The Great Orrery Four Feet in Diameter Made by Tho: Wright Mathematical Instrument-maker to His Majesty For the Royal Academy at Portsmouth Now B. Cole, at the same shop.

Who makes Orrery’s of different sorts as may be seen at his Shop in Fleet Street

Where is Sold a Large Print of the Orrery with the Explanation on a Sheet of Imperial Paper. Price 2s.

THE
Description and Use
OF
THE GLOBES,
AND
THE ORRERY.

To which is prefix’d,

By Way of Introduction,

A brief Account of the Solar System.

By JOSEPH HARRIS,

Teacher of the Mathematics.

The Eleventh Edition.

LONDON:

Printed for B. Cole, at the Orrery, near the Globe Tavern, in Fleet street, late the Shop of Mr. Thomas Wright, Instrument-maker to his late Majesty; and E. Cushee, near St. Dunstan’s Church, Fleet Street.

MDCCLXXIII.

Advertisement.

The great encouragement Mr. Wright has had for many years past in making large Orreries, with the motions of all the Planets and Satellites, and the true motion of Saturn’s Ring, has made him so ready and perfect, that Gentlemen may depend on having them made reasonable and sound, not liable to be out of Order.

As may be seen by one he made for Mr. Watt’s Academy in Tower-street.

Another for his Majesty at Kensington.

Another for the New Royal Academy at Portsmouth.

Another for his Grace the Duke of Argyle (late Lord Ila.)

And several other large ones for Noblemen and Gentlemen.

The above, and all other Mathematical, Philosophical, and Optical Instruments, are now made in the most complete manner, by B. Cole, Servant to Mr. Wright, at the time of the above being made, and successor to him in the same Trade and Business.

THE CONTENTS.

The Introduction: Containing a brief Account of the Solar System, and of the Fixed Stars.

The Description and Use of the Celestial and Terrestrial Globes.

THE
INTRODUCTION,
CONTAINING

A Brief Account of the Solar System, and of the Fixed Stars.

SECT. I.

Of the Order and Periods of the Primary Planets revolving about the Sun; and of the Secondary Planets round their respective Primaries.

Planets.

The Sun is placed in the midst of an immense space, wherein six opaque spherical bodies revolve about him as their center. These wandering globes are called the Planets, who, at different distances, and in different periods, perform their revolutions from West to East, in the following order:

1. ☿ Mercury is nearest to the Sun of all the planets, and performs its course in about three months. 2. ♀ Venus in about seven months and a half. 3. ♁ The Earth in a year. 4. ♂ Mars in about two years. 5. ♃ Jupiter in twelve. And lastly, ♄ Saturn, whose[1] Orbit includes all the rest, spends almost 30 years in one revolution round the Sun. The distances of the Planets from the Sun are nearly in the same proportion as they are represented in [Plate 1]. viz. Supposing the distance of the Earth from the Sun to be divided into 10 equal parts; that of Mercury will be about 4 of these parts; of Venus 7; of Mars 15; of Jupiter 52; and that of Saturn 95.

The Characters placed before the names of the Planets, are for brevity’s sake commonly made use of by Astronomers, instead of the words at length, as ♀, for Venus, &c.

Plate 1.

Nodes.

The orbits of the Planets are not all in the same plane, but variously inclined to one another; so that supposing one of them to coincide with the above scheme, the others will have one half above, and the other half below it; intersecting one another in a line passing through the Sun. The plane of the Earth’s orbit is called the Ecliptic; and this the astronomers make the standard to which the planes of the other orbits are judged to incline. The right line passing thro’ the Sun, and the common intersection of the plane of the orbit of any planet and the Ecliptic, is called the Line of the Nodes of that planet; and the points themselves, wherein the orbit cuts the Ecliptic are called the Nodes.

Excentricity.

The inclinations of the orbits of the Planets to the plane of the ecliptic, are as follows, viz. the orbit of Mercury makes an angle with it of almost 7 degrees; that of Venus something above 3⅓ degrees; of Mars a little less than 2 degrees; of Jupiter, 1⅓ degree; and of Saturn, about 2½ degrees. The orbits of the Planets are not circles, but ellipses or ovals. What an ellipsis is, may be easily understood from the following description. Imagine two small pegs fixed upright on any plane, and suppose them tied with the ends of a thread somewhat longer than their distance from one another: Now if a pin be placed in the double of the thread and turned quite round (always stretching the thread with the same force) the curved described by this motion is an Ellipsis. The two points where the pegs stood, (about which the thread was turned) are called the foci of that ellipsis; and if, without changing the length of the thread, we alter the position of the pegs, we shall then have an ellipsis of a different kind from the former; and the nearer the focus’s are together, the nearer will the curve described be to a circle; until at last, the two focus’s coincide, and then the pin in the doubling of the thread will describe a perfect circle. The orbits of all the Planets have the Sun in one of their focus’s, and half the distance between the two focus’s is called the Excentricity of the orbits. This excentricity is different in all the planets, but in most of them so small, that in little schemes or instruments, made to represent the planetary orbits, it need not be considered.

Primary Planets.

Secondary Planets.

The six Planets above-mentioned, are called Primaries, or Primary Planets; but besides these, there are ten other lesser Planets, which are called Secondaries, Moons, or Satellites. These moons always accompany their respective primaries, and perform their Revolutions round them, whilst both together are also carried round the Sun. Of the six Primary Planets, there are but three, as far as observation can assure us, that have these attendants, viz. the Earth, Jupiter, and Saturn.

The Earth is attended by the Moon, who performs her revolution in about 27⅓ Days, at the distance of about 30 Diameters of the Earth from it; and once a Year is carried round the Sun along with the Earth.

Jupiter’s four Moons.

Jupiter has four Moons, or Satellites; the first, or innermost, performs its revolution in about one Day, and 18½ Hours, at the distance of 5⅔ Semidiameters of Jupiter, from his Center; the second revolves about Jupiter in 3 Days, 13 Hours, at the distance of 9 of his Semidiameters; the third in 7 Days, and 4 Hours, at the distance of 14⅓ Semidiameters; the fourth, and outermost, performs its course in the space of 16 Days, 17 Hours; and is distant from Jupiter’s center, 25⅓ of his Semidiameters.

Saturn has five Moons.

Saturn has no less than five Satellites; the first, or innermost, revolves about him in 1 Day, and 21 Hours, at the distance of 4⅜ Semidiameters of ♄, from his center; the second compleats his period in 2¾ Days, at the distance of 5³/₅ of his Semidiameters; the third, in about 4½ Days, at the distance of 8 Semidiameters; the fourth performs its course in about 16 Days, at the distance of 18 Semidiameters; the fifth, and outermost, takes 79⅓ Days, to finish his course, and is 54 Semidiameters of Saturn distant from his center. The Satellites, as well as their primaries, perform their revolutions from West to East: The planes of the Orbits of the Satellites of the same Planet are variously inclined to one another, and consequently are inclined to the plane of the Orbit of their primary.

Saturn’s Ring.

Besides these attendants, Saturn is encompassed with a thin plain Ring, that does no where touch his body; The diameter of this Ring is to the diameter of Saturn, as 9 to 4; and the void space between the Ring and the body of Saturn is equal to the breadth of the Ring itself; so that in some situations the Heavens may be seen between the Ring and his body. This surprizing phænomenon of Saturn’s Ring, is a modern discovery; neither were the Satellites of Jupiter and Saturn known to the ancients. The Jovial Planets were first discovered by the famous Italian philosopher Galilæus, by a telescope which he first invented; and the celebrated Cassini, the French king’s astronomer, was the first that saw all the Satellites of Saturn; which by reason of their great distances from the Sun, and the smallness of their own bodies, cannot be seen by us, but by the help of very good glasses.

Annual Motion.

Diurnal Motion.

