E110  Scientia Navalis, volume 1
(Naval Science, volume 1)
Originally published with the full title: Scientia navalis seu tractatus de construendis ac dirigendis navibus Pars prior complectens
theoriam universam de situ ac motu corporum aquae innatantium. Auctore Leonhardo Euler
prof. honorario academiae imper. scient. et directore acad. reg. scient. Borussicae. Instar
supplementi ad tom. I. novorum commentar. acad. scient. imper. Petropoli typis academiae
scientiarum MDCCXLIX.
Summary:
(based on C. Truesdell's An idiot's fugitive essays on science: methods, criticisms, training,
circumstances and his introduction to Opera Omnia Series II, Volume 12)
Together with E111, Euler
establishes his principles of hydrostatics, providing a basis for the scientific foundation
for the theory of naval architecture. Together, these are second among the great treatises on rational
mechanics by which Euler created the field as we now know it.
Among the topics mentioned in these two volumes are:
 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 threedimensional motion of a general rigid body in response to an applied torque;
 the theory of small oscillations of floating bodies;
 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.
In particular, this volume looks at 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; this definition is still commonly used today.
More specifically, Euler considers:
 the equilibrium of floating bodies;
 the restitution of floating bodies to equilibrium;
 the stability of floating bodies in equilibrium;
 the effects of external forces upon floating bodies;
 the resistance of water to moved plane figures;
 the resistance of water to moved bodies;
 the progressive motion of floating bodies.
a.s.
In addition to the dedication (to Graf Rasumowski), which is dated January 25, 1749, it contains 7 chapters
listed above.
Publication:

Originally published as a book in 1749

Opera Omnia: Series 2, Volume 18
 A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
Documents Available:
 Original Document: To reduce the size of each file, E110 is archived in several parts:
 E110 is discussed in Ed Sandifer's How Euler Did It February
2004 column published online by the MAA.
 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 E110 include:
 Fuller AT., “Maxwell, James, Clerk Cambridge manuscripts  extracts relating to control and stability .2..” International Journal of Control, 36 (4), pp. 547574 (1982).
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