a circular ring is in the centre of the circle; of an ellip- | tie or oval ring, in the centre of the ellipse; and of a hollow cylindric tube, it is in the imaginary axis of the tube. In a drum, for instance, the centre of gravity is a point in the centre of the drum, where there is nothing but air. When a circular object is placed on level ground, or a horizontal plane, it remains at rest on a point of its surface, because the line of direction from its centre, which is its centre of gravity, falls perpendicularly downwards to the point on which it is in contact with the earth and at rest; and because it could not possibly get its centre of gravity nearer the earth by changing its position. When a similar circular object is placed on an inclined plane, it will not remain at rest, but roll over, because the line of direction from its centre of gravity falls perpendicularly downwards in front of the point on its surface which touches the plane. On this account it rolls over, as if it were seeking a spot on which it might have the line of direction from its centre of gravity passing through its point of contact with the earth. Hence a circular body continues rolling down an inclined plane till it find a level spot on which the line of direction passes through its point of rest. In a bar of iron, six feet long, and of equal breadth and thickness, the centre of gravity is just three feet from each end, or exactly in the middle. If the bar be supported at this point, it will balance itself, because there are equal weights on both ends. This point, therefore, is the centre of gravity. If a bar of iron be loaded at one end with a ball of a certain weight, then the centre of gravity will not be at the middle, but situated near the heavy end of the bar. But if we attach a ball of the same weight to both ends, the centre of gravity is again in the middle of the bar. A remarkable illustration of the principles now detailed, is exhibited in the case of the earth and moon. The earth revolves round the sun, in consequence of a cause already explained, namely, the sun's attraction; but instead of the centre of the earth describing the oval or elliptic orbit round the sun, it is the centre of gravity of the earth and moon that describes it. We shall briefly explain the reason for this. The earth, in its course, is encumbered with the moon, a body of about the seventieth of its mass; in other words, the moon is like a small ball stuck at one end of a bar, having the earth or a larger ball at the other end-the bar between being the mutual attraction of the earth and moon. On this account, the centre of gravity of the earth and moon is at a point somewhere between the centres of the earth and moon. This point lies not far below the earth's surface. Therefore, if the earth were to fall towards the sun, it would be this point which would proceed most directly towards it. In suspending an irregularly shaped body from different points successively, we may learn where the centre of gravity of the body is placed, by observing that the line of direction in each case passes through the same point, which point is the centre of gravity. For example, let a painter's palette, which is an irreguJarly shaped body, be suspended from the thumbhole, as in the annexed cut, fig. 5, and the line of direction will necessarily be from A to B. Next suspend it from a point at D, and a new line of direction will Fig. 5. be obtained, crossing the line A B. The place where the two lines intersect, is thus the centre of gravity. The point of suspension, on being removed to C, will give the same place of intersection in the original line of direction; and a similar result will follow any other change of the suspension point. In the various natural structures displayed in the animal and vegetable kingdoms, the centre of gravity is always so situated, as to produce a just equilibrium and a harmony of parts. Every animal is properly balanced on its limbs, and every tree has a tendency to grow in a direction perpendicular to its base, whether it grow from a level or an inclined plane. Some animals are enabled to move in opposition to the law of gravity, as, for instance, flies creeping on the ceiling of an apartment; but in such cases, other powers in nature are exerted to preserve the secure footing of the animals. THE PENDULUM. A Gravity, which causes bodies to fall, also causes them to swing backwards and forwards, when suspended freely by a string or rod from a point, and when once moved to a side, to give them an occasion of falling. A body suspended in this manner is called a Pendulum. Pendulums usually consist of a rod or wire of metal, at the lower end of which a heavy piece or ball of brass or other metal is attached. When a pendulum swings, it is said to oscillate or vibrate; and the path which its ball pursues in swinging, from its resemblance in figure to an inverted arch or bow, is called its arc. In the accompanying cut, fig. 6, a pendulum of the most common construction is represented. A is the axis or point of suspension. B is the rod. C is the ball, or a round, flattish piece of metal, which is fastened to the rod by a screw behind, and by which screw it can be raised