E332 -- Recherches sur le mouvement des rivieres

(Research concerning the flow of rivers)

(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 stream-lines," 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 stream-line 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.

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