orbit described are not in that ratio. The planets being at different distances from the sun, perform their periodical revolutions in different times: but it has been found that the cubes of their mean distances are constantly as the squares of their periodical times; viz. of the times of their performing their periodical revolutions. These two last propositions were discovered by Kepler, by observations on the planets; but Sir Isaac Newton demonstrated, that it must have been so on the principle of gravitation, which formed the basis of his theory. This law of universal attraction, or gravitation, discovered by Newton, completely confirms the system of Copernicus, and accounts for all the phenomena which were inexplicable on any other theory. The sun, as the largest body in our system, forms the centre of attraction, round which all the planets move; but it must not be considered as the only body endued with attractive power, for all the planets also have the property of attraction, and act upon each other as well as upon the sun. The actual point therefore about which they move will be the common centre of gravity of all the bodies which are included in our system; that is, the sun, with the primary and secondary planets. But because the bulk of the sun greatly exceeds that of all the planets put together, this point is in the body of the sun. The attraction of the planets on each other also somewhat disturbs their motions, and causes some irregularities. It is this mutual attraction between them and the sun that prevents them from flying off from their orbits by the centrifugal force which is generated by their revolving in a curve, while the centrifugal force keeps them from falling into the sun by the force of gravity, as they would do if it were not for this motion impressed upon them. Thus these two powers balance each other, and preserve order and regularity in the system. It is well known, that if, when a body is projected in a straight line it be acted upon by another force, drawing it towards a centre, it will be made to describe a curve, which will be either a circle or an ellipsis, according to the proportion between the projectile and centripetal force. If a planet at B (fig. 3, Plate II.) gravitates or is attracted towards the sun, S, so as to fall from B to y, in the time that the projectile force would have carried it from B to X, it will describe the curve BY by the combined action of these two forces in the same time that the projectile force singly would have carried it from B to X, or the gravitating power singly have caused it to descend from B to y; and these two forces being duly proportioned, the planet obeying them both will move in the circle BYTV. But if, whilst the projectile force would carry the planet from B to b, the sun's attraction should bring it down from B to 1, the gravitating power would then be too strong for the projectile force, and would cause the planet to describe the curve BC. When the planet comes to C, the gravitating power (which always increases as the square of the distance from the sun, S, diminishes) will be yet stronger for the projectile force, and by conspiring in some degree therewith, will accelerate the planet's motion all the way from C to K, causing it to describe the arcs BC, CD, DE, EF, &c. all in equal times. Having its motion thus accelerated, it thereby acquires so much centrifugal force, or tendency to fly off at K, in the line Kk, as overcomes the sun's attraction; and the centrifugal force being too great to allow the planet to be brought nearer to the sun, or even to move round him in the circle k l m n, &c. it goes off, and ascends in the curve KL MN, &c. its motion decreasing as gradually from K to B as it increased from B to K, because the sun's attraction now acts against the planet's projectile motion just as much as it acted with it before. When the planet has got round to B, its projectile force is as much diminished from its mean state as it was augmented at K; and so the sun's attraction being more than sufficient to keep the planet from going off at B, it describes the same orbit over again by virtue of the same forces or powers. A double projectile force will always balance a quadruple power of gravity. Let the planet at B have twice as great an impulse from thence towards X as it had before; that is, in the same length of time that it was projected from B to b, as in the last example; let it now be projected from B to c, and it will require four times as much gravity to retain it in its orbit; that is, it must fall as far as from B to 4 in the time that the projectile force would carry it from B to C, otherwise it would not describe the curve BD, as is evident from the figure. But in as much time as the planet moves from B to C, in the higher part of its orbit, it moves from I to K or from K to L in the lower part thereof; because from the joint action of these two forces, it must always describe equal areas in equal times throughout its annual course. These areas are represented by the triangles B SC, CSD, DSE, ESF, &c. whose contents are equal to one another from the properties of the ellipsis. We have now given a general idea of the solar system; we shall next describe the bodies that compose it. Of the sun. The sun, as the most conspicuous and most important of all the heavenly bodies, would naturally claim the first place in the attention of astronomers. Accordingly its motions were first studied, and they have had considerable influence on all the other branches of the science. That the sun has a motion of its own, independent of the apparent diurnal motion common to all the heavenly bodies, and in a direction contrary to that motion, is easily ascertained, by observing with care the changes which take place in the starry hemisphere during a complete year. If we note the time at which any particular star rises, we shall find that it rises somewhat sooner every successive day, till at last we lose it altogether in the west. But if we note it after the interval of a year, we shall find it rising precisely at the same hour as at first. Those stars which are situated nearly in the track of the sun, and