E332  Recherches sur le mouvement des rivieres
(Research concerning the flow of rivers)
Summary:
(based on Clifford A. Truesdell's introduction to Opera Omnia Series II, Volume 12)
This work contains the discovery of the "Bernoulli equation for the streamlines," now called "Lagrange's equation." In fact, this is the earliest occurrence of the equation in its modern form. Euler derives it as a result of the new general equations of hydrodynamics, and he shows that it holds with values of the constant that in general differ from one streamline to another. Euler also argues that in large channels or rivers, the particles near the bottom are pushed by different forces than the forces that act on the particles near the top. He thus looks into the forces that act on individual particles of water, and he starts to explain this theory in the case that a vertical section is taken along the length of the river since it is the foundation of all other cases.
According to C. G. J. Jacobi, a treatise with
this title was presented to the Berlin Academy on May 6, 1751.
Publication:

Originally published in Mémoires de l'académie des sciences de Berlin 16, 1767, pp. 101118

Opera Omnia: Series 2, Volume 12, pp. 272  288
 According to Jacobi, the manuscript of the printed
treatise can be found in the archive of the Berlin Academy.
Documents Available:
 Original publication: E332
 E332 can be viewed or downloaded from Digitalisierte Akademieschriften und Schriften zur Geschichte der Königlich Preußischen Akademie der Wissenschaften, which includes serial publications of the Prussian Academy of Science in the 18th and 19th Centuries.
 Emma Sorrell and Erik Tou of Carthage College have completed an English translation of this paper.
 The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E332 include:
 Arnold DH., “The mecaniquephysique of Poisson, Simeon, Denis  the evolution and isolation in France of his approach to physical theory (18001840) .10. some perspective on Poisson contributions to the emergence of mathematical physics.” Archive for History of Exact Sciences, 29 (4), pp. 287307 (1984).
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