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    Re: Point Venus, May 1774
    From: Fred Hebard
    Date: 2007 Apr 27, 17:29 -0400

    It's a joy to read your posts.
    On Apr 27, 2007, at 5:10 PM, alex wrote:
    > 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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