for the United States government by A. A. Humphreys and H. L. Abbot, by Robert Gordon's gaugings of the Irrawaddy, and by Allen J. C. Cunningham's experiments on the Ganges canal. The friction of water, investigated for slow speeds by Coulomb, was measured for higher speeds by William Froude (1810-1879), whose work is of great value in the theory of ship resistance (_Brit. Assoc. Report._, 1869), and stream line motion was studied by Professor Osborne Reynolds and by Professor H. S. Hele Shaw. (X.) HYDROSTATICS Hydrostatics is a science which grew originally out of a number of isolated practical problems; but it satisfies the requirement of perfect accuracy in its application to phenomena, the largest and smallest, of the behaviour of a fluid. At the same time, it delights the pure theorist by the simplicity of the logic with which the fundamental theorems may be established, and by the elegance of its mathematical operations, insomuch that hydrostatics may be considered as the Euclidean pure geometry of mechanical science. 1. _The Different States of a Substance or Matter._--All substance in nature falls into one of the two classes, solid and fluid; a solid substance, the land, for instance, as contrasted with a fluid, like water, being a substance which does not flow of itself. A _fluid_, as the name implies, is a substance which flows, or is capable of flowing; water and air are the two fluids distributed most universally over the surface of the earth. Fluids again are divided into two classes, termed a liquid and a gas, of which water and air are the chief examples. A _liquid_ is a fluid which is incompressible or practically so, i.e. it does not change in volume sensibly with change of pressure. A _gas_ is a compressible fluid, and the change in volume is considerable with moderate variation of pressure. Liquids, again, can be poured from one open vessel into another, and can be kept in an uncovered vessel, but a gas tends to diffuse itself indefinitely and must be preserved in a closed reservoir. The distinguishing characteristics of the three kinds of substance or states of matter, the solid, liquid and gas, are summarized thus in O. Lodge's _Mechanics_:-- A solid has both size and shape. A liquid has size but not shape. A gas has neither size nor shape.