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    Re: Position lines, crossing.
    From: George Huxtable
    Date: 2006 Dec 16, 00:28 -0000

    Going back to the problem that engaged our attention recently, as
    stated by John Cole-
    | Here is the problem that Guy Schwartz asked about and which gave
    | to this very interesting discussion about cocked hats. It is problem
    | 3-2, p. 22, in "100 Problems in Celestial Navigation" by Leonard
    | (1999, Celestaire, Inc.).
    | 1993 May 14
    | 0602 fix  40 31N, 153 08W
    | C=185
    | S=3.6
    | I.C. -1.0
    | Ht. eye 8 ft.
    | Alpheratz 14h  28m 17s GMT  Hs=36  05.1
    | Kochab 14h  29m  52s  Hs=42  40.1
    | Rasalhague 14h 31m 20s   Hs =49  54.2
    | Altair 14h 33m 01s  Hs=58  56.1
    | Venus 14h 37m 04s  Hs=16 18.6
    | Moon LL 14h 39m 33s  Hs=33 15.8
    | Question: What is 14 May 1440 fix? How reliable is it?
    | Answer: 14 01N, 153 09W.
    Earlier, in Navlist 1867, John had written, in relation to Guy
    Schwartz's posting-
    "Perhaps you can share your calculations? I worked this problem and my
    position lines for the Moon, Venus, and Kochab form a very tight
    triangle symmetrically inside a slightly larger triangle for Altair,
    Alpheratz, and Raselhague. This gives me 40 03 N, 153 09 W.  The book
    gives the answer 40 01 N, 153 09 W. I calculated my results using
    spreadsheets of my own design and checked the azimuths using Pub 229."
    Comment from George-
    I have now got round to checking that problem, and my plot rather
    agrees with John's conclusions. I would guess an effective centre of
    the six crossing lines to be at about 14 deg 00.5' N, 153 deg 10' W.
    That's within a mile or so of the dead-reckoning position following
    the previous fix, which gives one a bit of confidence, and all six
    position lines pass within a couple of miles of the spot.
    That plot took into account the shift of the vessel between
    observations, but as they were closely-spaced enough to cover only 0.7
    miles along the track, it would have made little difference if that
    shift had been neglected.
    John's results and mine, if correct, imply a serious discrepancy with
    the plot that Guy Schwartz provided as an attachment to Navlist 1848,
    on 9 December. It may be wise for Guy to examine his procedures to
    discover the reason for that disagreement. I will help if I can.
    Anyway, that plot of Guy's, right or wrong, has provided a welcome
    opportunity for me to exercise my favourite hobby-horse, about cocked
    hats. And, it seems, a lesson to a few list members to discover some
    realities, new to them, about those cocked hats.
    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.
    That is indeed rather different from the conclusion that
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