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    Re: Precise index correction: was- Eye problems and IE, IC
    From: George Huxtable
    Date: 2006 Jul 14, 03:25 -0500

    Referring to my last posting, Bill responded-

    | ...Much of it, although some list members appear
    | to have experienced just that, seems to run counter to common
    wisdom.

    Well, no harm in that, then, if it's shaken some ingrained
    preconceptions; depending on whether what I wrote was correct, and
    those preconceptions were wrong. I hope Bill has tried the tests I
    suggested, by now, to see whether they accord with his "common
    wisdom".

    Bill has told us that he obtains, consistently, a lower value for 4SD
    (where SD = Sun semidiameter) from his observations of adjacent Sun
    images, than he would expect. I can suggest two reasons that ought to
    be at least taken into account, at the precision level he is
    attempting to work to.

    One is the vertical squash of the Sun due to atmospheric refraction
    effects. With a standard unperturbed local atmosphere, the refraction
    change, between the bottom edge of the Sun and the top (that is, over
    about half a degree), is, at 10 deg altitude, 0.25', at 20deg,  0.06',
    at 30 deg,  0.01'. You can see how it becomes negligible as the
    altitude increases. Bill's recent observations all seem to be in the
    range where such effects can be neglected. But that's only half the
    story. The atmosphere seldom behaves exactly according to the book. We
    are all familiar with occasionally seeing an obviously squashed Sun,
    quite high in the sky, which is the result of a layer of air with a
    non-standard temperature gradient. The discrepancies that Bill sees
    correspond to a distortion level much smaller than would be apparent
    to the eye. I would not be surprised if those small distortions were
    rather common, even at elevated angles, but have no way of knowing
    whether that is indeed the case. The possibility should be borne in
    mind. It's only in the vertical direction that such squash is likely
    to occur; horizontal squash ought to be rare or non-existent. So if
    one wished to measure Sun semidiameter (for itself, not just as an
    adjunct to checking index error) then it should be done by a
    horizontal angle.

    The other is the quantization error. Although the Sun's semidiameter
    is precisely known and predicted (to a hundredth of an arc-second, in
    the Astronomical Almanac), in the Nautical Almanac it's simply rounded
    to the nearest 0.1 arc-minutes figure. So, between early May and late
    August, it's given a constant value of 15.8', which is just saying
    that it is nearer to 15.8 than to 15.7 or 15.9. There's  a possible
    error of  between = .05 and - .05, which can stay the same for weeks
    at a time. So, during a period when it was high by nearly .05, there
    can be weeks at a time when the value of 4SD can be consistently high
    by nearly 0.2'; quite enough to make Bill's precise observations
    scatter around a value that's significantly lower than 4SD taken from
    the Almanac. If he want's to do his job properly he should use a more
    precise value for SD; there must be a website that provides it.

    I wonder what is the rationale for rejecting observations that differ
    from 4SD by more than 0.4, as seems to be done by Bill and Alex;
    especially in the light of that quantisation error. If that is done,
    it will always skew the average of what remains. Who set that
    arbitrary limit, I wonder? Is the intention to show up cases of
    abnormal refraction? The scientific approach would be to never
    "reject" data unless it's so clearly out-of-line that it must be due
    to some error. The urge to reject stuff tjust because it's on the
    outer fringes of a scatter distribution should be resisted. That's the
    whole point of taking multiple measurements, that the averaging
    process reduces their impact.

    George.

    contact George Huxtable at george@huxtable.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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