tive and not positive, the nearest of them may be at twice or ten times that distance.

The number of comets which have been observed since the Christian era, amounts to 700 Scarcely a year has passed without the observation of one or two. And since multitudes of them must escape observation, by reason of their traversing that part of the heavens which is above the horizon in the day time, their whole number is probably many thousands. Comets so circumstanced, can only become visible by the rare coincidence of a total eclipse of the Sun a coincidence which happened, as related by Seneca, 60 years before Christ, when a large comet was actually observed very near the Sun.

But M. Arago reasons in the following manner, with respect to the num. ber of comets :-The number of ascertained coinets, which, at their least distances, pass within the orbit of Mercury, is thirty. Assuming that the comets are uniformly distributed throughout the solar system, there will be 117,649 times as many comets included within the orbit of Herschel, as there are within the orbit of Mercury. But as there are 30 within the orbit of Mercury, there must be 3,529,470 within the orbit of Herschel!

Of 97 comets whose elements have been calculated by astronomers, 24 passed between the Sun and the orbit of Mercury; 33 between the orbits of Mercury and Venus; 21 between the orbits of Venus and the Earth; 15 between the orbits of Ceres and Jupiter. Forty-nine of these comets move from east to west, and 48 in the opposite direction.

The total number of distinct comets, whose paths during the visible part of their course had been ascertained, up to the year 1832, was one hundred and thirty-seven.

What regions these bodies visit, when they pass beyond the limits of our view; upon what errands they come, when they again revisit the central parts of our system; what is the difference between their physical constitution and that of the Sun and planets; and what important ends they are destined to accomplish, in the economy of the universe, are inquiries which naturally arise in the mind, but which surpass the limited powers of the human understanding at present to determine.

CHAPTER XX.

OF THE FORCES BY WHICH THE PLANETS ARE
RETAINED IN THEIR ORBITS.

Having described the real and apparent motions of the bodies which compose the solar system, it may be interesting next to show, that these motions, however varied or complex they may seem, all result from one simple principle, or law, namely, the

What is the number of comets which have been observed since the Christian era? Why must some of them escape observation? How great is probably their actual number? In what case alone can comets which traverse the horizon in the day time become visible? Mention an instance of a comet thus becoming visible? What is the reasoning of M. Arago in regard to the number of comets? _Describe the track among the orbits of the planets, of the 97 comets whose elements have been calculated by astronomers. In what direction do they move? What, up to the year 1832, was the whole number of distinct comets, whose path, during the visible part of their course, has been determined? By what principle, or law, are the planets reLained in their orbits?

LAW OF UNIVERSAL GRAVITATION.

It is said, that Sir Isaac Newton, when he was drawing to a close the demonstration of the great truth, that gravity is the cause which keeps the heavenly bodies in their orbits, was so much agitated with the magnitude and importance of the discovery he was about to make, that he was unable to proceed, and desired a friend to finish what the intensity of his feelings did not allow him to do. By gravitation is meant, that universal law of attraction, by which every particle of matter in the system has a tendency to every other particle.)

This attraction, or tendency of bodies towards each other, is in proportion to the quantity of matter they contain. The Earth, being immensely large in comparison with all other substances in its vicinity, destroys the effect of this attraction between smaller bodies, by bringing them all to itself. The attraction of gravitation is reciprocal. All bodies not only attract other bodies, but are themselves attracted, and both according to their respective quantities of matter. The Sun, the largest body in our system, attracts the Earth and all the other planets, while they in turn attract the Sun. The Earth, also, attracts the Moon, and she in turn attracts the Earth. A ball, thrown upwards from the Earth, is brought again to its surface; the Earth's attraction not only counterbalancing that of the ball, but also producing a motion of the ball towards itself.)

This disposition, or tendency towards the Earth, is manifested in whatever falls, whether it be a pebble from the hand, an apple from a tree, or an avalanche from a mountain. All terrestrial bodies, not excepting the waters of the ocean, gravitate towards the centre of the Earth, and it is by the same power that animals on all parts of the globe stand with their feet pointing to its centre.

