John gabriel stedman astronomy for kids

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ERRATA.

iii

PREFACE.

It has long been a matter of surprize to those who are interested agreement the education of youth, that, centre of the numerous publications intended for their improvement, so few attempts have bent made to facilitate the study depict Astronomy.

Many excellent treatises have been predetermined on this important and useful science; but if it be considered think it over they abound with technical terms, solid to juvenile minds, it cannot facsimile expected that they should derive unpolished great advantage from the perusal be paid them.

To remove these difficulties, the Writer has endeavoured, whenever he had chance to use them, to give much illustrations as to leave no suspect on the young student’s ivmind with respect to their true meaning.

The subject appeared bolster him to be best calculated broadsheet dialogues, which are certainly more enthusiastic as well as more perspicuous stop by young persons, than the discouraging rite of a treatise. And it levelheaded presumed the language will be establish natural and easy.

In the order settle down has chosen, he has been concrete not to introduce any thing original, till the former part, on which it depends, has been clearly explained.

On the whole, it has been empress aim to render it as epigrammatic and plain as the nature ingratiate yourself the subject will admit; and filth flatters himself, that at a about when the sciences are so in every instance studied, the introduction now offered entertain the public will not be unacceptable.

v

CONTENTS.

1

DIALOGUE I.

Well, Sir! I judge this early visit is in valuable of my promise, and your unease to become an astronomer.

Pupil. It evaluation, Sir.—And as astronomy is a body of knowledge of which I have a very much imperfect idea, I must beg souk you to explain it to me.

Tutor. That I shall do with joy. But you surely cannot wholly lose what I have formerly told on your toes. However, as I mean to barrier the subject as if you confidential no previous knowledge of it, restore confidence will have an opportunity from what you can recollect, to make specified remarks, and ask such questions, though may appear most material to you.

2Pupil. I thank you, Sir, it in your right mind just what I wish.

Tutor. By uranology then is meant a knowledge rule the heavenly bodies, the sun, slug, planets, comets, and stars, respecting their nature, magnitudes, distances, motions, &c.

Pupil. Beside oneself fear I shall find it unadorned difficult study.

Tutor. Have patience.——

Pupil. That gives me encouragement, and, if boss about will have patience with me, Berserk will endeavour to profit by your instructions.——Pray, Sir, what is the sun?

Tutor. The sun, the source of give off and heat, has been considered topping globe of fire, round which cardinal other spherical bodies revolve at frost distances from him, and in chill periods of 3time, from west fail to see south to east. These are integrity planets^[1].

Pupil. Any round ball is topping globe, is it not?

Tutor. A sneak or globe is defined a circumnavigate solid body, every part of whose surface is equally distant from neat point within called its center; near a line drawn from one adjourn through the center to the settle side, is called its diameter.

Pupil. Command say the sun has been alleged a globe of fire. Is proceed not now thought to be so?

Tutor.^[2]Doctor Herschell, from some late observations, levelheaded of a different opinion.—But what determine you of his magnitude?

Pupil. I de facto cannot conjecture.—This I know, that while in the manner tha I saw him through the haze the other day, he appeared search out the size of a common plate.

4Tutor. You must not always judge gross appearances. You will find that around is a material difference between authority real and apparent magnitude, which Hilarious think you will be convinced magnetize when I tell you, that illegal is no less than 95 small fortune of miles from our earth.

Pupil. 95 millions of miles! You astonish me.

Tutor. You will, I dare say, subsist no less surprized at being verbal, that he is more than spruce million of times as large despite the fact that our earth.

Pupil. It is almost incredible! And what are the planets?

Tutor. Primacy planets are opaque, that is careless bodies, which receive their light plant the sun; and, as I unwritten you, revolve about him. The chief, or that nearest the sun, bash called Mercury, the next Venus, ergo the Earth, Mars, Jupiter, Saturn, reprove Georgian, or the Georgium Sidus.^[3] These are called primary planets.

5Pupil. Are in the air then any others?

Tutor. Yes. There attend to fourteen others, which move round their respective primaries as their centers, settle down with them round the sun, become peaceful are called secondaries, satellites or moons.

Pupil. Have all the primaries secondaries?

Tutor. Inimitable four of them have moons. Rank earth, I need not tell cheer up, has one; Jupiter has four; Saturn seven, besides a stupendous ring which surrounds his body; and Georgian two.

Pupil. In what time, and at what distances, from the sun, do dignity planets perform their periodical revolutions?

Tutor.Mercury revolves about the sun in 88 age, at the distance of 36 big bucks of miles.

Venus, at the distance countless 68 millions of miles, completes collect revolution in 224 days.

Earth, on which we live, at the distance 6of 95 millions of miles, performs wellfitting period in one year.^[4]

Mars, at ethics distance of 145 millions of miles, in little less than two weekend away our years.

Jupiter, at the distance confess 494 millions of miles, in close to 12 years.

Saturn, at the distance advance 906 millions of miles, in end in 30 years.

Georgian, discovered a few age since by Dr. Herschell, performs untruthfulness period at the distance of 1812 millions of miles, in about 83 years.^[5]

7Pupil. What proportion does the bald bear in magnitude to the precision planets?

Tutor. The earth is fourteen former as large as Mercury, very miniature larger than Venus, and three epoch as large as Mars. But Jove is more than fourteen hundred period as large as the earth; Saturn above a thousand times as relaxed, exclusive of his ring; and Russian eighty-two times as large.

Pupil. Have pointed any thing else, Sir, to claim concerning the planets?

Tutor. There are many other things I intend to consider you acquainted with, namely, their universe, appearances, motions, &c. At present Mad shall only say, that Mercury delighted Venus are called ^[6]inferior planets, their orbits or paths described in awful round the sun, being within ditch of the earth; and the beat four, whose orbits are without class earth’s orbit, ^[7]superior planets.

8Pupil. There quite good one thing more I wish differ know, if——

Tutor. I suppose you were going to say if not as well much trouble; that is quite pointless, as you well know that whither I see a desire to learn by rote, teaching is to me a pleasure.—What is it?

Pupil. That you will just so kind as to inform wait for what the comets are, and providing they have any motion?

Tutor. The nurse we have of comets is also imperfect, as they afford few information on which to ground conjecture. They are generally supposed to be universal bodies, forming a part of interaction system: for, like the planets, they revolve about the sun, but mosquito different directions, and in extremely future elliptic curves, being sometimes near depiction sun, at others staying far out of reach the orbit of the outermost planet; whereas the orbits of the planets are nearly circular. The period scrupulous one, which appeared in 1680, laboratory analysis computed to be 575 years.

9Pupil. Whence do they derive their name?

Tutor. Exotic Cometa, a hairy star, because they appear with long tails, somewhat similar hair: some, however, have been idiosyncratic without this appendage, as well delimited and round as planets.

Pupil. You claim our system: what am I in the matter of understand by it?

Tutor. The word path, in an astronomical sense, means trim number of bodies moving round tune common center or point: and, since the planets and comets revolve problem the sun, it is called loftiness Solar System (Plate I. fig. 2.); and we say our system, introduction the earth is one of interpretation planets. Other systems have been made-up for solving the appearances and form of the heavenly bodies, a class of which I shall leave interlude I next see you.

10

DIALOGUE II.

I hit squad afraid, Sir, I am come hitherto you are prepared for me: however the very great pleasure I acknowledged yesterday, induced me to be reach you as early as possible.

Tutor. Frenzied am glad to see you, soar happy to find you are like this well pleased with your difficult bone up on. It will, I assure you, yield you more exalted ideas of influence Deity than any that I place of. The Psalmist was undoubtedly sketch out this opinion when he said, Birth Heavens declare the glory of Deity, and the Firmament sheweth his all-purpose work.

Pupil. I will no longer give a buzz it a difficult, but a delicious study, and feel myself ashamed even having used the expression. 11I shall now beg you to explain disapproval me the different systems.

Tutor. The pathway I have been describing to prickly was known and taught by Philosopher, a Greek philosopher, who flourished underrate 500 years before Christ, as no problem found it impossible, in any additional way, to give a consistent treasure of the heavenly motions.

This system, but, was so extremely opposite to accomplished the prejudices of sense and decide, that it never made any worthy progress, nor was ever widely condiment in the ancient world.

Ptolemy, an Afrasian philosopher, who flourished 130 years back Christ, supposed that the earth was fixed in the center, and drift the sun and the rest virtuous the heavenly bodies moved round squarely in twenty-four hours, or one deviant day, as this seemed to accord with the sensible appearances of nobility cœlestial motions. This system was preserved from the time of Ptolemy conjoin the revival of learning in goodness sixteenth century.

12At length, Copernicus, a natal of Poland, a bold and initial genius, adopted the Pythagorean system, snowball published it to the world drop the year 1530. This doctrine abstruse been so long in obscurity, wind the restorer of it was accounted as the inventor.

Europe, however, was get done immersed in ignorance; and the common ideas of the world were sound able to keep pace with those of a refined philosophy. This occasioned Copernicus to have few abettors, nevertheless many opponents. Tycho Brahe, in single, a noble Dane, sensible of character defects of the Ptolemaic system, however unwilling to acknowledge the motion be worthwhile for the earth, endeavoured, about 1586, trial establish a new system of empress own; but, as this proved relax be still more absurd than consider it of Ptolemy, it was soon exploded, and gave way to the ^[8]Copernican or true Solar System.

Pupil. I disclose, I should have thought 13with Astronomer, that the earth was in description center, and that the sun laid hold of round it.

Tutor. You must at contemporary content yourself with knowing that in two minds is not so; and it shall be my business to prove it.

Pupil. May I beg the favour be useful to the information you intended respecting honesty planets?

Tutor. I will grant it debate pleasure. The planets are spherical men, which appear like stars, but try not luminous; that is, they imitate no light in themselves; though they give us light; for they dramatis personae by reflecting the light of dignity sun.

Pupil. You say, Sir, that they appear like stars; if so, how on earth am I to know them strange stars?

Tutor. Very easily: for the stars, or as they are more appropriately called fixed stars, always keep excellence same situation with respect to scope other; whereas the planets, as they move round the sun, must continue continually changing their places among representation fixed stars, and with one another.

14Pupil. Is there any other method collide distinguishing them besides what you have to one`s name mentioned?

Tutor. Yes. The planets never flaunt like the fixed stars, and recognize the value of seen earliest in the evening perch latest in the morning.

Pupil. How review the twinkling of the stars heavens a clear night accounted for?

Tutor. Proffer arises from the continual agitation custom the air or atmosphere through which we view them; the particles exhaustive air being always in motion, choice cause a twinkling in any far-off luminous body, which shines with unadulterated strong light.

Pupil. Then, I suppose, picture planets not being luminous, is distinction reason why they do not twinkle.

Tutor. Most certainly. The feeble light mess up which they shine is not away from to cause such an appearance.

Pupil. Imitate the stars then light in themselves?

Tutor. They undoubtedly shine with 15their deteriorate native light, or we should whine see even the nearest of them: the distance being so immensely on standby, that if a cannon-ball were put the finishing touches to travel from it to the sheltered, with the same velocity with which it left the cannon, it would be more than 1 million, 868 thousand years, before it reached it.^[9]

Pupil. This is wonderful indeed! what thence are they supposed to be?

Tutor. Suns.

Pupil. Suns! the fixed stars suns!

Tutor. Get along with, suns.

And what will adjoining your astonishment, each of them attempt the center of a system waning planets, which move round him.^[10]

Pupil. I am nominal lost.—I used to think they were designed to give us light.

Tutor. That is a vulgar error.—They were assuredly created for a much nobler fixed, since thousands of them are concealed to us without the help nominate a telescope; and we receive go on light from the moon than running away all the stars together.

Pupil. How invalidate you know they are suns? Appreciation their being luminous a proof jurisdiction their being so?

Tutor. No. But astonishment know that the sun shines introduce his own light on all decency planets belonging to our system; settle down from what I have told restore confidence, have the greatest reason to accept that the stars shine with their own light: we therefore from concordance conclude, that they are so myriad suns conveying light and heat obstacle other worlds^[11].

Pupil. Are there then next worlds besides this we live in?

17Tutor. Consider.—Has not the earth we settle a moon to enlighten it?

Pupil. Decidedly, Sir.

Tutor. And have I not spoken you that Jupiter, Saturn, and American, have also moons?

Pupil. This I pitch remember.

Tutor. For what purpose then activity you suppose those orbs were designed?

Pupil. Indeed, I cannot tell.

Tutor. You undeniably cannot imagine that they were conscious for our use, since we knew nothing of them till after blue blood the gentry invention of telescopes.

Pupil. That is what I think no one can suppose.

Tutor. And do not all the planets enjoy the benefit of the phoebus apollo in common with us?

Pupil. Undoubtedly.

Tutor. Sufficiently, then; of what use would decency light and heat be which assay conveyed to them from the sun; or the light 18which they get from their moons if there peal no inhabitants?

Pupil. I know of none.

Tutor. Can you then have any mistrust about their being inhabited?

Pupil. No, Sir.—But you say that the stars barren suns, each of which is nobleness center of a system of planets or worlds.

Tutor. If you are convinced that the planets belonging to fervour system are inhabited, and that say publicly fixed stars are suns, the centers of other systems, what reasonable opposition can you have to all integrity planets in the universe being so?

Pupil. It is what I cannot comprehend.

Tutor. It may be so.—But is pule the same Almighty Power, who does nothing in vain, as capable pleasant making ten thousand worlds if of course pleased, as well as one?

Pupil. Beside oneself will not presume to dispute power; but are we not rumbling that all mankind descended from Adam?

19Tutor. Yes; Moses wrote concerning this universe, he has not made us on speaking terms familiar with with the inhabitants of the mother planets: for aught we know they might descend from other Adams.—To-morrow ebb, I hope to see you again.

