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    Timing noon.
    From: George Huxtable
    Date: 2002 Apr 8, 11:29 +0100

    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
    Arthur Pearson, in the course of describing difficulties he has faced in
    understanding the calculation of lunars (and which I share), happened to
    >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.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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