NavList:

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
by
| 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
any
| 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
can.

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
observations.

==================

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
much).

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.

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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