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    Re: Point Venus, May 1774
    From: Alexandre Eremenko
    Date: 2007 Apr 25, 11:01 -0700

    This is a continuation of my previous message
    with the same title.
    My calculation outlined in the previous message implies
    that the going of the Clock from May 2 to May 6 was
    approx 22m33sec per day.
    What sort of "astronomical clock" was this, I don't know.
    And why did not they use chronometers instead.
    2. Moon's altitude. Here something happens that I cannot
    understand. The average error in Moon's altitude
    was +6' on May 2 (average of 5)
    and +7'8 on May 6.
    The stated Index errors were +1' and +3', respectively.
    Which leaves us with unaccounted 5'.
    The only plausible explanation I have for this 5'
    is that they had a substantial dip, which they did not record
    in their account...
    3. The Lunars. According to my computation,
    the average error of the Lunar on May 2
    was -3' and on May 6 it was the same -3',
    with sigma=0.3.
    I think this is a decent sigma.
    (My average sigma over VERY many observations with modern sextant
    is 0.18).
    However their stated index ERROR was +2'45" and +2'17".
    I stress that this they call quadrant ERROR and they have a clear,
    visible + sign in front of it.
    While my computation gives the error in their lunar -3' (not corrected
    for IC).
    Of course it is tempting to assume that they confused "error"
    with "correction".
    But such assumption implies that their altitude error was actually
    wrong by 7' and 10', which is unbelievable, even if they used
    a very bad quadrant.
    Of course, it is possible that I am missing something.
    But what?
    Here is a complete computation for of one observation on May 6.
    Time by their clock: 0h9m54s (of May 7)
    Sun UL ZenithDist 52d20'
    I compute: Alt(UL)=37d40, minus UL/refr. corr'n =37d23'.
    (Correction is from modern almanac, I suppose Sun SD and refraction
    did not change from 1774).
    >From this I find with Frank's calculator GMT=19:11:52, May 6.
    Thus the error of the clock is 4h58m2s.
    Same calculator says that their Lunar distance of 42d55'1/4
    has error -3.2.
    Same calculator says that Moon alt was 72d24.5 (Moon's center,
    as seen from the center of the Earth
    in the absence of air).
    They measured Moon's alt as 72d00' (LL)
    Using the HP from THEIR almanac I compute corrections from
    MODERN almanac and obtain the cleared alt of Moon center 72d32'3.
    So the error in the Moon alt is +7.8.
    What I am doing wrong here?
    So far I investigated 3 series of observations.
    All have small sigmas in all errors,
    but the systematic errors of unclear origin are much
    larger than I expected.
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