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 Hepi oxovμévæv, 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.

G.H.

Α

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HISTORICAL INTRODUCTION.
CAL

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 ?"
(Horace, Epist. I. x.)

"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

HISTORICAL INTRODUCTION.

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velocity and form of a jet of water, as deduced from the experiments of Galileo and himself with the ornamental waterworks of the gardens of the Duke of Tuscany; repeated later in 1684 by Mariotte in the gardens of Versailles.

In the writings of Stevinus of Bruges (c. 1600) we find many fundamental theorems of our science clearly enunciated and explained; but the modern exact Theory of Hydrostatics is generally held to originate with Pascal (1653), in his two treatises, Traité de l'équilibre des liqueurs and Traité de la pesanteur de la masse de l'air; in which the fundamental principles are first clearly enunciated and illustrated, and the true theory and use of the barometer of Torricelli is explained.

The elastic properties of a gas were investigated by Boyle and Mariotte, about 1660, and subsequently completed by Charles and Gay Lussac; and now the fundamental principles of the equilibrium of fluids being clearly enunciated and established, the analysis was carried on and completed by Newton, Cotes, Bernoulli, d'Alembert, and other mathematicians of the 18th century; while the applications of steam in the 19th century has been the cause of the creation of the subject of Thermodynamics, first placed on a sound basis by Joule's experiments, in which the relations are investigated between the heat expended and the work produced by means of the transformations of a fluid medium.

Hydrostatics is a subject which, growing originally out of a number of isolated practical problems, satisfies the requirements of perfect accuracy in its application to the largest and smallest phenomena of the behaviour of fluids; and at the same time delights the pure theorist

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THE DIFFERENT STATES OF MATTER.

by the simplicity of the logic with which the fundamental theorems may be established, and by the elegance of its mathematical operations; so that the subject may be considered as the Euclidean Pure Geometry of the Mechanical Sciences.

Montucla's Histoire des Mathématiques, t. iii., from which the preceding historical details are chiefly derived, may be consulted for a more elaborate account of the work of the pioneers in this subject of Hydrostatics and Hydraulics.

2. The Different States of Matter or Substance.

A FLUID, as the name implies, is a substance which flows, or is capable of flowing; water and air are the two fluids most universally distributed over the surface of the Earth.

All substances in Nature fall into the two classes of SOLIDS and FLUIDS; a Solid substance (the land for instance), as contrasted with a Fluid, being a substance which does not flow, of itself.

FLUIDS are again subdivided into two classes, LIQUIDS and GASES, of which water and air are the chief examples.

A LIQUID is a fluid which is incompressible, or nearly so; that is, it does not sensibly change in volume with variations of pressure.

A GAS is a fluid which is compressible, and changes in volume with change of pressure.

Liquids again can be poured from one vessel into another, and can be kept in open vessels; but gases tend to diffuse themselves, and must be preserved in closed vessels.

THE DIFFERENT STATES OF MATTER.

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The distinguishing characteristics of the three Kinds of Substances or States of Matter, the SOLID, LIQUID, and GAS, are summarized as follows in Lodge's Mechanics, p. 150:

A SOLID has both size and shape;
A LIQUID has size, but not shape;

A GAS has neither size nor shape.

3. The Changes of State of Matter.

By changes of temperature (and of pressure combined) a substance can be made to pass from one of these states to another; thus, by gradually increasing the temperature, a solid piece of ICE can be melted into the liquid state as WATER, and the water again can be evaporated into the gaseous state as STEAM.

Again, by raising the temperature sufficiently, a metal in the solid state can be melted and liquefied, and poured into a mould to assume any required form, which will be retained when the metal is cooled and solidified again; while the gaseous state of metals is discerned by the spectroscope in the atmosphere of the Sun.

Thus mercury is a metal which is liquid at ordinary temperatures, and remains liquid between about -40° C. and 357° C.; the melting or freezing point being - 40° C., and the vapourizing or boiling point being 357° C.

Conversely, a combination of increased pressure and of lowered temperature will if carried far enough reduce a gas to a liquid, and afterwards to the solid state.

This fact, originally the conjecture of natural philosophers, has of late years, with the improved apparatus of Cailletet and Pictet, been verified experimentally with air, oxygen, nitrogen, and even hydrogen, the last of the gases to succumb to liquefaction and solidification.