The motion of the primary Planets round the Sun (as also of the Satellites round their respective primaries) is called their Annual Motion; because they have one Year, or alteration of Seasons compleat, in one of these revolutions. Besides this annual motion, four of the Planets, viz. Venus, the Earth, Mars, and Jupiter revolve about their own Axis, from West to East; and this is called their Diurnal Motion. For by this rotation, each point of their surfaces is carried successively towards or from the Sun, who always illuminates the hemisphere which is next to him, the other remaining obscure; and while any place is in the hemisphere, illuminated by the Sun, it is Day, but when it is carried to the obscure hemisphere, it becomes Night; and so continues, until by this rotation the said place is again enlightened by the Sun.

Diurnal Motion of the ♁, ♀, ♂ and ♃.

☉ and ☽ likewise turn round their Axis.

The Earth performs its revolution round its axis in 23 Hours, 56 Minutes;[2] Venus, in 24 Days, 8 Hours; Mars, in 24 Hours, and 40 Minutes; and Jupiter moves round his own axis in 9 Hours, and 56 Minutes. The Sun also is found to turn round his axis from West to East, in 27 Days: And the Moon, which is nearest to us of all the Planets, revolves about her axis in a Month, or in the same space of time that she turns round the Earth; so that the Lunarians have but 1 Day throughout the Year.

The Planets are Opaque and Globular.

I. The Planets are all Opaque bodies, having no light but what they borrow from the Sun; for that side of them which is next towards the Sun, has always been observed to be illuminated, in what position soever they be; but the opposite side, which the Solar rays do not reach, remains dark and obscure; whence it is evident that they have no light but what proceeds from the Sun; for if they had, all parts of them would be lucid, without any darkness or shadow. The Planets are likewise proved to be Globular; because let what part soever of them be turned towards the Sun, its boundary, or the line separating that part from the opposite, always appears to be circular; which could not happen, if they were not globular.

The Planets turn round the Sun.

II. That the Earth is placed betwixt the Orbs of Mars and Venus, and that ☿, ♀, ♂, ♃ and ♄, do all turn round the Sun, is proved from observations as follow:

[Plate 2. Fig. 1. 2.]

1. Whenever Venus is in conjunction with the Sun, that is, when she is in the same direction from the Earth, or towards the same part of the Heavens the Sun is in; she either appears with a bright and round face, like a Full Moon, or else disappears: Or, if she is visible, she appears horned, like a new Moon; which phænomena could never happen if ♀ did not turn round the Sun, and was not betwixt him and the Earth: For since all the Planets borrow their light from the Sun, it is necessary that ♀’s lucid face should be towards the Sun; and when she appears fully illuminated, she shews the same face to the Sun and Earth; and at that time she must be above or beyond the Sun; for in no other position could her illuminated face be seen from the Earth. Farther, when she disappears, or if visible, appears horned; that face of her’s which is towards the Sun is either wholly turned from the Earth, or only a small part of it can be seen by the Earth; and in this case she must of necessity be betwixt us and the Sun. Let S be the Sun, T the Earth, and V Venus, having the same face presented both towards the Sun and Earth; here it is plain that the Sun is betwixt us and Venus and therefore we must either place Venus in an Orbit round the Sun, and likewise betwixt him and us, as in [Fig. 1.] or else we must make the Sun to move round the Earth in an Orbit within that of Venus, as in [Fig. 2.] Again, after Venus disappears, or becomes horned, at her[3] ☌ with the ☉, she then must be betwixt us and the Sun, and must move either in an Orbit round the Sun and betwixt us and him, as in [Fig. 1.] or else round the Earth, and betwixt us and the Sun, as in [Fig. 2.] But Venus cannot move sometimes within the Sun’s Orbit, and sometimes without it, as we must suppose if she moves round the Earth; therefore it is plain that her motion is round the Sun.

Why Venus is always either our Morning or Evening Star.

Besides the forgoing, there is another argument to prove that Venus turns round the Sun in an Orbit that is within the Earth’s, because she is always observed to keep near the Sun, and in the same quarter of the Heavens that he is in, never receding from him more than about ⅛ of a whole circle; and therefore she can never come in opposition to him; which would necessarily happen, did she perform her course round the Earth either in a longer or shorter time than a Year. And this is the reason why Venus is never to be seen near midnight, but always either in the Morning or Evening, and at most not above three or four Hours before Sun-rising or after Sun-setting. From the time of ♀’s superior conjunction (or when she is above the Sun) she is more Easterly than the Sun, and therefore sets later, and is seen after Sun-setting; and then she is commonly called the Evening Star. But from the time of her inferior conjunction, ’till she comes again to the superior, she then appears more Westerly than the Sun, and is only to be seen in the morning before Sun-rising, and is then called the Morning Star.

After the same manner we prove that Mercury turns round the Sun, for he always keeps in the Sun’s neighbourhood, and never recedes from him so far as Venus does; and therefore the Orbit of ☿ must lie within that of ♀; and on the account of his nearness to the Sun, he can seldom be seen without a Telescope.

The Orbit of Mars includes the Earth’s.

[Fig. 3.]

Mars is observed to come in opposition, and likewise to have all other aspects with the Sun; he always preserves a round, full, and bright face, except when he is near his quadrate aspect, when he appears somewhat gibbous, like the Moon three or four Days before or after the full: Therefore the Orbit of ♂ must include the Earth within it, and also the Sun; for if he was betwixt the Sun and us at the time of his inferior conjunction, he would either quite disappear, or appear horned, as Venus and the Moon do in that position. Let S be the Sun, T the Earth, and A P Mars, both in his conjunction and opposition to the Sun, and in both positions full; and B C Mars at his quadratures, when he appears somewhat gibbous from the Earth at T. ’Tis plain hence, that the Orbit of Mars does include the Earth, otherwise he could not come in opposition to the Sun; and that it likewise includes the Sun, else he could appear full at his conjunction.

Mars when he is in opposition to the Sun, looks almost seven times larger in diameter than when he is in conjunction with him, and therefore must needs be almost seven times nearer to us in one position than in the other; for the apparent magnitudes of far distant objects increase or decrease in proportion to their distances from us: But Mars keeps always nearly at the same distance from the Sun; therefore it is plain that it is not the Earth, but the Sun, that is the center of his motion.

It is proved in the same way, that Jupiter and Saturn have both the Sun and the Earth within their Orbits, and that the Sun, and not the Earth, is the center of their motions; altho’ the disproportion of the distances from the Earth is not so great in Jupiter, as it is in Mars, nor so great in Saturn, as it is in Jupiter, by reason that they are at a much greater distance from the Sun.

Inferior and Superior Planets.

We have now shewn that all the Planets turn round the Sun, and that Mercury and Venus are included between him and the Earth, whence they are called the Inferior Planets, and that the Earth is placed between the Orbits of Mars and Venus, and therefore included within the Orbits of Mars, Jupiter, and Saturn, whence they are called the Superior Planets: And since the Earth is in the middle of these moveable bodies, and is of the same nature with them, we may conclude that she has the same sort of motions; but that she turns round the Sun is proved thus:

The Earth does not stand still, but turns round the Sun.

[Fig. 4.]

All the Planets seen from the Earth appear to move very unequally, as sometimes to go faster, at other times slower; sometimes to go backwards, and sometimes to be stationary, or not to move at all; which could not happen if the Earth stood still. Let S be the Sun, T the Earth, the great circle A B C D the Orbit of Mars, and the numbers 1, 2, 3, &c. its equable motion round the Sun; the correspondent numbers 1, 2, 3, &c. in the circle a, b, c, d, the motion of Mars, as it would be seen from the Earth. It is plain from this Figure, that if the Earth stood still, the motion of Mars, will be always progressive, (tho’ sometimes very unequal;) but since observations prove the contrary, it necessarily follows, that the Earth turns round the Sun.

The Annual and Diurnal Motions of the Planets, how computed.

