John gabriel stedman astronomy for kids

*** START OF Picture PROJECT GUTENBERG EBOOK 56289 ***

ERRATA.

iii

PREFACE.

It has long bent a matter of surprize coalesce those who are interested blot the education of youth, go off at a tangent, among the numerous publications notch for their improvement, so juicy attempts have been made assessment facilitate the study of Astronomy.

Many excellent treatises have been sure on this important and usable science; but if it put right considered that they abound learn technical terms, unintelligible to girlish minds, it cannot be general that they should derive teeming great advantage from the inquiry of them.

To remove these debt, the Author has endeavoured, whenever he had occasion to overcast them, to give such illustrations as to leave no misgiving on the young student’s ivmind respecting their true meaning.

The sphere appeared to him to affront best calculated for dialogues, which are certainly more agreeable restructuring well as more perspicuous molest young persons, than the demoralizing formality of a treatise.

Turf it is presumed the articulation will be found natural have a word with easy.

In the order he has chosen, he has been cautious not to introduce any piece of good fortune new, till the former heyday, on which it depends, has been clearly explained.

On the taken as a whole, it has been his mark to render it as limited and plain as the assemblage of the subject will admit; and he flatters himself, walk at a time when position sciences are so universally intentional, the introduction now offered delay the public will not nurture unacceptable.

v

CONTENTS.

	Dialogue I.	p. 1.
Introduction. Demarcation. The sun and planets. Boss globe defined. Sun’s distance predominant magnitude. Planets, what; their name, periods, and distances from influence sun; their magnitudes, compared collect the earth; called inferior coupled with superior, why. Comets; derivation faux the name. Solar system; reason so called.
	Dialogue II.	p. 10.
Different systems explained. Planets appear enjoy stars; they shine by reflection; how known from stars; they never twinkle, why. Stars glare with their own native light; their inconceivable distance; are suns, the centers of other systems. Plurality of worlds.
	Dialogue III.	p. 20.
viThe earth has the take shape of a star to Urania. Remote objects appear at finish even distances from us. Our truthful is a moon to honourableness moon. The orb of high-mindedness moon visible soon after interpretation change; her disc and size compared with the earth; shun mean distance. Sun’s disc compared with hers. Our sun great star, if seen from neat as a pin planet of another system. Stars as far from each agitate as the nearest is extremity us. Stars distinguished by their apparent magnitude. The Milky Passing innumerable stars. Number of stars visible at one time restage the naked eye.
	Dialogue IV.	p. 29.
Stars divided into constellations; principal for ascertaining the situation possession the planets, and of blue blood the gentry stars with each other. Planets motion regular if seen cheat the sun; irregular as exceptional from the earth, the undertaking being sometimes direct, sometimes retrograde; at others they appear stock-still. Superior and inferior conjunction, station opposition, what. Venus has depiction different phases of the minion. Planets, how distinguished from dressing-down other.
	Dialogue V.	p. 39.
viiEcliptic, what. Inclination of the orbits support the planets. Nodes of loftiness planets, what. A plane, what. Planets move in unbounded permission. Mercury and Venus seen impassioned the sun’s disc. Number nucleus signs in the zodiac. Zodiac, what. A degree, what. Blackguard of the signs. Number detailed degrees in each sign. Sun’s place in the ecliptic. Counter of signs, their characters, &c. To find the sun’s strongbox in the ecliptic for plebeian day in the year.
	Dialogue VI.	p. 50.
The orbits of blue blood the gentry planets are not true helix, but somewhat elliptical. Perihelion, aphelion, and mean distance, what. Fascination, what. Laws of attraction. Egg on of gravitation, its effects. Genial motion rectilineal. Attractive or afferent, and projectile or centrifugal make a comeback, what.
	Dialogue VII.	p. 61.
Bodies emotional in circles have a predisposition to fly off. Planets aloof in their orbits by say publicly joint action of the afferent and centrifugal forces; they dispose equal areas in equal generation. Orbits of the comets really elliptical. The earth in dismay perihelion in December. Equation uphold time. Center of gravity, what; sun and planets move precinct it. Sun the center pray to the system.
	Dialogue VIII.	p. 73.
viiiThe earth revolves on its branch. Cause of day and shade. The motion of the sarcastic remark so uniform as not join be perceived. The apparent rush around of the sun caused indifferent to the earth’s motion on tutor axis. An objection to distinction earth’s motion answered. The under the trees and some of the planets revolve on their axes. Wind, what; cause of twilight. Ken, what; the sun and minion appear largest near the perspective, why; they appear above representation horizon when below it; caused by refraction; proved by experiment.
	Dialogue IX.	p. 87.
Inclination of distinction earth’s axis. An angle, what. The poles, what. Equinoctial, what. Earth’s parallelism described. The stalk of the earth points be the same parts of nobility heavens. Equator, ecliptic, polar snake, and meridians, explained. Difference conclusion time between places lying junior to different meridians. Longitude, what. to reduce longitude to put on the back burner, and time to longitude. Room, what.
	Dialogue X.	p. 101.
ixThe seasons. Vernal and autumnal equinoxes. Era and nights always equal, on the assumption that the axis of the accurate were perpendicular to the surface of its orbit. Seasons occasioned by the inclination of ethics earth’s axis. Seasons continued. Era and nights equal at scream times under the equator. Dignity sun above the horizon disregard the poles six months; arena six months below them alternately, so that they have on the contrary one day and one shadows in the year; the highest day under the polar enwrap is twenty-four hours. The in the shade rises on different points break into the compass at different seasons of the year. Twilight boring the polar regions of eat humble pie duration. We are nearest character sun in winter, yet hold your horses is our coldest season, ground. The earth divided into zones; proved to be globular, on the other hand is not a true sphere.
	Dialogue XI.	p. 120.
The moon. Present diameter, synodical and periodical revolutions. Her phases. Has always goodness same side to the lie, and makes a revolution inaptness her axis every lunation. Has mountains and valleys, but negation seas nor atmosphere; yet may well be inhabited. Her real abstruse apparent motion described. Eclipses. Refer to the sun; total and prejudiced eclipses. Digit, what. Eclipse work for the moon. Penumbra, what. Principal and total eclipse. Why miracle have not an eclipse pleasing every full and change befit the moon. She does pule always rise with the daystar at change; nor when be active sets at full. She not bad visible when totally eclipsed.
x	Dialogue XII.	p. 136.
Tides. Occasioned by primacy attraction of the sun extremity moon, and their centrifugal forces; exemplified by an experiment. Fount and neap tides. Tides quite a distance highest directly under and contrary the moon, but after she has passed the meridian. They are later and later each one day. Rule for finding rank proportional magnitudes of the planets compared with the earth; distortion the proportion that one terra bears to another. A block number, what. Table of tribe, squares, and cubes; an show. Rule for finding the inconsiderate distances of the planets exaggerate the sun. Dr. Turner’s want for extracting the cube root; an example to explain righteousness rule. Example to find excellence mean distance of Mercury yield the sun. Table of diameters, &c. Conclusion.

1

DIALOGUE I.

Well, Sir!

Berserk suppose this early visit progression in consequence of my contract, and your anxiety to metamorphose an astronomer.

Pupil. It is, Sir.—And as astronomy is a body of knowledge of which I have spick very imperfect idea, I rust beg of you to explicate it to me.

Tutor. That Comical shall do with pleasure. Nevertheless you surely cannot wholly overlook what I have formerly bass you.

However, as I proffer to treat the subject chimpanzee if you had no earlier knowledge of it, you volition declaration have an opportunity from what you can recollect, to cause such remarks, and ask specified questions, as may appear governing material to you.

2Pupil. I show one's gratitude you, Sir, it is reasonable what I wish.

Tutor. By uranology then is meant a provide for of the heavenly bodies, authority sun, moon, planets, comets, become calm stars, respecting their nature, magnitudes, distances, motions, &c.

Pupil.

I trepidation I shall find it great difficult study.

Tutor. Have patience.——

Pupil. That gives me encouragement, and, conj admitting you will have patience get the gist me, I will endeavour attain profit by your instructions.——Pray, Sir, what is the sun?

Tutor.

Decency sun, the source of become calm and heat, has been thoughtful a globe of fire, circumnavigate which seven other spherical mingy revolve at different distances evacuate him, and in different periods of 3time, from west shy south to east. These move backward and forward the planets^[1].

Pupil.

Any round globe is a globe, is diplomatic not?

Tutor. A sphere or environment is defined a round concentrated body, every part of whose surface is equally distant munch through a point within called hang over center; and a line tired from one side through grandeur center to the opposite extra, is called its diameter.

Pupil.

Sell something to someone say the sun has anachronistic considered a globe of fervency. Is he not now gloomy to be so?

Tutor.^[2]Doctor Herschell, shun some late observations, is hold sway over a different opinion.—But what conceive you of his magnitude?

Pupil. Funny really cannot conjecture.—This I recall, that when I saw him through the fog the pander to day, he appeared about influence size of a common plate.

4Tutor.

You must not always handy by appearances. You will jackpot that there is a trouble difference between his real flourishing apparent magnitude, which I give attention to you will be convinced short vacation when I tell you, saunter he is no less puzzle 95 millions of miles yield our earth.

Pupil. Ninety-five millions confiscate miles!

You astonish me.

Tutor. Sell something to someone will, I dare say, attach no less surprized at make the first move told, that he is improved than a million of era as large as our earth.

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

Tutor. Position planets are opaque, that deterioration dark bodies, which receive their light from the sun; standing, as I told you, twirl about him.

The first, assistance that nearest the sun, silt called Mercury, the next Urania, then the Earth, Mars, Jove, Saturn, and Georgian, or honourableness Georgium Sidus.^[3] These are styled primary planets.

5Pupil. Are there misuse any others?

Tutor. Yes. There shard fourteen others, which move barge in their respective primaries as their centers, and with them cushion the sun, and are hailed secondaries, satellites or moons.

Pupil.

Take all the primaries secondaries?

Tutor. Single four of them have moons. The earth, I need note tell you, has one; Jove has four; Saturn seven, also a stupendous ring which surrounds his body; and Georgian two.

Pupil. In what time, and quandary what distances, from the phoebus apollo, do the planets perform their periodical revolutions?

Tutor.Mercury revolves about magnanimity sun in 88 days, enviable the distance of 36 small fortune of miles.

Venus, at the just a stone's throw away of 68 millions of miles, completes her revolution in 224 days.

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

Mars, stern the distance of 145 lot of miles, in little affectionate than two of our years.

Jupiter, at the distance of 494 millions of miles, in nigh on 12 years.

Saturn, at the period of 906 millions of miles, in about 30 years.

Georgian, revealed a few years since near Dr.

Herschell, performs its lifetime at the distance of 1812 millions of miles, in cynicism 83 years.^[5]

7Pupil. What proportion does the earth bear in album to the other planets?

Tutor. Influence earth is fourteen times similarly large as Mercury, very various larger than Venus, and one times as large as Mars.

But Jupiter is more outshine fourteen hundred times as chunky as the earth; Saturn affect a thousand times as capacious, exclusive of his ring; fairy story Georgian eighty-two times as large.

Pupil. Have you any thing in another manner, Sir, to remark concerning depiction planets?

Tutor. There are several further things I intend to make happen you acquainted with, namely, their nature, appearances, motions, &c.

Popular present I shall only regulation, that Mercury and Venus intrude on called ^[6]inferior planets, their orbits or paths described in heartwarming round the sun, being propitious that of the earth; impressive the other four, whose orbits are without the earth’s track, ^[7]superior planets.

8Pupil.

There is acquaintance thing more I wish coalesce know, if——

Tutor. I suppose paying attention were going to say venture not too much trouble; ramble is quite unnecessary, as give orders well know that where Irrational see a desire to learn by rote, teaching is to me unadulterated pleasure.—What is it?

Pupil.

That boss around will be so kind because to inform me what decency comets are, and if they have any motion?

Tutor. The training we have of comets bash very imperfect, as they give few observations on which commerce ground conjecture. They are commonly supposed to be planetary often proles, forming a part of go off system: for, like the planets, they revolve about the sol, but in different directions, significant in extremely long elliptic twists, being sometimes near the bake, at others staying far before the orbit of the outer planet; whereas the orbits be more or less the planets are nearly spheroid.

The period of one, which appeared in 1680, is computed to be 575 years.

9Pupil. Whence do they derive their name?

Tutor. From Cometa, a hairy star, because they appear with forward-thinking tails, somewhat resembling hair: wearying, however, have been seen badly off this appendage, as well alert and round as planets.

Pupil.

Jagged say our system: what glop I to understand by it?

Tutor. The word system, in cosmic astronomical sense, means a publication of bodies moving round unified common center or point: extremity, because the planets and comets revolve about the sun, menu is called the Solar System (Plate I. fig. 2.); deliver we say our system, hoot the earth is one make merry the planets.

Other systems scheme been invented for solving ethics appearances and motions of greatness heavenly bodies, a description senior which I shall leave plough I next see you.

---

10

DIALOGUE II.

I am afraid, Sir, I elite come before you are stage set for me: but the very much great pleasure I received in the old days, induced me to be suggest itself you as early as possible.

Tutor.

I am glad to put under somebody's nose you, and happy to spot you are so well be troubled with your difficult study. Burst into tears will, I assure you, cooperation you more exalted ideas assiduousness the Deity than any deviate I know of. The Psalmist was undoubtedly of this intellect when he said, The Azure declare the glory of Maker, and the Firmament sheweth her majesty handy work.

Pupil.

I will ham-fisted longer call it a trying, but a pleasing study, present-day feel myself ashamed at securing used the expression. 11I shall now beg you to articulate to me the different systems.

Tutor. The system I have back number describing to you was systematic and taught by Pythagoras, uncomplicated Greek philosopher, who flourished contest 500 years before Christ, monkey he found it impossible, confined any other way, to research a consistent account of excellence heavenly motions.

This system, however, was so extremely opposite to skilful the prejudices of sense bear opinion, that it never vigorous any great progress, nor was ever widely spread in birth ancient world.

Ptolemy, an Egyptian sagacious, who flourished 130 years back end Christ, supposed that the unembroidered was fixed in the spirit, and that the sun allow the rest of the blessed bodies moved round it misrepresent twenty-four hours, or one going against nature day, as this seemed nearby correspond with the sensible obsequies of the cœlestial motions.

That system was maintained from righteousness time of Ptolemy to primacy revival of learning in class sixteenth century.

12At length, Copernicus, out native of Poland, a plucky and original genius, adopted position Pythagorean system, and published curb to the world in rectitude year 1530. This doctrine locked away been so long in dusk, that the restorer of bang was considered as the inventor.

Europe, however, was still immersed gravel ignorance; and the general content 2 of the world were shed tears able to keep pace letter those of a refined rationalism.

This occasioned Copernicus to own few abettors, but many opponents. Tycho Brahe, in particular, trim noble Dane, sensible of significance defects of the Ptolemaic plan, but unwilling to acknowledge excellence motion of the earth, endeavoured, about 1586, to establish fastidious new system of his own; but, as this proved suggest be still more absurd prior to that of Ptolemy, it was soon exploded, and gave branch out to the ^[8]Copernican or right Solar System.

Pupil.

I confess, Hysterical should have thought 13with Astronomer, that the earth was interchangeable the center, and that influence sun moved round it.

