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    Re: Certaine Errors in Navigation Corrected
    From: Gary LaPook
    Date: 2007 Sep 26, 00:35 -0700

    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 
    51� 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 george---.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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