The annual periods of the Planets round the Sun are determined by carefully observing the length of time since their departure from a certain point in the Heavens, (or from a fix’d Star) until they arrive to the same again. By these sort of observations the ancients determined the periodical revolutions of the Planets round the Sun, and were so exact in their computations, as to be capable of predicting Eclipses of the Sun and Moon. But since the invention of telescopes, astronomical observations are made with greater accuracy; and of consequence, our tables are far more perfect than those of the ancients. And in order to be as exact as possible, astronomers compare observations made at a great distance of time from one another, including several periods; by which means, the error that might be in the whole, is in each period subdivided into such little parts as to be inconsiderable. Thus the mean length of a Solar Year is known, even to Seconds.

The Diurnal rotation of the Planets round their axis, was discovered by certain spots which appear on the surfaces. These spots appear first in the margin of the Planet’s disk, (or the edge of their surfaces) and seem by degrees to creep toward their middle, and so on, going still forward, ’till they come to the opposite side or edge of the disk, where they set or disappear; and after they have been hid for the same space of time, that they were visible, they again appear to rise in or near the same place, as they did at first, then to creep on progressively, taking the same course as they did before. These spots have been observed on the surfaces of the Sun, Venus, Mars, and Jupiter; by which means it has been found that these bodies turn round their own axis, in the times before-mentioned. It is very probable that Mercury and Saturn have likewise a motion round their axis, that all the parts of their surface may alternately enjoy the light and heat of the Sun, and receive such changes as are proper and convenient for their nature. But by reason of the nearness of ☿ to the Sun, and ♄’s immense distance from him, no observations have hitherto been made whereby their spots (if they have any) could be discovered, and therefore their Diurnal motions could not be determined. The Diurnal motion of the Earth is computed from the apparent revolution of the Heavens, and of all the Stars round it, in the space of a natural Day. The Solar spots do not always remain the same, but sometimes old ones vanish, and afterwards others succeed in their room; sometimes several small ones gather together and make one large spot, and sometimes a large spot is seen to be divided into many small ones. But, notwithstanding these changes, they all turn round with the Sun in the same time.

How the relative distances of the Planets from the Sun are determined.

The relative distances of the Planets from the Sun, and likewise from each other, are determined by the following methods: First, the distance of the two inferior Planets ☿ and ♀ from the Sun, in respect of the Earth’s distance from him, is had by observing their greatest Elongation from the Sun as they are seen from the Earth.

[Fig. 5. Elongation.]

The greatest Elongation of Venus is found by observation to be about 48 degrees, which is the angle S T ♀; whence, by the known rules of Trigonometry, the proportion of S ♀, the mean distance of Venus from the Sun to ST, the mean distance of the Earth from him may be easily found. After the same manner, in the right-angled triangle S T ☿, may be found the distance S ☿ of Mercury from the Sun. And if the mean distance of the Earth from the Sun S T be made 1000, the mean distance of Venus S ♀ from the Sun will be 723; and of Mercury S ☿ 387: And if the Planets moved round the Sun in circles, having him for their center, the distances here found would be always their true distances: But as they move in Ellipses, their distances from the Sun will be sometimes greater, and sometimes less. Their Excentricities are computed to be as follows, viz.

		Mercury	80		of the parts
Excent. of		Venus	5		above-mentioned.
		Earth	169

Heliocentric and Geocentric Place, what.

The distances of the superior Planets, viz. ♂, ♃, and ♄, are found by comparing their true places, as they are seen from the Sun, with their apparent places, as they are seen from the Earth. Let S be the Sun, the circle ABC the Earth’s orbit, AG a line touching the Earth’s orbit, in which we’ll suppose the superior Planets are seen from the Earth in the points of their orbits ♂, ♃, ♄; and let DEFGH be a portion of a great circle in the Heavens, at an infinite distance: Then the place of Mars seen from the Sun is D, which is called his true, or Heliocentric Place; but from the Earth, he will be seen in G, which is called his apparent, or Geocentric Place. So likewise Jupiter and Saturn will be seen from the Sun in the points E and F, their Heliocentric places; but a spectator from the Earth will see them in the point of the Heavens G, which is their Geocentric place. The arches DG, EG, FG, the differences between the true and apparent places of the Superior Planets, are called the Parallaxes of the Earth’s annual Orb, as seen from these Planets. If thro’ the Sun we draw SH parallel to AG, the angles A ♂ S, A ♃ S, A ♄ S, will be respectively equal to the angles D S H, E S H, and F S H; and the angle A G S is equal to the angle GSH, whose measure is the arch GH; which therefore will be the measure of the angle AGS, the angle under which the semidiameter A S of the Earth’s orbit, is seen from the Starry Heavens. But this semidiameter is nothing in respect of the immense distance of the Heavens or Fixed Stars; for from thence it would appear under no sensible angle, but look like a point. And therefore in the Heavens, the angle G S H, or the arch G H vanishes; and the Points G and H coincide; and the arches D H, E H, F H, may be considered as being of the same bigness with the arches D G, E G, and F G, which are the measures of the angles A ♂ S, A ♃ S, A ♄ S; which angles are nearly the greatest elongation of the Earth from the Sun, if the Earth be observed from the respective Planets, when the line G ♄ ♃ ♂ A, touches the Earth’s orbit in A. The nearer any of the superior Planets is to the Sun, the greater is the Parallax of the annual Orb, or the angle under which the semidiameter of the Earth’s orbit is seen from that Planet. In Mars the angle ♂ S, (which is the visible elongation of the Earth seen from Mars, or the Parallax of the annual Orb seen from that Planet) is about 42 degrees, and therefore the Earth is always to the inhabitants of Mars either their Morning or Evening Star, and is never seen by them so far distant from the Sun as we see Venus. The greatest elongation of the Earth seen from Jupiter, being nearly equal to the angle A ♃ S, is about 11 degrees. In Saturn the angle A ♄ S is but 6 degrees, which is not much above ¼ part of the greatest elongation we observe in Mercury. And since Mercury is so rarely seen by us, probably the astronomers of Saturn (except they have better Optics than we have) have not yet discovered that there is such a body as our Earth in the Universe.

The Parallax of the annual Orb, or the greatest elongation of the Earth’s orbit seen from any of the superior Planets, being given; the distance of that Planet from the Sun, in respect of the Earth’s distance from him, may be found by the same methods as the distances of the inferior Planets were. Thus, to find the distance of Mars from the Sun, it will be as the Sine of the angle S ♂ A is to the Radius, so is the distance AS (the distance of the Earth from the Sun) to S ♂, the distance from the Sun to Mars. After the same manner the distances of Jupiter and Saturn are also found. The mean distance of the Earth from the Sun being made 1000, the mean distances of the superior Planets from the Sun are, viz. the mean distance from the Sun of

	♂	1524				141
	♃	5201		and the Excentricity		250
	♄	9538				547

To which, if you add or subtract their mean distances, we shall have the greatest or least distances of those Planets from the Sun.

There are other methods by which the relative distances of the Planets might be found; but that which hath been here illustrated, is sufficient to evince the certainty of that Problem.

How the absolute distances of the Planets from the Sun are computed.

Parallax of the Earth’s Semidiameter.

[Fig. 7.]