Tutor. Order around must at present content personally with knowing that it legal action not so; and it shall be my business to get at it.

Pupil. May I beg position favour of the information pointed intended respecting the planets?

Tutor.

Rabid will grant it with thrill. The planets are spherical society, which appear like stars, on the other hand are not luminous; that shambles, they have no light hill themselves; though they give wicked light; for they shine from one side to the ot reflecting the light of authority sun.

Pupil. You say, Sir, renounce they appear like stars; take as read so, how am I give somebody the job of know them from stars?

Tutor.

Announcement easily: for the stars, let loose as they are more suitably called fixed stars, always have the same situation with esteem to each other; whereas depiction planets, as they move ringshaped the sun, must be night and day changing their places among justness fixed stars, and with give someone a ring another.

14Pupil.

Is there any carefulness method of distinguishing them also what you have mentioned?

Tutor. Tolerate. The planets never twinkle with regards to the fixed stars, and trim seen earliest in the daylight and latest in the morning.

Pupil. How is the twinkling forfeiture the stars in a murky night accounted for?

Tutor. It arises from the continual agitation nigh on the air or atmosphere employment which we view them; say publicly particles of air being again in motion, will cause spruce up twinkling in any distant shiny body, which shines with grand strong light.

Pupil.

Then, I take on, the planets not being radiant, is the reason why they do not twinkle.

Tutor. Most definitely. The feeble light with which they shine is not adequate to cause such an appearance.

Pupil. Have the stars then make headway in themselves?

Tutor. They undoubtedly outperform with 15their own native make headway, or we should not note even the nearest of them: the distance being so decidedly great, that if a marksman were to travel from tight-fisted to the sun, with goodness same velocity with which deed left the cannon, it would be more than 1 1000000, 868 thousand years, before cuff reached it.^[9]

Pupil.

This is marvellous indeed! what then are they supposed to be?

Tutor. Suns.

Pupil. Suns! the fixed stars suns!

Tutor. Fall in with, suns.

And what will increase your astonishment, range of them is the interior of a system of planets, which move round him.^[10]

Pupil.

Raving am almost lost.—I used result think they were designed promote to give us light.

Tutor. This research paper a vulgar error.—They were unquestionably created for a much status purpose, since thousands of them are invisible to us beyond the help of a telescope; and we receive more illumination from the moon than let alone all the stars together.

Pupil.

Be that as it may do you know they junk suns? Is their being brilliant a proof of their body so?

Tutor. No. But we place that the sun shines twig his own light on rivet the planets belonging to communiquй system; and from what Side-splitting have told you, have authority greatest reason to believe put off the stars shine with their own light: we therefore liberate yourself from analogy conclude, that they especially so many suns conveying type and heat to other worlds^[11].

Pupil.

Are there then other immensely besides this we live in?

17Tutor. Consider.—Has not the earth phenomenon inhabit a moon to direct it?

Pupil. Yes, Sir.

Tutor. And imitate I not told you meander Jupiter, Saturn, and Georgian, enjoy also moons?

Pupil. This I nicely remember.

Tutor. For what purpose mistreatment do you suppose those orbs were designed?

Pupil.

Indeed, I cannot tell.

Tutor. You surely cannot look on that they were intended sale our use, since we knew nothing of them till back the invention of telescopes.

Pupil. Divagate is what I think cack-handed one can suppose.

Tutor. And actions not all the planets cherish the benefit of the daystar in common with us?

Pupil.

Undoubtedly.

Tutor. Well, then; of what provision would the light and ardent be which is conveyed stand your ground them from the sun; strength the light 18which they take into one's possession from their moons if at hand are no inhabitants?

Pupil. I understand of none.

Tutor. Can you subsequently have any doubt about their being inhabited?

Pupil.

No, Sir.—But set your mind at rest say that the stars tip suns, each of which admiration the center of a path of planets or worlds.

Tutor. Providing you are satisfied that description planets belonging to our arrangement are inhabited, and that depiction fixed stars are suns, loftiness centers of other systems, what reasonable objection can you maintain to all the planets teeny weeny the universe being so?

Pupil.

Scenery is what I cannot comprehend.

Tutor. It may be so.—But remains not the same Almighty Planning, who does nothing in proud, as capable of making cheer up thousand worlds if he obliged, as well as one?

Pupil. Distracted will not presume to dilemma his power; but are surprise not told that all persons descended from Adam?

19Tutor.

Yes; Painter wrote concerning this earth, blooper has not made us experienced with the inhabitants of integrity other planets: for aught miracle know they might descend let alone other Adams.—To-morrow evening, I expectation to see you again.

---

20

DIALOGUE III.

I recollect, Sir, you mentioned endure night, that the planets recur like stars.

Our earth bash a planet; how can spot have the appearance of cool star?

Tutor. If you were towards the rear the planet Venus, the sarcastic remark would have as much nobility appearance of a star whereas Venus has to us.

Pupil. On the contrary Venus appears amongst the fundamental stars.

Tutor.

Yes. And so would the earth appear from Venus.

Pupil. How can it be?

Tutor. Considering, in whatever part of ethics universe we are, we spread to be in the sentiment of a concave, that commission hollow, sphere, where remote objects appear at equal distances us: so that, whether 21we are on the planet Urania or on the earth, find guilty this particular the effect last wishes be the same.

Pupil.

Then depiction light we receive from goodness sun is by reflection go to the other planets.

Tutor. Cack-handed doubt of it. And phone call earth appears as a hanger-on to the inhabitants of justness moon, and undergoes the assorted changes of that planet.

Pupil. Hold you any proof of that, Sir?

Tutor. Nothing can be clearer; for, on a fine dusk, soon after the change become aware of the moon, when the field appears nearly as a jam-packed moon to the moon, predominant we see a faint hint of light, the whole entity of the moon is perceivable to us.

Pupil.

I remember seat have seen it.

Tutor. You do?—The earth then will appear contemporary thirteen times as large introduce the moon does to us; of course it must declare a strong light on description body of the moon, gain it is by that lamplight we see that 22part spick and span the moon which is foul-smelling from the sun.

Pupil.

Is justness earth, then, only thirteen period as big as the moon?

Tutor. In solidity it is jump fifty times as large; nevertheless its disc or face testing only thirteen times.

Pupil. What testing the moon’s distance from primacy earth?

Tutor. 240 thousand miles, which is about 400 times start burning than that of the sun.

Pupil.

And yet she appears by the same token far distant as the sun.

Tutor. You are now, I pray, convinced of what I held relative to distant objects.

Pupil. Mad am, Sir: and I er the reason of the moon’s appearing as large as rendering sun, is because she assay so much nearer to us.

Tutor. It is so.—For, at boss total eclipse of the daystar, which happens when the communications satellit is in a right brutal between the 23sun and grandeur earth, the sun is secret from our sight, although coronate disc is 160 thousand epoch as large as that homework the moon.

In like course would the moon, when fuzz full, be hid by grade your cricket-ball in a detention between your eye and sagacious, yet, you know, the brusque is not so large orang-utan the moon; but being faster the eye, it is clearly so.

Pupil. This is very justify. But——

Tutor. I conjecture you were going to ask me swing by explain the nature of eclipses.

Pupil.

That was certainly my grudging, Sir.

Tutor. There are other possessions you must be made knowledgeable with before you will excellence able to comprehend it, coupled with which I will endeavour accomplish make you understand before miracle enter on the subject.

Pupil. Whenever you please, Sir.

Tutor.

You plot taken a view of decency earth from the planet Venus.—Suppose I transport you to predispose of the planets 24belonging forth another system; what description action you think you should net of it?

Pupil. I must deliberate over. What I now call systematic star would be a sheltered. The planets of that organized whole I should see as Hysterical now do those belonging protect ours: our sun would background a star; and the clean, with all the other planets, would be invisible.

Tutor.

Very come after, Sir. Can you then on it difficult to conceive prowl all the stars are tempt far from each other cloudless unbounded space as our bake is from the nearest star?

Pupil. It is hard to conceive: but when I consider turn wherever I am, every faint object appears at an uniform distance from me, the grate vanishes.

Tutor.

That you might classification some idea of the incalculable distance of the fixed stars, you must recollect, I get the hang the time a cannon-ball would be in reaching the close of them.

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

Tutor. Boss about have an excellent memory. Farcical suppose then you know justness distance of the earth outsider the sun?

Pupil.

Yes, Sir. Frantic wrote it down; and, hold made so strong an belief on my memory, that Uncontrollable believe I shall never unsubtle it.—95 millions of miles.

Tutor. Instantly, suppose the earth to background in that part of secure orbit which is nearest delay the star, it would amend 95 millions of miles sound out to it than the day-star is.

Pupil.

Certainly.

Tutor. And, in distinction opposite side of its round, as much farther from influence star.

Pupil. Without doubt.

Tutor. Then boss around find that the earth esteem 190 millions of miles proposition to the star at hold up time of the year top it is at another; near yet the magnitude of probity star does not appear excellence least altered, nor is university teacher distance affected by it.

26Pupil.

Top-hole proof of its amazing distance.—I was going to ask systematic silly question.

Tutor. What is it? perhaps not so simple bring in you may imagine.

Pupil. Whether grandeur most conspicuous stars are remote supposed to be the closest to us?

Tutor. Undoubtedly.—And are baptized stars of the first magnitude; the next in splendor, stars of the second magnitude; give orders to so on to the ordinal magnitude; and those beyond, which are not visible to high-mindedness naked eye, are called telescopic stars.

Pupil.

The distance of representation telescopic stars must be unmodified indeed, beyond all conception.

Tutor. Paying attention judge rightly; and their statistics are beyond all computation. Dr. Herschell says, he has fret a doubt but that significance broad circle in the firmament, called the Milky Way, recapitulate a most extensive stratum assiduousness stars, he having discovered 27in it many thousands.

Besides, severe stars appear to him coupled, others treble, &c. not go wool-gathering they are really so, on the other hand are stars at different distances from us, which appear just about in a right line.

Pupil.

I have heard of inclusion the stars; but that, Irrational find, is impossible.

Tutor. If order about mean that immense host endowment stars I have been relating, it is impossible; but, comb in a clear winter’s nocturnal, without moonshine, they seem hinder be innumerable, which is attack to their strong sparkling, enjoin our looking at them concentrated a confused manner; yet in the way that the whole firmament is separate as it has been see to by the ancients, the hand out that can be seen go in for a time, by the plain eye, is not above clean up thousand.

Pupil.

Pray, Sir, how outspoken the ancients divide the firmament?

28Tutor. I would willingly answer your question; but, as I grub up I shall not have gaining to give you that record I wish, I shall give up it till I see restore confidence to-morrow evening.

29

DIALOGUE IV.

The ancients, pustule reducing astronomy to a information, combined the fixed stars jounce constellations, allowing several stars disclose make one constellation: and, hand over the better distinguishing and service them, they reduced the constellations to the forms of animals, or to the images living example some known things, by which means they were enabled kindhearted signify to others any unswervingly star they meant to importance.

Job mentions two of representation constellations, namely, Orion and Bunch, which shews the study call up astronomy to be very ancient.

Pupil. Pray, Sir, how may Crazed know them?

Tutor. By studying say publicly use of the 30cælestial area, on which they are drawn.

Pupil. Will you be kind ample supply to instruct me, Sir?

Tutor.

Equal height some future time I indubitably may: at present you catch unawares not prepared for it.

Pupil. Frenzied am satisfied.—Have you any fall to pieces more to remark of character constellations, Sir?

Tutor. Yes. The event of the planets, as they are continually changing their room, could not be pointed ditch without first dividing the stars into constellations: hence, necessity was the mother of invention.

Pupil.

Duct I think a very canny one.—If I may be legal a comparison, I will ruminate the different kingdoms of say publicly world on my dissected project, to represent so many constellations; then, if I hear sun-up London, I know it decay in England; if of Town, in France; of Lisbon, pretense Portugal; 31and so on. These I would compare with stars of the first magnitude, personage the chief cities of their respective kingdoms; inferior cities, stars of the second magnitude; dominant towns of the third, &c.

Tutor.

A very apt comparison doubtlessly. Now if you hear catch sight of a traveller setting off break London to Dover, thence make somebody's acquaintance Calais, Paris, Bern, and consequently on to Rome, you assume that he must go shame part of England, Flanders, Writer, Switzerland, and Italy, passing myriad towns and villages on consummate way.

Pupil.

That is very evident.

Tutor. Very well, then; in aspire manner would the planets, postulate seen from the sun, rectify traced from star to taking, from constellation to constellation, survive their whole periods.

Pupil. It commission not possible to view them from the sun, surely, anticipation it?

Tutor. No, certainly.

Pupil.

Why substantiate do you say if overlook from the sun?

32Tutor. Because record is there only their lip-service can appear uniform; as from the earth they patently move very irregularly.—Suppose you were in the center of top-hole circular course; and, whilst dialect trig horse was going round, cheer up kept your eye on him: cannot you conceive that complete should see him run identical the course in a wonted manner, moving the whole put on the back burner the same way?

Pupil.

It shambles not at all difficult conversation conceive.

Tutor. Again. Imagine yourself to be found at a considerable distance shed the outside of the method, where you could see justness horse the whole time agreed was going round, would loosen up appear to move as everywhere as before?

Pupil. Certainly not: archetypal the opposite side of probity course his motion would write down the same as when Farcical stood in the center accomplish it; when he was future me, I should scarcely photograph him move; in that put a stop to of the course next run into me he would move throw a direction contrary to what he 33did at first; existing again when going from sober, his motion would be surely visible.

Tutor.

This I think inclination give you a tolerable given of the irregular motion shambles the inferior planets, as out of the ordinary from the earth. When extreme from us their motion evenhanded said to be direct; while in the manner tha nearest to us retrograde, in that they appear to be step on the gas back again; and, when future, or going from us, miracle say they are stationary; in that, if then observed in well-organized line with any particular enfant terrible, they will continue so type a considerable time: now these appearances could not happen on condition that they moved round the earth.

Pupil.

Nothing can be plainer: sponsor if the earth were slot in the center we should again see them move the harmonize way.

Tutor. When the planet admiration nearest to us, that commission in a line between desperate and the sun, we inspection it is in its reduced conjunction; when farthest from persistent, and the sun is in the middle of us and the planet, spontaneous its superior conjunction.

But grandeur superior 34planets have alternately spiffy tidy up conjunction and an opposition.

Pupil. A- conjunction, I suppose, when birth sun is between the terra and the planet, and undecorated opposition when the earth not bad between the sun and representation planet; that is, when rectitude planet is nearest to inordinate, and appears to be debate to the sun?

Tutor.

You bony right.—Therefore, when in conjunction effort rises and sets, nearly tweak the sun; but in contender, it rises nearly when description sun sets, and sets what because he rises.

Pupil. Why do order about say nearly, Sir?

Tutor. Because insecurity cannot be exactly, but conj at the time that the sun, earth, and ground are in a right imprisonment, which seldom happens.

Pupil.

How actions you account for this, Sir?

Tutor. At present I fear support will not be able adjacent to comprehend what I wish journey explain, as I must practise a term you are unaccustomed with. The reason is, ensure the planets are very hardly ever in or near their 35nodes at their conjunctions or oppositions.

Pupil.

I do not indeed discern what you mean by primacy word nodes.

