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    Re: Circle of reflection
    From: Clive Sutherland
    Date: 2009 Mar 10, 18:19 -0000

    I commend your interest in the reflecting Circle it is a fascinating device
    and much neglected by modern historians. These are a few notes I have made
    about using this one.  
    The CIRCLE shown in Wolfgang�s Photograph is indeed the one I built some
    years ago. It is very nice of Wolfgang to show it. It was taken by him at
    the Nation Maritime Museum in Greenwich when George, Wolfgang and I were
    visiting their reserve collection. I built it because George and I wanted to
    discover what limitations there were in the angles that could be measured
    and generally to see how well this instrument functioned.
    I made no attempt to replicate a particular model.  The Circle was home made
    and the design was largely based what could be viewed in museums, which
    wasn�t much, and otherwise based on ignorance and guesswork. It was made
    from scrap materials and cheap components. However it worked surprisingly
    well considering, But I would design it differently if I had to do it again..
    The configuration chosen was constrained of by the diameter of the telescope
    on the one hand, (a one inch 'golfing' telescope requires one inch tall
    mirrors) and the computer printer (A4) page width on the other, for printing
    the scales. The Main Scale had to be printed in one piece.
    Observing with it takes a bit of getting used to as you need to remember
    accurately a sequence of hand movements, that are repeated many times. One
    mistake and you have to start all over again!  A bit like learning to play a
    As a land surveying instrument it worked well. With only a few doublings I
    could achieve a precision of about +- <1 min (the Vernier reads to 5 min).
    I do not have any filters fitted so it isn�t any good for Lunars but I have
    been experimenting with crossed polarisers and one day perhaps I will have
    another go. 
    When observing, the size of the mirrors fitted do cause problems. First
    because they obscure some directions and second because secondary
    reflections can be seen when you hunt for the targets you are trying to use..
    It is very necessary to set the angle to be expected onto the first index
    position before searching. 
    Once the correct alignment is found then the second inner scale can be used
    to remember this angle for all further repetitions. The way is, I think
    described in the paper by Mendoza y Rios referred to by you in [NavList
    This is probably an unnecessary bit of History for anyone interested.
    Because the �CIRCLE� is divided over the complete circle it is self
    calibrating. That a circle is 360� (400 gon or whatever) is axiomatic. It
    can never be approximate.
    That is not to say there can be no errors, it is just that if there are
    positive errors over one part of the arc then there must be negative errors
    somewhere over the other part. 
    A measurement is taken by walking the Telescope arm and the Index arm
    alternately, repeating the same measurement either side of the telescope
    arm, until several turns of the circle are traversed. 
    Only the first and last reading needs to be recorded and the subsequent
    averaging gives the angle measurement. The more repetitions, especially
    complete turns of the circle, gives better precision to measurement.
    Personally I am not sure Mayer appreciated the full implications of this but
    it is certain that Borda did and he and his contemporaries made use of this
    fact by perfecting their Doubling and Averaging procedures over the full
    range of the 720� calibration many times over. (The factor of 2 appears in
    this number  because like the Sextant two reflections are involved).  It is
    worth remembering that this instrument was developed before Gauss invented
    Statistical analysis and whether their measurements were believed by their
    sponsors depended  entirely on  the reputation of the surveyor.* 
    * A book called  �The measure of all things� by Ken Alder ISBN 0 316 85989.3
    describes the use of this instrument by Delambre and Mechain for determining
    the length of the degree of latitude from  Dunkerque to Barcelona (in the
    middle of not only the French revolution but also the Franco Spanish war!)
    It took them seven years to do it  and they finished in 1799. The book is a
    real gem
    Regards to All,
    > -----Original Message-----
    > From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf
    > Of Andres Ruiz
    > Sent: 09 March 2009 10:40
    > To: NavList@fer3.com
    > Subject: [NavList 7602] Re: Circle of reflection
    > Diving in the list I have found some references to the circle:
    > - In [NavList 1501] Alex Eremenko write: In Bremerhaven museum I saw some
    > very interesting reflecting circles (by Pistor and Martens), equipped with
    > detacheable oil lamps on each vernier.
    > Alex, have you got any pics to share?
    > And Frank Reed said that in Mystic there are some circles.
    > Bowditch and Chauvenet Vol.2 have included a description of this
    > instrument. Really, they were used in the States?
    > [NavList 7580]:
    > ---1. It's pleasing to note that the Royal Society is again providing
    > copies of its historical papers free of charge. Normally, they are only
    > available
    > rather expensively, through Jstor. I don't know how long this will last.
    > --> George, See http://royalsociety.org/ : "Royal Society Publishing is
    > pleased to announce that our online journal content is now hosted on the
    > HighWire H2O platform and, to celebrate, all our published content will be
    > FREE to access until 31 March 2009."
    > ---2. Even for those that may have no technical interest in that paper
    > itself,
    > it's worth taking a look at the quality of the engravings. ...
    > Nevertheless, to my mind they compete with any work-of-art as
    > things of beauty. Is that just my odd mind? What do others think?
    > --> I am totally agree with George, the engravings are very beautiful,
    > something like a 1800�s CAD 3D
    > [NavList 7581]:
    > Clive, is it possible to hear your comments about your circle?...
    > Andr�s Ruiz
    > Navigational Algorithms
    > http://www.geocities.com/andresruizgonzalez
    > > 
    > No virus found in this incoming message.
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    > 07:14:00
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