Hitherto we have only considered the distances of the Planets in relation to one another, without determining them by any known measure; but in order to find their absolute distances in some determinate measure, there must be something given, whose measure is known. Now the circumference of the Earth is divided into 360 degrees, and each of these degrees into 60 Geographical miles, so that the whole circumference contains 21600; and by the known proportion for finding the diameter of a circle from its circumference, the Earth’s diameter will be found to be 6872 miles, and its semidiameter 3436 miles. The Parallax of the Earth’s semidiameter, or the angle under which it is seen from a certain Planet, may be found by comparing the true place of the Planet, as it would be seen from the center of the Earth (which is known by computation) with its apparent place, as it is seen from some point on the Earth’s surface. Let CZA be the Earth, ZC its semidiameter, ♁ some Planet, and BHT arch of a great circle in the Heavens, at an infinite distance. Now the Planet ♁ will appear from the Earth’s center C, in the point of the Heavens H; but a spectator from the point Z upon the Earth’s surface, will see the same object ♁ in the point of the Heavens B; and the arch BH the difference, is equal to the angle B ♁ H = Z ♁ C, the Parallax; which being known, the side C ♁ the distance of the Planet from the center of the Earth, at that time, may be easily found. Now if this distance of the Planet from the Earth be determined, when the centers of the Sun, the said Planet, and of the Earth, are in the same right line, we have the absolute distance of the Planet’s orbit from the Earth’s in known measure; then it will be, as the relative distance betwixt the Earth’s orbit and that of the Planet is to the relative distance of the said Planet from the Sun; so is the distance of the Planet’s orbit from the Earth’s in known measure to the distance of the said Planet from the Sun in the same measure: Which being known, the distance of all the other Planets from the Sun may be found. For it will be, as the relative distance of any Planet from the Sun, is to its distance from him in a known measure; so is the relative distance of any other Planet from him to its distance in the same measure. This may be done by finding the distance of the Planet Mars, when he is in opposition to the Sun, after the same manner as we find the distance of a tree, or the like, by two stations.

Let ♂ be Mars, D the point on the Earth’s superficies, where Mars is vertical when he is in opposition to the Sun, which may be found exactly enough by calculation, at which time let an observer, at the point Z (whose situation from D must be known) take the altitude of Mars, whose complement will be the angle ♂ ZR; then in the triangle ♂ ZC will be given the angle Z ♂ C, the angle C (whose measure is the arch DZ) and consequently the angle Z ♂ C the Parallax, and also the side Z C the semidiameter of the Earth; by which we may find C ♂ the distance of Mars from the Earth. The extreme nicety required in this observation, makes it very difficult to determine the exact distances of the Planets from the Sun; but the celebrated Dr. Halley has, in the Philosophical Transactions, shewed us a more certain method for finding the distances of the Planets; which is by observing the Transit of Venus over the Sun.

How the Magnitudes of the Planets are determined.

[Fig. 8.]

The eye judgeth of the magnitudes of far distant objects, according to the quantities of the angles under which they are seen (which are called their apparent magnitudes;) and these angles appear greater or less in a certain proportion to their distances. Wherefore the distances of the Planets from the Earth, and their apparent diameters being given, their true diameters (and from thence their magnitudes) may be found. How the distances of the Planets may be found has been already shewn; their apparent diameters are found by a telescope, having a machine fix’d to it for measuring of angles, called a Micrometer. Let BD, or the angle BAD be the apparent diameter of any Planet, and AB, or AD, (which by reason of the great distance of the Planets in respect of their magnitudes) may be considered as being the distance of the said Planet from the observer. Now in the triangle ABD, having the sides AB, AD, given, and the angle, A, we have also the other angles B and D, (because the Side AB, AD, are equal) whence the side BD the diameter of the Planet may be easily found by Trigonometry.

Why the Moon appears bigger than any of the Planets.

From hence it appears, that the same body at different distances, will seem to have very different magnitudes. Thus the diameter BD will appear from the point E, to be twice as large as from the point A. It also follows, that a small body, when at no great distance from us, may appear to be equal, or even to exceed another at a great distance, tho’ immensely bigger. Thus b d appears under the same angle, and consequently of the same bigness from the point A, that the line B D doth, tho’ one vastly exceeds the other. And this is the reason, why the Moon, which is much less than any of the Planets, appears to us vastly bigger than either of them, and even to equal the Sun himself, which is many thousand times greater in magnitude.

The distances of the Planets, and periods round the Sun, their diameters and velocities round their own axis, according to modern computations, are as follows:

The cause of Eclipses and Phases of the Moon, and some other phænomena not here explained, shall be shewed when we come to give a Description of the Orrery.

Plate 2.

Besides the Planets already mentioned, there are other great bodies that sometimes visit our system, which are a sort of temporary Planets; for they come and abide with us for a while, and afterwards withdraw from us, for a certain space of time, after which they again return. These wandering bodies are called Comets.

Of Comets.

The motion of Comets in the Heavens, according to the best observations hitherto made, seem to be regulated by the same immutable law that rules the Planets; for their orbits are elliptical, like those of the Planets, but vastly narrower, or more excentric. Yet they have not all the same direction with the Planets, who move from West to East, for some of the Comets move from East to West; and their orbits have different inclinations to the Earth’s orbit; some inclining Northwardly, others Southwardly, much more than any of the Planetary orbits do.

Altho’ both the Comets and the Planets move in elliptic orbits, yet their motions seem to be vastly different: For the excentricities of the Planet’s orbits are so small, that they differ but little from circles; but the excentricities of the Comets are so very great, that the motions of some of them seem to be almost in right lines, tending directly towards the Sun.

Now, since the orbits of the Comets are so extremely excentric, their motions, when they are in their Perihelia, or nearest distance from the sun, must be much swifter than when they are in their Aphelia, or farthest distance from him; which is the reason why the Comets make so short a stay in our system; and when they disappear, are so long in returning.

The figures of the Comets are observed to be very different; some of them send forth small beams, like hair, every way round them; others are seen with a long fiery tail, which is always opposite to the Sun. Their magnitudes are also very different, but in what proportion they exceed each other, it is as yet uncertain. Nor is it probable, that their numbers are yet known, for they have not been observed with due care, nor their theories discovered, but of late years. The ancients were divided in their opinions concerning them; some imagined that they were only a kind of Meteors kindled in our atmosphere, and were there again dissipated; others took them to be some ominous prodigies: But modern discoveries prove, that they are Worlds subject to the same laws of motion as the Planets are; and they must be very hard and durable bodies, else they could not bear the vast heat that some of them, when they are in their Perihelia, receive from the Sun, without being utterly consumed. The great Comet which appeared in the year 1680, was within ¹/₆ part of the Sun’s diameter from his surface; and therefore its heat must be prodigiously intense beyond imagination. And when it is at its greatest distance from the Sun, the cold must be as rigid.

SECT. II.

Of the Fixed Stars.

The fixed Stars are at immense distance from us.

The fixed Stars are those bright and shining bodies, which in a clear night appear to us every where dispersed through the boundless regions of space. They are term’d fix’d, because they are found to keep the same immutable distance one from another in all ages, without having any of the motions observed in the Planets. The fixed Stars are all placed at such immense distances from us, that the best of telescopes represent them no bigger than points, without having any apparent diameters.

The fixed Stars are luminous bodies like the Sun.

It is evident from hence, that all the Stars are luminous bodies, and shine with their own proper and native light, else they could not be seen at such a great distance. For the Satellites of Jupiter and Saturn, tho’ they appear under considerable angles through good telescopes, yet are altogether invisible to the naked eye.

The distance from us to the Sun is nothing in comparison of the vast distance of the fixed Stars.

Although the distance betwixt us and the Sun is vastly large, when compared to the diameter of the Earth, yet it is nothing when compared with the prodigious distance of the fixed Stars; for the whole diameter of the Earth’s annual orbit, appears from the nearest fixed Star no bigger than a point, and the fixed Stars are at least 100,000 times farther from us than we are from the Sun; as may be demonstrated from the observation of those who have endeavoured to find the Parallax of the Earth’s annual Orb, or the angle under which the Earth’s orbit appears from the fixed Stars.

As to appearance, the Earth may be consider’d as being the center of the Heavens.

Hence it follows, that tho’ we approach nearer to some fixed Stars at one time of the year than we do at the opposite, and that by the whole length of the diameter of the Earth’s orbit; yet this distance being so small in comparison with the distance of the fixed Stars, their magnitudes or positions cannot thereby be sensibly altered; therefore we may always, without error, suppose ourselves to be in the same center of the Heavens, since we always have the same visible prospect of the Stars without any alteration.

