NavList:

Referring to my last posting, Bill responded-

| ...Much of it, although some list members appear
| to have experienced just that, seems to run counter to common
wisdom.

Well, no harm in that, then, if it's shaken some ingrained
preconceptions; depending on whether what I wrote was correct, and
those preconceptions were wrong. I hope Bill has tried the tests I
suggested, by now, to see whether they accord with his "common
wisdom".

Bill has told us that he obtains, consistently, a lower value for 4SD
(where SD = Sun semidiameter) from his observations of adjacent Sun
images, than he would expect. I can suggest two reasons that ought to
be at least taken into account, at the precision level he is
attempting to work to.

One is the vertical squash of the Sun due to atmospheric refraction
effects. With a standard unperturbed local atmosphere, the refraction
change, between the bottom edge of the Sun and the top (that is, over
about half a degree), is, at 10 deg altitude, 0.25', at 20deg,  0.06',
at 30 deg,  0.01'. You can see how it becomes negligible as the
altitude increases. Bill's recent observations all seem to be in the
range where such effects can be neglected. But that's only half the
story. The atmosphere seldom behaves exactly according to the book. We
are all familiar with occasionally seeing an obviously squashed Sun,
quite high in the sky, which is the result of a layer of air with a
non-standard temperature gradient. The discrepancies that Bill sees
correspond to a distortion level much smaller than would be apparent
to the eye. I would not be surprised if those small distortions were
rather common, even at elevated angles, but have no way of knowing
whether that is indeed the case. The possibility should be borne in
mind. It's only in the vertical direction that such squash is likely
to occur; horizontal squash ought to be rare or non-existent. So if
one wished to measure Sun semidiameter (for itself, not just as an
adjunct to checking index error) then it should be done by a
horizontal angle.

The other is the quantization error. Although the Sun's semidiameter
is precisely known and predicted (to a hundredth of an arc-second, in
the Astronomical Almanac), in the Nautical Almanac it's simply rounded
to the nearest 0.1 arc-minutes figure. So, between early May and late
August, it's given a constant value of 15.8', which is just saying
that it is nearer to 15.8 than to 15.7 or 15.9. There's  a possible
error of  between = .05 and - .05, which can stay the same for weeks
at a time. So, during a period when it was high by nearly .05, there
can be weeks at a time when the value of 4SD can be consistently high
by nearly 0.2'; quite enough to make Bill's precise observations
scatter around a value that's significantly lower than 4SD taken from
the Almanac. If he want's to do his job properly he should use a more
precise value for SD; there must be a website that provides it.

I wonder what is the rationale for rejecting observations that differ
from 4SD by more than 0.4, as seems to be done by Bill and Alex;
especially in the light of that quantisation error. If that is done,
it will always skew the average of what remains. Who set that
arbitrary limit, I wonder? Is the intention to show up cases of
abnormal refraction? The scientific approach would be to never
"reject" data unless it's so clearly out-of-line that it must be due
to some error. The urge to reject stuff tjust because it's on the
outer fringes of a scatter distribution should be resisted. That's the
whole point of taking multiple measurements, that the averaging
process reduces their impact.

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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