Chapter II: Part 2

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.

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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.”

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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.

TUTOR. It does so; and the inhabitants of London by this motion are carried at the rate of 560 miles an hour[13].

[Footnote 13: The hourly motion under the equator is 900 miles.]

PUPIL. What an astonishing rapidity!

TUTOR. Now, the sun with the rest of the heavenly bodies must move round the earth, or the earth must revolve on its axis in 24 hours, to cause that appearance.

PUPIL. That is plain.

TUTOR. Well then, great as you may suppose the velocity of the earth on its axis to be, if the sun move round the earth his hourly motion will be nearly 25 millions of miles; and beyond conception would be that of the fixed stars. Which now do you think is most probable, that the sun and stars should move round the earth, or that they, by the simple motion of the earth, should appear to be in motion?

PUPIL. The latter, to be sure, Sir.—I have one difficulty remaining, which is this; if a lark rise from a field near London and remain in the air a quarter of an hour, if the earth move at the rate of 560 miles an hour, it will go 140 miles whilst the lark is suspended, and yet it continues over the field,—how can this be?

TUTOR. This objection to the motion of the earth has been made by those who were older and who thought themselves wiser too than yourself. They either did not know or did not consider, that the atmosphere which surrounds the earth is a part of itself, and gravitates towards it, and therefore partakes of the earth’s motion and carries the lark along with it. Besides, as the Sun, Venus, Mars, and Jupiter are known to revolve on their axes, we have reason to suppose that the other planets, together with the earth, must have the same motion[14].

[Footnote 14: Dr. Herschell says that several of the fixed stars
revolve on their axes.]

PUPIL. How is it known that they do revolve on their axes; and in what time do they perform their revolutions?

TUTOR. By the assistance of telescopes dark spots have been seen on the disc of the sun, by the motion of which it is found that he revolves on his axis in 25-1/4 days; Venus performs her diurnal revolution in about 23 ho. 21 min.; Mars goes round his axis in 24 ho. 39 min.; and Jupiter in 9 ho. 56 min.; as to the rest, no spot or any fixed point has been discovered to ascertain the length of their day; Mercury being too near the sun, and Saturn and the Georgium Sidus too remote for our observations.

PUPIL. I can no longer doubt of the earth’s motion: and, if it will not be improper, a description of the atmosphere will give me pleasure.

TUTOR. That I can have no objection to. The atmosphere is a thin, invisible fluid, most dense or heavy near the earth, but grows gradually rarer or lighter the higher we ascend, so much so, that at the tops of some high mountains it is difficult to breathe. It serves not only to suspend the clouds, furnish us with wind and rain, and answer the common purposes of breathing, but is also the cause of the morning and evening twilight, and of all the glory and brightness of the firmament.

PUPIL. How, pray?

TUTOR. If there were no atmosphere, the sun would yield no light but when our eyes were directed towards him; and the heavens would appear dark and as full of stars as on a dark winter’s night; but the atmosphere being strongly illuminated by the sun, reflects the light back upon us, and makes the whole heavens to shine so strongly, that the faint light of the stars is obscured, and they are rendered invisible.

PUPIL. I find then the atmosphere is of more use than I imagined. But how is it the cause of the twilight?

TUTOR. The atmosphere is about 45 miles above the surface of the earth, therefore the sun’s rays falling upon the higher parts of it before rising, by reflection causes a faint light, which increases till he appears above the horizon; and in the evening it decreases after he sets, till he is 18 degrees below the horizon, where the morning twilight begins, and the evening twilight ends.

PUPIL. By the horizon, I think you mean that distant boundary of our sight where the heavens and the earth seem to join all around us, as it appears from an eminence.

TUTOR. The very same. ’Tis that imaginary circle which intercepts from our view the sun, moon, and stars each night; and when, by the rotation of the earth, they appear to descend below it, we say they are set; as on the contrary, each morning, when they appear above it, we say they rise.

“To find the spacious line, cast round thine eyes,
“And where the earth’s high surface joins the skies,
“Where stars first set, and first begin to shine,
“There draw the fancy’d image of this line.”

PUPIL. A very pleasing description, indeed.

