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).
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 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]
The metre is the base unit of length in the International System of Units (SI).
A sextant is a doubly reflecting navigation instrument that measures the angular distance between two visible objects. The primary use of a sextant is to measure the angle between an astronomical object and the horizon for the purposes of celestial navigation.
Jean-Charles, chevalier de Borda was a French mathematician, physicist, and Navy officer.
Jean Baptiste Joseph, chevalier Delambre was a French mathematician, astronomer, historian of astronomy, and geodesist. He was also director of the Paris Observatory, and author of well-known books on the history of astronomy from ancient times to the 18th century.
The history of geodesy deals with the historical development of measurements and representations of the Earth. The corresponding scientific discipline, geodesy (/dʒiːˈɒdɪsi/), began in pre-scientific antiquity and blossomed during the Age of Enlightenment.
A theodolite is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching.
Pierre François André Méchain was a French astronomer and surveyor who, with Charles Messier, was a major contributor to the early study of deep-sky objects and comets.
The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes.
Arc measurement, sometimes degree measurement, is the astrogeodetic technique of determining of the radius of Earth – more specifically, the local Earth radius of curvature of the figure of the Earth – by relating the latitude difference and the geographic distance surveyed between two locations on Earth's surface. The most common variant involves only astronomical latitudes and the meridian arc length and is called meridian arc measurement; other variants may involve only astronomical longitude or both geographic coordinates . Arc measurement campaigns in Europe were the precursors to the International Association of Geodesy (IAG).
The Paris meridian is a meridian line running through the Paris Observatory in Paris, France – now longitude 2°20′14.02500″ East. It was a long-standing rival to the Greenwich meridian as the prime meridian of the world. The "Paris meridian arc" or "French meridian arc" is the name of the meridian arc measured along the Paris meridian.
The French Geodesic Mission to the Equator, also called the French Geodesic Mission to Peru and the Spanish-French Geodesic Mission, was an 18th-century expedition to what is now Ecuador carried out for the purpose of performing an arc measurement, measuring the length of a degree of latitude near the Equator, by which the Earth radius can be inferred. The mission was one of the first geodesic missions carried out under modern scientific principles, and the first major international scientific expedition.
A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 0.5 Hz.
In astronomy, sextants are devices depicting a sixth of a circle, used primarily for measuring the position of stars. There are two types of astronomical sextants, mural instruments and frame-based instruments.
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 reflecting instruments are used in many professions, they are primarily associated with celestial navigation as the need to solve navigation problems, in particular the problem of the longitude, was the primary motivation in their development.
Étienne Lenoir (1744–1832) was a French scientific instrument maker and inventor of the repeating circle.
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 scientists looked for measures that were universal and could be based on natural phenomena rather than royal decree or physical prototypes. Rather than the various complex systems of subdivision then in use, they also preferred a decimal system to ease their calculations.
Carlos Ibáñez e Ibáñez de Ibero, 1st Marquis of Mulhacén, was a Spanish divisional general and geodesist. He represented Spain at the 1875 Conference of the Metre Convention and was the first president of the International Committee for Weights and Measures. As a forerunner geodesist and president of the International Geodetic Association, he played a leading role in the worldwide dissemination of the metric system. His activities resulted in the distribution of a platinum and iridium prototype of the metre to all States parties to the Metre Convention during the first meeting of the General Conference on Weights and Measures in 1889. These prototypes defined the metre right up until 1960.
Earth's circumference is the distance around Earth. Measured around the equator, it is 40,075.017 km (24,901.461 mi). Measured around the poles, the circumference is 40,007.863 km (24,859.734 mi).
The arc measurement of Delambre and Méchain was a geodetic survey carried out by Jean-Baptiste Delambre and Pierre Méchain in 1792–1798 to measure an arc section of the Paris meridian between Dunkirk and Barcelona. This arc measurement served as the basis for the original definition of the metre.
Jean-Joseph Tranchot was a French military cartographer. He is most well-known for his topographical survey of the Rhineland under Napoleon, and his assistance in measuring the meridian arc of France with astronomer Pierre Méchain to determine to length of the meter.
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