Repeating circle

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The repeating circle is an instrument for geodetic surveying, invented by Etienne Lenoir in 1784,[1] while an assistant of Jean-Charles de Borda, who later improved the instrument. It was notable as being the equal of the great theodolite created by the renowned instrument maker, Jesse Ramsden. It was used to measure the meridian arc from Dunkirk to Barcelona by Delambre and Méchain.

The repeating circle is made of two telescopes mounted on a shared axis with scales to measure the angle between the two. The instrument combines multiple measurements to increase accuracy with the following procedure:

Align the instrument so its plane includes the two points to be measured, and aim each telescope at a point (diagram:1). Keeping the angle between the telescopes locked, rotate the left (black) telescope clockwise to aim at the right point (diagram:2). Note the position of the right (gray) telescope, and rotate it back to the left point (diagram:3).

At this stage, the angle on the instrument is double the angle of interest between the points. Repeating the procedure causes the instrument to show 4x the angle of interest with further iterations increase it to 6x, 8x, and so on. In this way, many measurements can be added together, allowing some of the random measurement errors to cancel out.[2]

12 inch repeating circle.
Repeating circle on display at the Musée national de la Marine.

See also[edit]


  1. ^ Daumas, Maurice, Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers, Portman Books, London 1989 ISBN 978-0-7134-0727-3
  2. ^ Alder, Ken, The Measure Of All Things, 2002 ISBN 0-7432-1675-X