Repeating circle
Encyclopedia
The repeating circle is an instrument for geodetic surveying, invented by Etienne Lenoir
in 1784, 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:
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.
Etienne Lenoir (instrument maker)
Etienne Lenoir was a French scientific instrument maker and inventor of the repeating circle.When hired by Jean-Charles de Borda around 1772 to work on the reflecting circle, he was about thirty years old and nearly illiterate. However, his intelligence and mechanical genius allowed him to...
in 1784, while an assistant of Jean-Charles de Borda
Jean-Charles de Borda
Jean-Charles, chevalier de Borda was a French mathematician, physicist, political scientist, and sailor.-Life history:...
, who later improved the instrument. It was notable as being the equal of the great theodolite
Theodolite
A theodolite is a precision instrument for measuring angles in the horizontal and vertical planes. Theodolites are mainly used for surveying applications, and have been adapted for specialized purposes in fields like metrology and rocket launch technology...
created by the renowned instrument maker, Jesse Ramsden
Jesse Ramsden
Jesse Ramsden FRSE was an English astronomical and scientific instrument maker.Ramsden was born at Salterhebble, Halifax, West Riding of Yorkshire, England. After serving his apprenticeship with a cloth-worker in Halifax, he went in 1755 to London, where in 1758 he was apprenticed to a...
. It was used to measure the meridian arc
Meridian arc
In geodesy, a meridian arc measurement is a highly accurate determination of the distance between two points with the same longitude. Two or more such determinations at different locations then specify the shape of the reference ellipsoid which best approximates the shape of the geoid. This...
from Dunkirk to Barcelona
Barcelona
Barcelona is the second largest city in Spain after Madrid, and the capital of Catalonia, with a population of 1,621,537 within its administrative limits on a land area of...
by Delambre and Méchain
Mechain
Mechain was a medieval cantref in the Kingdom of Powys. It lay almost in the centre of the kingdom, bordering with cantref Caereinion to the south, the two cwmwds of the cantref of Mochnant to the north, and part of the cantref of Deuparth and the cwmwds of Deuddwr and Ystrad Marchell to the...
.
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:
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.