the hydraulic jump flow was derived 10 years later and first published by him in 1841 as part of a series of lecture notes for the École nationale des ponts et chaussées. His notes formed a comprehensive treatise in hydraulic engineering. They were re-edited several times and used at the École des Ponts et Chaussées and École Centrale des Arts et Manufactures, and available at the École Polytechnique et École des Mines de Paris. Altogether Bélanger's 1828, and 1841 contributions to modern open channel hydraulics were remarkable and influenced the works by Jacques Antoine Charles Bresse, Henry Darcy, Henry Émile Bazin, Adhémar Jean Claude Barré de Saint-Venant, and Joseph Valentin Boussinesq, as well as Philipp Forchheimer and Boris Bakhmeteff. Contribution to applied mechanics From 1851, as a full professor at the École Polytechnique, he developed a new university curriculum in mechanics (cours de Mécanique) in response to a re-structure of the engineering programme at École Polytechnique. Linking kinematics and dynamics, he argued that the mechanics is based upon three principles: inertia, action-reaction and constant ratio force to acceleration at any point. Among the innovations, he considered statics as a limited case of dynamics which was most innovative in France at the time. His basic ideas were first developed in his 1847 lecture notes, and they influenced many leading scholars in France and overseas. For example, Franz Reuleaux (1829–1905) respected highly text; Ernst Mach (1838–1916) listed Bélanger's 1847 treatise among a few basic references in Mechanics. An unusual aspect of Bélanger’s career was his most successful involvement in both professional engineering (1816–1838) and academic teaching (1838–1864), as well as his capabilities to develop fundamental new textbooks, widely respected in France and overseas (Chanson 2010). Published works session 1841-1842 References Further reading [The Bélanger backwater equation is equation (6.6) on Page 224] 1790 births 1874 deaths 19th-century French mathematicians Corps des ponts École des Ponts ParisTech alumni École Polytechnique alumni Academic staff of École Polytechnique People from Valenciennes