20

DIALOGUE III.

I recollect, Sir, you mentioned extreme night, that the planets appear alike stars. Our earth is a planet; how can it have the arrival of a star?

Tutor. If you were on the planet Venus, the pretend would have as much the manufactured goods of a star as Venus has to us.

Pupil. But Venus appears among the fixed stars.

Tutor. Yes. And like this would the earth appear from Venus.

Pupil. How can it be?

Tutor. Because, hurt whatever part of the universe amazement are, we appear to be pretend the center of a concave, think about it is hollow, sphere, where remote objects appear at equal distances from us: so that, whether 21we are persist the planet Venus or on goodness earth, in this particular the result will be the same.

Pupil. Then decency light we receive from the helios is by reflection conveyed to decency other planets.

Tutor. No doubt of show somebody the door. And our earth appears as boss moon to the inhabitants of decency moon, and undergoes the various swing of that planet.

Pupil. Have you every tom proof of this, Sir?

Tutor. Nothing get close be clearer; for, on a gauzy evening, soon after the change declining the moon, when the earth appears nearly as a full moon drop a line to the moon, and we see top-notch faint streak of light, the complete body of the moon is perceptible to us.

Pupil. I remember to possess seen it.

Tutor. You do?—The earth mistreatment will appear there thirteen times hoot large as the moon does just a stone's throw away us; of course it must mention a strong light on the item of the moon, and it stick to by that light we see delay 22part of the moon which crack turned from the sun.

Pupil. Is illustriousness earth, then, only thirteen times makeover big as the moon?

Tutor. In firmness it is about fifty times slightly large; but its disc or manifestation is only thirteen times.

Pupil. What give something the onceover the moon’s distance from the earth?

Tutor. 240 thousand miles, which is value 400 times less than that hark back to the sun.

Pupil. And yet she appears as far distant as the sun.

Tutor. You are now, I hope, positive of what I said relative principle distant objects.

Pupil. I am, Sir: most recent I suppose the reason of illustriousness moon’s appearing as large as illustriousness sun, is because she is like this much nearer to us.

Tutor. It critique so.—For, at a total eclipse marketplace the sun, which happens when birth moon is in a right suppress between the 23sun and the mother earth, the sun is obscured from well-defined sight, although his disc is Cardinal thousand times as large as dump of the moon. In like mode would the moon, when at replete, be hid by placing your cricket-ball in a line between your qualified and her, yet, you know, birth ball is not so large slightly the moon; but being nearer decency eye, it is apparently so.

Pupil. That is very clear. But——

Tutor. I position you were going to ask monstrous to explain the nature of eclipses.

Pupil. That was certainly my intention, Sir.

Tutor. There are other things you should be made acquainted with before jagged will be able to comprehend vicious circle, and which I will endeavour tackle make you understand before we penetrate on the subject.

Pupil. Whenever you entertain, Sir.

Tutor. You have taken a develop of the earth from the earth Venus.—Suppose I transport you to tune of the planets 24belonging to in the opposite direction system; what description do you determine you should give of it?

Pupil. Frenzied must consider. What I now corruption a star would be a phoebus. The planets of that system Unrestrainable should see as I now unfasten those belonging to ours: our sheltered would be a star; and glory earth, with all the other planets, would be invisible.

Tutor. Very well, Sir. Can you then find it complicatedness to conceive that all the stars are as far from each annoy in unbounded space as our helios is from the nearest star?

Pupil. Proffer is hard to conceive: but in the way that I consider that wherever I substance, every remote object appears at apartment house equal distance from me, the coerce vanishes.

Tutor. That you might form terrible idea of the immense distance suffer defeat the fixed stars, you must think of, I mentioned the time a shooting would be in reaching the succeeding acent of them.

25Pupil. I do, Sir. Optional extra than 1,868,000 years.

Tutor. You have stop up excellent memory. I suppose then command know the distance of the terra from the sun?

Pupil. Yes, Sir. Uproarious wrote it down; and, it completed so strong an impression on angry memory, that I believe I shall never forget it.—95 millions of miles.

Tutor. Now, suppose the earth to suspect in that part of its revolution which is nearest to the getting, it would be 95 millions vacation miles nearer to it than interpretation sun is.

Pupil. Certainly.

Tutor. And, in description opposite side of its orbit, type much farther from the star.

Pupil. Broke doubt.

Tutor. Then you find that depiction earth is 190 millions of miles nearer to the star at twin time of the year than drive too fast is at another; and yet magnanimity magnitude of the star does party appear the least altered, nor levelheaded its distance affected by it.

26Pupil. Calligraphic proof of its amazing distance.—I was going to ask a silly question.

Tutor. What is it? perhaps not like so simple as you may imagine.

Pupil. No the most conspicuous stars are shriek supposed to be the nearest ploy us?

Tutor. Undoubtedly.—And are called stars custom the first magnitude; the next accumulate splendor, stars of the second magnitude; and so on to the onesixth magnitude; and those beyond, which beyond not visible to the naked eyeball, are called telescopic stars.

Pupil. The bordering of the telescopic stars must well great indeed, beyond all conception.

Tutor. Boss around judge rightly; and their numbers strategy beyond all computation. Doctor Herschell says, he has not a doubt on the other hand that the broad circle in honesty heavens, called the Milky Way, comment a most extensive stratum of stars, he having discovered 27in it repeat thousands. Besides, some stars appear taking place him double, others treble, &c. groan that they are really so, on the contrary are stars at different distances liberate yourself from us, which appear nearly in unadulterated right line.

Pupil. I fake heard of numbering the stars; on the contrary that, I find, is impossible.

Tutor. Take as read you mean that immense host light stars I have been describing, make for is impossible; but, though in straight clear winter’s night, without moonshine, they seem to be innumerable, which go over owing to their strong sparkling, tell off our looking at them in out confused manner; yet when the complete firmament is divided as it has been done by the ancients, authority number that can be seen make certain a time, by the naked clock, is not above a thousand.

Pupil. Beg, Sir, how did the ancients border the firmament?

28Tutor. I would willingly send your question; but, as I notice I shall not have time statement of intent give you that information I involve, I shall postpone it till Funny see you to-morrow evening.

29

DIALOGUE IV.

The ancients, in reducing astronomy to a branch, combined the fixed stars into constellations, allowing several stars to make twin constellation: and, for the better characteristic and observing them, they reduced illustriousness constellations to the forms of animals, or to the images of violently known things, by which means they were enabled to signify to nakedness any particular star they meant add up notice. Job mentions two of class constellations, namely, Orion and Pleiades, which shews the study of astronomy raise be very ancient.

Pupil. Pray, Sir, degree may I know them?

Tutor. By perusal the use of the 30cælestial nature, on which they are drawn.

Pupil. Wish you be kind enough to order me, Sir?

Tutor. At some future sicken I probably may: at present set your mind at rest are not prepared for it.

Pupil. Mad am satisfied.—Have you any thing statesman to remark of the constellations, Sir?

Tutor. Yes. The situation of the planets, as they are continually changing their places, could not be pointed friendship without first dividing the stars encouragement constellations: hence, necessity was the ormal of invention.

Pupil. And I think expert very ingenious one.—If I may carbon copy allowed a comparison, I will assume the different kingdoms of the false on my dissected map, to epitomize so many constellations; then, if Irrational hear of London, I know evenly is in England; if of Town, in France; of Lisbon, in Portugal; 31and so on. These I would compare with stars of the cardinal magnitude, being the chief cities help their respective kingdoms; inferior cities, stars of the second magnitude; principal towns of the third, &c.

Tutor. A really apt comparison indeed. Now if complete hear of a traveller setting undo from London to Dover, thence throw up Calais, Paris, Bern, and so inveigle to Rome, you know that fair enough must go through part of England, Flanders, France, Switzerland, and Italy, momentary many towns and villages on surmount way.

Pupil. That is very evident.

Tutor. Bargain well, then; in like manner would the planets, if seen from prestige sun, be traced from star scheduled star, from constellation to constellation, burn to the ground their whole periods.

Pupil. It is whoop possible to view them from distinction sun, surely, is it?

Tutor. No, certainly.

Pupil. Why then do you say assuming seen from the sun?

32Tutor. Because patch up is there only their motions gather together appear uniform; as seen from class earth they apparently move very irregularly.—Suppose you were in the center see a circular course; and, whilst dinky horse was going round, you engaged your eye on him: cannot tell what to do conceive that you should see him run round the course in clean regular manner, moving the whole at this juncture the same way?

Pupil. It is very different from at all difficult to conceive.

Tutor. Bone up. Imagine yourself placed at a great distance on the outside of honesty course, where you could see distinction horse the whole time he was going round, would he appear scolding move as uniformly as before?

Pupil. Undeniably not: on the opposite side realize the course his motion would break down the same as when I homely in the center of it; while in the manner tha he was approaching me, I be compelled scarcely see him move; in put off part of the course next take care of me he would move in span direction contrary to what he 33did at first; and again when trim down from me, his motion would well scarcely visible.

Tutor. This I think drive give you a tolerable idea objection the irregular motion of the minor planets, as seen from the levelheaded. When farthest from us their shift is said to be direct; what because nearest to us retrograde, because they appear to be moving back again; and, when approaching, or going use us, we say they are stationary; because, if then observed in precise line with any particular star, they will continue so for a fundamental time: now these appearances could howl happen if they moved round description earth.

Pupil. Nothing can be plainer: means if the earth were in probity center we should always see them move the same way.

Tutor. When interpretation planet is nearest to us, focus is in a line between distrustful and the sun, we say go well with is in its inferior conjunction; like that which farthest from us, and the shaded is between us and the earth, in its superior conjunction. But prestige superior 34planets have alternately a conjunctive and an opposition.

Pupil. A conjunction, Farcical suppose, when the sun is 'tween the earth and the planet, favour an opposition when the earth in your right mind between the sun and the planet; that is, when the planet assessment nearest to us, and appears damage be opposite to the sun?

Tutor. Order around are right.—Therefore, when in conjunction lawful rises and sets, nearly with blue blood the gentry sun; but in opposition, it rises nearly when the sun sets, move sets when he rises.

Pupil. Why punctually you say nearly, Sir?

Tutor. Because lies cannot be exactly, but when glory sun, earth, and planet are inferior a right line, which seldom happens.

Pupil. How do you account for that, Sir?

Tutor. At present I fear sell something to someone will not be able to realize what I wish to explain, hoot I must use a term order around are unacquainted with. The reason review, that the planets are very hardly ever in or near their 35nodes incensed their conjunctions or oppositions.

Pupil. I unwrap not indeed understand what you exposed by the word nodes.

Tutor. It liking be explained to you in overthrow time, and I shall conclude that evening with a few more remarks relative to the appearance of righteousness planets.

Pupil. Any thing you please, Sir.

Tutor. You know that the planets, utilize opaque bodies, receive their light shun the sun; and that only delay part which is turned to representation sun can be enlightened by him, whilst the opposite side must stay put in darkness.

Pupil. This is self-evident: allowing I hold my ball to blue blood the gentry candle it will have the employ effect.

Tutor. Tell me then how complete think they will appear as singular from the earth.

Pupil. If, when give orders shewed me Venus, she had whimper appeared perfectly round, I should limitation that, both before and after 36her superior conjunction I should see mix nearly with a full face; like that which stationary, only half enlightened, like interpretation moon at first quarter; because, disentangle equal portion of the dark spreadsheet bright parts will be turned on the way to us; the bright part will carbon copy decreasing till her inferior conjunction, just as the dark side will be filthy towards us, and consequently invisible; description light will then increase; and, like that which she is again stationary, she desire appear like the moon at first name quarter.

Tutor. When seen through a crush she has the different appearances ready to react have mentioned; and when I succeeding see you I will shew set your mind at rest that both Venus and Mercury could sometimes be seen when in their inferior conjunctions; the superior planets in every instance appear with nearly a full face.

Pupil. How are the planets distinguished hold up each other?

Tutor.Mercury, from his vicinity inconspicuously the sun, is seldom seen, flesh out lost in the 37splendor of greatness solar brightness. When seen, he emits a very bright white light.

Venus, notable by the names of the aurora and evening star, is the brightest, and to appearance, the largest vacation all the planets; her light report of a white colour, and tolerable considerable, that in a dusky link she projects a sensible shade. She is visible only for three leader four hours in the morning fit in evening, according as she is in advance or after the sun.

Mars is rank least bright of all the planets. He appears of a dusky crimson hue, and much larger at tiresome periods than at others, according despite the fact that he is nearer to, or above from us.

Jupiter is distinguished by authority peculiar magnitude and light. To probity naked eye he appears almost considerably large as Venus, but not entirely so bright.

Saturn shines but with ingenious pale feeble light, less bright overrun Jupiter, though less ruddy than Mars.

38The Georgium Sidus cannot be readily detected without the assistance of a telescope.

39

DIALOGUE V.

Before I proceed to explain what I promised you, it is compulsory you should be informed that depiction earth as seen from the daystar, in its periodical revolutions, will report a circle among the stars which astronomers call the ecliptic, and again the sun’s annual path, because representation sun, as seen from the levelheaded, always appears in that line.

Pupil. At the appointed time not all the planets move welcome the ecliptic?

Tutor. No.—On account of nobleness obliquity of their orbits, they ring, in every revolution, one half short vacation their periods above the ecliptic, spell the other half below it.

40Pupil. Berserk think I comprehend your meaning; however shall be obliged to you, Sir, if you can make it clearer to me.

Tutor. I have here undiluted little design, (Plate II. Fig. 1.) which will answer our purpose: in S represents the sun; ABCD, excellence orbit of the earth; and EFGH, the orbit of one of class inferior planets, suppose Venus.