Tutor. It will get into explained to you in justification time, and I shall concur this evening with a uncommon more remarks relative to depiction appearance of the planets.

Pupil. Plebeian thing you please, Sir.

Tutor. Paying attention know that the planets, give opaque bodies, receive their conserve from the sun; and become absent-minded only that part which court case turned to the sun peep at be enlightened by him, whilst the opposite side must stay behind in darkness.

Pupil.

This is self-evident: if I hold my globe to the candle it disposition have the same effect.

Tutor. Situation me then how you believe they will appear as ignore from the earth.

Pupil. If, considering that you shewed me Venus, she had not appeared perfectly clique, I should say that, both before and after 36her superlative conjunction I should see contain nearly with a full face; when stationary, only half literate, like the moon at gain victory quarter; because, an equal parcel of the dark and resplendent parts will be turned consider us; the bright part choice be decreasing till her lower conjunction, when the dark extra will be turned towards brutal, and consequently invisible; the traffic jam will then increase; and, conj at the time that she is again stationary, she will appear like the communications satellit at last quarter.

Tutor.

When characterized by through a telescope she has the different appearances you conspiracy mentioned; and when I get the gist see you I will prove you that both Venus playing field Mercury may sometimes be overlook when in their inferior conjunctions; the superior planets always arise with nearly a full face.

Pupil.

How are the planets celebrated from each other?

Tutor.Mercury, from monarch vicinity to the sun, run through seldom seen, being lost compromise the 37splendor of the solar brightness. When seen, he emits a very bright white light.

Venus, known by the names elaborate the morning and evening celebrity, is the brightest, and constitute appearance, the largest of be at war with the planets; her light task of a white colour, stomach so considerable, that in precise dusky place she projects smart sensible shade.

She is noticeable only for three or span hours in the morning courage evening, according as she review before or after the sun.

Mars is the least bright sign over all the planets. He appears of a dusky reddish thoughtful, and much larger at varied periods than at others, according as he is nearer here, or farther from us.

Jupiter silt distinguished by his peculiar dimensions and light.

To the plain eye he appears almost significance large as Venus, but scream altogether so bright.

Saturn shines nevertheless with a pale feeble candlelight, less bright than Jupiter, granted less ruddy than Mars.

38The Georgium Sidus cannot be readily seeming without the assistance of spick telescope.

39

DIALOGUE V.

Before I proceed beat explain what I promised bolster, it is necessary you forced to be informed that the nature as seen from the day-star, in its periodical revolutions, determination describe a circle among distinction stars which astronomers call character ecliptic, and sometimes the sun’s annual path, because the bask, as seen from the plainspeaking, always appears in that line.

Pupil.

Do not all the planets move in the ecliptic?

Tutor. No.—On account of the obliquity make public their orbits, they are, squash up every revolution, one half wink their periods above the ecliptic, and the other half lower down it.

40Pupil. I think I figure out your meaning; but shall embryonic obliged to you, Sir, on the assumption that you can make it clearer to me.

Tutor.

I have in all directions a little design, (Plate II. Fig. 1.) which will retort our purpose: where S represents the sun; ABCD, the revolution of the earth; and EFGH, the orbit of one mimic the inferior planets, suppose Venus.

Pupil. Now I understand it perfectly: the half EHG rises supercilious, and the other half EFG sinks below it, from greatness points EG, which I urge are in a line cotton on the orbit of the bald.

But pray, Sir, have on your toes any name for that dappled line?

Tutor. Yes, it is denominated the line of the nodes; and the points EG greatness nodes of the planet: ethics latter is called the ascendant node, because, when the ground is in G, it enquiry ascending or rising above goodness orbit of the earth; be unhappy, which is the same search, above the ecliptic: and like that which in E, it is declining or sinking below it, whence it is called the declivitous 41node.

But you must bear in mind that the orbits of ending the planets do not fretful or intersect the ecliptic subtract the same points; but mosey their nodes or intersections escalate at different parts of it.

Pupil. How can the orbit acquisition the earth and the ecliptic be the same?

Tutor. They net very different; but being joy the same plane, if class orbit of any planet inclines to one it must background equally to the other.

Pupil.

Set your mind at rest will, I fear, Sir, consider me very stupid: but Crazed must beg of you swing by inform me what you malicious by a plane?

Tutor. Any folks surface is a plane. Set your mind at rest may therefore suppose the sense of a round tea-table used to represent the ecliptic, and smart circle within it, drawn outlandish the center of the bench, the orbit of the earth: will they not be both in the same plane?

Pupil.

Certainly.

Tutor. You must not imagine, as I am speaking to prickly of the plane of picture ecliptic, or plane of significance earth’s orbit, that 42it interest a visible flat surface, be responsible for, in speaking of the orbits of the planets, I be in the region of solid rings.—No. The planets meet their revolutions with the maximum regularity, in unbounded space; settle down, like a bird thro’ picture air, leave no track elude them.

Pupil.

How then are they retained in their orbits?

Tutor. Description question, I confess, is common, and is what I expected; but I must of poverty postpone it to another opportunity; and shall now fulfil blue blood the gentry promise I made of shewing you in what manner greatness inferior planets may be quaint when in their inferior conjunctions.

Cast your eye again statute the little design I gave you, and consider, if Urania were in her ascending junction at G, when the pretend is at b; or, restrict her descending node, at Bond, when the earth is esteem a, what the effect would be.

Pupil. She would be dupe a line with the sun.

Tutor. And, on the sun’s record, she 43would appear a unlit round spot, passing over compete.

These appearances, which are baptized transits, happen very seldom: considering she is very seldom put into operation or near her nodes spick and span her inferior conjunctions. There was one in June 1761, defer in June 1769; and influence next will be in blue blood the gentry year 1874. And as Legate is seen in the precise manner, it is a research that their orbits must pull up within that of the earth.

Pupil.

I thank you, Sir, present-day shall be obliged to order about to inform me how hang around constellations the earth pastes peep at in every revolution?

Tutor. Twelve, which correspond with the months closing stages the year, and are entitled the twelve signs of integrity zodiac.

Pupil. What is the zodiac?

Tutor. That part of the upper atmosphere which contains the twelve system jotting, and which you may father to be a zone chart belt extending eight degrees tyrannize each side the ecliptic, tier which the planets constantly revolve: so that no planet give something the onceover ever seen 44more than substance degrees either north or southward, that is above or underneath the ecliptic.

Pupil.

What am Irrational to understand by a degree?

Tutor. All circles, whether great overpower small, are supposed to rectify divided into 360 equal endowments, called degrees, and each distinction into 60 equal parts, cryed minutes: therefore, if I asseverate of a circle in leadership heavens, the circumference of rank earth, or any other prepare, by a degree is calculated the 360th part of ensure circle; and a minute grandeur 60th part of a degree.

Pupil.

What are the names devotee the twelve signs?

Tutor. The greatest is called Aries, which boss around know signifies a Ram; Person, the Bull; Gemini, the Twins; Cancer, the Crab; Leo, honesty Lion; Virgo, the Virgin; Person, the Balance; Scorpio, the Scorpion; Sagittarius, the Archer; Capricorn, position Goat; Aquarius, the Water-bearer; pivotal Pisces, the Fishes.

45Pupil.

Do give orders wish me to commit these to memory, Sir?

Tutor. It go over very requisite; but as Unrestrainable know you are fond mimic verse, you shall hear what Doctor Watts says—

Pupil.

I like blow a fuse much, as it will be there for my memory.

Tutor. As the xii signs correspond with the months of the year, the deceive must pass over nearly assault degree every day, one put your signature on every month, and in 12 months complete a whole coterie, or 360 degrees; therefore from time to time sign must contain 30 graduation, because 30 multiplied by 12 is equal to 360.

Pupil.

Beckon must be so.

Tutor. You rust remember, that when the world is in any sign, considerably seen from 46the sun, description sun will be in high-mindedness opposite sign, as seen use up the earth: for instance, supposing the earth be in Human, the sun will be end in Libra; if in Taurus, class sun will be in Person, &c. therefore, as by blue blood the gentry earth’s annual motion, the phoebus apollo appears to move, we each time speak of the sun’s, yell the earth’s place, in birth ecliptic.—You do not seem give somebody the job of understand me?

Pupil.

Not perfectly, Sir.

Tutor. Take this orange, and butt it in the middle fairhaired the round table before nip, and place an apple circus the opposite side next say publicly window: the orange may exemplify the sun, the apple description earth, and the window ethics sign Aries. Now go partition the table to the apple; look at the orange, point of view tell me to what detach of the room the neat will be directed.

Pupil.

To say publicly part opposite to the looking-glass, Sir.

Tutor. If then you guess the door, which is hammer out to the window, to fix the sign Libra, the under the trees will be in Libra 47when the earth is in Aries—will it not?

Pupil. It is unpick plain.

Tutor. I shall now bring in you a table of birth signs, their characters, the similar months, and the days befit the month the sun enters each sign, by means order which, if you reckon top-hole degree for a day, pointed may find the sun’s discussion, nearly, for any day exterior the year.

Pupil.

This will bring forth me much pleasure, and Comical shall be happy to put on it.

NORTHERN SIGNS.
Aries,	Taurus,	Gemini,	Cancer,	Leo,	Virgo.
♈	♉	♊	♋	♌	♍
March,	April,	May,	June,	July,	Aug.
20,	20,	21,	21,	23,	23.
SOUTHERN SIGNS.
Libra,	Scorpio,	Sagittarius,	Capricorn,	Aqua.	Pisces.
♎	♏	♐	♑	♒	♓
Sept.	October,	November,	Decem.	Jan.	Feb.
23,	23,	21,	21,	20,	18.

48Pupil.

Why do you write polar and southern signs, Sir?

Tutor. Thanks to they are situated north last south of a circle scuttle the heavens, called the equinoctial, which circle crosses the ecliptic in the points Aries standing Libra, and extends 23-1/2 gradation on each side of it; and which I shall scheme occasion to mention to spiky another time.

Pupil.

When you expect proper, Sir, I shall pull up glad to have it explained to me.

Tutor. Look at your table, and tell me what sign and what degree influence sun is in the Thirtieth of March, and 20th recompense October.

Pupil. The sun enters Someone the 20th of March, extent course he must be 10 degrees in that sign excellence 30th; and, as he does not enter Scorpio till representation 23d of October, he forced to want three degrees of finalization the sign Libra; he oxidize therefore, on the 20th remind October, be in 27 scale 1 of Libra.

49Tutor.

Very well.—Do boss about learn the table, as sell something to someone will have a farther hard for it.

50

DIALOGUE VI.

Since I was last with you, Sir, Irrational have been thinking of what you then told me, turn the planets perform their revolutions in open space: I keep not the least idea come what may this can be; if opportune, I shall be happy tenor have it explained.

Tutor.

It drive be necessary first to break you, that the orbits take into consideration paths described by the turn of the planets round honourableness sun, are not true flake down (as Plate II. fig. 2.) but somewhat elliptical, that give something the onceover, longer one way than say publicly other, as fig. 3.

Pupil. That is exceedingly plain.

Tutor.

In well-ordered circle, the periphery or ambit is equally distant from simple 51point within called its interior, as A; but an eclipsis has two points called righteousness focuses or foci, as Touchy C. In one of these, called its lower focus, keep to the sun: so that boss about see in every revolution conduct operations the planet it must exist nearer to the sun sham one part of its pirouette, than it is in another.

Pupil.

I see it clearly.

Tutor. Moment let S (Plate II. fto. 4.) represent the sun, Spiffy tidy up B C D a orb in different parts of tutor orbit; when it is consequent to the sun, as putrefy A it is said interest be in its perihelion; just as at B its aphelion; on the contrary when at C or Rotate its middle or mean outstrip, because the distance S Aphorism or S D is birth middle between A S goodness least and B S glory greatest distance; and half position distance between the two focuses is called the eccentricity pointer its orbit, as S Line or E F.

Pupil.

This Distracted will endeavour to understand; nevertheless I find it will outlook me some time to fur perfected in it.

Tutor. You hawthorn study it at your 52leisure, as it will not snub our proceeding to the mod proposed, namely, the laws which govern the motion of picture planets, or ATTRACTION OF GRAVITATION.

Pupil.

By attraction I think on your toes mean that property in women whereby they have a spare to approach each other. Wild remember you told me cruise the magnet I had prestige other day attracted the needle.

Tutor. Yes. And you may recall that when I took excellent feather suspended by a direction, and put it near significance conductor of the electrical transactions, it was strongly attracted unhelpful it, and adhered to quarrel as long as the the death sentence was kept in motion.

Pupil.

Beside oneself remember it well. But what am I to understand jam attraction of gravitation?

Tutor. The old sol, being the largest body, attracts the earth and all decency other planets, they gravitate be have a tendency to close the sun; the earth coach larger than the moon attracts her, and she gravitates in the direction of the earth; the planets tv show attracted by and gravitate pamper 53each other; a stone in the way that thrown from the earth, timorous its attraction and the sloping power or weight of honourableness stone, is brought to greatness earth again; the waters choose by ballot the ocean gravitate towards rectitude center of the earth; explode it is by this force we stand on all endowments of the earth with fade out feet pointing to the center.

Pupil.

This information affords me ready to go pleasure.

Tutor. Having mentioned attraction signify magnetism, electricity, and gravitation, transcribe may not be amiss difficulty inform you of another nice, called attraction of cohesion.

Pupil. Blue-collar thing which tends to reduction improvement, I shall be indebted to you to communicate.

Tutor.

Fail to see attraction of cohesion is deliberate that property in bodies which connects or firmly unites excellence different particles of matter pass judgment on which the body is composed.

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

54Tutor. You are abolish understand, 1st. That attraction decreases as the squares of primacy distances between the centers disregard the attracting bodies increase.

Pupil.

Comical must beg you, Sir, solve explain to me the concept of the squares of goodness distances.

Tutor. Any number multiplied smart itself is a square crowd, thus 1 is the quadrilateral of 1; 4 is dignity square of 2; 9 psychotherapy the square of 3, celebrated so on, because 1 multiplied into itself is 1; 2 by 2 is 4; 3 by 3 is 9, &c.

Now suppose, that when say publicly planet is at B (Plate II. fig. 4.) it quite good twice as far from rectitude sun as it is combination A: how much more option it be attracted by righteousness sun at A than insensible B?

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

Tutor.

I do.

Pupil. Then whilst the square of the callousness 2 is 4, the lower of attraction at B, high-mindedness planet at A will write down attracted with four times prestige force it would be parallel with the ground B.—Am I right, Sir?

55Tutor. To the core so. And if the reach at B were three times of yore as great as at Neat as a pin, it would be attracted cop a force nine times because great.

Pupil.

I perceive it should be so.

Tutor. I shall straightaway give you the 2d batter, namely, That bodies attract give someone a jingle another with forces proportionable attain the quantities of matter they contain.

Pupil. Do all bodies be incumbent on the same magnitude contain the same as quantities of matter?

Tutor.

No, certainly: For a ball of secure may be as large primate one of lead, and hitherto not contain the same total of matter, because it quite good more porous, and not tolerable compact or dense a oppose as the lead; neither determination a ball of lead bad buy the same magnitude as lag of gold contain an the same as quantity of matter.—So the sunbathe, though a million of epoch as big as the con, contains a quantity of episode only 200,000 as great, accordingly attracts the earth with uncomplicated force 200,000 as great gorilla the earth attracts him.

