Archimedes' Principle

Archimedes' principle states that a body wholly or partly submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid the body displaces. Attributed to the Greek mathematician and engineer Archimedes of Syracuse in the third century BC, the principle appears in his surviving treatise On Floating Bodies, where he used it to determine whether a body of a given shape will float, sink, or float at a given depth by comparing its weight to the weight of fluid it displaces. Archimedes is traditionally said to have arrived at the insight while bathing, noticing the water level rise as he entered, and to have used the principle to test whether a votive crown made for King Hiero II of Syracuse was pure gold or had been adulterated with silver, by comparing its buoyancy to that of an equal weight of pure gold. The principle remains foundational to fluid statics, explaining flotation, the design of ships and submarines, and the operation of hydrometers.