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, structure, space, models, and change. History On ...

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 caus ...

, and Navy officer.

Biography

Borda was born in the city of

Dax Dax or DAX may refer to: Business and organizations * DAX, stock market index of the top 40 German companies ** DAX 100, an expanded index of 100 stocks, superseded by the HDAX ** TecDAX, stock index of the top 30 German technology firms * Dax ...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 Military engineering is loosely defined as the art, science, and practice of designing and building military works and maintaining lines of military transport and military communications. Military engineers are also responsible for logistics b ...

. For that, he was elected to the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...

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

Caribbean The Caribbean (, ) ( es, El Caribe; french: la Caraïbe; ht, Karayib; nl, De Caraïben) is a region of the Americas that consists of the Caribbean Sea, its islands (some surrounded by the Caribbean Sea and some bordering both the Caribbean Se ...

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 a major war of the American Revolution. Widely considered as the war that secured the independence of t ...

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

French Navy The French Navy (french: Marine nationale, lit=National Navy), informally , is the maritime arm of the French Armed Forces and one of the five military service branches of France. It is among the largest and most powerful naval forces in t ...

. 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 Jacques-Noël Sané (18 February 1740, Brest – 22 August 1831, Paris) was a French naval engineer. He was the conceptor of standardised designs for ships of the line and frigates fielded by the French Navy in the 1780s, which served during the ...

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 system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Electoral systems are used in politics to elect governments, while non-political elections ma ...

that is referred to as the

Borda count The Borda count is a family of positional voting rules which gives each candidate, for each ballot, a number of points corresponding to the number of candidates ranked lower. In the original variant, the lowest-ranked candidate gets 0 points, the ...

. The

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

Napoleon Bonaparte Napoleon Bonaparte ; it, Napoleone Bonaparte, ; co, Napulione Buonaparte. (born Napoleone Buonaparte; 15 August 1769 – 5 May 1821), later known by his regnal name Napoleon I, was a French military commander and political leader who ...

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 The Borda count electoral system can be combined with an instant-runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method (also called Total Vote Runoff or TVR). Both methods are designed to satisfy the C ...

. 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 letter l ...

, 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 movement of a craft or vehicle from one place to another.Bowditch, 2003:799. The field of navigation includes four general categories: land navigation, ...

and

position fixing Geopositioning, also known as geotracking, geolocalization, geolocating, geolocation, or geoposition fixing, is the process of determining or estimating the geographic position of an object. Geopositioning yields a set of geographic coordinates ...

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 Radiohead ...

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'', basis of the

metric system The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...

to correspond to the

arc measurement of Delambre and Méchain 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 ...

. As an instrument maker, he improved the reflecting circle (invented by

Tobias Mayer Tobias Mayer (17 February 172320 February 1762) was a German astronomer famous for his studies of the Moon. He was born at Marbach, in Württemberg, and brought up at Esslingen in poor circumstances. A self-taught mathematician, he earned a l ...

) and the

repeating circle Developed from the reflecting circle, 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 ...

(invented by his assistant, Etienne Lenoir), the latter 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 de ...

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 ci ...

Delambre Jean Baptiste Joseph, chevalier Delambre (19 September 1749 – 19 August 1822) 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 th ...

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 A quarter is one-fourth, , 25% or 0.25. Quarter or quarters may refer to: Places * Quarter (urban subdivision), a section or area, usually of a town Placenames * Quarter, South Lanarkshire, a settlement in Scotland * Le Quartier, a settlement i ...

should be divided into 100

angular units In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two ...

, currently known as the ''

gradian In trigonometry, the gradian, also known as the gon (from grc, γωνία, gōnía, 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 degree ...

'', 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 Arc measurement, sometimes degree measurement (german: Gradmessung), 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 ...

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 time system used in France for a few years beginning in 1792 during the French Revolution, whic ...

) 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 In trigonometry, the gradian, also known as the gon (from grc, γωνία, gōnía, 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 degree ...

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 is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...

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, also known as Karta Pintingga (literally 'Island of the Dead' in the language of the Kaurna people), is Australia's third-largest island, after Tasmania and Melville Island. It lies in the state of South Australia, southwest ...

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 1754 – 16 September 1803) was a French explorer, cartographer, naturalist and hydrographer, most notable for his explorations in Australia and the southern Pacific. Biography Early career Born a comm ...

. *

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, it contains the geographic South Pole. Antarctica is the fifth-largest contine ...

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 philosopher and mathematician. His ideas, including support for a liberal economy, free and equal pu ...

. 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