said-
    >Only from you I hear that the purported triumph of chronometer in Cook's
    >hand is rather the result of the deliberate propaganda or the dull
    >repetition of unverified assertions lasting for century(ies).
    This was in response to my earlier posting, in which I had said-
    >>This was how Cook managed his one good chronometer. It was valuable to
    >>him to interpolate for time between island landfalls. On its own, without
    >>such cross-checking for errors, it would have been pretty useless long
    >>before the end of the voyage. Not to mention its occasional stoppings.
    >>This is an aspect of the Cook chronometers that hasn't been properly
    >>emphasised, except by Derek Howse.
    What I should have done, in that earlier mailing, was to provide a
    reference to where Derek Howse's analysis of the performance of the
    chronometers is to be found. It's in a book "Background to Discovery;
    Pacific exporation from Dampier to Cook.", ed. Derek Howse, Univ. of
    California Press, Berkeley, 1990. This is, I think proceedings of a
    conference, and the relevant chapter V, by Howse, is :Navigation and
    Astronomy in the Voyages", from page 160 to 184. That chapter gives a good
    summary of the navigator's art in that period.
    Howse doesn't have a lot to say about the chronometers and their behaviour,
    but provides two illuminating graphs, summarising the behaviour of the
    chronometers on the two vessels: fig.5.4 for his second voyage of 1772 to
    1776, and fig 5.5 for his third voyage 1776 to 1780.
    Let's concenrate on the performance of Cook's chronometers in his second
    voyage, aboard Resolution. He had an Arnold and the famous Kendall copy,
    K1. Within a few months of departure, which was in Spring '72, the Arnold
    had packed up at Cape Town, and was of no further use. K1 had started off
    with a very low rate, losing slightly at less than -1 sec per day (where a
    - sign implies a losing rate, running slower than mean time). By Cape Town
    an increasing rate-of-gain had set in, and by mid-'73 had reached about +10
    sec per day. It then held that rate of +10 to +12 sec per day throughout
    the rest of the voyage until it ended in mid-'75.
    Not bad going, for the first really-portable seagoing chronometer ever, you
    might think. And I would agree.
    But what has to be appreciated is that a rate of +10 sec per day implies
    that over the 365 days of a year the clock will have got further ahead of
    GMT by 3650 seconds, just over an hour, corresponding to a longitude error
    of 15 degrees. And if no corrections had been made to the indicated times
    of the chronometer, by measuring observed rates, its accumulated error as
    estimated by Howse would have been over 2.5 hours when Cook returned. It's
    clear, then, that for such a long voyage as Cook was making, the use of a
    chronometer of that date would be quite impractical without some regular
    recalibration, both of the rate and (by lunars or Jupiter satellites) the
    During the voyage, whenever the ship found harbour, the rate of the
    chronometer would be found. This can be done rather precisely, just
    requiring two clear nights. It can be very simple: a vertical post set in
    the ground as a backsight, and another used as a foresight. The time
    between any star disappearing in line with the posts on one night, and the
    same thing the next night, is exactly one sidereal day, which is precisely
    related to a mean day. The chronometer doesn't need to leave the ship; the
    time signals can be made by gunshot.
    What do we find in Cook's journal about the error in his chronometer
    (watch) when he returned to England? There are two slightly-different
    versions of that closing section of his journal. One states that when they
    made the land above Plymouth, on 29 July 1775, "the error of Mr Kendals
    Watch in Longitude was only 7' 45", which was too far to the West". Such an
    error in longitude was only an error of half-a minute of time. The other
    version states "Error of the watch on our arrival in Portsmouth 16' 26
    1/2". This figure was clearly an error in longitude, corresponding to just
    over a minute of time. Those numbers seem quite compatible with each other,
    but NOT with Howse.
    Presumably, it's on the basis of those remarks that the story seems to have
    grown up about the amazing accuracy of K1 over that voyage. Clearly,
    there's a great incompatibility between those remarks and the built-up
    error that arises when you integrate the rates provided by Howes. Perhaps
    (and I think probably) the errors quoted in the journal on Cook's return
    would have been the chronometer reading AFTER a big correction  had been
    made for known errors, as recorded over the voyage. Remember, Resolution
    had made several island landfalls on her way North from Cape Town,
    including a stop at Horta in the Azores. Presumably, by that date the
    longitude of Horta was reasonably well-known, so there can't have been much
    doubt, on leaving, about the error in the chronometer.
    One event which seldom gets a mention is that at the Pacific Island of
    Nomuka, near Tonga in mid-'74, the chronometer (which needed daily winding)
    was allowed to run down, and had to be restarted. So there is no way of
    making a direct comparison between the chronometer time on departure, and
    on return three years later.
    Unfortunately, Howse died a few years ago. He made no comment, in the paper
    I have cited, on the immense discrepancies that it shows up. I haven't
    tried to duplicate Howse's analysis, but there's useful and interesting
    work to be done there, using Beaglehole's edition of the Journals.
    Here in Oxford, it's 5 minutes short of New Year, and a filthy night. The
    fireworks are popping off already.
    A happy new year to all
    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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