#### English Title

Research concerning the motion of rivers

#### Enestrom Number

332

#### Fuss Index

571

#### Original Language

French

#### Published as

Journal article

#### Published Date

1767

#### Written Date

1751

#### Content Summary

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. (Based on Clifford Truesdell's introduction to *Opera Omnia* Series II, Volume 12.)

#### Original Source Citation

Mémoires de l'académie des sciences de Berlin, Volume 16, pp. 101-118.

#### Opera Omnia Citation

Series 2, Volume 12, pp.272-288.

#### Record Created

2018-09-25