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    Re: How Many Chronometers?
    From: Paul Hirose
    Date: 2009 May 09, 15:19 -0700

    George Huxtable wrote:
    > But I remain puzzled about Toynbee's discussion of the implications of the
    > differences between those observations. If Paul's explanation is correct,
    > they relate to nothing more than different assessments of the apparent
    > diameter of the Sun, but Toynbee seems to think there's more substance in it
    > than that.
    Actually, I think the differences between the members of each pair are
    due to personal error in making the coincidence. Toynbee says, "On
    referring to the above table it will be noticed that in Mr. Quihampton's
    case, the [Sun W Moon] lunars invariably give the greater, but in mine
    almost as invariably the lesser error. This may arise from a constant
    error in the observer, or his instrument; but the means of our [Sun E
    Moon] and [Sun W Moon] errors nearly agree."
    He also says, "I think it has also proved that there is a constant
    character in lunars taken by the same observer, using the same
    instrument in the same state; whereby any person having practised this
    method for a short time, may readily show how much a single set of
    lunars gives the Greenwich time in error. For instance, Mr. Quihampton's
    [Sun W Moon] and [Sun E Moon] lunars differ in the Greenwich time about
    one minute and twenty seconds; now the half of this, or forty seconds of
    time, may be called his constant error; mine differ about twenty-nine
    seconds, so that my constant error is fifteen seconds of time, which
    applied to any single set of observations will give the Greenwich time
    very nearly correct: hence an observer having ascertained his constant
    error, has the true longitude from a single set, taken either [Sun E
    Moon] or [Sun W Moon]."
    Incidentally, Charles Shadwell's book "Notes on the Management of
    Chronometers and the Measurement of Meridian Distances" (1855) is on
    Google books. (A "meridian distance" is the longitude difference between
    two places.)
    Cotter called this work a "classic". At the Google site I noticed it was
    republished in 2008. The MNRAS reviewed the original back in 1855:
    Shadwell throws some light on the question of how many chronometers were
    carried: "In Her Majesty's Navy it is usually customary to furnish every
    ship with one chronometer. If the captain supplies a private one in
    addition, then the Government give another, so as to make three
    chronometers in all. It is argued, that if a ship have but one
    chronometer, it would be unwise implicitly to trust it; and, therefore,
    great caution is necessary in navigation. If the ship had two, and they
    happened to differ, it would be impossible to tell which was right. If,
    however, she had three, the coincidence of any two of them would throw a
    strong probability on the truth of their results; while the mean of the
    three may probably be more safely relied on than any one of them taken
    singly: added to which, the examination of their intercomparisons, as
    pointed out above, gives the means of detecting which of the three is
    An appendix of his book has the chronometer rate log from HMS Fly during
    four years exploring the Australian coast. That ship carried 12
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