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    Re: Advancing position circles: Huxtable vs. Zevering
    From: George Huxtable
    Date: 2010 Mar 2, 09:19 -0000

    As predicted, in his latest posting Herman Zevering has failed to provide 
    his own solution to the example with which he was challenged, in The Journal 
    of Navigation, and in my posting of 26 Feb. This is because his proposed 
    procedure gives the wrong answer.
    
    Here is the example, once again-
    
    ====================================
    
    To test his procedure, I proposed a simple example, as follows, which
    presumed a spherical Earth-
    
    1. An observer, at position P1, measures the altitude of a star S1, at (Dec1
    = 0º, GHA1 = 0º), to be 30º.
    2. Then he travels due North by 60 nautical miles,  ( = 1º ) to P2.
    3. From there, he observes another star S2 (then at Dec2 = N 1º, GHA2 = W
    45º) to be at an altitude of 45º.  Where on Earth is he then?
    
    I showed that there were two solutions for P2.
    One was in the Northern hemisphere, at Lat N 46º, Long W 45º, in which case
    P1 was 1º further South, at Lat N 45º, Long W 45º.
    The other was in the Southern hemisphere, at Lat S 44º, Long W 45º, with P1
    situated 1º further South, at Lat S 45º, Long W 45º.
    
    Navlist members can check that those solutions meet conditions 1, 2, and 3
    of the example precisely, by computed altitude tables or by spherical
    geometry, as they prefer.
    
    I then challenged Zevering to apply his proposed procedure to that problem,
    and provide us with initial and final positions for the observer, the
    initial altitude of star S1, and the final altitude of star S2. My own
    estimate was that his final position would be 17' in error, in longitude,
    after a travel of only 60 miles.
    
    ===========================
    
    Readers may like to note that I did not propose any method for solving that 
    problem. All I have done is to present the exact solutions to it, as Navlist 
    members, including Herman Zevering, can check for themselves. If Zevering's 
    method can arrive at those same solutions, all will be well. Does it? I keep 
    on asking....
    
    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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