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    Re: Rocky Mountain Lunar Distance
    From: George Huxtable
    Date: 2002 Dec 16, 19:31 +0000

    Well done, Arthur Pearson!
    
    Instead of sitting in an armchair arguing it out (I plead guilty to that),
    you have gone out and tried it. And given a good coherent account of it for
    the rest of us to follow. Thank you, Arthur.
    
    It's left me with a few assorted questions and comments.
    
    1.I've never used a "bubble horizon" with a sextant, and wonder what
    performance can be expected from it on land. Is Arthur's experience of the
    bubble horizon being "a real challenge" a common one, and does an error of
    7 minutes strike other users as the sort of accuracy (or inaccuracy) one
    has to expect? For measuring such on-land altitudes, would an aircraft
    bubble-sextant have done better?
    
    2. If the afternoon Sun altitude had been measured halfway through the
    set-of-four lunar distances, then this could have been treated as an
    observed altitude (which it was) rather than an altitude to be calculated.
    Did Arthur also observe a Moon altitude at or near that time? I appreciate
    that he was demonstrating the art of calculated altitudes, rather than
    mmeasured ones (and has done it well). It would be interesting to see any
    figures.
    
    3. On returning to civilisation, did Arthur check his wristwatch against
    Zone time, to retrospectively confirm the time-accuracy of his afternoon
    sun observation? Just for cross-checking. It depends, of course, on how
    reliable was the timekeeping of his wristwatch, over that interval.
    
    4. I hope Arthur doesn't mind too much if I quibble somewhat about the way
    he treated his four lunar-distance observations. His rejection of the first
    two (because although more than a minute apart they gave identical values)
    would not find favour in a science lab. The lunar distance changes only by
    about half-a-degree in an hour, or in a minute of time by about 0.5
    arc-minutes (maybe somewhat less if parallactic retardation is
    significant). Even if the error of each observation was as little as 0.25
    arc-minutes, it would be quite unsurprising to find two observations, 1
    minute of time apart, giving exactly the same lunar distance. Arthur
    should, I suggest, plot out all four observations against time, and draw a
    best-line between them by eye, with a slope that he can work out in
    advance. That line will probably steer a path roughly midway between those
    first two observations. It would be easier for us to check on this if all
    the raw data was provided.
    
    If this plot was made, and all four observations taken account of in this
    way, my guess is that the resulting longitude would come within 45 minutes
    or so of the true value, which wouldn't be a bad value for a lunar,
    especially at first attempt. Captain Cook would have been pleased with
    him...
    
    5. Arthur quotes the expression for LHA Moon as-
    (LHA Sun +/- difference between GHA Sun and GHA Moon)
    but the ambiguities in this could cause trouble and it should be expressed
    more exactly as-
    LHA Moon =LHA Sun + GHA Moon - GHA Sun (adding or taking off 360� where
    necessary).
    
    GHA values have been provided the nautical almanac since 1952. Earlier
    almanacs gave Right Ascensions (RA) instead, which were in terms of time
    rather than angle, and measured Eastwards rather than Westwards, from a
    different base. Because of that, LHA Moon was  derived from-
    LHA Moon = LHA Sun + 15*( RA Sun - RA Moon) where the 15 is to convert time
    in hours to degrees, and the subtraction is the other way round.
    
    6. Arthur says-
    >David Thompson explored western Canada and his navigational procedures
    >are documented by J. Gottfred at
    >http://www.northwestjournal.ca/dtnav.html.  Thompson�s use of calculated
    >altitudes is elaborately reconstructed by Gottfried who provides a
    >comprehensive set of diagrams and trigonometric formulas in explanation
    >of the technique.  It is interesting to note that Thompson worked his
    >own sights to a full solution in the field.
    
    Well, I have read Jeff Gottfred's account, and it that he quotes no
    longitudes obtained by Thompson. Thompson may indeed have calculated
    longitudes in the field, but I can't find that in Gottfred's paper. I may
    have missed something, though.
    
    I agree with Arthur's conclusions about insensitivity to errors, but point
    out that he has demonstrated this just for one particular configuration of
    Moon and Sun, and it will not be true to quite the same extent with
    differing geometries.
    
    I do hope that Arthur enjoyed the skiing part of his trip, and that he will
    take his observing gear with him next time too, though it can't be much fun
    lugging a sextant about on skis.
    
    George Huxtable.
    
    
    ------------------------------
    
    george---.u-net.com
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.
    ------------------------------
    
    
    

       
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