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    Precise index correction: was- Eye problems and IE, IC
    From: George Huxtable
    Date: 2006 Jul 13, 07:45 -0500

    I have started a new threadname, as this is no longer addressing
    specific eye problems.

    Just let's start by eliminating one possible confusion, as these
    matters are already complex enough. In the same posting, Bill has used
    the same abbreviation, SD, which I take to refer to Standard Deviation
    and to Semi Diameter. Those terms should instead be spelled out, to
    avoid that confusion.


    For new readers-

    Bill has told us that when he turns the focus adjustment on the
    telescope of his sextant, he sees noticeable changes in its index
    error, that the side error can also be affected, and that this is
    corroborated by the similar experience of others.

    I have expressed doubts about the existence of any mechanism by which
    this could occur; though there's no way that I can dispute that Bill
    saw what he tells us he saw.

    Bill concluded-

    | ... I claim every scope I have handled (with the
    | possible exception of Alex's inverting scope, where focus is changed
    | sliding a press-fit tube in and out) exhibits a shift.  I do believe
    it is a
    | variable that I need to be aware of with my equipment.
    | Step outside and try it for yourself. If your scope(s) don't exhibit
    | shift, then we must all be wrong. <G>
    | I would encourage other readers to try the experiment and report in.

    Well, unfortunately, I can't do that. My own sextant, perfectly
    adequate for astro-navigating a small craft from A to B, is a plastic
    Ebbco. It's reading scale and optics are just not of the level of
    quality that would allow for such sub-minute observations that Bill is
    trying to make. And my old eyes are imprecise, to a similar extent.
    Also, it has a draw-tube, not screw-adjust, for the focus, if that
    really makes any difference.

    However, I have made some tests with it, that Bill or anyone else can
    replicate, which quite convince me that a sextant's index error and
    side error are completely insensitive to any misadjustments of the
    telescope optics.

    With the telescope removed, look at a distant object; Sun, star, or a
    building on a far skyline, centred in the horizon mirror, with the
    naked eye. Adjust  the drum for exact coincidence with its reflected
    image. When doing that, no doubt your eye will have been roughly
    centred, along the line where the telescope would have been. But now
    shift your eye into a different position, with respect to the sextant,
    still keeping the object centred in the horizon mirror. Of course,
    that means angling the sextant, rather than your sight-line. Make a
    gross misalignment, so that the sightline to your eye diverges 10 or
    20 degrees from the plane of the sextant. Do you see the slightest
    shift between the two images? Nod the sextant up and down, to the
    greatest extend that the geometry allows, before an obstruction
    intervenes? Is there any shift then? The answer will be no, I suspect.

    But then that was just an observation with the naked eye, not reliable
    to better than a minute or thereabouts. We need to do better, and we

    With your eye offset in that way, use the telescope (prefocussed at
    infinity). How? Just hold it by your other hand, in your sightline.
    It's allowing you to see a magnified image, looking into the horizon
    mirror. That magnification may show up a small offset between the
    images, that was too small to see before. If so, adjust it out (which
    will need three hands). Again, angle the sextant around, and nod it up
    and down, with respect to your sightline. Not the slightest
    displacement, between the two images, I predict. Holding the sextant
    still(ish), angle the telescope about, to the extent that its field of
    view allows, up, down, sideways. No displacement there, either. Try
    turning the telescope about its axis. No change. Change the focus, so
    that the images start to get slightly fuzzy at the edges. Because of
    the reduced sharpness, no longer will you observe offset between the
    images so clearly, but to the extent that you can, I predict that you
    will see none.

    And if Bill, having tried it out, agrees that these gross
    misalignments do not separate the two images, how does he imagine that
    a tiny eccentricity of his eyepiece will do it?

    I think that the real problem here is that he is working at the very
    limits of his perception .If the effect he reports is really,
    incontrovertibly, reproducibly, measurably seen, by more than a single
    observer, then something new has been unearthed, that none of us can
    explain, and it needs to be understood. As a devout sceptic, however,
    I will meanwhile continue to question the validity of those


    That's not to say that changing the focus has no effect at all,
    however. When focussed correctly, the Sun image has its edges as sharp
    and clear as can be got. Under those conditions the angular gap
    between the two tangent lines (reflected image over direct image, and
    vice versa) should be 4 semidiameters, as precisely as possible.
    Defocusing in either direction will make it fuzzier, and you have to
    judge some brightness contour at which to place that tangent. I
    suspect the eye will place the presumed edge of the Sun slightly
    further out from its centre in those circumstances, so the gap between
    the tangent lines will become slightly greater that 4 semidiameters.
    However, that fuzziness will put one of those tangent lines up, and
    the other down, by equal amounts, so their average (which is what
    gives the index error) should be unchanged. Just a bit less sharply
    defined, that's all.

    It's interesting, however, that Bill reports that his observed
    4-semidiamers gap, presumably made with optimum focus, comes out as
    consistently less than the prediction on the almanac. How much less,
    he has not made clear. That might tell us something about Bill's
    perception of where he puts the edge of the Sun. It suggests that he
    puts the Sun's diameter as slightly less than it really is; just the
    opposite to what conventional "irradiation" would lead one to expect.


    I have wondered why, according to Alex, "textbooks recommend" using
    Sun or star, rather than horizon, for obtaining index error. I have
    suggested circumstances where that might be the case, but others where
    the horizon might be just as good.

    However, there seems to be one argument in favour of taking two Sun
    (or Moon) observations, 4 semidiameters apart, and averaging them.
    It's this. The process of  averaging two rather-independent
    observations reduces the overall statistical error by a factor of
    root-2, compared with a single observation.. Well, you might say, you
    could just look at a star or the horizon and measure it twice, not
    once, and average them. But making exactly the same measurement once
    again isn't as good. The eye and brain are faced with exactly the same
    picture and make the same mental adjustments and interpolations, so
    averaging two identical observations won't reduce the scatter (or not

    Indeed, by making two Sun observations about 32' apart, one such error
    is entirely eliminated. This is a cyclic error varying with the drum
    angle, which Frank referred to in a recent posting as drum
    eccentricity. By making two measurements, almost exactly half a
    rotation apart, drum eccenticity is eliminated from any effect on
    index error.


    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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