weigh about 2 pounds 4 ounces. And on the surface of the moon, our pound would weigh only the fifth part of a pound. As a body in descending to the earth receives in 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 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 velocity with which the body was projected upwards. 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 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 other. B Fig. 2. Any square or angular body which we may place on the ground, will remain stationary, or safely at rest, provided an ideal line, drawn from its centre of gravity, and passing to the ground in a direction perpendicular to the earth's surface, fall within its base, as in fig. 2. A point below A is the centre of gravity; and from that point the line of direction goes downward to B, which is within the edges of the base. An object of this form, and so placed, will stand. If the line of direction from the centre of gravity fall without the outer edge of the base, as in fig. 3, from A to B, then the object will not remain balanced on its base; it will fall over, and attain some position in which the line of direction falls within the boundary of the base on which it stands. By keeping this simple principle in view, stability and safety will generally be secured in the erection of objects of art, such as houses, monumental Fig. 3. 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 an U nexed 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. Lately an improvement has been effected in stage-coach building, by which a chief part of the load is placed as low as the axle of the wheels; and by this means the danger of overturning is almost entirely averted. The centre of gravity of a body is not always in the substance of the body. Thus, the centre of gravity of but air. a circular ring is in the centre of the circle; of an elliptic 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 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. D 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 irregularly 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. B 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. 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. 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 path or arc 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. D B Fig. 6. 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, immediately 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 suspension. 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 a small 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 arc 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 arc 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 In the various natural structures displayed in the longer, however, in exact proportion as we extend the mal and vegetable kingdoms, the centre of gravity | rod. The vibration, it must always be recollected, is analogous to the falling of bodies. The spaces fallen through by a body in 1, 2, 3, or 4 seconds, are not in proportion to 1, 2, 3, 4, and so on, but in the proportion of 1, 4, 9, 16, 25, and so on, or the squares of the time occupied in falling. In the case of pendulums, it is found that their lengths are as the squares of the times of vibration. Thus, if the times occupied by one vibration of two pendulums be 1 and 2 seconds respectively, the lengths of the pendulums will be as 1 and 4; so if the time of one vibration of several pendulums be as 1, 2, 3, 4, their lengths are as 1, 4, 9, and 16. The vibrations of the pendulum being produced by terrestrial gravitation, it follows, as a natural result, that, if the force of gravitation be weakened, so will the tendency of the ball of the pendulum to fall or swing be weakened. This result is distinctly observable in different parts of the earth. At the equator, the earth, as already mentioned, bulges out to a thickness of 26 miles on the diameter, or 13 miles from the surface to the centre; and as the attraction of gravitation proceeds from the centre, the force of this attraction is consequently weaker at the surface at the equator than it is at the surface at the poles. At every part of the surface between the equator and poles, there is a proportionate increase of gravity. Besides the effect produced by the greater distance of the surface from the centre at the equator, centrifugal force, which is strongest at the equator, assists in weakening the attractive force at that place. In consequence of these combined causes, a pendulum of a given length vibrates more slowly at the equator than at the poles. In proportion as we advance on the surface of the earth from the equator towards the poles, so does the pendulum swing or vibrate more quickly. In order, therefore, to preserve uniformity of speed in pendulums at different parts of the globe, that is, in order that they may all vibrate in one second, their length must be regulated according to the distance of the places from the equator. Thus, each degree of latitude has its own length of pendulum. From a knowledge of these laws we are enabled, by this instrument, not only to detect certain variations in that attraction in various parts of the earth, but also to discover the actual amount of the attraction at any given place. To compare the force of gravity in different parts of the earth, it is only necessary to swing the same pendulum in the places under consideration, and to observe the rapidity of its vibrations. The proportion