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    Re: Circle of reflection
    From: George Huxtable
    Date: 2009 Mar 14, 22:22 -0000

    
    Brad wrote-
    
    While I do understand the advantages of a repeating circle of reflection 
    over a non-repeating circle of reflection, I cannot understand why a 
    non-repeating circle of reflection offers any advantage (other than the 
    handle orientation) over a sextant.  Would someone help me out with this?
    
    ====================
    
    Yes. If you have a complete circle, you aren't limited to having a single 
    index arm and Vernier (nonius). If you have two Verniers, 180� apart, then 
    averaging the two readings can compensate for any eccenticity error. 
    Averaging three did a bit more to compensate for unevenness in scale 
    division.
    
    Up to the introduction of engine-dividing from the 1780s, the inaccuracy of 
    hand-dividing was the limiting factor in all such angle measurement. That 
    was the original reason for the introduction of the repeating circle. 
    Engine-division became common, and economical, in London before it did on 
    the continent, which is why circular instruments prospered there for longer..
    
    Brad is quite right. Once engine-division had been introduced, the marginal 
    increase in precision obtained by averaging out remaining imperfections 
    became small, and in my view hardly worthwhile, especially for a 
    non-repeating circle. In those instruments there could be some advantage in 
    reducing scatter, simply because each altitude was the average of three 
    readings, which were to some extent independent, if only partially so.
    
    I wonder how popular they really were, among real navigators at sea. I can 
    see why they might be popular to put on show by museum curators, because 
    polished up well and lacquered, abounding with handles and stirrups, with a 
    multiplicity of scales, they add an eye-catching glitter to a museum 
    display. I can also see how this complexity might appeal to lecturers at 
    navigation colleges. But I can't visualise a hard-boiled navigator taking a 
    reflecting circle out on the poop on a rough night for a lunar; not if he 
    had a decent sextant on hand as an alternative.
    
    Reflecting circles weren't used just for lunar distance, they were also used 
    for precise hydrographic surveying, particularly by the French. I remember 
    reading an account of d'Entrecasteaux using a circle when surveying from 
    ship in Tasmania, probably a Borda repeating type. Clive has pointed out the 
    use of a non-reflecting repeating circle (Borda) in ultra-precise land 
    survey.
    
    Brad is asking a sensible question, one which puzzles me too. Why didn't 
    those Troughton non-repeating instruments die out, soon after 1780?.What was 
    their attraction, and their advantage?
    
    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. 
    
    
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