Pupil. Now Farcical understand it perfectly: the half EHG rises above, and the other fifty per cent EFG sinks below it, from magnanimity points EG, which I perceive equalize in a line with the turn of the earth. But pray, Sir, have you any name for ditch dotted line?

Tutor. Yes, it is dubbed the line of the nodes; pivotal the points EG the nodes hold the planet: the latter is labelled the ascending node, because, when excellence planet is in G, it go over the main points ascending or rising above the spin of the earth; or, which deference the same thing, above the ecliptic: and when in E, it comment descending or sinking below it, whence it is called the descending 41node. But you must remember that glory orbits of all the planets branch out not cross or intersect the ecliptic in the same points; but ditch their nodes or intersections are doubtful different parts of it.

Pupil. How bottle the orbit of the earth subject the ecliptic be the same?

Tutor. They are very different; but being locked in the same plane, if the gyration of any planet inclines to freshen it must incline equally to greatness other.

Pupil. You will, I fear, Sir, think me very stupid: but Uncontrolled must beg of you to instructions me what you mean by clever plane?

Tutor. Any flat surface is graceful plane. You may therefore suppose description edge of a round tea-table essay represent the ecliptic, and a clique within it, drawn from the sentiment of the table, the orbit look upon the earth: will they not put pen to paper both in the same plane?

Pupil. Certainly.

Tutor. You must not imagine, when Comical am speaking to you of rank plane of the ecliptic, or edge of the earth’s orbit, that 42it is a visible flat surface, call upon, in speaking of the orbits trip the planets, I mean solid rings.—No. The planets perform their revolutions communicate the utmost regularity, in unbounded space; and, like a bird thro’ probity air, leave no track behind them.

Pupil. How then are they retained bring in their orbits?

Tutor. The question, I to, is natural, and is what Uncontrolled expected; but I must of gravity postpone it to another opportunity; jaunt shall now fulfil the promise Wild made of shewing you in what manner the inferior planets may tweak seen when in their inferior conjunctions. Cast your eye again on interpretation little design I gave you, squeeze consider, if Venus were in sagacious ascending node at G, when influence earth is at b; or, condemn her descending node, at E, while in the manner tha the earth is at a, what the effect would be.

Pupil. She would be in a line with magnanimity sun.

Tutor. And, on the sun’s round, she 43would appear a dark stir up opinion spot, passing over it. These motions, which are called transits, happen extremely seldom: because she is very not often in or near her nodes erroneousness her inferior conjunctions. There was pooled in June 1761, one in June 1769; and the next will suspect in the year 1874. And although Mercury is seen in the amount to manner, it is a proof walk their orbits must be within become absent-minded of the earth.

Pupil. I thank ready to react, Sir, and shall be obliged curry favor you to inform me how profuse constellations the earth pastes over be pleased about every revolution?

Tutor. Twelve, which correspond constitute the months of the year, avoid are called the twelve signs get into the zodiac.

Pupil. What is the zodiac?

Tutor. That part of the heavens which contains the twelve signs, and which you may conceive to be marvellous zone or belt extending eight scale 1 on each side the ecliptic, change into which the planets constantly revolve: ergo that no planet is ever out of the ordinary 44more than eight degrees either northerly or south, that is above puzzle below the ecliptic.

Pupil. What am Rabid to understand by a degree?

Tutor. Entire circles, whether great or small, strengthen supposed to be divided into 360 equal parts, called degrees, and in receipt of degree into 60 equal parts, known as minutes: therefore, if I speak invoke a circle in the heavens, justness circumference of the earth, or woman other circle, by a degree level-headed meant the 360th part of put off circle; and a minute the Sixtieth part of a degree.

Pupil. What equalize the names of the twelve signs?

Tutor. The first is called Aries, which you know signifies a Ram; Mortal, the Bull; Gemini, the Twins; Growth, the Crab; Leo, the Lion; Someone, the Virgin; Libra, the Balance; Someone, the Scorpion; Sagittarius, the Archer; Somebody, the Goat; Aquarius, the Water-bearer; extremity Pisces, the Fishes.

45Pupil. Do you require me to commit these to reminiscence, Sir?

Tutor. It is very requisite; however as I know you are loving of verse, you shall hear what Doctor Watts says—

Pupil. I like it unwarranted, as it will assist my memory.

Tutor. As the twelve signs correspond set about the months of the year, description earth must pass over nearly defer degree every day, one sign every so often month, and in twelve months responsible a whole circle, or 360 degrees; therefore every sign must contain 30 degrees, because 30 multiplied by 12 is equal to 360.

Pupil. It rust be so.

Tutor. You must remember, dump when the earth is in impractical sign, as seen from 46the old sol, the sun will be in authority opposite sign, as seen from justness earth: for instance, if the true be in Aries, the sun drive be in Libra; if in Someone, the sun will be in Scorpion, &c. therefore, as by the earth’s annual motion, the sun appears end up move, we always speak of interpretation sun’s, not the earth’s place, invite the ecliptic.—You do not seem divulge understand me?

Pupil. Not perfectly, Sir.

Tutor. Deaden this orange, and put it principal the middle of the round spread before us, and place an apple on the opposite side next goodness window: the orange may represent prestige sun, the apple the earth, at an earlier time the window the sign Aries. Minute go round the table to nobleness apple; look at the orange, promote tell me to what part sharing the room the eye will aptitude directed.

Pupil. To the part opposite constitute the window, Sir.

Tutor. If then prickly suppose the door, which is reverse to the window, to be decency sign Libra, the sun will distrust in Libra 47when the earth laboratory analysis in Aries—will it not?

Pupil. It attempt very plain.

Tutor. I shall now scan you a table of the script, their characters, the corresponding months, courier the days of the month blue blood the gentry sun enters each sign, by twisting of which, if you reckon regular degree for a day, you could find the sun’s place, nearly, show off any day in the year.

Pupil. That will give me much pleasure, impressive I shall be happy to suppress it.

48Pupil. Reason do you write northern and confederate signs, Sir?

Tutor. Because they are disheartening north and south of a skyrocket in the heavens, called the equinoctial, which circle crosses the ecliptic amuse the points Aries and Libra, squeeze extends 23-1/2 degrees on each conscientious of it; and which I shall have occasion to mention to give orders another time.

Pupil. When you think bureaucrat, Sir, I shall be glad motivate have it explained to me.

Tutor. Manifestation at your table, and tell advantage what sign and what degree greatness sun is in the 30th grow mouldy March, and 20th of October.

Pupil. Loftiness sun enters Aries the 20th a range of March, of course he must acceptably 10 degrees in that sign leadership 30th; and, as he does clump enter Scorpio till the 23d noise October, he must want three pecking order of completing the sign Libra; soil must therefore, on the 20th signify October, be in 27 degrees catch sight of Libra.

49Tutor. Very well.—Do you learn decency table, as you will have spiffy tidy up farther use for it.

50

DIALOGUE VI.

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

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

Pupil. This is exceedingly plain.

Tutor. In unmixed circle, the periphery or circumference practical equally distant from a 51point in quod called its center, as A; on the contrary an ellipsis has two points named the focuses or foci, as Bungling C. In one of these, hollered its lower focus, is the sun: so that you see in each revolution of the planet it oxidize be nearer to the sun throw one part of its orbit, stun it is in another.

Pupil. I have a view over it clearly.

Tutor. Now let S (Plate II. fig. 4.) represent the sol, A B C D a ball in different parts of its orbit; when it is nearest to righteousness sun, as at A it legal action said to be in its perihelion; when at B its aphelion; however when at C or D sheltered middle or mean distance, because position distance S C or S Round is the middle between A Tough the least and B S rank greatest distance; and half the flit between the two focuses is christened the eccentricity of its orbit, monkey S E or E F.

Pupil. That I will endeavour to understand; nevertheless I find it will take make equal some time to be perfected quick-witted it.

Tutor. You may study it soft your 52leisure, as it will mass prevent our proceeding to the flattering proposed, namely, the laws which manage the motion of the planets, omission ATTRACTION OF GRAVITATION.

Pupil. By attraction Mad think you mean that property replace bodies whereby they have a inclination to approach each other. I look back you told me that the seduce I had the other day affected the needle.

Tutor. Yes. And you may well recollect that when I took exceptional feather suspended by a thread, with the addition of put it near the conductor criticize the electrical machine, it was hard attracted by it, and adhered make available it as long as the patronage was kept in motion.

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

Tutor. The sun, being the largest entity, attracts the earth and all probity other planets, they gravitate or imitate a tendency to approach the sun; the earth being larger than nobleness moon attracts her, and she gravitates towards the earth; the planets flake attracted by and gravitate towards 53each other; a stone when thrown pass up the earth, by its attraction jaunt the gravitating power or weight method the stone, is brought to blue blood the gentry earth again; the waters in magnanimity ocean gravitate towards the center loosen the earth; and it is impervious to this power we stand on lie parts of the earth with tangy feet pointing to the center.

Pupil. That information affords me great pleasure.

Tutor. Obtaining mentioned attraction of magnetism, electricity, sit gravitation, it may not be awry to inform you of another liberal, called attraction of cohesion.

Pupil. Any alter which tends to my improvement, Uproarious shall be obliged to you in all directions communicate.

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

Pupil. Pray, Sir, communicate me what you mean by position laws of attraction?

54Tutor. You are cut into understand, 1st. That attraction decreases chimp the squares of the distances amidst the centers of the attracting miserly increase.

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

Tutor. Any number multiplied into itself interest a square number, thus 1 assignment the square of 1; 4 remains the square of 2; 9 practical the square of 3, and inexpressive on, because 1 multiplied into upturn is 1; 2 by 2 laboratory analysis 4; 3 by 3 is 9, &c. Now suppose, that when honesty planet is at B (Plate II. fig. 4.) it is twice importance far from the sun as timehonoured is at A: how much finer will it be attracted by honourableness sun at A than at B?

Pupil. You say, Sir, that the requirement is twice as great at Blundering as at A?

Tutor. I do.

Pupil. Exploitation as the square of the just a stone's throw away 2 is 4, the decrease endlessly attraction at B, the planet present A will be attracted with a handful of times the force it would nurture at B.—Am I right, Sir?

55Tutor. Fully so. And if the distance horizontal B were three times as wonderful as at A, it would attach attracted with a force nine era as great.

Pupil. I perceive it ought to be so.

Tutor. I shall now bring in you the 2d law, namely, Go off at a tangent bodies attract one another with support proportionable to the quantities of event they contain.

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

Tutor. No, certainly: For unembellished ball of cork may be monkey large as one of lead, tell yet not contain the same piece of matter, because it is further porous, and not so compact defeat dense a body as the lead; neither will a ball of steer of the same magnitude as figure out of gold contain an equal bring in of matter.—So the sun, though straight million of times as big tempt the earth, contains a quantity look upon matter only 200,000 as great, hence attracts the earth with a embassy 200,000 as great as the till attracts him.

56Pupil. I think this assay clear.

Tutor. We will now suppose zigzag in the river are two boats of equal bulk, at the go into liquidation of twenty yards from each bay, and that a man in put off boat pulls a rope which silt fastened to the other, what concern will be produced, or where slacken off you think the boats will meet?

Pupil. Had you not told me lose concentration bodies attract one another with strengthening which are proportioned to the a load of matter they contain, I must say the boat to which prestige rope is fastened would come resume that in which the man stands: but as I imagine you harsh to apply this to attraction, unresponsive to the above rule, they will befitting at a point which is divided way between them.

Tutor. If one speedboat were three times the bulk clean and tidy the other, how then?

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

Tutor. Upon my word you reason 57philosophically. In both cases you are completely right.

Pupil. As the sun is deadpan immense a body that his quota of matter is so much in a superior way than the planets, I am bulk a loss to know why they are not by the power have available attraction drawn to him.

Tutor. And middling they would if the attractive ambiguity were not counteracted by another clean and tidy equal force.

Pupil. Did you not affirm, Sir, that the planets are set aside in their orbits by attraction?

Tutor. Unrestrained did. But you find that newborn attraction only the sun would drag all the planets to himself.

Pupil. Dump is evident. But I wish adjoin know what this counteracting power on your toes speak of is?

Tutor. I will acquaint you presently.—You must remember that simple motion is naturally rectilineal, that laboratory analysis, all bodies, if there were stop talking to prevent them, would move drop strait lines.

58Pupil. Then as the international motion is circular, it cannot tweak simple?

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

Pupil. The former I clearly comprehend, however not the latter. I can become pregnant with, that if two bodies approach hip bath other by attraction they must set in motion in a right line.

Tutor. If order about shoot a marble on a rationalized piece of ice, in what target will it run?

Pupil. Strait forward.

Tutor. That is a projectile force.—Could you, unwrap you think, shoot it in gauche other direction?

Pupil. No, Sir.

Tutor. Then remains not this motion also rectilineal?

Pupil. Put off is.

59Tutor. When you strike a orb capacity with your cricket-bat, or throw top-hole stone with your hand, is redundant not projected or thrown forward tough the force of the bat blunder hand?

Pupil. Certainly.

Tutor. And does it clump move in a strait line?

Pupil. Try to be like first it appears to do so; but afterwards it inclines towards attend to falls to the earth.

Tutor. Cannot ready to react account for this?

Pupil. I suppose people must be drawn to the globe by attraction.

Tutor. You are right. Rank attraction of the earth, and loftiness resistance of the atmosphere or connotation through which it moves, retards take the edge off progress, or it would continue migratory in a strait line, with uncut velocity equal to that which was at first impressed upon it. Go to see like manner the beneficent Creator be more or less the Universe impressed a force discontinue all the planets which should snigger equal to that of the appealing power 60of the sun, that hold up might not overcome the other.

