Galileo, Floating Bodies and the Balance

Abstract

A natural way of interpreting Archimedes’ account of floatation is by analogy with a balance. When a body is wholly or partially immersed in water it displaces water, which is raised as a result. Floating occurs when the tendency of the raised water to move downwards is balanced by the weight of the body. Galileo came to realize that if this comparison with the balance is to be retained the analogy must be with a balance with unequal rather than equal arms. If a balance with unequal arms is subject to a small displacement about its equilibrium position the resulting velocities of the bodies at the extremities of each arm are inversely proportional to their weight. Likewise, a slight vertical depression of a block of wood floating in a vessel will result in a displacement of water such that the velocity of the displaced wood or water is inversely proportional to its weight. This analysis yields Archimedes principle. However, it is confined to considerations of weight and of vertical displacements, as the approach of Archimedes had been, and was not well-equipped to deal with the isotropic hydrostatic forces noted by Stevin.