Repeating circle

12-inch repeating circle.

Borda reflecting circle, on display at Conservatoire national des arts et métiers.

Developed from the reflecting circle, 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 Jean Baptiste Delambre and Pierre Méchain (see: meridian arc of Delambre and Méchain).

Construction and operation[]

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:

Mode of operation:
(1) The instrument is aligned so its plane includes the two points to be measured, and each telescope is aimed at a point;
(2) Keeping the angle between the telescopes locked, the left (black) telescope is rotated clockwise to aim at the right point;
(3) the right (gray) telescope's position is noted, and it is rotated back to the left point.

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 4× the angle of interest, with further iterations increasing it to 6×, 8×, and so on. In this way, many measurements can be added together, allowing some of the random measurement errors to cancel out.^[2]

See also[]

• Reflecting circles
• Meridional definition
• Grade (angle)

References[]

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