# Prony, Gaspard-François-Clair-Marie Riche De

# PRONY, GASPARD-FRANçOIS-CLAIR-MARIE RICHE DE

(*b.* Chamelet, France, 22 July 1755; *d.* Asnièrcs, France. 29 July 1839)

*engineering.*

Prony’s father, a prominent lawyer, wished his son to follow him into a legal career and had him trained in the classics. But after convincing his father and after spending more than a year studying mathematics, in 1776 Prony entered the École des Ponts et Chaussées, from which he graduated in 1780. He won the admiration of its director Perronet, who in 1783 had Prony brought from the provinces to Paris to assist him. Prony’s defense of Perronet’s bridge at Neuilly led to his first memoir, on the thrust of arches (1783). and to friendship with Monge, who personally initiated him in advanced analysis and descriptive geometry. In this memoir using Phillipe de La Hire’s formula for the conditions of rupture of masonry arches, he argued that the Pont de Neuilly was structurally sound in spite of the thinness of its pillars and the breadth of its arches because it had sufficient strength to resist tipping caused by the flow of the river, bursting caused by the thrust of the arches, and crumbling caused by the jolting of heavily loaded wagons.

In 1790 Prony published the first volume of *Nouvelle architecture hydraulique*, which applies rational mechanics to engineering practice at an elementary level. It was a textbook for beginners, specifically for the students of the École des Ponts et Chaussées, of which he had just been appointed inspector of studies. He used Lagrangian analysis to prove theorems of statics, which he then represented graphically by use of descriptive geometry and for which he gave numerical methods of calculation that permitted the reader to solve problems without recourse to theory. In dynamics and hydrodynamics Prony, who used the calculus liberally, followed the same procedure. This textbook presented statics as the science of hydraulic machines, which Prony viewed as lifters of fluids. The second volume (1796) reverted to a nonanalytical and descriptive level in the vein of Bélidor’s *Architecture hydraulique* (1737–1739).

During the Revolutionary period, which he survived thanks to Lazare Carnot’s protection in 1793, Prony had an active career. In 1791 he was appointed director of the cadastral survey of France and in 1792 he supervised the drawing up of new logarithmic and trigonometric tables incorporating decimal divisions. Using the concept of the division of labor which he got from reading Adam Smith’s *An Inquiry Into the Nature and causes of the Wealth of Nations* (1776), he allocated the work of calculating the tables among several hundred men who knew only the elementary rules of arithmetic. In 1794 at the creation of the École Centrale des Travaux Publics (École Polytechnique) Prony became professor of analysis, a position that he held until 1815, when he resigned, reducing his commitment to that of *examinateur de sortie*. This position led him to write during this period several textbooks on analysis and mechanics, for instance “Cours d’analyse appliquée à la mécanique” (*Journal de l’ École Polytechnique*, 1st cahier, 1794, 92–119, and 2nd cahier, 1795, 1–23) and *Leçons de mécanique analytique données à l’Ecole … Polytechnique … seconde partie* (Paris, 1815). In the manual *Mecanique philosophique* (1799) he proposed to do for mechanics what Fourcroy had done for chemistry in *Philosophie chimique* (1792), namely to give a taxonomy of the theorems of mechanics. Although his textbooks on analytical mechanics drew largely on Lagrange’s *Mécanique analylique* (1788), they had a practical orientation and employed geometrical representations freely. In them, Prony reasoned on the manipulative level rather than on the conceptual one. Prony was named to the Institut de France on its founding in 1795. At the death of Antoine de Chezy in 1798, Prony succeeded him as the director of the École des Ponts et Chaussées and held this position until his death. He guided the school through great changes and modernized its curriculum for an industrial age. Drafting yielded to applied analytical mechanics; professional engineering scientists took the place of student teachers.

