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George endeavours to pick a fight with:
> ... I am aware that attempts at technical discussion with Peter
> have in the past degenerated into personal abuse, but will try once again,
> hoping that he can constrain himself to navigational matters.

Well I'm sorry, George, but I won't be drawn into this.  Except that
you are begging to be told that no one else on this List manages to
engender so much animosity.  Even from gentle souls who are otherwise
quite unfailingly polite and courteous to all.
>
> In his arguments, there are indeed several grains of truth and sense, but
> from these is created a structure that doesn't stand up.

What follows is large-scale agreement with almost everything I have
proposed!  Nevertheless, there are some problems with George's
analysis:

> ... it should be noted that whenever such a claim is made, that the
> true position is three times more likely to be outside rather than inside a
> cocked hat, it is (or should be) noted that any systematic errors have been
> first corrected for.

Sorry George, but this seems to be quite illogical nonsense.  You
don't seem to have grasped the basic idea, and have thus tried to put
the cart before the horse.  You CAN'T 'correct systematic errors
first' since their correction leads to a single point - a fix
position.  How are you then going to go about correcting for your ...
whatever you like to call the other, erratic variety?

This is WHY erratic error gets corrected at source, leaving an
assumption that what remains must be ... constant, or systematic, or
whatever you feel happy about naming it.

When it comes to the "structure that doesn't stand up", George first
resorts to an old ruse: that of finding some extreme example at which
a general truth may falter.  This is a regular tactic, is it not?

> First, let's deal with measuring a Sun noon altitude ...

No, let's not.  Indeed, since there is no apparent rise or fall at
this special case then by definition it does not apply.  You can try
to use the technique if you like, but this is really another subject,
one that has already had yet another good trashing here recently.
Let's move on.

> But all that's been done, by that "fitting to a slope" procedure, is to
> eliminate the problem caused by the steadily changing altitude ...

Dear oh dear.  I hate to be the bearer of sad tidings, and hope your
tender feelings won't be overly bruised, but you just don't get it,
George.  Have you ever tried the technique out?  That could be a LOT
more instructive than me trying to explain it to you a zillion times
already.

1. The technique quite literally draws a picture of your sights.
Rather than just a list of numbers you can SEE the pattern of your
sights.  Now if you have a few observations that follow that line
fairly well, but another that doesn't, then a reasonable assumption is
that the odd-fellow-out is a cock-up.

2. If you don't use the technique, then firstly you have no idea about
how good your sights are or not (ie; the spread; the overall
conformity to the fact of the line, or lack thereof), but secondly,
and more importantly, your single random sight taken could have been
that cock-up.  Or not.  How do you know?  Rather than endlessly
bleating afterwards about how you don't know where you are since there
is three times more chance of being outside the shape of the LOPs than
within it, isn't there some intrinsic appeal to being in a position to
quite usefully analyse those sights, close to source, and then move
forward to produce a position line that has been thus endorsed as
likely to be reasonably free of erratic error?

3.  The GREAT advantage of the technique is that the cock-up(s) can be
eliminated.  If an individual sight can't be fitted to the line while
others can then it doesn't have any place on that line.  Quite
literally.  The problem with your statistical approach is that it
embraces cock-ups equally with the others, and therefore pollutes the
good ones to no useful end.  Since there is a quite limited number of
sights that can be recorded within about 5 minutes (more with a scribe
than without), then consider what happens with your averaging
technique when most deviate little from the line but one or two
deviate quite a lot.  The average result is shifted to a significant
extent, away from those good sights towards the weirdo(s).  THIS IS
NOT HELPFUL.  THIS IS COUNTER-PRODUCTIVE.  Sorry to shout, but you
seem to have a problem hearing this simple message.

4.  There are other advantages.  This subject has been discussed
before, and off the top of my head I'm not sure I can remember them
all.  Should be in the archives ...  One I can remember is that having
best fitted the sights to the line then ANY POINT along that line can
be adopted, and the altitude/time read off the axes and adopted.  This
could be for calculational convenience or, for example, because you
want to adopt some instance in time.  You might want to ensure an
observation at the exact moment the azimuth of the body is due east or
west (eg; to calculate longitude).  This could be quite tricky to
achieve otherwise, but by taking sights over a 5-minute period
including the moment then that moment can be easily adopted later,
even if all of the sights were on either side of the moment (which
would be probable).

5.  Something else I remember from when this subject has been
discussed here before is that there was some worry about that line of
apparent rise or fall being in fact a curve.  Then we were informed
that at some extreme conjunction there could be a bending of the line
by 0.9 of a minute of arc at its ends.  I wouldn't worry too much
about that.

6.  As someone who has long adopted this as standard procedure, I can
say that typically the technique results in a position line that is
more correct than any of the individual sights.  That's the only
reason I use it, since it adds a little (well OK, quite a bit!) more
plotting work.  Because in practice it works very well.  It was also a
technique taught to students of surveying when they were instructed in
position finding via astronomical observations, as just one of the
techniques that could enable them to derive a position correct to the
nearest second of arc.  It works.  George seems to assume that this is
some offbeat idea I've dreamt up that should stand or fall depending
on how well he can theorise about how many holes he can pick in it.
Just ain't so.  It works very well, regardless of George.

You really might consider giving the proposal a go first, George.
Just pop outside and try it for yourself.  Put off judgement until you
understand the matter a little better.  There is too little science
(or common sense) in your negatively tendentious approach.  And far
too much prejudice.

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