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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
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.
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 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.
In Professor Dewar's lecture at the Royal Institution, June 1892, liquid air and oxygen were handed round in wine glasses, liquefaction in this case being produced by extreme cold, about 192° C.
All three states of matter of the same substance are simultaneously observable in a burning candle; the solid state in the unmelted wax of the candle, the liquid state in the melted wax around the wick, and the gaseous state in the flame.
Although the three states are quite distinct, the change from one to the other is not quite abrupt, but gradual, during which process the substance partakes of the qualities of both of the adjacent states, as for instance the asphalte pavement in hot weather; metals and glass become plastic near the melting point, and steam is saturated with water at the boiling point.
4. Plasticity and Viscosity.
All solid substances are found to be plastic more or less at all temperatures, as exemplified by the phenomena of punching, shearing, and the flow of metals, investigated experimentally by Tresca (vide fig. 8); but what distinguishes the plastic solid from the viscous fluid is that the plastic solid requires a certain magnitude of stress (shear) to make it flow while the viscous fluid requires a certain length of time for any shearing stress, however small, to permanently displace the parts to an appreciable extent. (K. Pearson, The Elastical Researches of Barré de Saint Venant, p. 253.)
According to Maxwell (Theory of Heat, p. 303), " When a continuous alteration of form is only produced by stresses exceeding a certain value, the substance is called a solid, however soft (plastic) it may be.
DEFINITION OF A FLUID.
"When the very smallest stress, if continued long enough, will cause a constantly increasing change of form, the body must be regarded as a viscous fluid, however hard it may be."
Mallet, in his Construction of Artillery, 1856, p. 122, and Maxwell (Theory of Heat, chap. XXI.) illustrate this difference between a soft solid and a hard liquid by a jelly and a block of pitch; also by the experiment of placing a candle and a stick of sealing wax on two supports; after a considerable time the sealing wax will be found bent, but the candle remains straight, at ordinary temperatures.
A quicksand behaves like a fluid, and, in opposition to the process of melting and founding metals, it requires to be artificially solidified in tunnelling operations; this is now affected either by a Freezing Process, in which pipes containing freezing mixtures are pushed into the quicksand, or else by the injection of powdered cement or lime-grouting, which solidifies in combination with the sand.
5. We are now prepared to give in a mathematical form
The Definition of a Fluid.
"A FLUID is a substance which yields continually to the slightest tangential stress in its interior; that is, it can be very easily divided along any plane (given plenty of time, if the fluid is viscous)."
Corollary. It follows that, when the fluid is at rest, the tangential stress in any plane in its interior must vanish, and the stress must be entirely normal to the plane-this is the mechanical axiom which is the foundation of the Mathematical Theory of Hydrostatics.