TUTOR. You will remember that this is called the _rational horizon_; but that which respects land and water is called the _sensible horizon_. The former divides the heavens into two equal parts, and is 90 degrees distant from a point directly over our heads, called the _zenith_, and the opposite point of the heavens directly under our feet, called the _nadir_.—But I must resume the subject of the atmosphere.

PUPIL. Had I not thought you had finished your description of the atmosphere, I should not have presumed to interrupt you.

TUTOR. What I have told you respecting the horizon is necessary for you to be acquainted with; therefore, the suspension is immaterial.—You must, I make no doubt, have observed the sun and moon at rising and setting to appear larger than when higher above the horizon.

PUPIL. I have, frequently, Sir.

TUTOR. And cannot you tell the reason of it?

PUPIL. No, Sir.

TUTOR. The reason is this: In viewing them, when near the horizon, you see them through a thicker medium than when they are higher, that is, you see them through a greater quantity of the atmosphere; and you not only see them larger, but really above the horizon whilst they are actually below it.

PUPIL. How do you account for this, Sir?

TUTOR. Light, like material bodies, if it meet with no obstruction, will move in right lines; now, the rays of the sun in coming to the earth must pass through a great quantity of the atmosphere, which being a fluid, refracts or bends the rays of light, by which refraction it is that we are favoured with the sight of the sun 3-1/4 minutes every morning before he rises above the horizon, and every evening after he sinks below it, which in one year amounts to more than 40 hours. This refraction is greatest near the horizon, and ends in the zenith.

PUPIL. Pray, Sir, can you make this clearer by an experiment?

TUTOR. I have just thought of one. Take a bason filled with water, and a strait stick or piece of wire; put it perpendicularly into the water, that is, that it lean neither way, and there will be no refraction; incline it a little towards the edge of the bason and it will appear a little bent at the surface of the water; incline it still more, and the refraction will be greater.

PUPIL. I have often seen this appearance when I have put my stick into water, but did not before know the cause.

TUTOR. You may try one more experiment. Pour the water out of the bason, and set the bason on the floor; put a guinea into it, and let it represent the sun.—Why do you smile?

PUPIL. Because I have not the sun’s representative to try the experiment with.

TUTOR. Well, well, put a shilling into the bason and call it the moon, and it will answer the same purpose:—Walk backward till you just lose sight of it, then the right line from your eye continued over the edge of the bason must pass beyond the money at the bottom of it.

PUPIL. That is evident.

TUTOR. Keep your position, and desire some friend to pour the water gently into the bason so as not to remove the money, and you will clearly distinguish it. Now, if you call the edge of the bason the horizon, the water the atmosphere, and the shilling the moon, is it not clear that you will see it above the horizon, when it is really below it?

PUPIL. I think so, Sir.

TUTOR. Well, try the experiment, and let me know the result when I next see you.

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DIALOGUE IX.

TUTOR.

I presume, Sir, you have made the experiment I recommended to you.

PUPIL. I have, Sir; and am so well convinced of what you told me, that nothing farther need be said on the subject.

TUTOR. As that is the case, I shall proceed.—I dare say you do not forget what the plane of the ecliptic is.

PUPIL. I do not, Sir; but have a perfect recollection of it.

TUTOR. Now, remember, that the axis of the earth is not upright or perpendicular to the plane of the ecliptic, but inclines to, or leans towards it, 23-1/2 degrees, and makes an angle with it of 66-1/2 degrees.

PUPIL. An angle signifies a corner; but that cannot be the meaning here.

TUTOR. That is what is generally understood by an angle: but, in geometry, it means the meeting of any two lines which incline to one another, in a certain point. Now, if you conceive the axis of the earth to be one line, and the plane of the ecliptic the other, the point where they meet or cross each other will form an angle.

PUPIL. I think I understand it; but how can it contain 23-1/2 or 66-1/2 degrees?

TUTOR. You know what a degree is.

PUPIL. If I remember right it is the 360th part of a circle.

TUTOR. It is so: and the measure of an angle is an arc or part of the circumference of a circle, whose angular point is the center: and so many 360th parts as any arc contains, so many degrees the measure of the angle is said to be; thus, Z C P (Plate III. fig. 1.) makes an angle of 23-1/2 degrees, because the arc Z P contains 23-1/2 360th parts of the whole circle. Then if A B represent the plane of the ecliptic, and N C S the axis of the earth, as D N contains the same number of degrees as Z P, will not its inclination from a perpendicular be 23-1/2 degrees?