The Napoleonic period, during which Prony made several field trips to Italy to study river control and to draw up a project for the drainage of the Pontine Marshes, formed a highly productive part of his theoretical engineering career. To instruct engineers, he published treatises on earth thrust (*Recherches sur la poussée des terres*, 1802), on the measure of the how of liquids through orifices (*Le jaugeage des eaux courantes*, 1802), and on their flow in pipes and in canals (*Recherches physico-mathématiques sur la theorie des eaux courantes*, 1804). In his treatise on earth thrust, Prony simplified Coulomb’s analysis by assuming that the curve of maximum thrust is a straight line rather than some unknown curve that could only be found by using the calculus of variations. This simplification led him to conclude that the line of maximum thrust bisects the complement of the angle of repose. In his treatise on the gauging of water, Prony gave practical advice on how one should go about measuring water flow in such a way that the measurements are independent of hypotheses formulated concerning the laws of fluid flow. To measure, the engineer should use a pitot tube to find the speed of flow of the water through an orifice cut into a weir around which is built a system of channels to assure stagnant water behind the weir. To find all that is known about the flow of fluids through orifices, Prony referred the reader to Giovanni Battista Venturi, *Recherches expérimentales sur le principe de la communication laterale du mouvement dans les fluides, applique a l’explication de differens phenomenes hydrauliques* (Paris, 1797). In his study of flowing water Prony had a triple objective: build on solid principles of mechanics, respect experiment, and present results in a way that does not require difficult calculations on the part of the reader. He limited his study to cases where fluids flow along sufficient distances to assure constant speed and equality between the accelerating force of gravity and the resisting force of cohesion and friction. Drawing on memoirs by Charles Augustin Coulomb (1800) and Pierre-Simon Girard (1803 and 1804), Prony derived where *U* is the average speed, *R* the mean radius (cross-sectional area/wetted perimeter), *I* the slope, and *a, b, c* constants. He presented the results of his study in graphical and numerical form for the use of the field engineer.

In 1805 when Prony became *inspecteur général des ponts et Chaussées*, he obtained a seat on the général council of the Ponts et Chaussées, which gave technical and administrative direction to the Corps of the Ponts et Chaussées—no project could be undertaken without its prior approval. In this post, which he held for life, he greatly influenced the course of civil engineering in France and encourged the construction of numerous bridges.

Under the Bourbon and Orleans monarchs Prony continued an active engineering career, which became gradually one of a highly placed technical consultant rather than a field engineer. He did not abandon all engineering research, however. In 1821 he developed the Prony brake while conducting tests on steam engines. He discovered that the work delivered by a motor, to the shaft of which was applied a heavy frictional drag by means of a brake, was measured by the moment of the weight that kept the brake from rotating with the shaft. He showed that the equation for the work delivered is independent of the nature of friction and of the equation relating friction and force.

France’s various governments recognized Prony’ useful service to the state. Even though he refused to accompany Napoleon to Egypt, Napoleon made him a member of the Legion of Honor when he founded it. Charles X made him baron, and Louis Philippe raised him to the peerage. Prony was the true successor of Jean-Rodolphe Perronet, becoming France’s leading engineer and engineering educator during the period 1800–1840.