The power of terrestrial gravitation is greatest at the earth's surface, whence it decreases both upwards and downwards; but not both ways in the same proportion. It decreases upwards as the square of the distance from the Earth's centre increases so that at a distance from the centre equal to twice the semi-diameter of the Earth, the gravitating force would be only one fourth of what it is at the surface. But below the surface, it decreases in the direct ratio of the dis

Who discovered this great truth, and how was he affected in view of it? What is meant by gravitation? To what is it proportioned? Give some example. How is it known that the attraction of gravitation is reciprocal? Give some examples to illustrate this principle. Where is the power of terrestrial gravitation the greatest? From this point, does the power decrease equally, both upwards and downwards? What is the law of decrease upwards? Give an example. What is the law of decrease downwards? Give an example.

tance from the centre; so that at a distance of half a semidiameter from the centre, the gravitating force is but half what it is at the surface.

Weight and Gravity, in this case, are synonymous terms. We say a piece of lead weighs a pound, or 16 ounces; but if by any means it could be raised 4000 miles above the surface of the Earth, which is about the distance of the surface from the centre, and consequently equal to two semi-diameters of the Earth above its centre, it would weigh only one fourth of a pound, or four ounces; and if the same weight could be raised to an elevation of 12,000 miles above the surface, or four semi-diameters above the centre of the Earth, it would there weigh only one sixteenth of a pound, or one ounce.

The same body, at the centre of the Earth, being equally attracted in every direction, would be without weight; at 1000 miles from the centre it would weigh one fourth of a pound; at 2000 miles, one half of a pound; at 3000 miles, three fourths of a pound; and at 4000 miles, or at the surface, one pound.

It is a universal law of attraction, that its power decreases as the square of the distance increases. The converse of this is also true, viz. The power increases, as the square of the distance decreases. Giving to this law the form of a practical rule, it will stand thus:

The gravity of bodies above the surface of the Earth, decreases in a duplicate ratio, (or as the squares of their distances) in semi-diameters of the earth, from the earth's centre. That is, when the gravity is increasing, multiply the weight by the square of the distance; but when the gravity is decreasing, divide the weight by the square of the distance.

Suppose a body weighs 40 pounds at 2000 miles above the Earth's surface, what would it weigh at the surface, estimating the Earth's semi-diameter at 4000 miles? From the centre to the given height, is 1 semi-diameters: the square of 13, or 1.5 is 2.25, which, multiplied into the weight, (40,) gives 90 pounds, the answer.

Suppose a body which weighs 256 pounds upon the surface of the Earth, be raised to the distance of the Moon, (240,000 miles,) what would be its weight. Thus, 4000)240,000(60 semi diameters, the square of which is 3600. As the gravity, in this case, is decreasing, divide the weight by the square of the distance, and it will give 3600)256(1-16th of a pound, or 1 ounce.

2. To find to what height a given weight must be raised to lose a certain portion of its weight.

RULE. Divide the weight at the surface, by the required weight, and extract the square root of the quotient. Ex. A boy weighs 100 pounds, how high must he be carried to weigh but 4 pounds? Thus, 100 divided by 4, gives 25, the square root of which is 5 semi-diameters, or 20,000 miles above the

centre.

Bodies of equal magnitude do not always contain equal

What is the relation between weight and gravity? Illustrate it by some examples. What, then, is the general law in regard to the increase and decrease of attraction? How may this law be expressed, in the form of a practical rule? Suppose, for example, the semi-diameter of the Earth be estimated, in round numbers, at 4000 miles, and that a body, elevated 2000 miles above its surface, should weigh 40 pounds, what would the same body weigh, if brought to the Earth's surface? Suppose a body which weighs 256 pounds upon the surface of the Earth, be raised to the distance of the Moon, what would be its weight at such an elevation? [The pupil should be required to give the calculation, as well as the answer.] By what rule can we determine the height to which a body must be raised, in order to its losing a certain portion of its weight? Give an example. Do bodies of the same magnitude always contain equal quantities of matter?

quantities of matter; a ball of cork, of equal bulk with one of lead, contains less matter, because it is more porous. The Sun, though fourteen hundred thousand times larger than the Earth, being much less dense, contains a quantity of matter only 355,000 times as great, and hence attracts the Earth with a force only 355,000 times greater than that with which the Earth attracts the Sun.