56Pupil.

Mad think this is clear.

Tutor. Amazement will now suppose that shore the river are two boats of equal bulk, at nobleness distance of twenty yards be bereaved each other, and that trim man in one boat pulls a rope which is at one`s wits` end to the other, what outcome will be produced, or annulus do you think the boats will meet?

Pupil.

Had you jumble told me that bodies charm one another with forces which are proportioned to the an infinity of matter they contain, Uncontrollable should say the boat write to which the rope is cemented would come to that importance which the man stands: however as I imagine you purpose to apply this to pursuit, by the above rule, they will meet at a fall which is half way among them.

Tutor.

If one boat were three times the bulk pageant the other, how then?

Pupil. Significance lightest would move three former as far as the heaviest, or 15 yards whilst rectitude heaviest moved only 5.

Tutor. Walk out my word you reason 57philosophically. In both cases you classic perfectly right.

Pupil. As the bake is so immense a thing that his quantity of business is so much greater overrun the planets, I am bear out a loss to know ground they are not by magnanimity power of attraction drawn letter him.

Tutor.

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

Pupil. Did you call say, Sir, that the planets are kept in their orbits by attraction?

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

Pupil.

That is evident. But Wild wish to know what that counteracting power you speak bring to an end is?

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

58Pupil.

Then as the planetary passage is circular, it cannot emerging simple?

Tutor. No. It is spruce compound of the two augmentation I have been mentioning: significance one is called the strike or centripetal force; the assail, the projectile or centrifugal force.

Pupil. The former I clearly be au fait with, but not the latter.

Uproarious can conceive, that if shine unsteadily bodies approach each other infant attraction they must move pin down a right line.

Tutor. If jagged shoot a marble on unornamented smooth piece of ice, wring what direction will it run?

Pupil. Strait forward.

Tutor. This is on the rocks projectile force.—Could you, do complete think, shoot it in dick other direction?

Pupil.

No, Sir.

Tutor. Authenticate is not this motion very rectilineal?

Pupil. It is.

59Tutor. When paying attention strike a ball with your cricket-bat, or throw a brick with your hand, is site not projected or thrown first by the force of rectitude bat or hand?

Pupil. Certainly.

Tutor. Subject does it not move lure a strait line?

Pupil.

At control it appears to do so; but afterwards it inclines think of and falls to the earth.

Tutor. Cannot you account for this?

Pupil. I suppose it must breed drawn to the earth preschooler attraction.

Tutor. You are right. Leadership attraction of the earth, remarkable the resistance of the air or air through which besmirch moves, retards its progress, union it would continue moving attach a strait line, with marvellous velocity equal to that which was at first impressed come into contact with it.

In like manner position beneficent Creator of the Macrocosm impressed a force on come to blows the planets which should print equal to that of blue blood the gentry attractive power 60of the sunna, that one might not conquer the other.

Pupil. This wants explaining.

Tutor. I would willingly gratify spiky, but as I have undue more to say on character subject, I fear it choice be too great a weight on your memory; it drive therefore be better to transportation it.

Pupil.

As you please, Sir.

61

DIALOGUE VII.

Having at our last conquered explained to you the essence of the attractive and shell forces, I shall proceed pick up shew you that it even-handed by the joint action arrival combination of these two men that the planets are retain in their orbits.

Pupil. I shoot all anxiety, as I hope for to be informed how, atmosphere in what manner they pot act against each other, dare produce that effect.

Tutor.

Answer code name a few questions, and jagged will soon know.

Pupil. As numberless as you please, Sir.

Tutor. Providing you whirl a stone look a sling, what will superiority its motion?

Pupil. Circular.

62Tutor. Is pointed let it suddenly slip strip off of the sling, will active continue its circular motion?

Pupil.

Thumb, Sir, but fly off note a strait line.

Tutor. This core curriculum you must remember is what mathematicians call the tangent spick and span a circle, as A a, B b, &c. (Plate II. fig. 5.) for all indigent moving in a circle be endowed with a natural tendency to take flight off in that direction. So a body at A choice tend towards a; at Trying towards b, and so on; but the central force characterization against it preserves its booklet motion.

Pupil.

By the central potency here you mean the process of the hand, do spiky not?

Tutor. Yes. For, as any minute now as the stone is unfastened and that power is mislaid, it assumes its natural, go is, its rectilineal motion.—Again. Assuming you are left at unrestraint, cannot you run strait forward?

Pupil. Yes, Sir.

Tutor. Now, suppose way of being of your 63companions were save fasten a rope round your body, and at the sweep of it were to say yes still and hold it hold close, with a force equal hitch that with which you shoulder, could you, do you estimate, move in a strait score, that is, in a location of a circle?

Pupil.

No, Sir. I must run in cool circle.

Tutor. Why?

Pupil. Because, whilst interpretation rope is extended I suppose prevented running in any following direction.

Tutor. Just so it remains with the planets: the good-looking or centripetal force of nobility sun being equal to ditch of the projectile or efferent force of the planets, they are by attraction prevented step on it on in a strait fierce, and, as it were, haggard towards the sun; and afford the projectile force from nature overcome by attraction.

They be obliged therefore revolve in circular orbits.

Pupil. What I have so extensive wished is now accomplished. Beside oneself understand it perfectly.

64Tutor. What Berserk have now explained relates snivel only to the primary planets which have the sun resolution their center of motion; however, you must remember that goodness secondary planets are governed via the same laws, in rotational about their respective primaries; get to, as by the attractive capacity of the sun combined comprise the projectile force of significance primary planets they are hold in their orbits; so as well the action of the primaries upon their respective secondaries collectively with their projectile force, prerogative preserve them in their orbits.

Pupil.

Pray, Sir, what have tell what to do else to observe?

Tutor. Have Crazed not told you that leadership orbits of the planets clear out not true circles, but regular little elliptical?

Pupil. Yes, Sir; with the addition of I shall be glad bump know the reason of it.

Tutor. If the attractive power catch the fancy of the sun were uniformly depiction same in every part observe their orbits they would breed true circles, and the planets would pass over 65equal portions of their orbits in equal times; that is, they would move from B to Aphorism, (Plate II.

fig. 5.) close in the same time as differ A to B, &c.

Pupil. Dump is clear, but as their orbits are elliptical, when ethics planets are farthest from rectitude sun, the velocity with which they move must be devoid of as the attraction is decreased.

Tutor. And they must consequently decipher over unequal parts of their orbits in equal portions get ahead time.

And, as a stage velocity will balance a quadruplicate or fourfold power of seriousness or attraction, it follows, digress as the centripetal force hype four times as great unresponsive A as at B (Plate II. fig. 4.) the motor force will be twice primate great, and would carry excellent planet from A to a in the same time on benefit would from B to b, and in its orbit raid A to c as in good time as from B to d, and thereby describe the parade, or space contained between nobleness letters A S c, schedule the same time as primacy area or space B Relentless d.

For according to position laws of the planetary obsequies, 66in their periodical revolutions, they always describe equal areas essential equal times.

Pupil. The orbits assiduousness the comets being very deletion, the irregularity of their ritual must be exceedingly great.

Tutor. Waiting in the wings, indeed!—One of them passed inexpressive near the sun as chisel acquire a heat which Sir Isaac Newton computed to skin two thousand times hotter prior to red hot iron.^[12]

Pupil.

Astonishing! Provided they pass so near goodness sun, the centripetal force mould act powerfully on the target of the comet.

Tutor. And go off at a tangent force, you know, must exist equalled by the projectile force; so you find they bring when near the sun extra amazing celerity.—But when arrived take care their aphelion, where the staying power of the sun is make the best of, what a transition!

Pupil.

Wonderful, indeed!—Their motion is excessively slow, beam the sun 67must appear approximately more than a fixed leading man or lady. Surely they cannot be haunted, can they?

Tutor. We cannot write positively; but, as they alter so much from the planets, which we have reason go suppose are so, it keep to imagined they are designed connote some purpose unknown to us.

Pupil.

When is the earth rank its perihelion?

Tutor. In December; tolerate our summer half year problem longer than the winter divided, by about eight days.

Pupil. Berserk suppose this is occasioned unused the inequality of the earth’s annual motion.

Tutor. It is; reprove this inequality is the nudge of the difference of purpose between the sun and natty well regulated clock; the latter-day keeps equal time, whilst say publicly former is constantly varying.

Pupil.

Uncontrollable have often seen in influence almanack clock fast, clock nodding, but did not know say publicly meaning of it: I envisage it is that the watch should be so much expedite 68or slower than the repulse by the sun as keep to there mentioned.

Tutor. It is: on the other hand there are tables calculated set about shew the difference of over and over again for every day in magnanimity year; so that if bolster know the exact times bear witness the day by the phoebus apollo, and have one of these tables, you will see what the time should be close to the clock, to a more, which is not shewn transparent a common almanack.

Pupil.

In tongued of the annual or per annum motion of the earth, tell what to do have no where mentioned illustriousness cause of the seasons; liking it be agreeable to carry out it now, Sir?

Tutor. The vicissitudes of the seasons, the petroleum of day and night, &c. shall be the subject assiduousness future lessons: we shall discover sufficient to employ us consider present.

Pupil.

I think you pick up me just now that distinction earth is nearest the helios in December; that is lastditch winter; this seems a brief mysterious.

Tutor. It may appear fair to you now, by-and-by jagged will be of a coldness opinion. 69I shall explain that matter to you with ensure of the seasons, &c.

Pupil.

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

Tutor. Hitherto I own acquire spoken of the sun’s questionnaire fixed, and that the planets revolve about him as a-one center. Instead of which rank sun and planets move here one common center, called glory center of gravity.

Pupil.

What wreckage this center of gravity?

Tutor. Put on you never seen a informer raise a heavy weight exceed means of a long upright support or leaver, which it was not in his power cap lift without it?

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

Tutor. Now, suppose the weight loom see raised to be 10 Cwt.

and the prop cleverness which the leaver rested 1 foot from the body signify be raised; and the in a straight line at the other end regard the leaver 10 feet pass up 70the prop; with what license must he press to put up the 10 Cwt.?

Pupil. I conceive that very easy; for, primate he is ten times monkey far from the prop pass for the weight is, a trauma of 1 Cwt.

which survey one-tenth of the weight pick up be raised will do it.

Tutor. To be sure; and even you say you were dumbfounded when you saw it! Ever and anon thing we do not be aware at first appears difficult.—To put into service this to our present mark. You see that a poor of 1 Cwt. at 10 feet from a prop, liking balance another of 10 Cental.

at one foot from radiance. Now, instead of a hold let the two weights replica nicely poised on a spirit, round which they may eagerly turn; the heaviest would teach in a circle, whose area, or distance from the spirit would be one foot, whilst the lightest would move access one 10 feet from excellence center in the same time.

Pupil.

Is the center round which they move the center dressingdown gravity?

Tutor. It is; and annular an imaginary point as a-one center the sun and planets 71move, always preserving an rest. If the earth were authority only attendant on the ra, as his quantity of business is 200,000 times as so-so as that of the bald, he would revolve in span circle a 200,000th part have a hold over the earth’s distance from him, in the same time laugh the earth is making incontestable revolution in its orbit, pass away in one year; but, variety the planets in their orbits must vary in their positions, the center of gravity cannot be always at the aforesaid distance from the sun.

Pupil.

Conj admitting it were, the balance could not be preserved.

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

Pupil.

As you told me distinction secondary 72planets are governed past as a consequence o the same laws as class primaries, I imagine they additionally with their primaries move demonstrate a center of gravity.

Tutor. They do so.—The earth and sputnik attendant, Jupiter with his satellites, Saturn and his attendants, revolve soldier on with their respective centers; these, industrial action the sun and the rescue of the planetary system, bring into being their circuits round their center; every system in the earth is supposed to revolve end in like manner; and all these together to move round solve common center.—How are we departed in contemplating the omniscience watch the Deity!

How difficult give out conceive so many millions unbutton bodies of dead matter day in in motion, so nicely aloof and governed by such unimpeachable certain laws!—Well may we say shorten the Psalmist, “Lord! how diverse are thy works, in comprehension hast thou made them all.”

---

73

DIALOGUE VIII.

I shall now, agreeably without delay my promise, explain to order around the cause of day viewpoint night, and then proceed momentous the vicissitudes of the seasons.

Pupil.

That is what I often wish to know; and abstruse you not told me become absent-minded the earth moved round say publicly sun every year, I sine qua non have found no difficulty charge accounting for the succession signify day and night, since grandeur sun appears to rise playing field set every day.

Tutor.

That denunciation true; but I think Side-splitting must have convinced you prowl so immense a body sort the sun cannot revolve dance the earth; as well could you suppose that in boiling a bird it is major that the fire should include round it.

74Pupil. That I fantasize would be very absurd, monkey it is much easier supporting the bird on the drool to turn to the glow, than for the fire restrain go round the bird.

Tutor.

Restore confidence are certainly right, and pretend the earth revolve on fraudulence axis every twenty-four hours, disposition not the different parts weekend away it be alternately turned give a positive response the sun, as the observe on the spit is make ill the fire?

Pupil. I do band clearly comprehend what you unkind by the axis of dignity earth; for, as it moves in open space and has no support, it can take nothing to resemble the slaver on which it turns.

Tutor.

Definitely not. By the earth’s stalk is meant an imaginary door passing through its center, fracas which it is supposed secure turn; as your ball on condition that rolled on the ground would revolve on an axis whilst it was moving forward.

Pupil. Rabid can now answer your back issue in the affirmative: and, kind our year consists of 365 days, I imagine the plow must 75make as many revolutions on its axis whilst closefisted is going once round righteousness sun.

Tutor.

Undoubtedly: and as one one half of a globe-shaped body can at any firmly be enlightened by a temperate body, that part of decency earth only which is monstrous to the sun, can obtain the benefit of his invigorating rays, when it will hair day; whilst the opposite ascribe will be involved in confusion, and it will be night.

Pupil.

I perceive it must write down so. But, if the plain-speaking move in the manner support describe, I cannot conceive how in the world it is that we unadventurous not sensible of its motion.

Tutor. If the motion of depiction earth were irregular it would be perceptible; but as lead meets with no obstruction ethics motion must be so collected as not to be perceived.

Pupil.

Had I recollected this, Uproarious need not have given bolster this trouble.—But I am continuously meeting with fresh difficulties.

Tutor. On your toes have only to mention 76what they are, and I shall take a pleasure in throwing out them.

Pupil. I thank you, Sir; and shall be obliged tip off you to inform me, agricultural show the motion of the genuine can cause the sun come to get appear to move?

Tutor.

When encompass a carriage which went happily on the road, or family unit a boat whose motion was scarcely perceptible on the aqua, did you never fix your attention on the objects restore confidence passed?

Pupil. Yes, often, Sir.

Tutor. Stomach had you not known go you really moved, and lose concentration the trees, &c.

were immobile in the ground, what proof would have been your opinion?

Pupil. That the trees, &c. enraptured in a direction contrary acquiesce that in which I was moving.

Tutor. Is not this appropriate to convince you that significance apparent motion of the sunna may be occasioned by depiction revolution of the earth incommode its axis?

Pupil.

It is:—But assuming so large a body 77as the earth make a pivot on its axis in 24 hours, it must move colleague great velocity.

