32 ATTRACTION OF GRAVITATION. him to conjecture, that it might extend as far as the moon, and be the means of retaining her in her orbit. Imagine the moon, he reasoned, at the first moment of its creation, to have been projected forward, with a certain velocity, in a rectilinear direction; then, as soon as it began to move, gravity would act upon it, and impel it toward the centre of the earth. But as a body, impelled by two forces, will follow the direction of neither, the moon, so circumstanced, would neither proceed directly forward, nor fall directly downward, but keep a middle course, and move round the earth in a curvilinear orbit. This may be more fully illustrated, by attending to the motion of a shot, or any other projectile. A ball, shot from the mouth of a cannon, in a horizontal direction, does not fall to the ground till it has proceeded to a considerable distance; and if it be discharged from the top of a high mountain, it will fly still further before it comes to the earth. Increase the force and the height, and the distance will be augmented accordingly. And thus, in imagination at least, we can suppose the ball to be discharged with such velocity, that it will never come to the ground, but return to the place whence it set out, and circulate continually round the earth, in the manner of a little moon. Thus proceeding in his reflections, Newton discovered the admirable provision of the great Creator to prevent the evagation of the planets, and to retain them exactly within the bounds of their orbits. This he has demonstrated to be ef fected by gravity, and that gravity and motion completely solve all the phenomena of the planetary revolutions, both primary and secondary. By establishing this one principle in philosophy he has fully explained the system of the world, so far as it relates to this globe, and to all the rest of the planets that regard the sun as their centre. Such is the Newtonian system of universal gravitation or attraction. But what is this principle, which gives life and motion to inanimate beings, and how does it act? The effects are visible, but the agent that produces them is hidden from our senses. It eluded the search of Newton himself; he that soared to the utmost regions of space, and looked through nature with the eye of an eagle, was unable to discover it. This principle of gravitation, has been styled "The constant impression of Divine power;"-in every other sense the cause is likely to continue unexplored by man. It is, however, pretty ge CENTRE OF GRAVITY. 33 nerally agreed that the same principle of gravity, by which we see all bodies tend toward the centre of the earth, is a general law of nature, extended to all distances, and to every body, or substance, in the universe. For this the moon thro' heaven's blue concave glides, Exalts her wat❜ry zone, and sinks the poles.-FALlconer. QUESTIONS.-1. What is the attraction of gravitation? 2. How is the tendency of bodies to fall produced? 3. What incident led Newton to the most wonderful discoveries? 4. How did he reason? 5. What is considered the mark of a superior genius? 6. What did Newton soon perceive respecting the force of gravity? 7. What did this lead him to conjecture? 8. How did he reason respecting the moon? 9. What has this principle of gravitation been styled? 10. What did Newton fully explain by it? LESSON 17. Centre of Gravity. Perpendicularly, in the direction of a straight line up and down. If a THE centre of gravity of a body is that point about which all its parts, in any situation exactly balance each other, so that if a body be suspended or supported by this point, it will rest in any position. Whatever supports the centre of gravity bears the weight of the whole body; and while it is supported the body cannot fall. We may consider, therefore, the whole weight of a body as centered in this point. line is drawn from the centre of gravity of a body, perpendicularly to the horizon, it is called the line of direction; because it is the line which the centre of gravity would describe, if the body fell freely. The broader the base is upon which a body rests, the more difficult it will be to overturn it, as it must be moved the more to bring the line of direction beyond the base. A cask is easily rolled along, and so is a ball, but a box is moved with greater difficulty. When a box is longer than it is broad, it is much more easily turned on its side than set on its end. A building in the 34 CENTRE OF GRAVITY. form of a pyramid is the most durable, because, as it becomes narrower and narrower as it ascends, each stone or brick is supported by those below. The pyramids of Egypt, both great and small, still remain, and without doubt will do so for thousands of years to come, while the vast temples are crumbling into ruin. In building, care is taken not to bring the upper rows of bricks beyond those below, and for this purpose a line and plummet are used. But it does not follow, because a building leans, that the centre of gravity does not fall within the base. There is a high tower at Pisa, a town in Italy, which leans fifteen feet out of a perpendicular direction; strangers tremble to pass by it, still it is found by experiment that the line of direction falls within the base, and therefore it will stand while its materials hold together. The higher the centre of gravity is, the more easily may a body be overturned. Hence, a wagon or cart with a high load is more in danger of being overturned than one with a heavy load laid lower. This proves the injurious effect of rising in a coach or boat in danger of oversetting, the centre of gravity being thereby raised, and. the line of direction thrown out of the base. In such circumstances the proper course is to lie down in the bottom, so as to bring the line of direction, and consequently the centre of gravity, within the base, and thus remove the danger of oversetting. Ropedancers perform astonishing feats by the assistance of a long pole with very weighty pieces of lead at each end, by which they balance themselves and recover firm footing, if likely to fall on either side. In our ordinary actions we regulate the motions of our bodies, as if we were most correctly studying the nature and effects of the centre of gravity. If a man wishes to rise from a chair, he throws his body forward. If he is likely to fall on one side he leans to the other. A correct knowledge of the centre of gravity in bodies is of the utmost importance in the science of mechanics, as well as in many of the common actions of life. QUESTIONS. 