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Andres: 

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
guitar.  

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
7571].  

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,

CLIVE

> -----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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