slightly concave. In a water-wheel, whether the water is the moving power, as where a stream acts to drive machinery, or the resistance, as in the case of the paddle-wheels of a steam-boat, the impulse on the flat faces of the vanes or float-boards is proportioned to the area. When a wheel with float-boards has its lower part merely dipping into a stream of water, to be driven by the momentum of the water as it floats along, it is called an undershot wheel. When the water reaches the wheel near the middle of its height, and turns it by falling on the float-boards of one side, as they sweep downwards in a curved trough fitting them, the weight of the water also is called into play; and this modification is called a breast-wheel. When the float-boards are shut in by flat sides, so as to form cavities or buckets round the wheel, into which the water is allowed to fall at the top of the wheel, and to act almost by its weight only, the modification is called the overshot wheel. To have a maximum of effect from wheels acted on by the moving force of water, they are generally made to turn with a velocity about one-third as great as that of the water; and wheels moved by the simple weight of water usually have their circumference turning with a velocity of about three feet per second. The subject of water-wheels is one of the most important in practical mechanics; seeing that, where water power is supplied ready to hand, it would be useless waste to employ steam power. Oars for boats are made flat, and often a little concave, that the water may be prevented from sliding off the oars, and the mutual action between them and water may be as great as possible. The webbed feet of water-fowls are oars in advancing they collapse like a shutting umbrella, but open outwards in the thrust backwards, so as to offer a broad concave surface to the water. The sails of ships, when they are receiving a fair wind, are seen to bulge or swell a little, and are supposed thereby to receive a stronger impulse. 370. The resistance between a meeting solid and fluid being nearly proportioned to the breadth and surface of the solid, it follows that large bodies, because containing much more matter, in proportion to their breadth and surface, than smaller bodies of similar form, are less resisted, in proportion to their weights, than smaller bodies. The science of measure tells us that a bullet, or other regular solid, of two inches diameter, has eight times as much matter in it as a similar solid of one inch diameter, while it has only four times Resistance of the Air. 221 the surface. If, therefore, a bullet of eight pounds, and a bullet of one pound, be shot off with equal velocity, the larger has only half as much surface in proportion to its weight, and therefore in proportion to its momentum, as the other. Consequently, it will go much further against the resistance of the air than the other. For this reason large spherical shot, smaller cannon-balls, musketbullets, pistol and swan-shot, and the common small-shot of the sportsman, all discharged with the same velocity, have always a shorter range as they are smaller in size. Even water is sometimes thrown from a gun or powerful syringe to stun birds, that they may be obtained with uninjured plumage; but as it soon divides very minutely in the air, it reaches only to a short distance. 371. Water, falling through the air from a great height, goes on suffering a gradual division into smaller and smaller portions, which at last may be said to be nearly all surface; and these are then seen sinking slowly as a mist. The different sizes of rain drops are explained partly by the height from which they have fallen, and partly by the amount of atmospheric disturbance during the fall. In calm weather, with the clouds near the surface of the earth, as during a thunderstorm, for example, the drops are very large and heavy compared with their size on a wet, windy day. The toy called the water-hammer is merely a small quantity of water hermetically inclosed in a tube which is exhausted or empty of air : when, by turning the tube, the water is made to fall from one end to the other, as there is no air to break up its cohesion, it falls as one mass, and makes a sharp noise like the blow of a hammer. 372. The largeness of the surface in proportion to the quantity of solid matter, explains why a spider's thread or a single filament of silk floats so long in the air before it falls; why there are almost constantly suspended in the air those very minute particles which appear as motes in the sunbeam; and there is reason to believe that the insidious transporters of infectious diseases are often invisible particles, wafted, it may be, great distances from their putrid source; why the fine dust, sent aloft during the eruption of volcanoes, is often carried by the wind to a distance of hundreds of miles; why, in the deserts of Africa, the strong winds often transport fine sand from place to place, overwhelming caravans, and forming new mountains, which succeeding blasts are again to lift; why, in the bottom of a river, or in a tide's way, fine mud is found only where the current is slow, sand where it is quicker, pebbles or large stones where it is quicker still, while in rapids and waterfalls only massive rocks can 222 Examples of the Power of Fluids in Motion. resist the fluid force. The explanation of the floating of clouds in the atmosphere, which is very much lighter than the watery particles forming the clouds, is not very apparent. It seems probable, however, that the support required to keep them afloat is in part due to aërial currents underneath, in somewhat the same way as the motion of a fan supports the toy known as the Japanese butterfly. 