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    Re: Old style lunar
    From: Alexandre Eremenko
    Date: 2004 Dec 12, 00:55 -0500

    On Sat, 11 Dec 2004, Fred Hebard wrote:
    > Perhaps Alex
    > could further massage these data for us.
    1. To decide anything on the source of Thompson errors,
    it is desirable to pull the almanac data for the date of his
    actual observations. I am a bit confused: who of us has a 1800
    (and prhaps 1801 almanac? Can we ask this person to post the data?
    > Errors for stars east and west of the moon often cancel each
    > other out.
    Not the errors in the almanac!
    It is the measurement errors that cancel, not the errors in almanac.
    Index error is a good example.
    Suppose you overshot. Then the distance you measured from a star
    E of the moon will give incorrect Moon's position,
    somewhat West oif its true position.
    Similarly, measuring  the distance from a star W of the Moon
    will give Mooin's position East of the true one.
    Then you average and your errors cancel.
    But the errors in almanac have different effect.
    Notice that the 1800 almanac distances to stars East and West of
    the moon always have opposite sign (with one exception,
    which is a gross blunder, possibly a misprint in the almanac)
    Let us consider an idealized situation when the stars are
    exactly on the Moon's path and positions of the stars are known
    precisely. Consider two stars, Moon in between.
    Then the error in Moon's position will lead to the errors
    in distances which are exactly opposite to each other.
    Now suppose we measured both distances EXACTLY with our sextant
    and want to deduce longitude (or chronometer corr., does not matter)
    Averaging the two reduction results will give you nothing.
    Both will give the same error in time/longitude.
    3. The errors shown in the posting are typically
    more than 0.5' in the distance. That is 15' in longitude.
    This "almost" explains Thompson standard deviation of 20'
    in longitude, but comes a bit short of it.
    To decide whether the main reason of his errors was the
    almanac, we
    need the almanac errors
    on the specific dates of his observations.

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