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    Re: Certaine Errors in Navigation Corrected
    From: Gary LaPook
    Date: 2007 Dec 04, 00:44 -0800
    Gary LaPook writes:

    I have now read the article on the ION disk  and it does not use the method shown by Wright to calculate great circle distances  so I still do not know why it works.

    gl
    I just ordered the ION CD and I see by the table of contents that it
    contains an article entitled "GREAT CIRCLE SAILING (GRAPHIC SOLUTION)
    William M. Fraser Vol. 15 No. 01, 1968. "Has anybody read this article
    and does it describe the same method as used by Wright? hopefully with
    an explanation as to why it works.
    
    gl


    glapook{at}PACBELL.NET wrote:
    I just ordered the ION CD and I see by the table of contents that it
    contains an article entitled "GREAT CIRCLE SAILING (GRAPHIC SOLUTION)
    William M. Fraser Vol. 15 No. 01, 1968. "Has anybody read this article
    and does it describe the same method as used by Wright? hopefully with
    an explanation as to why it works.
    
    gl
    
    
    Vol. 15 No. 01, 1968
    
    On Sep 26, 12:41 am, glap...{at}PACBELL.NET wrote:
      
    Gary adds:
    
    That is why it would have been better if Wright had started out with
    the general method first before showing the special cases.
    
    gl
    
    On Sep 26, 12:35 am, "Gary J. LaPook" <glap...---.net> wrote:
    
        
    Gary replies.
          
    We can agree that the first two special cases he gives, (the first with
    both points on the same meridian;  and the second case with both points
    on the equinoctial) are trivial with the distance being the difference
    in latitude in the first case and the difference in longitude in the second.
          
    The case you bring up Wright  illustrates with the computation of the
    distance between London and Cape Blanco each having the same latitude of
    51º 32' north. Because they have the same latitude the general method
    can be simplified but it still works. You start out the same way and
    draw in the points and the lines representing London "B, C, E, and F."
    You draw in the lines and points for Cape Blanco "D, I, K, and L."
    Applying the general method, you set your dividers to the space between
    "L" and "F" and leaving one leg on "F" you swing the other leg to place
    a point on the line "B- C" at that distance from "F" towards "C" just
    like we did in the example with Jerusalem where we plotted "P."  Doing
    it now with the Cape Blanco example let's plot "P2."  Still using the
    general method, we set our dividers to the distance between "K" and "L."
    and set one leg on "E" and placing the other leg on the line "E-F" we
    plot "Q2" just like we plotted "Q" in the Jerusalem example. But wait,
    since the latitude of Cape Blanco is the same as the latitude of
    London, "K-L" is equal to "E-F" so when we plot "Q2" if falls on "F."
    Still following the general method, we use our dividers to measure the
    space between "P2" and "Q2" which turns out to be the same as "F-P2"
    which is the same as "L-F."  So when both points have the same latitude
    we can skip several steps and go right to the circle scale with "L-F."
    Does that help?
          
    gl
          
    George Huxtable wrote:
          
    Thanks to Gary LaPook for bringing to our attention that treatise by Wright,
    and the puzzle his diagrams represent.
            
    There's been little or no reponse so far, and perhaps that's because others,
    not just me, have been struggling to understand what's behind Wright's
    construction.
            
    I agree with Wright that his first construction, in the case where the
    departure point and the destination are at the same latitude, gives an exact
    answer. He proposes a second, different, construction when those latitudes
    differ. However, if you then apply that second construction to the
    special-case where the latitudes are in fact the same, it should boil down
    to the same thing as the first construction. I'm not sure that it does. So
    I'm not convinced yet that he has got things right. Could there be another
    typo in his text, perhaps, or in the labelling of his diagram?
            
    George.
            
    contact George Huxtable at geo...---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
            
    
    
    
    
      


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