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DIALOGUE I. The Doitrine of the SPHERE; or, a general Description of the Circles thereof.

* Cleonicus. TITELL, my Euphrosyne, I make no Queftion but

V the Conversations we had when I was with you last, have made a notable Impression on your Mind, and fupplied you with Matter of ample Meditation and Amusement.

Euphrosyne. Greatly fo, in each Respect, dear Cleonicus; and fo agreeable were those Studies, and so advantageous to my Mind and Understanding, that I shall ever reflect with Pleasure and Gratitude on the Care and Pains you then took to instruct me in those more than human (I may truly say divine) Speculations. You are a Stranger to the longing Expectation I have had for your Return, that I might have the Happiness of making a farther Progress and Proficiency therein.

Cleon. You speak in most engaging Accents; we will now apply every Opportunity to that Purpose; and as we then contemplated the Heavens in a natural and practical Way; fo now we will farther consider the Advantages Art has supplied us with, to make those Things still

more * Now returned again from the University, where he is supposed to have been to pursue his Studies since the last Dialogue was finished.

more easy and practically useful. To which End we have three excellent Instruments contrived, viz. the ARMILLARY SPHERE, the ORRERY, and the GLOBES.

Euphrof. I should much delight to be acquainted with the Nature and Uses of these Instruments, Cleonicus,

Cleor. That you will attain with great Ease; for there is nothing in them which a Genius much inferior to yours is not capable of apprehending.

Euphrof. No Compliments, I beg of you, Cleonicus ; I shall put you to prove your Words; for, if I can once understand these Machines, I shall have a great Opinion of myself as an Astronomer.

Cleon. And justly you may ; nor will you then be the first Woman who has understood Astronomy well. Astronomy is a noble Science, worthy the Fair-Sex, and highly deserving the Encomium of the Poet.

Astronomy! bail, Science heavenly born!
Thy Schemes the Life affift, the Mind atorn.
Thy Aids the Heaven's feald Volumes wide impart;
And taught the Seaman first bis useful Art;
Gave changing Seafons their determin'd Space,

And fix'd to Hours and Years their measur'd Race.
Euphrof. So useful a Science urges me with Impatience
to the Study of it; and, pray, which of the afore-named -
Instruments do we first begin with, to employ the remain-
ing Hours of the Day?
· Cleon. The ARMILLARY SPHERE, by the Knowledge
of which you will naturally be led to the understanding
of the Orrery and the Globes, on which you may practile
all the useful Problems of Astronomy.

Euphrof. Pray what is that you call the Armillary Sphere?

Cleon. I will presently shew you ; I have bought one at London, as I came home, which cost me 20 Guineas, on Purpose to give you the better Idea of such things as may prove the future Subject of our Speculations. Here it is, Sifter.

Euphrof. Afine and curious Machine, indeed! But I see nothing but Circles variously connected together; pray, what am I to understand by them?

Cleon. You will see more hereafter ; but we will first consider the Nature and Use of the Circles; a due Underitanding of which, is the Ground of all practical Aftro, pomy,

Instrumtudy of it; and Science urges meafurd Race.

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Euphrol. That's doubtless the Case; but a Parcel of bare Circles seem an uncouth Subject for Study; they feein fo variously combined and intermixed, that I fear I fall never understand them.

Cleon. So I remember you once said of the various Conjugations and kinds of Verbs in the French Grammar, and yet you have found, that nothing but Attention and Resolution was necefl.ry to make you a perf et. Mistress of them. The like you will find of this Study, which is much easier : I shall only repeat the Words of Manilius, to encourage you thereto.

A subrle and surprizing Task is frown;
Nivch have i pajt, yet fill you lead me on.
Thepi Things rem dark, whilft I the rest explore,
E jy my Procepts, and complain no more.
'Tis Got you feurch for, by my Aid you try
To climb, aud vierú the Inside of the Sky's
Corfin'd ly Fate, you search its boundless Sway,
Ad se k is know the Laws you must obey :
The narrow Bounds of your own Breast you pass,
Enjoy the I Vorld, and rove in the vasi Space:
Pai ful, but always noble Things are hard,
Great is the Talk, but equal the Reward:
Nor let the various Maze thy Thoughts repress,
Entir, ard you are certain to puifs.

Book IV. Euphrof. I do not in the least dispond; I only with your Patience, Cleonicus, may hold out with mine. To make a Beginning on this Inftrument, t'erefore, pray tell me why it is called an Armillary Sphere?

