sents a lever of this kind, the fulcrum is the end fixed against the wall, or upon which another man stands: the weight is at the top part of the ladder, and the power is the strength of the man applied to raise it.

The wheels in a clock, and in watch-work, are levers of this kind, because the power that moves them acts near the centre of motion, by a pinion, and the resistance it has to overcome, acts against the teeth at the circumference.

Of the Inclined Plane.

384. The Inclined Plane, is merely a plane surface inclined to the horizon; but a mechanical power of great use in moving weights from one level to another; as for example, for rolling up casks, wheel-barrows, &c. It is formed by placing boards or earth in a sloping direction.

D

B

C

The force wherewith a body (C) descends upon an inclined plane, is to the force of its absolute gravity by which it would descend perpendicularly in free space, as the height (B D) of the plane is to its length (D A).

Thus, when a plane is inclined to the horizon one-third of its whole length, any body will be kept from rolling down that plane, by a power equal to a third part of the weight of the body: if D A be six feet and B D two feet; then if C be six pounds, a power of two pounds will support it: if the height of the plane be equal to half its length a power equal to half the weight of the body will support it: but a plane, perpendicularly situated, ought not to come under the denomination of this article, because the plane in such a direction contributes nothing to the support or hindrance of the falling body, which descends with its whole force of gravity, unless prevented by a power equal to its whole weight,

It is obvious from the foregoing illustrations, that the less the angle of elevation, or the gentler the ascent is, the greater will be the weight which a given power can draw up; for the steeper the inclined plane is, the less does it support of the weight; and the greater the tendency which the weight has to roll, consequently the more difficult for the power to support it; hence the advantage gained by this mechanical power, is as great as its length (A D) exceeds its, perpendicu lar height (BD).

To the inclined plane may be reduced all hatchets, chissels, and other edged tools, which are sloped on one side only.

Of the Wedge.

385. The wedge is merely two equally inclined planes united at their bases, and the advantage gained, by this mechanical power, is in proportion as the length of the two sides, A B, A C, of the wedge, is greater than the back B C, or as the length on one side AB, is greater than half the back B D.

Wedges are used in splitting wood, stones, &c. When wood does not cleave at any distance before the wedge, there will be an equilibrium between the power, driving the wedge downward and the resistance of the wood acting against the sides of the wedge, when the power is to the resistance as half the thickness of the wedge at the back is to the length of either of its sides; because the resistance then acts perpendicularly to the sides of the wedge. But when the resistance on each side acts parallel to the back, the power that balances the resistance on both sides, will be as the length of the whole back of the wedge is to double its perpendicular height. When the wood cleaves at any distance before the wedge (as it generally does), the power of impelling the wedge will not be to the resistance of the wood, as the length on the back of the wedge is to the length of both its sides, but as half the length of the back is to the length of either side of the cleft, estimated from the top or acting part of the wedge.

The wedge is a very great mechanical power, in splitting wood and rocks, which it would be impossible to effect by the lever, wheel and axle, or pulley: the force of the blow or stroke upon the wedge, shakes the cohering parts of the most compact body of stone, and makes them separate more easily.

Most of the instruments used in the common purposes of life are to be referred to the principle of the wedge.

Of the Screw.

386. The screw is an inclined plane used with a lever or winch to assist in turning it. It is a com

pound engine of great force, either in pressing bodies together, or in raising great weights. The screw may be conceived to be made by cutting a piece of paper in the form of an inclined plane, and then wrapping it round a cylinder; when the edge of the paper will form a spiral line round the cylinder, which will answer to the thread of the

screw.

The advantage gained by this oballyo ap mideme mechanical power is in proportion as the circumference of the circle made by the lever or winch F L, is greater than the interval or distance between the spirals or threads of the screw A. To estimate the force then, of this machine, let us suppose that I desire to screw down the press G upon B, every turn I make once round with both

handles, I shall drive the press only one spiral nearer to B ;. so that if there are twenty-two spirals, I must make twentytwo turns of the handles F L before I come to the bottom. In pressing down the screw I cut with a force as much superior to the resistance of the body I desire to press, as the circumference of the circle, which my hands describe in turning the machine, exceeds the distance between the two little spirals of the screw.