or lowered on the rod. D D is the Fig. 6. path or are which the ball traverses in swinging. When the pendulum is at rest, it hangs perpendicularly, as here represented, and the place which the ball is seen to occupy is called the point of rest. The pendulum remains at rest till its ball is drawn aside to allow it an opportunity of swinging on its axis. Being raised to any height on one side, and set at liberty, the ball, by the force of gravity, has a tendency to fall to the ground; but being confined by the suspending rod, it is compelled to make a sweep to that point where it was formerly hanging at rest, immedi ately beneath the point of suspension. But it does not stop here; it has acquired a velocity sufficient to carry it onward in an ascending course to nearly as high a point on the opposite side as that from which it was let fall. Of its own accord, it again falls downwards in the same arc, and rises to near the point where it set off; and thus, of itself, continues to swing to and fro, or vibrate, for a certain length of time, till its force is expended, and it finally comes to a state of rest in its original dependent situation under the point of suspen sion. small At every sweep of the pendulum (when not meddled with, or assisted by any external force), the length of the path or are traversed by the ball is in degree diminished. This arises from two causes-the obstruction offered by the atmosphere, and the friction on its axis or point of suspension. These causes, therefore, sooner or later, bring the pendulum to a state of rest, unless external force of some kind continues to be applied to urge it to sustain its action. The ball of a pendulum in swinging, as has been mentioned, describes the figure of an arc. This are is a certain portion of a circle. The extent of this portion depends on the force exerted in setting the pendulum in motion, or in drawing it aside to let it fall. A circle being divided by mathematicians into 360 degrees or parts, the ball may be made to swing over five, ten, twenty, or any other number of degrees under 180, which is half a circle. The extent of the are traversed under ordinary circumstances, is from ten to twenty degrees. A pendulum with a long rod vibrates slower than one with a short rod. The time does not become longer, however, in exact proportion as we extend the rod. The vibration, it must always be recollected, is the malleable metals are gold, silver, copper, zinc at | trial objects, but they have all necessarily failed, as no the temperature of boiling water, lead, iron, and some human effort can destroy gravity in bodies, or altogether others. Some of the metals possess the opposite quality prevent friction in movement. of brittleness. Gold is the most malleable of all metals, and it may be hammered so thin as to be translucent, or permeable to light. By ductility is understood that property by which metals may be drawn to wire. The most malleable metals are not the most ductile. Tin and lead may be rolled into thin leaves, but cannot be drawn into wire. The most ductile metal is platina, which can be drawn into wire as fine as the threads of a cobweb. Tenacity is the quality by which bodies are not easily torn asunder. Steel is the most tenacious of all substances; a wire of this metal, the hundredth of an inch in diameter, will support a weight of 134 lbs.; while one of the same size of platina will sustain only 16 lbs., and one of lead only 2 lbs. MOTION AND FORCES GENERAL EXPLANATIONS. Motion is the changing of place, or the opposite of rest. Matter, according to the definitions which have been given of its properties, is substance devoid of life and volition, and which is perfectly passive, or inert. It has been described as possessing the property of inertia, and in this respect it is said to possess an unwillingness or reluctance to move; but these phrases are only figurative, and are used for the purpose of conveying a forcible idea of the passiveness of its character. It is also, in consequence of this property of inertia, or passiveness to submit to any condition to which it is subjected, that a body, when once in motion, will continue to move continually with the same velocity and in the same direction, till it be disturbed by some external cause. In regard to bodies on the earth, of which a state of rest is the ordinary condition, motion is produced by certain agencies, or impelling causes, either belonging to the phenomena of nature or to art. The property of capillary attraction causes a motion in liquids under certain circumstances; the winds blow, and cause motion; rivers, in flowing down their channels, and the action of the tides, likewise produce motion; thus, there exist many natural causes of motion, which are taken advantage of by man in the economy of arts and manufactures. Motion in the animal economy is produced by a principle of life; but of the nature of this kind of motion mankind are ignorant, and nothing here requires to be said regarding it. The causes of motion which have to engage our attention are those which consist of forces, whether natural or artificial, and which forces have the property of impelling inanimate objects from a state of rest to a