Abstract

This article makes a case for Euler as the first discoverer of what has come to be known as d’Alembert’s paradox. Suppose a body is immersed in an unbounded fluid and moves with constant velocity relative to the fluid, which is otherwise undisturbed: d’Alembert’s paradox asserts that, contrary to experimental evidence, the fluid exerts no drag force on the body if the fluid is inviscid and incompressible. Euler demonstrates this, for a two-dimensional body or an axisymmetric body whose axis aligns with its motion, in his extensive 1745 commentary on New Principles of Gunnery, a book published in 1742 by Benjamin Robins. After a rigorous analysis, Euler recognizes that the absence of a drag force conflicts with experience for fluids like air and water, and he uses Robins’ experiments with musket balls to explain this anomaly as a consequence of greater fluid pressure fore of the body than aft of it, due to a corresponding fore–aft asymmetry in the density of the fluid. Essentially, he resolves the apparent paradox by removing the assumption of the fluid’s incompressibility.