# Claude Louis Marie Henri Navier

### Quick Info

Dijon, France

Paris, France

**Claude-Louis Navier**was a French mathematician best known for the Navier-Stokes equations describing the behaviour of a incompressible fluid.

### Biography

**Claude-Louis Navier**'s father was a lawyer who was a member of the National Assembly in Paris during the time of the French Revolution. However Navier's father died in 1793 when Navier was only eight years old. At this time the family were living in Paris but after Navier's father died, his mother returned to her home town of Chalon-sur-Saône and left Navier in Paris to be cared for by her uncle Emiland Gauthey.

Emiland Gauthey was a civil engineer who worked at the Corps des Ponts et Chaussées in Paris. He was considered the leading civil engineer in France and he certainly gave Navier an interest in engineering. Despite encouraging Navier to enter the École Polytechnique, Gauthey seems not to have been that successful in teaching Navier, who may just have been a late developer, for he only just scraped into to École Polytechnique in 1802. However, from almost bottom place on entry, Navier made such progress in his first year at the École Polytechnique that he was one of the top ten students at the end of the year and chosen for special field work in Boulogne in his second year.

During this first year at the École Polytechnique, Navier was taught analysis by Fourier who had a remarkable influence on the young man. Fourier became a life-long friend of Navier as well as his teacher, and he took an active interest in Navier's career from that time on. In 1804 Navier entered the École des Ponts et Chaussées and graduated as one of the top students in the school two years later. It was not long after Navier's graduation that his granduncle Emiland Gauthey died and Navier, who had left Paris to undertake field work, returned to Paris, at the request of the Corps des Ponts et Chaussées, to take on the task of editing Gauthey's works. Anderson writes in [3]:-

Over the next 13 years, Navier became recognised as a scholar of engineering science. He edited the works of his granduncle, which represented the traditional empirical approach to numerous applications in civil engineering. In that process, on the basis of his own research in theoretical mechanics, Navier added a somewhat analytical flavour to the works of Gauthey. That, in combination with textbooks that Navier wrote for practicing engineers, introduced the basic principles of engineering science to a field that previously had been almost completely empirical.Navier took charge of the applied mechanics courses at the École des Ponts et Chaussées in 1819, being named as professor there in 1830. He did not just carry on the traditional teaching in the school, but rather he changed the syllabus to put much more emphasis on physics and on mathematical analysis. In addition, he replaced Cauchy as professor at the École Polytechnique from 1831. His ideas for teaching were not shared by all, however, and soon after his appointment to the professorship at the École Polytechnique Navier became involved in a dispute with Poisson over the teaching of Fourier's theory of heat.

A specialist in road and bridge building, he was the first to develop a theory of suspension bridges which before then had been built to empirical principles. His major project to build a suspension bridge over the Seine was, however, to end in failure. The real reason that the project ran into difficulties was that the Municipal Council never supported it. Despite this it went ahead but, when the bridge was almost complete, a sewer ruptured at one end causing a movement of one of the bridge supports. The problem was not considered a major one by the Corps des Ponts et Chaussées who reported that repairs were straightforward, but the Municipal Council were looking for an excuse to stop the project and they had the bridge dismantled.

Navier is remembered today, not as the famous builder of bridges for which he was known in his own day, but rather for the Navier-Stokes equations of fluid dynamics. He worked on applied mathematics topics such as engineering, elasticity and fluid mechanics and, in addition, he made contributions to Fourier series and their application to physical problems. He gave the well known Navier-Stokes equations for an incompressible fluid in 1821 while in 1822 he gave equations for viscous fluids.

We should note, however, that Navier derived the Navier-Stokes equations despite not fully understanding the physics of the situation which he was modelling. He did not understand about shear stress in a fluid, but rather he based his work on modifying Euler's equations to take into account forces between the molecules in the fluid. Although his reasoning is unacceptable today, as Anderson writes in [3]:-

The irony is that although Navier had no conception of shear stress and did not set out to obtain equations that would describe motion involving friction, he nevertheless arrived at the proper form for such equations.Navier received many honours, perhaps the most important of which was election to the Académie des Sciences in Paris in 1824. He became Chevalier of the Legion of Honour in 1831.

Finally we should say a little of Navier's political position. Of course he lived through a period when there was great political movements throughout Europe and in France in particular. The two men who had the most influence on Navier's political thinking were Auguste Comte, the French philosopher known as the founder of sociology and of positivism, and Henri de Saint-Simon who started the Saint-Simonian movement which proposed a socialist ideology based on society taking advantage of science and technology.

Comte had been educated at the École Polytechnique, entering in 1814, where he had studied mathematics. Navier appointed him as one of his assistants at the École Polytechnique and this connection was to see Navier become an ardent supporter of the ideas of Comte and Saint-Simon. Navier believed in an industrialised world in which science and technology would solve most of the problems. He also took a stand against war and against the bloodletting of the French Revolution and the military aggression of Napoleon.

From 1830 Navier was employed as a consultant by the government to advise on how science and technology could be used to better the country. He advised on policies of road transport, the construction of both roads and railways. His many reports show both his remarkable abilities as an engineer coupled with his strong political views on building an industrialised society for the advantage of all.

### References (show)

- R M McKeon, Biography in
*Dictionary of Scientific Biography*(New York 1970-1990). See THIS LINK. - A B de Saint-Venant, C Navier,
*Résumé des leçons donnée à l'École des ponts et chaussées*(Paris, 1864). - J D Anderson,
*A History of Aerodynamics*(Cambridge, 1997). - E F Kranakis, Navier's theory of suspension bridges, From ancient omens to statistical mechanics,
*Acta Hist. Sci. Nat. Med.***39**(Copenhagen, 1987), 247-258. - J Langins, From Bélider to Navier through the École Polytechnique : the consolidation of the science of mathematical engineering in France (Spanish),
*Mathesis***8**(1) (1992), 13-29. - A Picon, Navier and the introduction of suspension bridges in France,
*Construction History***4**(1988), 21-34.

### Additional Resources (show)

Other websites about Claude-Louis Navier:

### Honours (show)

Honours awarded to Claude-Louis Navier

Written by J J O'Connor and E F Robertson

Last Update May 2000

Last Update May 2000