state of motion, of stopping them when in motion, or of altering the character of their motion. These forces are also called powers. Motion, according to the mode in which the force acts, is susceptible of innumerable variations. According as the moving body is affected, it may move rapidly or slowly; proceed in a straight line, turn in a circle or curve; it may move with uniform or irregular speed, or be retarded or accelerated. The body may also move upon or in respect of another body which is also moving. Some of these peculiarities in motion will immediately engage our attention; meanwhile, it has to be explained, that, for the sake of convenience in language, and accuracy in the application of terms, certain words are used to define the nature of motion in bodies, and the forces affecting them. Any instance of rest which comes under our observation, is only rest in a relative, not an absolute, sense; Motion is said to be common to two or more bodies that is, it is rest as relates to the earth, but not rest as when they move in contact or together; or when, relates to the universe; for though the stone which though not in contact, they are carried along in a simifalls to the ground lies at rest on the earth, the earth lar manner, and with the same velocity; that is, when is always in motion, and therefore the stone is no more they have a motion in common, or participate in the at rest than the insect which sits upon a moving wheel same motion. Motion is said to be absolute, when a is at rest. Hence, in speaking of bodies coming appa-body actually moves from one point of space to another, rently to a state of rest, we must always recollect, that or when it moves towards, or when it passes, another it is only relative, not positive or absolute rest. It is which is at rest. Therefore, setting aside the idea of supposed that there is no such thing as absolute rest in the earth moving, we should say that a vessel moving creation. All the planets are in motion round the sun; on the sea has an absolute motion, while the land is and the sun itself has a motion on its own axis; it is fixed or stationary. Motion is said to be relative, when also believed by many astronomers that the sun has an the motion of one moving body is considered in referonward or progressive motion in space, besides its rota-ence to that of another moving body. Thus, if two tory movement; and thus, perhaps, revolves round some distant centre, with all its planets in its train. Common experience would lead to the conviction that rest is more natural for matter than motion; but this conviction is founded on a limited consideration of circumstances. The reason why we see ordinary moving bodies coming to a state of rest-such as a wheel stopping after having been whirled on its axle, a ball stopping after rolling on the ground, or an object falling to the earth after being thrown upwards-is, that they are sooner or later arrested in their progress by the earth's attraction or their own gravity, by the friction or rubbing against some other body, or by the opposition presented to them by the atmosphere. Except for these three prevailing causes of impediment and stoppage, all bodies once set in motion would go on moving for ever. Taking this expanded view of things, and dismissing the erroneous impressions arising from what is obvious only to our limited experience, we find that there is nothing more remarkable in perpetual motion than in perpetual rest. It is only, however, in the great works of creation, or the heavenly bodies, that perpetual motion is observable. The planetary bodies are under the ever. acting impulses of centrifugal and centripetal forces, and are not impeded by friction, or by the atmosphere, for they move in space, or in a comparative vacuum. Many ingenious attempts have been made to produce bodies move in the same direction, their relative motion is the difference of their motions; if they move in opposite directions, it is the sum of their separate motions, When a force, applied to any material object, is resisted or counteracted, so that no motion ensues, it is called a pressure; and forces so counteracted are said to balance each other, or to be in equilibrium. The degree of speed in the motion of bodies is called velocity. Velocity is measured by the space or distance passed over, with an invariable motion, and in a given time, as one second. Thus, if a body, in one second, with an invariable motion, pass over twenty feet, its velocity is said to be twenty feet per second. When a motion is invariable, it is said to be uniform ; if it be gradually increasing, it is said to be accelerated; and if it gradually decrease, it is said to be retarded. A force is said to be an accelerating or retarding force, according as it produces an accelerated or retarded motion. The Forces are either instantaneous or continued. former is an impulse, like a stroke; the latter acts without intermission. When a continued force remains always of the same intensity, it is called a constant force. Other continued forces are said to be variable. A body, in moving, possesses a force which is called its momentum, or motal force. Momentum is very different from velocity. A