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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Circle of reflection
From: George Huxtable
Date: 2009 Mar 14, 10:20 -0000
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@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---