373. A like explanation may be given of the operation of levigating, by which heavy substances, insoluble in water—such as the emery used in polishing—are obtained in the state of the finest powder. Any such substance is first ground or powdered in the ordinary way, and then diffused in a vessel of water. The grosser parts first fall to the bottom, and if the water be then passed into another vessel, the deposit in that will be of smaller portions; in a third vessel, with longer time allowed for subsidence, the deposit will be of smaller particles still, and so on, if desired. The fine powder of flint used in the manufacture of porcelain is obtained by levigation, as is also that of putty powder, calamine, whiting (chalk), and other powders used in medicine and in the arts. The power of running water is seen in the rapid destruction of embankments, if the water be allowed to accumulate and run over the top. The particles of the earth or clay on the top, while dry, press on one another with all their weight, and form a tolerably resisting barrier; but if the water reach them, they half float, and are so easily carried along by the powerful friction of the passing water, that a small channel or gap is quickly rendered the outlet of a resistless torrent. Where rivers, like the Po in Lombardy, have in many places to be retained in their channels at a higher level than the surrounding fields by earthen banks, a small gap cut in the embankment might flood the whole of the low country. Some disastrous cases have occurred in the fen districts of England by failure of embankments or sluices. 374. Thus, by means of air or water, substances of different specific gravities in mixture may be easily separated. If pieces of cork and lead be let fall together through the air, the lead will reach the ground first, and may be swept away before the cork arrives. So the farmer, by winnowing in either a natural or artificial current of air, readily separates the grain from the chaff, and, if he desire it, may even divide the grain itself into portions of different quality. Similar to this is the operation of separating sand or mud from golddust by water. A current of water made to pass over the soil containing gold-dust, carries away the lighter rubbish, and leaves the Oblique Fluid Action. 223 gold. A lead ball with a string attached to it, an arrow loaded at the point, or a shuttle-cock with its cork and feathers, always moves with the heavier mass in front, because the resistance of the air has least influence on the greater momentum. "Oblique fluid action." 375. When a fluid and a solid meet obliquely, the resultant impulse is still perpendicular to the surface of the solid, as if they met directly, but is less forcible as the obliquity of the approach is greater. Suppose the double line, a b (fig. 95), to represent the edge of a smooth board placed in a current of fluid running with a certain speed in the direction of the lines with arrow points, fp and h; the pressure P Fig. 95 -f -9 on the board will be direct or at right angles to the board, and proportioned to the area of the surface. If then the board be placed obliquely to the current, in the position, a c, evidently the breadth of current acting on the board will be as much less than previously as the line, a d, is shorter than the line, a b (mathematically stated, the line, a d, is called the sine of the angle of obliquity-(See the Appendix). Then, further, the part of the current striking the board, and reduced to the breadth, a d, strikes it not directly but obliquely, and therefore only with force represented by the line, a e, instead of a d. (See Art. 130.) That line, e a, is again the sine of the angle of obliquity, with the line, a d, for radius. If the a e 376. From this it appears that the wind blowing upon the sail of a ship, however obliquely, as from e to d (fig. 96), always presses it directly, or perpendicularly to its surface, with a part of its force. wind approaching the sail, a b, be represented, as to direction and strength, by the line, e d, it will act on the sail as if it came from ƒ, but with a force smaller in the proportion of ƒ d to b e d. The effect, therefore, is the same as if the sail were pulled by a rope, d c. And all the sails being adjusted so as to receive the wind in the direction here shown, a little behind their back-surfaces, they Fig. 96. 224 all act to produce the same result as if pushes were made in the direction, fd, or as if ropes were pulling from each in the direction, dc, or parallel to it. Now the side force, cd, would urge the vessel sideways, as well as forwards, were it not that the form of vessels causes them to pass forward at least twenty times more easily in the direction of their sharp bow, than sideways across their broadside or keel. Thus a force urging equally sideways and forwards causes a ship to advance twenty miles in the direction of her keel for one mile which she deviates sideways. The deviation sideways, which in sailing-vessels must take place to a certain extent whenever the wind is at all oblique, is called the lee-way. A vessel having to sail from 6 to a, while the wind blows directly against her course, or from a to b, is obliged to sail close to the wind, as represented in last para›c_graph, first, it may be supposed, to e, as represented in fig. 97, with the left or larboard side to the wind, then to tack, as it is called, or turn round, at e, and to sail to d, with the right or starboard side to the wind; then to go on the larboard tack again to c, and thence to port at a. A ship tacking, as e here represented, makes an approach of one mile towards her port for about two which she sails through the water. Oblique Action of the Wind on a Ship's Sails. a b Fig. 97. In making way against a contrary wind, the sails of a ship have to be pointed so nearly edgeways to the wind, that, unless very flat, a portion of their surface becomes useless. The Chinese manner of rigging has, in this respect at least, some advantages, for in it bamboo reeds attached across the sails render these as flat as boards. A ship with several masts may sail faster when the wind is more or less from a side, than when directly astern, because in the former case all the sails are acting, although not to the best advantage individually, while, in the latter, the sails in front are becalmed by those behind them. With a side wind, a ship may move a little faster than the wind itself, as is often the case with the outer extremities of a windmill's vanes. 377. Oblique fluid action is well illustrated by the action of the rudder of a ship, which enables a single man to direct the course of a huge vessel before a stormy wind. The helm or rudder is a sort of door or gate hanging by strong hinges from the stern-post of the ship, and moved by a lever called the tiller. In small vessels the |