hence that branch of natural philosophy, Mechanics, has been carried almost to the acmè of perfection. It remains for us, in this division of our volumes, to give a very slight sketch of the leading subjects comprehended under each department of natural philosophy, and then point out the works in which they may severally be most successfully studied by persons of all ages.

Under the article Mechanics, has usually been included an illustration of matter and its properties, considered as the substratum of the science, as that which acts on our senses, either immediately, or by the perceptible effects which it produces upon other bodies: matter is divided into that which is capable of being seen, by reflecting the rays of light to our eyes; and that which, by its transparency, is always invisible; such is the atmospheric air, with which we, and all terrestrial bodies, are perpetually surrounded, and such are the chemical gases, hereafter to be described.

Hence we come to the properties of matter; as solidity, impenetrability, divisibility, mobility, and inertia, which belong to all bodies whatever. From these, we are led to the consideration of motion, and to the laws by which it is governed when accelerated, and when retarded; to shew that in these and other cases which occur, it is to be estimated by the spaces run over, and that the velocity of motion is measured by the space passed over in a given time. From this, we are led to consider the effect produced on the motions of bodies, by the action of one or more forces in the same, or different directions, and in what instances motion is carried on in straight lines, and in what in a curve.

The different kinds of attraction claim the attention of those who study mechanics as a science, though it is with the attraction of cohesion and gravitation that they are chiefly concerned, of which the latter is introductory to the knowledge of central forces, divided into (1.) the centrifugal, which is defined as the tendency that bodies revolving round a centre, have to fly off from it in a tangent to the curve they move in: and (2.) the centripetal force, or that which is continually

impelling to a centre, such is the attraction of gravitation, whether the centre be that of the earth, to which all terrestrial bodies, and the moon likewise, have a tendency; or that of the sun, to which the earth and other planets, with their satellites, tend, and would fall, if the action of the centrifugal force were suspended.

The principle of gravitation being established, without pretending to say what that principle is, the student is led to reflect upon the centre of gravity, which exists in bodies, and in which the whole weight of a body may be said to be collected, because, if that be supported, the whole body is supported; and upon the line of direction, or that path through which a body, left to itself, falls towards the centre of attraction, whether it be of the earth or the sun.

These preliminaries being understood and established, and which are amply illustrated in a hundred different elementary works, the student goes on to the consideration of the mechanical powers, viz. the lever, the wheel and axle, the pulley, the inclined plane, the wedge, and the screw; since to these simple machines, all others, however complicated, may be reduced: we shall here describe them as briefly as possible.

The Lever is only a straight bar of iron, wood, or other material, supported on, and moveable round a point called the fulcrum, or prop. In regard to this mechanical power, three things are to be considered, viz. the fulcrum by which it is supported; the weight to be raised, or resistance to be overcome; and the power by which this is effected.

The lever is distinguished into three kinds: 1. When, in the lever A B, the prop F, Plate I. fig. 1, is placed between the power P and the weight W. The lever is supposed capable of turning about on F, and there will be an equilibrium, or the two ends will balance one another, when the weight W, multiplied into the distance F B, is equal to the power P, multiplied in the distance AF. For two bodies will always balance one another, when their momenta, or

quantities of force are equal. Now the momentum of a body is always in proportion to its weight multiplied into its velocity.

Suppose A B, fig. 2, to be the lever, and turned into the situation CD, as the end A is farthest from the fulcrum F, it must have travelled over a greater space in coming to D, than B has in coming to C; but the velocities are as the spaces passed over in the same time, therefore the velocity of A must be greater than that of B: of course as much greater as the velocity of A is than that of B, of so much less weight must A be, to balance the larger weight B with a less velocity. If the lever be divided into twenty-eight parts, of which FA is twenty, and BF eight, then a weight of two pounds at A, will balance a weight of five pounds at B, because the weights and velocities taken on each side the fulcrum, and multiplied together, balance each other as 2 x 20 5 x 8.

