Naval Science, volume 1
Eneström notes that this work was essentially completed by 1738, citing Euler's letter to Johann Bernoulli dated 20 December 1738.
Together with E111, Euler establishes his principles of hydrostatics, providing a basis for the scientific foundation for the theory of naval architecture. These volumes are among the great treatises on rational mechanics by which Euler created the field as we now know it. More specifically, these two volumes include: the idea of centroid and metacenter as distinct from center of gravity; a theory of stability based on the direction of the restoring torque in a small displacement; the earliest treatment of three-dimensional motion of a general rigid body in response to an applied torque; solutions of specific problems based on local use of Newton's law of resistance. Euler also shows that the principle, written in modern notation as F = – ∫p dS and p = rgh (where p is pressure, r is density, g is the force of gravity per unit mass, and F is the force), is both necessary and sufficient for the equlibrium of incompressible fluids near the Earth's surface. It is on this principle that he builds a "mansion of analysis" that includes all the elementary parts of hydrostatics as we know them today. In addition, Euler proves that one can obtain a complete solution to the problem of finding the restoring moment for a body in any position by first finding all the positions of equilibrium; once this is done, determine the direction of the turning moment that is acting on the body when it is infinitesimally displaced from each of these equilibrium positions. The first volume considers the general theory of the location and motion of bodies floating in water. In Chapter 3, Euler gives a general and precise definition of stability that applies to all systems that are in equilibrium, which is still commonly used today. More specifically, in this volume Euler considers: the equilibrium and stability of floating bodies; the restitution of floating bodies to equilibrium; the effects of external forces upon floating bodies; the resistance of water to moved bodies; the progressive motion of floating bodies. (Based on Clifford Truesdell's An idiot's fugitive essays on science: methods, criticisms, training, circumstances and his introduction to Opera Omnia Series II, Volume 12.)
Original Source Citation
St. Petersburg: Imperial Academy of Sciences, Volume 1, pp. 1-444.
Opera Omnia Citation
Series 2, Volume 18, pp.1-426.