## BIBLIOGRAPHY

I. Original Works. A complete bibliography of Prony’s writings includes over 100 titles; fortunately the library of the École des Ponts et Chaussées possesses Prony’s library and many of his **MSS** ; the *Catalogue des livres composant la bibliothèque de l’ École des ponts et Chaussées* (Paris, 1872) and the *Catalogue des manuscrits de la bibliothèque de l’ École des ponts et Chaussées* (Paris, 1886) give the necessary references; this library has bound together most of Prony’s articles under the title *Ses opuscules, ou collection de toutes les brochures publiées par Riche de Prony*, 4 vols. Parisot’s notice on Prony (cited below) lists Prony’s major works. With A.-A. Parmentier, J.-P.-F. Guillot-Duhamel, J.-G. Garnier, *et al*., Prony edited *Mémoires des sociétés savantes et littéraires de la République*, 2 vols. (Paris, 1801–1802). L. B. Francoeur, *Traité élémentaire de mécanique* (Paris, 1801), consists of Prony’s notes. Prony briefly describes his method for measuring the work of a machine in “Note sur un moyen de mesurer l’ effect dynamiqye des machines de rotation,” in *Annales de chimie et de physique*, **19** (1822), 165–173, and more fully in “Rapport sur la nouvelle et l’ ancienne machines à vapeur établies, à Paris, au Gros-Caillou” in *Annales des mines*, **22** (1826), 3–100, plus 3 plates. At the Archives Nationales, Paris, the following references are of interest: F^{14} 2304^{2}, Prony’s dossier, briefly details his career; F^{17} 1084^{13} contains documents concerning the printing and distribution of Prony’s *Mécanique philosphique;*^{14} 1023 contains a report by Prony on the Pontine Marshes; ^{14} 1031^{2} contains correspondence with Prony on his mission in Italy; ^{14} 11055 has a few letters by Prony; ^{14} 11057 has *Sommaires des Leçons du cours de mécanique de M. De Prony* (1811) and a series of documents by Prony, Navier, and Coriolis concerning an 1830 reform of the École des Ponts et Chaussées and measurement of the effect of steam engines; F^{17} 1393 has documents concerning Prony and the cadastral survey of France. Some letters by Prony are at the Bibliothèque Nationale, Paris , n.a. fr. 2479, 2762, 2769, 15778, 22431. The archives of the École Polytechnique, Paris, carton 1829, has a report by Prony that remarks on Cauchy’s teaching. The Académie des Sciences, Paris, has **MSS** by Prony and a MS report by Monge on Prony’s memoir on arch thrust in the carton for 1783. This memoir, “Sur l’application de la mécanique des voûtes au Pont de Neuilly,” is at the library of the École es Ponmts et Chaussées, **MS** no. 2215.

II. Secondary Literature. Parisot, “Prony,” in Michaud’s *Biographie universelle* LXXVIII (Paris, 1846), 79–91, gives an excellent survey of Prony’s life. *Bulletin de la Société d’ encouragement pour l’industrie nationale*, **139** nos. 3 and 4 (Mar.-Apr. 1940), 66–98, commemorates Prony’s death, and **139/140** (July 1940-June 1941), p. 166, details Prony’s descendants. Other obituaries are J.-B. Tarbé de Vauxclairs, in *Moniteur universel*, no. 219 (7 Aug. 1839), 1605, and in *Annales des ponts et Chaussées …, mémoires et documents*, **18** (2nd sem., 1839), 394–400; C. Dupin, “Éloge de M.le Bon de Prony…,” in *Chambre des paris, Impressions diverses, session* 1840, no. 48 (Paris, 1840), sess of 2 Apr.; and F. Arago, “Discours funéraire de Prony,” in *Oeuvres complètes* …, III (Paris, 1855), 584–592. Archives Nationales, Paris, F^{14} 10906^{1} 11041 ^{180} is the collection of the registers of the deliberations of the Conseil général des Ponts et Chaussées. At the École des Ponts et Chaussess, Paris, office of the secretary, is “Registre des proces verbaux des séances du conseil de l’ École des ponts et Chaussées. …” See also A. Lorion, “Une mésaventure de Prony a Venise sous l’ Empire (juillet 1805), “ in *Revue de l’Institut Napoléon*, no. 93 (Oct. 1964), 164–168; and M.d’ Ocagne, *Hommes et choses de science*, 3rd sers. (Paris, 1936), 174–179. C.-A. Vieilh de Boisjoslin, *Biographie universelle et portative des contemporains*, **4** (Paris, 1830), 1024–1027; and M. Edgeworth, *Lettres intimes …* (Paris, 1896), letters dated 18 Nov. 1802, 1 Dec. 1802, and 3 May 1820, give details concerning Prony. J. V. Poncelet, “Examen critique et historique des principales théories ou solutions concernant l’equilibre des voûtes “ in *Comptes rendus hebdomadaires des seances de l’Académie des sciences*, **35** (1852), 494–502, gives the context of Prony’s work on arches. C. S. Gillmor, *coulomb and The Evolution of Physics and Engineering in Eighteenth-century France* (Princeton, 1971), 100–115, 189–190; and H. Rouse and S. Ince, *History of Hydraulics* (New York, 1963), 139–143, discuss Prony briefly.

See also Jacques Payen, “La pratique des machines a vapeur au temps de Carnot,” in *Actes du colloque “Sadi Carnot et l’ essor de la thermodynamique”* (Paris, in press), which discusses tests that Prony made on steam engines and during which he first used the Prony brake.

Robert M. McKeon

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