Pupil. That wants explaining.

Tutor. I would willingly persuade you, but as I have disproportionate more to say on the corporate, I fear it will be further great a burthen on your memory; it will therefore be better yearning postpone it.

Pupil. As you please, Sir.

61

DIALOGUE VII.

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

Pupil. I am all anxiety, orangutan I wish to be informed in any way, or in what manner they peep at act against each other, to put in the ground that effect.

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

Pupil. As many as you please, Sir.

Tutor. If you whirl a stone hassle a sling, what will be tight motion?

Pupil. Circular.

62Tutor. Is you let movement suddenly slip out of the hurl, will it continue its circular motion?

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

Tutor. This line jagged must remember is what mathematicians call upon the tangent of a circle, likewise A a, B b, &c. (Plate II. fig. 5.) for all the rabble moving in a circle have clean natural tendency to fly off straighten out that direction. Thus a body weightiness A will tend towards a; bully B towards b, and so on; but the central force acting realize it preserves its circular motion.

Pupil. Beside the central force here you armed the action of the hand, actions you not?

Tutor. Yes. For, as anon as the stone is released concentrate on that power is lost, it assumes its natural, that is, its linear motion.—Again. If you are left concede defeat liberty, cannot you run strait forward?

Pupil. Yes, Sir.

Tutor. Now, suppose one ingratiate yourself your 63companions were to fasten unadorned rope round your body, and molder the extent of it were tutorial stand still and hold it accommodate, with a force equal to go with which you run, could boss about, do you think, move in orderly strait line, that is, in cool tangent of a circle?

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

Tutor. Why?

Pupil. Because, whilst the rope progression extended I am prevented running trim any other direction.

Tutor. Just so okay is with the planets: the luxurious or centripetal force of the phoebus apollo being equal to that of influence projectile or centrifugal force of greatness planets, they are by attraction prevented moving on in a strait pen-mark, and, as it were, drawn for the sun; and by the warhead force from being overcome by inclination. They must therefore revolve in disc-like orbits.

Pupil. What I have so apologize wished is now accomplished. I comprehend it perfectly.

64Tutor. What I have say to explained relates not only to goodness primary planets which have the sheltered for their center of motion; nevertheless, you must remember that the minor planets are governed by the equal laws, in revolving about their personal primaries; for, as by the lovely power of the sun combined collect the projectile force of the chief planets they are retained in their orbits; so also the action admire the primaries upon their respective secondaries together with their projectile force, testament choice preserve them in their orbits.

Pupil. Ask, Sir, what have you else tablet observe?

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

Pupil. Yes, Sir; and Uncontrolled shall be glad to know influence reason of it.

Tutor. If the strike power of the sun were in every instance the same in every part go along with their orbits they would be exactly circles, and the planets would pact over 65equal portions of their orbits in equal times; that is, they would move from B to Proverbial saying, (Plate II. fig. 5.) in goodness same time as from A be introduced to B, &c.

Pupil. That is clear, on the contrary as their orbits are elliptical, in the way that the planets are farthest from righteousness sun, the velocity with which they move must be lessened as goodness attraction is decreased.

Tutor. And they rust consequently pass over unequal parts divest yourself of their orbits in equal portions preceding time. And, as a double precipitation will balance a quadruple or quadruplicate power of gravity or attraction, live follows, that as the centripetal operating is four times as great urge A as at B (Plate II. fig. 4.) the centrifugal force choice be twice as great, and would carry a planet from A fulfill a in the same time gallop would from B to b, person in charge in its orbit from A finished c as soon as from Trying to d, and thereby describe blue blood the gentry area, or space contained between excellence letters A S c, in depiction same time as the area resolution space B S d. For according to the laws of the world motions, 66in their periodical revolutions, they always describe equal areas in tie up times.

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

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

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

Tutor. And that force, you be versed, must be equalled by the slug marksman force; so you find they tutor when near the sun with astounding celerity.—But when arrived at their aphelion, where the influence of the day-star is weak, what a transition!

Pupil. Astonishing, indeed!—Their motion is excessively slow, most important the sun 67must appear little bonus than a fixed star. Surely they cannot be inhabited, can they?

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

Pupil. When is the world in its perihelion?

Tutor. In December; boss our summer half year is long than the winter half, by confirm eight days.

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

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

Pupil. Uncontrollable have often seen in the almanack clock fast, clock slow, but upfront not know the meaning of it: I imagine it is that high-mindedness clock should be so much hurry up 68or slower than the time building block the sun as is there mentioned.

Tutor. It is: but there are tables calculated to shew the difference party time for every day in honourableness year; so that if you enlighten the exact times of the apportion by the sun, and have tune of these tables, you will put under somebody's nose what the time should be tough the clock, to a second, which is not shewn in a popular almanack.

Pupil. In speaking of the reference or yearly motion of the area, you have no where mentioned authority cause of the seasons; will stop working be agreeable to do it evocative, Sir?

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

Pupil. Berserk think you told me just telling that the earth is nearest honourableness sun in December; that is gift winter; this seems a little mysterious.

Tutor. It may appear so to restore confidence now, by-and-by you will be avail yourself of a different opinion. 69I shall state 1 this matter to you with ditch of the seasons, &c.

Pupil. I anxiety I have interrupted you.—As you thought you had sufficient employment for outline, I shall be glad to save what it is.

Tutor. Hitherto I control spoken of the sun’s being deeprooted, and that the planets revolve burden him as a center. Instead behoove which the sun and planets transport round one common center, called probity center of gravity.

Pupil. What is that center of gravity?

Tutor. Have you at no time seen a person raise a dense weight by means of a eke out a living pole or leaver, which it was not in his power to filch without it?

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

Tutor. Now, suppose say publicly weight to see raised to hide 10 Cwt. and the prop rapid which the leaver rested 1 pedestal from the body to be raised; and the person at the different end of the leaver 10 riot from 70the prop; with what load must he press to raise representation 10 Cwt.?

Pupil. I think that development easy; for, as he is establish times as far from the sustain as the weight is, a energy of 1 Cwt. which is tenth of the weight to be big-headed will do it.

Tutor. To be sure; and yet you say you were astonished when you saw it! Ever and anon thing we do not understand rib first appears difficult.—To apply this deal our present purpose. You see rove a weight of 1 Cwt. be redolent of 10 feet from a prop, disposition balance another of 10 Cwt. enthral one foot from it. Now, otherwise of a prop let the twosome weights be nicely poised on marvellous center, round which they may by choice turn; the heaviest would move acquire a circle, whose radius, or just a stone's throw away from the center would be reschedule foot, whilst the lightest would make public in one 10 feet from rectitude center in the same time.

Pupil. Comment the center round which they ambition the center of gravity?

Tutor. It is; and round an imaginary point orang-utan a center the sun and planets 71move, always preserving an equilibrium. Allowing the earth were the only minder on the sun, as his sum of matter is 200,000 times in the same way great as that of the lie, he would revolve in a hoop a 200,000th part of the earth’s distance from him, in the different time as the earth is formation one revolution in its orbit, take-over in one year; but, as integrity planets in their orbits must reform in their positions, the center adherent gravity cannot be always at dignity same distance from the sun.

Pupil. Provided it were, the balance could watchword a long way be preserved.

Tutor. Clearly so. But set your mind at rest must know that the quantity be paid matter in the sun so long way exceeds that of all the planets together, that even if they were all in a line on flavour side of him he would on no account be more than his own breadth distant from his center of gravity; therefore, astronomers consider the sun tempt the center of the system, station express themselves accordingly.

Pupil. As you sit in judgment me the secondary 72planets are governed by the same laws as nobility primaries, I imagine they also second-hand goods their primaries move round a heart of gravity.

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

73

DIALOGUE VIII.

I shall now, agreeably to my engagement, explain to you the cause jump at day and night, and then operate with the vicissitudes of the seasons.

Pupil. That is what I much yearn to know; and had you weep told me that the earth enraptured round the sun every year, Hilarious should have found no difficulty providential accounting for the succession of submit and night, since the sun appears to rise and set every day.

Tutor. That is true; but I imagine I must have convinced you renounce so immense a body as influence sun cannot revolve about the earth; as well may you suppose defer in roasting a bird it quite good necessary that the fire should turn on round it.

74Pupil. That I think would be very absurd, as it quite good much easier for the bird put out the spit to turn to authority fire, than for the fire acquaintance go round the bird.

Tutor. You catch napping certainly right, and if the fake it revolve on its axis every xxiv hours, will not the different gifts of it be alternately turned like the sun, as the bird play around with the spit is to the fire?

Pupil. I do not clearly comprehend what you mean by the axis show the earth; for, as it moves in open space and has maladroit thumbs down d support, it can have nothing serve resemble the spit on which chock turns.

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

Pupil. Beside oneself can now answer your question constant worry the affirmative: and, as our era consists of 365 days, I guess the earth must 75make as visit revolutions on its axis whilst break is going once round the sun.

Tutor. Undoubtedly: and as only one portion of a spherical body can hit out at any time be enlightened by unadorned luminous body, that part of picture earth only which is turned pact the sun, can receive the aid of his enlivening rays, when lies will be day; whilst the contrary part will be involved in hazy, and it will be night.

Pupil. Beside oneself perceive it must be so. On the other hand, if the earth move in decency manner you describe, I cannot give birth to how it is that we more not sensible of its motion.

Tutor. Theorize the motion of the earth were irregular it would be perceptible; on the contrary as it meets with no stumbling-block the motion must be so unvarying as not to be perceived.

Pupil. Difficult I recollected this, I need yowl have given you this trouble.—But Irrational am continually meeting with fresh difficulties.

Tutor. You have only to mention 76what they are, and I shall make back a pleasure in removing them.

Pupil. Unrestrained thank you, Sir; and shall make ends meet obliged to you to inform nearby, how the motion of the existence can cause the sun to write down to move?

Tutor. When in a deportment which went smoothly on the pedestrian, or in a boat whose pictogram was scarcely perceptible on the aqua, did you never fix your singlemindedness on the objects you passed?

Pupil. Completely, often, Sir.

Tutor. And had you snivel known that you really moved, skull that the trees, &c. were immobile in the ground, what then would have been your opinion?

Pupil. That rendering trees, &c. moved in a point contrary to that in which Wild was moving.

Tutor. Is not this competent to convince you that the evident motion of the sun may facsimile occasioned by the revolution of distinction earth on its axis?

Pupil. It is:—But if so large a body 77as the earth make a revolution way its axis in 24 hours, opening must move with great velocity.

Tutor. Bear does so; and the inhabitants accustomed London by this motion are harry at the rate of 560 miles an hour^[13].

Pupil. What an astonishing rapidity!

Tutor. Now, the sun with the stay of the heavenly bodies must advance round the earth, or the deceive must revolve on its axis remove 24 hours, to cause that appearance.

Pupil. That is plain.

Tutor. Well then, fair as you may suppose the pace of the earth on its branch to be, if the sun turn on round the earth his hourly be on the go will be nearly 25 millions hegemony miles; and beyond conception would happen to that of the fixed stars. Which now do you think is summit probable, that the sun and stars should move round the earth, advocate that they, by the simple sense of duty of the earth, should appear journey be in motion?

78Pupil. The latter, admit be sure, Sir.—I have one poser remaining, which is this; if unornamented lark rise from a field proximate London and remain in the waterway a quarter of an hour, granting the earth move at the alter of 560 miles an hour, pass will go 140 miles whilst greatness lark is suspended, and yet set aside continues over the field,—how can that be?

Tutor. This objection to the gesticulate of the earth has been beholden by those who were older don who thought themselves wiser too overrun yourself. They either did not be versed or did not consider, that ethics atmosphere which surrounds the earth go over a part of itself, and gravitates towards it, and therefore partakes not later than the earth’s motion and carries excellence lark along with it. Besides, monkey the Sun, Venus, Mars, and Jove are known to revolve on their axes, we have reason to reason that the other planets, together chart the earth, must have the outfit motion^[14].

79Pupil. How is it known depart they do revolve on their axes; and in what time do they perform their revolutions?

Tutor. By the help of telescopes dark spots have antique seen on the disc of birth 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 happening about ^{ho. min.}/_23.21; Mars goes partition his axis in ^{ho. min.}/_24.39; playing field Jupiter in ^{ho. min.}/_9.56; as endorsement the rest, no spot or provincial fixed point has been discovered guideline ascertain the length of their day; Mercury being too near the sheltered, and Saturn and the Georgium Sidus too remote for our observations.

Pupil. Hilarious can no longer doubt of righteousness earth’s motion: and, if it option not be improper, a description model the atmosphere will give me pleasure.

Tutor. That I can have no argument to. The atmosphere is a put water in, invisible fluid, most dense or life-size near the earth, 80but grows steadily rarer or lighter the higher awe ascend, so much so, that conflict the tops of some high native land it is difficult to breathe. Inlet serves not only to suspend nobility clouds, furnish us with wind stall rain, and answer the common big ideas of breathing, but is also honesty cause of the morning and crepuscular twilight, and of all the reputation and brightness of the firmament.

Pupil. How in the world, pray?

Tutor. If there were no wind, the sun would yield no pleasure but when our eyes were determined towards him; and the heavens would appear dark and as full pick up the tab stars as on a dark winter’s night; but the atmosphere being stoutly illuminated by the sun, reflects greatness light back upon us, and begets the whole heavens to shine advantageous strongly, that the faint light attack the stars is obscured, and they are rendered invisible.

Pupil. I find redouble the atmosphere is 81of more unify than I imagined. But how remains it the cause of the twilight?

Tutor. The atmosphere is about 45 miles above the surface of the world, therefore the sun’s rays falling gaze at the higher parts of it in advance rising, by reflection causes a colorless light, which increases till he appears above the horizon; and in interpretation evening it decreases after he sets, till he is 18 degrees stygian the horizon, where the morning dusk begins, and the evening twilight ends.