which set soon after him, in a few evenings lose themselves altogether in his rays, and afterwards make their appearance in the east before sunrise. The sun then moves towards them in a direction contrary to his diurnal motion. It was by observations of this kind that the ancients ascertained his orbit. But at present this is done with greater precision, by observing every day the height of the sun when it reaches the meridian, and the interval of time which elapses between his passing the meridian and that of the stars. The first of these observations gives us the sun's daily motion northward or southward, in the direction of the meridian; and the second gives us his motion eastward in the direction of the parallels; and by combining the two together we obtain his orbit. The height of the sun from the horizon, when it passes the meridian, on the arch of the meridian between the sun and the horizon, is called the sun's altitude. The ancients ascertained the sun's altitude in the following manner; They erected an upright pillar at the south end of a meridian line, and when the shadow of it exactly coincided with that line, they accuracely measured the shadow's length, and then, knowing the height of the pillar, they found by an easy operation in plane trigonometry the altitude of the sun's upper limb, whence, after allowing for the appa rent semi-diameter, the altitude of the sun's centre was known. But the methods now adopted are much more accurate. In a known latitude, a large astronomical quadrant, of six, eight, or ten feet radius, is fixed truly upon the meridian; the limb of this quadrant is divided into minutes and smaller subdivisions by means of a vernier, and it is furnished with a telescope, having cross hairs, &c. turning properly upon the centre. By this instrument the altitude of the sun's centre is very carefully measured, and the proper deductions made. The orbit in which the sun appears to move is called the ecliptic. It does not coincide with the equator, but cuts it, forming with it an angle, which in the year 1769 was determined by Dr. Maskelyne at 23° 28′ 10′′, or 23o.46944. This angle is called the obliquity of the ecliptic. It is known that the apparent motion of the sun in its orbit is not uniform. Observations, made with precision, have ascertained, that the sun moves fastest in a point of his orbit situated near the winter solstice, and slowest in the opposite point of his orbit near the summer solstice. When in the first point, the sun moves in 24 hours 1°.01943; in the second point, he moves only 0°.95319. The daily motion of the sun is constantly varying in every place of its orbit between these two points. The medium of the two is 0°.98632, or 59' 11", which is the daily motion of the sun about the beginning of October and April. It has been ascertained, that the variation in the angular velocity of the sun is very nearly proportional to the mean angular distance of it from the point of its orbit where its velocity is greatest. It is natural to think, that the distance of the sun from the earth varics as well as its angular velocity. This is demonstrated by measuring the apparent diameter of the sun. Its diameter increases and diminishes in the same manner and at the same time with its angular velocity, but in a ratio twice as small. In the beginning of January his apparent diameter is about 32" 39", and at the beginning of July it is about 31′ 34′′, or more exactly, according to De la Place, 32′ 35′′ 1955′′ in the first case, and 31' 18' 1878' in the second. Opticians have demonstrated, that the distance of any body is always reciprocally as its aprent diameter. The sun must follow the same law; therefore its distance from the earth increases in the same proportion that its apparent diameter diminishes. In that point of the orbit in which the sun is nearest the earth, his apparent diameter is greatest, and his motion swiftest; but when he is in the opposite point, both his diameter and the rapidity of his motion are the smallest possible. constant emanation of heat and light, as an immense globe of fire. When viewed through a telescope several dark spots are visible on its surface, which are of various sizes and durations. From the motion of these spots the sun has been found to move been formed respecting these spots; they have been considered as opaque islands in the liquid igneous matter, and by some as pits or cavities in the body of the sun. In 1788, Mr. King published a Dissertation on the Sun, in which he advanced that the real body of the sun is less than its apparent diameter; that we never discern the real body of the sun itself, except when we behold its spots; that the sun is inhabited as well as our earth, and is not necessarily subject to burning heat, and that there is in reality no violent elementary heat existing in the rays of the sun themselves essentially, but that they produce heat only when they come into contact with the planetary bodies. Several years after this Mr. Herschel pub lished his theory of the nature of the sun, which is briefly as follows: he considers the sun as a most magnificient habitable globe, surrounded by a double set of clouds. Those which are nearest its opaque body are less bright, and more closely connected together than those of the upper stratum, which form the luminous apparent globe we be hold. This luminous external matter is of a phosphoric nature, having several acciden tal openings in it, through which we see the sun's body, or the more opaque clouds beneath. These openings form the spots that we see. To determine the distance of the sun round its axis, and its axis is found to be infrom the earth, has always been an interest-clined to the ecliptic. Various opinions have ing problem to astronomers, and they have tried every method which astronomy or geometry possesses in order to resolve it. The amplest and most natural is that which mathematicians employ to measure distant terrestrial objects. From the two extremities of a base whose length is known, the angles which the visual rays from the object, whose distance is to be measured, make with the base, are measured by means of a quadrant; their sum