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    Re: October Lunar
    From: George Huxtable
    Date: 2008 Oct 13, 00:24 +0100

    Frank Reed found some points to agree with in my comments on Jeremy's lunar,
    bur argued with others.  Some may be worth pursuing.
    I had written-
    "And this takes us into rather deeper waters. The discrepancy that Jeremy
    reports, though consistent, is only a small angle, of 1'."
    To which he replied-
    "Through a sight tube or a low-power scope, that would be a fair statement,
    but with a 7x scope, which Jeremy has, an angular difference of a minute of
    arc is plainly visible. "
    Well, it's still only a small angle of 1', that discrepancy, just as I
    wrote. Indeed, such an angle may well be plainly visible in a 7x scope, but
    the aim is not just to see it, but to measure it, systematically. And it's
    near, but not (I agree) at, the limits of such measurement. Jeremy appears
    able to produce repeatability of better than that amount, but something
    appears to be failing in a systematic way.
    To my comment-
    "To measure a planet against the Moon's limb calls for a bit of judgment,
    because the image of the star is not a precise point, and the image of the
    limb is not an infinitely-sharp boundary."
    "Yes, and because the plains and mountain ranges on the Moon vary the
    outline (at average sextant scope resolutions) by anywhere from one to two
    seconds of arc, that is the absolute limit on any historical lunars (a
    modern computation could include limb effects)."
    Errors of a second or two are quite irrelevant to the present discussion; a
    I wrote-
    The eye does its best with them, but it's beset with the problem of
    "irradiation" "
    "This is irrelevant to this Moon-Venus lunar. Except under extreme
    circumstances, irradiation is a minor issue."
    That's an assertion; can Frank back it up? And is irradiation irrelevant
    when assessing index-error using the Sun, the measurement that may be at the
    root of the problem we're discussing? Irradiation is a real effect. It's
    been dropped from upper-limb predictions, in the Almanac, not because it's
    negligible, or unreal, but because it's so variable between different
    To my conclusion-
    "Whenever we near the limits of what we can perceive, some such degree of
    personal judgment comes in. It sets a limit to the inherent accuracy
    available in an observation, and being systematic rather than random,
    repetition and averaging aren't going to help."
    Frank responded-
    "That's a good point in general terms. It's fine rhetoric. But it does not
    apply here."
    Dismissing it as "fine rhetoric", and claiming, on dubious grounds that it
    doesn't apply, don't allow that matter to be avoided, particularly the
    question of systematic error, which I will return to later.
    Frank continued
    "The "limits" of what we can perceive are well-known. The resolution of the
    human visual system is about one minute of arc for standard optical
    resolution tests at unit magnification (with corrective lenses or adjusted
    focus as necessary --in other words, when wearing eyeglasses or contacts--
    and assuming no exotic uncorrected eye defects)."
    That's a gross over-simplification: that everyone's eye is the same. There's
    a wide spectrum of visual perception. I would put, at one end of the scale,
    the astronomer Hevelius, from Danzig, in the late 1600s, who amazed his
    contemporaries by the precision of his star catalogue, obtained without use
    of the new-fangled telescopes, or Copernicus' mother, who, shown Venus
    through such a telescope, asked why it was upside-down. Out of contention,
    at the other end of the scale, is my own eyesight, raddled by age and
    retinal lasering.
    All we can say about the eyesight of the observer in question is that it's
    good enough for a watchkeeper's certificate (which must mean reasonably
    But we're discussing, not perception (whether or not you can perceive
    something) but whether you can measure it, and that demands judgment, in
    placing one image with respect to another, if they are not completely sharp
    (and no optical system is completely sharp).
    Frank continues, in familiar vein-
    "It has been my experience that observers with well-adjusted sextants
    equipped with 7x scopes, with reasonably good conditions (on land, no
    clouds, no haze) can observe lunar distances with an accuracy of about 0.25
    minutes of arc (standard deviation) on each individual sight, and when four
    are averaged, the results are generally twice as good (0.13' s.d.). These
    are typical results for Sun and planet lunars. My results with stars have
    been worse and seemingly directly dependent on the magnitude of the star.
    Your mileage may vary."
    These are claims we have heard from Frank before, is just such anecdotal
    terms. Who ARE these observers, then? This question has been asked again and
    again on this list. Nobody, other than Frank Reed, has put his hand up and
    claimed such ability. As for averaging four observations, and getting
    twice-as-good results, that only applies (as Frank must know well) when any
    errors are random ones, varying unpredictably from one observation to
    another, and when all systematic errors are exactly known and corrected for,
    to an extent that makes their sum negligible compared with 0.125 arc
    contact George Huxtable, now at george{at}hux.me.uk
    (switched from george---.u-net.com)
    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
    To post, email NavList@fer3.com
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