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    Re: Point Venus, May 1774
    From: Alexandre Eremenko
    Date: 2007 Apr 27, 14:10 -0700

    This is the continuation of my messages of April 24 and April 25
    on the Point Venus observations of Cook's expedition on May 2-6 1774.
    
    1. I fixed the "clock problem". The Clock was not so bad after all.
    Except an unexplained leap of 1 minute on May 1 (see my message on
    April 24)
    it was slowing down by 1m 22.6s per day plus-minus a fraction of one
    second.
    The astronomers of the expedition checked its going against the Sun,
    and they determined the rate perfectly, and this is confirmed (to 1s)
    by my computations.
    This was a Syderial Clock (showing GHA Aries, rather than Mean solar
    time).
    
    2. I can prove that what they call "Quadrant error"  (for the
    instrument used in measuring
    the lunar distance) in their observation journal is in fact the
    CORRECTION, not "error".
    They don't say which instrument exactly was this.
    To prove this, I reduce their own observation using their own almanac,
    and this correction (which they call error) and obtain the same
    longitude AS THEY COMPUTED.
    
    3. The residual error of their lunars (after applying the correction
    mentioned above in part 2),
    was -0.5' on May 2, -0.6' on May 3 and -0.45' on May 6. These are the
    averages of 5-10
    observations each time and sigma in each series is from 0.2' to 0.4'.
    These errors are the errors of OBSERVATION, have nothing to do with
    the
    almanac.
    These errors are SYSTEMATIC, every single shot is an overshot.
    Exactly the same picture as I had for years with my own observations.
    Averaging does not help at all in this situation.
    
    4. The resulting error in longitude is a sum of the observation error
    described in section 3,
    and the error resulting from the almanac. On these dates these two
    errors ADDED.
    On May 2, the almanac contributed 30' and the observation error
    contributed 14',
    giving the total error in longitude  of 44' in longitude.
    On May 3, the almanac error contributed 32' and observation error 17'
    to the total of approx. 50'
    On May 6, the almanac contributed 20' and the observation error 23' ,
    and there was probably
    some smaller reduction error.
    Thus we see that the role of the observation errors was roughly of the
    same
    magnitude as the errors in almanac.
    
    5. The only thing about these observations that I still don't
    understand is the errors
    in the Moon altitudes.  They are very large and also systematic.
    6' on May 2,
    15' on May 3 (!) and
    8' on May 6.
    For this I have no clue.
    These numbers do not take into account their "quadrant error" which
    was less than 3'
    for this quadrant all the time.
    
    Alex.
    
    
    
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