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    Re: The Noon Fix
    From: George Huxtable
    Date: 2009 Apr 10, 09:55 +0100

    I reminded Jim Wilson about this question-
    "But you didn't answer my question about the sextant correction, and how you 
    could know, in advance, what it was going to need resetting to, before the 
    time interval was known. That's still puzzling me."
    And he answered-
    "Your puzzlement is gradually seeping in. I noted that I calculated Dh at 
    the time of maximum altitude for simplicity, implicitly assuming that the 
    slope of the adjusted line was the same as the original. If I were to also 
    calculate it at a time prior to LAN, then I could establish the true slope 
    of the adjusted line. With that defined, the exact time of LAN could be 
    determined posthumously.
    I hope this clears it all up."
    But it doesn't, really. I don't really follow what Jim is telling me, and 
    wonder whether we are at cross-purposes.
    Let me explain, again, what's bothering me, which seems a simple matter. Jim 
    measures a Sun altitude, somewhat short of its highest point, and notes the 
    time. He then waits until the Sun has gone over the top, and then come down 
    a bit again, to reach, not exactly the same altitude as before, but an 
    altitude that's been somewhat adjusted. The adjustment (Δhs) is (Sn - d)ΔWT, 
    where(Sn - d) is the rate of movement between the observer and the body, 
    where Sn is the northerly component of speed, and d is the rate of change of 
    declination, here positive if the change is northerly. Multiplying this by 
    the time between observations ΔWT gives the resultant change in sextant 
    The contradiction, here, is that to make the adjustment, you need to know 
    ΔWT. But you don't yet know ΔWT, the watch-time gap between the 
    observations, until both observations have been made. But you can't make the 
    second observation until you know the adjustment. Stalemate.
    There's no problem in doing the job with hindsight, if the curve of altitude 
    against time has been plotted. But Jim was emphasising a simple procedure 
    that used just one pair of observations, and I still can't see how that's to 
    be done. Perhaps I'm missing something simple.
    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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