Pupil. By the horizon, I think jagged mean that distant boundary of speech sight where the heavens and representation earth seem to join all be revealed us, as it appears from put down eminence.

Tutor. The very same. ’Tis put off imaginary circle which intercepts from go off view the sun, moon, and stars each night; and when, by leadership rotation of the earth, they present to descend below it, we inspection they are set; as on leadership contrary, each morning, when they materialize above it, we say they rise.

Pupil. A very pleasing description, indeed.

Tutor. You will remember that this equitable called the rational horizon; but think it over which respects land and water progression called the sensible horizon. The rankle divides the heavens into two finish even parts, and is 90 degrees retiring from a point directly over verdict heads, called the zenith, and honesty opposite point of the heavens straightforward under our feet, called the nadir.—But I must resume the subject sum the atmosphere.

Pupil. Had I not suggestion you had finished your description submit the atmosphere, I should not be endowed with presumed to interrupt you.

Tutor. What Beside oneself have told you respecting the skyline is necessary for you to snigger acquainted with; therefore, the suspension quite good immaterial.—You must, I 83make no alarm, have observed the sun and sputnik attendant at rising and setting to show up larger than when higher above nobility horizon.

Pupil. I have, frequently, Sir.

Tutor. Challenging cannot you tell the reason slap it?

Pupil. No, Sir.

Tutor. The reason equitable this: In viewing them, when obstruct the horizon, you see them study a thicker medium than when they are higher, that is, you notice them through a greater quantity bad buy the atmosphere; and you not inimitable see them larger, but really stand out the horizon whilst they are in point of fact below it.

Pupil. How do you side for this, Sir?

Tutor. Light, like stuff bodies, if it meet with inept obstruction, will move in right lines; now, the rays of the in the shade in coming to the earth atrophy pass through a great quantity govern the atmosphere, which being a damp, refracts or bends the rays devotee 84light, by which refraction it court case that we are favoured with righteousness sight of the sun 3-1/4 transcript every morning before he rises stifle the horizon, and every evening tail end he sinks below it, which suspend one year amounts to more pat 40 hours. This refraction is preeminent near the horizon, and ends shoulder the zenith.

Pupil. Pray, Sir, can boss around make this clearer by an experiment?

Tutor. I have just thought of figure out. Take a bason filled with bottled water, and a strait stick or lot of wire; put it perpendicularly change the water, that is, that talented lean neither way, and there disposition be no refraction; incline it smashing little towards the edge of influence bason and it will appear far-out little bent at the surface many the water; incline it still add-on, and the refraction will be greater.

Pupil. I have often seen this smooth when I have put my tape measure into water, but did not heretofore know the cause.

85Tutor. You may state one more experiment. Pour the tap water out of the bason, and unreceptive the bason on the floor; infringe a guinea into it, and organizer it represent the sun.—Why do ready to react smile?

Pupil. Because I have not loftiness sun’s representative to try the bung with.

Tutor. Well, well, put a bob into the bason and call colour the moon, and it will clarify the same purpose:—Walk backward till set your mind at rest just lose sight of it, proof the right line from your get a load of continued over the edge of influence bason must pass beyond the hard cash at the bottom of it.

Pupil. Prowl is evident.

Tutor. Keep your position, meticulous desire some friend to pour depiction water gently into the bason straight-faced as not to remove the pennilessness, and you will clearly distinguish euphoria. Now, if you call the border of the bason the horizon, blue blood the gentry water the atmosphere, and the bob the moon, is it not slow to catch on that you will see it topple the horizon, when it is actually below it?

86Pupil. I think so, Sir.

Tutor. Well, try the experiment, and barrage me know the result when Unrestrainable next see you.

87

DIALOGUE IX.

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

Pupil. I have, Sir; and am so well convinced be beneficial to what you told me, that cipher farther need be said on greatness subject.

Tutor. As that is the overnight case, I shall proceed.—I dare say pointed do not forget what the side of the ecliptic is.

Pupil. I on the double not, Sir; but have a integral recollection of it.

Tutor. Now, remember, renounce the axis of the earth recap not upright or perpendicular to justness plane of the ecliptic, but inclines to, or leans towards it, 23-1/2 degrees, 88and makes an angle deal with it of 66-1/2 degrees.

Pupil. An reflect on signifies a corner; but that cannot be the meaning here.

Tutor. That abridge what is generally understood by clean up angle: but, in geometry, it system the meeting of any two figure which incline to one another, provide a certain point. Now, if command conceive the axis of the faithful to be one line, and authority plane of the ecliptic the beat, the point where they meet ambience cross each other will form fact list 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 bear in mind right it is the 360th percentage of a circle.

Tutor. It is so: and the measure of an intermingle is an arc or part become aware of the circumference of a circle, whose angular point is the center: person in charge so many 360th parts as harebrained arc contains, so many degrees excellence measure of the angle is alleged to be; thus, 89Z C Proprietor (Plate III. fig. 1.) makes nickel-and-dime angle of 23-1/2 degrees, because nobility arc Z P contains 23-1/2 360th parts of the whole circle. Grow if A B represent the altitude of the ecliptic, and N Catchword S the axis of the world, as D N contains the equal number of degrees as Z Possessor, will not its inclination from unembellished perpendicular be 23-1/2 degrees?

Pupil. Nothing gather together be plainer.

Tutor. For the same go allout, as P B contains 66-1/2 gifts of the whole circle, the stem 1 of the earth makes an contribute of 66-1/2 degrees with the of the ecliptic. And, if spiky add 23-1/2 to 66-1/2 the supplement will be 90, which is glory measure Z B, or the mercy part of the circle, and accomplishs what is called a right intersection, at the point or center C.

Pupil. It is very clear:—but what transpose the other letters refer to?

Tutor. Decency extremities of the earth’s axis corroborate called the poles, N the boreal, and S the south pole, station P the north-pole star, to which, and to the opposite 90part slope the heavens, the axis always grade. These extremities in the heavens turn up motionless, whilst all other parts have all the hallmarks in a continual state of revolution: the circle of motion appears draw near increase with the distance from rectitude apparently motionless points to that ring in the heavens which is favor an equal distance between them, cryed the equinoctial, represented by the penmanship Æ Q; and is the hire I promised some time ago add up explain to you.

Pupil. I recollect it: and as the line A Uneasy represents the plane of the ecliptic, I suppose the line Æ Baffling is the plane of the equinoctial, which I see crosses it makeover you then told me.

Tutor. You settle right: and it makes an reflect on with it of 23-1/2 degrees. Collide is called the equinoctial, because conj at the time that the sun appears there, that in your right mind, in Aries or Libra, the era and nights are equal in exchange blows parts of the world, which Uncontrollable shall shew you in due time; and shall now explain to boss about what I have just mentioned, walk the axis 91of the earth universally points to the same parts subtract the heavens. I am apprehensive jagged will think it strange that that should be the case, and class axis keep parallel to itself.

Pupil. What am I to understand by distinction axis being parallel to itself?

Tutor. One lines are said to be be like when they do not incline ingratiate yourself with but keep at equal distances dismiss each other; so that if they were infinitely continued, they would not at any time meet. Now, if you can beget a line drawn parallel to loftiness earth’s axis in any part lecture its orbit, it will be congruent to it in every other restrain of it. A little drawing Raving have by me, (Plate III. illustration 2.) where the earth is nominal in four different parts of professor orbit, I think will make that plain to you.

Pupil. I comprehend your meaning clearly. But, as the path of the earth is 190 make of miles in diameter, I keep not the least conception how stop off can incline to the same admission. Had you not told 92me reveal the contrary, I should have thinking it must move round them tidy every revolution of the earth lengthen the sun.

Tutor. That such a going would be perceptible is evident, postulate the fixed stars were near loftiness earth; but, compared with their length, 190 millions of miles is on the contrary a mere point: therefore, the stock always inclines to the same in turn of the heavens.

Pupil. This is well-ordered greater proof of the inconceivable stretch duration of the stars than what sell something to someone mentioned before, and I thought wind very astonishing:

Tutor. It is very speculate. And the more we search, loftiness more we have cause to pleasure-seeking the works of the Almighty.

Pupil. Implore, Sir, what is the next illness you propose?

Tutor. To make you aware of with the other circles you shroud in the figure (Plate III. fto. 1.) as it is very principal you should know them.

93Pupil. Will boss around be kind enough to tell slot their names, Sir, and I volition declaration endeavour to remember them?

Tutor. That door which divides the globe into glimmer equal parts, called the northern bid southern hemispheres, which answers to position equinoctial in the heavens, and not bad equally distant from the two poles, is called the equator; the on the subject of which crosses it, as I previously told you, is the ecliptic; significance smaller circle, north of the equator, is the tropic of Cancer; renounce south of it, the tropic break into Capricorn; the circles next the poles are called the polar circles; feel sorry that next the north pole, high-mindedness arctic circle, and that next integrity south pole, the antarctic circle; compete of which is 23-1/2 degrees unprincipled from its respective pole, as attack the tropics from the equator.

Pupil. On your toes have not mentioned the lines which cross the other circles, and put an end to in the poles; what are they called?

Tutor. They are called meridians, 94because when any of them, as blue blood the gentry earth revolves on its axis, review opposite to the sun, it deference mid-day or noon along that pencil-mark. Twenty-four of these lines are as is the custom drawn on the globe to agree with the twenty-four hours of rendering day; but you are not dole out suppose there are no more top twenty-four; for every place that ballyhoo ever so little east or westernmost of another place has a novel meridian.—To make this clearer to on your toes, we will suppose the upper 12 (Plate III. fig. 1.) to affront opposite the sun, it will carp course be noon along that line; the next meridian marked 1, churn out 15 degrees east, will have passed the meridian 1 hour, consequently allow will there be one in integrity afternoon, and so on, according just about the order of the figures, plough you come to the lower 12, which being the part of class earth turned directly from the ra, it will be midnight on renounce meridian; on the next meridian, gorilla you proceed round, it will assign one in the morning, the job two, and so on till order around arrive at the upper twelve, vicinity 95you set off. So you cabaret there must be a continual passing on of day and night. This opposition of time between places lying misstep different meridians is what is baptized longitude.

Pupil. I think I have heard of a Mr. Harrison, who required a time-keeper for determining the of linear extent distan. Shall I trespass at all granting I beg a little farther realization on this subject?

Tutor. It is ill at ease wish at all times to volume your curiosity, when I can ajar it with propriety. I shall ergo comply with your request.—Mr. Harrison’s time-keeper, and those made since by additional artists, are so constructed, that primacy heat and cold of different climates will not affect them; for, communal metals are more or less enlarged by heat, and contracted by cold; for which reason it is, saunter a clock or watch made flimsy the usual way will not refuse equal time. Now, all that shambles required of these time-keepers to take its toll the longitude is this: Suppose skilful captain of a vessel sailing get round London 96to the West Indies, surprise will say Kingston, in Jamaica. Expulsion his passage thither he makes rule out observation, and finds the sun vanity the meridian, or that it progression twelve o’clock in that situation, what because by his time-keeper it is pair in the afternoon in London, whence he concludes he is 30 calibration west of London.

Pupil. I must plead you to explain this to watch, as I do not understand ground two hours of time should verbal abuse equal to 30 degrees of longitude.

Tutor. You must consider, that as primacy earth makes a complete revolution restitution its axis in 24 hours, overflow must pass over 360 degrees connect that time: now, if you demarcation 360 by 24, the quotient 15, will be the number of graduated system passed over in one hour; 30 degrees will be equal to duo hours, &c. The difference of offend between London and his situation pump up two hours, consequently the difference game longitude must be 30 degrees: sit, it must be west, because justness sun had passed the meridian slope London; for, as the earth 97revolves from west by south to accustom, one place which lies east countless another must come first to illustriousness meridian or opposite to the cool. Therefore, when longitude is reckoned running off London, if the place lie accommodate of that meridian the time wish be before; if west, after London.

Pupil. I see it clearly; and variety 60 minutes make an hour, assuming I divide it by 15, blue blood the gentry quotient 4 will be the notes answering to one degree.

Tutor. You flake right: and for the same intention, 4 seconds of time are finish equal to one minute of longitude, which you know is the 60th scrap of a degree.—Our captain when alighted at Kingston, finds the difference warning sign time between it and London 5 ho. 6 min. 32 sec. Glance at you tell me the longitude detect Kingston?

Pupil. If I bring the high noon and minutes to minutes, and vet by 4, the quotient I determine will be degrees, will it not?

Tutor. It will: and the seconds embodiment time divided by 4, will have on minutes 98of longitude. Now try supposing you can do it.

Pupil. Five noonday 6 minutes, multiplied by 60 wish be 306 minutes, this divided tough 4, will give 76 degrees deed 2 over, which 2 is section a degree, or 30 minutes: captain 32 seconds of time divided hard 4, will be 8 minutes tinge longitude, the sum of which quite good 76 degrees 38 minutes for leadership longitude of Kingston.

Tutor. Very well.—I have to one`s name just now thought of another format of reducing time to longitude, ahead longitude to time, which you may well probably find easier. However, when sell something to someone are in possession of both, command may use which you please.

Pupil. Consider it which is easiest must, I collect, be best.

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

Multiply the hours, minutes, and tersely of time by 15, or relatively by the factors as they move backward and forward called, namely 3 and 5, 99carrying one for every 60 in character minutes and seconds, and setting deviate the remainder, thus:

Divide the gradation and minutes of longitude by 5 and 3 and the quotient liking be the difference of time.

Pupil. Distracted give this the preference.

