Since I was last with you, Sir, I have been thinking of what you then told me, that the planets perform their revolutions in open space: I have not the least idea how this can be; if convenient, I shall be happy to have it explained.

Tutor. It will be necessary first to inform you, that the orbits or paths described by the revolution of the planets round the sun, are not true circles (as Plate II. fig. 2.) but somewhat elliptical, that is, longer one way than the other, as fig. 3.

Pupil. This is exceedingly plain.

Tutor. In a circle, the periphery or circumference is equally distant from a point within called its center, as A; but an ellipsis has two points called the focuses or foci, as B C. In one of these, called its lower focus, is the sun: so that you see in every revolution of the planet it must be nearer to the sun in one part of its orbit, than it is in another.

Pupil. I see it clearly.

Tutor. Now let S (Plate II. fig. 4.) represent the sun, A B C D a planet in different parts of its orbit; when it is nearest to the sun, as at A it is said to be in its perihelion; when at B its aphelion; but when at C or D its middle or mean distance, because the distance S C or S D is the middle between A S the least and B S the greatest distance; and half the distance between the two focuses is called the eccentricity of its orbit, as S E or E F.

Pupil. This I will endeavour to understand; but I find it will take me some time to be perfected in it.

Tutor. You may study it at your leisure, as it will not prevent our proceeding to the thing proposed, namely, the laws which govern the motion of the planets, or ATTRACTION OF GRAVITATION.

Pupil. By attraction I think you mean that property in bodies whereby they have a tendency to approach each other. I remember you told me that the magnet I had the other day attracted the needle.

Tutor. Yes. And you may recollect that when I took a feather suspended by a thread, and put it near the conductor of the electrical machine, it was strongly attracted by it, and adhered to it as long as the machine was kept in motion.

Pupil. I remember it well. But what am I to understand by attraction of gravitation?

Tutor. The sun, being the largest body, attracts the earth and all the other planets, they gravitate or have a tendency to approach the sun; the earth being larger than the moon attracts her, and she gravitates towards the earth; the planets are attracted by and gravitate towards each other; a stone when thrown from the earth, by its attraction and the gravitating power or weight of the stone, is brought to the earth again; the waters in the ocean gravitate towards the center of the earth; and it is by this power we stand on all parts of the earth with our feet pointing to the center.

Pupil. This information affords me great pleasure.

Tutor. Having mentioned attraction of magnetism, electricity, and gravitation, it may not be amiss to inform you of another kind, called attraction of cohesion.

Pupil. Any thing which tends to my improvement, I shall be obliged to you to communicate.

Tutor. By attraction of cohesion is meant that property in bodies which connects or firmly unites the different particles of matter of which the body is composed.

Pupil. Pray, Sir, inform me what you mean by the laws of attraction?

Tutor. You are to understand, 1st. That attraction decreases as the squares of the distances between the centers of the attracting bodies increase.

Pupil. I must beg you, Sir, to explain to me the meaning of the squares of the distances.

Tutor. Any number multiplied into itself is a square number, thus 1 is the square of 1; 4 is the square of 2; 9 is the square of 3, and so on, because 1 multiplied into itself is 1; 2 by 2 is 4; 3 by 3 is 9, &c. Now suppose, that when the planet is at B (Plate II. fig. 4.) it is twice as far from the sun as it is at A: how much more will it be attracted by the sun at A than at B?

Pupil. You say, Sir, that the distance is twice as great at B as at A?

Tutor. I do.

Pupil. Then as the square of the distance 2 is 4, the decrease of attraction at B, the planet at A will be attracted with four times the force it would be at B.—Am I right, Sir?

Tutor. Perfectly so. And if the distance at B were three times as great as at A, it would be attracted with a force nine times as great.

Pupil. I perceive it must be so.

Tutor. I shall now give you the 2d law, namely, That bodies attract one another with forces proportionable to the quantities of matter they contain.

Pupil. Do all bodies of the same magnitude contain equal quantities of matter?

Tutor. No, certainly: For a ball of cork may be as large as one of lead, and yet not contain the same quantity of matter, because it is more porous, and not so compact or dense a body as the lead; neither will a ball of lead of the same magnitude as one of gold contain an equal quantity of matter.—So the sun, though a million of times as big as the earth, contains a quantity of matter only 200,000 as great, therefore attracts the earth with a force 200,000 as great as the earth attracts him.

Pupil. I think this is clear.

Tutor. We will now suppose that in the river are two boats of equal bulk, at the distance of twenty yards from each other, and that a man in one boat pulls a rope which is fastened to the other, what effect will be produced, or where do you think the boats will meet?

Pupil. Had you not told me that bodies attract one another with forces which are proportioned to the quantities of matter they contain, I should say the boat to which the rope is fastened would come to that in which the man stands: but as I imagine you mean to apply this to attraction, by the above rule, they will meet at a point which is half way between them.

Tutor. If one boat were three times the bulk of the other, how then?

Pupil. The lightest would move three times as far as the heaviest, or 15 yards whilst the heaviest moved only 5.

Tutor. Upon my word you reason philosophically. In both cases you are perfectly right.

Pupil. As the sun is so immense a body that his quantity of matter is so much greater than the planets, I am at a loss to know why they are not by the power of attraction drawn to him.

Tutor. And so they would if the attractive power were not counteracted by another of equal force.

Pupil. Did you not say, Sir, that the planets are kept in their orbits by attraction?

Tutor. I did. But you find that by attraction only the sun would draw all the planets to himself.

Pupil. That is evident. But I wish to know what this counteracting power you speak of is?

Tutor. I will tell you presently.—You must remember that simple motion is naturally rectilineal, that is, all bodies, if there were nothing to prevent them, would move in strait lines.

Pupil. Then as the planetary motion is circular, it cannot be simple?

Tutor. No. It is a compound of the two forces I have been mentioning: the one is called the attractive or centripetal force; the other, the projectile or centrifugal force.

Pupil. The former I clearly comprehend, but not the latter. I can conceive, that if two bodies approach each other by attraction they must move in a right line.

Tutor. If you shoot a marble on a smooth piece of ice, in what direction will it run?

Pupil. Strait forward.

Tutor. This is a projectile force.—Could you, do you think, shoot it in any other direction?

Pupil. No, Sir.

Tutor. Then is not this motion also rectilineal?

Pupil. It is.

Tutor. When you strike a ball with your cricket-bat, or throw a stone with your hand, is it not projected or thrown forward by the force of the bat or hand?

Pupil. Certainly.

Tutor. And does it not move in a strait line?

Pupil. At first it appears to do so; but afterwards it inclines towards and falls to the earth.

Tutor. Cannot you account for this?

Pupil. I suppose it must be drawn to the earth by attraction.

Tutor. You are right. The attraction of the earth, and the resistance of the atmosphere or air through which it moves, retards its progress, or it would continue moving in a strait line, with a velocity equal to that which was at first impressed upon it. In like manner the beneficent Creator of the Universe impressed a force on all the planets which should be equal to that of the attractive power of the sun, that one might not overcome the other.

Pupil. This wants explaining.

Tutor. I would willingly gratify you, but as I have much more to say on the subject, I fear it will be too great a burthen on your memory; it will therefore be better to postpone it.

Pupil. As you please, Sir.