_T. Conder Sculp^t._]

PUPIL. Nothing can be plainer.

TUTOR. For the same reason, as P B contains 66-1/2 parts of the whole circle, the axis of the earth makes an angle of 66-1/2 degrees with the plane of the ecliptic. And, if you add 23-1/2 to 66-1/2 the sum will be 90, which is the measure Z B, or the fourth part of the circle, and makes what is called a right angle, at the point or center C.

PUPIL. It is very clear:—but what do the other letters refer to?

TUTOR. The extremities of the earth’s axis are called the poles, N the north, and S the south pole, and P the north-pole star, to which, and to the opposite part of the heavens, the axis always points. These extremities in the heavens appear motionless, whilst all other parts seem in a continual state of revolution: the circle of motion appears to increase with the distance from the apparently motionless points to that circle in the heavens which is at an equal distance between them, called the equinoctial, represented by the letters Æ Q; and is the same I promised some time ago to explain to you.

PUPIL. I recollect it: and as the line A B represents the plane of the ecliptic, I suppose the line Æ Q is the plane of the equinoctial, which I see crosses it as you then told me.

TUTOR. You are right: and it makes an angle with it of 23-1/2 degrees. It is called the equinoctial, because when the sun appears there, that is, in Aries or Libra, the days and nights are equal in all parts of the world, which I shall shew you in due time; and shall now explain to you what I have just mentioned, that the axis of the earth always points to the same parts of the heavens. I am apprehensive you will think it strange that this should be the case, and the axis keep parallel to itself.

PUPIL. What am I to understand by the axis being parallel to itself?

TUTOR. Two lines are said to be parallel when they do not incline to but keep at equal distances from each other; so that if they were infinitely continued, they would never meet. Now, if you can conceive a line drawn parallel to the earth’s axis in any part of its orbit, it will be parallel to it in every other part of it. A little drawing I have by me, (Plate III. fig 2.) where the earth is represented in four different parts of its orbit, I think will make this plain to you.

PUPIL. I comprehend your meaning clearly. But, as the orbit of the earth is 190 millions of miles in diameter, I have not the least conception how it can incline to the same points. Had you not told me to the contrary, I should have thought it must move round them in every revolution of the earth about the sun.

TUTOR. That such a motion would be perceptible is evident, if the fixed stars were near the earth; but, compared with their distance, 190 millions of miles is but a mere point: therefore, the axis always inclines to the same points of the heavens.

PUPIL. This is a greater proof of the inconceivable distance of the stars than what you mentioned before, and I thought that very astonishing:

Wonders on wonders constantly arise,
Whene’er we view the earth, or sea, or skies.

TUTOR. It is very true. And the more we search, the more we have cause to admire the works of the Almighty.

PUPIL. Pray, Sir, what is the next thing you propose?

TUTOR. To make you acquainted with the other circles you see in the figure (Plate III. fig. 1.) as it is very necessary you should know them.

PUPIL. Will you be kind enough to tell me their names, Sir, and I will endeavour to remember them?

TUTOR. That line which divides the globe into two equal parts, called the northern and southern hemispheres, which answers to the equinoctial in the heavens, and is equally distant from the two poles, is called the _equator_; the other which crosses it, as I before told you, is the _ecliptic_; the smaller circle, north of the equator, is the _tropic of Cancer_; that south of it, the _tropic of Capricorn_; the circles next the poles are called the _polar circles_; or that next the north pole, the _arctic circle_, and that next the south pole, the _antarctic circle_; each of which is 23-1/2 degrees distant from its respective pole, as are the tropics from the equator.

PUPIL. You have not mentioned the lines which cross the other circles, and terminate in the poles; what are they called?

TUTOR. They are called _meridians_, because when any of them, as the earth revolves on its axis, is opposite to the sun, it is mid-day or noon along that line. Twenty-four of these lines are usually drawn on the globe to correspond with the twenty-four hours of the day; but you are not to suppose there are no more than twenty-four; for every place that lies ever so little east or west of another place has a different meridian.—To make this clearer to you, we will suppose the upper 12 (Plate III. fig. 1.) to be opposite the sun, it will of course be noon along that line; the next meridian marked 1, being 15 degrees east, will have passed the meridian 1 hour, consequently it will there be one in the afternoon, and so on, according to the order of the figures, till you come to the lower 12, which being the part of the earth turned directly from the sun, it will be midnight on that meridian; on the next meridian, as you proceed round, it will be one in the morning, the next two, and so on till you arrive at the upper twelve, where you set off. So you see there must be a continual succession of day and night. This difference of time between places lying under different meridians is what is called longitude.

