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    Re: "Attainment of Precision" article (1964)
    From: Gary LaPook
    Date: 2009 Jul 08, 04:37 -0700

    I've grown partial to this method of finding the I.E. since I get a much
    sharper edge on the limb of the sun than with the sea horizon.
    When I calculate the error I avoid using negative readings for the "off
    the arc" reading. Many mentally convert a reading of say 31' on the
    micrometer with the index below zero as negative 29.' Rather than taking
    a chance of making an error in this mental conversion, I  would consider
    it as "31' minus 60'",somewhat like using logarithms. I then add this
    number to the "on the arc" reading, subtract 60 from the total and then
    divide by two to find the I.E.
    As an example consider a sextant with no I.E. on a day when the S.D. of
    the sun is 16.' The on the arc reading will be 32' and the off the arc
    reading will be "28' minus 60."
    32+ 28 = 60; subtract 60 leaves zero which divided by two still equals
    Now consider a sextant with a 10' on the arc I.E. on the same day. The
    on the arc reading will be 42' while the off the arc reading will be
    "38' minus 60." 42 + 38 = 80; minus 60 leaves 20 which divided by two
    gives you the I.E. of 10.'
    George Huxtable wrote:
    > Nicolas asked, about Frank's comment
    > "frankreed@HistoricalAtlas.com wrote:
    >> If you want a really good value for IC, shoot the Sun or the Moon
    >> limb-to-limb ... it's usually more effective than the standard sea horizon
    >> test (but the standard test is usually quite sufficient and it's the one
    >> that should always be taught)."
    > "could you please explain why the limb-to-limb method is more effective?
    > And can you explain how this is done? What I mean is: are you
    > superimposing opposite limbs onto each other (so calibrating the sextant
    > at the sun's/moon's diameter), or the same limbs (so calibrating for
    > zero at two spots in your field of view)? I take it it is the latter
    > method. Do you have any data supporting the effectiveness?"
    > ==========================
    > The main difficulty with using the sea horizon to check index error is that
    > the horizon is often hazy or disturbed (especially when seen from a small
    > craft).
    > A standard method for checking using the Sun is to put the reflected image
    > of the Sun above the direct image so that they just kiss,
    > tangent-to-tangent; then below it, and split the difference. That is, using
    > opposite limbs, not similar limbs.
    > It calls for, ideally, a very-dark-glass cap to fit to the telescope
    > eyepiece, as was once a standard accessory, to make both Sun images
    > viewable. (That carries a possible danger that the undiminished focussed
    > heat from the Sun can crack it; an acknowledged eye-hazard with some
    > astronomical telescopes, but I've never heard of it actually happening with
    > the smaller telescope that's found on a sextant.) Alternatively, it calls
    > for a very dark shade in the direct-view, as is always available for the
    > reflected-view, and not all sextants are so fitted. And any difference in
    > refraction between those shades can skew the result.
    > It's quite hard to do it the other way, by superimposing precisely two
    > images of the Sun, one exactly on top of the other, because when making the
    > final adjustment, it's difficult to be sure which image-edge is which. Doing
    > the job by averaging two displaced images, because it combines two
    > independent observations, has its errors reduced by root-2 because of that
    > averaging.
    > But it doesn't provide any useful calibration of the sextant by taking the
    > difference between the two readings,  about 1 degree apart, as Nicolas
    > suggests. The extrapolation is too great, combined with the sensitivity to
    > the observer's judgment of where the Sun-edge happens to lie.
    > ===========================
    > The Moon is another matter, and I don't see how it is possible to determine
    > index error precisely by aligning opposite limbs of the Moon , because of
    > its partial lighting, except at full Moon. It would call for tilting the
    > scope into the plane given by the line between the horns, which in itself is
    > no real problem. The difficulty comes in that those horns are just at the
    > boundary between sharp-edge and shadowed-edge, and I doubt whether those
    > opposite limbs would provide a pair of sufficiently-sharp targets to do the
    > job well, though to be honest I have never tried the Moon for that purpose
    > in real life. Perhaps Frank has done so, and will explain.
    > George.
    > 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.
    > >
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