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    Re: Certaine Errors in Navigation Corrected
    From: Gary LaPook
    Date: 2007 Dec 09, 17:52 -0800

    Gary LaPook replies:
    
    Thank you George for you interest in this matter and I still have no 
    idea why it works. So far six list members of the list have asked me for 
    copies of the entire book and I have emailed it to them. Hopefully one 
    of them will come up with an explanation.. I am especially mystified 
    that I have found no mention of his method in any of the texts I have 
    consulted. You would have thought it would have rated at least a mention 
    in Bowditch.
    
    George, your post confused me because I had also checked Wright's 
    figures for the Cape Blanco case and came up in agreement with his 
    value. I think you may have read his text incorrectly because I read it 
    as giving the longitude of Cape Blanco as 331º and all of his longitudes 
    are east. This is where he plotted it on his diagram, 331º east which 
    is, as you point out, at 29º west of his prime meridian. This gives the 
    difference in longitude of 51º and using this value with the latitudes 
    of both places of 51º 32' north and using trig I come up with a distance 
    of 1864 NM just as you did and it is within 4 NM of Wright's calculation.
    
    
    I have attached the 10 pages from this book which contain his complete 
    explanation and this includes the page that was missing from my original 
    post.
    
    
    The copy of Certaine Errors that I now have contains an errata sheet on 
    page 12 which I am attaching  which may also be helpful.
    
    gl
    
    
    
    George Huxtable wrote:
    
    >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---.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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