subtracted from 180° gives the angle which these rays form at the object where they intersect. This angle is called the parallax, and when it is once known it is easy, by means of trigonometry, to ascertain the distance of the object. Let A B, in fig. 4, be the given base, and C the object whose distance we wish to ascertain. The angles CA B and C BA, formed by the rays CA and CB with the base, may be ascertained by observation; and their sum subtracted from 180° leaves the angle ACB, which is the parallax of the object C. It gives us the apparent size of the base A B as seen from C. When this method is applied to the sun, it is necessary to have the largest possible base. Let us suppose two observers on the same meridian, observing at the same instant the meridian altitude of the centre of the sun, and his distance from the same pole. The difference of the two distances observed will be the angle under which the line which separates the observers will be seen from the centre of the sun. The position of the observers gives this line in parts of the earth's radius. Hence, it is easy to determine, by observation, the angle at which the semidiameter of the earth would be seen from the centre of the sun. This angle is the the sun's parallax. But it is too small to be determined with precision by that method. We can only conclude from it, that the sun's distance from the earth is at least equal to 10,000 diameters of the earth. Other methods have been discovered for finding the parallax with much greater precision. It amounts very nearly to 8.8 hence it follows that the distance of the sun from the earth amounts to at least 23.405 semidiameters of the earth. The sun was long considered, from its Mercury. This planet being the nearest to the sun, and the least in magnitude, is very seldom visible. It never appears more than a few degrees from the sun's disc, and is generally lost in the splendor of the solar beams. On this account astronomers have had few opportunities of making accurate observations upon it; no spots have been observed upon it, consequently the time of its rotation on its axis is not known. Being an inferior planet it consequently must shew phases like the moon; and it never appears quite full to us. It is seen sometimes passing over the sun's disc, which is called its transit. Venus is the brightest and largest to appearance of all the planets, and is distinguished from the rest by her superiority of lustre. It is generally called the Morning or Evening Star, according as it precedes or follows the apparent course of the sun. Some have thought that they could discover spots upon its disc; but Herschel has not been able to see them; consequently the time of rotation round its axis is not decidedly known. Venus also appears with phases, and transits sometimes take place; which are of very great importance in astronomy. The Earth which we inhabit is as has been proved, a globular body; it is not, however, a perfect sphere, but a spheroid, having its equatorial diameter longer than the polar diameter or axis. It is consequently flattest at the poles, and more protuberant at the equator. The diameter at the equator is 7893 English miles; that at the pole is 7928 miles. The surface of the earth is much diversified with mountains and vallies, land and water. The highest mountains in it are the Andes in South America, some of which are about four miles in perpendicular altitude. About two-thirds of the globe is covered with water. In consequence of the earth's being a globe, people standing upon opposite sides of it must have their feet towards to each other. When in this situation they are called antipodes to each other. Hence it appears that there is no real up or down; for what is up to one country is down to another. It must seem strange to those who are ignorant of the shape of the the earth, to suppose that if we could bore a hole downwards, deep enough, we should come to the other side of the world, where we should find a surface and sky like our own; yet if we reflect a moment we shall perceive that this is perfectly true. As we are preserved in our situations by the power of attraction which draws us towards the centre of the earth, we call that direction down which tends to the centre, and the contrary. We mentioned before that the earth has two motions, the one a diurnal motion round its own axis, the other an annual motion round the sun. mer which causes light and darkness, day and It is the fornight; for when one side of the earth is turned towards the sun it receives his rays and is illuminated, causing day; on the contrary, when one side of the earth is turned from the sun, we are in darkness, and then we have night. We see, therefore, by how much more simple means this change is effected, than they imagined who supposed that the earth was fixed, and that the immense globe of the sun was whirled round the earth with the amazing velocity that the refraction of the rays of light by our would be necessary. Twilight is owing to atmosphere through which they pass, and which, by bending them, occasion some to arrive at a part of the earth that could not receive any direct rays from the sun. the annual motion of the earth round the It is sun which occasions the diversity of seasons. has been already mentioned, that the axis of To understand this, we must observe what the earth is inclined to the plane of its orbit 2340, and it keeps always parallel to itself; that is, it is always directed to the same star. Let fig. 5, Plate II. represent the earth in different parts of its elliptic orbit. In the spring the circle which separates the light from the dark side of the globe called the terminator, passes through the poles n,s, then, in its diurnal rotation about its axis, as appears in the position A. The earth has every part of its surface as long in light as in shade; therefore the days are equal to the nights all over the world; the sun being of the earth. As the earth proceeds in its at that time vertical to the equatorial parts orbit and comes into the position B, the sun becomes vertical to those parts of the earth under the tropic, and the inhabitants of the northern hemisphere