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Timing noon.

This is a spin-off, prompted by Arthur Pearson's recent contribution to the
thread "It works." Because it has connections to other aspects of
navigation as well as to lunars, I have started a new thread, "Timing
noon".

Arthur Pearson, in the course of describing difficulties he has faced in
understanding the calculation of lunars (and which I share), happened to
say-

>1. During the day, one establishes latitude by a noon sight.
>2. The same sight that is used to determine latitude is used to
>establish the Watch Time of Local Apparent Noon.

This was not a vital part of the point he was making but I think it is
worth picking up.

====================

Here I wish to challenge a widely-held and long-cherished misconception
about measuring the time of local apparent noon. Let me put it like this-

The worst possible time to try to determine the moment of local apparent
noon at sea is at, or near, local apparent noon itself. It's impossible!

On land, it's a different matter. A telescope can be set up to swing about
a precisely East-West axis, in a North-South vertical plane, and the time
of passing the crosswires gives the answer for noon.

At sea, there's no way to establish such a precise azimuth. Instead, the
observer has to observe the changes in the Sun's altitude, which will be
maximum at (or anyway near to) local apparent noon. Near to rather than at,
because the vessel may have a North-South component of velocity, and the
Sun can also be moving North in Spring, South in Autumn, at a speed of up
to one knot. This can distort the shape of the curve of Sun altitude
against time, shifting the moment of zero slope away from noon. We can
ignore, for now, such complications by presuming that measurements are
being made from an anchored vessel at the time of a solstice, so there's no
North-South motion of the vessel, or the Sun, and no displacement of the
maximum altitude from noon..

Here comes the difficulty. At the moment of noon, the altitude of the Sun
is neither rising or falling. Before, it was rising, slower and slower.
After, it is falling, slowly at first, then more quickly. Around the moment
of noon, changes are imperceptible. There is no one moment at which it is
possible to say- "now, it's stopped going up, and now, it's started going
down". No two observers will ever agree about it.

Perhaps the true-believer will argue back with me, and say "well, perhaps
not exactly AT the moment of noon, but a few minutes before then, the Sun
will clearly be rising, if slowly, and a few minutes later it will clearly
be falling, if slowly, so all one needs to do is to split the difference
between them". At that point, he has already conceded the principle. He has
adopted the principle of measuring equal-altitudes either side of noon.

The further away from noon, before and after, those equal altitudes are
measured, the faster will the Sun be rising or falling, so the more
precisely will the observer be able to measure the moments when the
altitudes become equal. You can illustrate it by drawing a sine-curve.

It isn't even necessary to measure two equal altitudes. Observe the maximum
altitude of the Sun at noon (which can be determined very precisely, even
if its time can't) and then measure time and altitude later in the evening
when the Sun is well to the West. A bit of not-too-difficult trig then
gives an accurate value for the time elapsed between the moment of noon and
the moment of that second observation.

The conclusion is inescapable: to determine the moment of noon, one or more
measurements of altitude, well-separated from noon, are required.

I regret that in making this diversion, I may be taking attention away from
the valid point that Arthur Pearson was making. But the opportunity to nail
this widespread misunderstanding about determining the moment of noon was
too good to miss. I wouldn't be surprised to hear some howls from
listmembers, outraged that their cherished belief has been questioned. We
shall see.

George Huxtable.





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george@huxtable.u-net.com
George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
Tel. 01865 820222 or (int.) +44 1865 820222.
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