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    Re: The repeating reflecting circle.
    From: George Huxtable
    Date: 2005 Jan 14, 23:48 +0000

    Alex Eremenko tells us he's found an interesting volume, which was referred
    to in Chauvenet. This was Simms' Treatise on Mathenatical Instruments, of
    I presume this was William Simms, a partner in the famous firm of Troughtom
    and Simms.
    I can't locate that volume in the Bodleian library (which is a bit of a
    surprise) but have found Simms' "The Sextant", written a few years later.
    This is a VERY mathematical treatment, and rather hard going, but very
    thorough. It may appeal to Alex. Nothing about dipmeters, though, and
    little about circles.
    My guess is that Simms must have been the intellectual in the partnership,
    with Troughton supplying the craft skills.
    Alex kindly offers to make available a scan or copy of the pages relevant
    to the dipmeter, and if he finds that possible, it would be most welcome.
    Troughton was well-known for his reflecting circles, but these were (most,
    if not all) NOT repeating circles. The telescope was fixed to the frame, so
    it wasn't possible to automatically sum up a series of repeated
    observations, as with Mayer, Borda, and Mendoza Rios. Instead, they the
    instrument was used rather like an ordinary sextant. The main difference
    from a sextant was that the arc was extended to a complete circle, and the
    index arm carried three separate verniers, spaced 120 deg apart around the
    circle. All three were read and averaged for each observation, which
    reduced scale errors and eccentricity errors.
    Surprisingly, in view of his involvement in the firm, Simms doesn't seem to
    rate such instruments very highly, because reading off the extra verniers
    slowed things down without adding much in the way of increased accuracy.
    On the other hand, Alex writes-
    >And it also has a prohibited range of angles.
    >(at about 30 degrees), and Simms says this explicitly and
    >explains that for these angles it can be used only as a simple
    >sextant (the advantages specific to reflecting circles are
    >thus lost for this prohibited range).
    That appears to argue against my statement above, that the Troughton
    circles was not, in general, a repeating device. Perhaps some were, then.
    I've also had a good look at Mendoza Rios' paper "On an improved Reflecting
    Circle" by Mendoza Rios (Phil. Trans, June 4, 1801). One remarkable aspect
    of his instrument is his Vernier (he calls it a "Nonius") for interpolating
    the divisions round his circle. This Vernier is not the usual short arc of
    10 of 15 deg length, but extends right around the complete circle!
    Alex remarks on the quality of Mendoza's engravings as being "better than
    photos", and I must agree. Really beautifully and accurately done, to my
    mind those engravings are works of art in themselves.
    My estimation from those engravings was that the range of "prohibited
    angles" would be centred somewhere near 20 degrees.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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