in fact the circumference of a wheel, often move 30 miles The diameter of this circle is sometimes 70 feet;

an hour.

the breadth of the sails from 5 to 6 feet.

In the lever, we have to consider three circumstances: 1. The fulcrum or prop supporting the lever, as an axis of motion; 2. The power employed to raise or support the weight; and 3. The resistance, or weight to be raised.

The power and the weight are supposed to act at right angles to the lever, unless otherwise expressed; and, according to the position of the fulcrum or prop, and the power, with respect to each other, we may have—

1st. The prop between the power and the weight, as in the use of a crowbar; 2dly. The weight may be situate between the prop and the power, as in the rudder of a ship or an oar of a boat; 3dly. The prop may be at one end, and the weight at the other, the power being applied between them; as when a man raises a ladder, or the beautiful mechanism in a watch or a clock, where the power acts near the centre of motion by a pinion, and the resistance to be overcome lies at the circumference, upon the teeth.

In the wheel and axle we have an example of a perpetual lever, as in a capstan. Indeed all windlasses, cranes, mills, windmills, and water-mills are framed on the principle of this machine.

Pulleys are either fixed or moveable; by the former we merely change the direction of a power, as when a man pulls up a stone to the top of a building, in which case, though the man does not move from his place, all his power is concentrated in the stone as it goes up. In the moveable pulley, we double the power, and see, in a stone lifted by this means, the strength of one man on the ground equivalent to that of two men applied in lifting the stone to the top of a building. A pair of blocks with a rope we call a tackle.

Every one knows that he ascends a gentle slope easier than when there is much of acclivity. Inclined planes, as embankments of earth, should always be made a little below the angle of repose, or less than an angle of thirty-five degrees. In haw-haws of very stiff clay, the slope may be

forty-five degrees. If the force of traction on a level road be one-twentieth, and the slope of a road one in ten feet, an additional force of one-tenth the load is requisite to draw the carriage up, besides what is required to overcome the friction. Hence the requisite force of traction is += on the slope. In other words, if 1 horse would do the work on the level, 3 would be requisite to go over the hill. On the gradients or slopes of railways, with a friction of only th the load, and the incline 1 in 30, nine times the force required on the level is requisite to overcome the ascent. In great slopes, two engines are used; and in very steep ascents, stationary engines are employed to raise the train.

The screw is nothing more than an inclined plane rolled about a cylinder. If the distance of the centres of two threads of the screw be of an inch, and the radius of the lever by which it is turned round be 24 inches, the circumference of the screw will be nearly 150-8 inches; therefore, if we apply a power of 150 lb. to this lever, the force of the screw will be expressed by this proportion; : 150.8 × 150: 1 : 90,480 lb. = 4011 tons. We see the great power of the screw exemplified in stamping, in the smith's vice, coiningmachinery, and in many domestic agents, as presses. The common corkscrew is merely a screw without a spindle or body. In the combination where the cork is drawn by a second screw or toothed rod and a wheel or pinion, we have an instrument that dispenses with the human power of the deltoid muscle, which the common screw requires in drawing a cork.

The wedge is a great mechanical power, used in splitting wood and rocks, which are rent asunder by the force of a blow that separates the compact body; and, when the vertical angle of the wedge is small, it retains every new position between the resisting forces into which it is driven, and every yielding or separation of the mass is rendered permanent. All nails are wedges made with the greatest economy of their material.

Steam. This power is applied in many ways: to give motion to machinery of all sorts; to move ponderous engines

and trains on railways; to navigate ships; to discharge water from mines, &c. Wonderful are the revolutions this new power has created in mining, manufactures, locomotive intercourse by land, and connecting by short spaces of time the ends of the earth one with another. Some years ago the steam-engine was applied to plough land. The medium pressure of the atmosphere and of steam at the boiling heat of water is about equal to a column of 30 inches of quicksilver, or to 34 feet of water, or to 15 lb. on the square inch of surface pressed. But, allowing for friction, &c., the effective pressure may be taken at 12 lb. on the square inch; the working pressure about 10 lb., but usually assumed at from 7 to 9.42 lb.; and this force, multiplied by the number of feet the piston moves in each minute, is the momentum or lifting power each minute. The piston works twice the length of the cylinder at each stroke, and at a maximum in a 9-feet stroke, 14 each minute, travels 252 feet, or with a 6-feet stroke, at 21 each minute, it travels 210 feet. And the lifting power per minute, divided by the power of one horse, determines the number of horses equal to the engine's duty. Steam-engines are divided into different classes, as the atmospheric, high-pressure, and condensing, of which our limits do not admit even short descriptions. Suffice it to say, the horse's power is reckoned as a motive force of 33,000 lb. (i. e. 528 cubic feet of water) raised to a height of one foot in a minute.

In complicated machinery, friction isor of the force, unless diminished by mechanical means.

As a source of labouring power, water is one of the most beneficent gifts of the Creator, acting by its own weight only, by its momentum only, by both these combined, or by its pressure. In the former we see its power applied to wheels; in the latter, by its action on a piston. If we have a stream of water 5 feet wide and 2 feet deep, flowing at the rate of 4 miles an hour, and can make it fall a height of 10 feet, its labouring force is 220,000 lb. a minute, or 13,200,000 lb. an hour. Here is a great force, easily formed in many places of this fair island. Rivers flow with velocities in pro

portion to the elevation of their sources and volumes of water; but their velocity is retarded by constant obstructions and impediments, though not influenced by friction like water in pipes. The Ganges has only a fall of 4 inches in a mile; the Nile 6 inches in 1000 miles; the bed of the Thames is actually lower at London than below Gravesend, nevertheless its waters all run into the German Ocean. In rivers water ordinarily runs 3 miles an hour; their ordinary declivity is about 4 inches a mile: and this explains why the Rhone, drawing its waters from an elevation of 1000 feet above the level of the Mediterranean, does not pour them out with the velocity of water issuing from the bottom of a reservoir 1000 feet deep, or at the rate of 170 miles an hour. Many methods may be resorted to in order to make the mechanical power of water of great utility, whether it runs only one way, or is subject to the action of tides. Lowell, near Boston, is the seat of very flourishing manufactories, wrought by the water power of a canal, which falls 30 feet in 2500 yards. It is 60 feet wide and 8 feet deep, and affords 1250 cubic feet of water per second, which drives wheels of 30 feet diameter. The mud of great rivers, where they unite with the sea, forms in time deltas, and these little islands in time unite with the mainland and form plains. Thus streams do more in one century than the united labour of millions of men could effect in many ages.

144

CHAP. VII.

HYDROSTATICS AND HYDRAULICS.

THE concluding paragraph of the last chapter briefly introduces the subjects to be noticed in this.

SECTION I.

HYDROSTATICS.

HYDROSTATICS treats of the equilibrium of fluids, or the principles of the equal distribution of fluid pressure. Hydraulics treats of fluids in motion. Taken conjointly, their theory is denominated Hydrodynamics — a branch of physical science and practical mechanics of the utmost utility.

The general principle of hydrostatics is, that, when a fluid mass, in a state of equilibrium, is subjected to the action of any forces, every particle of the fluid is pressed in all directions; and conversely, when every particle of a fluid is pressed equally in all directions, the whole mass is in a state of equilibrium.

The surface of every fluid at rest, or in a state of equilibrium, is parallel to the horizon, or at right angles to the direction of gravity. The subject of levelling on a grand scale depends on this proposition; for it is evident that two or more places are on a level when they are equally distant from the centre of the earth, and a line which is equally distant from the centre of the earth in all its parts is called the line of true level; therefore, because the earth is a sphere, that line must be an arc of the circumference.