If, instead of the weights W and P, the end B of the lever, fig. 1, be put under a stone, log of wood, &c. and a man pull or press down the point A, he can, with an exertion equal to two pounds, or two hundred weight, raise a weight of five pounds, or five hundred weight. By a lever of this kind, the advantage gained is in proportion as the part A F is longer than FB; if the proportion be as fifty or eighty to one, a man may move a block of stone fifty or eighty times heavier than he could by his main strength only. To this kind of lever may be reduced all kinds of crows, scissars, pincers, candle-snuffers, and other instruments of this sort, which are compounded of two levers of the first kind.

2. A lever is said to be of the second kind, when the weight W is between the fulcrum F, and the power P, as in fig. 3. In this case, the weight and power balance each other, or the lever is in equilibrium, when the power is in proportion to the weight, as the distance of the weight from the fulcrum is to the distance of the power from it, or when P:W::FA: Aa. To this sort of lever are referred doors turning on hinges, oars, and such kinds of knives as are

used by turners, patten-makers, &c. which are fixed at one end, thereby forming a fulcrum, while the other end is moved by the hand, or power; and the body to be cut, or the resistance to be overcome, is the weight. With respect to an oar; the blade acting against the water is the fulcrum, the boat to be moved is the weight, and the power is the hand acting at the other end of the oar. A pair of bellows consists of two levers of this kind. The fulcrum, or centre of motion, is where the ends of the boards are fixed near the pipe, the power is applied at the handles, and the resistance of the air acting against the middle of the boards, may be considered as the weight. The rudder of a vessel acts in

the same way as an oar.

The principle of this lever shews the reason why two men, carrying a burden on a long pole between them, bear shares of the load which are to one another in the inverse proportion of their distances from it; for, if the weight be removed to the centre of the lever x, then a person at F, and another at a, would bear equal weights; but, if the pole be nine feet long, and the burden of a hundred and eighty pounds, be put at the distance of four feet from one end, and five feet from the other, the man at the short end will bear a hundred pounds, and the other man only eighty pounds. The same principle is applicable to the case of two horses of unequal strength, which may be so yoked to the carriage, that each horse shall draw a weight exactly proportional to his strength; this is done by so dividing the beam, that the point of traction may be as much nearer to the stronger horse than to the weaker, as the strength of the former exceeds that of the latter.

3. A lever is of the third kind, when the power P, fig. 4, is between the weight W, and the fulcrum F. In this kind of lever, the power and weight balance each other, when the power is in proportion to the weight, as the distance of the weight from the prop is to the distance of the power from it; that is, when P:W::GF: g F.

To this sort of lever are generally referred the bones of a man's arm; for when he lifts a weight by the hand, the muscle that exerts its force to raise that weight, is fixed to the bone about one tenth part as far below the elbow as the hand is; and the elbow being the centre round which the lower part of the arm turns, the muscle must therefore exert a force ten times as great as the weight that is raised. This lever is never used where power is required to be gained; for in it the intensity of the power applied, must always exceed the intensity of the weight to be raised, or resistance to be overcome. The wheels of clocks and watches act upon the principle of a lever of the third kind.

In making experiments on the mechanic powers, we must take care that the instruments used are perfectly balanced among themselves, before the weights and powers are applied. Thus the bar used in making experiments on levers, should have the short arm so much thicker than the long one, as will be sufficient to balance it on the prop.

The balance, an instrument of extensive use in comparing the weights of bodies, is a lever of the first kind, whose arms are of equal length. The statera, or Roman steel-yard, is likewise a lever of the first kind, and is used for finding the weights of different bodies by a single weight, placed at different distances from the centre of motion D, fig. 5; for the shorter arm DG, exactly counterpoises the longer arm DX, which is divided into as many parts as it will contain, each equal to DG; the single weight P, suppose one pound, will serve for weighing any thing as heavy as itself, or as many times heavier as there are divisions in the arm DX; which divisions are divided into halves, quarters, &c. for the convenience of being accurate to those divisions of a pound.

The Wheel and Axle. In this mechanical power, the power is applied to the wheel, and the weight drawn up by a rope winding round an axle, of course the velocity of the power is to that of the weight as the circumference of the wheel is to the circumference of the axle, and the advantage