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George-



Perhaps I can make it clearer by avoiding the distraction of numbers.

Take a sextant observation. Record the observed altitude of ONE object, ONE reading.
Reduce that sight to a position. i.e., Perhaps it is the sun, 1800 miles away 
on a bearing of 235 degrees. it doesn't matter what, where, how much, this 
is, whether it is a position, a fix, a whatever. Don't get distracted by the 
numbers, just ake and reduce one sight on one object.

Do not make any more sightings or observations. That's done now.

Repeat your reduction, but add 20" to the observed altitude. Mark this position.

Repeat your reduction one more time, this time subtracting 20" from your observed altitude.

You now have three positions generated from three reductions. Compare the locations they give you.

Q: How far apart are they?

All else being equal, the difference in your positions is the amount of 
inaccuracy that you have generated by imitating a 20" instrument error. If 
the three positions are all "identical" enough for your needs, then a 20" 
instrument error is good enough for the instrument you will require. If the 
three positions are not sufficiently identical, then you will need a better 
instrument, or at least one of more precisely known error and quality.

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

The "real" observation will be off from a benchmarked location based on all 
errors, and because of that, even the "real" observation will be off by a 
factor of combined instrument, eye, and observer errors. If everything is 
done perfectly under perfect conditions, the observation and location will 
STILL be off from the actual position, by an amount caused by the total of 
instrument plus eye errors. If you have fuzzy eyes, or a fuzzy head, a fine 
instrument will not matter. And vice versa.

I am saying that those two factors cannot be told apart, from any one 
observation, or any series of observations, unless one can swap out the eye 
(for another eye) and the instrument (for another instrument) to compare them 
to other eyes and instruments. Or, if one can get either calibrated in some 
manner. I don't know any way to "calibrate" an eye, aside from using it with 
various instruments of known accuracy at various known positions, so that 
when you are done all you can say is "The only variable left was the eye, and 
this was the error range found from it."

In the case of "I have this sextant of unknown error and accuracy and I'm new 
to sextant use", then there is no way to determine user error distinctly from 
sextant error absent other information, is there? Not for certainty.

If there is, please, that's the information we're looking for. Share your 
thoughts on how it might be found.

   

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