continues to move downwards to the stage, in consequence of the velocity it had acquired previously to that time.)

To comprehend the accuracy of this machine, it must be understood that the velocities of gravitating bodies are supposed to be equal, whether they are large or small, this being the case when no calculation is made for the resistance of the air. Consequently, the weight of a quarter of an ounce placed on the large weight A, is a representative of all other solid descending bodies. The slowness of its descent, when compared with freely gravitating bodies, is only a convenience by which its motion can be accurately measured, for it is the increase of velocity which the machine is designed to ascertain and not the actual velocity of falling bodies.

Now it will be readily comprehended, that in this respect, it makes no difference how slowly a body falls, provided it follows the same laws as other descending bodies, and it has already been stated, that all estimates on this subject are made from the known distance a body descends during the first se cond of time.

It follows, therefore, that if it can be ascertained, exactly how much faster a body falls during the third, fourth, or fifth second, than it did during the first second, by knowing how far it fell during the first second, we should be able to estimate the distance it would fall during all succeeding seconds.

If, then, by means of a pendulum beating seconds, the weight A should be found to descend a certain number of inches during the first second, and another certain number during the next second, and so on, the ratio of increased descent would be precisely ascertained, and could be easily applied to the falling of other bodies; and this is the use to which this instrument is applied.

By this machine, it can also be ascertained, how much the actual velocity of a falling body depends on the force of gravity, and how much on acquired velocity, for the force of gravity gives motion to the descending weight only until it arrives at

After the small weight is taken off by the ring why does the large weight ontinue to descend? Does this machine show the actual velocity of a falling body, or only its increase? How does Mr. Atwood's machine show how much the celerity of a body depends upon gravity, and how much on acquired velocity?

the ring, after which the motion is continued by the velocity it had before acquired. }

From experiments accurately made with this machine, it has been fully established, that if the time of a falling body be divided into equal parts, say into seconds, the spaces through which it falls in each second, taken separately, will be as the odd numbers, 1, 3, 5, 7, 9, and so on, as already stated. To make this plain, suppose the times occupied by the falling body to be 1, 2, 3, and 4 seconds; then the spaces fallen through will be as the squares of these seconds, or times, viz. 1, 4, 9, and 16, the square of 1 being 1, the square of 2 being 4, the square of 3, 9, and so on. The distance fallen through, therefore, during the second second, may be found, by taking 1, the distance corresponding to one second, from 4, the distance corresponding to 2 seconds, and is therefore 3. For the 3d second, take 4 from 9, and therefore the distance will be 5. For the fourth second, take 9 from 16, and the distance will be 7, and so on. During the first second, then, the body falls a certain distance, during the next second, it falls three times that distance, during the third, five times that distance, during the fourth, seven times that distance, and so continually in that proportion.

It will be readily conceived, that solid bodies falling from great heights, must ultimately acquire an amazing velocity by this proportion of increase. An ounce ball of lead, let fall from a certain height towards the earth, would thus acquire a force ten or twenty times as great as when shot out of a rifle. By actual calculation, it has been found that were the moon to lose her projectile force, which counterbalances the earth's attraction, she would fall to the earth in four days and twenty hours, a distance of 240,000 miles. And were the earth's projectile force destroyed, it would fall to the sun in sixty-four days and ten hours, a distance of 95,000,000 of miles.

Every one knows by his own experience the different

Suppose the times of a falling body are as the numbers 1, 2, 3, 4, what will be the numbers representing the spaces through which it falls? Suppose a body falls 16 feet the first second, how far will it fall the third second? Would it be possible for a rifle ball to acquire a greater force by falling, than if shot from a rifle ? How long would it take the Moon to come to the earth according to the law of increased velocity? How long would it take the earth to fall to the sun?

effects of the same body falling from a great or a small height. A boy will toss up his leaden bullet and catch it with his hand, but he soon learns, by its painful effects, not to throw it too high. The effects of hail-stones on window glass, animals, and vegetation, are often surprising, and sometimes calamitous illustrations of the velocity of falling bodies.

It has been already stated that the velocities of solid bodies falling from a given height, towards the earth, are equal, or in other words, that an ounce ball of lead will descend in the same time as a pound ball of lead.

This is true in theory, but there is a slight difference in this respect in favor of the velocity of the larger body, owing to the resistance of the atmosphere. We, however, shall at present consider all solids of whatever size, as descending through the same spaces in the same times, this being exactly true when they pass without resistance.