The quantity of matter in the Sun is 780 times greater than that of all the planets and satellites belonging to the Solar System; consequently their whole united force of attraction is 780 times less upon the Sun, than that of the Sun upon them.

The Centre of Gravity of a body, is that point in which its whole weight is concentrated, and upon which it would rest, if freely suspended. If two weights, one of ten pounds, the other of one pound, be connected together by a rod eleven feet long, nicely poised on a centre, and then be thrown into a free rotary motion, the heaviest will move in a circle with a radius of one foot, and the lightest will describe a circle with a radius of ten feet: the centre around which they move is their common centre of gravity. See the Figure. Thus the Sun and planets move around an imaginary point as a centre, always preserving an equilibrium.

CENTRE OF GRAVITY.

Fig. 21.

If there were but one, body in the universe, provided it were of uniform density, the centre of it would be the centre of gravity towards which all the surrounding portions would uniformly tend, and they would thereby balance each other. Thus the centre of gravity, and the body itself, would forever remain at rest. It would neither move up nor down; there being no other body to draw it in any direction. In this case, the terms up and down would have no meaning,

What are the comparative bulks and densities of the Sun and the Earth? How great is the quantity of matter in the Sun, compared with that of all the planets belonging to the solar system? What is the centre of gravity of a body? Give an example. How does this illustration apply to planetary motion? If there were but one single body in the universe, where would the centre of gravity be? What motion would the body have? What wouli the terms up and down, in such case, mean?

except as applied to the body itself, to express the direction of the surface from the centre.

Were the Earth the only body revolving about the Sun, as the Sun's quantity of matter is 355,000 times as great as that of the Earth, the Sun would revolve in a circle equal only to the three hundred and fifty-five thousandth part of the Earth's distance from it: but as the planets in their several orbits vary their positions, the centre of gravity is not always at the same distance from the Sun. i

The quantity of matter in the Sun so far exceeds that of all the planets together, that were they all on one side of him he would never be more than his own diameter from the common centre of gravity; the Sun is therefore justly considered as the centre of the system.

The quantity of matter in the Earth being about 80 times as great as that of the Moon, their common centre of gravity is 80 times nearer the former than the latter, which is about 3000 miles from the Earth's centre.

The secondary planets are governed by the same laws as their primaries, and both together move around a common centre of gravity.

Every system in the universe is supposed to revolve, in like manner, around one common centre.

ATTRACTIVE AND PROJECTILE FORCES.

All simple motion is naturally rectilinear; that is, all bodies put in motion would continue to go forward in straight lines, as long as they met with no resistance or diverting force.

On the other hand, the Sun, from his immense size, would, by the power of attraction, draw all the planets to him, if his attractive force were not counterbalanced by the primitive impulse of the planetary bodies to move in straight lines.

The attractive power of a body drawing another body towards the centre, is denominated Centripetal force; and the tendency of a revolving body to fly from the centre in a tangent line, is called the Projectile or Centrifugal force. The joint action of these two central forces gives the planets

If the Earth were the only body revolving about the Sun, what would be their relative distances from their common centre of gravity? If, instead of the Earth alone, the Earth with all the planets and satellites of the system were on one side, and the Sun alone on the other, at what distance from their common centre of gravity must the Sun be, 10 balance them all? Where is the centre of gravity between the Earth and Moon? How do you know this? By what laws are the secondary planets governed, and the other systems of the universe? What is meant by all simple motion being rectilinear? Why does rot the Sun, by its great attraction, bring all bodies to its surface? Explain what is meant by centripetal and centrifugal forces. What results from the joint action of these two forces}

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