PUPIL. I think I have heard of a Mr. Harrison, who made a time-keeper for determining the longitude. Shall I trespass at all if I beg a little farther information on this subject?

TUTOR. It is my wish at all times to satisfy your curiosity, when I can do it with propriety. I shall therefore comply with your request.—Mr. Harrison’s time-keeper, and those made since by other artists, are so constructed, that the heat and cold of different climates will not affect them; for, all metals are more or less expanded by heat, and contracted by cold; for which reason it is, that a clock or watch made in the usual way will not keep equal time. Now, all that is required of these time-keepers to ascertain the longitude is this: Suppose a captain of a vessel sailing from London to the West Indies, we will say Kingston, in Jamaica. On his passage thither he makes an observation, and finds the sun on the meridian, or that it is twelve o’clock in that situation, when by his time-keeper it is two in the afternoon in London, whence he concludes he is 30 degrees west of London.

PUPIL. I must beg you to explain this to me, as I do not understand why two hours of time should be equal to 30 degrees of longitude.

TUTOR. You must consider, that as the earth makes a complete revolution on its axis in 24 hours, it must pass over 360 degrees in that time: now, if you divide 360 by 24, the quotient 15, will be the number of degrees passed over in one hour; 30 degrees will be equal to two hours, &c. The difference of time between London and his situation is two hours, consequently the difference of longitude must be 30 degrees: and, it must be west, because the sun had passed the meridian of London; for, as the earth revolves from west by south to east, one place which lies east of another must come first to the meridian or opposite to the sun. Therefore, when longitude is reckoned from London, if the place lie east of that meridian the time will be before; if west, after London.

PUPIL. I see it clearly; and as 60 minutes make an hour, if I divide it by 15, the quotient 4 will be the minutes answering to one degree.

TUTOR. You are right: and for the same reason, 4 seconds of time are equal to one minute of longitude, which you know is the 60th part of a degree.—Our captain when arrived at Kingston, finds the difference of time between it and London 5 ho. 6 min. 32 sec. Can you tell me the longitude of Kingston?

PUPIL. If I bring the hours and minutes to minutes, and divide by 4, the quotient I think will be degrees, will it not?

TUTOR. It will: and the seconds of time divided by 4, will be minutes of longitude. Now try if you can do it.

PUPIL. Five hours 6 minutes, multiplied by 60 will be 306 minutes, this divided by 4, will give 76 degrees and 2 over, which 2 is half a degree, or 30 minutes: and 32 seconds of time divided by 4, will be 8 minutes of longitude, the sum of which is 76 degrees 38 minutes for the longitude of Kingston.

TUTOR. Very well.—I have just now thought of another method of reducing time to longitude, and longitude to time, which you may probably find easier. However, when you are in possession of both, you may use which you please.

PUPIL. That which is easiest must, I think, be best.

TUTOR. I will give it you, and let me have your opinion of it.

To reduce time to longitude.

Multiply the hours, minutes, and seconds of time by 15, or
rather by the factors as they are called, namely 3 and 5,
carrying one for every 60 in the minutes and seconds, and
setting down the remainder, thus:

ho. min. sec.
5 6 32 difference of
3 time.
────────────────
15 19 36
5
────────────────
Degrees 76 38 0 longitude.
════════════════

Divide the degrees and minutes of longitude by 5 and 3 and the
quotient will be the difference of time.

PUPIL. I give this the preference.

TUTOR. As longitude is seldom mentioned without being accompanied with latitude, that you may not be ignorant of its meaning when you meet with it, I shall just tell you that it is the distance of any place from the equator, reckoned in degrees and minutes on the meridian, and is either north or south as the place lies north or south of the equator. The latitude of any place is equal to the elevation of the pole above the horizon. The latitude of the heavenly bodies is reckoned from the ecliptic, and terminates in the arctic and antarctic circles: and their longitude begins at the point Aries.