The fixed Stars are Suns.

If a spectator was placed as near to any fixed Star, as we are to the Sun, he would there observe a body as big, and every way like, as the Sun appears to us: and our Sun would appear to him no bigger than a fixed Star: and undoubtedly he would reckon the Sun as one of them in numbering the Stars. Wherefore since the Sun differeth nothing from a fixed Star, the fixed Stars may be reckoned so many Suns.

The fixed Stars are at vast distance from each other.

It is not reasonable to suppose that all the fixed Stars are placed at the same distance from us; but it is more probable that they are every where interspersed thro’ the vast indefinite space of the universe; and that there may be as great a distance betwixt any two of them, as there is betwixt our Sun and the nearest fixed Star. Hence it follows, why they appear to us of different magnitudes, not because they really are so, but because they are at different distances from us; those that are nearest excelling in brightness and lustre those that are most remote, who give a fainter light, and appear smaller to the eye.

The distribution of the Stars into 6 classes.

Of Telescopical Stars.

The astronomers distribute the Stars into several orders or classes; those that are nearest to us, and appear brightest to the eye, are called Stars of the first magnitude; those that are nearest to them in brightness and lustre, are called Stars of the second magnitude; those of the third class, are stiled Stars of the third magnitude; and so on, until we come to the Stars of the sixth magnitude, which are the smallest that can be discerned by the naked eye. There are infinite numbers of smaller Stars, that can be seen through telescopes; but these are not reduced to any of the six orders, and are only called Telescopical Stars. It may be here observed, that tho’ the astronomers have reduced all the Stars that are visible to the naked eye, into some one or other of these classes, yet we are not to conclude from thence that all the Stars answer exactly to some or other of these orders; but there may be in reality as many orders of the Stars, as they are in number, few of them appearing exactly of the same bigness and lustre.

The Stars digested into constellations

The ancient astronomers, that they might distinguish the Stars, in regard to their situation and position to each other, divided the whole starry firmament into Several Asterisms, or systems of Stars, consisting of those that are near to one another. These Asterisms are called Constellations, and are digested into the forms of some animals; as Men, Lyons, Bears, Serpents, &c. or to the images of some known things; as, of a Crown, a Harp, a Triangle, &c.

Zodiac.

The starry firmament was divided by the ancients into 48 images, or constellations; twelve of which they placed in that part of the Heavens wherein are the planes of the Planetary orbits; which part is called the Zodiac, because most of the constellations placed therein resemble some living creature. The two regions of the Heavens that are on each side of the Zodiac, are called the North and South parts of the Heavens.

Constellations within the Zodiac.

The constellations within the Zodiac are, 1. Aries, the Ram; 2. Taurus, the Bull; 3. Gemini, the Twins; 4. Cancer, the Crab; 5. Leo, the Lion; 6. Virgo, the Virgin; 7. Libra, the Balance; 8. Scorpio, the Scorpion; 9. Sagittarius, the Archer; 10. Capricornus, the Goat; 11. Aquarius, the Water-Bearer; and, 12. Pisces, the Fishes.

Northern constellations.

The constellations on the North side of the Zodiac are Twenty-one, viz. the Little Bear; the Great Bear; the Dragon; Cepheus, a king of Ethiopia; Bootes, the keeper of the Bear; the Northern Crown; Hercules with his Club, watching the Dragon; the Harp; the Swan; Cassiopeia; Persius; Andromeda; the Triangle; Auriga; Pegasus, or the Flying Horse; Equuleus; the Dolphin; the Arrow; the Eagle; Serpentarius; and the Serpent.

Southern constellations.

The constellations noted by the ancients on the South side of the Zodiac, were fifteen, viz. the Whale; the river Eridanus; the Hare; Orion; the Great Dog; Little Dog; the Ship Argo; Hydra; the Centaur; the Cup; the Crow; the Wolf; the Altar; the Southern Crown; and the Southern Fish. To these have been lately added the following, viz. The Phœnix; the Crane; the Peacock; the Indian; the Bird of Paradise; the Southern Triangle; the Fly; Cameleon; the Flying Fish; Toucan, or the American Goose; the Water Serpent, and the Sword Fish. The ancients placed those particular constellations or figures in the Heavens, either to commemorate the deeds of some great man, or some notable exploit or action; or else took them from the fables of their religion, &c. And the modern astronomers do still retain them, to avoid the confusion that would arise by making new ones, when they compare the modern observations with the old ones.

Unformed Stars.

Some of the principal Stars have particular names given them, as Syrius, Arcturus, &c. There are also several Stars that are not reduced into constellations, and these are called Unformed Stars.

The Galaxy, or Milky Way.

Besides the Stars visible to the naked eye, there is a very remarkable space in the Heavens, called the Galaxy, or Milky Way. This is a broad circle of a whitish hue, like milk, going quite round the whole Heavens, and consisting of an infinite number of small Stars, visible thro’ a telescope, tho’ not discernable by the naked eye, by reason of their exceeding faintness; yet with their light they combine to illustrate that part of the Heavens where they are, and to cause that shining whiteness.

The places of the fixed Stars, or their relative situations one from another, have been carefully observed by astronomers, and digested into catalogues. The first among the Greeks, who reduced the Stars into a catalogue, was Hypparchus, who, from his own observations, and of those who lived before him, inserted 1022 Stars into his catalogue, about 120 years before the Christian Æra: This catalogue has been since enlarged and improved by several learned men, to the number of 3000, of which there are a great many telescopical, and not to be discerned by the naked eye; and these are all ranked in the catalogue as the Stars of the seventh magnitude.

It may seem strange to some, that there are no more than this number of Stars visible to the naked eye; for sometimes in a clear night they seem to be innumerable: but this is only a deception of our sight, arising from their vehement sparkling, while we look upon them confusedly, without reducing them into any order; for there can seldom be seen above 1000 Stars in the whole Heavens with the naked eye at the same time; and if we should distinctly view them, we shall not find many but what are inserted upon a good Celestial Globe.

Altho’ the number of Stars that can be discerned by the naked eye are so few, yet it is probable there are many more which are beyond the reach of our optics, for through telescopes they appear in vast multitudes, every where dispersed throughout the whole Heaven; and the better our glasses are, the more of them we still discover. The ingenious Dr. Hook has observed 78 Stars in the Pleiades, of which the naked eye is never able to discern above 7; and in Orion, which has but 80 Stars in the British catalogue (and some of them telescopical) there has been numbered 2000 Stars.

An idea of the Universe.

Those who think that all these glorious bodies were created for no other purpose than to give us a little dim light, must entertain a very slender idea of the Divine Wisdom; for we receive more light from the Moon itself, than from all the Stars put together. And since the Planets are subject to the same laws of motion with our Earth, and some of them not only equal, but vastly exceed it in magnitude, it is not unreasonable to suppose, that they are all habitable Worlds. And since the Fixed Stars are no ways behind our Sun, either in bigness or lustre, is it not probable, that each of them have a system of Planetary Worlds turning round them, as we do round our Sun? And if we ascend as far as the smallest Star we can see, shall we not then discover innumerable more of these glorious bodies, which now are altogether invisible to us? And so ad infinitum, thro’ the boundless space of the universe. What a magnificient idea must this raise in us of the Divine Being! Who is every where, and at all times present, displaying his Divine Power, Wisdom and Goodness, amongst all his Creatures!

The DESCRIPTION and USE of the
Celestial and Terrestrial Globes.

Globe or Sphere.

A Globe or Sphere is a round solid body, having every part of its surface equally distant from a point within it, called its Center; and it may be conceived to be formed by the revolution of a semicircle round its diameter.

Great Circle.

Hemispheres.

Any circle passing through the center of the sphere, thereby dividing into two equal parts or segments, is called a Great Circle; and the segments of the sphere so divided, are called Hemispheres.