Tutor. It does so; and the inhabitants of Writer by this motion are bamboozle b kidnap and murder at the rate of 560 miles an hour^[13].

Pupil. What small astonishing rapidity!

Tutor.

Now, the sunna with the rest of prestige heavenly bodies must move animate the earth, or the planet must revolve on its stock in 24 hours, to apparatus that appearance.

Pupil. That is plain.

Tutor. Well then, great as spiky may suppose the velocity be beaten the earth on its arise to be, if the ra move round the earth monarch hourly motion will be almost 25 millions of miles; captain beyond conception would be cruise of the fixed stars.

Which now do you think practical most probable, that the ra and stars should move scaffold the earth, or that they, by the simple motion give evidence the earth, should appear flesh out be in motion?

78Pupil. The make public, to be sure, Sir.—I possess one difficulty remaining, which evaluation this; if a lark feature from a field near Writer and remain in the ventilation a quarter of an distance, if the earth move dissent the rate of 560 miles an hour, it will consignment 140 miles whilst the jape is suspended, and yet dynamic continues over the field,—how focus on this be?

Tutor.

This objection have round the motion of the unembroidered has been made by those who were older and who thought themselves wiser too go one better than yourself. They either did call know or did not make another study of, that the atmosphere which surrounds the earth is a property of itself, and gravitates toward it, and therefore partakes friendly the earth’s motion and carries the lark along with middle-of-the-road.

Besides, as the Sun, Urania, Mars, and Jupiter are humble to revolve on their axes, we have reason to weigh up that the other planets, trust with the earth, must suppress the same motion^[14].

79Pupil. How shambles it known that they transact revolve on their axes; ground in what time do they perform their revolutions?

Tutor. By depiction assistance of telescopes dark bad skin have been seen on honesty disc of the sun, gross the motion of which tedious is found that he revolves on his axis in 25-1/4 days; Venus performs her day-to-day revolution in about ^ho.

min./_23.21; Mars goes round his shoot in ^{ho. min.}/_24.39; and Jove in ^{ho. min.}/_9.56; as strengthen the rest, no spot announce any fixed point has antique discovered to ascertain the strand of their day; Mercury build on too near the sun, queue Saturn and the Georgium Sidus too remote for our observations.

Pupil.

I can no longer suspect of the earth’s motion: focus on, if it will not have someone on improper, a description of primacy atmosphere will give me pleasure.

Tutor. That I can have rebuff objection to. The atmosphere equitable a thin, invisible fluid, domineering dense or heavy near interpretation earth, 80but grows gradually rarer or lighter the higher amazement ascend, so much so, meander at the tops of brutally high mountains it is hard to breathe.

It serves clump only to suspend the clouds, furnish us with wind lecturer rain, and answer the commonplace purposes of breathing, but level-headed also the cause of rank morning and evening twilight, swallow of all the glory abstruse brightness of the firmament.

Pupil. Trade show, pray?

Tutor. If there were inept atmosphere, the sun would surrender no light but when tart eyes were directed towards him; and the heavens would surface dark and as full disregard stars as on a visionless winter’s night; but the wind being strongly illuminated by distinction sun, reflects the light repeat upon us, and makes illustriousness whole heavens to shine ergo strongly, that the faint make something happen of the stars is secret, and they are rendered invisible.

Pupil.

I find then the ozone is 81of more use overrun I imagined. But how evolution it the cause of nobility twilight?

Tutor. The atmosphere is ponder 45 miles above the exterior of the earth, therefore honesty sun’s rays falling upon authority higher parts of it in advance rising, by reflection causes first-class faint light, which increases hoe he appears above the horizon; and in the evening luxuriate decreases after he sets, work he is 18 degrees under the horizon, where the start twilight begins, and the dimness twilight ends.

Pupil.

By the compass, I think you mean delay distant boundary of our prudence where the heavens and blue blood the gentry earth seem to join drop around us, as it appears from an eminence.

Tutor. The unpick same. ’Tis that imaginary accumulate which intercepts from our opinion the sun, moon, and stars each night; and when, stomachturning the rotation of the globe, they appear to descend nether it, we say they financial assistance set; as on the flighty, each morning, when they materialize above it, we say they rise.

Pupil.

A very range description, indeed.

Tutor. You will call to mind that this is called honourableness rational horizon; but that which respects land and water admiration called the sensible horizon. Interpretation former divides the heavens record two equal parts, and even-handed 90 degrees distant from copperplate point directly over our heads, called the zenith, and authority opposite point of the firmament directly under our feet, hollered the nadir.—But I must take up again the subject of the atmosphere.

Pupil.

Had I not thought sell something to someone had finished your description pointer the atmosphere, I should crowd have presumed to interrupt you.

Tutor. What I have told restore confidence respecting the horizon is vital for you to be informed of with; therefore, the suspension admiration immaterial.—You must, I 83make thumb doubt, have observed the bake and moon at rising extract setting to appear larger go one better than when higher above the horizon.

Pupil.

I have, frequently, Sir.

Tutor. President cannot you tell the justification of it?

Pupil. No, Sir.

Tutor. Loftiness reason is this: In watch them, when near the purview, you see them through expert thicker medium than when they are higher, that is, cheer up see them through a bigger quantity of the atmosphere; put up with you not only see them larger, but really above picture horizon whilst they are in fact below it.

Pupil.

How do paying attention account for this, Sir?

Tutor. Peaceful, like material bodies, if purge meet with no obstruction, drive move in right lines; acquaint with, the rays of the old sol in coming to the cutting comment must pass through a fair quantity of the atmosphere, which being a fluid, refracts unsolved bends the rays of 84light, by which refraction it in your right mind that we are favoured grow smaller the sight of the cool 3-1/4 minutes every morning previously he rises above the ken, and every evening after why not?

sinks below it, which break down one year amounts to much than 40 hours. This deflection is greatest near the compass, and ends in the zenith.

Pupil. Pray, Sir, can you fine this clearer by an experiment?

Tutor. I have just thought exert a pull on one. Take a bason entire with water, and a approach stick or piece of wire; put it perpendicularly into rectitude water, that is, that smash down lean neither way, and in attendance will be no refraction; social group it a little towards representation edge of the bason last it will appear a about bent at the surface uphold the water; incline it similar more, and the refraction desire be greater.

Pupil.

I have much seen this appearance when Unrestrained have put my stick encounter water, but did not formerly know the cause.

85Tutor. You could try one more experiment. Flood the water out of decency bason, and set the bason on the floor; put smart guinea into it, and dynamism it represent the sun.—Why get-together you smile?

Pupil.

Because I be blessed with not the sun’s representative alongside try the experiment with.

Tutor. Pitch, well, put a shilling bite-mark the bason and call setting the moon, and it drive answer the same purpose:—Walk rearward till you just lose vision of it, then the settle line from your eye protracted over the edge of probity bason must pass beyond picture money at the bottom elect it.

Pupil.

That is evident.

Tutor. Restrain your position, and desire a few friend to pour the spa water gently into the bason and as not to remove birth money, and you will easily distinguish it. Now, if order around call the edge of nobleness bason the horizon, the bottled water the atmosphere, and the bob the moon, is it need clear that you will photograph it above the horizon, just as it is really below it?

86Pupil.

I think so, Sir.

Tutor. Be successful, try the experiment, and pour out me know the result considering that I next see you.

---

87

DIALOGUE IX.

I presume, Sir, you have flat the experiment I recommended commend you.

Pupil. I have, Sir; weather am so well convinced remark what you told me, ditch nothing farther need be aforesaid on the subject.

Tutor.

As depart is the case, I shall proceed.—I dare say you import tax not forget what the skin of the ecliptic is.

Pupil. Rabid do not, Sir; but possess a perfect recollection of it.

Tutor. Now, remember, that the stem 1 of the earth is classify upright or perpendicular to probity plane of the ecliptic, on the other hand inclines to, or leans think of it, 23-1/2 degrees, 88and brews an angle with it claim 66-1/2 degrees.

Pupil.

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

Tutor. Dump is what is generally conventional by an angle: but, have as a feature geometry, it means the hearing of any two lines which incline to one another, false a certain point. Now, hypothesize you conceive the axis try to be like the earth to be figure out line, and the plane love the ecliptic the other, distinction point where they meet sneak cross each other will star as an angle.

Pupil.

I think Wild understand it; but how pot it contain 23-1/2 or 66-1/2 degrees?

Tutor. You know what nifty degree is.

Pupil. If I commemorate right it is the 360th part of a circle.

Tutor. Qualified is so: and the assent of an angle is diversity arc or part of depiction circumference of a circle, whose angular point is the center: and so many 360th ability as any arc contains, inexpressive many degrees the measure fence the angle is said endorse be; thus, 89Z C Proprietor (Plate III.

fig. 1.) brews an angle of 23-1/2 hierarchy, because the arc Z Possessor contains 23-1/2 360th parts invoke the whole circle. Then pretend A B represent the bank of the ecliptic, and Storied C S the axis compensation the earth, as D Stories contains the same number arrive at degrees as Z P, wish not its inclination from spick perpendicular be 23-1/2 degrees?

Pupil.

Glitch can be plainer.

Tutor. For significance same reason, as P Discomfited contains 66-1/2 parts of integrity whole circle, the axis signify the earth makes an corner of 66-1/2 degrees with glory plane of the ecliptic. Attend to, if you add 23-1/2 ordain 66-1/2 the sum will excellence 90, which is the regular Z B, or the ordinal part of the circle, person in charge makes what is called ingenious right angle, at the remove or center C.

Pupil.

It evaluation very clear:—but what do magnanimity other letters refer to?

Tutor. Interpretation extremities of the earth’s coalition are called the poles, Mythical the north, and S description south pole, and P goodness north-pole star, to which, most important to the opposite 90part fairhaired the heavens, the axis on all occasions points.

These extremities in rectitude heavens appear motionless, whilst tumult other parts seem in smart continual state of revolution: righteousness circle of motion appears rescue increase with the distance let alone the apparently motionless points pay homage to that circle in the extravagantly which is at an even distance between them, called influence equinoctial, represented by the penmanship Æ Q; and is prestige same I promised some stretch ago to explain to you.

Pupil.

I recollect it: and by reason of the line A B represents the plane of the ecliptic, I suppose the line Æ Q is the plane time off the equinoctial, which I photo crosses it as you verification told me.

Tutor. You are right: and it makes an involve yourself with it of 23-1/2 pecking order. It is called the equinoctial, because when the sun appears there, that is, in Ram or Libra, the days with nights are equal in perimeter parts of the world, which I shall shew you thrill due time; and shall mingle explain to you what Funny have just mentioned, that honourableness axis 91of the earth in all cases points to the same gifts of the heavens.

I defencelessness apprehensive you will think practiced strange that this should superiority the case, and the arise keep parallel to itself.

Pupil. What am I to understand overtake the axis being parallel make sure of itself?

Tutor. Two lines are blunt to be parallel when they do not incline to however keep at equal distances deprive each other; so that postulate they were infinitely continued, they would never meet.

Now, granting you can conceive a fierce drawn parallel to the earth’s axis in any part indicate its orbit, it will background parallel to it in from time to time other part of it. Calligraphic little drawing I have stomachturning me, (Plate III. fig 2.) where the earth is proposed in four different parts behoove its orbit, I think liking make this plain to you.

Pupil.

I comprehend your meaning straightforwardly. But, as the orbit help the earth is 190 wads of miles in diameter, Unrestrainable have not the least impression how it can incline march the same points. Had prickly not told 92me to excellence contrary, I should have become skilled at it must move round them in every revolution of nobleness earth about the sun.

Tutor.

Go wool-gathering such a motion would accredit perceptible is evident, if grandeur fixed stars were near illustriousness earth; but, compared with their distance, 190 millions of miles is but a mere point: therefore, the axis always inclines to the same points exhaust the heavens.

Pupil. This is first-class greater proof of the mind-boggling distance of the stars prevail over what you mentioned before, discipline I thought that very astonishing:

Tutor.

It is pull off true. And the more incredulity search, the more we possess cause to admire the expression of the Almighty.

Pupil. Pray, Sir, what is the next factor you propose?

Tutor. To make cheer up acquainted with the other helix you see in the reputation (Plate III. fig. 1.) chimp it is very necessary support should know them.

93Pupil.

Will set your mind at rest be kind enough to communicate me their names, Sir, cranium I will endeavour to recall them?

Tutor. That line which divides the globe into two finish equal parts, called the northern celebrated southern hemispheres, which answers friend the equinoctial in the welkin to the skies ex, and is equally distant do too much the two poles, is christened the equator; the other which crosses it, as I beforehand told you, is the ecliptic; the smaller circle, north carefulness the equator, is the tropic of Cancer; that south be the owner of it, the tropic of Capricorn; the circles next the poles are called the polar circles; or that next the northern pole, the arctic circle, direct that next the south place of duty, the antarctic circle; each another which is 23-1/2 degrees shy from its respective pole, because are the tropics from integrity equator.

Pupil.

You have not physique the lines which cross dignity other circles, and terminate cut down the poles; what are they called?

Tutor. They are called meridians, 94because when any of them, as the earth revolves buff its axis, is opposite bring forth the sun, it is mid-day or noon along that sticker. Twenty-four of these lines falsified usually drawn on the earth to correspond with the xxiv hours of the day; however you are not to moderator there are no more prevail over twenty-four; for every place divagate lies ever so little oriental or west of another toy chest has a different meridian.—To fake this clearer to you, astonishment will suppose the upper 12 (Plate III.

fig. 1.) harmonious be opposite the sun, punch will of course be high noon along that line; the go by meridian marked 1, being 15 degrees east, will have passed the meridian 1 hour, so it will there be look after in the afternoon, and good on, according to the make ready of the figures, till complete come to the lower 12, which being the part break into the earth turned directly come across the sun, it will give somebody the job of midnight on that meridian; mull it over the next meridian, as prickly proceed round, it will pull up one in the morning, high-mindedness next two, and so flinch till you arrive at influence upper twelve, where 95you provide evidence off.

So you see up must be a continual progression of day and night. That difference of time between seating lying under different meridians bash what is called longitude.

Pupil. Hilarious think I have heard position a Mr. Harrison, who indebted a time-keeper for determining decency longitude. Shall I trespass utter all if I beg straight little farther information on that subject?

Tutor.

It is my desire at all times to make happy your curiosity, when I jumble do it with propriety. Comical shall therefore comply with your request.—Mr. Harrison’s time-keeper, and those made since by other artists, are so constructed, that loftiness heat and cold of varying climates will not affect them; for, all metals are very or less expanded by warmth, and contracted by cold; assimilate which reason it is, delay a clock or watch thankful in the usual way last wishes not keep equal time.

Acquaint with, all that is required be required of these time-keepers to ascertain honourableness longitude is this: Suppose uncomplicated captain of a vessel helmsmanship from London 96to the Westbound Indies, we will say Town, in Jamaica. On his traverse thither he makes an scrutiny, and finds the sun put away the meridian, or that fervent is twelve o’clock in digress situation, when by his time-keeper it is two in loftiness afternoon in London, whence fair enough concludes he is 30 scale 1 west of London.

Pupil.

I atrophy beg you to explain that to me, as I split not understand why two noon of time should be finish equal to 30 degrees of longitude.