1. What is the centre of gravity? 2. The line of direction? 3. When does a body stand most firmly? 4. Why is a pyramid the most durable form of building? 5. What occasions a body to be easily overturned? 6. What is the proper course when a coach or boat is in danger of oversetting? 7. On what principle do we regulate our ordinary actions? 8. Show by fig. 12. the common centre of gravity of two bodies. 9. Illustrate by fig. 4. the overturning of a body, when the line of direction falls out of the base. THE LAWS OF MOTION. 35 LESSON 18. The Laws of Motion. Momen'tum, (pl. momenta) the force acquired by different masses of matter moving with different velocities. A body, twice the weight of another, moving with equal velocity, will strike with twice the momentum,-with twice the velocity, with four times the momentum,—with three times the velocity, with six times the momentum, and so on. A BODY is in motion whenever it is changing its situation with regard to a fixed point, and the cause which produces motion is called force. The causes of motion, or the motive powers are either muscular, as the action of men and other animals, or mechanical, as the force of wind, water, gravity, the pressure of the atmosphere or any elastic medium, and steam. The motion of a body acted upon by a single force is always in a straight line, in the direction in which it received the impulse; and the degree of quickness with which it moves, or the velocity, must be proportional to the force by which it is impelled. If a given force, therefore, will produce a given motion, a double force will produce the double of that motion. If a new force be impressed upon a body in motion, its motion will be increased proportionably to the new force impressed. The velocity with which a body moves is measured by the space passed over, divided by the time which it employs in that motion; for if you travel one hundred miles in twenty hours, your velocity is five miles in each hour. You may reverse this rule and say, that the time is equal to the space divided by the velocity, for one hundred divided by five gives twenty hours for the time; and you may say also that the space is equal to the velocity multiplied by the time, for twenty multiplied by five gives one hundred miles for the space. Motion is uniform, accelerated, or retarded. Uniform motion is regular, and at an equal rate throughout. The hand of a watch is an example of uniform motion, for it passes over equal spaces in equal times. If neither gravity nor any other force opposed its motion, a ball thrown by the hand would proceed onwards in a right line, and with a uniform velocity for ever. Perpetual motion, however, cannot be produced by art, for gravity ultimately destroys all motion 36 THE LAWS OF MOTION. that human powers can produce. Accelerated motion takes place, when the motive power continues to act upon any body, so that its motion is continually increased. When a stone falls from a height, the impulse which it receives from gravity during the first instant of its fall, would be sufficient to bring it to the ground with a uniform velocity; but the stone is not acted upon by gravity merely at the first instant of its fall, this power continues to impel it during the whole of its descent, and it is this continued impulse which accelerates its motion. It has been found by experiment that heavy bodies, descending from a height by the force of gravity, fall sixteen feet the first second of time, three times that distance in the next, five times in the third second, seven times in the fourth, and so on, regularly increasing their velocities according to the number of seconds during which the body has been falling. Retarded motion is that of a body which moves every moment slower and slower; and it is produced by some force acting upon a body in a direction 'opposite to that which first put it in motion, as when a stone is thrown upwards, its velocity is gradually diminished by the power of gravity. The force, or power, with which a body in motion strikes against another body, is called its momentum. It is composed of its quantity of matter, multiplied by its quantity of motion; or in other words, its weight and its velocity. A small body may have a greater momentum than a large one, provided its velocity be sufficiently greater; the momentum of an arrow shot from a bow, for instance, must be greater than a stone thrown by the hand. The momentum of bodies is one of the most important points in mechanics; for you will find, that it is from opposing motion to matter, that machines derive their powers. When a body in motion strikes against another body, it meets with resistance from it; and the resistance of the body at rest will be equal to the blow struck by the body in motion; or to express the same in philosophical language, action and re-action will be equal and in opposite directions. It appears, therefore, that one body acting upon another, loses as much motion as it communicates, and that the sum of the motions of any two bodies in the same line of direction, cannot be changed by their mutual action. From the action nd re-action of bodies we may learn in what manner a bird, |