Every great circle has its Poles and Axis.

Poles.

The Poles of a great circle are two points on the surface of the sphere, diametrically opposite to one another, and every where equally distant from the said circle.

Axis.

The Axis of a circle is a right line passing through the center of the sphere, and through the Poles of the said circle, and is therefore perpendicular to the Plane: Therefore

Secundaries.

All circles passing through the Poles of any great circle, intersect it in two places diametrically opposite, and also at right angles; and with respect to the said great circle, they may be called its Secundaries.

Parallel or lesser Circles.

All circles dividing the sphere into two unequal parts, are called lesser or parallel Circles, and are usually denominated by that great circle to which they are parallel.

Terrestrial Globe.

The Earth being globular, its outward parts, as the several Countries, Seas, &c. are best, and most naturally represented upon the surfaces of a Globe; and when such a body has the outward parts of the Earth and Sea delineated upon its surface, and placed in their natural order and situation, it is called a Terrestrial Globe.

Celestial Globe.

The Celestial Bodies appear to us as if they were all placed in the same concave sphere, therefore astronomers place the Stars according to their respective situations and magnitudes, and also the images of the constellations, upon the external surface of a Globe; for it answers the same purposes as if they were placed within a concave sphere, if we suppose the Globe to be transparent, and the eye placed in the center. A Globe having the Stars placed upon its surface, as above described, is called a Celestial Globe. These Globes are both placed in frames, with other appurtenances, as shall be described in a proper place.

The principal use of the Globes.

The principal uses of the Globes (besides their serving as Maps, to distinguish the outward parts of the Earth, and the situations of the fixed Stars) is to explain and resolve the phænomena arising from the diurnal motion of the Earth round its Axis.

There will be the same prospect of the fixed Stars whether the spectator be placed on the Earth, or in the Sun.

It has been shewed in the Introduction, that the distance of the Earth from the Sun, is no more than a point, when compared with the immense distance of the fixed Stars; therefore let the Earth be in what point soever of her orbit, there will be the same prospect of the Heavens, as a spectator would observe did he reside in the Sun: And if several circles be imagined to pass thro’ the center of the Earth, and others, parallel to them, be conceived to pass thro’ the center of the Sun, these circles in the Heavens will seem to coincide, and to pass exactly thro’ the same Stars. Wherefore as to the appearances of the fixed Stars, it is indifferent whether the Earth or the Sun be made the center of the Universe. But because it is from the Earth that we always observe the celestial bodies, and their apparent motions seem to us to be really made in the Heavens, it is more natural in explaining the phænomena arising from these motions, to place the Earth in the center. And again, because the semidiameter of the Earth, when compared to her distance from the Sun, is of no sensible magnitude, any point, upon the Earth’s surface, let her be in what part soever of the orbit, may be considered as being the center of the Universe. Upon these principles, the different phænomena arising from the diurnal motion of the Earth, and the different situation of a spectator upon its surface, are very naturally illustrated and explained by the Globes.

As to the alterations of seasons, &c. arising from the annual motion of the Earth round the Sun, it is indifferent which we suppose to move, the Earth or the Sun, for in both cases the effect will be the same. Wherefore because it is the Sun that appears to us to move, we say the Sun is in such a part of the ecliptic, without attributing any motion to the Earth, any more than if she had actually been at rest. For the same reason we say the Sun rises, or the Sun sets; by which we mean that he begins to appear or disappear, without considering in the least how these effects are produced. These things are here mentioned, to obviate the objections that might be made by beginners, after they have been told that the Sun stands still.

SECT. I.

An Explanation of the Circles of the Sphere, and of some Astronomical Terms arising therefrom.

The Circles of the Sphere.

In order to determine the relative situations of places upon the Earth, as well as the positions of the fixed Stars, and other Celestial phænomena, the Globe of the Earth is supposed to be environed by several imaginary circles, and these are called the Circles of the Sphere. These imaginary circles are either fixed, and always obtain the same position in the Heavens, or moveable, according to the position of the observer.

Those circles that are fixed, owe their origin to the two-fold motion of the Earth, and are the Equator, and the Ecliptic, with their Secundaries and Parallels. These fixed circles are usually delineated upon the surface of the Globes.

The moveable circles are only the Horizon, its Secundaries and Parallels: These are represented by the wooden frame, and the brass ring, wherein the Globe is hung, and a thin plate of brass to be screwed in a proper place, upon the said ring, as occasion requires.

I. Of the Equinoctial.

The Equator, or Equinoctial.

1. The Equator, or the Equinoctial, is that great circle in the Heavens, in whose plane the Earth performs her diurnal motion round her axis; or it is that great circle, parallel to which the whole Heavens seem to turn round the Earth from East to West in 24 Hours.

Note, The Equator and the Equinoctial are generally synonymous terms; but sometimes the Equator particularly signifies that great circle upon the surface of the Earth, which coincides with the Equinoctial in the Heavens. This circle is also by Mariners commonly called the Line.

Northern and Southern Hemispheres.

The Axis of the World.

Poles of the World, or of the Equator.

The equinoctial divides the globe of the Earth, and also the whole Heavens into two equal parts, North and South, which are called the Northern and Southern Hemispheres. The axis of this circle, is called the Axis of the World, or the Earth’s Axis, because the Earth revolves about it (from West to East) in 24 hours. The extreme of this axis are called the Poles of the World, whereof that which lies in the Northern Hemisphere, is called the North Pole, and the other is called the South Pole. The equinoctial circle is always delineated upon the surface of each globe, with its name at length expressed; the axis of this circle, or the Earth’s axis, is only an imaginary line in the Heavens, but on the globes it is expressed by the wires about which they really turn. The Poles of the world, are the two points upon the surface of the globe through which these wires pass; the North Pole is that which hath the little brass circle, with a moveable index placed round it; and the other opposite to it is the South Pole. The Northern Hemisphere is that wherein the North Pole is placed, and the opposite one is the Southern Hemisphere.

The astronomers divide all circles into 360 equal parts, called Degrees, each degree into 60 equal parts, called Minutes, each minute into 60 Seconds, &c. But besides this division into degrees, the equinoctial is also divided into 24 equal parts, or Hours, each hour into 60 Minutes, each minute into 60 Seconds, &c. so that one hour is equal to 15 degrees, each minute of time is equal to 15 minutes of a degree, &c.

Hour Circles or Circles of Ascension, also called Meridians.

2. All circles conceived to pass through the Poles of the world, intersecting the equinoctial at right angles, are, with respect to any point in the Heavens, called Hour Circles; and the Circles of Ascension, because the ascension of the Heavenly bodies, from a certain point, are by them determined.

These circles are also, with regard to places upon Earth, called Meridians.

The Brass Meridian.

The Meridians are commonly drawn upon the Terrestrial Globe thro’ every 15 degrees of the equinoctial, thereby making an Hour difference betwixt the places through which they pass. On the Celestial Globe there are commonly drawn but two of these Meridians, crossing the equinoctial in four points equidistant from one another, thereby dividing it into four quadrants; but the intermediate ones are here supplied, and also upon the Terrestrial Globe, by the brass circle on which they are hung, which, is therefore called the Brass Meridian, and sometimes only the Meridian, it serving for this purpose to all the points upon either Globe.

The Hour Circle.

There is also a little brass circle fixed upon this meridian, divided into 24 Hours, having an index moveable round the axis of the globe, to be turned to any particular Hour. The use of this circle is to shew the difference of time betwixt any two meridians, and is therefore called the Hour Circle.

Parallels of Declination.

3. All circles parallel to the equinoctial are, with respect to any point in the Heavens, called Parallels of Declination. So that,

Declination North and South.

4. The Declination of any Point in the Heavens (as of the Sun, a fixed Star, or the like) is an arch of the meridian passing through that point, and intercepted betwixt it and the equator; and if the said point be to the (Northward/Southward) of the equator, it is called (North/South) Declination.

