conjunction the centre of the moon is exactly or nearly in a line joining those of the earth and sun; in which case, the moon intercepting the rays of light coming from the sun towards the earth, the sun, to an inhabitant of the earth who may be situated near the direction of the line, on the side nearest to the luminary, is observed to suffer an eclipse.

11. Attentive and continued observations of the heavens show that some of the stars have movements independent of that general revolution which all of them appear to perform daily about the earth. These are the planets, which are ten in number, though only six can be seen by the unassisted eye, and their designations in the order of their distances from the sun are as follow:- Mercury, Venus, Mars, Vesta, Juno, Pallas, Ceres, Jupiter, Saturn, and Uranus; the Earth, which is also a planet, and is situated between Venus and Mars, being omitted in the enumeration. Two of the planets, Mercury and Venus, when visible, appear on the same side of the meridian as the sun is; and the former but a short time before his rising or after his setting: if first seen nearly in conjunction with the sun in the west, these planets then gradually recede from him towards the south, Mercury to an angular distance not exceeding 28 degrees, and Venus to a distance not exceeding 48 degrees: they afterwards appear to return towards him, and after having been for some days invisible, they may be seen in the east before sunrise; at first they appear to recede from that luminary towards the south; and subsequently, the greatest angular distances or elongations being equal to those which were attained in their former positions, they return towards it. After being again for a time invisible, they re-appear in the west as before, and the like phenomena are repeated. In the interval between the disappearance in the west and the next appearance in the east, both planets are occasionally, by the aid of the telescope, seen to pass like dark spots across the disk of the sun; the telescope moreover shows that each of these, like the moon, assumes the form of a crescent, a semicircle, an ellipse, and nearly a complete circle; the several phases succeeding each other in regular order. The inferences are that these planets are globular, and that they revolve about the sun within the orbit of the earth, Mercury being that which is nearest to him.

12. The other planets are seen at times nearly in conjunction with the sun, and at other times diametrically opposite to him in the heavens, and it is therefore inferred that they revolve about the sun in orbits, on the exterior of that which is described by the earth. The comets also, which occasionally

appear in the heavens, are observed to have such movements as indicate that they, like the planets, revolve about the sun. All the planets, moreover, are seen to move in different directions with respect to the fixed stars: sometimes they appear to recede from certain of these towards the west, sometimes towards the east, and, again, to remain for a time stationary, or nearly so. The telescope shows that their disks are nearly circular, or segments of circles, and from the movements of the spots which have been observed on most of their surfaces, it is inferred that they are globular bodies, which, like the earth, constantly turn on axes of rotation. The motions of the spots observed on the sun show that this luminary has a similar movement on an axis. The planets Jupiter, Saturn, and Uranus are, by the aid of the telescope, observed to be accompanied by satellites, which revolve about them as the moon revolves about the earth; and Saturn is, moreover, accompanied by a ring which revolves in its own plane about the planet.

13. The stars called fixed have, from the earliest ages, been reduced into groups under the figures chiefly of men and animals; and representations of such groups, or constellations as they are called, may be seen on any celestial globe. A certain zone of the sphere of stars, extending several degrees northward and southward of the sun's apparent annual path, is called the zodiac, and twelve groups of stars immediately about that path bear the name of the zodiacal constellations. The designations of these are as follow: · Aries (v), Taurus (8), Gemini (п), Cancer (), Leo (a), Virgo (my), Libra (), Scorpio (m), Sagittarius ( 4 ), Capricornus (w), Aquarius (), and Pisces (x).

14. An approximate knowledge of the magnitude of the earth may be, and very early was, obtained by the aid of a simple trigonometrical proposition, from the measured length of the shadow cast at noon by a column or obelisk erected at each of two places, lying in a direction nearly due north and south of each other. Thus, it being assumed that the earth is a sphere, and the sun so remote that the rays of light which fall upon the earth at the two stations A and B may be considered as parallel to one another, let the plane of the paper represent that of a terrestrial meridian, whose circumference passes through the stations, and let Aa, Bb, be the obelisks there set up. Then, if sam, sbn be two parallel rays proceeding from the sun at noon, am, Bn, which may be considered as straight lines, will denote the lengths of the shadows; and in the triangles aam, bân, right angled at A and B, the lengths of Aa and Am, вb and вn being known,

S

the angles Aam, Bbn may be computed. But c representing the centre of the earth, if EC be drawn parallel to sa or sb, the angles ACE, BCE will be respectively equal to Aam, Bbn; therefore the difference between these last angles is equal to the angle ACB. Hence, the arc AB being measured, the following proportion will give the length of the earth's circumference:

b

A m

B

n

E

C

ACB (in degrees): 360°: AB circumference (24850 miles, nearly.)

