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    Re: Lunar distance accuracy
    From: Alexandre Eremenko
    Date: 2007 Nov 4, 23:18 -0500

    
    Frank,
    
    > "So you're saying these observations
    > exhibit excess kurtosis "
    
    Frank. I really don't want to discuss theoretical
    questions of statistics on this list.
    I think the plots of distributions of errors tell
    EVERYTHING to anyone who cares to look at them.
    While trying to characterize the error with a single
    number (error of the average, average error, sigma,
    most probable error, median error, whatever) is
    somewhat misleading.
    
    > Alex, your messages are not getting "lost".
    
    Good. So you saw the plots of distributions.
    These plots tell you everyhting I have to say
    (and everything I know) about
    Lunars accuracy. If you disagree with this, then tell
    me what exactly is the point of disagreement.
    a) You think these plots are somehow not typical and
    DO NOT reflect the real accuracy of the lunar distance
    observations (from sea and land, with a hand held sextant,
    by an observer with experience)?
    Or
    b) you agree that these distributions are sort of typical,
    and really show what can be practically achieved?
    And in this last case (b), the only disagreement is how
    to derive a SINGLE number from these distributions,
    the number which characterizes the accuracy?
    
    If we are in situation (a) please give me a reference
    for better data.
    
    If we are in situation (b), let me state two rough
    conclusions from these plots:
    1. Observations at sea a substantially less accurate
    than those on land.
    2. Even on land, under good conditions,
    errors of up to 0'5 in a single distance
    shot are unavoidable, and occur in about 1/10 of all
    shots.
    
    These are the conclusions I make from these graphs.
    
    > For a long time, I thought that you personally, Alex,
    > were shooting lunars because
    > you wanted to determine the arc error of your
    > instrument.
    
    For this I was shooting star distances.
    I have to say that I failed to determine any arc error
    of the instrument. Freiberger and
    Cassnes Plath independently issued certificates that say
    that my instrument has no perceptible error.
    So in my Lunars I assume this (as White did:-)
    
    > "game"-- then mounting the instrument on a stand
    
    Lunars is a poor method of determining arc error.
    Because there are only few distances that you can
    shoot on any given night. And for arc error, it is desirable
    that all shots are made under the same conditions,
    with index error unchanged etc.
    
    Years ago, one list member (George perhaps?) challenged
    us by asking whether anyone succeeded in determining
    the arc error of his (modern) sextant himself, by distances
    or any other observations.
    No one responded to this challenge. I tried and failed.
    But perhaps my sextant really does not have any
    perceptible arc error.
    
    Alex.
    
    
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