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    Re: Certaine Errors in Navigation Corrected
    From: Gary LaPook
    Date: 2007 Sep 26, 00:41 -0700

    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"  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
    > 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 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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