15. The processes by which the earth's form and magnitude are with precision determined, as well as those which are employed in finding the magnitudes of the sun, moon, and planets, the distances of the moon from the earth, and of the earth and planets from the sun, will be presently explained. It is sufficient to observe here, that since the planetary bodies, when viewed through a telescope, present the appearance of well-defined disks, subtending, at the eye of the spectator, angles of sensible magnitude, while the stars called fixed, though examined with the most powerful instruments, are seen only as lucid points; it will follow that the sun, the earth, and the planets constitute a particular group of bodies, and that a sphere supposed to encompass the whole of the planetary system may be considered as infinitely small when the imaginary sphere of the fixed stars is represented by one of any finite magnitude. Hence, in describing the systems of circles by which the apparent places of celestial bodies are indicated, it is permitted to imagine that either the earth or the sun is a point in the centre of a sphere representing the heavens: and, in the latter case, the earth and all the planets must be supposed to revolve in orbits whose peripheries are at infinitely small distances from the sun.

P

B

16. If the earth's orbit (supposed to be a plane) be produced to the celestial sphere, it will there form the circumference of a circle which is called the trace of the ecliptic (let it be EL): this is represented on the common celestial globes; and on those machines, the representations of the zodiacal stars near which it appears to pass will serve, when the stars are recognised, as indications of its position in

E

R

L

the heavens. A line passing through the sun at C (the centre of the sphere) perpendicularly to the plane of the ecliptic, meets the heavens in the points designated p and q, which are called the poles of the ecliptic. Now, if planes be supposed to pass through p and q, these planes will be perpendicular to that of the ecliptic, and they will cut the celestial sphere in the circumferences of circles which are called circles of celestial longitude: these are also represented on the celestial globes.

17. The trace of the ecliptic in the heavens is imagined to be divided into twelve equal parts called signs, which bear the names of the zodiacal constellations before mentioned. They follow one another in the same order as those constellations, that is, from the west towards the east; and the movement of any celestial body in that direction is said to be direct, or according to the order of the signs: if the movement take place from the east towards the west, it is said to be retrograde, or contrary to the order of the signs.

18. It has been shown in art. 7. that the path (the ecliptic) of the earth about the sun is inclined to the plane which is perpendicular to the axis of the diurnal rotation; the axis pg must, therefore, be inclined to the latter axis. Now, the centre of the earth being at c infinitely near, or in coincidence with that of the sun, agreeably to the above supposition, let PQ be the axis of the diurnal rotation; then the plane A B passing through C perpendicularly to P Q and produced to the heavens will be the plane last mentioned: it will cut the surface of the earth (which is assumed to be a sphere or spheroid) in the circumference of a circle called the terrestrial equator, and that of the sphere of the fixed stars in the circumference A y B of the celestial equator. The plane of this circle will cut that of the ecliptic in a line, as y c^, which is called the line of the equinoxes, of which one extremity in the heavens is called the point of the vernal equinox. If planes pass through PQ they will be perpendicular to the equator, and their circumferences in the celestial sphere form what are called circles of declination: such is the circle P R Q which is made to pass through s, the supposed place of a star. Of these circles that which passes through the line of the equinoxes is called the equinoctial colure, and that which, being at right angles to the former, passes through p, is called the solsticial colure. The last-mentioned planes Iwill cut the surface of the earth in the circumferences of circles, if the earth be a sphere, or in the perimeters of ellipses if it be a spheroid; and these are called the meridians of the stations, or remarkable points which they pass through on

the earth. This is, however, only the popular definition of a terrestrial meridian: if from every point in the circumference of a circle of declination in the celestial sphere lines be let fall in the directions of normals, or perpendiculars, to the earth's surface, a curve line supposed to join the points in which the normals meet that surface will be the correct terrestrial meridian; and if the earth be not a solid of revolution this meridian is a curve of double curvature. If any point, ass, be the place where a perpendicular raised from any station on the surface of the earth meets the celestial sphere, s will be the zenith of that station; R will express its geographical longitude, and R s its geographical latitude. The arc T or the angle y CT on the plane of the ecliptic is designated the longitude of any star s, through which and the axis pq the plane of a circle is supposed to pass; and the arc T s, or the angle TC s, is called the latitude of such star: ps or qs is called its ecliptic polar distance. A plane passing through any point, parallel to the ecliptic Ev L, will cut the celestial sphere in the circumference of a circle which is called a parallel of celestial latitude. The arc R, or the angle CR on the plane of the equator, is designated the right-ascension of any star s, through which and the axis PQ the plane of a circle of declination is supposed to pass; and the arc RS or the angle R C S is called the declination of such star: PS or QS is called the polar distance. A plane passing through any point, parallel to that of the equator AB, will cut the celestial sphere in the circumference of a small circle which is called a parallel of declination.

19. The ecliptic and the circular arcs perpendicular to it form one system of co-ordinates: the equator and its perpendicular arcs form another system; and the knowledge of the number of degrees in the arcs v T and T S, VR and RS, whether obtained by direct observation, or from astronomical tables, is sufficient to determine the place s of a star in the celestial sphere. It may be necessary to observe that the system of the equator and its perpendiculars is continually changing its position by the annual movement of the earth about the sun; but on account of the smallness of the orbit when compared with the magnitude of the celestial sphere, and the axis PQ being always parallel to itself (art. 8.), omitting certain deviations which will be hereafter mentioned, that change of position creates no sensible differences, except such as depend on the deviations alluded to, in the situations of the stars with respect to these co-ordinates.

20. A third system of co-ordinates is formed by a plane