Having at our last meeting explained to you the nature of the attractive and projectile forces, I shall proceed to shew you that it is by the joint action or combination of these two forces that the planets are retained in their orbits.

Pupil. I am all anxiety, as I wish to be informed how, or in what manner they can act against each other, to produce that effect.

Tutor. Answer me a few questions, and you will soon know.

Pupil. As many as you please, Sir.

Tutor. If you whirl a stone in a sling, what will be its motion?

Pupil. Circular.

Tutor. Is you let it suddenly slip out of the sling, will it continue its circular motion?

Pupil. No, Sir, but fly off in a strait line.

Tutor. This line you must remember is what mathematicians call the tangent of a circle, as A a, B b, &c. (Plate II. fig. 5.) for all bodies moving in a circle have a natural tendency to fly off in that direction. Thus a body at A will tend towards a; at B towards b, and so on; but the central force acting against it preserves its circular motion.

Pupil. By the central force here you mean the action of the hand, do you not?

Tutor. Yes. For, as soon as the stone is released and that power is lost, it assumes its natural, that is, its rectilineal motion.—Again. If you are left at liberty, cannot you run strait forward?

Pupil. Yes, Sir.

Tutor. Now, suppose one of your companions were to fasten a rope round your body, and at the extent of it were to stand still and hold it tight, with a force equal to that with which you run, could you, do you think, move in a strait line, that is, in a tangent of a circle?

Pupil. No, Sir. I must run in a circle.

Tutor. Why?

Pupil. Because, whilst the rope is extended I am prevented running in any other direction.

Tutor. Just so it is with the planets: the attractive or centripetal force of the sun being equal to that of the projectile or centrifugal force of the planets, they are by attraction prevented moving on in a strait line, and, as it were, drawn towards the sun; and by the projectile force from being overcome by attraction. They must therefore revolve in circular orbits.

Pupil. What I have so long wished is now accomplished. I understand it perfectly.

Tutor. What I have now explained relates not only to the primary planets which have the sun for their center of motion; but, you must remember that the secondary planets are governed by the same laws, in revolving about their respective primaries; for, as by the attractive power of the sun combined with the projectile force of the primary planets they are retained in their orbits; so also the action of the primaries upon their respective secondaries together with their projectile force, will preserve them in their orbits.

Pupil. Pray, Sir, what have you else to observe?

Tutor. Have I not told you that the orbits of the planets are not true circles, but a little elliptical?

Pupil. Yes, Sir; and I shall be glad to know the reason of it.

Tutor. If the attractive power of the sun were uniformly the same in every part of their orbits they would be true circles, and the planets would pass over equal portions of their orbits in equal times; that is, they would move from B to C, (Plate II. fig. 5.) in the same time as from A to B, &c.

Pupil. That is clear, but as their orbits are elliptical, when the planets are farthest from the sun, the velocity with which they move must be lessened as the attraction is decreased.

Tutor. And they must consequently pass over unequal parts of their orbits in equal portions of time. And, as a double velocity will balance a quadruple or fourfold power of gravity or attraction, it follows, that as the centripetal force is four times as great at A as at B (Plate II. fig. 4.) the centrifugal force will be twice as great, and would carry a planet from A to a in the same time it would from B to b, and in its orbit from A to c as soon as from B to d, and thereby describe the area, or space contained between the letters A S c, in the same time as the area or space B S d. For according to the laws of the planetary motions, in their periodical revolutions, they always describe equal areas in equal times.

Pupil. The orbits of the comets being very elliptical, the irregularity of their motions must be exceedingly great.

Tutor. Great, indeed!—One of them passed so near the sun as to acquire a heat which Sir Isaac Newton computed to be two thousand times hotter than red hot iron.^[12]

Pupil. Astonishing! If they pass so near the sun, the centripetal force must act powerfully on the body of the comet.

Tutor. And that force, you know, must be equalled by the projectile force; so you find they move when near the sun with amazing celerity.—But when arrived at their aphelion, where the influence of the sun is weak, what a transition!

Pupil. Wonderful, indeed!—Their motion is excessively slow, and the sun must appear little more than a fixed star. Surely they cannot be inhabited, can they?

