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    Point Venus, August 1773
    From: Alexandre Eremenko
    Date: 2007 Apr 29, 15:28 -0400

    
    
    This time I try to find out what's happened
    in Point Venus in August 1773, that is about a year
    befre, during Cook's first visit of Point Venus
    in his SECOND voyage.
    
    Something very interesting has happened indeed:-)
    
    The set consists of 12 shots of Sun-Moon distances.
    Unlike in May 1774, they use astronomical quadrant
    this time for the altitude of Moon, and some
    unspecified quadrant/sextant for the altitude of Sun.
    This time they say what the height above sea level was,
    and again I prefer to use the Sun
    altitude to derive the time
    of observations.
    
    So the scheme of my computations remains the same.
    1. I reduce the Sun alt by adding SD, refraction and dip
    corrections (from modern almanac).
    2. Using terraserver position and Sun corrected alt
    I derive the time (GMT) of observation.
    3. Using terraserver coordinates and this GMT
    I derive Lunar distance error and Moon atl error,
    and Clock error. (Having certainly corrected their
    observed Moon altitudes with the modern almanac).
    
    Here are the results.
    Lunar distances are perfect.
    Just outstanding (by my standard, which may differ from
    Frank's much higher standard.)
    The average error in the first series (6 observations)
    is -0.2' and sigma is 0.65.
    The average error in the second series (6 observations)
    is -0.2' and sigma is 0.1' (!!)
    
    The most amazing thing about the whole business is
    WHAT HAS HAPPENED BETWEEN THE FIRST and the SECOND series.
    
    The time interval between them is 5 minutes.
    During this time, they re-checked IC for all three
    instruments. And the thing I find most puzzling is
    that IC of their sextant used to take the Lunars
    changed from +1' to -3'42" (This is what they
    recorded !!!)
    
    Was it dropped??
    More likely is that the observer noticed a substantial
    side error/lack of parallelism or whatever while
    shooting the first series. So he adjusted the sextant
    and re-checked the IC.
    Other instruments IC were re-checked at the same time,
    and they did not change.
    
    Another possibility is that they used another sextant
    for this second series (and did not record this fact).
    Anyway, the Lunars of both series seem outstanding to me.
    
    2. Moon's altitude. There are still problems with
    Moon's altitude, though not so severe as on
    May 1774.
    The average error is -3.8' and sigma is 2'.
    (I recall that this time this was a stationary
    "astronomical quadrant", of hudge radius
    and using artificial horizon (a plumb line).
    The stated error/correction is 0.5'.
    
    I can only conjecture that taking the Moon altitude
    was considered not very important business
    which was delegated to some apprentice midshipman
    (or perhaps even a boy) who was not really thinking
    of high precision, but rather about Thaitian girls
    passing by:-)
    
    Unlike Frank's XX century apprentices who shoot
    everythig with less than 0.2' error, without any
    preliminary experience:-)
    
    3. Derived longitude.
    This time the "residual error" of shooting
    was of the opposite sign to the almanac error.
    The almanac error on this day was 0.9'
    and should had contributed 25' in the longitude error.
    The shooting error, as I said before was only about -0.2,
    and its contribution to longitude was 5'5.
    
    The actual errors in their longitude are
    14.6' for the first series and 2.6'
    for the second.
    
    Which is just within best possible theoretical
    precision of the Lunars method, using ordinary tools
    almanacs and reduction methods.
    
    I may add that WHEN NEEDED, they COULD shot altitudes
    to 0.5'. This is seen from their latitude observations.
    Their latitude deviates from Terraserver by only 0.5'.
    Perhaps by even less, because I am not 100% sure
    in the Terraserver position of their observation
    place.
    
    Alex.
    
    
    
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