light body and a heavy body may move at the same velocity, but the momentum of the heavy one. The light one, on coming to a state of the other, by its momentum, will strike forcibly on the top, his velocity becomes so much increased, before he tum is proportionate to the mass and velocity of bodies, and, by multiplying the weight by the number of feet ing body is increased, or accelerated, in regular arit produced by ordinary forces, it will be appropriate to when the supports which upheld them are withdrawn. THE PHENOMENA OF FALLING BODIES-WEIGHT. in nature, by which particles and masses of matter are inch for the sake of even numbers, we find that the the first second, and the result is the amount of fes tion, to arrive at a correct result as to the height faller opposition from the atmosphere in their descent. It's o of coin, for instance a guinea, and a onsequence of the different size and density of rect so much e endangere As a body in descending to the earth receives in that creasing accessions to its velocity during every successive second, so when a body is projected upwards from the surface of the earth, its velocity decreases in the same proportion, till it comes to a state of momentary y increasing rest, when it instantly begins to descend with a gradually increasing velocity, which at any point in the descent is equal to its velocity at the same point when ascending. In this calculation, however, we omit the influence of the atmosphere, which would cause the final velocity in the descent to be less than the original Tren te velocity with which the body was projected upwards. ense or co cha stare timme. Lege .cmbers THE CENTRE OF GRAVITY. Terrestrial gravitation, as already explained, does not act on the mere surface of bodies, or according to their bulk, but is exerted in reference to all the particles or atoms individually which compose the mass of a body. As the earth is nearly of a spherical form, its attraction is the same nearly as if it proceeded entirely from the centre. On account of the great size of the earth, compared with that of any ordinary body at its surface, its attractive force acts in straight lines, sensibly parallel, proceding from the earth's centre. In the case of liquids, in which the atoms slightly cohere, the atoms have liberty to spread themselves over the earth, and to seek the lowest situation for repose. In the case of solids, a different operation is observable. In them, the particles of matter stick so closely together, that they are not at liberty to obey the law of gravitation individually, but rally, as it were, round a common centre, upon which the force of attraction may be considered to act for the general behoof. This centre is called the centre of gravity, the centre of inertia, or the centre of parallel forces. Every solid body or dense mass possesses a centre of gravity, which is the point upon or about which the body balances itself, and remains in a state of rest, or selecty k equilibrium, in any position. The centre of gravity may be described as a point in solids which always seeks its lowest level, in the same manner that the lowest level is sought for by water; for it is only by propping up the body, that the centre of gravity is prevented from displaying the same mode of action. The centre of gravity in round, square, or other regular shaped bodies, of uniform density in all their parts, is the centre of these bodies. When a body is shaped irregularly, or when there are two or more bodies connected, the centre of gravity is the point about which they will balance each arises from i Ving differet ut od of leat ik Lining an con however, f botes the sum other. edifices, spires, and obelisks, as well as in the lading of coaches, carts, and other vehicles, and the piling of timber or any kind of goods in heaps. In every instance, the base ought to be sufficiently broad to admit of the line of direction from the centre of gravity falling within it. A small degree of experience seems to point out the propriety of erecting all kinds of structures with a base wide enough to secure stability; nevertheless, in opposition both to experience and the simple principles of science, we often find that stage-coaches are laden in such a manner that their centre of gravity is liable to too great a change of position, and that they are overturned, to the personal injury, and even loss of life, of the passengers. The error in these instances consists in raising the centre of gravity too high. At first, perhaps, the centre of gravity is so comparatively low, that, in the case of swaying to a side, the line of direction would fall within the edge of the wheel, and no danger would ensue ; but it is common to go on piling masses of goods or luggage, or placing a number of passengers, on the roof of the vehicle, so that the centre of gravity becomes considerably elevated; so high, indeed, that when the carriage is swayed, or jolts to one side, the line of direction is thrown beyond the wheel, and the vehicle will consequently fall over. In the annexed cut, fig. 4, a loaded vehicle is represented crossing an inclined plane, or we may suppose that its wheel on one side has come Fig. 4. in contact with a