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    Re: Index Error
    From: George Huxtable
    Date: 2004 May 5, 17:46 +0100

    Robert Eno asked-
    >A method I have long used for determining index error when taking practice
    >observations on land is to use the sun's limbs by setting the sextant at
    >32' on arc, touching up the reflected and actual sun's limbs, recording
    >the number, then doing the same off arc. One half the difference between
    >the value on and off arc should give you your index error; the sign being
    >the greater of the two values. I have found this to be a reasonably
    >accurate method for determining index error; as long as the sun is at
    >least 30 or more degrees above the horizon.
    >Here's the problem: theoretically, if one adds the reading off and on arc,
    >subtracts the index error and divides by four, then the result should
    >equal the tabulated value for semi diameter in the Nautical Almanac.
    >I have seldom found this to be true. The result often differs from the
    >tabulated value by up to 0.4' of arc. That's a lot.
    If the error is in such a direction that the Sun looks bigger than it's
    "supposed to", a plausible reason is "irradiation", a perception, in the
    eye, that the boundary between bright patches and darker ones appears to be
    shifted toward the darker side, so that bright objects appear bigger than
    they really are.
    I was someewhat sceptical that this was a real effect, until the following
    trick (which I've explained on Nav-l before) demonstrated its reality to
    me. With a bright background, such as a sunlit cloud, a lit lampshade, even
    a white computer screen, hold up one hand in front of it, and bring finger
    and thumb gradually together, a few inches from your eye. Just as they
    touch, you will see a dark shadow jump across the bright gap between them.
    This is caused by irradiation, but in the converse situation to what Robert
    Eno describes, because it's a narrowing sliver of brightness between two
    dark objects, rather than the sliver of dark between two bright Sun images
    that he sees.
    It happens because if there's any sliver of brighness at all, visible
    between finger and thumb, irradiation expands its edges to make it look
    wider than it really is. Only at the moment that the gap closes, so no
    light at all can shine through it, does the effect disappear, and that's
    what causes the sudden change in the appearance of the gap. The effect can
    give rise to a boundary-shift of bright objects by a large fraction of a
    minute at the eye, though this is reduced, in its effect on the object
    viewed, by the magnification of the telescope. For lunar distances, which
    demand the ultimate in angular precision, it's a good argument for using a
    the highest-magnification that the vessel's motion will allow.
    Because aligning of the Sun's limb with the horizon involves three areas of
    different brightness, Sun disc, sky above horizon, sea below it, and this
    configuration changes between upper-limb and lower-limb observations, at
    one time the Nautical Almanac gave corrections for UL and LL observations
    that had been separately adjusted to allow for the differing effects of
    irradiation. Later, it was recognised that this depended so much on the eye
    of the observer, and (particularly) the magnification of his telescope,
    that the attempt was abandoned, about 20 years ago I think.
    As for me, as long as I can see a sharp, straightish horizon in the
    distance, without intervening swell-peaks, I am happy to use the horizon to
    check my index error, though some purists may deride that procedure for
    reasons that I fail to follow. True, the horizon isn't (quite) at infinity,
    but the resulting parallax between the views in the two sextant mirrors is
    no more than an arc-second or two. But then, I'm a fellow that finds a
    plastic sextant sufficiently good for the altitudes I measure on my small
    boat, so I do not seek ultimate accuracy. On the other hand, confidence in
    the stability of a plastic sextant comes from frequent checking of index
    error, so there's a big advantage in keeping that operation simple. Not
    that I think there's anything wrong with the technique that Robert Eno
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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