To comprehend the reason of this we have only to consider, that the attraction of gravitation in acting on a mass of matter acts on every particle it contains and thus every particle is drawn down equally and with the same force. The effect of gravity, therefore, is in exact proportion to the quantity of matter the mass contains, and not in proportion to its bulk. A ball of lead of a foot in diameter, and one of wood of the same diameter, are obviously of the same bulk; but the lead will contain twelve particles of matter where the wood contains one, and consequently will be attracted with twelve times the force, and therefore will weigh twelve times as much.

If then, bodies attract each other in proportion to the quantities of matter they contain, it follows that if the mass of the earth were doubled, the weights of all bodies on its surface would also be doubled; and if its quantity of matter were tripled, all bodies would weigh three times as much as they do at present.

It follows also, that two attracting bodies, when free to move, must approach each other mutually. If the two bodies

What familiar illustrations are given of the force acquired by the velocity of falling bodies? Will a small and a large body fall through the same space in the same time? On what parts of a mass of matter does the force of gravity act? Is the effect of gravity in proportion to bulk, or quantity of matter? Were the mass of the earth doubled, how much more should we weigh than we do now?

contain like quantities of matter, their approach will be equal ly rapid, and they will move equal distances towards each other. But if the one be small and the other large, the small one will approach the other with a rapidity proportioned to the less quantity of matter it contains.

It is easy to conceive, that if a man in one boat pulls at a rope attached to another boat, the two boats, if of the same size, will move towards each other at the same rate; but if the one be large and the other small, the rapidity with which each moves will be in proportion to its size, the large one moving with as much less velocity as its size is greater.

A man in a boat pulling a rope attached to a ship, seems only to move the boat, but that he really moves the ship is certain, when it is considered, that a thousand boats pulling in the same manner would make the ship meet them half way.

It appears, therefore, that an equal force acting on bodies containing different quantities of matter, move them with different velocities, and that these velocities are in an inverse proportion to their quantities of matter.

In respect to equal forces, it is obvious that in the case of the ship and single boat, they were moved towards each other by the same force, that is, the force of a man pulling by a rope. The same principle holds in respect to attraction, for all bodies attract each other equally, according to the quantities of matter they contain, and since all attraction is mutual, no body attracts another with a greater force than that by which it is attracted.

Suppose a body to be placed at a distance from the earth weighing two hundred pounds; the earth would then attract the body with a force equal to two hundred pounds, and the body would attract the earth with an equal force, otherwise their attraction would not be equal and mutual. Another body weighing 10 pounds, would be attracted with a force equal to 10 pounds, and so of all bodies according to the quantity of

Suppose one body moving towards another, three times as large, by the force of gravity, what would be their proportional velocities? How is this illustrated? Does a large body attract a small one with any more force than it is attracted? Suppose a body weighing 200 pounds to be placed at a distance from the earth, with how much force does the earth attract the body? With what force does the body attract the earth?

matter they contain; each body being attracted by the earth with a force equal to its own weight, and attracting the earth with an equal force.

If the man in the boat pulled the rope with the force of 100 pounds, it is plain that the force on each vessel would be 50 pounds for suppose each end of the rope to be thrown over a pulley, and a weight of 50 pounds attached to these ends, it would take just 100 pounds in the middle of the rope to balance them.

It is inferred from these principles, that all attracting bodies which are free to move, mutually approach each other, and therefore that the earth moves towards every body which is raised from its surface, with a velocity and to a distance proportional to the quantity of matter thus elevated from its surface. But the velocity of the earth being as many times less than that of the falling body as its mass is greater, it follows that its motion is not perceptible to us.

The following calculation will show what an immense mass of matter it would take, to disturb the earth's gravity in a perceptible manner.

If a ball of earth equal in diameter to the tenth part of a mile, were placed at the distance of the tenth part of a mile from the earth's surface, the attracting powers of the two bodies would be in the ratio of about 512 millions of millions to one. For the earth's diameter being about 8000 miles, the two bodies would bear to each other about this proportion. Consequently if the tenth part of a mile were divided into 512 million of millions of equal parts, one of these parts would be nearly the space through which the earth would move towards the falling body. Now in the tenth part of a mile there are about 6400 inches, consequently this number must be divided into 512 millions of millions of parts, which would give the eighty thousand millionth part of an inch through which the earth would move to meet a body of the tenth part of a mile in diameter.

Suppose a man in one boat, pulls with the force of 100 pounds at a rope fastened to another boat, what would be the force on each boat? How is this illustrated? Suppose the body falls towards the earth, is the earth set in motion by its attraction? Why is not the earth's motion towards it perceptible? What distance would a body, the tenth part of a mile in diameter, placed at the distance of a tenth part of a mile, attract the earth towards it?