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    Re: "Vernier acuity" of horizon IC tests
    From: Bill Morris
    Date: 2009 Jul 6, 22:51 -0700

    I have now made the appeal to experiment that I suggested in post 8984, I used 
    a SNO-T sextant whose silky smooth micrometer has well under 6 seconds of 
    error. (Those interested can find a calibration chart for its micrometer in a 
    blog on my web site www.sextantbook.com under "Interesting overhaul problems" 
    Look at "A worm turns").
    
    A prelimary experiment showed that the arm-ache coefficient was going to be 
    substantially exceeded if I made the thirty observations beloved by 
    statisticians, so I clamped the sextant in the soft jaws of a small vice held 
    on top of a theodolite tripod.
    
    I used a land horizon about 6 km away and the viewing was very good. At one 
    point, a small insect crept across the landscape near the horizon and with 
    the x 6 'scope I was able to make out that it was a person on a 4-wheel farm 
    bike.
    
    Starting with the naked eye at arms length, the first thing I noticed was that 
    there was in fact a very tiny area of overlap of the images, so that I may 
    not in fact have been testing naked eye vernier acuity at all. In the SNO-T 
    horizon mirror, there is a narrow band of paint overlap, about half a 
    millimetre, on the back of the mirror extending on to the clear glass. This 
    is true ( or should be true) of most sextants, as the paint protects the edge 
    of the silvering. Exceptions  might be those instruments with sealed mirror 
    cells.Its relevance is not clear to me.
    
    For those who are totally ignorant of statistics, rather than 90 percent 
    ignorant like me, standard deviation is a measure of the spread of results 
    about their mean and assumes a "normal", "Gaussian" or "bell-shaped" 
    distribution. Variance is the square of the standard deviatoon.
    
    A series of 30 naked eye observations had a mean of 1.467 minutes and a 
    standard deviation of 0.458. After I had done the two telescope series, I did 
    another 30 naked eye observations.
    
    This time the mean was 1.30 and the SD was 0.415. A variance ratio test gave 
    an F value of 1.218 against a tabular value for 29 degrees of freedom of 
    1.85, so we may infer that the SDs are not significantly different at the 10 
    percent level.
    
    A series of 30 observations with a x 4 Galilean telescope gave a mean of 0.743 
    minutes with an SD of 0.187.
    
    The figures with a x 6 Keplerian telescope were a mean of 0.593 and  and SD 
    0.129. Comparing these two series, the variance ratio F was 2.10, which 
    exceeds the tabulated value at the 10 percent level, but not at 2 percent. 
    For our purposes, we can say that the telescope SDs are significantly 
    different from each other and it is clear just on inspection that both differ 
    significantly (F exceeds 4)from the naked eye results.
    
    It seems that if using the horizon, we should check index error with the same 
    means that we plan to use for the observations and that in general we will 
    get better results by using the highest magnification that suits the 
    circumstances. This latter may well be open to argument. We'll see...
    
    Bill Morris
    Pukenui
    New Zealand
    
    
    
    
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