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    Re: Sun Moon Lunars to 155 degrees
    From: George Huxtable
    Date: 2010 Mar 30, 12:57 +0100

    Brad wrote-
    
    
    "For the same lunar distance at 155 degrees 13.1 minutes, I used Frank's
    online calculator and a time of 15-48-12.  I injected the altitudes exactly
    as given in the log into the LL (lower limb) fields of the calculator.
    Frank's calculator states that the error in the lunar is now Zero minutes!
    The error in longitude is a mere 1.3 minutes.
    
    Therefore, if you know precisely what Frank means by his altitude fields,
    you can determine more about the data presented in the log.  The solution
    that Frank provides states "Cleared using observed altitude".
    
    Finally the calculator states an error of 3.8 minutes in Moon altitude and
    3.4 minutes in the Sun's altitude. In attempting to use 3.6 minutes as an
    index correction, it is shown that the error in alitudes are in opposite
    directions."
    
    =======================
    
    Brad needs to be careful here. Frank's online lunar calculator is intended
    for a rather different purpose.
    
    It needs to know the observer's position (latitude and longitude), and GMT,
    and then it will predict a lunar distance, which an observer can compare
    with his observation.
    
    Brad has taken a stated position, and an observed lunar distance, and using
    the program backwards, has adjusted the GMT until it gives the right value
    for lunar distance. He has found a suitable time, at which the calculated
    lunar distance corresponds to Bayly's observation, providing an error on
    longitude of just 1.3 arc-minutes. Indeed, another 5 seconds-worth of
    adjustment to GMT would have reduced that error to zero.
    
    That is a perfectly valid thing to do, IF the observer's position is known.
    But to Bayley, his position wasn't known. His latitude was known (or at
    least assumed, well enough). But his longitude wasn't known. It depended on
    the result of the lunar observation, the value of GMT. And ALSO depended
    (and this is the crucial matter) on his measurement of local time, which
    presumably was obtained, at that same moment as the lunar, from the
    altitude of the Sun, though there's nothing on that page to tell us so.
    
    If Brad had started from a different position, in longitude, he would have
    got a different value for GMT. So, without that crucial observation for
    Local Apparent Time, he has, as yet, ascertained nothing. I think (and no
    doubt he will correct me here if I have it wrong) that Brad has not yet
    deduced the LAT obtained from that Sun altitude. When he has done this, and
    differenced GMT and LAT (allowing for equation of time), Adventure's
    longitude will be the result. That is unlikely to be very different from
    the initial assumption of longitude that Brad has started from, but only
    because that assumption was based on Bayly's competent observations, for
    both Greenwich Time and Local Time. Both are needed. If the resulting
    longitude does differ greatly from the presumed value, then a reiteration
    is called for, because position changes affect the clearing process (a
    bit).
    
    If we do take Bayly's position, it's interesting that the value for
    Greenwich Time that it produces is about two-and-a half hours ahead of the
    reading of his chronometer. I had warned, in a previous postin, that times
    on that chronometer should not be taken at face value, because of its poor,
    and worsening, slow running since the voyage started the year before. And I
    reckoned, from the graph that Howes produced, that it was likely to be
    running something like 2.5 hours slow, by that stage in the voyage. Which
    is just what it's turned out to be. No doubt, Howes deduced that graph from
    just the sort of observations, aboard Adventure, that we are looking at
    now, which just goes to show that we are all self-consistent.
    
    And also shows that without lunars to correct it, that chronometer would
    have become a useless tool by that stage of the voyage. No doubt there will
    be a table of corrections to their chronometers, at various dates, to be
    found in Wales and Bayly.
    
    George.
    
    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.
    
    .
    
    
    
    
    

       
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