Cleon. Because of the various Circles of which it is composed, which are like so many Rings or Hoops, which in Latin are called Armillæ in eneral; thou h this Word properly signified a Bracelet, an Ornament formerly worn on the Arm, and given by Caprains to their Soldiers, and by such as held any Poft, &c. Hence you see the Propriety of the Name.

Euphref. I do ; and mult next ak you what this Sphere is difigned to represent in general ?

Cleon. This Sphere, by its real Circles, represents the imarinary Circles of the concave Expanse of the Sky, by which Attronomers divide the Heavens into the



Cleon. "Day, it is callethis Inteld out with

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Yame Parts or Portions, as you see these Circles divide the Sphere.

Euphrof. I suppose you mean, if my Eye could be placed in the Center of this Sphere, I should see its Circles upon, or against those very Parts of the Heavens where those imaginary Circles of the Astronomers are supposed to be.

Cleon. Most happily conceived, my Euphrosyne ; your Genius is turned for the Science. The Sphere, you observe is moveable within the Frame, and the large Circle (HOR) supported thereby ; which Circle, you lee, with some others, are graduated, or divided into their proper Degrees.

Euphrof. I take notice of those graduated Circles; but must confess I have but an imperfect Notion of those Divisions and their Uses, and should be glad to have them farther explained to me,

Cleon. To understand that aright is a fundamental Ar. ticle; in order to which you must know, that a Circle is generally divided into four equal Parts or Quarters, called Quadrants, and each of these Quadrants is again divided into go equal Parts, called Degrees, as you see is done on this broad Circle ; so that the whole Circle contains four Times go, or 360 Degrees.--Again, each Degree is supposed to be subdivided into 60 equal Parts, called Seconds, and each Second into 60 others, called Thirds; and so on. But these last Divisions are too small to be actually made; and therefore a Degree is generally divided but into Halves and Quarters ; that is, at every 15th Minute : But I have formerly acquainted you with this Manner of dividing a Circle, and need not again repeat it to my Euphrosjne.

Euphrof. I understand you well, and those Degrees, I fee, are numbered at every joth Division; but I also observe, this Method of numbering Degrees is not the same in all the graduated Circles of this Sphere.

Cleon. No, it is not; but differs in almost all them, according to their different Nature and Use.

Euphros. Pray, how many kinds of Circles are there? And what are their Names?

Cleon. All the Circles of the Sphere are but of two Sorts, viz. Great and small Circles. The greater Circles divide the Sphere into two equal Parts, or Hemispheres ;

the Sphe The Shemispheresnis


and lesser Cire'es divide it into two unequal Parts, or Segments.

Euphrof. How many are che great Circles of the Sphere?

Cleon. They are in Number fix, Four of which are graduated, vimeo

1. The HORISON, (HOR) which is this broad Circle, fupported by the Frame within which moves

2. The general MERIDIAN, (HZRD) which is this upright, graduated Circle, ftanding at right Angles to the Horizon; and within this moves the Sphere itself,

3. The EQUINOCTIAL, (AQ) which divides the Sphere into the Northern and Southern Hemispheres.

4. The ECLIPTIC, which is this large Circle, on which you fe the Characiers of the 12 Signs, and which cuts the Equinoctial in two opposite Points at the Horizon.The o her two are called COLURES; the first of which is callid,

5. The Equinoctial COLURE, which is the great Circle that passes through those two Points of the Equinoctial, where the Ecliptic intersects it.

6. The Solftitial COLURE, which is that great Circle you fee just undur the General Meridian; ta which, and the other Colure, all the other Circles are fixed.

Exhrof. So far I understand you very well : But now tell me which, and how many are the lefler Circles of the Sphere?

Clean. They are four, viz. Two Tropic, and two Polar Circles.

1. The Tropic of Cancer, (ab) which lies parallel to the Equinoctial on the North Side, at the Distance of 231 Degrees, and touches the Ecliptic in the Beginning of Cancer.

2. The Tropic of Capricorn, (de) which is situated, you see, at the fame Distance froin the Equinoctial, and parallel to it, on the South Side ; touching the Ecliptic in the Beginning of Capricorn.

3. The Arctic Circh, fef) parallel to the Equinoctial on the North, at the Distance of 661 Degrees.

4. The Antarctic Circle, (8 h) which, you fee, is parallel to, and at the same Distance from the Equinoctial on the South Side. And thus you have the Names of the principal Circles of the Sphere,

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