stone S, which has raised it above the level of the other wheel, so as to incline the body of the vehicle very considerably from the horizontal. The centre of gravity is represented in two different positions, a lower with the line of direction L C, and a higher with the line of direction U C. Had the vehicle not been high laden, the line of direction would have remained as L C, and as it falls within the wheel or base, the vehicle would have maintained its balance; but being now laden to a considerable height, the line has risen to about the place where it is marked descending from C to U, beyond the base; consequently the vehicle must overturn. There are instances in which bodies will not be overturned, although the line of direction falls considerably beyond the base. These exceptions to a common rule are observable in the case of rapidly and smoothly moving bodies, in which centrifugal force acts as a counterpoise to the weight of the body. A familiar example of this kind occurs in the case of skaters, in making their circular turns on the ice, in which they bend or lean greatly beyond the perpendicular position without falling. A notice of this peculiarity in moving bodies will engage our attention, under the head Centrifugal Force. The tendency which leaning bodies have to fall, may also be counteracted in some measure by the cohesion of parts. Thus, there are many instances of walls, steeples, and towers, inclining sensibly from the vertical line, and yet, by the strength of the cement which binds them, they have stood for ages. Whatever raises the centre of gravity, or narrows the base, allows the line of direction to pass more easily without it, and diminishes the stability. Hence the imprudence of rising up in carriages or boats, when in danger of being upset; and hence, as we have just mentioned, the danger of high-loading of vehicles. L an improvement has been effected in stage-coach bu ing, by which a chief part of the load is placed as as the axle of the wheels; and by this means the da of overturning is almost entirely averted. The centre of gravity of a body is not always in substance of the body. Thus, the centre of gravity of the heavy one. The light one, on coming to a state of rest, will perhaps fall harmlessly on the ground, while the other, by its momentum, will strike forcibly on the earth, or destroy any object which opposes it. Momentum is proportionate to the mass and velocity of bodies, and, by multiplying the weight by the number of feet moved over per second, we find that the momentum is the product. Thus, if a body of twelve ounces move with a velocity of twenty feet per second, its momentum is (twelve times twenty) two hundred and forty. In ordinary language, the term impetus is used to signify the violent tendency of a moving body to any point. Before entering upon a consideration of motion as produced by ordinary forces, it will be appropriate to describe the effects produced upon bodies when simply falling-that is, moving downwards towards the earth, when the supports which upheld them are withdrawn. THE PHENOMENA OF FALLING BODIES-WEIGHT. Attraction, as already explained, is a force inherent in nature, by which particles and masses of matter are drawn towards each other. This force, it has also been stated, increases in proportion to the quantity of matter which the attracting body contains, and it also increases as the bodies approach each other. Further, it has been mentioned that this powerful and subtile quality in matter is the cause of the falling or drawing of bodies downwards towards the earth, and thus produces what is termed weight or gravity. Gravity, then, is simply the tendency which any substance has to press down wards in obedience to the law of attraction, as exemplified in the phenomena of bodies falling from heights to the ground, when the supports which upheld them are removed. All falling bodies tend directly towards the centre of the earth, in a straight line from the point where they are let fall. If, then, a body be let fall in any part of the world, the line of its direction will be perpendicular to the earth's centre. Consequently, two bodies falling on opposite sides of the earth, fall towards each other. Suppose any body to be disengaged from a height opposite to us, on the other side of the earth, its motion in respect to us would be upward, while the downward motion from where we stand, would be upward in respect to those who stand opposite to us, on the other side of the earth. In like manner, if the falling body be a quarter, instead of half the distance round the earth from us, its line of direction would be directly across or sidewise, that is, at right angles with the lines already supposed. It will be obvious, therefore, that what we call up and down are merely relative terms, and that what is down in respect to us, is up in respect to those who live on the opposite side of the globe. Consequently, down every where means towards the centre of the earth, and up signifies from the centre of the earth. The velocity or rapidity of every falling body is uniformly accelerated, or increased, in its approach towards the earth, from whatever height it falls, if the resistance of