E225 -- Principes generaux de l'etat d'equilibre des fluides

(General principles concerning the state of the equilibrium of fluids)

(based on Clifford A. Truesdell's introduction to Opera Omnia Series II, Volume 12)
This work, the first of a series of three that constitute Euler's masterful treatise on fluid mechanics (the others being E226 and E227), contains a formulation of hydrostatics, a special case of Euler's theory of fluid motion. It represents a turning point in the history of physics and the continuum view of matter put foward as a basic principle, and it has sometimes been cited as the origin of the theory that the normality of pressure implies its equality in all directions. Euler proves that for dynamical principles, there is no essential difference between compressible and incompressible fluids. He also It is broken down into three parts.

In part 1 (General Principles), Euler develops the principles on which all of hydrostatics (or the science of the equilibrium of fluids) is founded. He considers fluids that have the same degree of density everywhere and also those fluids that are made up of particles of varying density. He shows that the property that most essentially distinguishes fluid bodies from solids is that "a fluid mass cannot be in equilibrium unless it is subject at all points of its surface to forces equal and perpendicular to the surface...[provided] that the interior particles...are not subject to any force." He also looks at the following problem: Suppose that the forces acting on all the elements of the fluid are given, in addition to the relation that at each point connects the density and the elasticity of the fluid. Find the pressures that must occur in all points of the fluid mass if it is to be in equilibrium.
In part 2 (On the equilibrium of fluids according to the hypothesis of natural gravity), he develops the theory of the barometer, saying that "neither the elasticity nor the density can vanish entirely at any altitude." Moreover, a wind must arise whenever the heat at equal heights is different since the pressures on each particle of air cannot be balanced by its weight.

Finally, in part 3 (On the equilibrium of fluids according to the hypothesis of gravity directed towards one or more centers), Euler proves that the force from a fixed center is a function of distance and that somtimes figures of equilibrium might approximate those of earth or another planet.


According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on October 11, 1753.

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