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    Re: "Vernier acuity" of horizon IC tests
    From: Frank Reed
    Date: 2009 Jul 4, 18:09 -0700

    Greg, you wrote:
    "An unorthodox method that I use for adjusting and determining index error is 
    to tweak the side error adjustment just enough to split a star into two 
    images with the sextant set at zero (with a bright star I even use a weak 
    shade to present a point of light instead of an asterisk of light). With the 
    two stars side by side I seem to do a better job of zeroing my index error."
    
    Bill B., if I remember correctly, suggested using fainter stars for this, 
    which strikes me as equivalent to your use of shades to eliminate the flares 
    in the image. I've tried this, and I agree that it's effective. And yes, I've 
    also found, and others seem to agree, that leaving a little so-called "side 
    error" is helpful with these sorts of observations. Just as you say, it's 
    easier to align the images side by side than to superimpose them.
    
    And you wrote:
    "A fussy navigator would probably tweak the side error back but I leave mine 
    off so that I can periodically recheck index error. Question: What kind of 
    errors get generated on high altitude observations if side error is a few 
    minutes out?"
    
    Yeah, you're right about the 'fussy navigator' here, and I think this is 
    mostly because so many navigation manuals insist on it. They emphasize that 
    one should eliminate "side error" with the same insistence as the other 
    adjustable errors. But this is really over-kill. If the side-by-side gap as 
    seen through the sextant is k minutes of arc, and the observed angle is d, 
    then the error in minutes of arc in any angular measurement is given by
      error=(1/6876)*k^2/tan(d).
    So suppose k is 5' which is probably more than you need for the trick you 
    describe above. Then if d is 30', the error is about 0.4 minutes of arc. 
    That's the error you would find in measuring the diameter of the Sun or Moon 
    using the sextant with that large side-by-side gap. But suppose that d is ten 
    times bigger, 5 degrees. Then the error would be just about ten times 
    smaller, only 0.04', negligible, and dropping roughly in inverse proportion 
    to the measured angle. So there are really no practical observations affected 
    by "side error" at all. When this has come up before, I think I said that 
    checking IC by the Sun's diameter on and off the arc would be influenced by 
    this error, but it's not true. The error cancels out. So don't fuss over that 
    side gap. It doesn't matter.
    
    -FER
    PS: The error formula above if everyhing is done in pure angles (in "radians") 
    would be error = (1/2)*k^2/tan(d). Dividing by 3438 turns one factor of k 
    into a pure angle and leaves the other in minutes of arc so the result is in 
    minutes of arc. 
    
    
    
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