Euphrof. That's doubtlefs the Cafe; but a Parcel of bare Circles feem an uncouth Subject for Study; they feem fo varioufly combined and intermixed, that I fear I fhall never underftand them. Clean. So I remember you once faid of the various Conjugations and kinds of Verbs in the French Grammar, and yet you have found, that nothing but Attention and Refolution was neceff.ry to make you a perf &t Mistress of them. The like you will find of this Study, which is much cafier: I fhall only repeat the Words of Manilius, to encourage you thereto. A fubtle and furprizing Tafk is shown; Much have I past, yet fiill you lead me on. Book IV. Euphrof. I do not in the leaft defpond; I only with your Patience, Cleonicus, may hold out with mine. To make a Beginning on this Inftrument, therefore, pray tell me why it is called an Armillary Sphere? Cleon. Because of the various Circles of which it is compofed, which are like fo many Rings or Hoops, which in Latin are called Armil'e in general; thou h this Word properly fignified a Bracelet, an Ornament formerly worn on the Arm, and given by Captains to their Soldiers, and by fuch as held any Poft, &c. Hence you fee the Propriety of the Name. Euphrof. I do; and must next afk you what this Sphere is defigned to reprefent in general? Cleon. This Sphere, by its real Circles, reprefents the imaginary Circles of the concave Expanfe of the Sky, by which Aftronomers divide the Heavens into the fame Tame Parts or Portions, as you fee thefe Circles divide the Sphere. Euphrof. I fuppofe you mean, if my Eye could be placed in the Center of this Sphere, I fhould fee its Circles upon, or against thofe very Parts of the Heavens where thofe imaginary Circles of the Aftronomers are fuppofed to be. Cleon. Moft happily conceived, my Euphrofyne; your Genius is turned for the Science.-The Sphere, you obferve is moveable within the Frame, and the large Circle (HOR) fupported thereby; which Circle, you fee, with fome others, are graduated, or divided into their proper Degrees. Euphrof. I take notice of thofe graduated Circles; but muft confefs I have but an imperfect Notion of those Divifions and their Uses, and should be glad to have them farther explained to me. Cleon. To understand that aright is a fundamental Article; in order to which you must know, that a Circle is generally divided into four equal Parts or Quarters, called Quadrants, and each of thefe Quadrants is again divided. into 90 equal Parts, called Degrees, as you fee is done on this broad Circle; fo that the whole Circle contains four Times go, or 360 Degrecs.Again, each Degree is fuppofed to be fubdivided into 60 equal Parts, called Seconds, and each Second into 60 others, called Thirds; and fo on. But thefe laft 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 Euphrofyne. Euphrof. I understand you well, and thofe Degrees, I fee, are numbered at every 10th Divifion; but I also observe, this Method of numbering Degrees is not the fame in all the graduated Circles of this Sphere. Clean. No, it is not; but differs in almost all them, according to their different Nature and Ufe. Euphrof. 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 fmall Circles. The greater Circles divide the Sphere into two equal Parts, or Hemifpheres ; and and leffer Circles divide it into two unequal Parts, or Segments. Euphrof. How many are the great Circles of the Sphere? Cleon. They are in Number fix. Four of which are graduated, viz. 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, (EQ) which divides the Sphere into the Northern and Southern Hemispheres. 4. The ECLIPTIC, which is this large Circle, on which you fe the Characters of the 12 Signs, and which cuts the Equinoctial in two oppofite Points at the Horizon.The other two are called COLURES; the first of which is called, 5. The Equinoctial COLURE, which is the great Circle that paffes through thofe two Points of the Equinoctial, where the Ecliptic interfects it. 6. The Solflitial COLURE, which is that great Circle you fee just under the General Meridian; to which, and the other Colure, all the other Circles are fixed. Euphrof. So far I understand you very well: But now tell me which, and how many are the leffer Circles of the Sphere ? Clean. They are four, viz. Two Tropic, and two Polar Circles. I. 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 fituated, you fee, at the fame Dittance from the Equinoctial, and parallel to it, on the South Side; touching the Ecliptic in the Beginning of Capricorn. 3. The Arctic Circle, (ef) parallel to the Equinoctial on the North, at the Diftance of 66 Degrees. 4. The Antarctic Circle, (gh) which, you fee, is parallel to, and at the fame Distance from the Equinoctial on the South Side.And thus you have the Names of the principal Circles of the Sphere, Euphrof. I thank you, Cleonicus: But there is that ftrait, curious Rod or Wire in the Middle of the Sphere, about which it turns; is it not what you call the Axis of the Sphere? Cleon. Yes, Euphrofyne, it is; and it reprefents the Axis of the World, and the two Extremities thereof, (N and S) are called the Poles of the World; the former (N) the North Pole, which is above our Horizon; and the latter (S) the South Pole, below the Horizon. Euphrof. But this fmall Circle, fixed on the Meridian about the North Pole, I prefume, you call the HourCircle; from the Hours I fee engraved thereon, and the Hand on the Axle, pointing to them. Cleon. You judge aright, 'tis called the Hour-Circle; and is rather an Appendage to the Sphere, than a Part of it: The Ufe of which, and of all the Circles of the Sphere, great and small, we will more fully consider, and apply, in the next enfuing Opportunities; the Daylight being too far gone to admit any Thing farther on this Subject at present. DIALOGUE II. Of the HORIZON, and its Various Ufes. You Euphrofyne. YOU gave me Yesterday an Account of the Spheres, and the Names of the Circles which compofe it, Cleonicus; I fhall be glad to have a more diftinct and particular Explanation of the Nature and Ufe of thofe Circles, that I may the more compleatly comprehend the Defign of the Machine. Cleon. I'll now begin to inform you of the Name, Nature, and Ufe of all the Circles; how they divide the Sphere; and the Terms of feveral Points and Parts of the Machine derived therefrom.-And first of all, let us confider this broadeft Circle, the Horizon. Euphrof. With Pleasure I attend you, Cleonicus; pray then, whence has it the Name? And what does it import? Cleon. The Word is derived from the Greek, and the Ufe Ufe of the Circle is contained in its Name; for it comes from a Word which fignifies to bound, limit, or terminate ; as the Horizon is appointed to fhew that Circle in the Heavens, which bounds or terminates the Sight of the Spectator any where fituated on the Earth. Euphrof. I fuppofe you mean, that diftant Boundary of our Sight, where the Heavens and the Earth seem to join all around us, as it appears from the Top of an high Mountain or Tower. Cleon. The very fame, Euphrofyne; 'tis that imaginary Circle which intercepts from our View the Sun, Moon, and Stars, each Night; and when they defcend below it, we fay, they fet; as on the contrary, each Morning, when they appear above it, we fay, they rife. Euphrof. How far is this Circle diftant from us in the Heavens? Cleon. It is every Way distant from the Point over our Heads in the Heavens juft 90 Degrees; and therefore divides the Heavens into two equal Parts, called the Upper and the Lower Hemispheres. Euphrof. By the upper Hemisphere, I fuppofe, you mean all that Part of the Heavens which is open to our View; and by the under or lower Hemisphere, all that Part which is hid from our Sight. Cleon. Very right, Sifter, I do: And the two Points, (Z and D) which are equally diftant from the Horizon on every Part above and below it, are called the Poles of the Horizon; and further, this which is above it, (Z) and over the Head of the Spectator, is called the Zenith; as that (D) which is under his Feet, is called the Nadir. Of this great Circle Manilius thus fings: To find the fpacious Line, caft round thine Eyes, For now this half, and now that half of Sky, This |