the atmosphere be not reckoned. If a rock be rolled from the summit of a steep mountain, its motion is at first slow and gentle, but as it proceeds downwards, it moves with perpetually increased velocity, seeming to gather fresh speed every moment, until its force is suel that every obstacle is overcome; trees and rocks are dashed from its path, and its motion does not cease until it has rolled to a great distance on the plain. The same principle of increased velocity in bodies as they descend from a height, is illustrated by pouring treacle, honey, or any thick syrup, from an elevated vessel. The bulky stream, which is perhaps two inches in diameter where it leaves the vessel, is reduced to the size of a straw or thread on reaching its destination; but what it wants in bulk is made up in velocity, for the small thread-like stream at the bottom will fill a vessel just as soon as the large and slow moving stream at the outlet; the velocity is indeed so great, that the stream has not time to sink at once into the mass below, bat falls in overlaying folds. From the same principle, a person may leap from a chair without danger; but if he jump from the housetop, his velocity becomes so much increased, before he reaches the ground, as to endanger his life by the fall. It is found by experiment, that the motion of a falling body is increased, or accelerated, in regular arithmetical progression. In other words, in every second of time during its descent, it acquires an additional rate of speed, the rate regularly increasing by the accumulation of the preceding additions. It is ascertained that a dense or compact body, when falling freely, passes through a space of 16 feet 1 inch during the first second of time. Leaving out the odd inch for the sake of even numbers, we find that the space fallen through in a given time is determined by the following arithmetical computation. Ascertain the number of seconds which a body occu pies in falling. Take the square of that number (that is, the number multiplied by itself), and multiply the square by 16, which is the number of feet faller during the first second, and the result is the amount of feet which the body altogether falls. For example, if a ball occupy 3 seconds in falling, we take the square of 3, which is 9; then we multiply 9 by 16, which gives 144 as the result, and that is the number of feet fallen. Again, if we find that the bail occupies 4 seconds in falling, we take the square of 4, which is 16, and multiply ing 16 by 16, the result is 256, which is the number of feet fallen. And so on, always following the same rule of computation. It is not always easy, by the above mode of calculation, to arrive at a correct result as to the height fallen by bodies, and all that can be expected is an approxi mation to a true result. This arises from bodies being of different bulks, and receiving different degrees of opposition from the atmosphere in their descent. It is a common supposition that large and heavy bodies fall more quickly than small and light ones. This opinion, which was maintained even by philosophers, until Galileo rectified the mistake, perhaps originates in the error of confounding momentum with velocity. Be this as it may, it is now an ascertained truth in science, that all bodies, of whatever density, fall with the same velocity. Thus, a ball containing a pound of lead falls with the same velocity as a ball containing an ounce. This equality in the rate of falling is, however, disturbed by the quality of figure and bulk of bodies. A solid ball of gold will fall more quickly than the same quantity of gold beat out into a thin leaf, because in the case of the leaf the resistance from the atmosphere on a large sur face impedes the descent. Thus the atmosphere prevents bulky and porous substances from falling with the same velocity as those which are compact. If the atmosphere were removed, all bodies, whether light or heavy, large or small, would descend with the same velocity. This fact is ascertained by experiments performed with the air-pump. When a piece of coin, for instance a guinea, and a feather, are let fall at the same instant of time, from a hook which has held them at the top of the exhausted receiver of an air-pump, they are observed to fall at an equal rate, and to strike the bottom at the same moment. Hence it is demonstrated, that were it not for the resistance of the atmosphere, a bag full of feathers, and one of coins, would fall from a given height with the same velocity, and in the same space of time. It has been stated that the attraction of gravitation increases in proportion to the quantity of matter which the attracting body contains. Thus, the mass of our planet, the carth, exerts a force of attraction which produces the phenomena of weight, and the falling of bodies with a certain velocity. In consequence of the different size and density of the sun and planetary bodies, attraction is much stronger in some of them than others, and consequently the weight of bodies differs in each. On the surface of the sun, our pound weight would weigh upwards of 27 pounds, and a body would fall upon it 434 feet the first second. On the surface of Jupiter, our pound would |