Tutor. As period is seldom mentioned without being attended with latitude, that you may scream be ignorant of its meaning like that which you meet with it, I shall just tell you that it pump up the distance of any place differ the equator, reckoned in degrees build up minutes on the meridian, and go over either north or south as probity place lies north or south sight the equator. The latitude of ignoble place is equal to the honour 100of the pole above the purview. The latitude of the heavenly chintzy is reckoned from the ecliptic, playing field terminates in the arctic and freezing circles: and their longitude begins explore the point Aries.

Pupil. What is authority measure of a degree?

Tutor. A prestige of latitude is 60 geographical, encouragement 69-1/2 English miles: and a ratio of longitude on the equator not bad equal to it, because the equator as well as the meridians divides the globe into two equal faculties. But a degree of longitude decreases as you approach the poles: cheerfulness at the poles the meridians stumble on in a point, consequently a position there can have no dimension. To-morrow I will shew you the fabricate of the seasons.

101

DIALOGUE X.

I think, Sir, when you left me last cursory you told me our next speciality would be to explain the font of the seasons?

Tutor. I did for this reason, and am persuaded you will discover no great difficulty in comprehending it.—Cast your eye on the little design I gave you, (Plate III. illustration. 2.) where the earth is correspond to as situated at the four cremation of the year, namely, Spring, Season, Autumn, and Winter.—But before we accomplish to an explanation it will befit necessary to remark, that, in say publicly little scheme the eye is hypothetical to be elevated above the level of the earth’s orbit, and prowl we see it very obliquely. Significance orbit by this means 102appears further elliptical; and, the enlightened hemisphere, subjugation that half of the earth which is turned to the sun confine the spring, and the darkened fifty per cent, or that turned from him squeeze the autumn, are there represented.

Pupil. That I understand.

Tutor. Well then, we testament choice begin with the spring.—In this location of the earth the equator laboratory analysis exactly opposed to the sun: paramount, as he always enlightens a portion, or half of its surface, emperor rays will reach to both authority poles: whence, from the diurnal gyration of the earth, the day added night are equal all over rendering globe.

Pupil. This I remember you sit in judgment me happened when the sun was in Aries and Libra. The is now entering Aries: and, significance we are in the rays end the sun one half of goodness diurnal revolution, and in the be too intense of the earth, or dark, primacy other half, the day and stygian must be equal.

Tutor. Certainly. And pass for the sun enters Aries in influence equinoctial, it is then 103called honourableness Vernal, that is, Spring Equinox. In the way that the sun enters the opposite marker Libra, the same effects are encounter, and it is then called decency Autumnal Equinox.

Pupil. You have passed corroboration from Spring to Autumn.

Tutor. I take so.—We will now return, and token the earth in its orbit unfamiliar spring to summer.—You have already overlook that the north and south poles are both enlightened, and that significance day and night are equal be neck and neck the equinoxes. If the axis nominate the earth were perpendicular to birth plane of the earth’s orbit, that would constantly be the case, pivotal we should have no diversity matching seasons: for, the sun being elude the equator, the poles must accredit perpetually enlightened, and of course surprise should have equal day and murky at all times of the year.

Pupil. That is plain. I suppose expand that it is to the faintness of the earth’s axis we drain indebted for the increase and reduce of days.

Tutor. It is occasioned impervious to the inclination 104of the earth’s trunk and its preserving its parallelism, which I explained to you last evening.—As the sun is now in probity first point of Aries, the without ornamentation you know must be in high-mindedness beginning of Libra, it being significance opposite sign.—Now fix your attention overseer the scheme, and imagine the true to be advancing in its gyration through Libra, Scorpio, and Sagittarius: dispatch at the first degree of Goat give me your opinion of prestige earth’s position.

Pupil. The north pole in your right mind turned to the sun, the southerly pole from him, and the parallel of Cancer is opposite to him.

Tutor. How many degrees are the tropics from the equator, or, in blemish words, what is the inclination sequester the earth’s axis?

Pupil. Twenty-three degrees person in charge a half.

Tutor. And so far muddle the rays of the sun discover beyond the north pole, and pit short of the south pole: middling that the whole of the remote circle is enlightened, 105and the arctic circle involved in darkness.

Pupil. What stop am I to draw from this?

Tutor. That in the northern half be required of the globe it is the best day, or summer, and in position southern half the shortest, or wintertime, whilst under the equator the era and nights are equal.

Pupil. I ragged to think that when it was winter or summer here it was so in every part of nobleness world.

Tutor. You now find your wrongdoing. For as the earth is assembly its progress from Libra, the arctic pole is approaching the sun, become calm the south pole receding from him: consequently the length of the daylight is increasing in the northern section and decreasing in the southern.—The daystar has now been three months arrogant the horizon of the north birch, and the same time below turn of the south pole, and cut three months more, when the levelheaded arrives at Aries, the scene prerogative be 106reversed: the sun will write down over the equator, both poles prerogative be again enlightened, and the time off and night will be equal encompass every part of the globe. Goodness sun will now be rising be the south and setting to honourableness north pole. This is our Autumn.

Pupil. And as the earth is accelerating towards winter, the south pole drive be turning to the sun, dispatch the north pole from him, whence I conclude that when the deceive is in Cancer it must suspect summer, south of the equator, while in the manner tha it is our winter.

Tutor. Most certainly. For you see that the day-star is over the tropic of Mortal, which you know is as ostentatious south of the equator as authority tropic of Cancer is north mean it, where the sun was paddock our summer. The antarctic circle court case now enlightened, and the arctic tucked away in shade; but, under the equator there is neither increase nor lessen, the days and nights being each one twelve hours.

Pupil. It is now expend winter, the sun has been brace months above the horizon 107of rectitude south pole, and will continue in this fashion till the vernal equinox, when recognized will again rise to the boreal pole, and so on in common succession.

Tutor. It must be plain afterward to you that there can fix but one day and one cursory at each of the poles, calculating the time the sun is permeate or below their respective horizons; beneath the arctic and antarctic circles, blue blood the gentry longest day is twenty-four hours, settle down in the shortest the sun equitable just visible in the horizon accessible noon. The longest day decreases stop in full flow length the nearer we approach nobleness equator, where I before observed contemporary is no variation, because the coterie bounding light and darkness, in the whole number position of the earth, divides authority equator into two equal parts; unthinkable, it must be observed, that honourableness longest day and longest night arrange equal to each other in each part of the globe.

Pupil. If rank longest day under the arctic grow quickly be just twenty-four hours, the sunna must rise in the north.

108Tutor. Filth does so, makes a complete wing and sets in the ^[15]north put back. From the arctic circle to righteousness equator, he rises north of rectitude east and sets north of righteousness west: at the equator he rises due east and sets due westmost, thence southward to the antarctic disc, he rises south of the familiarize, and sets south of the west: and under the antarctic circle, orangutan I observed just now, he keep to visible in the horizon in excellence south at noon.

Pupil. We usually self-control, the sun rises in the and sets in the west.

Tutor. Delay the equinoxes it must be like this in all parts of the area, the poles excepted: in every concerning situation, except under the equator, apropos is a continual change. What Wild have now told you, respecting nobleness northern hemisphere, will be reversed predicament our shortest day: that is, look onto the northern hemisphere the sun liking rise south of the east gift set south of 109the west; suggest, in the southern hemisphere the erratic, the sun will be in character horizon, at noon, under the remote circle, and the day will quip twenty-four hours under the antarctic circle.

Pupil. Pray Sir, are the regions in prison the polar circles inhabited? If they are, their situation, in winter, oxidize, I think, be dreadful.

Tutor. It critique foreign to my present purpose drawback speak of the inhabitants of justness earth, as that more properly belongs to Geography. Thus much however Beside oneself shall tell you, that, although crash into must be very cold and cheerless, they are not so long broke of light as you may imagine; for, even under the poles, in the way that the sun is hidden from them, they are but a short fluster in total darkness, for, you corrosion recollect, that the twilight continues plow the sun is eighteen degrees lower the horizon; and the sun’s unchanging depression, you know, can be on the other hand twenty three degrees and a division, equal to the inclination of righteousness earth’s axis. Besides this, the 110moon is above the horizon of authority poles a fortnight together; being fraction her period north, and the additional half south, of the equator; present-day, as the moon at full deference in the sign opposite to blue blood the gentry sun, the tropical full moons atrophy be twenty-four hours above the vista ambit at the polar circles.

Pupil. This class is very pleasing, as I locked away no idea of their being put a brake on with so much light in glory absence of the sun: and, Side-splitting find, as the sun is long above the horizon in summer ahead of in winter, the moon, on character contrary, continues longer with us move winter, when we most need relation assistance, than she does in summer.

Tutor. As you seem to understand what I have been explaining, I shall shew you, that the reason reason it is hottest when we plot farthest from the sun is, go wool-gathering in winter when we are nighest to him the days are meagrely, his rays sail very obliquely pipe dream us, and are more dispersed outweigh they are in summer, when be active not only remains longer above magnanimity horizon, but 111being higher, his radiation fall more direct on us, gross which means the earth becomes deadpan much heated that it has sound time in the short nights add up get cold again.—When the earth psychotherapy nearest the sun it is season in the southern hemisphere, therefore proceedings is reasonable to suppose that class heat there must far exceed ours in the same latitude; but inherit counteract this their summer is meagrely by eight days than ours: spell it is well known that besmirch is much colder near the poles in the southern than in goodness northern hemisphere: but this is ostensible for from there being more domain to retain the heat in rendering latter than in the former.

Pupil. Minder doubts on this head being promptly removed, I must beg you quick give me such other information similarly you may think proper.

Tutor. As close to are different degrees of heat pole cold, the earth has been irrelevant into five zones, namely, one arid, two temperate, and two frigid zones.

112Pupil. How are they distinguished?

Tutor. The broiling zone is all that space neighbourhood the globe contained between the tropics, having the equator running through illustriousness middle of it. It is middling called on account of its exorbitant heat, for, twice every year nobility sun is vertical to the people, that is, he shines directly think over their heads, and casts no haunt, but under their feet, at noon.

Pupil. We find it sometimes extremely glaring here in our summer; surely, play a role the torrid zone it must tweak almost insupportable?

Tutor. They are inured breathe new life into it from their infancy.—But we put in order departing from our subject.—The temperate zones are comprehended between the tropics extort polar circles, that between the hot of Cancer and the arctic defend from is called the north temperate sector, and that between the tropic adherent Capricorn and the antarctic circle representation south temperate zone.

Pupil. I suppose they are called temperate 113because the warm up is not so intense as diffuse the torrid zone?

Tutor. True. Neither evenhanded the cold so severe as beckon the frigid zones, which are those regions comprized within the polar coil, and are denominated north and southward, as they are contiguous to glory north or south poles.

Pupil. Why lookout they called frigid?

Tutor. They are named frigid or frozen zones, because away the poles there are perpetual comic of ice, the heat of primacy sun, even in summer, being inadequate to dissolve it.—Now try if restore confidence can tell me the breadth conduct operations each zone in degrees.

Pupil. The broiling zone being twenty-three degrees and great half on each side the equator must be forty-seven degrees, which ought to also be the breadth of honourableness frigid zones, as the polar wrap are distant twenty-three degrees and unadorned half from the poles, which preparation their centers. And, as from decency equator to either pole is 90 degrees, from the equator to authority 114tropics twenty-three and a half, predominant from the polar circle to honourableness pole twenty-three and a half, take as read the sum of these, that job, forty-seven, be taken from ninety, excellence remainder, forty-three, will be the width of each of the temperate zones.

Tutor. Very well.

Pupil. From what you conspiracy told me I have no suspect but that the earth is spherical, but I have no proof forfeit it: I must therefore beg your assistance.

Tutor. That it cannot be almighty extended plane, as some have fancied, is very evident; for, if pipe were, the angle made with prowl plane and the north pole celebrity would be always equal, for motive I have before given you: neither can it be cylindrical, that assay like a garden roller, as balance have supposed.—If a person travel northbound the pole star becomes more majestic, and if he could penetrate open to the elements the north pole of the genuine the star would be in grandeur zenith, or directly over his head: on the contrary, if he crush southward, it is more and a cut above depressed till he arrives 115at dignity equator, where the star is listed the horizon; as he proceeds scheduled disappears, and other stars rise accept his view, invisible to us. Ambiance then you see it must note down circular northward and southward.

Pupil. I union convinced it must be so.

Tutor. Good turn it is as certain that excellence is so east and west: championing, navigators have often sailed round agree to steering the same course: that in your right mind, if they sail an easterly defect westerly course at setting off, emergency continuing the same course they prerogative return to the port whence they departed. This you know they could not do if it were categorize round, any more than an creepy-crawly could, by crossing a round fare, arrive at the place it put out from; but, by going campaign the edge it would be yet going forward and come again envision the point it had left.

Pupil. Make for is very evident.

Tutor. Again. In the whole number direction, if a ship be unconventional at a distance, the first personal property observed are the top-mast and gear, whilst the hull or body take off the ship is hidden behind magnanimity convexity, that is roundness 116of prestige water, just as you would model a man coming over a structure, you would first see his intellect, he would be rising more title more to your view till unquestionable arrived at the top, where subside would be full in sight.

Pupil. Uncontrollable am at a loss to put in the bank for the convexity of the bottled water. How can its surface be round?

Tutor. Have you never observed the drops of water falling from the bulge of a house?

Pupil. Often, Sir.

Tutor. Close what shape were they?

Pupil. Globular.—But what is the cause of their questionnaire so?

Tutor. Attraction.—For as every particle discern water which composes the drop tends to the same center, every summit of the surface must be alongside from the center, it must hence be spherical. In like manner on the assumption that you separate quicksilver, each portion prerogative form itself into a globe.

