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    Re: Cocked hats, again.
    From: George Huxtable
    Date: 2007 Mar 17, 16:49 -0000

      Gary has written, in Navlist 2353,
    
      Regarding your other post today, I too learned that your position
    was
      always inside the triangle with the most likely point being the
    center.
      We now know that was bad information.
    
    And has been asked, by Peter Fogg, rather aggressively and
    persistently-
    
    Are you sure someone said those words: "always inside the triangle"? I
    have never come across such a statement.  Could the statement have
    been more along the lines of the calculable fix lying at the centre of
    the position lines? In which case it wasn't bad info at all.
    
    Gary was referring to what he had been taught, not quoting from a
    book, so none of us is in a position to question his recollection, or
    demand evidence. However, it corresponds exactly to what I had been
    taught, and to the recollection of several others I have asked, and I
    have no doubt that Gary described his teaching correctly..
    
    Peter's admission, that he had never read such a statement, indicates
    the limits to Peter's reading, and does not put Gary's account into
    question.
    
    Over the years, I have acquired an assortment of texts on navigation,
    some of questionable merit, and am able to quote the chapter and verse
    that Peter Fogg demanded, as shown below.
    
    No attempt has been made to distinguish between references to cocked
    hats arising from compass bearings to three landmarks, and those
    arising from three astro position lines. Any reference to the
    possibility of the true position being outside the triangle is indeed
    hard to find.
    
    Here goes-
    
    Little Ship Navigation, Rantzen, 1961, page 122. "...The crossing
    lines define a triangle, known as a cocked hat. ...The position of the
    ship is somewhere in this triangle..."
    
    Sea Navigation, Gates, 1968, page 51. "Rarely, of course, will the
    three position lines intersect at a common point, and more usually
    they will form a small triangle or 'cocked hat'.... The ship's
    position is then assumed to be at the centre of the triangle. If the
    triangle is a large one (even after checking the observations), then
    the position of the ship is taken as the apex of the triangle nearest
    to danger."
    
    Learn to Navigate, Mosenthal, 1998, page 42. "Your are more likely to
    end up with a cocked hat like this [diagram shown here]. You normally
    take the middle of the cocked hat as your position. Unless you are
    near a danger, when you take the 'worst' position- the point nearest
    the danger."
    
    Navigation for yachtsmen, Blewitt, 1973, page 52. "When your cocked
    hat is small, you can put yourself in the middle of it. This is not
    necessarily logical, but in practice is the best you can do." If the
    cocked hat is larger she suggests a position at a point marked X on
    one of the sides of the triangle, corresponding to the bearing of
    which you have most confidence. No suggestion that the true position
    might possibly be outside the triangle.
    
    Dutton's navigation and pilotage, 1969, [highly reliable on most
    matters] art. 2016. Referring to LOPs, "In practice they will seldom
    intersect at a point but will produce a small polygon, which usually
    contains the position of the ship." However, in the case of a
    triangle, if we agree on the 1 in 4 probability, that's far from
    "usually".
    
    Admiraly Manual of Navigation, vol 3, 1938, page 166, states- "...
    when a cocked hat is obtained, it is customary to place the ship's
    position in the most dangerous position that can be derived from the
    observations..." However, in the previous paragraph, an interesting,
    and somewhat contradictory statement is made "... it can be seen that
    the chance of F's falling inside the cocked hat is only 1 in 4". Here
    then, is the first official backing for the 1 in 4 figure that I have
    come across.
    
    And here we should give credit to Cotter, better known for his
    "History of Nautical Astronomy". In "The complete Coastal Navigator",
    1964, page 187, he writes- "In the general case, where the errors e1,
    e2, and e3 are not known either in magnitude or sign, the possibility
    or chance of P lying within the cocked hat is only 1 in 4."
    
    On that evidence, perhaps Peter Fogg will retract.
    
    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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