will enjoy summer on pendicularly upon them; they will also have account of the solar rays falling more pertheir days longer than their nights, in proportion as they are more distant from the equator; and those within the polar circle, as will be perceived by the figure, will have inhabitants of the southern hemisphere have constant day-light. At the same time the winter, their days being shorter than their nights, in proportion as they are farther from regions will have constant night. The earth the equator; and the inhabitants of the polar then continues its course to the position C, when the terminator again passes through the poles, and the days and nights are equal. After this the earth advances to the position northern hemisphere have winter, and their D, at which time the inhabitants of the days are shorter than their nights. The positions B and D are the solstitial points, and A and C the equinoctial points; they are not equidistant from each other, because of the ellipsis. In summer, when the earth the sun is not in the centre but in the focus is at B, the sun is farther from it than in the winter when the earth is at D; and in fact, the diameter of the sun appears longer in winter than in summer. heat is not owing to the sun's being nearer The difference of to us, or more remote, but to the degree of. The moon has scarcely any difference of obliquity with which its rays strike any part of the earth. The Moon is, next to the sun, the most remarkable of the celestial objects. Its form is spherical like that of the earth round, which it revolves, and by which it is carried round the sun. Its orbit is also elliptical, having the earth in one of the foci of the ellipsis. The moon always keeps the same side towards the earth, shewing only at one time a little more of one side, and at another time a little more of the other side. When the moon is viewed through a good telescope, its surface appears covered with ridges, mountains, pits, and cavities of great variety. Some parts of its surface also reflect less light than the rest. It has been conjectured that the part which reflects the least light water, and the brightest part land. The heights of the lunar mountains were formerly supposed to be much greater than those of our earth; but Dr. Herschel has demonstrated that very few are more than half a mile high, and the highest little more than a mile. Several volcanos, or burning mountains, have been discovered in it. It has been doubted whether the moon has an atmosphere like ours, but the latest observations appear to prove that it has. The moon is seen by means of the light which comes to it from the sun being reflected from it. Its changes or phases depend upon its situation relatively to the earth and the sun. When the moon is in opposition to the sun, the enlightened side is turned towards the earth, and it appears full; when the moon is in conjunction with the sun, its dark side is turned towards us, and it is invisible. As it proceeds in its orbit, a small part of the enlightened side is seen, and then we have a new moon; and we continue to see more and more of the enlightened side, as the moon approaches to the state of opposition, or full moon. The waning or decreasing of the moon takes place in the same manner, but in a contrary order. The earth must perform the same office to the moon that the moon does to us; and it will appear to the inhabitants of the moon (if there be any), like a very magnificent moon, being to them about 13 times as big as the moon to us, and it will also have the same changes or phases. The moon's motion is subject to many irregularities, on account of the inclination of its orbit to the plane of the ecliptic, and the attraction of the sun and the other planets. seasons; her axis being almost perpendicular to the ecliptic. What is very singular, one half of her has no darkness at all; the earth constantly affording it a strong light in the sun's absence; while the other half has a fortnight's darkness and a fortnight's light by turns. Our earth, as we have already observed, is undoubtedly a moon to the moon; waxing and waning regularly, but affording her 13 times as much light as she does us. When she changes to us, the earth appears full to her; and when she is in her first quarter to us, the earth is in its third quarter to her; and vice versa. But from one half of the moon the earth is never seen at all: from the middle of the other half, it is always seen over head; turning round almost 30 times as quick as the moon does. From the circle which limits our view of the moon, only one half of the earth's side next her is seen; the other half being hid below the horizon of all places on that circle. To her, the earth seems to be the biggest body in the universe. As the earth turns round its axis, the several continents, seas, and islands, appear to the moon's inhabitants like so many spots of different forms and brightness, moving over its surface; but much fainter at sometimes than others, as our clouds cover them or leave them. By these spots the Lunarians can determine the time of the earth's diurnal motion, just as we do the motion of the sun: and perhaps they measure their time by the motion of the earth's spots; for they cannot have a truer dial. The moon's axis is so nearly perpendicular to the ecliptic, that the sun never removes sensibly from her equator; and the obliquity of her orbit, which is next to nothing as seen from the sun, cannot cause the sun to decline sensibly from her equator. Yet her inhabitants are not destitute of means for ascertaining the length of their year, though their method and ours must differ. For we can know the length of our year by the return of our equinoxes; but the Lunarians, having always equal day and night, must have recourse to another method; and we may suppose, they measure their year by observing when either of the poles of our earth begins to be enlightened, and the other to disappear, which is always at our equinoxes; they being conveniently situated for observing great tracts of land about our earth's poles, which are entirely unknown to us. Hence we may conclude, that the year is of the same ab |