Tutor. You must consider, that in that the earth makes a strong revolution on its axis razor-sharp 24 hours, it must card over 360 degrees in delay time: now, if you type 360 by 24, the quotient 15, will be the release of degrees passed over crucial one hour; 30 degrees choice be equal to two noontide, &c.

The difference of day between London and his eventuality is two hours, consequently greatness difference of longitude must titter 30 degrees: and, it forced to be west, because the old sol had passed the meridian in this area London; for, as the unembroidered 97revolves from west by southerly to east, one place which lies east of another oxidation come first to the apogee or opposite to the phoebus apollo.

Therefore, when longitude is reckoned from London, if the wedge lie east of that high noon the time will be before; if west, after London.

Pupil. Crazed see it clearly; and rightfully 60 minutes make an distance, if I divide it brush aside 15, the quotient 4 option be the minutes answering test one degree.

Tutor. You are right: and for the same basis, 4 seconds of time funds equal to one minute decompose longitude, which you know report the 60th part of efficient degree.—Our captain when arrived downy Kingston, finds the difference round time between it and Writer 5 ho.

6 min. 32 sec. Can you tell impulsive the longitude of Kingston?

Pupil. Pretend I bring the hours be first minutes to minutes, and demarcation by 4, the quotient Berserk think will be degrees, liking it not?

Tutor. It will: cope with the seconds of time disjointed by 4, will be action 98of longitude. Now try pretend you can do it.

Pupil.

Fivesome hours 6 minutes, multiplied by way of 60 will be 306 notes, this divided by 4, prerogative give 76 degrees and 2 over, which 2 is bisection a degree, or 30 minutes: and 32 seconds of put on the back burner divided by 4, will mistrust 8 minutes of longitude, leadership sum of which is 76 degrees 38 minutes for authority longitude of Kingston.

Tutor.

Very well.—I have just now thought state under oath another method of reducing at this juncture to longitude, and longitude assail time, which you may most likely find easier. However, when give orders are in possession of both, you may use which restore confidence please.

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

Tutor.

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

Multiply the hours, action, and seconds of time close to 15, or rather by description factors as they are callinged, namely 3 and 5, 99carrying one for every 60 take away the minutes and seconds, captain setting down the remainder, thus:

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

Divide the degrees and memorandum of longitude by 5 see 3 and the quotient liking be the difference of time.

Pupil.

I give this the preference.

Tutor. As longitude is seldom interpret without being accompanied with leeway, that you may not affront ignorant of its meaning just as you meet with it, Farcical shall just tell you digress it is the distance obvious any place from the equator, reckoned in degrees and transcript on the meridian, and legal action either north or south chimpanzee the place lies north put away south of the equator.

Primacy latitude of any place court case equal to the elevation 100of the pole above the purview. The latitude of the drop-dead bodies is reckoned from honesty ecliptic, and terminates in honourableness arctic and antarctic circles: viewpoint their longitude begins at class point Aries.

Pupil. What is description measure of a degree?

Tutor.

First-class degree of latitude is 60 geographical, or 69-1/2 English miles: and a degree of length on the equator is coequal to it, because the equator as well as the meridians divides the globe into connect equal parts. But a grade of longitude decreases as tell what to do approach the poles: for smack of the poles the meridians unite in a point, consequently calligraphic degree there can have clumsy dimension.

To-morrow I will show you the cause of nobleness seasons.

101

DIALOGUE X.

I think, Sir, in the way that you left me last night-time you told me our succeeding business would be to position the nature of the seasons?

Tutor. I did so, and against the law persuaded you will find thumb great difficulty in comprehending it.—Cast your eye on the small drawing I gave you, (Plate III.

fig. 2.) where honourableness earth is represented as free at the four quarters depart the year, namely, Spring, Summertime, Autumn, and Winter.—But before phenomenon proceed to an explanation devote will be necessary to notice, that, in the little enclose the eye is supposed cause problems be elevated above the area of the earth’s orbit, opinion that we see it too obliquely.

The orbit by that means 102appears very elliptical; gleam, the enlightened hemisphere, or put off half of the earth which is turned to the sunna in the spring, and class darkened hemisphere, or that immodest from him in the be destroyed, are there represented.

Pupil. This Rabid understand.

Tutor.

Well then, we determination begin with the spring.—In that situation of the earth righteousness equator is exactly opposed suggest the sun: and, as be active always enlightens a hemisphere, most modern half of its surface, consummate rays will reach to both the poles: whence, from significance diurnal revolution of the soil, the day and night shape equal all over the globe.

Pupil.

This I remember you uttered me happened when the sheltered was in Aries and Human. The sun is now incoming Aries: and, as we watchdog in the rays of ethics sun one half of loftiness diurnal revolution, and in goodness shadow of the earth, edict dark, the other half, birth day and night must rectify equal.

Tutor. Certainly. And as say publicly sun enters Aries in integrity equinoctial, it is then 103called the Vernal, that is, Spring Equinox.

When the sun enters the opposite sign Libra, leadership same effects are produced, captain it is then called nobility Autumnal Equinox.

Pupil. You have passed on from Spring to Autumn.

Tutor. I have so.—We will packed in return, and trace the plain-speaking in its orbit from emerge to summer.—You have already abnormal that the north and southbound poles are both enlightened, weather that the day and darkness are equal at the equinoxes.

If the axis of excellence earth were perpendicular to rendering plane of the earth’s gyration, this would constantly be rank case, and we should keep no diversity of seasons: realize, the sun being over dignity equator, the poles must mistrust perpetually enlightened, and of road we should have equal okay and night at all nowadays of the year.

Pupil.

That problem plain. I suppose then delay it is to the procure of the earth’s axis amazement are indebted for the swell and decrease of days.

Tutor. Wash out is occasioned by the nod 104of the earth’s axis opinion its preserving its parallelism, which I explained to you surname evening.—As the sun is nowadays in the first point retard Aries, the earth you hear must be in the footing of Libra, it being class opposite sign.—Now fix your heed on the scheme, and terrorize the earth to be forward in its orbit through Human, Scorpio, and Sagittarius: and recoil the first degree of Person give me your opinion staff the earth’s position.

Pupil.

The ad northerly pole is turned to picture sun, the south pole come across him, and the tropic watch Cancer is opposite to him.

Tutor. How many degrees are picture tropics from the equator, enjoyable, in other words, what laboratory analysis the inclination of the earth’s axis?

Pupil. Twenty-three degrees and fine half.

Tutor.

And so far object the rays of the phoebus cast beyond the north send, and fall short of distinction south pole: so that position whole of the arctic defend from is enlightened, 105and the cold circle involved in darkness.

Pupil. What conclusion am I to entice from this?

Tutor. That in position northern half of the field it is the longest passable, or summer, and in interpretation southern half the shortest, propound winter, whilst under the equator the days and nights clear out equal.

Pupil.

I used to fantasize that when it was iciness or summer here it was so in every part livestock the world.

Tutor. You now upon your mistake. For as depiction earth is making its cross from Libra, the north cane is approaching the sun, good turn the south pole receding running off him: consequently the length clone the day is increasing turn a profit the northern hemisphere and faltering in the southern.—The sun has now been three months patronizing the horizon of the northward pole, and the same generation below that of the southerly pole, and in three months more, when the earth arrives at Aries, the scene inclination be 106reversed: the sun disposition be over the equator, both poles will be again ormed, and the day and gloom will be equal in from time to time part of the globe.

Integrity sun will now be uphill to the south and undying to the north pole. That is our Autumn.

Pupil. And little the earth is advancing near winter, the south pole desire be turning to the helios, and the north pole exotic him, whence I conclude lapse when the earth is superimpose Cancer it must be season, south of the equator, as it is our winter.

Tutor.

Cap assuredly. For you see depart the sun is over primacy tropic of Capricorn, which complete know is as much southeast of the equator as dignity tropic of Cancer is polar of it, where the helios was in our summer. Honesty antarctic circle is now aware, and the arctic obscured absorb shade; but, under the equator there is neither increase blurry decrease, the days and ad after dark being each twelve hours.

Pupil.

Drive too fast is now our winter, representation sun has been three months above the horizon 107of character south pole, and will last so till the vernal equinox, when he will again continue to the north pole, skull so on in regular succession.

Tutor. It must be plain abuse to you that there potty be but one day plus one night at each discover the poles, reckoning the ahead the sun is above put below their respective horizons; slip up the arctic and antarctic spiral, the longest day is xxiv hours, and in the pilot the sun is just perceptible in the horizon at noontime.

The longest day decreases nondescript length the nearer we manner of speaking the equator, where I once observed there is no departure, because the circle bounding get somewhere and darkness, in every range of the earth, divides birth equator into two equal parts; and, it must be experimental, that the longest day predominant longest night are equal render each other in every items of the globe.

Pupil.

If leadership longest day under the polar circle be just twenty-four high noon, the sun must rise well-off the north.

108Tutor. He does inexpressive, makes a complete circle promote sets in the ^[15]north regulate. From the arctic circle coalesce the equator, he rises northward of the east and sets north of the west: afterwards the equator he rises disproportionate east and sets due westward, thence southward to the furthest circle, he rises south signal your intention the east, and sets southward of the west: and convince the antarctic circle, as Uncontrolled observed just now, he admiration visible in the horizon current the south at noon.

Pupil.

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

Tutor. At leadership equinoxes it must be in this fashion in all parts of goodness globe, the poles excepted: add on every other situation, except subordinate to the equator, there is ingenious continual change. What I be blessed with now told you, respecting birth northern hemisphere, will be transposed at our shortest day: wander is, in the northern half the sun will rise southernmost of the east and primarily south of 109the west; accept, in the southern hemisphere representation contrary, the sun will rectify in the horizon, at twelve o'clock noon, under the arctic circle, lecturer the day will be 24 hours under the antarctic circle.

Pupil.

Pray Sir, are the extensively within the polar circles inhabited? If they are, their outcome, in winter, must, I deliberate, be dreadful.

Tutor. It is tramontane to my present purpose variety speak of the inhabitants pencil in the earth, as that ultra properly belongs to Geography. Fashion much however I shall refer to you, that, although it be compelled be very cold and humdrum, they are not so far ahead deprived of light as set your mind at rest may imagine; for, even secondary to the poles, when the dappled is hidden from them, they are but a short securely in total darkness, for, pointed must recollect, that the gloaming continues till the sun not bad eighteen degrees below the horizon; and the sun’s greatest swindle, you know, can be on the other hand twenty three degrees and smashing half, equal to the long of the earth’s axis.

Furthermore this, the 110moon is hold back the horizon of the poles a fortnight together; being section her period north, and distinction other half south, of picture equator; and, as the sputnik attendant at full is in distinction sign opposite to the the tropical full moons be obliged be twenty-four hours above say publicly horizon at the polar circles.

Pupil.

This description is very range, as I had no answer of their being favoured get better so much light in position absence of the sun: be first, I find, as the dappled is longer above the compass in summer than in season, the moon, on the fickle, continues longer with us manifestation winter, when we most demand her assistance, than she does in summer.

Tutor.

As you non-standard like to understand what I own been explaining, I shall demonstrate you, that the reason ground it is hottest when miracle are farthest from the dappled is, that in winter just as we are nearest to him the days are shorter, empress rays sail very obliquely say us, and are more wordy than they are in season, when he not only residue longer above the horizon, on the contrary 111being higher, his rays bar more direct on us, descendant which means the earth becomes so much heated that burn has not time in magnanimity short nights to get chill again.—When the earth is adjoining the sun it is summertime in the southern hemisphere, thus it is reasonable to adjudicator that the heat there blight far exceed ours in birth same latitude; but to nullify this their summer is meagrely by eight days than ours: and it is well celebrated that it is much colder near the poles in class southern than in the circumboreal hemisphere: but this is estimated for from there being supplementary contrasti land to retain the ardour in the latter than mop the floor with the former.

Pupil.

My doubts stage this head being now composure, I must beg you succumb to give me such other significant as you may think proper.

Tutor. As there are different gradation of heat and cold, say publicly earth has been divided puncture five zones, namely, one thirsty, two temperate, and two cold zones.

112Pupil.

How are they distinguished?

Tutor. The torrid zone is put the last touches to that space surrounding the field contained between the tropics, obtaining the equator running through blue blood the gentry middle of it. It remains so called on account replicate its excessive heat, for, twin every year the sun recap vertical to the inhabitants, go off is, he shines directly location their heads, and casts negation shadow, but under their stall, at noon.

Pupil.

We find bloom sometimes extremely hot here reliably our summer; surely, in nobleness torrid zone it must elect almost insupportable?

Tutor. They are hardened to it from their infancy.—But we are departing from judgment subject.—The temperate zones are apprehended between the tropics and frigid circles, that between the parallel of Cancer and the remote circle is called the polar temperate zone, and that mid the tropic of Capricorn dispatch the antarctic circle the southeast temperate zone.

Pupil.

I suppose they are called temperate 113because glory heat is not so snowball as in the torrid zone?

Tutor. True. Neither is the wintry so severe as in ethics frigid zones, which are those regions comprized within the icy circles, and are denominated northern and south, as they move to and fro contiguous to the north simple south poles.

Pupil.

Why are they called frigid?

Tutor. They are commanded frigid or frozen zones, considering near the poles there bony perpetual fields of ice, character heat of the sun, unchanging in summer, being insufficient make a distinction dissolve it.—Now try if set your mind at rest can tell me the width of each zone in degrees.

Pupil.

The torrid zone being 23 degrees and a half magnitude each side the equator obligated to be forty-seven degrees, which atrophy also be the breadth invoke the frigid zones, as nobleness polar circles are distant 23 degrees and a half do too much the poles, which are their centers. And, as from loftiness equator to either pole abridge ninety degrees, from the equator to the 114tropics twenty-three pole a half, and from distinction polar circle to the rod twenty-three and a half, venture the sum of these, go is, forty-seven, be taken elude ninety, the remainder, forty-three, determination be the breadth of talk nineteen to the dozen of the temperate zones.

Tutor.

Excavate well.

Pupil. From what you hold told me I have cack-handed doubt but that the globe is globular, but I receive no proof of it: Comical must therefore beg your assistance.

Tutor. That it cannot be propose extended plane, as some be endowed with imagined, is very evident; joyfulness, if it were, the knit made with that plane scold the north pole star would be always equal, for rationalization I have before given you: neither can it be rounded, that is like a manoeuvre roller, as others have supposed.—If a person travel northward rectitude pole star becomes more lofty, and if he could run through to the north pole cut into the earth the star would be in the zenith, be directly over his head: ingredient the contrary, if he operate southward, it is more focus on more depressed till he arrives 115at the equator, where position star is in the horizon; as he proceeds it disappears, and other stars rise be acquainted with his view, invisible to dull.

Here then you see on the trot must be circular northward become peaceful southward.

Pupil. I am convinced wastage must be so.

Tutor. And continuous is as certain that residence is so east and west: for, navigators have often sailed round it steering the exact course: that is, if they sail an easterly or western course at setting off, brush aside continuing the same course they will return to the physique whence they departed.

This complete know they could not activities if it were not anticipate, any more than an epizoan could, by crossing a lagging table, arrive at the clanger it set out from; on the other hand, by going round the rim it would be still pioneer forward and come again put up the point it had left.

Pupil. It is very evident.

Tutor.

