4. These circumstances indicate a general revolution of all the stars about an axis passing through the earth perpendicularly to the planes of the circular arcs apparently described by them: but it is very improbable that so many different bodies should perform the revolution in the same time, preserving their apparent distances unchanged; and, on the ground that the like phenomena would result from a rotation of the earth about the same axis, the latter hypothesis is adopted by astronomers. In the present age a certain star (a Polaris) nearly indicates the northern extremity of the axis in the heavens, and an arc supposed to be traced through two bright stars (y and a of the southern cross) tends directly towards the opposite extremity.

5. The stars appearing to be at the same distance from the spectator, they are, for convenience, imagined to be attached to the concave surface of a hollow sphere of which his eye is the centre; and hence the general movement of the stars about the earth is sometimes called the diurnal rotation of the celestial sphere. The sun appears daily to rise and set: the moon also, when visible, exhibits the like phenomena; but these two celestial bodies, and certain stars which are not always visible, have proper movements which prove them to be quite distinct from the other bodies of the universe.

6. At a certain season, in any part of the world, a very distinguishable cluster of stars, which may have been observed to rise very near the eastern part of the horizon, will be on the meridian of the observer a short time before the rising of the sun on continuing to observe the cluster, its apparent elongation from the sun will constantly increase, and, in two or three months from the time of the first observation, it will appear at morning dawn to be setting in the west. During several months it will not be visible, but it will afterwards appear near the east a little while before the sun is there; and at the end of one year from the first observation it will be again seen on the meridian near the time of his rising. The like phenomena are exhibited by all the stars which rise in or near the east; and from this change in the sun's position with respect to such stars, it may be inferred either that those stars, and with them all the others, have been carried towards the west independently of the diurnal movement, or that the sun has, during the year, moved eastward about the earth. The moon is observed to change her place in like manner; for if on any night her distance eastward from some star be remarked, on the following night the distance in that direction will be sensibly increased: the distance

will go on continually increasing and, in about a month, the moon will be in the same position as at first with respect to the star. That an annual and monthly, as well as a diurnal revolution of all the stars should take place simultaneously, is highly improbable; and it may therefore be inferred that the moon revolves about the earth from west to east: the phenomena above mentioned may seem to indicate a like movement of the sun; but since they will be the same whether the sun revolve about the earth in one year, or the earth about the sun in the same time, the latter hypothesis, which alone is consistent with the laws of general attraction among the great bodies of the universe, may be immediately adopted.

7. It is well known that the sun's angular elevation above the horizon at noon experiences, from mid-winter to midsummer, a continual increase, and, from mid-summer to midwinter, a continual decrease. Now, by observing what groups of stars appear to rise and set very near the sun during a year, the trace of his apparent route in the heavens may be distinguished; and hence it may be readily ascertained in what groups the sun is at the times when his elevations above the horizon are the least and the greatest. These groups, or constellations, are on opposite sides of the celestial sphere with respect to the earth; and it may be perceived that a mean between the greatest and least elevations of the sun at noon is nearly equal to the elevation of that luminary at the noon of the day which is the middle of the interval between mid-winter and mid-summer, or between mid-summer and mid-winter: it may be observed also, that the greatest elevation of any star, which, rising in the east and setting in the west, appears to describe daily about the earth a path whose plane is perpendicular to the axis of the diurnal rotation, is equal to that mean elevation of the sun; and it may from these circumstances be presumed, that the path of the sun in his apparent yearly revolution about the earth, or the path of the earth about the sun, is a plane curve having a certain inclination to the plane last mentioned. The angular elevations of the points which the moon appears to occupy in the celestial sphere are sometimes greater than the greatest, and sometimes less than the least elevations of the sun; and it may from thence be inferred that the moon's orbit has a certain inclination to that in which the earth revolves about the sun.

8. Since the angular distance of the sun below the plane passing through the earth perpendicularly to the axis of rotation is at noon, on the day of mid-winter, equal to the angular

distance of the sun above that plane at noon on the day of midsummer, and that on the two days of the year which are equally distant from those days the sun is in the plane perpendicular to the axis of rotation; it follows, if the earth be supposed to revolve annually about the sun, that the axis of the diurnal rotation must on those four days be in positions parallel to one another; also, since the changes in the angular distance of the sun from that plane take place gradually, it may be inferred that the axis of rotation continues always strictly or nearly parallel to itself.

9. If the moon be at first observed near the west about the time that the sun is setting, her angular distance from that luminary will on every succeeding evening be found to have increased, and at the end of about fourteen days, she may be observed rising near the east, when the sun is on the western side of the horizon: she is then said to be in opposition to the sun from that time, she appears to approach the sun towards the east, the intervals between the times at which the two luminaries rise continually diminishing; and, at the end of about a month from the first observation, the moon is in conjunction with the sun. After remaining invisible for a few days, she re-appears in the west at a small distance from the setting sun, and the like phenomena are repeated.

10. During this revolution of the moon about the earth the form exhibited by the outline of her face gradually changes. At the time of new moon, when, in the western part of the horizon, she first emerges from the sun's rays, she assumes the form of a slender crescent of light, and this crescent daily increases in breadth, till, at the time of opposition, it becomes a complete circle: afterwards the breadth diminishes till the moon is about to become invisible from her proximity to the sun in the east, when the figure is again that of a slender crescent. These phases are exactly such as are presented by a globular body enlightened on half_its surface by the sun, the circle bounding the light and shadow being in different positions with respect to the observer; and hence it is inferred that the figure of the moon is exactly or nearly that of a sphere.

It happens occasionally that, at the time of opposition, the centre of the moon is exactly or nearly in the direction of a line drawn from the centre of the sun through that of the earth, and produced towards her; and then, the shadow of the earth falling on the moon, the inhabitants of the side of the earth which is nearest to her observe her to be eclipsed, or deprived of the light which she would have received from the sun it happens also, occasionally, that at the time of

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 (r), Taurus (8), Gemini (п), Cancer (), Leo (a), Virgo (my), Libra (), Scorpio (m), Sagittarius (+), Capricornus (v), 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, Bb and вn being known,