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    Re: Point Venus, May 1774
    From: George Huxtable
    Date: 2007 Apr 25, 00:49 +0100

    Alex asked-
    |
    | 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.
    
    =======================
    
    Just a few comments before I head for bed.
    
    When he was in harbour, Cook used ordinary civil date for his journal, in
    which the day commenced at local midnight. However, the almanac used a day
    which was 12 hours later than that.
    
    Being about 150 deg West of Greenwich, and having travelled Westward from
    Greenwich, his timing would be about 10 hours behing Greenwich for the
    corresponding day. That is, when it was Greenwich noon, it was about 2 am at
    Tahiti, on the same day. There was no international date line then, and even
    if there had been, Cook hadn't reached it yet.
    
    The quadrant was 1 foot radius, made by Bird (so it would have been the best
    obtainable) It had been set on a vertical post placed in a barrel of wet
    sand, which had been inset into the ground.
    
    There was an astronomical clock and an alarm clock (from the Royal
    Observatory), and a journeyman clock bespoke of Mr Shelton.
    
    The astronomical clock, made by Shelton and furnished with a gridiron
    pendulum....   ...The pendulum was adjusted to exactly the samelength as it
    had been at Greenwich.
    
    According to Beaglehole, 40 years ago, Shelton's clock is still going
    accurately in the Royal Society's rooms.
    
    As an astronomical clock, it will have been intended to keep sidereal time,
    about 4 min per day faster than Sun time. But its rate would change, between
    Greenwich and Tahiti, in a way that would have been unpredictable at the
    time, because of gravity differences. So it needed either adjusting, or at
    least rating, using star transits.
    
    That's enough. Bed.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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