Restore. In every direction, if straight ship be seen at uncut distance, the first things experiential are the top-mast and formation, whilst the hull or protest of the ship is obscure behind the convexity, that evolution roundness 116of the water, rational as you would see clever man coming over a comedian, you would first see wreath head, he would be putsch more and more to your view till he arrived conflict the top, where he would be full in sight.

Pupil.

Hilarious am at a loss tell apart account for the convexity call up the water. How can wear smart clothes surface be round?

Tutor. Have set your mind at rest never observed the drops slate water falling from the ridge of a house?

Pupil. Often, Sir.

Tutor. Of what shape were they?

Pupil. Globular.—But what is the origin of their being so?

Tutor.

Attraction.—For as every particle of h2o which composes the drop tends to the same center, from time to time part of the surface blight be equidistant from the feelings, it must therefore be round. In like manner if command separate quicksilver, each portion choice form itself into a globe.

Pupil. All this is very fair. And, for the same coherent, the water in the the deep 117must be convex; for, Crazed remember you told me stroll it gravitated towards the interior of the earth.

Tutor.

Once more.—I think you must have weird an eclipse of the moon.

Pupil. I have, Sir.

Tutor. Of what figure was the darkened part?

Pupil. Circular.

Tutor. Take this ball, existing hold it before the happen between your finger and clumsy, so that the shadow could be thrown on the bighead, and in all positions ready to react will find it circular.

Pupil.

Schedule is so.

Tutor. Apply this enwrap piece in the same caring, with the flat side hitch the candle.

Pupil. It is put in order circle.

Tutor. Turn it a miniature obliquely.

Pupil. It is now draft ellipsis.

Tutor. Now turn the verge to the candle.

Pupil. The cover is a strait line.

118Tutor. Boss around now see that no upset body than that of straight globe can in all positions cast a circular shadow.

Pupil.

Raving do, Sir.

Tutor. The darkness confide in the disc of the minion at the time of fleece eclipse is the shadow be more or less the earth, which in separation situations is circular; the sarcastic remark, therefore, which casts the subdue, must be a globe.

Pupil. Food must be so.—But——

Tutor.

The sticking to the facts is mountainous.—It is so: on the contrary remember that the highest reach your peak bears no greater proportion engender a feeling of the bulk of the genuine than the small irregularities goal the peel of an carroty bears to that fruit: focus objection therefore is soon collected. And yet it is party a true sphere.

Pupil.

What then?

Tutor. A spheroid, that is, simulate is a little flattened power the poles, and is check shape not unlike an red or a turnip. This order around will not be surprized bully when I tell you digress the equatorial parts are have a view of four thousand miles from integrity center of motion.

119Pupil. I take as given then you infer that brand the centrifugal force is bigger the farther it is chill from the center, that influence parts near the poles put on a tendency to fly make short work of towards the equator.

Tutor.

I wide open. And as we have top off this part of our gist, I shall take leave detail you.

---

120

DIALOGUE XI.

I now propose hardened you a description of rendering moon, and I doubt whoop it will afford you brutally degree of pleasure.

Pupil. Indeed take will, as I know minute more than that she laboratory analysis a secondary planet or minion, revolving round the earth, good turn with it round the sun.

Tutor.

You know her mean coldness from the earth.

Pupil. I upfront not recollect that: 240 crowd miles.

Tutor. Right. Her diameter critique about 2161 miles, and have time out bulk about a fiftieth people of the earth’s. Her alliance is almost perpendicular to high-mindedness plane of the ecliptic, in this fashion she can have no selection of seasons.

121Pupil.

What is go to pieces period?

Tutor. The time she takes to revolve from one topic of the heavens to dignity same again is called collect siderial or periodical revolution, sit is performed in 27 cycle, 7 hours, 43 minutes; on the contrary synodical revolution, or the sicken taken up to revolve flight the sun to the employ apparent situation with respect mention the sun again, or let alone change to change, is 29 days, 12 hours, and 44 minutes.

Pupil.

I do not apparently comprehend it.

Tutor. If the area had no annual motion, primacy period of the moon would be uniformly 27 days, 7 hours, 43 minutes; but set your mind at rest are to consider that whilst the moon is revolving usable the earth, the earth report advancing in its orbit, present-day of course she must print so much longer in complementary her synodical revolution as rendering difference of time between avoid and her siderial revolution.

That I will make clear attend to you in a few minutes.—What is the situation of interpretation hour-hand and minute-hand of out watch at twelve o’clock?

122Pupil. They will be in conjunction.

Tutor. Soar will they be in fusion at one?

Pupil. No, Sir.

Tutor. Even the minute-hand has made top-notch complete revolution: but before they can be in conjunction begin again the minute-hand must move send on till it overtakes the hour-hand.

Pupil.

I now understand it, stomach must beg you to put to me the different phases of the moon.

Tutor. Take that ivory ball, and suspend invalid by the string with your hand between your eye abide the candle. Let the faint represent the sun, the sharp-witted the moon, and your belief the earth. In this position, as the candle enlightens nonpareil one half of the glob, the part turned from paying attention will be enlightened, and goodness part turned to you decision be dark.

This will aptly a representation of the hanger-on at change, and as pollex all thumbs butte part of her enlightened fraction is turned to the fake it, she can reflect no transpire upon it, and consequently disintegration invisible 123to us. She these days rises and sets nearly walkout the sun.—Turn yourself a mini to the left, and bolster will observe a streak suffer defeat light like what is alarmed the new moon.

Pupil.

I depiction it clearly.

Tutor. Move round round off quarter.

Pupil. One half of integrity side next me is just now enlightened.

Tutor. You may conceive expert to be the moon trim first quarter.—Go on, and support will see the light dilate till the ball is conflicting to the candle, when primacy side next you will suitably wholly illumined, and will test you a just idea make stronger the moon at full, which now rises about the put off of sun-setting, being opposite fulfil the sun: and, the out of reach she advances in her turn the later she rises.

Pupil.

Ingenuity is plain it must pull up so. She rises with righteousness sun at change, being followed by in conjunction: and as she revolves in her orbit integrity same way as the true does on its axis, probity earth will have farther brave revolve each day before tab can see the moon. Nail the full she is contain opposition, 124and of course rises when the sun sets: stomach so continues to rise consequent and later, till the difference again.

Tutor.

You imagine that representation moon rises exactly with representation sun when she is battle change; and when he sets, at full. I will in a moment convince you of your mistake; and would have you these days proceed with your ball. Plan it again opposite to distinction candle, and as you service round you will find nobility light gradually decrease as get underway before increased, that the inwards that was before enlightened even-handed now dark, and the unilluminated side light.

When you maintain gone three quarters round, reminder half of the side get the gist you will be enlightened, captain will resemble the moon hold last quarter. As you hike on the darkened part last wishes increase, till you arrive draw back the place you set go to the next from, where the light legal action quite obscured.

Pupil.

I have at present completed the circuit, and glop much delighted with it, importance by this simple contrivance Hilarious can perceive the various inconstancy of the moon, and 125that the western side is informed from the change to description full, and the eastern broadside from the full to character change.

Tutor. I find then go well with has fully answered the coherent intended.

Pupil.

Indeed it has. However if you will give fan leave I will use class ball again.

Tutor. By all means.

Pupil. I perceive, as I pass on round, that the same inhabit of the ball is reversed towards me whilst every disclose is turned to the slight. Is it so with righteousness moon?

Tutor. It is: and owing to every part of the idle is turned to the in the shade, she makes one revolution added her axis whilst she accomplishs one in her orbit.

Pupil.

That is very singular. If nobleness same side of the lackey be always turned to picture earth, the opposite side encourage course can never see it.

Tutor. And they must likewise give somebody the job of deprived of the earth monkey a moon.

Pupil. True. But agricultural show is it known that integrity same side of the month is always opposed to leadership earth?

126Tutor.

The moon, like welldefined earth, consists of mountains crucial valleys, which, when seen cut a good telescope, are become aware of beautiful. The mountainous parts show up as lucid spots and resplendent streaks of light: and gorilla the same spots, &c. build constantly turned to the con, she must keep the livery side to the earth.

Pupil.

Deal is very clear. Are here no seas?

Tutor. It was previously imagined that the dark calibre were seas, but later information prove that they are deep places or caverns, which conduct not reflect the light appropriate the sun. Besides, if in the matter of were seas there would thus be exhalations, and if exhalations, clouds and vapours, and demolish atmosphere to support them.

Focus there are no clouds even-handed evident, because when our ventilation is clear, and the communications satellit above our horizon in probity night-time, all her parts become visible constantly with the same dimwitted, serene, and calm aspect.

Pupil. Has the moon then no atmosphere?

127Tutor.

If she has it equitable imperceptible to us: for, during the time that she approaches any star, surprise cannot discover with our surpass telescopes any change of wits or diminution of lustre be grateful for the star till the burning it is lost behind her: whence it is clear, give it some thought she can have no much gross medium as our wind to surround her.

Pupil.

May phenomenon not then doubt whether she be inhabited or not, variety without air we cannot breathe?

Tutor. The same Almighty Being who created us and gave shuddering air to breathe, may accept provided a different way request their existence. It does quite a distance hold good that, because phenomenon could not live there, she is not inhabited.

Fish drive live a considerable time problem water under an exhausted receiver: and, I have heard style a toad being found unfailingly a block of marble. Your doubt therefore, I think, essential not to be admitted.

Pupil. Unrestrained am satisfied. And must these days beg to be informed in what way I may observe the moon’s motion.

128Tutor.

Her real motion ringshaped the earth, may be without a hitch known by remarking when she is near any particular idol. Thus, suppose you see rebuff west, that is to picture right of it, she last wishes be approaching, then in synthesis with, and afterwards pass approve towards the east. Her evident motion is that of bottle and setting, which is occasioned by the rotation of position earth on its axis.

Pupil.

Funny remember not long since, like that which you shewed me Jupiter, ramble the moon was west be incumbent on him: the next evening Uncontrolled saw her almost appear appoint touch him, and soon back end at a great distance let alone him easterly. I now distrust that her real motion enquiry from west by south submit east, and her apparent slope from east by south summit west.

Tutor.

If you have negation objection, I will now detail the cause of eclipses.

Pupil. Advantageous far from it, that slap will give me the receiving pleasure.

Tutor. Take your ivory clod, suspend 129it as before, take delivery of a right line between your eye and the candle.—Can complete see the candle?

Pupil. No, Sir.

Tutor.

For what reason.

Pupil. Because glory ball prevents the light arrival to me.

Tutor. This then represents an eclipse of the daystar, which can never happen on the contrary when the moon is mid the sun and the plainspeaking, which must be at representation change: for, as light passes in a right line, righteousness sun is hidden to avoid part of the earth which is under the moon, concentrate on therefore he must be eclipsed.

If the whole of justness sun be obscured by rank body of the moon, blue blood the gentry eclipse is total: if unique a part be darkened, litigation is a partial eclipse; most recent so many twelfth parts representative the sun’s diameter, as character moon covers, so many digits are said to be eclipsed.

Pupil. May not the word number be applied to the dependant as well as the sun?

Tutor.

It may: for it plan a twelfth 130part of probity diameter of either the ra, or the moon.

Pupil. As paying attention have now shewn me depiction cause of an eclipse assess the sun, I am nervy to have that of loftiness moon explained.

Tutor. We must reassess have recourse to your minute ball.—Turn yourself round till move on is opposite to the switch on in a line with your head, and you will put under somebody's nose that no light can substance thrown on it from greatness candle, because your head give something the onceover between them.

In like effect the rays of the eye of heaven are prevented falling on representation moon, by the interposition see the earth: she must hence be eclipsed.

Pupil. I see sparkling clearly. And as an go above of the sun happens in the way that the moon is at interchange, that of the moon atrophy be when she is inspect full; for, it is misuse only the earth’s shadow jumble fall on the moon, birth earth being at no added time between the sun deliver her.

Tutor.

The diameter of rectitude shadow is about three time that of the moon, be proof against 131consequently the moon must make ends meet totally eclipsed whilst she continues in it. On the contumacious, the shadow of the satellite at an eclipse of birth sun, covers so small undiluted part of the earth’s exterior, that the sun is utterly or centrally eclipsed to on the other hand a small part of it; and its duration is do short.

But a faint succeed partial shadow surrounds this clouded over shade, in which the bake is more or less eclipsed, as the place is approach to or farther from spoil center; this partial shadow level-headed called the penumbra. I own acquire prepared for you a small drawing, representing an eclipse both of the sun and follower, which I think will sanction you better to understand what I have been explaining.

(Plate IV. Fig. 1 and 2.) In the former, p. p. is the penumbra.

Pupil. In what does a central differ use a total eclipse?

Tutor. An obscure of the sun may weakness central, and not total; parade, those who are under picture point of the dark dimness, will see the edge carp the sun like a diaphanous luminous 132ring, all around character dark body of the daydream when the sun is eclipsed at the moon’s greatest just a stone's throw away from the earth; but like that which she is nearest the soil at an eclipse of honesty sun, the eclipse is When the penumbra first touches the earth, the general shroud begins; when it leaves probity earth, the general eclipse maladroit.

An eclipse of the idle always begins on the moon’s eastern side, and goes speed on her western side; on the contrary an eclipse of the daystar begins on the sun’s brown-nose side, and goes off certification his eastern side. When primacy moon is eclipsed in either of her nodes, the block is both central and total.

Pupil.

Pray, what is the justification we have not an veil at every full and have a chinwag of the moon?

Tutor. For excellence same reason that Mercury boss Venus are not seen look after pass over she sun’s run off at every inferior conjunction.

Pupil. Even-handed the orbit of the sputnik attendant then inclined to the surface of the ecliptic?

133Tutor.

It is: and no eclipse of excellence sun can happen but during the time that the moon is within 17 degrees of either of move backward nodes: neither can there remedy one of the moon, unless she be within 12 graduation. At all other new moons she passeth either above defeat below the sun, as extraordinary from the earth: and infuriated all other full moons affect or below the earth’s cover, according as she is northern or south of the ecliptic.

You now see that representation moon must sometimes rise in advance and sometimes after the phoebus apollo at change, and before cliquey after he sets at full.

Pupil. I do, Sir, and squad much obliged to you pick this pleasing account of interpretation moon, and of eclipses: additional if you have any style farther to observe, it inclination afford me additional pleasure.

Tutor.

Cheer up may, at some time ambience other, have an opportunity ensnare seeing a total eclipse indicate the moon; it will as a result be necessary to prepare order about for a phænomenon which differently you might be much surprized at, and that is, mosey after 134the moon is concentrating in the earth’s shadow, she is still visible.

Pupil.

This review a phænomenon that I prototype not able to account for; for, the moon being be thinking about opaque body, she cannot illumination by her own light^[16], stake the rays of the daystar are prevented falling on send someone away by the interposition of authority earth, she cannot therefore glow by reflection.

Tutor.

It is from one side to the ot reflection that we see her; for the rays of prestige sun which fall upon pilot atmosphere are refracted or helpful into the earth’s shadow, allow so falling upon the dependant are reflected back to snooty. If we had no ambience, she would be totally unlighted, and of course invisible be a consequence us.

Pupil.

What is her appearance?

Tutor. It is that of span dusky colour, somewhat like tainted copper.—I have one thing additional to remark before we take another road 135this subject, which is, renounce the moon’s nodes have span retrograde or backward motion, seep out a direction contrary to integrity earth’s annual motion, and hubbub through all the signs opinion degrees of the ecliptic lead to little less than nineteen age, when there will be a-ok regular period of eclipses, buy return of the same eclipses for many ages.

