A cubic foot of water weighs very nearly 1000 ounces avoirdupois, or 621⁄2 lbs. Hence the specific gravities of solids and liquids in the foregoing table have only to be multiplied by 1000 to give the weight in ounces of a cubic foot of the different substances.

Thus gold will contain 19,340 ounces in a cubic foot, being worth in money about £63,000 sterling; and a cubic foot of marble will weigh 2.84 × 1000 = 2840 ounces, or about 180 lbs. A cubic foot of ice, which has a specific gravity of o'92, will therefore weigh (0'92 x 1000) 920 ounces, which at once shows how much ice is lighter than its bulk or volume of water. A cubic foot of common air contains only about one ounce; while a cubic foot of hydrogen gas (the lightest substance known) contains less than a drachm.

Atmospheric air is thus about 4th part of the weight of water: and hydrogen only 12000th part.

SECTION II.-HYDRAULICS, OR THE PHENOMENA OF

LIQUIDS IN MOTION.

ANALYSIS OF THE SECTION.

The necessity of a plentiful water-supply to the animal and vegetable world renders the study of the laws of flowing liquids both interesting and useful. Water issuing from a vessel, or passing through pipes or channels, is regulated in its flow by the height of its source, and by the friction or resistance it meets on its way. The currents of rivers and the waves of the sea are thus brought under the laws of hydraulics. In naval architecture, the resistance of water to the motion of bodies immersed in it has to be carefully considered. On the other hand, the resistances that moving liquids are able to overcome lead to the employment of the fluid motions in nature as a source of workpower; as, for example, in water-wheels, water-engines, &c., as well as in raising water to a height for domestic purposes and for irrigation.

Hydraulics.

346. The special interest that, increasing with the advance of civilization, attaches to the distribution of water and the laws of flowing liquids which have to be observed for the purpose of such distribution, arises from the fact that, without a copious supply of pure water, life in large towns and cities would be insupportable, and the vast accumulations of human beings in the great capitals of modern times-Paris, New York, Berlin, Jeddo, and London-would become but so many plague-spots on the surface of our globe.

It was from the want of suitable material for the construction of pipes or conduits, and not from ignorance of the value of a plentiful water-supply, that the ancients were so little advanced in hydraulic engineering. Recourse was had to open canals, of which numerous traces remain on the banks of the Tigris and Euphrates, indicating the existence of a regular system of water distribution through the gigantic capitals of Assyria and Babylon.

In Phœnicia, in Judæa, in Egypt, there are numberless ruins of aqueducts, tanks, and wells; but the most magnificent examples of

208

Fluids issuing from Vessels.

artificial watercourses were the aqueducts of ancient Rome. About 300 B.C. the first aqueduct was completed, and by the later days of the empire there were as many as twenty, distributing to the Eternal City a daily supply exceeding sixfold the quantity allowed per head to the population of modern London. Their domestic consumption averaged probably much the same per head as that of our large cities-forty galions a day; but it is a most remarkable fact that the great bulk of the water was devoted to their public fountains, baths, gardens, and amphitheatres. Several of the Roman aqueducts exceeded forty miles in length, passing through hills in their way, and resting on tiers of splendid arches across the valleys. These were copied in other parts of the empire; and even in later times there are several examples-such as the Lisbon aqueduct (1713–32), the Croton aqueduct of New York, and others—of waterworks designed upon the principle of the ancient Romans.

In modern times, the applications of the arts have completely changed the conditions of the problem to be solved for the distribution of water, and have rendered a thorough acquaintance with the physical principles to be attended to in all such undertakings a matter of the greatest consequence.

"Fluids issuing from vessels, or moving in channels.”

347. It is an important, though apparently paradoxical fact, that the force required to drive a certain quantity of water through a

Fig. 92.

certain opening in a given time, must be increased fourfold instead of tvice, to drive double the quantity through the same or a like opening, in the same time. Thus, if, in a vessel of water, A (fig. 92), a small hole be pierced in the side at b, a foot below the surface of the water, the pressure of liquid there will cause a certain quantity, say a gallon, to spout forth. in one minute; but, in order that two gallons may issue in the same time from a similar opening below, that opening must be made not at two, but at four, feet below the water surface.

Again, if a quantity of water be squirted from a syringe, or forcepump, by a force of one pound pressing the handle of the piston, a

Fluids issuing from Vessels.

209

force of four pounds would be required to double the quantity of the discharge in the same time.

The reason of such facts is, that the double number of water particles moved would require double force if they were moved with only the same velocity; but because twice as many have to pass through the same sized opening in the same time, each must move with double speed, requiring another doubling of the force on that account, and the two doublings make a fourfold increase. So, in order to force a triple discharge, the power employed must be nine times as great; to force a quadruple issue it must be sixteen times as great; and so forth, in the proportion of squares.

B

348. Another phenomenon illustrates the same principle. If a tube be screwed into the lower part of a water cistern, B (fig. 93), and have its outer end turned up as a spouting nozzle, c, the water will jet upwards to the height of the water surface in the cistern, with a certain deduction for the resistance of the air and friction. Hence, by the law of falling bodies, the velocity of issue at e must be the same as that acquired by the liquid falling from the level of its surface. Thus, we may learn the velocity of the issue of water from the side or bottom of a reservoir in any case, and therefore, approximately, the quantity delivered through a pipe or opening of a given size.

Fig. 93.

349. It is a curious fact that more water issues from a vessel with thin sides through a short pipe, than through a simple aperture of the same diameter in the thin side-and still more if the pipe be funnel-shaped within, or a little wider towards its inner extremity. The explanation is, that the particles coming from all sides of the opening to escape, cross and impede one another in rushing through a simple opening, as proved by the narrow neck called the vena contracta, which the jet exhibits a little beyond the opening; but in a uniform tube, this narrowing of the jet could not happen without leaving a vacuum around the part, and the pressure of the atmosphere, preventing the formation of such vacuum, causes a quicker flow. The funnel-shape again leads the water by a more gradual inclination to the point of exit, and prevents the crossing among the particles which retards the flow; moreover, seeing that its external mouth surrounds the narrow neck of the jet, that part may be considered the commencement of the jet.