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George H, you wrote:
"Frank's apology is unnecessary. He didn't confuse me; not a bit. Neither in
my mind nor in my words, which were quite free from any confusion."

Well that's strange then. If you weren't confused by my wording, then what
on earth are you complaining about?

I wrote earlier that it's easy to deal with the motion of the vessel. And
George, you replied:
"Which may well be true, but nowhere has he explained how to do it."

Aw well, george, you know how it goes... You can't squeeze everything into
one post, right? There are a variety of ways of dealing with it, and I have
most certainly explained one good method before. I don't blame you for not
remembering that since it was very nearly three years ago (time does fly,
doesn't it?). The post was entitled "Latitude and Longitude by 'Noon Sun'"
and you can read it here:
http://fer3.com/arc/m2.aspx?i=024178&y=200506.
There are a few changes I would make to the description there based on some
recent numerical tests, but basically, that's the idea.

And you stated:
"Not many practical navigators would agree with Frank's claim that it isn't
impractical, when a simple pair of sights, mid-morning and noon, would do
the trick instead, and more precisely."

I agree that many navigators would have to be convinced. Navigators tend to
be a conservative lot, and for good reason. So let's try this line of
argument for convincing... you've been in a storm for a couple of days. Your
electronics are out. You really, REALLY want a position fix. When the
weather finally begins to break, it's cloudy all morning until, let's say,
1100 local apparent time. So what would you do? Ignore a method which will
give a good fix in both latitude AND longitude in forty minutes or less?
Wait three or four hours for an afternoon LOP?? And what if the clouds work
against you?

George, you added:
"Frank gives us no numbers to put into his "typical case", to allow his
claims of precision to be checked. What are its limits of applicability? He
doesnt say."

That's true, George. I rather thought you could work out a typical case on
your own. But I can help you do one, if you want.

And then, George, you came up with something slightly bizarre.
You proposed:
"So let me put forward another case, quite "typical" for mariners
in the trade I describe.
Take the case of a steamer, in the transatlantic trade, aiming to pass
North-about Ireland in lat 56 deg, in midwinter. She is en route for the
Clyde or the Mersey, in World War 2, with no radio aids."

er... George? Are you worried that I'm going to go back in time and sell
this method of navigation to navigators of the 1940s?? I promise you,
George, although my experiments in time travel are coming along well, I will
not change history by providing a useful navigation trick to the navigators
of those "steamers" in the "transatlantic trade". ;-)

You asked:
"If her skipper spends 40 minutes around noon on his longitude, I ask Frank
how good the result will be, to allow her to approach the unlit Scottish
coast in safety, after dark."

The longitude generated around noon will be approximately as accurate as I
said in the previous post. So if you expect a typical error of 1 n.m. in a
standard LAN sight for latitude, then you should expect a typical error of 5
n.m. in longitude by the approach I've described.

You also wrote:
"We have to remember that Frank's interest, in minimising the difficulties
of measuring longitude-around-noon, relates to his pushing of it as a
teaching method, because its principle is a simple one to grasp (which
indeed it is)."

Yep. I'm a pusher. A pusher of ideas. A pusher of knowledge! :-) But I do
have a quibble with your comment here. You appear to be suggesting that a
"proper navigator" should eschew such blasphemy BECAUSE it is easy. Ease is
not a fault. The fact that this can be worked without sight reduction tables
is a positive feature, no matter who you are, not a negative. And in
addition, understanding how this set of sights works leads to all sorts of
fascinating theoretical issues.

And you wrote:
"But much of this is old ground, which has been well-trodden on this list
before, and I doubt whether any minds are going to be changed."

I have faith in you, George. I've seen you change your mind before --though
it can take a while-- and I suspect you will make peace with this concept
when you finally realize that it can analyzed using the standard tools of
position line celestial navigation. Give it a try... :-)

On high altitude sights, I wrote:
"If the navigator knows that there are TWO ways to swing the arc, then this,
too, is no problem."

And George, you replied:
"Presumably, Frank refers to the swinging of the sextant about the line to
the body, rather than about the horizontal; a technique that any decent
observer always practices."

ANY decent navigator??!! Really now, George -- you do exaggerate here. The
VAST MAJORITY of navigators who learned celestial in the past century have
no idea that you can swing the arc by rotation about the line to the body.
They have no idea that this greatly facilitates high altitude sights. I have
a REAL challenge for you: can you find any manuals of navigation that spell
out the two methods of swinging the arc? I am aware of only ONE modern book
that describes this (Letcher's) though a few hint at it, and I have
encountered numerous navigators who consider it quite surprising that you
can 'swing the arc' in two different ways. You may recall that Joel Jacobs,
who is surely an expert in his own right on sextant use, once got quite
upset over my suggestion that you can swing the arc about the line to the
body.

And you wrote:
"But even so, accurately measuring a high body is no picnic."

I don't disagree with the assessment of "no picnic", but only when the
object is extremely close to the zenith --let's say above 88 degrees. Even
at 85 degrees, if you swing the arc properly, it's no problem. Incidentally,
there is another issue to be aware of with a series of sights around noon
that is more important than sighting difficulties when the Sun is very close
to the zenith. The whole process depends on the Sun's azimuth being near the
meridian throughout the set (the maximum azimuth offset from the meridian at
the beginning and end of the set should be not less than 5 and not more than
10 degrees, roughly). This means that you should take your sights over a
shorter interval when the Sun is very high. In practice, this should not be
a serious issue. In fact, it probably helps.

 -FER

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