- fully elaborates the concept of pressure and its applications;
- presents for the first time the general equations of hydrostatics;
- clarifies his idea of a gas thermometer; and
- presents for the first time the equations of equilibrium.

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.

a.s.

According to C. G. J. Jacobi, a treatise with this title was presented to the Berlin Academy on October 11, 1753.-
Originally published in
*Mémoires de l'académie des sciences de Berlin*11, 1757, pp. 217-273 -
*Opera Omnia*: Series 2, Volume 12, pp. 2 - 53

- Original publication: E225
- E225 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.

- 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 E225 include:
- Arnold DH., “The mecanique-physique of Poisson, Simeon, Denis - the evolution and isolation in France of his approach to physical theory (1800-1840) .10. some perspective on Poisson contributions to the emergence of mathematical physics.” Archive for History of Exact Sciences, 29 (4), pp. 287-307 (1984).
- Craik ADD., “The origins of water wave theory.” Annual Review of Fluid Mechanics, 36, pp. 1-28 (2004).
- Maltese G., “On the relativity of motion in Leonhard Euler's science.” Archive for History of Exact Sciences, 54 (4), pp. 319-348 (2000).