435 HYDEO MECHANICS HISTORICAL INTRODUCTION.* THE word Hydromechanics is derived from the Greek v8po-/ji-r)xaviKa., meaning the mechanics of water and fluids in general. The science is divided into three branches : Hydrostatics, which deals with the equilibrium of fluids; Hydrodynamics, which deals with the mathe matical theory of the motion of fluids, neglecting the viscosity ; and Hydraulics, in which the motion of water in pipes and canals is considered, and hydrodynamical questions of practical application are investigated. The science of hydromechanics was cultivated with less success among the ancients than any other branch of mechanical philosophy. When the human mind had made considerable progress in the other departments of physical science, the doctrine of fluids had not begun to occupy the attention of philosophers ; and, if we except a few proposi tions on the pressure and equilibrium of water, hydro- ni3chanics must be regarded as a modern science, which owes its existence and improvement to these great men who adorned the 17th and 18th centuries. rchi- Those general principles of hydrostatics which are to odes, this day employed as the foundation of that part of the science were first given by Archimedes in his work lie/at TOJV 6xovfjisv(i)v, or De Us quce vehuntur in humido, about 250 B.C., and were afterwards applied to experiments by Marinus Ghetaldus in his Promotus Archimedes (1603). Archimedes maintained that each particle of a fluid mass, when in equili brium, is equally pressed in every direction ; and he in quired into the conditions according to which a solid body floating in a fluid should assume and preserve a position of equilibrium. We are also indebted to him for that in genious hydrostatic process by which the purity of the precious metals can be ascertained, and for the screw engine which goes by his name. ex- In the Greek school at Alexandria, which flourished drian under the auspices of the Ptolemies, the first attempts iool. were made at the construction of hydraulic machinery. About 120 B.C. the fountain of compression, the siphon, and the forcing pump were invented by Ctesibius and Hero ; and, though these machines operated by the pressure of the air, yet their inventors had no distinct notions of the preliminary branches of pneumatical science. The siphon is a simple instrument ; but the forcing pump is a com plicated and abstruse invention, which could scarcely have been expected in the infancy of hydraulics. It was pro bably suggested to Ctesibius by the Egyptian Wheel or Noria, which was common at that time, and which was a kind of chain pump, consisting of a number of earthen pots carried round by a wheel. In some of these machines the pots have a valve in the bottom which enables them to descend without much resistance, and diminishes greatly the load upon the wheel ; and, if we suppose that this valve was introduced so early as the time of Ctesibius, it is not difficult to perceive how such a machine might have led that philosopher to the invention of the forcing pump. Notwithstanding these inventions of the Alexandrian school, its attention does not seem to have been directed to the motion of fluids. The first attempt to investigate this 3 n- subject was made by Sextus Julius Frontinus, inspector of us - the public fountains at Rome in the reigns of Nerva and Trajan ; and we may justly suppose that his work, entitled De Aquceductibus Urbis Roma? Commentating, contains all the hydraulic knowledge of the ancients. After describing 1 This historical sketch of the subject is a revised abridgment of that written by David Buchanan, and prefixed to the article HYDRO DYNAMICS iu the 8th edition of this work. the nine 2 great Roman aqueducts, to which he himself added five more, and mentioning the dates of their erection, he considers the methods which were at that time employed for ascertaining the quantity of water discharged from ajutages, and the mode of distributing the waters of an aqueduct or a fountain. He justly remarks that the flow of water from an orifice depended not only on the magnitude of the orifice itself, but also on the height of the water in the reservoir ; and that a pipe employed to carry off a portion of water from an aqueduct should, as circumstances required, have a position more or less inclined to the original direction of the current. But as he was unacquainted with the true law of the velocities of running water as depending upon the depth of the orifice, we can scarcely be surprised at the want of precision which appears in his results. It has generally been supposed that the Romans were ignorant of the art of conducting and raising water by means of pipes ; but it can scarcely be doubted, from the statement of Pliny and other authors, not only that they were acquainted with the hydrostatical principle, but that they actually used leaden pipes for the purpose. Pliny asserts that water will always rise to the height of its source, and he also adds that, in order to raise water up to an eminence, leaden pipes must be employed. 3 Castelli and Torricelli, two of the disciples of Galileo, Castelli applied the discoveries of their master to the science of hydrodynamics. In 1C 28 Castelli published a small work, Delia Misura deW acque correnti, in which he gave a very satisfactory explanation of several phenomena in the motion of fluids in rivers and canals. But he committed a great paralogism iu supposing the velocity of the water propor tional to the depth of the orifice below the surface of the vessel. Torricelli, observing that in a jet where the water Torri- rushed through a small ajutage it rose to nearly the same celli. height with the reservoir from which it was supplied, imagined that it ought to move with the same velocity as if it had fallen through that height by the force of gravity. And hence he deduced this beautiful and important pro position, that the velocities of fluids are as the square root of the head, allowing for the resistance of the air and the friction of the orifice. This theorem was published in 1643, at the end of his treatise De Motu gravium Projectorum. It was afterwards confirmed by the ex periments of Raphael Magiotti on the quantities of water discharged from different ajutages under different pressures ; and, though it is true only in small orifices, it gave a new turn to the science of hydraulics. After the death of the celebrated Pascal, who discovered PascaL the pressure of the atmosphere, a treatise on the equilibrium of fluids (Sur FEquilibre des Liqueurs] was found among 2 These nine aqueducts delivered every day 14,000 quinaria, or about 50,000,000 cubic feet of water, or about 50 cubic feet for the daily consumption of each inhabitant, supposing the population of Rome to have been a million. From measurements of Frontinus at the close of the 1st century, the total length of channels of aqueducts was 285 Roman miles (Roman mile =161 8 English yards). The supply mea sured by Frontinus amounted to 13,470 quinaries, outside Rome 3164, inside 10,306. Measured at the head the supply was 24,413 quinaries, the difference being due to waste, and to some of the channels having fallen into decay. Parker says : "It has been coni- pated by a French engineer that the supply to Rome was 332,306,624 gallons daily. If we assume the population at a million, the rate was 332 gallons daily per person. In our day we consider 40 gallons suffi cient, and many think this excessive." Modern supply varies from 24 to 50 gallons per head per day. 3 Plin. xxxvi. See also Palladius, De Re Rustica, ix. , xi. ; Horace,
Ei>ist., i. 10, 20; Ovid, Met., iv. 122.
