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    Re: Perpendicularity and other qstns.
    From: Alexandre Eremenko
    Date: 2004 Oct 13, 16:07 -0500

    Dear Herbert,
    I already admitted that my message you refer to was incorrect.
    Maybe worse, it was arrogant, and I apologize for this.
    And indeed, I should have thought more about messages
    on this subject before I wrote my own.
    
    I found my mistake as soon as I strated writing mathematical
    theory of this experiment, on Frank's request.
    In the process of writing,
    I realized that if the axis of rotation of
    the index
    arm passes through the plane of the index error
    (which is probably the case for many (most?) sextants)
    then the effect I described will be be absent.
    I repeat that I have never seen another sextant except my SNO-T.
    
    Then I saw the message with Frank's experiment on the kitchen
    floor. By that time I already did not need to stage this experiment
    myself because mathematical conclusions were in complete agreement
    with the experiment described by Frank.
    
    Only then I realized that your suggestions made before Frank's
    experiment were right. And what I was saying about "all sextants"
    was wrong: what I was saying only applies to some
    sextants, like SNO-T.
    
    So next time I will try to be more cautious in my statements.
    
    The mathematical demonstrations I have at this moment are of the
    following:
    
    1. If the axis of rotation of the index arm passes through the
    reflecting surface of the index mirror, then the perpendicularity
    test as described in most books is correct, and it does not matter
    from what height you look.
    
    2. If this axis does not pass through the reflecting surface,
    the test should be modified. This is the case with SNO-T and
    maybe with some other sextants.
    
    I am still not sure that this mathematical "theory"
    has to be posted on the list, because its conclusions
    apparently coinside with the "common knowledge" of the members
    of this list, and the "theory" adds nothing new to it. But of
    course
    I will post if there is still any need.
    
    So far I only have one practical recommendation for SNO-T and
    other sextants with this similar property (that the axis of
    rotation does not pass through the mirror surface).
    
    Put your sextant on the table horizontally. Set the index arm
    on 35 degrees. Put one visor on 0 on the arc, so that its
    front surface is aligned with the inner edge of the arc.
    Put the second visor on 120 deg on the arc, so that its front surface
    is 5mm BEHIND (that is "to the outside" of the arc)
    this inner edge of the arc. Now the test can be done in the usual
    manner. That is the height of the eye becomes irrelevant.
    
    I find this easier to do than to keep the height of the eye precisely.
    Which I tried for some time yesterday. (Using standard SNO-T
    visors, it could be easier with Celestaire cylinders.
    Piles of coins did not work: two piles of 16 dimes were found
    of unequal height, apparently because some dimes were bent,
    I could not determine which ones, and thus abandonned the dimes.
    I don't have dominoes or dice at home, so I cannot say anything
    about them).
    The recommended 5mm distance should be determined for each sextant
    experimentally. I found 5mm appropriate for my SNO-T.
    
    Alex.
    
    
    

       
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