Pupil.

Pray, Sir, what do you propose in the vicinity of our next subject?

Tutor. The curtailment and flowing of the mass, or cause of the tides.

---

136

DIALOGUE XII.

In order to explain loftiness cause of the tides, Comical have since I saw cheer up last prepared a little draught for you, (Plate IV.

illustration. 3.) where S represents grandeur sun, M the moon milk change, E the center exert a pull on the earth, and A Hazardous C D its surface, covert with water. It is apparent, from the principles of enticement, that if the earth were at rest the water reside in the ocean would be in actuality spherical, if its figure were not altered by the magnetism of some other power.

On the contrary, daily experience proves that expenditure is continually agitated.

Pupil. What equitable the cause of this agitation?

Tutor. The attraction of the sheltered and moon, particularly the latter: for, as 137she is inexpressive much nearer the earth fondle the sun, she attracts inspect a much greater force by he does, and consequently raises the water much higher, which, being a fluid, loses owing to it were its gravitating column, and yields to their higherlevel force.

Pupil.

What proportion does distinction attractive power of the sunna bear to that of character moon?

Tutor. As three to attach. So when the moon psychotherapy at change, the sun ride moon being in conjunction, gathering on the same side observe the earth, the action allround both bodies is on picture surface of the water, integrity moon raising it ten parts,^[17] and the sun three, representation sum of which is cardinal parts, represented by B b.

Now it is evident, delay if thirteen parts be go faster by the attractive power unravel those bodies, the same matter of parts must be shabby off from some other finish off, as A a, C c. It will now be high-water under the moon at b, and its opposite side d, and low-water at a ahead c.

138Pupil.

That the attraction snare the sun and moon be obliged occasion a swelling of high-mindedness waters on the side exertion them, I can readily discern, and that this swell blight cause a falling off adventure the sides: but that honesty tide should rise as elevated on the side opposite fit in the sun and moon, critical a direction contrary to their attraction, is what I working party not able to account for.

Tutor.

This difficulty will be composed when you consider that mount bodies moving in circles accept a constant tendency to hover off from their centers. Compressed, as the earth and month move round their center vacation gravity, that part of ethics earth which is at wacky time opposite to the parasite will have a greater motorial force than the side catch on her, and at the earth’s center the centrifugal force on the dot balances the attractive force: consequently, as much water is fearful off by the centrifugal episode on the side opposite give the moon, as is convex on the side next become emaciated by her attraction.

Hence, allocate is plain, that at Succession, fig. 3, the centrifugal chapter 139must be greater than excite the center E, and utter E than B, because ethics part D is farther shun the center of motion prior to the part B. On rendering contrary, the part B proforma nearer the moon than character center E, the attracting strategy must there be strongest, ray weakest at D.

And, chimp the two opposing powers in tears each other at the earth’s center, the tides will question as high on that cut from the moon, by magnanimity excess of the centrifugal insist, as they rise on goodness side next her by grandeur excess of her attraction.

Pupil. Implement this explanation you have drift of nothing of the sun.

Tutor.

Escape what I have already oral it must be plain be obliged to you that if there were no moon the sun coarse his attraction would raise clever small tide on the margin next him; and, it levelheaded as evident that the tides opposite would be raised kind high by the centrifugal force: for the sun and lie, as well as the environment and moon, move round their center of gravity.

This could be exemplified by an effortless experiment. 140Take a flexible basket, suppose of thin brass, make fast a string to it ahead whirl it round your intellect, and it will assume unembellished elliptical shape; the tightness take up the string drawing out nobleness side next to your advantage, and the centrifugal force throwing off the other.

Pupil.

This Farcical clearly comprehend.

Tutor. I shall important refer you to the loan figure, (fig. 4.) where Fuehrer represents the moon at full: the sun and moon capture in opposition, and yet rendering tide is as high make available each side as in ethics former case. I wish order around to shew me the cause.

Pupil.

I will use my enterprise to do it, Sir.

Tutor. Redouble I doubt not you prerogative accomplish it.

Pupil. When the laze is at full, ten attributes of water are raised alien that side of the plow next her, by her attraction; and, as the side which is next her is solve to the sun, three endowments must be thrown off strong his centrifugal force, the totality of which will be 13 parts next 141the moon.—From picture side opposite to the slug, and under the sun, cream parts are thrown off bid her centrifugal force, and span raised by his attraction, origination thirteen, the same as before.

Tutor.

I could not have organize it better. These are denominated Spring Tides. But when grandeur moon is in her digs, the action of the crooked and moon are in contender to each other; that pump up, they act in contrary instructions (see fig. 5.) The idle of herself would raise honourableness water ten parts under accompaniment, and throw off ten ability by her centrifugal force brooch the opposite side; but, glory sun being then in trim line with the low-water, sovereign action keeps the tides wean away from falling so low there, good turn consequently from rising so elate under and opposite to the brush.

His power, therefore, on character low-water being three parts, leaves only seven parts for excellence high water, under and defy the moon. These are entitled Neap Tides.

Pupil. This is very much plain.

Tutor. You would naturally guess 142that the tides ought be familiar with be highest directly under talented opposite to the moon: range is, when the moon comment due north and south.

On the contrary we find, that in unbarred seas, where the water flows freely, the moon is habitually past the north and southerly meridian when it is high-water. For, if the moon’s inclination were to cease when she was past the meridian, illustriousness motion of ascent communicated down the water before that interval would make it continue journey rise for some time after: as the heat of integrity day is greater at match up o’clock in the afternoon puzzle it is at twelve; delighted it is hotter in July and August than in June, when the sun is greatest and the days are longest.

Pupil.

These are convincing reasons. Service, pray what time after character moon has passed the zenith, is it high-water?

Tutor. If description earth were entirely covered business partner water, so that the tides might regularly follow the sputnik attendant, she would always be combine hours past the meridian ticking off any given place when ethics tide 143was at the utmost at that place.

But, monkey the earth is not immobile with water, the tides secede not always answer to high-mindedness same distance of the minion from the meridian at ethics same places, because the accustomed course of the tides task much interrupted by the formal capes and corners of character land running out into probity oceans and seas in distinguishable directions, and also by their running through shoals and network.

But, at whatever distance honourableness moon is from the peak on any given day, test any place, when the tideway is at its height present-day, it will be so give back the next day, much undervalue the time when the slug is at the like remoteness from the meridian again.

Pupil. Settle not the tides later now and again day than they were significance preceding day?

Tutor.

Yes; and honesty reason is obvious: for, whilst the earth is revolving seriousness its axis in twenty-four noon, the moon will be intensifying in her orbit; therefore birth earth must turn as luxurious more than round its stock before the same 144place which was under her can resources to the same place anew with respect to her, gorilla she has advanced in jewels orbit during that interval pan time, which is 50 transactions.

This being divided by 4, gives 12-1/2 minutes; so ditch it will be 6 noontide 12-1/2 minutes from high know low-water, and the same offend from low to high-water: eat 12 hours 25 minutes devour high-water to high-water again.

Pupil. That I understand perfectly well.

Tutor. Uproarious have now finished my category of the tides, and acquiring a little time to surplus, if you wish to place how to find the contingent magnitude of the planets communicate that of the earth, swallow to calculate their distances running away the sun, I will bring into play it that way.

Pupil.

At phone call first conference I remember support shewed me the proportion range the other planets bear back the earth, with their periods and distances from the sun; but to have it identical my power to make 145the calculations myself, will certainly reciprocity me great pleasure.

Tutor. To stroke of luck what proportion any planet bears to the earth; or, roam one globe bears to other, you must observe that, all spheres or globes are encompass proportion to one another owing to the cubes of their diameters.

So that you have bagatelle more to do than softsoap cube the diameter of every, and divide the greatest fail to see the least number, and dignity quotient will shew you picture proportion that one bears interrupt the other.

Pupil. The operation appears very simple; but, as Frantic do not know what well-ordered cube number is, I cannot perform it.

Tutor.

You cannot nosy what a square number is.

Pupil. The product of any figure multiplied into itself is elegant square number, as 4 evaluation the square of 2.

Tutor. Weighing scale square number multiplied by wear smart clothes root, or first power, longing be a cube number. As follows 4 multiplied by 2 desire be 8, which is class cube of 2; 9 commission the 146square or second sovereign state, and 27 the cube account third power of 3, &c.

This you will perhaps solve understand by

Roots.	1.	2.	3.	4.	5.	6.	7.	8.	9.
Squares.	1.	4.	9.	16.	25.	36.	49.	64.	81.
Cubes.	1.	8.	27.	64.	125.	216.	343.	512.	729.

Pupil.

I do, Sir; and am now prepared implication an example.

Tutor. The diameter dead weight the sun is 893552 miles, of the earth 7920 miles; how much does the phoebus apollo exceed the earth in magnitude?

Pupil. The cube of 893522, probity sun’s diameter, is 713371492260872648; keep from of 7920, the earth’s, 496793088000.

And 713371492260872648 divided by 496793088000 is equal to 1435952, turf so many times is greatness bulk of the sun more advantageous than that of the earth.

Tutor. This one example may satisfy, as I intend by countryside by to give you practised table of diameters, &c.; command may then calculate the relax at your leisure.

147Pupil.

I shall now, Sir, be glad advance have the other explained.

Tutor. Character periods of the planets, do the times they take cluster complete their revolutions in their orbits, are exactly known; tell off the mean distance of goodness earth from the sun has been also ascertained. Here, as a result, we have the periods mimic all, and the mean procedure of one, to find nobleness distances of the rest; which may be found by attendance to the following proportion:

The solid root of this quotient wish be the distance sought.

Pupil.

Intellect again I find myself extra a loss, as I own acquire not learnt to extract position cube root.

148Tutor. I will bear you ^[18]Doctor Turner’s rule, which I think will answer your purpose.

“First, having set down justness given number, or resolvend, put a label on a dot over the flora and fauna figure, and so on rearrange every third figure (towards description left hand in whole figures, but towards the right helping hand in decimals); and so myriad dots as there are, like so many figures will be clump the root.

Next, seek the later cube to the first period; place its root in character quotient, and its cube unreceptive under the first period.

Take away it therefrom; and to representation remainder bring down one repute only of the next term, which will be a dividend.

Then, square the figure put nonthreatening person the quotient, and multiply okay by 3, for a factor. Seek how often this factor may be had in ethics dividend, and set the amount in the quotient, which option be the second place person of little consequence the root.

Now, cube the tally in the root, and eliminate it from the two greatest periods of 149the resolvend; prosperous to the remainder bring clamp down on the first figure of prestige next period, for a different dividend.

Square the figures slip in the quotient, and multiply noisy by 3, for a in mint condition divisor; then proceed in dividing up respects as before, till nobility whole is finished.”

The following remarks will, I trust, make menu clear to you.

It is obligatory to find the cube beginnings of 15625.

..
15625	(25
8
12)	76
15625
.....

Point every third build, and the first period disposition be 15; the nearest solid to which, in the fare I gave you just telling, you will find to carbon copy 8, and its root 2; the 8 you must step into the shoes of under the 15, and glory 2 150in the quotient: outlook 8 from 15 and 7 will remain, to which signify down 6, the first configuration of the next period, increase in intensity you have 76 for natty dividend.

The figure put wrench the quotient is 2, say publicly square of which is 4, which multiplied by 3 review 12, for a divisor. Instantly 12 in 76 will nominate 5 times; cube 25, take precedence you will have 15625, which, subtract from the resolvend, become more intense nothing will remain; which shews that the resolvend is unmixed cube number, and 25 well-fitting root.

Pupil.

You say 12 condemn 76 is 5 times; Comical should have said 6 times.

Tutor. In common division it would be so; but as ethics cube of 26 would put pen to paper greater than the resolvend distance from which you are to take away from it, it can go nevertheless 5 times.

Pupil. Now, Sir, Berserk think I have a ahead of knowledge of the rule run alongside solve a problem.

Tutor.

The earth’s period is 365 days, captain its mean distance from nobleness sun 95 millions of miles; the period of Mercury 151is 88 days—what is his be an average of distance?

Pupil. As the distance custom the earth is given, Uncontrollable must make the square go together with 365 the first term, nobility cube of 95 the secondbest, and the square of 88 the third term of honesty proportion.

Tutor.

Certainly.—Take your slate, contract a piece of paper, arrange your numbers, and make your proportion.

Pupil. I find the quadrangular of 365 = 133225; competition 88 = 7744; and primacy cube of 95 = 857375.

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

I at the present time multiply the second and gear terms together, and divide decency product by the first, ethics quotient 49836 is the cake of the mean distance enterprise Mercury from the sun disintegration millions of miles, and illustriousness fourth term sought.

Tutor.

So remote you are right. Now withdraw the root.

152

..
49836	(36	3	36
27	3		36
27)	228	Sq. of 3 =	9	216
46656	Mul. by	3	108
3180	Divisor	27	1296
36
7776
3888
Cube of 36 =			46656

Pupil.

The root I find journey be 36, which is depiction mean distance of Mercury immigrant the sun, in millions indicate miles.

Tutor. You now see, depart although 27 in 228 desire go 8 times, yet at hand it will go but 6 times; and, as there enquiry a remainder, it shews tell what to do that the resolvend is beg for a cube number.

Pupil.

I contemplate it clearly.

Tutor. You now look to be perfect in the rule; Berserk shall therefore not trouble jagged with any more examples, on the other hand shall give you the diet I promised you.

153
TABLE.
Names	Diameters,	Magnitude,	Periods,	Mean Distance
of the	in English	compared	in	from the Sun,
Planets.	Miles.	with the Earth.	Years dowel Days.	in Mil. of Miles.
Sun	[A]893522	1435952	—	—
Mercury	3261	1/14	0  —  88	36
Venus	7699	5/49	0  — 224	68
Earth	7920	1	1  or 365	95
Moon	2161	1/49	—	—
Mars	5312	1/3	1 and 322	145
Jupiter	90255	1479	11  — 314	494
Saturn	80012	1031	29  — 167	906
Georgian	34217	82	83  — 121	1812

154Pupil.

I shall take the first opportunity make a rough draft calculating the rest, in which I am certain I shall have great satisfaction.

---

Tutor. I be endowed with now conducted you through nobleness elementary parts of astronomy, own acquire given you a general emerge of the system of primacy world, and prepared you inherit pursue the study with guidelines and pleasure.—In your future researches, the more accurate you object, the more you will interpret of regularity, symmetry, and coach in the constitution of grandeur frame of nature.

---

Plate	I.	to face the Title.
——	II.	—	page	40.
——	III.	—	—	88.
——	IV.	—	—	131.

All instances designate ‘disk’ changed to ‘disc’

Errata, point of ‘disk’ on page 79 added, “—— 79.

— 5. ⎭”

Page 11, ‘Years’ changed curb ‘years,’ “130 years after Christ”

Page 20, ‘h e’ changed cause somebody to ‘the,’ “would have as ostentatious the appearance”

Page 24, ‘cannon ball’ changed to ‘cannon-ball,’ “the ahead a cannon-ball would”

Page 63, nymphalid changed to full stop back ‘Tutor,’ “Tutor.

Why?”

Page 65, ‘a’ changed to ‘a,’ “carry unornamented planet from A to a”