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Frank,
Thanks. Actually I did not miss this method of index correction.
And I understand that most of my Lunars are not bad.
(Not worse than Cook's astronomers were doing on land:-)
And not worse than other published results that I know.

But I still see some scientific problem here: there is a clear
systematic bias that I cannot explain. Small, but it definitely exists.
I never get undershots. This clearly shows that there is a bias
of unknown origin.
So there must be some reason for this.

If the problem is with index correction, then this is another scientific
problem: why over 10 years I get systematically and consistently
a wrong index correction with every method that I use ?

The only logical explanation I can imagine is that one or two teeth
of the sextant arc near 0 are somehow defective, distorted. And the rest
of the scale
is perfect. The visual inspection shows that they look exactly the
same as other teeth, but of course a 0'3 distortion of teeth cannot be
visible with a naked eye.

Alex.

> During the period when you were not following NavList messages, I
> described a method for checking index correction which is more reliable
> and accurate than any other I have used. It's fairly simple, but it
> requires a "spotting scope" --a small telescope with a magnification of
> perhaps 30x. The method is simple. Remove the sextant's scope, and place
> it on its side on a table where you can see some suitably distant
> well-defined vertical pole or tower. Then put the spotting scope on a
> tripod in line with the usual optical path to the horizon mirror. You may
> need to build a cardboard shade or "umbrella", as Maskelyne put it, to
> keep out direct images. Then use the usual method to test the index error,
> lining up the direct and reflected images of that distant marker. Your
> results should be identical to the tenth of a minute of arc on roughly
> four out of five trials (based on my experience). I know of no better way
> to check index correction. I don't know if that would explain your 0.3'
> bias (which does not appear to be present in your current observations),
> but it might help.
>
> But in any case, your results with lunars are just fine. You're getting
> roughly two-thirds of individual observations within a quarter of a minute
> of arc (that's another way of saying that the s.d. is about 0.25' on
> single observations, which, of course, is what I have been saying for
> years). And your average on sets of four is within a tenth of a minute of
> arc most of the time. You mentioned a couple of weeks ago that you are
> somewhat "pessimistic" about lunars. Doesn't all of this make you even a
> little more "optimistic"?
>
> For others following along, if you shoot four lunars and average them
> (with a properly-adjusted modern sextant under good conditions with a 6x
> or better scope), as was common practice "back in the day", you can expect
> an error in your observed distance of about +/-0.1' most of the time. This
> is equivalent to an error in the resulting GMT of +/-12 seconds, which, of
> course, is equivalent to an error in the corresponding longitude of +/-3'
> at the equator, or at, e.g., 40 degrees latitude, an error of +/-2.3
> nautical miles in position.
>
> -FER
> PS: Also, Alex, that same method setting a spotting scope in line with the
> instrument on a table can be used to measure arc error if you add another
> sextant with a KNOWN arc error (or better yet zero arc error).
>
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