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An interesting posting from Geoffrey Kolbe, Subject: [NavList 1849] I
need some help please

I've changed the threadname to make it more relevant.

The relevant diagram is attached to [Navlist 1848]

He wrote-

"First, look at the Moon-Rasalhague position lines. They are almost
parallel, but about ten minutes apart (in the area of interest) and
the bodies are opposite each other. This indicates some systematic
error of about +5 minutes, which might be index error or an error in
dip due to some atmospheric effects. Anyhow, draw a line right in
between these position lines to bisect them and to  amalgamate the
Moon-Rasalhague sightings. This takes out the systematic error in
these sightings.

Now look at the Altair-Kochab pair. They are roughly opposite each
other, so you can bisect these two position lines, which will take out
the systematic error from these sightings.

Now all you have left is the Venus-Alpheratz pair. These bodies are
both in the same quarter of the sky, so you cannot take out the
systematic error by combining them - but bisect them anyway, so
forming a third amalgamated-position-line which runs pretty much
exactly North-South. However, note that from the Moon-Rasalhague
position lines, the systematic error seems to be around +5 minutes.
Your sextant is reading about 5 minutes too high. So, assume this
systematic error is present for all your sightings and move your
Venus-Alpheratz amalgamated position line 5 minutes to the West.

Now you have three amalgamation position lines all crossing at the
same point at around 40N17,153W13. That is where you are - roughly."

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

Well, what Geoffrey has done, in effect, is to presume, from
discrepancies between these position lines, that there is a systematic
error, which could be corrected by a shift of  5' "away". The logical
way to correct such an error, if it exists, would be to shift each of
those 6 observations, each by 5', in the opposite direction to that of
the object observed, to discover how those 6 lnew ines intersect.
Indeed, that procedure doesn't differ, that much, from what he has
described.

But how reliable is that deduction, from those observations, that
there must be a systematic error, to be corrected by shifting
everything 5' away? On the face of it, it seems unlikely. How could it
possibly come about? What sort of carelessness is going to give rise
to an index error that's wrong by all of 5'? What extreme temperature
gradients are going to cause an anomalous dip, differing by 5' from
the expected value? A minute or two is plausible, but 5' is outside
common experience, though not quite impossible. For sure, if Geoffrey
or I suspected such a common discrepancy in our own observations, we
would think it called for some investigation, at least. In this case,
we are hampered, in being provided with a set of altitudes which may
well have been contrived for the sake of creating a problem, and may
not be at all realistic.

So, in real life, what would be a more likely cause of that
discrepancy, between position lines of Moon and Rasalhague, observed
in nearly opposite directions? What about the random scatter that you
get in making any observation, up from the horizon, with all the
uncertainties that are involved, in other than millpond conditions?
What about error in chronometer time, which would systematically
affect computed position lines, but in quite a different pattern.

I don't disagree with Geoffrey, that the observations may perhaps be
compatible with a common error in altitude. And there's no doubt that
in applying the adjustments, as he has done, the apparent scatter in
the plots is significantly reduced, all 6 of the lines being shifted
closer to a common intersection. But in my view such an improvement
may be illusory, based on weak foundations. I would prefer to take the
observations as they stand and analyse them accordingly.

In the end, however, there's no great difference between Geoffrey's
final conclusion and mine, based on simple eyeball estimation. What he
hasn't done is to answer Gary's original question, "My fundamential
question is which sights form the enclosure of my position?". Mind
you, I didn't really answer it, either. I hope that Geoffrey isn't
going to claim that it's bounded by his new, much-reduced, triangle.

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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