Thus, supposing the distance of the spirals to be half an inch, and the length of the winch thirty-six inches, the circle described by the handle of the winch, when the power acts, will be two hundred and twenty-eight inches nearly, or about four hundred and fifty-six half-inches; and consequently, four hundred and fifty-six times as great as the distance between the spirals: and therefore a power at the handle whose intensity is equal to no more than a single pound, will ba lance four hundred and fifty-six pounds, acting against the screw; and as much additional force as is equal to overcome the friction, will raise the four hundred and fifty-six pounds; and the velocity of the power will be to the velocity of the weight, as four hundred and fifty-six is to one. Hence it appears, that, the longer the winch is, and the nearer the spirals are to each other, so much the greater is the force of the screw.

Almost all kinds of presses, common cork-screws, &c. act upon the principle of this mechanical power. When the

screw acts in a wheel, it is called a perpetual screw.

Screws properly applied, are used to support large buildings whilst the foundations are mending or renewed.

Of the Wheel and Axle.

387. The wheel and axle consist of a wheel fixed to an axle, or cylinder, so as to turn round together: sometimes a cylinder with projecting spokes. And the power being applied at the

circumference of the wheel, the weight (w) to be raised is fastened to a rope which coils round the axle or cylinder. But this machine is made in a variety of forms: the wheel may be perpendicular (P) and the axle horizontal, as in the diagram before us; or the axle may be perpendicular and the wheel horizontal.

The circumferences of different circles bear the same proportion to each other, as their respective diameters; consequently the advantage gained, by this mechanical power, is in proportion as the circumference of the wheel is greater than that of the axis, or as the diameter of the wheel is greater than the diameter of the axis. Hence the velocity of the power will be to that of the weight, as the circumference of the wheel is to that of the axis: and that, the power and the weight being in equilibrio, the power must be to the weight in the inverse ratio of the circumference of the wheel to that of the axis.

Suppose a water wheel twelve feet diameter turn an axle of one foot, the power acting at the circumference of the large wheel, moves over twelve times the space which the circumference of the axle moves: hence twelve cut, may be raised with the power of one cut.

The wheel and axis may be considered as a kind of perpetual lever, of which the fulcrum is the centre of the axis, and the long and short arms the diameter of the wheel, and the diameter of the axis. From this it is evident, that the longer the wheel, and the smaller the axis, the stronger is the power of this machine: but the weight must rise slower in proportion.

A capstan is a cylinder of wood with holes in it, into which are put bars, or levers, to turn it round: these are like the

spokes of a wheel without a rim. All windlasses, cranes, mills, windmills, and watermills, are framed on the principle of this machine; and the power whatever it be is applied to the circumference of a large wheel, whose circumference moves in consequence, perhaps ten miles an hour, while its axle, one tenth of its diameter, moves but one mile an hour; consequently the strength of one man at the circumference, will be equal to that of ten men at the axle: and when the axle is turned by a winch fastened to it, it will be more powerful, in proportion to the largeness of the circle it describes, compared with the diameter of the axle.

Of the Pulley.

388. The pulley is a wheel turning on an axis, with a drawing rope passing over it: the wheel (x) is usually called a sheeve, and is so fixed in a box or block (a), as to be moveable round a pin passing through its centre.

Pullies are of two kinds; 1. Fixed, as the upper pulley on the right

a

hand side of the diagram; and 2. Moveable, as the lower ones, which rise and fall with the weight.

The fixed pulley is used only to change the direction of a power, as in raising a weight to any height, without moving from the place in which one is, as a stone to the top of a building: it also enables several men to apply their strength together to the weight by means of the rope.

The moveable pulley doubles the power, and a man (P) may raise twice as much by his physical strength; whence by increasing the number of such pullies, the force may be increased in any ratio whatever. The advantage gained by it, is as two to one; conquently, a power of 10lbs. exerted by the hand will balance a weight of 20lbs.

The reason of this is evident, for in raising the weight one inch, one foot, or one yard, both sides of the rope must be shortened as much; that is to say, the hand must move through two inches, feet, or yards, which shews that the space through which the power moves, must always be in proportion to the advantage gained. In general, the advantage gained by pullies is found by multiplying the number of pul