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    Re: Calibrating a sextant scale
    From: George Huxtable
    Date: 2007 Nov 24, 23:43 -0000

    Alex wrote-
    
     4 years ago, when I joined the list, one of
    | the list members (I think it was George) wrote that he
    | challenges anyone to determine his (modern, metal)
    | sextant arc correction from
    | stars. I tried to do this. I made several hundred observations
    | of stars, and failed.
    
    Not sure that it was me, though it was a good question. I would like to ask
    some supplementary questions.
    
    Has anyone on this list, by measuring star-star distances or by any other
    method, ever discovered reproducible errors, outside the terms of a
    calibration certificate or maker's warranty, in a sextant? Has anyone made
    calibration measurements of his own, in which he has more confidence than in
    the manufacturer's scale readings, corrected as necessary by the box
    certificate? And if the answer is yes, what's the magnitude of those errors?
    
    =====================
    
    With the discussion about inter-star differences, I remembered that John
    Karl's new book, "Celestial Navigation in the GPS age", devoted several
    pages to helping users to calibrate or check their own sextants that way. He
    selected 12 pairs of bright stars (with rather a Northern-hemisphere bias),
    to provide a suitable spread of angles to calibrate, ranging from Bellatrix
    to Betelgeuse, at about 7 deg 30', as far as Betelgeuse to Spica, at over
    113 deg. For each such pair, he provides a table, showing how the refraction
    alters the odd minutes and fractions of that separation, based on the
    observer's latitude, and on the altitude of the first-named star. In the
    explanation he claims- "Since the observer's latitude and the star's
    altitude determine the altitudes of any other star ... the altitude of the
    second star is not needed". On the face of it, it seems a good simple
    scheme, dead easy for a user to implement.
    
    But on reflection, I'm not convinced. I have been worrying about that
    statement. I don't think it is true. It's all a bit more complicated than
    that, I fear.
    
    Given a latitude, and a star with known declination, and an observed
    altitude, it's true that one can deduce a local hour angle. That local hour
    angle will be the same in amount, corresponding to that altitude, whether
    the star is rising or falling in the sky, before or after culmination, but
    will be opposite in sign. And there will therefore be two completely
    different Greenwich hour angles. And therefore two completely different
    possible values for the local hour angle, and thus the altitude, of the
    second star. Therefore, as I see it, there should be two different tables
    for the refraction correction, depending on whether the first star is to the
    East or the West of the observer. The table as given, for, say, Bellatrix to
    Betelgeuse, tells only half the story. I haven't investigated the matter
    deeply enough to discover which half.
    
    Am I missing something, somewhere? Have I misunderstood? Can anyone help?
    John Karl himself, perhaps, if he still tunes in to Navlist, though we
    haven't heard from him recently.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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