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    Re: Certaine Errors in Navigation Corrected
    From: Gary LaPook
    Date: 2007 Oct 07, 13:05 -0700

    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.
    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"  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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