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    Re: Lunar distance measurement in ideal conditions: attainable accuracy.
    From: Alexandre Eremenko
    Date: 2013 Jan 18, 18:00 -0500

    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.
    > 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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