Now, Newton has shewn that this very law is competent to the explanation of that by which the Moon moves with the Earth in her orbit round the Sun; and it is a striking proof of the simplicity of the laws of motion, that one and the same principle governs the falling of a stone and the revolution of a planet.

Let us suppose the planets to be left to the power of this principle alone; that is, let us suppose the projectile force to be destroyed, and attraction only to act upon them; they would then be in the condition of falling bodies, and subject to the law just recited. The mathematician knowing their respective distances from the Sun, has calculated that if that were to happen,

A stone from the surface to the center of the

Earth in 21 minutes and 19 seconds.

It has been before observed, that the power of Attraction is proportioned to the distance of a body, from that which attracts it. Let us notice the proportions which

to find the number of feet fallen through in 3 seconds of time. Therefore, multiply 3 by itself, and the product is the square of 3, or 9;-by this number multiply 16, the number of feet a body falls in the first second of time, and the result is 144. So that the rule and the fact agree.

the Sun exerts upon Saturn and the Georgium SidusThe latter is twice as far from the Sun as the former; hence we might conclude that the power of attraction exerted by the Sun on Saturn, is twice as great as that exerted on the Georgium Sidus. But this is not the proportion. For the rule by which this power acts has been discovered; it is this, Attraction decreases as the squares of the distances from the attracting body increase; that is, a body at twice the distance from the attracting body, is attracted only by 1-4th part of the force. The Georgium Sidus therefore is attracted by 1-4th part of the force that Saturn is. Hence the greater the distance of a planet from the Sun, proportionably the less is its velocity, because it requires less projectile force to counteract the force of gravity and prevent the planet from falling to the Sun; round which

Mercury moves at the rate of 109,561 miles per hour

There yet remain a few observations on the motions of the planets, relating to the gravitating power of the Sun. If they moved round it in perfect circles and the Sun were in the centre, we can readily imagine that they would move through equal parts of those circles in equal times; for as each planet would, in that case, in every part of its orbit, be at the same distance from the Sun, its attractive power would always be alike, and the planet

would always move with the same velocity. But the Astronomer finding, from long continued observation, that the planets do not move in every part of their orbits with the same velocity, concluded that they could not move in circles. The observation that the planets do not always move with the same velocity, was the foundation of the law discovered by the famous Kepler, at which we have already hinted, but which we cannot wholly explain, because the illustration demands a knowledge of trigonometry and geometry. In a word, the planets move according to the laws of bodies revolving in ovals or ellipses; and Kepler discovering this, raised upon it a few simple and expressive rules, designating the planetary motions, and equally applicable to them. all. These rules must be correct; for by them the Astronomer is able precisely to calculate the return of a planet to any given point of its path.

Each planet revolves in an oval, and we have already shewn that the Sun is not in the centre of the oval, but in the lower focus. This being the case, each of the planets must be nearer to the Sun in one part of its orbit than in any other part; and when in the opposite part, the planet must be at its greatest distance from the Sun. Now it has been said that the attracting or gravitating power of one body for another, is proportioned to its distance; therefore, as the distance of every planet from the Sun is continually varying, the attractive power of the Sun must vary with the distance; and consequently, the rate at which it travels is increased and diminished according as its distance increases and diminishes; it moves quickest when nearest to the Sun, slowest in that part of its orbit which is most distant from the Sun. In the determination of this fact, observation and theory go hand in hand.

Hence, when it is said that Mercury moves in his orbit at the rate of 109,000 miles an hour, it is meant that he must on an average travel at that rate to complete his revolution in 87 days and 23 hours: it is his mean rate of travelling. When it is said that he is distant from the Sun 36 millions of miles-it is his mean distance. So also of the other planets.

As we are now noticing the discovery of the Astronomer, that the planets do not move through every part of their orbits with the same swiftness-an observation which I have already said was the foundation of the famous law of Kepler, I cannot refrain attempting to shew the nature of that law, even though it cannot be fully explained, without more mathematical knowledge than we can be supposed to possess. The law is this, a planet in moving round its orbit describes equal areas in equal times.

D

Let S be the Sun in the lower focus of the orbit of a planet. An area is the superficial dimension of any figure enclosed between lines. Let us suppose AS B to be an area, equal to another area CS D; they contain the same superficial quantity, though very different in shape. Then if these two areas are equal, and if a planet moves through equal areas in equal times, it will be the same time in moving from C to D as from A to B, though the space A to B is much the greater of the two.

The cause of the planet's much greater swiftness in this part of its orbit, is, that being nearer, and therefore more strongly attracted by the Sun, it moves with greater velocity than between C and D; for, being then furthest from the Sun, it is then least attracted and moves slowest.

The latter of the two preceding ovals or orbits is divided into 6 equal areas or portions, and supposing a planet to be 12 months in moving round the whole orbit, each of these divisions will be passed through in two months. Hence, as each division differs from that next to it, the rate at which a planet travels must vary continually.

Kepler, by the comparison of a multitude of observations on the planetary motions, also discovered the law by which their respective velocities are governed; namely, that the squares of their times of revolution are in proportion to the cubes of their mean distances from the Sun. For example, if one planet were four times as distant as another, it would revolve in a period eight times as long; for the cube of 4 is equal to the square of 8. Thus, Mars is about 4 times as remote from the Sun as Mercury, and the Georgium Sidus four times as remote as Jupiter, and their periods of revolution are nearly as long respectively.

All the planets move round the Sun from west to east; sometimes however they appear to move from east to west, which only occurs when they are in certain parts of their orbits. If we carry a ball round a hoop held in a horizontal direction, beginning at the west and proceeding to the east, we shall find that it appears after it has quitted the east, to move in a contrary direction. This motion is termed by the Astronomer retrograde-a planet is then said to be retrograde, or in retrogradation.