vi PREFACE. interest, in which the variation of gravity becomes perceptible. In accordance with modern ideas of mathematical instruction, a free use is made of the symbols and operations of the Calculus, where the treatment requires it, although an alternative demonstration by elementary methods is occasionally submitted; because, as it has well been said, "it is easier to learn the Differential Calculus than to follow a demonstration which attempts to avoid its use." Particular attention has been given to the applications of the subject in Naval Architecture, and the Transactions of the Institution of Naval Architects have been ransacked for appropriate illustrations. The diagrams, which have been drawn by Mr. A. G. Hadcock, late Royal Artillery, are intended to represent accurately to scale the objects described. No attempt has been made to rival the beautiful shaded figures of the French treatises, for fear of obscuring essential principles. A type of uniform size has been employed throughout: although adding considerably to the bulk, it is hoped that this uniformity will prove acceptable to the eyes of the readers, and counterbalance the disadvantage of the extra size of the book. P. 170, line 9 from the bottom, read " ... fo' a/s, then fo' is the depth of P. 436, last line, and p. 437, line 7, read P sin (OQ/OL). HYDROSTATICS. CHAPTER I. THE FUNDAMENTAL PRINCIPLES. 1. Introduction. HYDROSTATICS is the Science of the Equilibrium of Fluids, and of the associated Mechanical Problems. The name is derived from the compound Greek word υδροστατική, meaning the Science (ἐπιστήμη) of the Statics of Water; thus Hydrostatics is the Science which treats of the Equilibrium of Water, the typical liquid, and thence generally of all Fluids. The Science of Hydrostatics is considered to originate with Archimedes (B.C. 250) in his work Пepì oxovμévwv, now lost, but preserved in the Latin version of Guillaume de Moerbek (1269), "De iis quæ vehuntur in humido"; and recently translated into French by Adrien Legrand, "Le traité des corps flottants d'Archimède," 1891. Archimedes discovered the method of determining the density and purity of metals by weighing them in water, and extended the same principles to the conditions of equilibrium of a ship or other floating body. 2 HISTORICAL INTRODUCTION. Ctesibius, of Alexandria, and his pupil Hero (B.C. 120), the author of a treatise on Pneumatics, are considered the inventors of the siphon and forcing pump; Vitruvius may be consulted for these and other machines known to the Romans; while the leading principles of the flow of water as required in practical hydraulics are given by Frontinus in his work de aquæductibus urbis Roma commentarius (A.D. 100). The writings of Pliny (lib. xxx. c. vi.) prove that the Romans were acquainted with the hydrostatical principle that water will rise in a pipe to the height of its source, and that lead pipes must then be employed, stone or brick conduits not being sufficiently watertight; but being ignorant of the method of casting iron pipes strong enough to stand a considerable pressure or head of water, their large aqueducts were carried on the level, while leaden pipes were used only for the distribution of the water, specimens of which pipes have recently been discovered at Bath. A long detailed edict of Augustus concerning the waterworks of Venafrum is given in Mommsen's Corpus Inscriptionum Latinarum, vol. 10, part i.; and allusions to the mode of water supply are found in Horace and Ovid "Purior in vicis aqua tendit rumpere plumbum, Quam quæ per pronum trepidat cum murmure rivum ?" "Cruor emicat alte, Non aliter quam cum vitiato fistula plumbo Scinditur." (Ovid, Metamorphoses, iv. 122.) A great advance in the Theory of Hydraulics was made by Torricelli (1643), also the inventor of the barometer, who first enunciated the true theory of the |