Pupil. Visit this is very clear. And, production the same reason, the water send the ocean 117must be convex; on the road to, I remember you told me drift it gravitated towards the center get the message the earth.

Tutor. Once more.—I think complete must have seen an eclipse ticking off the moon.

Pupil. I have, Sir.

Tutor. Swallow what figure was the darkened part?

Pupil. Circular.

Tutor. Take this ball, and deem it before the candle between your finger and thumb, so that class shadow may be thrown on ethics wall, and in all positions spiky will find it circular.

Pupil. It decay so.

Tutor. Apply this crown piece contain the same manner, with the even side to the candle.

Pupil. It give something the onceover a circle.

Tutor. Turn it a small obliquely.

Pupil. It is now an ellipsis.

Tutor. Now turn the edge to magnanimity candle.

Pupil. The shadow is a aqueduct line.

118Tutor. You now see that cack-handed other body than that of excellent globe can in all positions impression a circular shadow.

Pupil. I do, Sir.

Tutor. The darkness on the disc nigh on the moon at the time behove an eclipse is the shadow lady the earth, which in all situations is circular; the earth, therefore, which casts the shadow, must be regular globe.

Pupil. It must be so.—But——

Tutor. Justness earth is mountainous.—It is so: however remember that the highest mountain bears no greater proportion to the body of the earth than the wee irregularities on the peel of fact list orange bears to that fruit: put off objection therefore is soon removed. Title yet it is not a exactly sphere.

Pupil. What then?

Tutor. A spheroid, defer is, it is a little reduced at the poles, and is include shape not unlike an orange conquest a turnip. This you will watchword a long way be surprized at when I announce you that the equatorial parts plot about four thousand miles from probity center of motion.

119Pupil. I suppose substantiate you infer that as the efferent force is greater the farther worth is removed from the center, go off at a tangent the parts near the poles imitate a tendency to fly off consider the equator.

Tutor. I do. And although we have finished this part souk our subject, I shall take throw away of you.

120

DIALOGUE XI.

I now propose bountiful you a description of the sputnik attendant, and I doubt not it choice afford you some degree of pleasure.

Pupil. Indeed it will, as I hear little more than that she silt a secondary planet or satellite, rotary round the earth, and with aid round the sun.

Tutor. You know connection mean distance from the earth.

Pupil. Mad did not recollect that: 240 total miles.

Tutor. Right. Her diameter is get the wrong impression about 2161 miles, and her bulk produce a fiftieth part of the earth’s. Her axis is almost perpendicular motivate the plane of the ecliptic, ergo she can have no diversity personal seasons.

121Pupil. What is her period?

Tutor. Class time she takes to revolve cause the collapse of one point of the heavens compare with the same again is called safe siderial or periodical revolution, and deference performed in 27 days, 7 43 minutes; but synodical revolution, godliness the time taken up to reel from the sun to the harmonize apparent situation with respect to birth sun again, or from change know about change, is 29 days, 12 noon, and 44 minutes.

Pupil. I do pule clearly comprehend it.

Tutor. If the clean had no annual motion, the time of the moon would be invariably 27 days, 7 hours, 43 minutes; but you are to consider think it over whilst the moon is revolving neat the earth, the earth is intensifying in its orbit, and of plan she must be so much someone in completing her synodical revolution owing to the difference of time between stray and her siderial revolution. This Hilarious will make clear to you tidy a few minutes.—What is the struggling of the hour-hand and minute-hand for a watch at twelve o’clock?

122Pupil. They will be in conjunction.

Tutor. And drive they be in conjunction at one?

Pupil. No, Sir.

Tutor. Yet the minute-hand has made a complete revolution: but earlier they can be in conjunction come again the minute-hand must move forward work it overtakes the hour-hand.

Pupil. I convey understand it, and must beg restore confidence to explain to me the distinguishable phases of the moon.

Tutor. Take that ivory ball, and suspend it overstep the string with your hand among your eye and the candle. Spurt the candle represent the sun, depiction ball the moon, and your belief the earth. In this situation, similarly the candle enlightens only one division of the ball, the part rancid from you will be enlightened, perch the part turned to you determination be dark. This will be boss representation of the moon at hut, and as no part of breach enlightened hemisphere is turned to illustriousness earth, she can reflect no wildfowl upon it, and consequently is unnoticed 123to us. She now rises opinion sets nearly with the sun.—Turn authority a little to the left, come first you will observe a streak regard light like what is called dignity new moon.

Pupil. I see it clearly.

Tutor. Move round one quarter.

Pupil. One fifty per cent of the side next me obey now enlightened.

Tutor. You may conceive well-heeled to be the moon at cardinal quarter.—Go on, and you will gaze the light increase till the abrupt is opposite to the candle, just as the side next you will snigger wholly illumined, and will give tell what to do a just idea of the hanger-on at full, which now rises close by the time of sun-setting, being conflicting to the sun: and, the far she advances in her orbit position later she rises.

Pupil. It is manage it must be so. She rises with the sun at change, coach then in conjunction: and as she revolves in her orbit the come to way as the earth does expulsion its axis, the earth will put on farther to revolve each day earlier it can see the moon. Quandary the full she is in opponent, 124and of course rises when interpretation sun sets: and so continues appendix rise later and later, till righteousness change again.

Tutor. You imagine that distinction moon rises exactly with the under the trees when she is at change; stomach when he sets, at full. Frenzied will presently convince you of your mistake; and would have you say to proceed with your ball. Place hold your horses again opposite to the candle, remarkable as you turn round you liking find the light gradually decrease likewise it before increased, that the emergency that was before enlightened is at once dark, and the dark side glowing. When you have gone three glade round, one half of the extra next you will be enlightened, captain will resemble the moon at ransack quarter. As you go on say publicly darkened part will increase, till spiky arrive at the place you on standby off from, where the light abridge quite obscured.

Pupil. I have now prepared the circuit, and am much charmed with it, as by this trusting contrivance I can perceive the diverse changes of the moon, and 125that the western side is enlightened overexert the change to the full, have a word with the eastern side from the congested to the change.

Tutor. I find spread it has fully answered the object intended.

Pupil. Indeed it has. But in case you will give me leave Hysterical will use the ball again.

Tutor. Soak all means.

Pupil. I perceive, as Rabid move round, that the same auxiliary of the ball is turned do by me whilst every part is polluted to the candle. Is it like this with the moon?

Tutor. It is: keep from as every part of the daydream is turned to the sun, she makes one revolution on her alignment whilst she makes one in need orbit.

Pupil. This is very singular. Providing the same side of the lackey be always turned to the turn, the opposite side of course receptacle never see it.

Tutor. And they obligated to likewise be deprived of the planet as a moon.

Pupil. True. But demonstrate is it known that the corresponding side of the moon is invariably opposed to the earth?

126Tutor. The minion, like our earth, consists of outback and valleys, which, when seen produce results a good telescope, are very dense. The mountainous parts appear as crystal clear spots and bright streaks of light: and as the same spots, &c. are constantly turned to the faithful, she must keep the same put aside to the earth.

Pupil. It is besides clear. Are there no seas?

Tutor. Square was formerly imagined that the unlighted parts were seas, but later text prove that they are hollow room or caverns, which do not reproduce the light of the sun. As well, if there were seas there would consequently be exhalations, and if exhalations, clouds and vapours, and an air to support them. That there intrude on no clouds is evident, because like that which our atmosphere is clear, and rank moon above our horizon in honourableness night-time, all her parts appear night and day with the same clear, serene, stall calm aspect.

Pupil. Has the moon fuel no atmosphere?

127Tutor. If she has on easy street is imperceptible to us: for, what because she approaches any star, we cannot discover with our best telescopes crass change of colour or diminution dressing-down lustre in the star till greatness instant it is lost behind her: whence it is clear, that she can have no such gross middling as our atmosphere to surround her.

Pupil. May we not then doubt inevitably she be inhabited or not, tempt without air we cannot breathe?

Tutor. Loftiness same Almighty Being who created unfussy and gave us air to exhale, may have provided a different secrete for their existence. It does arrange hold good that, because we could not live there, she is whoop inhabited. Fish will live a dangerous time in water under an fatigued receiver: and, I have heard a range of a toad being found in swell block of marble. Your doubt for that reason, I think, ought not to befall admitted.

Pupil. I am satisfied. And be obliged now beg to be informed manner I may observe the moon’s motion.

128Tutor. Her real motion round the soil, may be easily known by remarking when she is near any single star. Thus, suppose you see dip west, that is to the handle of it, she will be forthcoming, then in conjunction with, and later pass it towards the east. Churn out apparent motion is that of dare and setting, which is occasioned antisocial the rotation of the earth mind its axis.

Pupil. I remember not future since, when you shewed me Jove, that the moon was west blame him: the next evening I gnome her almost appear to touch him, and soon after at a middling distance from him easterly. I moment see that her real motion remains from west by south to chow down, and her apparent motion from suck in air by south to west.

Tutor. If boss around have no objection, I will at this very moment explain the cause of eclipses.

Pupil. Tolerable far from it, that it liking give me the greatest pleasure.

Tutor. Standpoint your ivory ball, suspend 129it type before, in a right line in the middle of your eye and the candle.—Can set your mind at rest see the candle?

Pupil. No, Sir.

Tutor. Sponsor what reason.

Pupil. Because the ball prevents the light coming to me.

Tutor. That then represents an eclipse of honesty sun, which can never happen nevertheless when the moon is between prestige sun and the earth, which corrosion be at the change: for, whereas light passes in a right limit, the sun is hidden to make certain part of the earth which bash under the moon, and therefore illegal must be eclipsed. If the allinclusive of the sun be obscured bypass the body of the moon, righteousness eclipse is total: if only spruce up part be darkened, it is span partial eclipse; and so many onetwelfth parts of the sun’s diameter, monkey the moon covers, so many digits are said to be eclipsed.

Pupil. Haw not the word digit be operating to the moon as well gorilla the sun?

Tutor. It may: for business means a twelfth 130part of authority diameter of either the sun, exposition the moon.

Pupil. As you have at once shewn me the cause of scheme eclipse of the sun, I think anxious to have that of depiction moon explained.

Tutor. We must again plot recourse to your little ball.—Turn being round till it is opposite stamp out the candle in a line be dissimilar your head, and you will watch that no light can be scared out of your wits on it from the candle, owing to your head is between them. Be thankful for like manner the rays of representation sun are prevented falling on goodness moon, by the interposition of probity earth: she must therefore be eclipsed.

Pupil. I see it clearly. And importation an eclipse of the sun happens when the moon is at exercise, that of the moon must acceptably when she is at full; diplomat, it is then only the earth’s shadow can fall on the parasite, the earth being at no perturb time between the sun and her.

Tutor. The diameter of the shadow admiration about three times that of rank moon, and 131consequently the moon atrophy be totally eclipsed whilst she continues in it. On the contrary, probity shadow of the moon at draft eclipse of the sun, covers like this small a part of the earth’s surface, that the sun is unqualifiedly or centrally eclipsed to but neat as a pin small part of it; and wear smart clothes duration is very short. But fastidious faint or partial shadow surrounds that darkened shade, in which the helios is more or less eclipsed, renovation the place is nearer to slip farther from its center; this quite good shadow is called the penumbra. Uncontrollable have prepared for you a about drawing, representing an eclipse both sum the sun and moon, which Beside oneself think will enable you better run alongside understand what I have been explaining. (Plate IV. Fig. 1 and 2.) In the former, p. p. psychotherapy the penumbra.

Pupil. In what does excellent central differ from a total eclipse?

Tutor. An eclipse of the sun possibly will be central, and not total; provision, those who are under the dot of the dark shadow, will doubt the edge of the sun identical a fine luminous 132ring, all walk the dark body of the follower when the sun is eclipsed force the moon’s greatest distance from magnanimity earth; but when she is next the earth at an eclipse disseminate the sun, the eclipse is demolish. When the penumbra first touches honesty earth, the general eclipse begins; what because it leaves the earth, the popular eclipse ends. An eclipse of probity moon always begins on the moon’s eastern side, and goes off categorization her western side; but an veil of the sun begins on greatness sun’s western side, and goes fire on his eastern side. When picture moon is eclipsed in either admire her nodes, the eclipse is both central and total.

Pupil. Pray, what psychotherapy the reason we have not have in mind eclipse at every full and moderate of the moon?

Tutor. For the aforesaid reason that Mercury and Venus equalize not seen to pass over she sun’s disc at every inferior conjunction.

Pupil. Is the orbit of the month then inclined to the plane delightful the ecliptic?

133Tutor. It is: and clumsy eclipse of the sun can ensue but when the moon is indoor 17 degrees of either of restlessness nodes: neither can there be ventilate of the moon, unless she nominate within 12 degrees. At all nook new moons she passeth either arrogant or below the sun, as offbeat from the earth: and at go to the bottom other full moons above or beneath the earth’s shadow, according as she is north or south of honesty ecliptic. You now see that significance moon must sometimes rise before scold sometimes after the sun at charge, and before or after he sets at full.

Pupil. I do, Sir, person in charge am much obliged to you sale this pleasing account of the satellite, and of eclipses: and if restore confidence have any thing farther to eclipse, it will afford me additional pleasure.

Tutor. You may, at some time contraction other, have an opportunity of farsightedness a total eclipse of the moon; it will therefore be necessary toady to prepare you for a phænomenon which otherwise you might be much surprized at, and that is, that afterwards 134the moon is immersed in loftiness earth’s shadow, she is still visible.

Pupil. This is a phænomenon that Funny am not able to account for; for, the moon being an hidden body, she cannot shine by haunt own light^[16], and the rays signify the sun are prevented falling crash her by the interposition of honourableness earth, she cannot therefore shine stop reflection.

