The planets do not move with equal ve locity in every part of their orbits,but they move faster when they are nearest to the Sun, and slower in the remotest part of their orbits ; and they all observe this remarkable law, that if a straight line be drawn from the planet to the sun, and this line be supposed to be carried along by the periodical motion of the planet, then the areas which are described by this right line and the path of the planet are proportional to the times of the pla net's motion. That is, the area described in two days is double that which is de scribed in one day, and a third part of that which is described in six days,though the arcs or portions of the orbit described are not in that ratio. The planets, being at different distances from the sun, per form their periodical revolutions in differ ent times : but it has been found that the cubes of their mean distances are con stantly as the squares of their periodical times ; viz. of the times of their perform ing 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 Coper nicus, 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 attrac tion, and act upon each other as well as upon the sun. The actual point there fore about which they move will be the common centre of gravity of all the bo dies 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 dis tubs their motions, and causes some ir regularities. 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 mo tion impressed upon them. Thus these two powers balance• each other, and pre serve 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 be tween 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 car ried it from B to X, it will describe the curve B Y, 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 II to y, and these two forces being duly proportioned, the planet obeying them both will move in the circle B Y V. But if, whilst the projectile force would carry the planet from B to b, the sun's attraction should bring it down from 13 to 1, the gravitating power would then be too strong for the projectile force, and would cause the planet to describe the curve B C. 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 planets motion all the way from C to K, causing it to describe the arcs B C, C D, D E, E F, &c. all in equal times. Having its motion thus ac celerated, it thereby acquires so much centrifugal force, or tendency to fly off at K, in the line K k, as overcomes the sun's attraction ; and the centrifugal force be ing to great too 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 K L MN, &c. its motion decreasing as gradu ally 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 projec tile force is as much diminished from its• mean state as it was augmented at R ; and so tlhy 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 B D, 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 repre
sented by the triangles B S C, C S D,DSE, E S F, &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 ann. The sun, as the most-con spicuous and most important of all the heavenly bodies, would naturally claim the first place in the attention of astronomers. Accordingly, its motions were first stu died, and they have had considerable in fluence on all the other branches of the science. That the sun has a motion of its own, independent of the apparent di urnal 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 com plete 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 in terval of a year, we shall find it rising pre cisely 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 or.
hit. 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 mo tion northward or southward, in the di rection of the meridian ; and the second gives us his motion eastward in the direc tion of the parallels ; and by combining the two together we obtain his orbit. The height of the sun from the horizon, when it passesthe 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 fol lowing manner :—They erected an up right pillar at the south end of a meridi an line, and when the shadow of it exact ly coincided with that line, they accurate ly measured the shadow's length,and then, knowing the height of the pillar, they found by an easy operation in plain trigo nometry, the altitude of the sun's upper limb, whence, after allowingfor the appa rent semidiameter, 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 mi nutes and smaller subdivisions, by means of a vernier, and it is furnished with a te lescope, having cross hairs, &c. turning properly upon the centre. By this instru ment 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 eclip tic. It does not coincide with the equa tor, but cuts it, forming with it an angle, which in the year 1769, was determined by Dr. Maskelyne at 23° 28' 10" or 23°.46944. This angle is called the obli quity 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 the point of his orbit situated near the winter solstice, and slowest in the oppo site point of his orbit near the summer solstice. When in the first point, the sun moves in `...A hours 1°.01943 ; in the se cond point he moves only 0°.95319. The daily motion of the sun is constantly va rying 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 begin ning of October and April. It has been ascertained, that the variation in the an gular 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 varies as well as its angular velocity. This is demonstrated by measuring the apparent diameter of the sun. Its dia meter 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 reciprocal ly as its apparent diameter. The sun must follow the same law; therefore its distance from the earth increases in the same pro portion that its apparent diameter dimi nishes. In that point of the orbit in which the sun is nearest the earth, his apparent diameter is greatest, and his motion swift est; but when he is in the opposite point both his diameter and the rapidity of his motion are the smallest possible.