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    Re: Sun Moon Lunars to 155 degrees
    From: George Huxtable
    Date: 2010 Mar 29, 00:35 +0100

    Brad shouldn't take the stated chronometer time too seriously. I attach a
    plot from the Howse and Hutchinson booklet "The clocks and watches of
    Captain James Cook", from Antiquarian Horology. Bayly, in Adventure, was
    using the Arnold chronometer, which was already, by then, losing  over 40
    seconds per day.
    The averaged rate of loss since the voyage commenced was something like 25
    seconds per day, and the voyage had been going for nearly a year. So,
    unless the timekeeper had been reset at some time during the voyage (and I
    have no idea if it had, or not)  its indicated time could, by then, be out
    by something like 2.5 hours.
    One of the purposes of the voyage (the first on which chronometers were
    carried) was to assess the usefulness of the new timekeepers. Such a long
    voyage was a hard test. The chronometers only remained useful because their
    errors could be reassessed by means of lunars and, on land, occultations
    and Jupiter moons, as the voyage progressed.
    It should be possible to deduce the longitude on that date from predictions
    without reference to the chronometer.Be careful about the date, however. I
    assume that the nautical day was probably being used, not the civil day or
    the astronomical day. Crazy business, but there it is.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    From: "Brad Morris" 
    Sent: Sunday, March 28, 2010 10:21 PM
    Subject: [NavList] Re: AW: Sun Moon Lunars to 155 degrees
    I took the data provided by Wolfgang (112572.wales 4 august 1777.pdf)and
    utilized it directly with Frank's online Lunar calculator.
    To Re-Iterate the data from the log, we find
    Date 4 Aug 1773
    TIME  01-18-59
    Lunar Distance (Sun) 155 degrees 13 minutes 7 seconds
    Sun's Alt LL 5 degrees 41 3/4 minutes
    Moon's Alt LL 10 degrees 31 7/8 minutes
    DR Longitude 227 degrees 40 minutes 30 seconds
    DR Latitude S20 degrees 49 minutes
    As the alitudes are given as lower limb, we should add 15.8 minutes to the
    sun's altitude and 15 minutes (?? don't know if this is correct) to the
    moon's altitude.  This yields Sun's alt 5 degrees 57.5 minutes and the
    Moon's alt 10 degrees 47.8 minutes
    Firstly, I injected all terms directly from the logbook into the online
    Lunar calculator.  The response was that there was more than 2 degrees of
    error in the lunar distance and about 194 degrees of error in longitude.
    That didn't seem reasonable, so I checked the "predicted" lunar distances
    for the day.
    Aha!  The distance, at DR, was 155 degrees 39 minutes at 15-00 and was 155
    degrees at 16-00.
    Conclusion #1:  The time recorded in the log may be the time on the face of
    the watch.  It may be UNCORRECTED!
    Next, I manipulated the time injected into the clearing of a lunar online,
    until the sun's altitude was spot on at 5 degrees 57.5 minutes.  Why?
    Because the motion of the sun would have been know better than that of the
    moon.  Using a time of 15-48-12, the sun's altitude is correct and the
    moon's altitude is given as 10 degrees 40.2 minutes (about 7 minutes of
    error in altitude).  The online calculator then states that the lunar
    distance is in error by less than 0.1 minutes and the error in longitude to
    be 1.6 minutes.
    Conclusion #2: Back to the time piece, it showed 01-18-59 while we can
    calculate 15-48-12.  Wow, that's a chronometer error of 14-29-13!!
    Question #1:  Is it fair to assume that the motion of the moon wasn't well
    enough understood in 1773 to be able to calculate moon altitudes?  7
    minutes seems like a large amount, although that is dependent on my
    estimate of 15 minutes semi diameter for date.
    Question #2: Is the chronometer error that far off or is it a matter of the
    astronomical day vs the sea day?
    Conclusion #3: After a quick look at the USNO site, the moon was full on 2
    August at 16-26 GMT.  As the date in the log is 4 August, the moon is
    indeed very near to full, no matter how we account for the astronomical vs
    sea vs civil day.  Most interesting then is that the sun would set (due to
    phase) before the moon would rise, preventing this from being an afternoon
    observation.    The moon is about to set and the sun has risen, making this
    an early morning observation.  At least that is the way I think about it at
    this time!
    Question #4: In the first column of the log, the navigator is giving the
    astrological "signs" and planet "signs".  What do these mean?
    Best Regards
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