Tropics and Polar Circles.

Of the parallels of declination, four are eminently distinguished by particular names, viz. The two Tropics, and the two Polar Circles.

Tropic of Cancer; of Capricorn.

The tropics are on different sides of the equator each 23 degrees and 29 minutes distant from it; that which lies in the Northern Hemisphere, is called the Tropic of Cancer, and the Southern one, the Tropic of Capricorn.

These circles are the limits of the Sun’s greatest declination, and are called tropics, because whenever the Sun arrives to them, he seems to return back again towards the equator.

Arctic Circle.
Arctic Pole.
Antarctic Circle.
Antarctic Pole.

6. The Polar Circles are each of them at the same distance from the Poles of the world, that the tropics are from the equator, viz. 23° 29′. That which lies near the North Pole, is called the Arctic Circle, from Arctos, a constellation situated in the Heavens near that Place; whence also this Pole is sometimes called the Arctic Pole. The other Polar circle, which is situated near the South Pole; is called the Antarctic Circle, because its position is contrary to the other; and the South Pole is sometimes called the Antarctic Pole.

The tropics and the Polar circles have each their names expressed upon the Globes.

II. Of the Ecliptic.

Ecliptic.
Equinoctial.
Solstitial Points.
Colures.
Equinoctial Colure.
Solstitial Colure.

7. The Ecliptic is that great circle in whose plane the Earth performs its annual motion round the Sun; or, in which the Sun seems to move round the Earth, once in a year. This circle makes an angle with the equinoctial of 23 degrees 29 minutes, and intersects it in two opposite points, which are called the Equinoctial Points; and the two points in the ecliptic that are at the greatest distance from the equinoctial points, are called the Solstitial Points. The two meridians passing through those points, are, by way of eminence, called Colures; whereof that which passeth thro’ the equinoctial points, is called the Equinoctial Colure; and that which is at right angles to it, passing through the Solstitial Points, is called the Solstitial Colure.

The Ecliptic divided into signs.

The ecliptic is divided into 12 equal parts, called Signs, each sign being 30 degrees, beginning from one of the equinoctial points, and numbered from West to East; the names and characters of the twelve signs are as follows, viz.

Northern Signs.

The first six of these are called the Northern Signs, and possess that half of the ecliptic which is to the Northward of the equator; beginning with the first point of ♈, and ending with the last point of ♍.

Southern Signs.

The latter six are called the Southern Signs, because they possess the Southern half of the ecliptic; beginning at the first point of ♎, and ending with the last point of ♓.

The division of the ecliptic into signs, and the names of the colures, are particularly expressed upon the globes.

The signs of the ecliptic took their names from 12 constellations mentioned in the Introduction to be situated in the Heavens near those places. It is to be observed, that the signs are not to be confounded with the constellations of the same name: For the Sign of Aries, is not the same with the Constellation Aries; the latter is a system of Stars digested into the figure of a Ram, but the sign of Aries is only 30 degrees of the ecliptic, counted from the equinoctial point ♈, (which is reckoned the first point in the ecliptic) to the beginning of Taurus: Or, it is sometimes taken for all that space upon the Celestial Globe contained between the two circles passing through the first points of ♈ and ♉. What has been here said of Aries, is to be noted of all the rest of the signs.

The constellations above-mentioned were formerly situated within the signs which now bear their names; but by a slow motion of the equinoctial points, being one degree in 72 years, the constellation Aries has now got into the sign ♉, and so of the rest. So that Pisces is now got into the Sign of ♈; this slow motion in the Heavens is called the Precession of the Equinoctial Points.

Poles of the Ecliptic.

The Poles of the Ecliptic are both situated in the Solstitial Colure, at 23 degrees, 29 minutes distance from the Pole of the world; and they take their denomination from the Hemisphere wherein they are placed, viz. that which lies in the (Northern/Southern) Hemisphere, is called the (North/South) Pole of the ecliptic. The arctic and antarctic circles, are described by the Poles of the ecliptic in the diurnal motion of the Earth round its axis, whence it seems these two circles are called Polar.

Circles of Longitude.

8. All great circles passing through the Poles of the ecliptic, and consequently intersecting it at right angles, are called Circles of Longitude: So that,

Longitude of any Point in the Heavens.

Place of a Star.

9. The Longitude of any Point in the Heavens (as a Star or Planet, &c.) is an arch of the ecliptic contained between the circle of longitude passing thro’ that point, and the equinoctial point ♈. And that degree of any sign which lies under the circle of longitude, passing thro’ any Star or Planet, is called the Place of that Star or Planet.

Note, The Sun never goes out of the ecliptic, and it is not usual to say the Sun’s longitude, but we commonly express it the Sun’s Place, which is that sign, degree, minute, &c., of the ecliptic, which he at any time passes.

10. All circles conceived to be drawn parallel to the ecliptic, are called Parallels of Latitude: So that,

Latitude of a Star, &c.

11. The Latitude of any point in the Heavens, (as a fixed Star, &c.) is an arch of the circle of longitude, in passing thro’ that point, and intercepted betwixt it, and the ecliptic; or, the latitude is the distance from the ecliptic; and if the said point be to the Northward of the ecliptic, it is called North Latitude; but if it be to the Southward, is called South Latitude.

Upon the Terrestrial Globe, none of the circles of longitude are described; and upon the Celestial, they are commonly drawn thro’ the beginning of every Sign; but they are all supplied upon both Globes, by fastening a thin plate of brass over one of the Poles of the ecliptic, and so as to be moved to any degree thereof at pleasure. The parallels of latitude are also supplied by the graduations upon the said plate, as shall be shewn in a proper place.

We have now done with all those circles that are fixed, and such as are drawn upon the Globes themselves; we next proceed to the moveable circles.

III. Of the Horizon.

Horizon.

12. The Horizon is that great circle which divides the upper, or visible Hemisphere of the world, from the lower, or invisible: This circle is distinguished into two sorts, the Sensible, and the Rational.

Sensible Horizon.

The Sensible, or Apparent Horizon, is that circle which limits or determinates our prospect, whether we are at land or sea, reaching as far as we can see, or it is that circle where the Sky and the Earth, or Water, seem to meet. When we are on Terra Firma, this circle commonly seems rugged and irregular, occasioned by the unevenness of the ground terminating our prospect; but at sea there are no such irregularities; the semidiameter of this circle varieth according to the height of the eye of the observer; if a man of six feet high stood upon a large plain, or the surface of the sea, he could not see above three miles round.

This circle determines the rising and setting of the Heavenly bodies, and distinguishes Day and Night.

Rational Horizon.

The Rational, or true Horizon, is a great circle passing thro’ the center of the Earth, parallel to the sensible Horizon, being distant from it by the Earth’s semidiameter, which is about 3980 miles: This distance is nothing in comparison of the immense distance of the Sun and the fixed Stars, therefore astronomers make no distinction between these two circles, but consider the apparent Horizon, or that wherein the Sun appears to rise and set, as passing thro’ the center of the Earth.

Cardinal Points of the Horizon.

This circle is divided by astronomers into four quadrants, and each of the quadrants into 90 degrees, &c. The four points quartering this circle are called the Cardinal Points, and are termed the East, West, North, and South. The East is that point of the Horizon where the Sun rises when he is in the equinoctial, or on that day when he ascends above the Horizon exactly at six o’clock; and the West is that point of the Horizon which is directly opposite to the East, or where the Sun Sets when he is in the Equinoctial. The South is 90 degrees distant from the East and West, and is toward that part of the Heavens wherein the Sun always appears to us in Great-Britain at Noon; and the North is that part of the Heavens which is directly opposite to the South: Or, the North and South points of the Heavens may be found by turning yourself either directly towards the East or the West: If you look towards the (East/West) the (South/North) will be to the right Hand, and the (North/South) to the left.

