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    Re: The repeating circle.
    From: Alexandre Eremenko
    Date: 2005 Jan 11, 17:06 -0500

    Dear George,
    
    I checked the Chauvenet volume again from
    my library and I am ready to discuss your question.
    I agree with what you say, there is indeed
    some prohibited range of angles for "cross observations",
    like in Fig. 28.
    
    I also looked at the paper
    "On an improved Reflecting Circle" by Mendoza Rios
    (Phil. Trans, June 4, 1801) which has much better
    pictures than Chauvenet. (Besides schematic diagrams,
    he has "real life" pictures of his instrument,
    they are of better quality than photos:-)
    Mendoza's
    description
    coincides with that of Chauvenet. In particular
    he has an exact counterpart of Fig 28.
    
    The pictures in Mendoza suggest however, that the range
    of prohibited angles conststs of rather small angles.
    (The line corresponding to EB in Fig 28 is much closer
    to the center in Mendoza pictures, and the mirror m is
    very small).
    
    Now I conjecture that the prohibited range is somewhere
    between 5 to 10 degrees, and such angles are rarely used
    both in altutudes and in lunar distances, for well known reasons.
    
    If nevertheless it is necessary to measure such angles,
    this also can be done by using Meyer's original procedure,
    where only configurations like Fig 29 are involved.
    
    This should not create much inconvenience in practice.
    Mendoza calls the method described on p 120 of Chauvenet
    the "Borda method".
    
    On another subject we discussed last fall:
    notice that Chauvenet mentions the possibility of
    using a reflecting circle as a dipmeter, and also mentions
    some specially constructed dipmeters by Troughton and Daussy
    (see p. 127).
    
    Alex.
    
    
    

       
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