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    From: Fred Hebard
    Date: 2004 Sep 29, 14:59 -0400

    On Sep 29, 2004, at 12:46 PM, Alexandre Eremenko wrote:
    
    > Subject: questions on sextants
    >
    > I am interested in sextants precision.
    > I read the earlier discussions in this list on the errors
    > of altitude measurement in the sea, but I want
    > to seperate the question of sextant precision
    > (as an instrument)
    > from the rest of the factors like dip, refraction, difficulties
    > on a small boat etc.
    > In other words, how precisely can you measure an angle
    > with a sextant under the best possible conditions?
    >
    > I could not find much on this question in the books.
    > Some authors hint that 0.1' is the best you can hope. Can this be
    > really
    > be achieved? Can 0.2' be achieved?
    >
    > Of course, this depends on the sextant:
    >
    > Is it true (as some say) that XIX century sextants were
    > more precise (because they were designed for Lunar distances,
    > where super-high precision of the measurement is crucial)?
    > And that in the modern times they don't care so much about
    > sextant precision because other errors (dip and refraction)
    > are larger anyway?
    >
    > Is it true that top of the line XX century sextants with brass frame
    > like
    > Plath, Cassens-Plath or Kalvin-Hughes permit more precise measurements
    > than cheaper aluminium-frame sextants (like Astra, Freiberger and
    > SNO-T)?
    >
    > I am doing some experiments with my aluminium SNO-T
    > (have no other sextant for comparison), but these
    > experiments are non-conclusive yet, probably because
    > of my lack of agility/experience in the measurement.
    >
    > I would also appreciate any suggestions on how can I really
    > test the instrumental error of my sextant.
    > The natural way to do this seems
    > to be star-to-star measurements. I read the two interesting
    > letters of April 6 by Frank on how to do this, but so far
    > I fail. (Unexpectedly, my star-to-star measurements turned
    > out to be much less precise than my Sun (art horizon) measurements! And
    > I have no idea why this is so.)
    > I will report the details of my experiments in another message,
    > if there is any interest to this "academic" question at all.
    >
    > Alex.
    >
    
    Alexandre,
    
    I am deeply interested in these questions.  You need to separate the
    question of sextant accuracy from precision.  Accuracy is how close you
    are to the target; precision is the repeatability of your shots.  An
    inaccurate sextant can be very precise and an accurate one imprecise.
    An inaccurate but precise sextant might give measurements that are all
    off by 1.0' of arc, but consistently off, all measuring between 0.9'
    and 1.1' in error.  An imprecise but accurate sextant might give
    measurements that averaged being off by 0.0' of arc, but the individual
    measurements might range from -1.0' to +1.0' in error.
    
    There may be some truth to the statement that the XIX century sextants
    were more accurate & precise than modern sextants.  They had a larger
    radius of the arc, 7 inches or 8 inches rather than 6".  In addition,
    the larger Hughes sextants often had no detectable errors at any angle
    while the smaller "Mate" series usually were off by at least 30" of arc
    at some angles.  Furthermore, the telescope mounts on the larger Hughes
    sextants were adjustable, but not on the "Mate", at least the later
    ones in the series.
    
    Early in my use of a sextant I tried star to star measurements to
    calibrate the instrument, but then switched to altitude shots, as these
    have a practical application, at least potentially.  I think it
    important that you become proficient with using the sextant, by
    whatever means, before attempting to calibrate it with star to star
    distances.
    
    For practical use in position-line celestial navigation, I agree that
    high accuracy is unnecessary and that not as much practice and care are
    required.
    
    I think an error of 0.2' of arc is about the best that can be obtained.
      A few times I have gotten very accurate and precise, to under 0.1' of
    arc.  More typically, my standard deviations lately range from 0.1' to
    0.3'.  These are with an artificial horizon, which shrinks the errors,
    I believe.  Here's a summary of my last few months of shots, usually
    three replicates per series:
    
    mean    std_dev
    -0.11   0.27
    0.22    0.09
    0.20    0.32
    -0.01   0.10
    1.08    0.62
    -0.22   0.22
    -0.36   0.07
    -0.36   0.30
    -0.78   0.22
    0.05    0.23
    -0.14   0.30
    -0.03   0.11
    -0.46   0.19
    -0.25   0.07
    -0.06   0.02
    0.01    0.14
    
    I'm still fiddling with this sextant, so the numbers haven't settled
    down as much as they might.
    
    Fred
    
    
    

       
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