Jean-Charles, chevalier de Borda (4 May 1733 – 19 February 1799) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...

, and Navy officer.

Biography

Borda was born in the city of Dax to Jean‐Antoine de Borda and Jeanne‐Marie Thérèse de Lacroix. In 1756, Borda wrote ''Mémoire sur le mouvement des projectiles'', a product of his work as a military engineer. For that, he was elected to the

French Academy of Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

in 1764. Borda was a mariner and a scientist, spending time in the

Caribbean The Caribbean ( , ; ; ; ) is a region in the middle of the Americas centered around the Caribbean Sea in the Atlantic Ocean, North Atlantic Ocean, mostly overlapping with the West Indies. Bordered by North America to the north, Central America ...

testing out advances in chronometers. Between 1777 and 1778, he participated in the

American Revolutionary War The American Revolutionary War (April 19, 1775 – September 3, 1783), also known as the Revolutionary War or American War of Independence, was the armed conflict that comprised the final eight years of the broader American Revolution, in which Am ...

. In 1781, he was put in charge of several vessels in the

French Navy The French Navy (, , ), informally (, ), is the Navy, maritime arm of the French Armed Forces and one of the four military service branches of History of France, France. It is among the largest and most powerful List of navies, naval forces i ...

. In 1782, he was captured by the English, and was returned to France shortly after. He returned as an engineer in the French Navy, making improvements to waterwheels and pumps. He was appointed as France's Inspector of Naval Shipbuilding in 1784, and with the assistance of the naval architect Jacques-Noël Sané in 1786 introduced a massive construction programme to revitalise the French navy based on the standard designs of Sané. In 1770, Borda formulated a ranked preferential

voting system An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and inf ...

that is referred to as the

Borda count The Borda method or order of merit is a positional voting rule that gives each candidate a number of points equal to the number of candidates ranked below them: the lowest-ranked candidate gets 0 points, the second-lowest gets 1 point, and so on ...

. The

used Borda's method to elect its members for about two decades until it was quashed by

Napoleon Bonaparte Napoleon Bonaparte (born Napoleone di Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French general and statesman who rose to prominence during the French Revolution and led Military career ...

who insisted that his own method be used after he became president of the Académie in 1801. The Borda count is in use today in some academic institutions, competitions and several political jurisdictions. The Borda count has also served as a basis for other methods such as the

Quota Borda system The Quota Borda system or quota preference score is a voting system that was devised by the British philosopher Michael Dummett and first published in 1984 in his book, ''Voting Procedures'', and again in his ''Principles of Electoral Reform''. ...

, Black's method and Nanson's method. In 1778, he published his method of reducing lunar distance for computing the

longitude Longitude (, ) is a geographic coordinate that specifies the east- west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lett ...

, still regarded as the best of several similar mathematical procedures for

navigation Navigation is a field of study that focuses on the process of monitoring and controlling the motion, movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navig ...

and position fixing in pre-chronometer days. They were used, for example, by

Lewis and Clark Lewis may refer to: Names * Lewis (given name), including a list of people with the given name * Lewis (surname), including a list of people with the surname Music * Lewis (musician), Canadian singer * " Lewis (Mistreated)", a song by Radiohe ...

to measure their latitude and longitude during their exploration of the North-western United States. Another of his contributions is his construction of the standard

metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...

, basis of the

metric system The metric system is a system of measurement that standardization, standardizes a set of base units and a nomenclature for describing relatively large and small quantities via decimal-based multiplicative unit prefixes. Though the rules gover ...

to correspond to the arc measurement of Delambre and Méchain. As an instrument maker, he improved the reflecting circle (invented by Tobias Mayer) and the repeating circle (invented by his assistant, Etienne Lenoir), the latter used to measure the

meridian arc In geodesy and navigation, a meridian arc is the curve (geometry), curve between two points near the Earth's surface having the same longitude. The term may refer either to a arc (geometry), segment of the meridian (geography), meridian, or to its ...

from

Dunkirk Dunkirk ( ; ; ; Picard language, Picard: ''Dunkèke''; ; or ) is a major port city in the Departments of France, department of Nord (French department), Nord in northern France. It lies from the Belgium, Belgian border. It has the third-larg ...

