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? Wha! would the terms up and down, in such case, mean?

except 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.

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, to 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 no 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 twc forces?

a circular motion, and retains them in their orbits as they revolve, the primaries about the Sun, and the secondaries about their primaries.

;

The degree of the Sun's attractive power at each particular planet, whatever be its distance, is uniformly equal to the centrifugal force of the planet. The nearer any planet is to the Sun, the more strongly is it attracted by him the farther any planet is from the Sun, the less is it attracted by him; therefore, those planets which are the nearer to the Sun must move the faster in their orbits, in order thereby to acquire centrifugal forces equal to the power of the Sun's attraction; and those which are the farther from the Sun must move the slower, in order that they may no* have too great a degree of centrifugal force, for the weaker attraction of the Sun at those distances.

The discovery of these great truths, by Kepler and Newton, established the UNIVERSAL LAW OF PLANETARY MOTION; which may be stated as follows:

1. Every planet moves in its orbit with a velocity varying every instant, in consequence of two forces; one tending to the centre of the Sun, and the other in the direction of a tangent to its orbit, arising from the primitive impulse given at the time it was launched into space. The former is called its Centripetal, the latter, its Centrifugal force. Should the centrifugal force cease, the planet would fall to the Sun by its gravity; were the Sun not to attract it, it would fly off from its orbit in a straight line.

2. By the time a planet has reached its aphelion, or that point of its orbit which is farthest from the Sun, his attraction has overcome its velocity, and draws it towards him with such an accelerated motion, that it at last overcomes the Sun's attraction, and shoots past him; then gradually decreasing in velocity, it arrives at the perihelion, when the Sun's attraction again prevails.

3. However ponderous or light, large or small, near or remote, the planets may be, their motion is always such that imaginary lines joining their centres to the Sun, pass over equal areas in equal times: and this is true not only with respect to the areas described every hour by the same planet, but the agreement holds, with rigid exactness, between the areas described in the same time, by all the planets and comets belonging to the Solar System.

From the foregoing principles, it follows, that the force of gravity, and the centrifugal force, are mutual opposing powers-each continually acting

To what is the Sun's attractive rower at each particular planet equal? Explain this more fully. By whom was the universal law of planetary motion established? Repeat the law.

against the other. Thus, the weight of bodies, on the Earth's equator, is diminished by the centrifugal force of her diurnal rotation, in the propor tion of one pound for every 290 pounds: that is, had the Earth no motion on her axis, all bodies on the equator would weigh one two hundred and eighty-ninth part more than they now do.

On the contrary, if her diurnal motion were accelerated, the centrifugal force would be proportionally increased, and the weight of bodies at the equator would be, in the same ratio, diminished. Should the Earth revolve upon its axis, with a velocity which would make the day but 84 minutes long, instead of 24 hours, the centrifugal force would counterbalance that of gravity, and all bodies at the equator would then be absolutely destitute of weight; and if the centrifugal force were further auiginented, (the Earth revolving in less time than 84 minutes,) gravitation would be completely overpowered, and all fluids and loose substances near the equator would fly off from the

surface.

The weight of bodies, either upon the Earth, or on any other planet having a motion around its axis, depends jointly upon the mass of the planet, and its diurnal velocity. A body weighing one pound upon the equator of the Earth, would weigh, if removed to the equator of the Sun, 27.9 lbs. Of Mercury, 1.03 lbs. Of Venus, 0.98 lbs. Of the Moon, lb. Of Mars, lb. Of Jupiter, 2.716 lbs. Of Saturn, 1.01 lbs.

CHAPTER XXI.

PRECESSION OF THE EQUINOXES-OBLIQUITY OF THE ECLIPTIC.

Of all the motions which are going forward in the Solar System, there is none, which it is important to notice, more difficult to comprehend, or to explain, than the PRECESSION OF THE EQUINOXES, as it is termed.

The equinoxes, as we have learned, are the two opposite points in the Earth's orbit, where it crosses the equator. The first is in Aries; the other, in Libra. By the precession of the equinoxes is meant, that the intersection of the equator with the ecliptic is not always in the same point:in other words, that the Sun, in its apparent annual course, does not cross the equinoctial, Spring and Autumn, exactly in the same points, but every year a little behind those of the preceding year.

This annual falling back of the equinoctical points, is called by astronomers, with reference to the motion of the heavens, the Precession of the Equinoxes; but it would better accord with fact as well as the apprehension of the learner, to call it, as it is, the Recession of the Equinoxes: for the equinoctial points do actually recede upon the ecliptic, at the rate of about 501" of a degree every year. It is the name

How is the weight of bodies on the Earth's equator affected by its diurnal rotation? What would be the effect if the diurnal motion of the Earth were accelerated? What would be the consequence if the Earth revolved about its axis in 84 minutes, cr in rss time? What are the equinoxes? What is meant by the precession of the equinoxes? hy is it called precession of the equinoxes, and what would be a better term?

only, and not the position, of the equinoxes which remains permanent. Wherever the Sun crosses the equinoctial in the spring there is the vernal equinox; and wherever he crosses it in the autumn there is the autumnal equinox, and these points are constantly moving to the west.

To render this subject familiar, we will suppose two carriage roads, extending quite around the Earth: one, representing the equator, running due east and west; and the other, representing the ecliptic, running nearly

in the same direction as the former, yet so as to cross it. with a small angle, (say of 2310,) both at the point where we now stand, for instance, and in the nadir, exactly opposite; let there also be another road, to represent the prime meridian, running north and south, and crossing the first at right angles, in the common point of intersection, as in the annexed figure.

Let a carriage now start from this point of intersec.

tion, not in the road leading

directly east, but along that of the ecliptic, which leaves the former a little to the north, and let a person be placed to watch when the carriage comes around again, after having made the circuit of the Earth, and see whether the carriage will cross the equinoctial road again precisely in the same track as when it left the goal. Though the person stood exactly in the former track, he need not fear being run over, for the carriage will cross the road 100 rods west of him, that is, 100 rods west of the meridian on which he stood. It is to be observed, that 100 rods on the equator is equal to 504 seconds of a degree.

If the carriage still continue to go around the Earth, it will, on completing its second circuit, cross the equinoctial path 200 rods west of the meridian whence it first set out; on the third circuit, 300 rods west; on the fourth circuit, 400 rods, and so on, continually. After 713 circuits, the point of intersection would be one degree west of its place at the commencement of the route. At this rate it would be easy to determine how many complete circuits the carriage must perform before this continual falling back of the intersecting point would have retreated over every degree of the orbit, until it reached again the point from whence it first departed. The application of this illustration will be manifest, when we consider, further, that,

The Sun revolves from one equinox to the same equinox again, in 365d. 5h. 48′ 47′′.81. This constitutes the natural, or tropical year, because, in this period, one revolution of the seasons is exactly completed. But it is, mean

The equinoctial points are continually moving; how, then, is their position define.1. Give, at length, a familiar illustration by which this subject may be understood. Suppose the carriage continues its circuit around the earth, where would it cross the equinoctial the 2d, 3d, and 4th times, &c.? After how many circuits would this falling back of the equinoctial points amount to one degree on the ecliptic? In what time does the Sun revolve from one equinox to the same equinox again? What is this "eriod called?