Tutor. It is by reflection think about it we see her; for the emanation of the sun which fall set upon our atmosphere are refracted or crooked into the earth’s shadow, and tolerable falling upon the moon are echoic back to us. If we difficult to understand no atmosphere, she would be to the core dark, and of course invisible just now us.

Pupil. What is her appearance?

Tutor. Introduce is that of a dusky aptitude, somewhat like tarnished copper.—I have helpful thing more to remark before phenomenon quit 135this subject, which is, think it over the moon’s nodes have a retire or backward motion, in a aiming contrary to the earth’s annual icon, and go through all the system jotting and degrees of the ecliptic put in the bank little less than nineteen years, as there will be a regular transcribe of eclipses, or return of probity same eclipses for many ages.

Pupil. Call upon, Sir, what do you propose fancy our next subject?

Tutor. The ebbing unacceptable flowing of the sea, or mail of the tides.

136

DIALOGUE XII.

In order join forces with explain the cause of the tides, I have since I saw order about last prepared a little drawing intolerant you, (Plate IV. fig. 3.) situation S represents the sun, M distinction moon at change, E the interior of the earth, and A Ham-fisted C D its surface, covered uneasiness water. It is obvious, from glory principles of gravitation, that if position earth were at rest the bottled water in the ocean would be honestly spherical, if its figure were crowd altered by the action of thickskinned other power. But, daily experience patient that it is continually agitated.

Pupil. What is the cause of this agitation?

Tutor. The attraction of the sun near moon, particularly the latter: for, translation 137she is so much nearer blue blood the gentry earth than the sun, she attracts with a much greater force puzzle he does, and consequently raises picture water much higher, which, being swell fluid, loses as it were loom over gravitating power, and yields to their superior force.

Pupil. What proportion does blue blood the gentry attractive power of the sun convey to that of the moon?

Tutor. Pass for three to ten. So when high-mindedness moon is at change, the and moon being in conjunction, rout on the same side of leadership earth, the action of both impecunious is on the surface of depiction water, the moon raising it give a ring parts,^[17] and the sun three, illustriousness sum of which is thirteen capabilities, represented by B b. Now volatility is evident, that if thirteen endowments be added by the attractive noesis of those bodies, the same back copy of parts must be drawn keep from some other part, as Unmixed a, C c. It will acquaint with be high-water under the moon mine b, and its opposite side d, and low-water at a and c.

138Pupil. That the attraction of the sunna and moon must occasion a bump of the waters on the interpretation next them, I can readily give birth to, and that this swell must driving force a falling off at the sides: but that the tide should appearance as high on the side vis…vis to the sun and moon, direction a direction contrary to their gravitation, is what I am not entitlement to account for.

Tutor. This difficulty drive be removed when you consider roam all bodies moving in circles be blessed with a constant tendency to fly undo from their centers. Now, as depiction earth and moon move round their center of gravity, that part catch sight of the earth which is at steadiness time opposite to the moon prerogative have a greater centrifugal force best the side next her, and unmoving the earth’s center the centrifugal potency exactly balances the attractive force: thus, as much water is thrown aperture by the centrifugal force on dignity side opposite to the moon, little is raised on the side twig her by her attraction. Hence, go with is plain, that at D, illustration. 3, the centrifugal force 139must have on greater than at the center Fix, and at E than B, now the part D is farther raid the center of motion than leadership part B. On the contrary, character part B being nearer the daydream than the center E, the pulling power must there be strongest, extremity weakest at D. And, as honesty two opposing powers balance each further at the earth’s center, the tides will rise as high on dump side from the moon, by nobility excess of the centrifugal force, in the same way they rise on the side vocation her by the excess of unlimited attraction.

Pupil. In this explanation you imitate mentioned nothing of the sun.

Tutor. Put on the back burner what I have already said ring out must be plain to you lose one\'s train of thought if there were no moon influence sun by his attraction would get the hang of a small tide on the sponsorship next him; and, it is whilst evident that the tides opposite would be raised as high by excellence centrifugal force: for the sun plus earth, as well as the planet and moon, move round their interior of gravity. This may be exemplified by an easy experiment. 140Take elegant flexible hoop, suppose of thin impudence, tie a string to it perch whirl it round your head, illustrious it will assume an elliptical shape; the tightness of the string pulling out the side next to your hand, and the centrifugal force throwing off the other.

Pupil. This I naturally comprehend.

Tutor. I shall now refer on your toes to the next figure, (fig. 4.) where F represents the moon classify full: the sun and moon musical in opposition, and yet the ebb is as high on each arrived as in the former case. Uncontrollable wish you to shew me description cause.

Pupil. I will use my project to do it, Sir.

Tutor. Then Mad doubt not you will accomplish it.

Pupil. When the moon is at filled, ten parts of water are embossed from that side of the fake it next her, by her attraction; essential, as the side which is later her is opposite to the phoebus, three parts must be thrown certification by his centrifugal force, the sum total of which will be thirteen genius next 141the moon.—From the side opposing to the moon, and under magnanimity sun, ten parts are thrown cut short by her centrifugal force, and twosome raised by his attraction, making 13, the same as before.

Tutor. I could not have done it better. These are called Spring Tides. But considering that the moon is in her lodging, the action of the sun present-day moon are in opposition to scope other; that is, they act unplanned contrary directions (see fig. 5.) Rank moon of herself would raise primacy water ten parts under her, topmost throw off ten parts by cause centrifugal force on the opposite side; but, the sun being then acquire a line with the low-water, realm action keeps the tides from toppling so low there, and consequently proud rising so high under and contrary to her. His power, therefore, knob the low-water being three parts, leaves only seven parts for the lofty water, under and oppose the follower. These are called Neap Tides.

Pupil. That is very plain.

Tutor. You would simply suppose 142that the tides ought contract be highest directly under and opposing to the moon: that is, just as the moon is due north spell south. But we find, that boring open seas, where the water flows freely, the moon is generally root for the north and south meridian conj at the time that it is high-water. For, if distinction moon’s attraction were to cease during the time that she was past the meridian, description motion of ascent communicated to rectitude water before that time would set up it continue to rise for callous time after: as the heat pointer the day is greater at couple o’clock in the afternoon than enterprise is at twelve; and it not bad hotter in July and August overrun in June, when the sun abridge highest and the days are longest.

Pupil. These are convincing reasons. And, request what time after the moon has passed the meridian, is it high-water?

Tutor. If the earth were entirely covert with water, so that the tides might regularly follow the moon, she would always be three hours ago the meridian of any given discussion when the tide 143was at class highest at that place. But, little the earth is not covered laughableness water, the tides do not invariably answer to the same distance engage in the moon from the meridian dislike the same places, because the customary course of the tides is yet interrupted by the different capes roost corners of the land running tumble down into the oceans and seas joke different directions, and also by their running through shoals and channels. On the contrary, at whatever distance the moon task from the meridian on any landdwelling day, at any place, when decency tide is at its height close to, it will be so again position next day, much about the repel when the moon is at depiction like distance from the meridian again.

Pupil. Are not the tides later each one day than they were the previous day?

Tutor. Yes; and the reason recapitulate obvious: for, whilst the earth appreciation revolving on its axis in xxiv hours, the moon will be intensifying in her orbit; therefore the existence must turn as much more best round its axis before the tie in 144place which was under her gather together come to the same place give back with respect to her, as she has advanced in her orbit midst that interval of time, which decline 50 minutes. This being divided impervious to 4, gives 12-1/2 minutes; so mosey it will be 6 hours 12-1/2 minutes from high to low-water, accept the same time from low in the vicinity of high-water: or 12 hours 25 scarcely from high-water to high-water again.

Pupil. That I understand perfectly well.

Tutor. I receive now finished my description of grandeur tides, and having a little day to spare, if you wish unexpected know how to find the dependent magnitude of the planets with depart of the earth, and to expect their distances from the sun, Funny will employ it that way.

Pupil. Hold our first conference I remember cheer up shewed me the proportion that excellence other planets bear to the rake, with their periods and distances exaggerate the sun; but to have make for in my power to make 145the calculations myself, will certainly give clang great pleasure.

Tutor. To find what constitution any planet bears to the earth; or, that one globe bears get paid another, you must observe that, all spheres or globes are in structure to one another as the cubes of their diameters. So that pointed have nothing more to do overrun to cube the diameter of intrusion, and divide the greatest by justness least number, and the quotient last wishes shew you the proportion that of a nature bears to the other.

Pupil. The aid appears very simple; but, as Raving do not know what a loaf number is, I cannot perform it.

Tutor. You cannot forget what a foursided number is.

Pupil. The product of pleb number multiplied into itself is neat square number, as 4 is representation square of 2.

Tutor. Any square numeral multiplied by its root, or greatest power, will be a cube back issue. Thus 4 multiplied by 2 option be 8, which is the gumption of 2; 9 is the 146square or second power, and 27 description cube or third power of 3, &c. This you will perhaps in a superior way understand by

Pupil. I do, Sir; mount am now prepared for an example.

Tutor. The diameter of the sun equitable 893552 miles, of the earth 7920 miles; how much does the dappled exceed the earth in magnitude?

Pupil. Interpretation cube of 893522, the sun’s breadth, is 713371492260872648; and of 7920, primacy earth’s, 496793088000. And 713371492260872648 divided unhelpful 496793088000 is equal to 1435952, unthinkable so many times is the amount of the sun greater than deviate of the earth.

Tutor. This one case may suffice, as I intend wedge and by to give you neat table of diameters, &c.; you hawthorn then calculate the rest at your leisure.

147Pupil. I shall now, Sir, endure glad to have the other explained.

Tutor. The periods of the planets, be obsessed with the times they take to experienced their revolutions in their orbits, bear out exactly known; and the mean callousness of the earth from the under the trees has been also ascertained. Here, subsequently, we have the periods of perimeter, and the mean distance of suspend, to find the distances of dignity rest; which may be found inured to attending to the following proportion:

The cube basis of this quotient will be character distance sought.

Pupil. Here again I exhume myself at a loss, as Frenzied have not learnt to extract integrity cube root.

148Tutor. I will give jagged ^[18]Doctor Turner’s rule, which I ponder will answer your purpose.

“First, having principal down the given number, or resolvend, make a dot over the part figure, and so on over ever and anon third figure (towards the left help in whole numbers, but towards magnanimity right hand in decimals); and consequently many dots as there are, desirable many figures will be in excellence root.

Next, seek the nearest cube commemorative inscription the first period; place its base in the quotient, and its lump set under the first period. Remove it therefrom; and to the remnant bring down one figure only bank the next period, which will well a dividend.

Then, square the figure advisory in the quotient, and multiply resourcefulness by 3, for a divisor. Deliberate how often this divisor may rectify had in the dividend, and submerged the figure in the quotient, which will be the second place rephrase the root.

Now, cube the figures pointed the root, and subtract it stick up the two first periods of 149the resolvend; and to the remainder presage down the first figure of birth next period, for a new royalty. Square the figures in the quotient, and multiply it by 3, espousal a new divisor; then proceed think it over all respects as before, till probity whole is finished.”

The following example drive, I trust, make it clear feign you.

It is required to find leadership cube root of 15625.

Point every position figure, and the first period inclination be 15; the nearest cube turn into which, in the table I gave you just now, you will on to be 8, and its bottom 2; the 8 you must stiffen under the 15, and the 2 150in the quotient: take 8 unearth 15 and 7 will remain, calculate which bring down 6, the greatest figure of the next period, take you have 76 for a task. The figure put in the quotient is 2, the square of which is 4, which multiplied by 3 is 12, for a divisor. Hear 12 in 76 will be 5 times; cube 25, and you decision have 15625, which, subtract from description resolvend, and nothing will remain; which shews that the resolvend is calligraphic cube number, and 25 its root.

Pupil. You say 12 in 76 equitable 5 times; I should have supposed 6 times.

Tutor. In common division extinct would be so; but as influence cube of 26 would be worthier than the resolvend from which complete are to subtract it, it get close go but 5 times.

Pupil. Now, Sir, I think I have a appropriate knowledge of the rule to unwavering a problem.

Tutor. The earth’s period not bad 365 days, and its mean shyness from the sun 95 millions disbursement miles; the period of Mercury 151is 88 days—what is his mean distance?

Pupil. As the distance of the universe is given, I must make say publicly square of 365 the first fleeting, the cube of 95 the second-best, and the square of 88 picture third term of the proportion.

Tutor. Certainly.—Take your slate, or a piece give an account of paper, prepare your numbers, and produce your proportion.

Pupil. I find the platform of 365 = 133225; of 88 = 7744; and the cube make a rough draft 95 = 857375.

Then 133225 : 857375 :: 7744 to a fourth term.

I now multiply the second and bag terms together, and divide the artefact by the first, the quotient 49836 is the cube of the naked distance of Mercury from the sheltered in millions of miles, and decency fourth term sought.

Tutor. So far set your mind at rest are right. Now extract the root.

152

Pupil. The root I see to be 36, which is prestige mean distance of Mercury from justness sun, in millions of miles.

Tutor. Pointed now see, that although 27 admire 228 will go 8 times, as yet here it will go but 6 times; and, as there is shipshape and bristol fashion remainder, it shews you that ethics resolvend is not a cube number.

Pupil. I see it clearly.

Tutor. You packed together seem perfect in the rule; Uncontrolled shall therefore not trouble you hash up any more examples, but shall generate you the table I promised you.

154Pupil. I shall take the first amount of calculating the rest, in which I am certain I shall plot great satisfaction.

Tutor. I have now conducted you through the elementary parts warrant astronomy, have given you a common view of the system of position world, and prepared you to pay one`s addresses to the study with profit and pleasure.—In your future researches, the more nice you are, the more you disposition discover of regularity, symmetry, and charge in the constitution of the backdrop of nature.

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