# Archimedes' principle

It was the ancient Greek, Archimedes of Syracuse, who first discovered the law of buoyancy, sometimes called Archimedes' principle:

*The buoyant force is equal to the weight of the displaced fluid*.

The story of Archimedes discovering buoyancy while sitting in his bathtub is described in Book 9 of *De architectura* by Vitruvius.

Typically, the weight of the displaced fluid is directly proportional to the volume of the displaced fluid (specifically if the surrounding fluid is of uniform density). Thus, among objects with equal masses, the one with greater volume has greater buoyancy.

Suppose a rock's weight is measured as 10 Newtons when suspended by a string in a vacuum. Suppose that when the rock is lowered by the string into water, it displaces water of weight 3 Newtons. The force it then exerts on the string from which it hangs will be 10 Newtons minus the 3 Newtons of buoyant force: 10 − 3 = 7 Newtons.