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    Re: Cocked hats, again.
    From: Gary LaPook
    Date: 2007 Apr 16, 03:13 -0700
    Gary LaPook wrote:

    Sorry it has taken me so long to get back to you on this. I never recieved this post. For some reason my junk mail filter depostied it in the junk mail box and I was going through it today prior to deleating them all when I found your post.

    I haven't been looking for sources  but I did run across one while looking for something else. U.S. War Department Technical Manual TM 1-206, "Celestial Air Navigation" March 4, 1941 section 54 entitled "Fix by position lines" sub paragraph (b)  states:

    "If three simultaneous position lines such as shown in figure 33 are determined, the true position may be reckoned to be somewhere within the shaded triangle."  Figure 33 shows three LOP's forming a triangle with the interior of the triangle shaded. in. (I can scan it in if you need to see the page.)

    Merriam-Webster's Online Dictionary, 10th Edition defines "reckoned" as:

    " to accept something as certain : place reliance <I reckon on your promise to help>";

    Cambridge Dictionary of American English says: "
    to consider or have the opinion that something is as stated ."

    So, that's one example where there is no qualification, no "sometimes," no "often" no "assumed." It may not use the word "always" but it is clear from the wording that that is clearly the import of the statement.

    P F wrote:
    Earlier Gary baulked when asked to provide evidence to back up his contention:
    > 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.

    George Huxtable contends:
    > 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.

    This is factually incorrect, my dear sweet old chap. You really should check your sources before rushing into print with what you imagine that you remember that someone once wrote - and in this case not so long ago! This goes to the heart of this matter, does it not? This is why evidence is needed - because our minds play these little tricks upon us, do they not?  It is only too easy to convince ourselves (whether unconsciously or not) that what we would like to remember is the fact, rather than fancy.

    This is what Gary actually wrote:
    > No, it read it a number of times from a number sources over a large
    > number of years.

    Now George attempts to do as much; to provide Gary's evidence (a quixotic crusade if ever I heard of one) accompanied by a few snide comments, as is his merry way. Let's have a look at this evidence:

    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..."

    I agree that this could be worded better. The addition of 'assumed to be' inserted between "is" and "somewhere" would do the trick. But it fails the Gary test: no " position ... always inside the triangle".

    Gary adds:

     The above quote is again an unqualified statement that  the position is inside the triangle and english grammer doesn't require the use of the word "always" to make the statement unqualified. It appears that this one also supports my position. Note, the author of that book didn't feel the need to use the word "assumed" as you would have liked him to have done.  Maybe you should write your own book on navigation.

    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."

    Well put. No problems here, that I can see. "Assumed to be" gets it right.
    Fails the Gary test: does not state: "position ... always inside the triangle".

    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."

    Gary adds:

    Both of these quotes support my position. Although there is the use of your favorite word "assumed" and another locution, "normally" the clear import is that you can be sure that you are within the confines of the triangle. This is clear from the statement that if you are near a danger then, in the interest of safety and conservatism, you abandon the "normal" "assumption" that you are in the center of the triangle and use the point, still within the triangle, that is closest to the danger as the position of the ship. It does not say "assume that you are within the triangle" the word "assume" only modifies the use of the "center" as the true location of the ship. Also, it does not state, even when discussing proximity to danger, that your true position may be outside the bounds of the triangle and possibly closer to the danger than the boundary defined by the positon lines. A clear reading of these quotes shows that they are also unqualified statements that the true position is within the triangle and the word "always" is not needed to make this stronger.

    Anyway, I  think this shows that there are many texts that state the position is found within the triangle so I think I have proved my point. I see below that you have found some other texts that say "not always" but that does not negate the proof above. Remember I did not say "every book ever published on navigation states that you will always be within in the triangle." I said I had read it many times in many sources and there are enough examples above to support my statement.

    This also seems fine. You DO normally, etc. Well put. I might add that this advice to assume a position on a position line closest to danger is good simple common sense, based on the evidence of that position line. Fails the Gary test: does not state: " position ... always inside the triangle".

    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."

    I am not impressed by how Mary puts this (why is it not logical - does she go on to say?) but, again, it fails the Gary test: no " position ... always inside 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."

    This is the most damning so far, as it directly contradicts the 25% / 75% theory. However, and crucially, it DOES NOT say: "always inside" [the shape].

    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

    Good. Well drafted. I'm not sure how customary it is, although makes excellent common sense.

    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.

    So this doesn't quite fit the Gary contention either.

    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."

    No assistance towards the Gary crusade here either, it seems.

    On that evidence, perhaps Peter Fogg will retract.

    Or perhaps not. Based on this lack of evidence. The need for retractions would seem to lie firmly in your camp, George. We shall all await them with bated breath.

    So, putting behind us that tedious and useless exercise - these sources mostly got it right; NONE could support Gary - you will note the silence from George on my recent, and more relevant, posts on this issue. What George does not say is sometimes more telling than what he does (not difficult in light of the above example).

    Neither George nor anyone else, it seems, has found much to quibble about with the central thrust of my contention, argued now on many fronts with examples and diagrams galore: that this 25% / 75% brou-ha-ha really is futile and pointless ... literally!

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