English Title

On the impact of bullets exploded against a plate


Leonhard Euler

Enestrom Number


Fuss Index


Original Language


Content Summary

This paper is a description of the physics behind the ballistic pendulum, a device used to measure the muzzle velocity of a bullet or a cannon ball. Essentially, the user makes a heavy pendulum with a known weight, then fires the projectile into the pendulum and measures how much the pendulum is swinging. Then, the law of conservation of momentum supplies the necessary formula for finding the velocity of the projectile. Benjamin Robins had invented the ballistic pendulum in 1727, and described it in his 1742 book, New principles of gunnery. Euler's 1745 translation of Robins' book (with corresponding commentary) became Euler's Neue Grundsätze der Artillerie (E77). Apparently, Euler didn't think that Robins had covered the ballistic pendulum sufficiently well, hence the need, almost 30 years later, to write this article. (Based on notes by Ed Sandifer)

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Journal article

Published Date


Written Date


Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 15, pp. 414-436.

Opera Omnia Citation

Series 2, Volume 14, pp.448-467.

Record Created


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Mathematics Commons