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    Point Venus, May 1774
    From: Alexandre Eremenko
    Date: 2007 Apr 24, 08:24 -0700

    What exactly happened in Point Venus in Thaiti
    in the first week of May, 1774?
    
    Point Venus, S 17d29'8, W 149d29.6 (from Terraserver)
    In the records we find the following data:
    
    date, time-by-the-clock,
    zenith distance of the Sun,
    altitude of the Moon,
    distance from the Sun to the Moon,
    Barometer, thermometer,
    derived longitude. Errors of the Quadrants (all three).
    No dip or alt above sea level is recorded.
    
    The question is what can we do with these data.
    Let me try to assess the reliability of each piece.
    
    Time-by-the-clock seems pretty useless;
    my preliminary investigation shows that this was a really
    lousy clock (see below).
    Zenith distance of the Sun seems to be the most reliable
    number. It was taken by an "astronomical quadrant"
    A stationary one, of the type of transit/theodolite,
    I suppose. And it took the zenith distance rather
    than altitude, so I suppose it is dip-independent.
    The Error of this quadrant is recorded as 21",
    a quantity one can neglect for the first approximation.
    (See below why I prefer to neglect their recorded IC,
    at least in the first step of this investigation).
    The altitudes and the distances were recorded
    "as read on the sextant scales", no corrections added,
    
    The main problem is to determine the GMT of each observation
    as precisely as we can.
    
    I used the following method. For the given date,
    I determine GMT from their presumably
    most precise observation, the Sun zenith distance.
    I use Frank's calculator to do this.
    
    The procedure is exactly the following.
    I take their Sun ZD, convert it to altitude,
    subtract refraction and add/subtract Sun SD,
    according to the limb observed.
    Then I find by trial-and-error, using the Frank
    calculator, the GMT of the moment when the Sun was
    on this altitude on that day, in their position
    (Terraserver position).
    
    Then I use this GMT, and this position, to compute
    the rest of the quantities: Moon alt, and Sun-Moon dist.
    Then I reduce their Moon alt using parallax, refraction
    and Moon SD.
    Then I record the errors:
    a) of their watch, as compared with GMT
    b) of their Moon altitude and
    c) of their Lunar distance.
    
    1. The clock was terrible. Going 1-2 MINUTES PER DAY!!!
    Irregularly. They should had better used a sandglass:-)
    I conclude from the citation below that the clock was
    regulated to sideral time, rather than mean solar time,
    but in any case, their time records do not help in
    determining the GMT with reasonable precision.
    
    It is very interesting, what Wales (the astronomer
    in this expedition) says about this clock:
    
    "...it may not amiss to take notice of some
    very extraordinary irregularities, which happened to
    the going of the Clocks..."
    
    "The Clock B lost 1m22s a day on syderal time at Otaheite,
    lat 17d29'1/4 S and long 210d25' E from April 23d
    to May 9th, 1774; but I here reject its loss
    between April 30-th and May 1st,
    as it appears to have lost exactly 1m more on that day
    than on any other;
    a circumstance I cannot account for PROPERLY,
    as I never, that I know of, left the case or face of
    the Clock unlocked." And  he continues:
    
    "There is however little doubt but that some WITTY
    Gentleman or other found means to open it, and put the
    Clock a minute back,
    I suppose to try whether or no the
    ASTRONOMER could find it out."
    
    (Astronomical Observations... p. xvi. Emphasized words
    are in his text). I suppose when he says 1m22s a day
    he means that the AVERAGE LOSS was 1m22s EVERY DAY.
    I only investigated 3 days so far (May 1-3).
    
    And I have to say that they were negligent in recording
    the date, but this is easy to fix.
    (For example, they never make clear whether they record
    the local date or Greenwich date, and how do they count the
    local date. Given that their longitude was
    "210 East" as they say:-) this makes the thing puzzling
    in the beginning. But I was able to fix all GMT dates
    beyond reasonable doubt:-)
    
    This message is too long. I will continue in the next one.
    
    Alex.
    
    

       
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