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    Re: Circle of reflection
    From: George Huxtable
    Date: 2009 Mar 14, 10:20 -0000

    It's pleasing to note a revival of interest in reflecting circles, on this
    list.
    
    In [7571, Andres referred to Mendoza's description of his circle, in -
    On an improved Reflecting Circle. Mendoza y R�os.
    http://rstl.royalsocietypublishing.org/content/91/363.full.pdf+html
    
    this is from phil. trans. 1801. It's still available free to download until
    the end of March.
    
    Mendoza was a Spanish naval officer who, in his later years (1800 to 1816)
    lived in London.
    
    Eva Taylor, in "Mathematical practitioners of Hanoverian England 1714 -1840"
    (1966) refers to Mendoza (biography 871), and to a paper in phil. trans.
    (1801.) "On a Improved Reflecting Circle, made by Troughton." That's a bit
    odd, because the 1801 paper cited above makes no such reference to
    Troughton, in its title. I wonder if there was another Mendoza paper that
    year.
    
    Mendoza's paper does mention Troughton, comparing Troughton's usual methods,
    adversely, with his own. Indeed, Troughton made many  circles, in most of
    which the telescope / horizon mirror assembly was firmly fixed to the
    circle's arc, against which, the index-mirror position could be read by
    averaging the readings of  three separate Verniers, disposed at 120�
    spacings around the arc. This process reduced many of the defects of
    division of the arc, but it discarded the principle of accumulating repeated
    observations, as angles around the circle. Troughton's, like the others,
    were reflecting circles, using the Hadley double-reflecting principle, but
    his were (mostly) not repeating circles, unlike those of Mayer, Borda, and
    Mendoza. With a Troughton circle, you had to read and record three Verniers
    for each observation, so if averaging many observations, you had a lot of
    work to do. With the repeating system, the additions were done
    automatically, so you just had to read a Vernier once, at the end.
    
    Nevertheless, it's possible that Mendoza's repeating circle had been
    constructed for him by Troughton.
    
    Mendoza ends his paper with these words, which are a bit ambiguous-
    "I have procured Reflecting Circles to be constructed, upon the principles
    here described, both with the telescope and the horizon glass upon a
    moveable index, and with the same pieces attached to the main frame of the
    instrument. The two methods have respectively answered my expectation: and I
    propose, at a future opportunity, to publish a description of the means
    which I wish to recommend for the mechanical improvement of the different
    parts, together with an account of some other essays which I have made on
    the same subject."
    
    In those words, he doesn't actually say that the repeating instrument
    described in his paper and illustrated in his engravings had really been
    made and tested. It could, at that stage, just have been a design "on
    paper", though it's hard to imagine the perspective engraving of the
    instrument being made without the real thing available for the artist to
    work from.
    
    However, I haven't seen, or heard of, that Mendoza design, with its clever
    "flying nonius", existing in any museum. Clearly, it didn't "catch on", but
    did it even ever exist, as hardware? If any list member has come across a
    Mendoza circle, it would be interesting to learn about it.
    
    Mendoza's design accumulated angles twice as quickly as did Borda's, by the
    clever trick of shifting one circular scale for all clockwise movements of
    the index (wuth respect to the telescope line), and shifting a different
    scale for all anticlockwise movements, then reading off the angular
    difference between the two scales. It called for the user to alternately
    free and lock a set of four clamps at the right moment, for each
    observation. If he made a mistake, it was necessary to start again.
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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