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    Re: Star-star distances for arc error
    From: George Huxtable
    Date: 2009 Jun 23, 14:02 +0100

    In [8767], Douglas Denny describes one of his sextants, in a way that 
    puzzles me a bit-
    "My Hughes sextant - beautifuly built, brass frame, with platinum divided 
    scale,  with drum/worm drive has a vernier to measure to 10 seconds of arc 
    but the certificate indicates accuracy of max error of 1 minute 30 seconds 
    at points on the scale."
    His reference to a "platinum divided scale" implied to me that it was a 
    Vernier sextant; but then the word "drum" goes with micrometer sextants 
    (which sometimes have their own little Vernier for interpolating between 
    drum divisions). My guess is that he has a Vernier instrument with a Hughes 
    patent endless-tangent knob, but not a micrometer drum (I've never come 
    across the two combined, but it might be possible). If it's a Vernier 
    instrument, divided to 10", then judging by my own such sextant, I would 
    expect the scale to be readable, reliably, to well within 20",  but without 
    being certain to 10".
    Douglas defends his earlier claim-
    "Attempting to use star separations to try to determine scale accuracy for 
    example would not be possible due to the variables in the measurements 
    themselves - including the refraction component even if calculated.
    Also, combining of two stars overlapping, with the inevitable abberrations 
    seen in the telscope image itself preclude this to being within one minute 
    at best.
    Also, the measurement can only be done to an accuracy of the divisions of 
    the sextant which in most cases is one minute of arc. "
    Frank Reed and I often differ about questions of precision, but in this case 
    I would endorse all that he has said (and also on another matter, of the 
    effect of a telescope on brightness, but that's for another posting). 
    Douglas has got a lot wrong, in my view.
    Right from my schooldays many years ago in a science lab, it became clear 
    that if markings on a scale were sharp and clear, and were far enough apart 
    that eye-resolution wasn't a problem, and any movements were smooth and 
    reproducible (all of which apply to the drum reading of a good sextant) then 
    anyone could interpolate between them, just by eye, to fifths, and a careful 
    worker, with a bit of skill and practice, to tenths. A vernier helps a bit, 
    but isn't necessary.
    Douglas writes- "If accuracy is required, the measurements are difficult to 
    achieve in the first place unless the sextant is clamped.".  It's true that 
    measuring star-star separations is difficult, requiring a steady hand and a 
    sharp eye. At my age, I have neither, sufficiently. One difficulty is in 
    identifying the correct star-pair, as one star looks much like another. And 
    having done so, superimposing star images is rather tricky, that's true. But 
    you don't have to superimpose them, you can brush one past another, to put 
    them just side by side, and cross them over (tricks of the trade).
    Because of the stars' motion across the sky, clamping a sextant can be 
    counterproductive, and gets in the way of such sweeping-past. An equatorial 
    mounting on a pillar stand, as some land geographers used in the days of 
    lunar longitudes, would work better. But the genius of the sextant is that 
    the sextant itself doesn't need to be aligned with anything, as long as both 
    objects can be got into view. To my mind, Douglas is overstating the 
    difficulties in such on-land observations, although skill is certainly 
    called for. Remember, generations of mariners found their longitudes from 
    lunar distances, from a vessel at sea, with a rolling deck underfoot, aiming 
    at angular precisions of less than a minute. By comparison, measurement from 
    on-land is a doddle.
    It surprises me that an optics professional brings in "the inevitable 
    abberrations seen in the telscope image itself". Yes, of course, all 
    telescopes suffer from aberrations, which degrade the image of a 
    point-source star to some extent, ending up with a resolved image disc of 
    finite size. But those aberrations affect both star images exactly the same; 
    they don't cause any shift between one and another. Then the eye has to 
    distinguish the shift of one such disc with respect to another. Is Douglas 
    really claiming that the eye can't detect such a shift of less than 1', when 
    using, say, a 6x scope? In which case, what sort of resolving power does he 
    expect that telescope to have?
    About refraction, Douglas complains-
    "and you are suggesting it is OK to measure two stars where the refraction 
    error alone can be greater than the measurement."
    No problem about that, none at all, if the refraction is predictable. And, 
    as long as the lower few-degrees of altitude are avoided, it is VERY 
    precisely predictable, which is what makes precision astronomy possible.
    As he states, the effect of refraction at an altitude of 40� is of the order 
    of 1'. If no correction were made for meteorology, even in extreme 
    depressions that wouldn't vary by more than 0.1'. And if only roughly 
    corrected for local temperature and pressure, no more than .01' variation 
    would remain. Would that satisfy Douglas Denny? Far from being "unknown 
    effects" of barometric pressure, the effects are precisely known and easy to 
    measure and correct for. The effects of humidity are quite negligible, as 
    Frank has pointed out..
    Low altitudes should certainly be avoided for this purpose, but there's no 
    need whatsoever to use low altitudes.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 
    Navigation List archive: www.fer3.com/arc
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