E-411 is a description of the physics behind the ballistic pendulum, a device 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. Euler's translation of Robins' book became Euler's Artillerie, E77, published in 1745, but Euler apparently didn't think that he had covered the ballistic pendulum sufficiently well, hence the need, almost 30 years later, to write E-411.
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