Tutor. We cannot speak positively; but, as they differ so much from the planets, which we have reason to suppose are so, it is imagined they are designed for some purpose unknown to us.

Pupil. When is the earth in its perihelion?

Tutor. In December; and our summer half year is longer than the winter half, by about eight days.

Pupil. I suppose this is occasioned by the inequality of the earth’s annual motion.

Tutor. It is; and this inequality is the cause of the difference of time between the sun and a well regulated clock; the latter keeps equal time, whilst the former is constantly varying.

Pupil. I have often seen in the almanack clock fast, clock slow, but did not know the meaning of it: I imagine it is that the clock should be so much faster or slower than the time by the sun as is there mentioned.

Tutor. It is: but there are tables calculated to shew the difference of time for every day in the year; so that if you know the exact times of the day by the sun, and have one of these tables, you will see what the time should be by the clock, to a second, which is not shewn in a common almanack.

Pupil. In speaking of the annual or yearly motion of the earth, you have no where mentioned the cause of the seasons; will it be agreeable to do it now, Sir?

Tutor. The vicissitudes of the seasons, the cause of day and night, &c. shall be the subject of future lessons: we shall find sufficient to employ us at present.

Pupil. I think you told me just now that the earth is nearest the sun in December; that is our winter; this seems a little mysterious.

Tutor. It may appear so to you now, by-and-by you will be of a different opinion. I shall explain this matter to you with that of the seasons, &c.

Pupil. I fear I have interrupted you.—As you said you had sufficient employment for us, I shall be glad to know what it is.

Tutor. Hitherto I have spoken of the sun’s being fixed, and that the planets revolve about him as a center. Instead of which the sun and planets move round one common center, called the center of gravity.

Pupil. What is this center of gravity?

Tutor. Have you never seen a person raise a heavy weight by means of a long pole or leaver, which it was not in his power to lift without it?

Pupil. Yes, Sir, and it excited my astonishment.

Tutor. Now, suppose the weight to see raised to be 10 Cwt. and the prop on which the leaver rested 1 foot from the body to be raised; and the person at the other end of the leaver 10 feet from the prop; with what weight must he press to raise the 10 Cwt.?

Pupil. I think that very easy; for, as he is ten times as far from the prop as the weight is, a pressure of 1 Cwt. which is one-tenth of the weight to be raised will do it.

Tutor. To be sure; and yet you say you were astonished when you saw it! Every thing we do not understand at first appears difficult.—To apply this to our present purpose. You see that a weight of 1 Cwt. at 10 feet from a prop, will balance another of 10 Cwt. at one foot from it. Now, instead of a prop let the two weights be nicely poised on a center, round which they may freely turn; the heaviest would move in a circle, whose radius, or distance from the center would be one foot, whilst the lightest would move in one 10 feet from the center in the same time.

Pupil. Is the center round which they move the center of gravity?

Tutor. It is; and round an imaginary point as a center the sun and planets move, always preserving an equilibrium. If the earth were the only attendant on the sun, as his quantity of matter is 200,000 times as great as that of the earth, he would revolve in a circle a 200,000th part of the earth’s distance from him, in the same time as the earth is making one revolution in its orbit, or in one year; but, as the planets in their orbits must vary in their positions, the center of gravity cannot be always at the same distance from the sun.

Pupil. If it were, the balance could not be preserved.

Tutor. Clearly so. But you must know that the quantity of matter in the sun so far exceeds that of all the planets together, that even if they were all in a line on one side of him he would never be more than his own diameter distant from his center of gravity; therefore, astronomers consider the sun as the center of the system, and express themselves accordingly.

Pupil. As you told me the secondary planets are governed by the same laws as the primaries, I imagine they also with their primaries move round a center of gravity.

Tutor. They do so.—The earth and moon, Jupiter with his satellites, Saturn and his attendants, revolve about their respective centers; these, with the sun and the rest of the planetary system, make their circuits round their center; every system in the universe is supposed to revolve in like manner; and all these together to move round one common center.—How are we lost in contemplating the omniscience of the Deity! How difficult to conceive so many millions of bodies of dead matter constantly in motion, so nicely balanced and governed by such unerring laws!—Well may we say with the Psalmist, “Lord! how manifold are thy works, in wisdom hast thou made them all.”