E77  Neue Grundsätze der Artillerie
(New Principles of Gunnery)
Originally published with the title: Neue Grundsätze der Artillerie enthaltend die Bestimmung der Gewalt des Pulvers nebst
einer Untersuchung über der Unterscheid (!) des Wiederstands der Luft in schnellen und
langsamen Bewegungen aus dem Englischen des Hrn. Benjamin Robins übersetzt und mit den
nöthigen Erläuterungen und vielen Anmerkungen versehen von Leonhard Euler Königlichem
Professor in Berlin. Berlin bey A. Haude Königl. und der Academie der Wissenschaften privil.
Buchhändler.
In English: The true principles of gunnery investigated and explained.
Comprehending translations of Professor Euler’s observations upon the new principles of
gunnery, published by the late Mr. Benjamin Robins, and that celebrated author’s Discourse upon
the track described by a body in a resisting medium, inserted in the memoirs of the Royal
academy of Berlin for the year 1753. To which are added, many necessary explanations and
remarks, together with Tables calculated for practice, the use of which is illustrated by proper
examples; with the method of solving that capital problem, which requires the elevation for the
greatest range with any given initial velocity.
Summary:
(based on Clifford A. Truesdell's introduction to Opera Omnia Series II, Volume 12)
This is a treatise on the ballistics annotations that Euler added to his translation of Robins' "little
budget of rules, experiments, and guesses," thus changing it into the first scientific work on gunnery.
But in this book, Euler also advances the theory of fluids. He investigates the physical nature of air and fire
and shows that the relationship between elasticity and density depends on the temperature. He also looks
at air resistance and the motion of bodies that are projected in the air. In addition, Euler clearly and
precisely states the problem of resistance, and he gives a "clear and explicit corpuscular derivation"
of the Newtonian law of resistance that is proportional to v^{2}sin^{2}a.
He also shows that the constant of proportionality is half as great for elastic molecules as it is for inelastic
molecules. Euler derives a law that connects resistance with the difference in speed between the fluid and
the body, expressing the resultant force as an integral over the profile of the body. It is in this work, too,
that for the first time, a fluid mass is divided into fillets, each of which can be treated as a tube,
representing the next great step in analytical fluid dynamics. Also, Euler uses intrinsic rather than fixed
coordinates. It is in this book also that Euler gives the first proof of the d'Alembert paradox.
a.s.
The original appeared in 1742 in London under the title: New principles of gunnery.
Publication:

Originally published as a book in 1745

Opera Omnia: Series 2, Volume 14, pp. 1  409
Documents Available:
 Archive.org has recently posted a version of E77 online. (This is a scan of Opera Omnia's 1922 reprinting and commentary.)
 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 E77 include:
 Ackroyd JAD., “The United Kingdom's contributions to the development of aeronautics part 1. from antiquity to the era of the Wrights.” Aeronautical Journal, 104 (1031), pp. 930 (Jan 2000).
 Johnson W., “Robins, Benjamin (18thcentury founder of scientific ballistics)some European dimensions and past and future perceptions.” International Journal of Impact Engineering, 12 (2), pp. 293323 (1992).
 Johnson W., “The origin of the ballistic pendulum  the claims of Cassini, Jacques (16771756) and Robins, Benjamin (17071751).” International Journal of Mechanical Sciences, 32 (4), pp. 345374 (1990).
 Steele, B "The Ballistics Revolution: Military and
Scientific Change from Robins to Napoleon" (Ph.D. dissertataion, University of Minnesota,
1994).
 Steele, B. "Muskets and Pendulums: Benjamin Robins, Leonhard Euler and the Ballistics Revolution." Technology and Culture 35 (2), pp. 348382
(Apr 1994).
 Steele, B. The Heirs of Archimedes: Science and the Art of War through the Age of Enlightenment (MIT Press, 2005).
 Steele, B. "Rational Mechanics as Enlightenment Engineering: Leonhard Euler and Interior Ballistics" in Gunpowder, Explosives, and the State: A
Technological History, B. Buchanan, ed. (Ashgate, 2006)
 Truesdell C., “The mechanical foundations of elasticity and fluid dynamics.” Journal of Rational Mechanics and Analysis, 1 (2), pp. 125291 (1952).
 Truesdell C., “The mechanical foundations of elasticity and fluid dynamics.” Journal of Rational Mechanics and Analysis, 2 (5), pp. 593616 (1953).
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