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    Re: Circular sextant?
    From: Brad Morris
    Date: 2017 Jul 30, 15:58 -0400
    One must be careful.  There are two types of reflecting circles.

    The first type operates much like a sextant, wherein one measurement of one angle occurs.  This is termed a "non-repeating" reflecting circle.  The advantage of the non-repeating circle over a similar sextant is that there are two verniers on one arm.  Each vernier has its own scale.  In practice, the readings are averaged.  The affect is to minimize eccentricity errors in the index arm axis of rotation.  Additionally, some non repeating reflecting circles can measure angles far beyond that of a sextant.  A sextant will typically measure to about 120° (scale markings extend further, but are un-useable).  My particular reflecting circle can measure angles out to 235°, that is, right up to 180° and beyond!!

    The second type of reflecting circle is termed a "repeating circle".  In this arrangement there are a pair of index arm.  Each arm moves independently.  In practice, the user takes several readings, and accumulates an overall angle.  Suppose the basic angle is 32°.  If 6 readings are taken, then the repeating circle will report 192° of accumulated angle (6×32°).  The user divides the accumulated angle by the number of readings.  Not only does this reduce eccentricity errors, but also helps to average outliers in the measurement.  

    Actual period reflecting circles are quite rare.  They were quite expensive, even back in the day.  To put it into perspective, my reflecting circle was manufactured before 1905, as it was used in a documented survey, to include the device serial number.  When purchased new, it had a list price in excess of $400.  That would put it out of the reach of all but the very serious and well heeled users.

    Brad







    On Jul 30, 2017 2:55 PM, "Tom Sult" <NoReply_TomSult@fer3.com> wrote:
    Some information on the reflecting circle. 

    On Jul 30, 2017, at 02:03, Peter Monta <NoReply_PeterMonta@fer3.com> wrote:

    Hi Bill,

    It's a reflecting circle.  Just as you say, it looks like a sextant, and it has the same operating principle.  The advantage is that it's self-calibrating, because the circular scale can be arbitrarily rotated and redundant measurements taken, permitting the target angle and the scale errors to be jointly estimated.  It's bulkier for a given radius, though, and I guess somewhat more expensive too.

    "Reflecting circle" on images.google.com pulls up a number of nice examples.  I think the name of Borda is associated with the device, but I'm sure others here know more of the history.

    Cheers,
    Peter

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