Barcelona Barcelona ( ; ; ) is a city on the northeastern coast of 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 c ...

by Delambre and Méchain. Cercle de reflexion img 2600

Tables of logarithms

With the advent of the metric system, after the French Revolution it was decided that the quarter circle should be divided into 100 angular units, currently known as the '' gradian'', instead of 90 degrees, and the gradian into 100 centesimal minutes of arc ( centigrades) instead of 60 arc-minutes. This required the calculation of trigonometric tables and logarithms corresponding to the new unit and instruments for measuring angles in the new system. Borda constructed instruments for measuring angles in the new units (the instrument could no longer be called a "sextant") which was later used in the arc measurement of the meridian between Dunkirk and Barcelona by Delambre to determine the radius of the Earth and thus define the length of the metre. The tables of logarithms of sines, secants, and tangents were also required for the purposes of navigation. Borda was an enthusiast for the metric system and constructed tables of these logarithms starting in 1792 but their publication was delayed until after his death and only published in the Year IX (1801) as ''Tables of Logarithms of sines, secants, and tangents, co-secants, co-sines, and co-tangents for the Quarter of the Circle divided into 100 degrees, the degree into 100 minutes, and the minute into 100 seconds'' to ten decimals, and including his tables of logarithms to 7 decimals from 10,000 to 100,000 with tables for obtaining results to 10 decimals. The division of the degree into hundredths was accompanied by the division of the day into 10 hours of 100 minutes (

decimal time Decimal time is the representation of the time of day using units which are decimally related. This term is often used specifically to refer to the French Republican calendar time system used in #France, France from 1794 to 1800, during the Fre ...

) and maps were required to show the new degrees of latitude and longitude. The Republican Calendar was abolished by Napoleon in 1806, but the 400-unit circle lived on as the Gradian.

Honours

*Five French ships were named ''Borda'' in his honour. *The crater Borda on the

Moon The Moon is Earth's only natural satellite. It Orbit of the Moon, orbits around Earth at Lunar distance, an average distance of (; about 30 times Earth diameter, Earth's diameter). The Moon rotation, rotates, with a rotation period (lunar ...

is named after him. *Asteroid 175726 has been called Borda in his honour. *His name is one of the 72 names inscribed on the Eiffel Tower. * Cape Borda on the northwest coast of

Kangaroo Island Kangaroo Island (, ) is Australia's third-largest island, after Tasmania and Melville Island, Northern Territory, Melville Island. It lies in the state of South Australia, southwest of Adelaide. Its closest point to the mainland is Snapper Poi ...

in South Australia is named in his honour. * Île Borda was the name given to Kangaroo Island in his honour by

Nicholas Baudin Nicolas Thomas Baudin (; 17 February 175416 September 1803) was a French people, French explorer, cartographer, naturalist and hydrographer, most notable for his explorations in Australia and the southern Pacific Ocean, Pacific. He carried a few ...

. *

electoral method * Borda Rock in

Antarctica Antarctica () is Earth's southernmost and least-populated continent. Situated almost entirely south of the Antarctic Circle and surrounded by the Southern Ocean (also known as the Antarctic Ocean), it contains the geographic South Pole. ...

is named after Jean-Charles de Borda.

Publications

*
Rapport sur le choix d'une unité de mesure, lu à l'Academie des sciences le 19 mars 1791 / imprimé par ordre de l'Assemblée nationale.
' With

Marquis de Condorcet Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (; ; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French Philosophy, philosopher, Political economy, political economist, Politics, politician, and m ...

. File:Rapport-1.jpg, Cover page of a 1791 copy of "Rapport sur le choix d'une unité de mesure" by Borda and the

File:Rapport-2.jpg, Page one of a 1791 copy of "Rapport sur le choix d'une unité de mesure" by Borda and the

File:Rapport-3.jpg, Pages 2-3 File:Rapport-4.jpg, Pages 4-5 File:Rapport-5.jpg, Pages 6-7 File:Rapport-6.jpg, Pages 8-9 File:Rapport-8.jpg, Pages 10-11 File:Rapport-7.jpg, Final page of a 1791 copy of "Rapport sur le choix d'une unité de mesure" by Borda and the

Notes

References