PUPIL. What is the measure of a degree?

TUTOR. A degree of latitude is 60 geographical, or 69-1/2 English miles: and a degree of longitude on the equator is equal to it, because the equator as well as the meridians divides the globe into two equal parts. But a degree of longitude decreases as you approach the poles: for at the poles the meridians meet in a point, consequently a degree there can have no dimension. To-morrow I will shew you the cause of the seasons.

------------------------------------------------------------------------

DIALOGUE X.

PUPIL.

I think, Sir, when you left me last night you told me our next business would be to explain the nature of the seasons?

TUTOR. I did so, and am persuaded you will find no great difficulty in comprehending it.—Cast your eye on the little drawing I gave you, (Plate III. fig. 2.) where the earth is represented as situated at the four quarters of the year, namely, Spring, Summer, Autumn, and Winter.—But before we proceed to an explanation it will be necessary to remark, that, in the little scheme the eye is supposed to be elevated above the plane of the earth’s orbit, and that we see it very obliquely. The orbit by this means appears very elliptical; and, the enlightened hemisphere, or that half of the earth which is turned to the sun in the spring, and the darkened hemisphere, or that turned from him in the autumn, are there represented.

PUPIL. This I understand.

TUTOR. Well then, we will begin with the spring.—In this situation of the earth the equator is exactly opposed to the sun: and, as he always enlightens a hemisphere, or half of its surface, his rays will reach to both the poles: whence, from the diurnal revolution of the earth, the day and night are equal all over the globe.

PUPIL. This I remember you told me happened when the sun was in Aries and Libra. The sun is now entering Aries: and, as we are in the rays of the sun one half of the diurnal revolution, and in the shadow of the earth, or dark, the other half, the day and night must be equal.

TUTOR. Certainly. And as the sun enters Aries in the equinoctial, it is then called the _Vernal_, that is, _Spring Equinox_. When the sun enters the opposite sign Libra, the same effects are produced, and it is then called the _Autumnal Equinox_.

PUPIL. You have passed on from Spring to Autumn.

TUTOR. I have so.—We will now return, and trace the earth in its orbit from spring to summer.—You have already seen that the north and south poles are both enlightened, and that the day and night are equal at the equinoxes. If the axis of the earth were perpendicular to the plane of the earth’s orbit, this would constantly be the case, and we should have no diversity of seasons: for, the sun being over the equator, the poles must be perpetually enlightened, and of course we should have equal day and night at all times of the year.

PUPIL. That is plain. I suppose then that it is to the inclination of the earth’s axis we are indebted for the increase and decrease of days.

TUTOR. It is occasioned by the inclination of the earth’s axis and its preserving its parallelism, which I explained to you last evening.—As the sun is now in the first point of Aries, the earth you know must be in the beginning of Libra, it being the opposite sign.—Now fix your attention on the scheme, and imagine the earth to be advancing in its orbit through Libra, Scorpio, and Sagittarius: and at the first degree of Capricorn give me your opinion of the earth’s position.

PUPIL. The north pole is turned to the sun, the south pole from him, and the tropic of Cancer is opposite to him.

TUTOR. How many degrees are the tropics from the equator, or, in other words, what is the inclination of the earth’s axis?

PUPIL. Twenty-three degrees and a half.

TUTOR. And so far are the rays of the sun cast beyond the north pole, and fall short of the south pole: so that the whole of the arctic circle is enlightened, and the antarctic circle involved in darkness.

PUPIL. What conclusion am I to draw from this?

TUTOR. That in the northern half of the globe it is the longest day, or summer, and in the southern half the shortest, or winter, whilst under the equator the days and nights are equal.

PUPIL. I used to think that when it was winter or summer here it was so in every part of the world.

TUTOR. You now find your mistake. For as the earth is making its progress from Libra, the north pole is approaching the sun, and the south pole receding from him: consequently the length of the day is increasing in the northern hemisphere and decreasing in the southern.—The sun has now been three months above the horizon of the north pole, and the same time below that of the south pole, and in three months more, when the earth arrives at Aries, the scene will be reversed: the sun will be over the equator, both poles will be again enlightened, and the day and night will be equal in every part of the globe. The sun will now be rising to the south and setting to the north pole. This is our Autumn.

