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    Re: Certaine Errors in Navigation Corrected
    From: George Huxtable
    Date: 2007 Dec 10, 00:07 -0000

    Gary LaPook has set us an interesting problem, and I have been struggling
    with it, on and off, to no avail. That is, to discover how Wright's
    geometrical construction happens to give the right answer to the
    great-circle distance between points A and B. That it does give an accurate
    answer, depending only on the precision with which the measuring has been
    done, I have little doubt.
    
    But I have a morsel of information to offer. I have checked over the results
    Wright states for great-circle distance between pairs of places, for which
    he provides lat and long, and they all come out highly accurate, except one.
    That one is between London, at 51 deg 32' North, 22 deg East of his presumed
    meridian, and Cape Blanco in Newfoundland, at the same latitude, but a
    longitude stated to be 33.5 degrees West of that meridian. For that, Wright
    quotes a distance of 1860 miles, but if I work out the distance between
    those points, I make it 2020.4 miles, a serious error of 160 miles.
    
    However, Wright shows his construction, and a close look shows what has gone
    wrong. Instead of point D being marked at the longitude of Cape Blanco, at
    33.5 deg West, it has, by some error, been marked instead at the wrong
    value, at only 29 deg West. No wonder it gives the wrong answer, then! But
    what that allows us to do is to check the great circle distance beetween
    London and that other point, not at Cape Blanco, but in the sea, at the same
    latitude as London and at a longitude of 29 deg West of his reference
    meridian. If we calculate that distance by trig., it gives 1864 miles, only
    differeing by 4 miles from Wright's geometrical result!
    
    Which adds further conviction to the correctness of Wright's procedure.
    
    Clearly, this problem has been bugging Gary for some time, and if he
    discovers the answer I hope he will share it and put us out of our misery.
    
    George.
    
    contact George Huxtable at george@huxtable.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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