Part 3

Aries, Taurus, Gemini, Cancer, Leo, Virgo. ♈ ♉ ♊ ♋ ♌ ♍ March, April, May, June, July, Aug. 20, 20, 21, 21, 23, 23.

SOUTHERN SIGNS.

Libra, Scorpio, Sagittarius, Capricorn, Aqua. Pisces. ♎ ♏ ♐ ♑ ♒ ♓ Sept. October, November, Decem. Jan. Feb. 23, 23, 21, 21, 20, 18.

PUPIL. Why do you write northern and southern signs, Sir?

TUTOR. Because they are situated north and south of a circle in the heavens, called the equinoctial, which circle crosses the ecliptic in the points Aries and Libra, and extends 23-1/2 degrees on each side of it; and which I shall have occasion to mention to you another time.

PUPIL. When you think proper, Sir, I shall be glad to have it explained to me.

TUTOR. Look at your table, and tell me what sign and what degree the sun is in the 30th of March, and 20th of October.

PUPIL. The sun enters Aries the 20th of March, of course he must be 10 degrees in that sign the 30th; and, as he does not enter Scorpio till the 23d of October, he must want three degrees of completing the sign Libra; he must therefore, on the 20th of October, be in 27 degrees of Libra.

TUTOR. Very well.—Do you learn the table, as you will have a farther use for it.

DIALOGUE VI.

PUPIL.

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.

DIALOGUE VII.

TUTOR.

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]

[Footnote 12: Dr. Herschel is of opinion, that bodies near the sun do not acquire so great a degree of heat as has been generally imagined.]

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.”

DIALOGUE VIII.

TUTOR.

I shall now, agreeably to my promise, explain to you the cause of day and night, and then proceed with the vicissitudes of the seasons.

PUPIL. That is what I much wish to know; and had you not told me that the earth moved round the sun every year, I should have found no difficulty in accounting for the succession of day and night, since the sun appears to rise and set every day.

TUTOR. That is true; but I think I must have convinced you that so immense a body as the sun cannot revolve about the earth; as well may you suppose that in roasting a bird it is necessary that the fire should move round it.

PUPIL. That I think would be very absurd, as it is much easier for the bird on the spit to turn to the fire, than for the fire to go round the bird.

TUTOR. You are certainly right, and if the earth revolve on its axis every twenty-four hours, will not the different parts of it be alternately turned to the sun, as the bird on the spit is to the fire?

PUPIL. I do not clearly comprehend what you mean by the axis of the earth; for, as it moves in open space and has no support, it can have nothing to resemble the spit on which it turns.

TUTOR. Certainly not. By the earth’s axis is meant an imaginary line passing through its center, on which it is supposed to turn; as your ball if rolled on the ground would revolve on an axis whilst it was moving forward.

PUPIL. I can now answer your question in the affirmative: and, as our year consists of 365 days, I imagine the earth must make as many revolutions on its axis whilst it is going once round the sun.

TUTOR. Undoubtedly: and as only one half of a spherical body can at any time be enlightened by a luminous body, that part of the earth only which is turned to the sun, can receive the benefit of his enlivening rays, when it will be day; whilst the opposite part will be involved in darkness, and it will be night.

PUPIL. I perceive it must be so. But, if the earth move in the manner you describe, I cannot conceive how it is that we are not sensible of its motion.

TUTOR. If the motion of the earth were irregular it would be perceptible; but as it meets with no obstruction the motion must be so uniform as not to be perceived.

PUPIL. Had I recollected this, I need not have given you this trouble.—But I am continually meeting with fresh difficulties.

TUTOR. You have only to mention what they are, and I shall take a pleasure in removing them.

PUPIL. I thank you, Sir; and shall be obliged to you to inform me, how the motion of the earth can cause the sun to appear to move?

TUTOR. When in a carriage which went smoothly on the road, or in a boat whose motion was scarcely perceptible on the water, did you never fix your attention on the objects you passed?

PUPIL. Yes, often, Sir.

TUTOR. And had you not known that you really moved, and that the trees, &c. were immoveable in the ground, what then would have been your opinion?

PUPIL. That the trees, &c. moved in a direction contrary to that in which I was moving.

TUTOR. Is not this sufficient to convince you that the apparent motion of the sun may be occasioned by the revolution of the earth on its axis?

PUPIL. It is:—But if so large a body as the earth make a revolution on its axis in 24 hours, it must move with great velocity.