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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
zero.

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.'

gl
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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