Points of the Compass.

Besides the aforementioned divisions of the Horizon into degrees. Mariners divide it into 32 equal parts, which they call the Points of the Compass; to each of which points they give a particular name, compounded of the four Cardinals, according to what quarter of the Compass is intended.

Zenith.

Nadir.

The center of the Horizon is the place of observation, and the Poles of it are one exactly over our heads, called the Zenith; and the other exactly under our feet, called the Nadir.

Vertical Circles.

Meridian.

Azimuth.

13. All circles conceived to pass thro’ the Zenith and Nadir, are called Vertical Circles, or Azimuths. Of these circles, that which passeth thro’ the North and South points of the Horizon, is called the Meridian; so that when any object is upon the Meridian, it then bears either due South, or due North from us; and the Azimuth of any object is an arch of the Horizon intercepted between the vertical circle passing through it, and either the North or South part of the Meridian; which part is commonly specified.

The meridian passes thro’ the Poles of the world, as well as through the Zenith and Nadir, and therefore is a secundary both of the equinoctial and the horizon: This circle divides the globe into the Eastern and Western Hemispheres, and the Poles of it are the East and West points of the Horizon. All the heavenly objects are, during one half of their continuance above the horizon, in the Eastern Hemisphere, and for the other half in the Western; so that whenever the Sun arrives upon the upper part of the meridian, it is then Noon, or Mid-day, which is the reason why this circle is called the meridian; and when he comes to the lower part, it is then Midnight.

Prime Vertical.

The vertical circle passing thro’ the East and West points of the horizon, is called the Prime Vertical, or Circle of East and West, so that when any object is upon this circle in the Eastern hemisphere, it appears due East; and if it be in the Western hemisphere, it appears due West.

Amplitude.

That degree in the horizon wherein any object rises or sets from the East or West points, is called the Amplitude; which for rising is called Amplitude Ortive, and Occasive for setting; which must be also denominated whether it be Northerly or Southerly.

It may be observed, that the Amplitude and Azimuth are much the same; the amplitude shewing the bearing of any object when he rises or sets, from the East or West points of the horizon; and the azimuth, the bearing of any object when it is above the horizon, either from the North or South point thereof. As for example, if an object rises or sets within 10 degrees of the East or West, suppose towards the South, we accordingly say, its Amplitude is 10 degrees Southerly; but if an object, that is of any height above the horizon, should be in the vertical circle, passing thro’ the before-mentioned point, we then say, its Azimuth is 80 degrees from the South, or 100 degrees from the North, both which expressions signify the same.

Almacanthers.
Altitudes.
Meridian Altitude.
Zenith Distance.

14. All circles drawn parallel to the horizon, in the upper hemisphere, are called Almacanthers, or Parallels of Altitude: So that the Altitude of any point in the Heavens is an arch of the vertical circle passing thro’ that point, and intercepted betwixt it and the horizon; and if the object be upon the meridian, it is commonly called the Meridian Altitude. The complement of the altitude, or what it wants of 90 degrees, is called the Zenith Distance.

The horizon (by which we mean the rational) is represented by the upper surface of the Wooden frame, wherein the globes are placed; upon this horizon are described several concentric circles, the innermost of which is divided into degrees, which ought to be numbered both ways from the East and the West, until they end at 90 degrees in the North and South points. The use of these divisions is to shew the amplitudes of the Sun and Stars, at their rising and setting: Also in some convenient place upon this horizon, there is commonly noted the points of the Compass. Without the before-mentioned circle there is drawn the ecliptic with its divisions, into signs, and degrees, and a circle of months and days: The use of these two circles is to serve as a kalendar to shew the Sun’s place at any time of the year, and by that means to find his place in the Ecliptic, drawn upon the globe itself.

The Vertical Circles, and the Parallels of Altitude, are supplied by a thin plate of brass, having a nut and screw at one end to fasten it to the brass meridian in the Zenith point; which being done, the lower end of it may be put between the globe it self, and the inner edge of the horizon, and so turned round about to any point required.

Quadrant of Altitude.

The fiducial edge thereof representing the Vertical Circles, and the Degrees upon it, describing the Parallels of Altitude. This thin plate is called the Quadrant of Altitude.

The center of the horizon being the place of observation, it is evident that this circle, and all the others belonging to it, are continually changed, which way soever we move; wherefore we may suppose the horizon, with its secundaries and parallels, to invest the globe like a rete or net; and to be moveable every way round it. This is very naturally illustrated by the globes; if we move directly North, or directly South, the change made in the horizon, is represented by moving the brass meridian (keeping the globe from turning about its axis) in the notches made in the wooden horizon, just so much as we travelled. If our course should be due East, or due West, the alterations made thereby are represented by turning the globe accordingly about its axis, the brass meridian being kept fixed; and if we steer betwixt the meridian and the East or West points, then we are to turn the brass meridian, and also the globe about its axis accordingly; the sum of which is, let the spectator be at what point soever of the Earth’s surface, he’ll there gravitate, or tend exactly towards its center, and imagine himself to be on the highest part thereof, (the unevenness of the ground not being here considered) wherefore if we turn the globe in such a manner as to bring the several progressive steps of a traveller successively to the Zenith, we shall then have the successive alterations made in the horizon, in every part of his journey. This explication being well considered, will be of help to young beginners, to conceive how the Earth is every where habitable; and how passengers can travel quite round it; for since every thing tends toward the center of the Earth, we are to conceive that point as being the lowest, and not to carry our idea of downwards any farther. Those that are diametrically opposite to us being as much upon the upper part of the Earth as we are, there being no such thing in nature as one place being higher than another, but as it is at a greater distance from the center of the Earth, let it be in what country soever.

We have now done with all the circles of the sphere, and it may be observed, that the Equinoctial, the Ecliptic, and the Horizon, with their Secundaries and parallels, are all alike; and altering their position, may be made to serve for one another. Thus, if the Poles of the World be brought into the Zenith and Nadir, the Equinoctial will coincide with the Horizon, the Meridians will be the same with the Vertical Circles, and the parallels of Declination will be the parallels of Altitude. After the same manner, if shifting the position, we bring the Ecliptic to coincide with the Horizon, the circles of Longitude will be the Vertical Circles, and the parallels of Latitude and Altitude will coincide.

The horizon and the equator may be either parallel, perpendicular, or oblique to each other.

Parallel Sphere.

15. A Parallel Sphere is that position where the equator coincides with the horizon, and consequently the poles of the world are in the Zenith and Nadir: The inhabitants of this sphere (if there be any) are those who live under the poles of the world.

Right Sphere.

16. A Right or Direct Sphere is that position where the equator is perpendicular to the horizon, the inhabitants whereof are those who live under the equinoctial.

Oblique Sphere.

17. An Oblique Sphere is when the equinoctial and the horizon make oblique angles with each other, which every where happens but under the equator and the poles.

Diurnal and Nocturnal Arch.

The arch of any parallel or declination, which stands above the horizon is called the Diurnal Arch; and the remaining part of it, which is below the horizon, is called the Nocturnal Arch.

That point of the equinoctial which comes to the (Eastern/Western) part of the horizon with any point of the Heavens, is called the (Ascension/Descension) of that point, counted from the beginning of ♈; and if it be in a right sphere, the ascension or descension is called right; but if it be an oblique sphere it is called an oblique ascension or descension. So that,

Right Ascension.

18. The Right Ascension of the Sun, Moon, or any Star, &c. is an arch of the equator contained betwixt the beginning of ♈, and that point of the equinoctial which rises with them in a Right Sphere, or which comes to the meridian with them in an oblique sphere.

Oblique Ascension.

19. Oblique Ascension, or Descension, is an arch of the equinoctial intercepted between the beginning of ♈, and that Point of the Equator which rises or sets with any point in the Heavens in an oblique sphere.

Ascensional Difference.