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    Re: Personal Equation and Index Error
    From: Bill Morris
    Date: 2016 Dec 21, 11:34 -0800
    David,
    
    I gave an account of my index error determinations here; http://fer3.com/arc/m2.aspx/Index-error-Morris-jun-2008-g5300, but since there was an error in the last sentence of the paragraphs quoted below, I give here a corrected abstract: 
    
    <<I made three sets of thirty careful observations for each method:
    using a sharply defined land horizon about 6 km away; using the sun's
    limbs; and using a 2nd magnitude star. To make things easier and to
    avoid fatigue, I clamped the sextant atop a theodolite tripod so I
    could make each observation a leisurely one. I also glued a simple but
    effective paper vernier over the micrometer index to reduce to some
    extent a tendency to bias the results in a more or less favourable
    direction when estimating tenths. Here are my results for the standard
    deviations:
    
            Method                    S.D.      95% range
    Horizon, reflected image up to direct image     0.142        0.56
    Horizon, direct image up to reflected image     0.157        0.62
    Sun's limbs                         0.155        0.61
    Star                                0.174        0.68
    
    For those who might think that statistics is a new form of contact
    adhesive, I should point out that the standard deviation is a measure
    of the dispersion of the results about the mean value; and 1.96
    standard deviations each way will capture 19 out of 20 or 95% of
    results. 1 S.D. each way will include about 64% of results. So, my
    sextant-eye-brain system will give an index error of more than 0.3
    minutes away from the best estimate, the mean, one time in twenty.
    About 45% of the time it will be more than 0.15 minbutes
    away from the mean.>>

    The sextant was a Soviet SNO-T, freshly overhauled and using a x 4 telescope.

    Bill Morris

    Pukenui

    New Zealand

       
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