of the force of gravity in the several places will be that of the squares of the velocity of the vibration. Observations to this effect have been made at several places, by Biot, Kater, Sabine, and others. The uniform vibration of the pendulum has rendered it useful in regulating the motion of clocks for measuring time. In the common clock, a pendulum, connected with the wheel-work, and impelled by weights, or a spring, regulates the motions of the minute and hour hands on the dial-plate, by which the time of day is pointed out. If no pendulum were employed, the wheels would go very irregularly. The pendulum is regulated in length, so as to vibrate sixty times, each time being a second, in the space of a minute. At each vibration, it acts upon the tooth of a wheel, which turns the rest of the machinery. In order that the pendulum may vibrate neither quicker nor slower than sixty times in a minute, in the latitude of London it must measure 39 inches and about the 7th of an inch from the point of suspension to the centre of oscillation. A pendulum at Edinburgh would require to be a small degree longer. The greatest possible nicety is required in the adjustment of the length, for a difference in extent amounting to the 1000th part of an inch, would cause an error of about one second in a day. Therefore, to make a pendulum go slower by one second a-day, it must be lengthened by the 1000th part of an inch; and to make it go quicker, it must be shortened in the same proportion. It is possible to cause short pendulums to regulate the movement of clocks the same as long pendulums; and this is done in cases where long pendulums would be inconvenient, or inelegant in appearance. This is accomplished by shortening the pendulum to a fourth of its ordinary length, by which it beats or vibrates twice instead of once in a second. The wheel-work is constructed to suit this arrangement. THE LAWS OF MOTION. Motion, as already mentioned, is the changing of place, or the opposite of rest. According to the general explanations which have been given, it appears that motion in bodies is as natural as rest, and that matter passively submits to remain in either of these states in which it may be placed, provided no external force or obstacle interfere to cause an alteration of condition. These and other fundamental laws of nature, in relation to rest and motion of matter, are laid down by Sir Isaac Newton in the following three propositions: 1st, Every body must persevere in its state of rest, or of uniform motion in a straight line, unless it be compelled to change that state by forces impressed upon it. 2d, Every change of motion must be proportional to the impressed force, and must be in the direction of that straight line in which the force is impressed. 3d, Action must always be equal and contrary to reaction; or the actions of two bodies upon each other must be equal, and their directions must be opposite. These propositions we shall treat separately. In the first of the series there are three points requiring consideration, namely, the permanency, the uniformity, and the straight line of direction of motion in bodies. As was formerly observed, it is impossible to show either permanency or uniformity of motion in bodies upon or near the earth; for all moving bodies are sooner or later brought to a state of rest by the force of attraction, friction, and the opposition of the atmosphere. It is only, therefore, in the case of the great works of nature, or planetary bodies, that the laws of motion are most clearly and fully illustrated. The tendency of a body to move in a straight line from the point whence it set out, is as much a property of matter as the uniformity of motion. If we conceive the idea of a body impelled into a state of motion by any given force, and at the same time conceive the idea that there is no obstacle to interrupt it, no attractive force to bend it aside, we shall then fully understand that a moving body must, as a matter of necessity, from its property of inertia, proceed in a straight line of direction-it must go on in an even path for ever. CENTRIFUGAL FORCE AND CIRCULAR MOTION. Bodies in flying round a centre have a tendency to proceed in a straight line, and this principle of motion, as already mentioned, is termed centrifugal force. Examples of this tendency are very familiar to our observation. When we whirl rapidly a sling with a stone in it, and suddenly allow the stone to fly off, it proceeds at first sensibly in a straight line, but is gradually pulled to the earth by attraction. In turning a circular grinding-stone rapidly with water in contact with it, we perceive a rim of water first rising on the stone and next flying off; and the more rapidly we turn the stone, so does the water fly off with the greater force. In grinding corn by two rapidly turning stones playing on each other, the grain poured in at an opening at the centre is quickly shuffled towards the edges of the stones, and expelled in the condition of meal or flour. If we put some water in a vessel, and rapidly turn it in one direction, we shall find that the water endeavours to escape, and rises up to the edges of the vessel, leaving a deep hollow in the middle. The tendency to fly off from a centre is made use of in the manufacture of pottery: Soft clay being placed on a revolving wheel, it quickly spreads towards the circumference of the machine, and is guided or moulded by the hand of the potter into the required form. In forming common |