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    Re: The Noon Fix
    From: George Huxtable
    Date: 2009 Apr 9, 00:09 +0100

    Oh, dear. I seem to have trodden on Frank Reed's favourite hobby-horse.
    Again.
    
    And it's brought on another attack of personal sneering, without which this
    mailing list would be a more pleasant place.
    
    Frank presumes to tell me."You've really missed out by not investigating
    this further". But has not found any error in anything I've said.
    
    Jim's contribution mentioned his "reference 1" as a basis for his arguments,
    but as we were not informed what reference 1 was, that was of little help.
    Since then, he has told us that it's a reference to his earlier ION paper,
    which I happen to have, so for me, that answers my question. So tell us,
    Frank, just what was wrong with asking?
    
    I wrote-
    
    ""What is hidden, under that catchy title of "The noon fix", or "longitude
    at noon", is that it's actually longitude AROUND noon"
    
    To which Frank replied-
    
    "But everyone knows this, George. It does not detract from the method in any
    way. "
    
    I didn't say that it did, did I, Frank? So what's the problem, then?
    
    What I pointed out was that it didn't take place AT noon, but over a period
    AROUND noon, and the longer that period was, the more accurate the result
    would be. And vice versa, of course.
    
    Frank continued- "The focus on time interval, here and in Bowditch, may be
    misleading. What matters is a change in the Sun's azimuth (just convert the
    method to its equivalent lines of position to see why). For reasonable
    accuracy, one should take sights over a sufficiently long period such that
    the Sun's azimuth changes by roughly twenty degrees. When the Sun is fairly
    low in the sky, that's fairly close to the suggested "30 minutes" on each
    side of noon. But when the Sun is higher, the time interval can be quite a
    bit shorter."
    
    Well, there are two factors to take into account here. One is change of
    azimuth, but azimuth isn't being measured, or considered. The other, which
    Frank has ignored, is change in altitude, the quantity we are working with.
    Observations made with a high noon Sun win out on both counts; the Sun
    swings up to a high altitude over the day, and near noon there's a rather
    sudden switch from rising to falling, combined with a sudden change in
    azimuth. Under these conditions, determining longitude from observations
    close to noon can be useful and reasonably precise. The extreme case is when
    the Sun passes through the zenith, when the change is instantaneous, and
    last year Jeremy reported an observation that came close to that.
    
    On the other hand, the method works much less well at higher latitudes, in
    Winter conditions. Not only is the azimuth changing more slowly, but so is
    the altitude, and it becomes harder to detect the moment when the altitude
    stops rising, and starts falling. The example I asked Frank to consider,
    last year, was an approach to the Clyde, at 56� lat, in Winter; a question
    that was repeatedly evaded, as readers may recall. But it's satisfying to
    note that at last, Frank seems to be accepting that a lengthened time-span
    is appropriate to those circumstances.
    
    Frank ended with this piece of complete nonsense-
    
    "Also, just from the standpoint of terminology, the idea that you have to
    take sights over a somewhat extended period to get longitude near noon is
    really not that different from the common procedure for getting latitude at
    noon. Most students, when learning the LAN sight, are taught to take
    occasional sights leading up to noon and then catch that moment when the Sun
    "hangs" at its maximum altitude. So even for latitude, it's really latitude
    "around noon". The difference for the longitude case is that we also want
    some sights after noon to make a complete noon curve."
    
    Near noon, the Sun's altitude hardly changes, as we all know. There's a
    world of difference between measuring it for latitude, when the quantity
    you're after hardly changes, so it hardly matters whether you "catch the
    moment" or not, and measuring for longitude, when you are trying to quantify
    those minute changes in its slope.
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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