# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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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
rise
| to this very interesting discussion about cocked hats. It is problem
| 3-2, p. 22, in "100 Problems in Celestial Navigation" by Leonard
Gray
| (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
Excel
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

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.

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.

That is indeed rather different from the conclusion that

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```
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