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Developed from the
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 4Ă the angle of interest, with further iterations increasing it to 6Ă, 8Ă, and so on. In this way, many measurements can be added together, allowing some of the random measurement errors to cancel out.
Developed from the reflecting circle
Reflecting instruments are those that use mirrors to enhance their ability to make measurements. In particular, the use of mirrors permits one to observe two objects simultaneously while measuring the angular distance between the objects. While r ...
, the repeating circle is an instrument for geodetic surveying, invented by Etienne Lenoir in 1784, while an assistant of Jean-Charles de Borda
Jean-Charles, chevalier de Borda (4 May 1733 â 19 February 1799) was a French mathematician, physicist, and Navy officer.
Biography
Borda was born in the city of Dax to JeanâAntoine de Borda and JeanneâMarie ThĂ©rĂšse de Lacroix.
In 175 ...
, who later improved the instrument. It was notable as being the equal of the great theodolite
The Ramsden surveying instruments are those constructed by
Jesse Ramsden and used in high precision geodetic surveys carried out in the period 1784 to 1853. This includes the five great theodolitesâgreat in name, great in size and great in accu ...
created by the renowned instrument maker, Jesse Ramsden
Jesse Ramsden FRS FRSE (6 October 1735 â 5 November 1800) was a British mathematician, astronomical and scientific instrument maker. His reputation was built on the engraving and design of dividing engines which allowed high accuracy measureme ...
. It was used to measure the meridian arc
In geodesy and navigation, a meridian arc is the curve between two points on the Earth's surface having the same longitude. The term may refer either to a segment of the meridian, or to its length.
The purpose of measuring meridian arcs is to ...
from Dunkirk
Dunkirk (french: Dunkerque ; vls, label= French Flemish, Duunkerke; nl, Duinkerke(n) ; , ;) is a commune in the department of Nord in northern France.Barcelona
Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ...
by Jean Baptiste Delambre and Pierre MĂ©chain
Pierre François AndrĂ© MĂ©chain (; 16 August 1744 â 20 September 1804) was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep-sky objects and comets.
Life
Pierre MĂ©chain was bo ...
(see: meridian arc of Delambre and MĂ©chain).
Construction and operation
The repeating circle is made of twotelescope
A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to obse ...
s 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 4Ă the angle of interest, with further iterations increasing it to 6Ă, 8Ă, and so on. In this way, many measurements can be added together, allowing some of the random measurement errors to cancel out.
See also
* Reflecting circles *Meridional definition
The history of the metre starts with the Scientific Revolution that is considered to have begun with Nicolaus Copernicus's publication of ''De revolutionibus orbium coelestium'' in 1543. Increasingly accurate measurements were required, and sc ...
* Grade (angle)
In trigonometry, the gradian, also known as the gon (from grc, ÎłÏÎœÎŻÎ±, gĆnĂa, angle), grad, or grade, is a unit of measurement of an angle, defined as one hundredth of the right angle; in other words, there are 100 gradians in 90 degr ...
References