The Principles of Archimedes*—It is well known that the mechanics of floating bodies, and the laws which govern their equilibrium, were established and enunciated by Archimedes, the Sicilian, in the third century before our era. The following propositions, demonstrated in the first book of his treatise on this subject, embody the fundamental principles of the hydrometer :—

(a) The surface of any fluid at rest is the surface of a sphere whose centre is the same as that of the earth.

(b) Of solids, those which, size for size, are of equal weight with a fluid will, if let down into the fluid, be immersed so that they do not project above the surface, but do not sink lower.