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.

(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 v2sin2a. 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.


The original appeared in 1742 in London under the title: New principles of gunnery.

Publication: Documents Available:

Return to the Euler Archive