PUPIL. And as the earth is advancing towards winter, the south pole will be turning to the sun, and the north pole from him, whence I conclude that when the earth is in Cancer it must be summer, south of the equator, when it is our winter.

TUTOR. Most assuredly. For you see that the sun is over the tropic of Capricorn, which you know is as much south of the equator as the tropic of Cancer is north of it, where the sun was in our summer. The antarctic circle is now enlightened, and the arctic obscured in shade; but, under the equator there is neither increase nor decrease, the days and nights being each twelve hours.

PUPIL. It is now our winter, the sun has been three months above the horizon of the south pole, and will continue so till the vernal equinox, when he will again rise to the north pole, and so on in regular succession.

TUTOR. It must be plain then to you that there can be but one day and one night at each of the poles, reckoning the time the sun is above or below their respective horizons; under the arctic and antarctic circles, the longest day is twenty-four hours, and in the shortest the sun is just visible in the horizon at noon. The longest day decreases in length the nearer we approach the equator, where I before observed there is no variation, because the circle bounding light and darkness, in every position of the earth, divides the equator into two equal parts; and, it must be observed, that the longest day and longest night are equal to each other in every part of the globe.

PUPIL. If the longest day under the arctic circle be just twenty-four hours, the sun must rise in the north.

TUTOR. He does so, makes a complete circle and sets in the [15]north again. From the arctic circle to the equator, he rises north of the east and sets north of the west: at the equator he rises due east and sets due west, thence southward to the antarctic circle, he rises south of the east, and sets south of the west: and under the antarctic circle, as I observed just now, he is visible in the horizon in the south at noon.

[Footnote 15: Here it must be observed that there will be a little
variation from sun-rising to sun-setting, as the earth is advancing
in its orbit.]

PUPIL. We usually say, the sun rises in the east and sets in the west.

TUTOR. At the equinoxes it must be so in all parts of the globe, the poles excepted: in every other situation, except under the equator, there is a continual change. What I have now told you, respecting the northern hemisphere, will be reversed at our shortest day: that is, in the northern hemisphere the sun will rise south of the east and set south of the west; and, in the southern hemisphere the contrary, the sun will be in the horizon, at noon, under the arctic circle, and the day will be twenty-four hours under the antarctic circle.

PUPIL. Pray Sir, are the regions within the polar circles inhabited? If they are, their situation, in winter, must, I think, be dreadful.

TUTOR. It is foreign to my present purpose to speak of the inhabitants of the earth, as that more properly belongs to Geography. Thus much however I shall tell you, that, although it must be very cold and dreary, they are not so long deprived of light as you may imagine; for, even under the poles, when the sun is hidden from them, they are but a short time in total darkness, for, you must recollect, that the twilight continues till the sun is eighteen degrees below the horizon; and the sun’s greatest depression, you know, can be but twenty three degrees and a half, equal to the inclination of the earth’s axis. Besides this, the moon is above the horizon of the poles a fortnight together; being half her period north, and the other half south, of the equator; and, as the moon at full is in the sign opposite to the sun, the tropical full moons must be twenty-four hours above the horizon at the polar circles.

PUPIL. This description is very pleasing, as I had no idea of their being favoured with so much light in the absence of the sun: and, I find, as the sun is longer above the horizon in summer than in winter, the moon, on the contrary, continues longer with us in winter, when we most need her assistance, than she does in summer.

TUTOR. As you seem to understand what I have been explaining, I shall shew you, that the reason why it is hottest when we are farthest from the sun is, that in winter when we are nearest to him the days are shorter, his rays sail very obliquely on us, and are more dispersed than they are in summer, when he not only remains longer above the horizon, but being higher, his rays fall more direct on us, by which means the earth becomes so much heated that it has not time in the short nights to get cold again.—When the earth is nearest the sun it is summer in the southern hemisphere, therefore it is reasonable to suppose that the heat there must far exceed ours in the same latitude; but to counteract this their summer is shorter by eight days than ours: and it is well known that it is much colder near the poles in the southern than in the northern hemisphere: but this is accounted for from there being more land to retain the heat in the latter than in the former.

PUPIL. My doubts on this head being now removed, I must beg you to give me such other information as you may think proper.