Person: De Borda, Jean Charles
Jean-Charles de Borda was a French soldier and mathematician who invented an important surveying instrument.
Mathematical Profile (Excerpt):
- The town, which was a famous spa with thermal springs, was on the Adour River, about 80 km north of the Pyrenees and the border with Spain.
- His parents were Jean-Antoine de Borda, Lord of Labattut, and Marie-Thérèse de la Croix.
- At the age of seven, Charles entered the Collège des Barnabites at Dax.
- The Barnabites were a religious order founded in the 16th century, taking their name from the ancient church of St Barnabas in Milan, and they were devoted to the study of the Letters of St Paul.
- Borda was sent there and studied classics, science, mathematics, and metaphysics, following a course which would lead to an career in the army.
- In 1748, when he was fifteen years old, Borda completed his studies at La Flèche.
- In 1753, at the age of twenty, Borda produced his first memoir on geometry and sent it to d'Alembert.
- While in this post Borda undertook research on ballistics and, on 29 May 1756, he submitted a memoir studying the theory of the projectiles to the Académie des Sciences in Paris.
- The Seven Years' War began in 1756 and the French defeated the Duke of Cumberland at the Battle of Hastenbeck in Hanover in July 1757.
- Borda was aide-de-camp of Marshal Maillebois during this battle.
- The course he entered should have lasted two years but Borda completed it in one year, then continued his career as a military engineer in the navy.
- He demonstrated that Newton's theory of fluid resistance was untenable and that the resistance is proportional to the square of the fluid velocity and to the sine of the angle of incidence.
- While describing his contributions to fluid mechanics we should also note the contributions he made to the study of waterwheels and pumps.
- Between 1765 and 1775 Borda made several crossings of the Atlantic.
- In 1771 he was sent on a scientific voyage on the frigate "La Flore" to undertake studies to improve methods of calculating the longitude and test certain marine chronometers.
- The American War of Independence began in 1776 and two years later France joined the conflict against Britain.
- It was for control of the seas that France and Britain fought during the American War of Independence, and Borda was heavily involved in the French naval actions.
- The French fleet was commanded by Charles-Hector, Count d'Estaing, with Borda as captain of the ship "La Seine" and in command of several of the ships.
- The fleet sailed in the Caribbean and off the American coast, won some notable victories, but Count d'Estaing was seriously wounded while unsuccessfully attacking Savannah in October 1779, and he returned to France with his squadron.
- Count de Grasse took over command of the French fleet and again won important victories but he lost the Battle of the Saints off Dominica in 1782.
- Borda captained "la Solitaire" and commanded six ships in this battle.
- He, and the leader of the fleet de Grasse, were both taken prisoner by the British.
- After a short period Borda was allowed to return to France but after this episode his health declined.
- Borda made good use of the differential calculus and of experimental methods to unify areas of physics.
- He also developed a series of trigonometric tables in conjunction with his surveying techniques.
- One of his instruments, the Borda repeating circle, was used during the time of the French Revolution to measure an arc of a meridian as part of a project to introduce the decimal system.
- This instrument was proposed by Borda around 1785 and it had developed from instruments designed for use on ships.
- The Borda repeating circle consisted of two small telescopes each fixed to rings which could rotate independenly against a scale.
- Of course the first scope was now an angle of 2θ from the angle determined by BBB so, decoupling the rings on which the scopes turned and moving it back to sight BBB one measured the angle 2θ.
- Repeating the process continued to double θ, so in theory the error could be made as small as one desired since the final answer was divided by the number of doublings to find θ.
- He described this instrument in Description and use of the repeating circle (1787) giving nautical applications.
- The accuracy of Borda's repeating circle allowed distances to be found by surveying using triangulation.
- When Borda was made Chairman of the Commission of Weights and Measures, which had as its members Condorcet, Lavoisier, Laplace and Legendre, he soon put his accurate surveying instrument to good use.
- It considered a proposal which had already been made to the French government to base the metre on the length of a pendulum which beat at the rate of one second.
- This proposal had found favour with Britain and the United States who considered it a truly international measure.
- Borda, however, reported on the 19 March 1791 that the Commission had decided on a different standard, namely that one metre should be one ten millionth of the distance from the North Pole to the equator.
- Borda argued that the day should be divided into 10 hours with an hour divided into 100 minutes each of 100 seconds.
- Under Borda's leadership the project to accurately measure the distance from the North Pole to the equator using the Borda repeating circle was carried out.
- The value they came up with was actually more accurate than the one achieved by the Delambre-Méchain survey of the arc of the meridian from Dunkerque to Barcelona.
- As Chairman of the Commission of Weights and Measures, Borda made other important proposals.
- Substitution weighing had its advent and found wider application during the French Revolution, when, under the direction of Jean-Charles de Borda, new standards for measures and weights, the metre scale and the kilogram, were introduced.
- There is another topic to which Borda made important contributions.
- Borda felt that Condorcet's proposal was fair but he suggested that it was not workable in practice as no winner might result.
- Borda proposed the system of ranking candidates by giving each points corresponding to their rank.
- This proposal, often used in elections today, has the deficiency that the candidate elected may not have been anyone's first choice.
- There was a vigorous argument between Borda and Condorcet as to which of the two voting systems was the best but of course since both systems had their strengths and weaknesses, such an argument was bound to be inconclusive.
- One of Borda's proposals which has not found favour was that a right angle should be divided into 100 degrees, each degree into 100 minutes and each minute into 100 seconds.
- Such a system required new trigonometrical tables to be constructed and Borda organised this.
- After his death in 1804 Delambre published Decimal trigonometrical tables which extended Borda's work.
- We should mention further achievements in Borda's career which we have not mentioned above.
- He was elected to the Académie de Bordeaux in 1767 and, two years later, to the Académie de Marine.
- In 1795 he was made a member of the Bureau des longitudes.
- Borda died shortly before the project to determine the length of the metre was completed.
- An International Commission was set up to try to make the metre an international measure, but Borda argued against this on the grounds that the measurements were based on the Earth and should therefore be equally acceptable to every nation on Earth.
Born 4 May 1733, Dax, France. Died 19 February 1799, Paris, France.
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Tags relevant for this person:
Astronomy, Geography, Physics, Statistics
Thank you to the contributors under CC BY-SA 4.0!
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive