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    Re: Lewis and Clark lunars: more 1803 Almanac data
    From: Ken Muldrew
    Date: 2004 Apr 19, 12:04 -0600

    On 17 Apr 2004 at 0:04, George Huxtable wrote:
    
    > That, I think, is what
    > Ken was getting at. I can't quite see, yet, how he arrives at that
    > misalignment of about 36deg from the numbers he quotes: perhaps he
    > will explain further.
    
    I'm afraid I've lost the more recent message where George has taken
    this up so I'll reply here. This morning I looked at the spreadsheet
    that I was using and I can't tell where I got the numbers that I
    posted as the slope on my spreadsheet is 0.295, as George gets as
    well. Since Paul Hirose has done the calculation correctly, I suggest
    we leave my sloppy work for the sorry mess that it is.
    
    I tried another approach last night to this problem that might be
    worth mentioning. I treated each observation from series A and C as
    individual measurements, clearing the distance with the assumption of
    a particular star and comparing that with the true distance for each.
    In this way I hoped to be able to see if there was a systematic error
    in the data. For example, if they used Rigel but their index error
    was off by 10' or so, then we would expect to see a relatively
    constant error in the difference between the cleared distance and the
    true distance equal to the systematic error (in fact, the error for
    Rigel diverges quite sharply). I'll just give my results for
    Aldebaran and Tabit (PI 3 Orion, the center of his bow).
    
            clr'd d true d  clr'd d true d
    GMT     Aldebaran       Tabit
    5.09    59.57   60.84   59.69   59.97
    5.32    59.64   60.95   59.75   60.07
    5.49    59.71   61.05   59.83   60.17
    5.59    59.73   61.09   59.83   60.21
    5.64    59.81   61.13   59.92   60.24
    5.69    59.83   61.16   59.93   60.27
    7.27    60.47   61.99   60.56   61.05
    7.36    60.55   62.05   60.64   61.11
    7.42    60.53   62.07   60.62   61.13
    7.49    60.54   62.11   60.63   61.16
    7.53    60.57   62.13   60.66   61.19
    7.57    60.57   62.15   60.66   61.20
    
    The error is smaller, and flatter for Tabit, but it still increases
    monotonically with time with a consistency that looks like they were
    not measuring to this star. Interestingly, if we look at the star
    below Tabit in Orion's bow (PI 5 Orion), the error is a reflection of
    the Tabit error about the zero line (so that if you were to add the
    two errors for each datapoint you would have zero error). Maybe they
    jumped back and forth between these two 3rd magnitude stars with
    different measurements?
    
    As an aside, perhaps my own beginner's errors can lend some support
    to the "wrong star" hypothesis. Just last night I was measuring some
    star-to-star distances and I got the wrong star by presetting my
    sextant and finding a star exactly where I expected. In fact I had
    read off the wrong number in the dark when pre-setting my sextant,
    but seeing the star where it was expected, I proceeded to bring the
    two stars together. It's really quite different from using binoculars
    or a telescope, where you scan the neighborhood of a star to see
    familiar landmarks. Because you have to keep two stars in your view
    at the same time, you don't have the luxury of panning about. If L&C
    had the star in their index mirror and the moon through their horizon
    glass, then they might have made this obvious error (at least, I can
    now see myself making such a glaring error).
    
    Ken Muldrew.
    
    
    

       
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