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64 66 59.9 Jupiter
112 12 51.3 Saturn
135 19 05.5 Uranus
177 48 01.1 (5.) Mean Longitude of the Perihelion, for the same Epoch, with the
Sidereal and Secular Variation. The Sign — indicates a Retro-
14 21 46.9 g 43.5
128 43 53.1 - 4 27.8 The Earth
99 30 05.0 19 39.8 Mars
332 23 56.7 26 22.4 Jupiter
11 08 34.4 11 3.9 Saturn
89 09 29.6 32 17.1 Uranus
167 32 06.0 3 59.3
(6.) Inclination of the Orbit to the Ecliptic, at the Beginning of 1801,
with the Secular Variation of the Inclination to the true Ecliptic. Mercury
9 60 69.1 18.2 Venus
3 23 28.5
- 4.6 The Earth
0 00 00.0
1 51 06.2
1 18 51.3
2 29 35.7
0 46 28.4
(7.) Longitude of the Ascending Node, at the Beginning of 1801, with
the Sidereal and Secular Motion.
Å5 67 36.9
0 00 00.0
13 2 31 10
0 00 38 48 26 18 37 46 59 58
Ceres Pallas Juno Vesta
(1.) Sidereal Revolution.
Years. 1681.3931 or 43 nearly. 1686.5388
4 1592.6608 1325.7431 33
(2.) Mean Distance.
263,000,000 miles. 263,000,000 252,000,000 225,000,000
(3.) Ratio of the Eccentricity to the Mean Distance. Ceres
(4.) Mean Longitude at the Beginning of 1820.
123 69 41.4 108 18 28.7 200 09 32.4 278 21 45.1
(5.) Longitude of the Perihelion at the same Epoch.
147 67 31.5 121 07 04.3
53 33 46.0 249 33 24.4
(6.) Inclination of the Orbit to the Eliptic.
io 37 26.3 34 34 55.1 13 04 09.7 7 08 09.0
(7.) Longitude of the Ascending Node, at the Beginning of 1810.
Each of the planets, after a certain period, returns to the same position with regard to the sun. This period is called the synodic revolution, from two Greek words, which signify, to come together. It is readily found from the motion of the planet, compared with the apparent motion of the
sun, or, which is the same thing, the real motion of the earth. Mercury, for instance, after coming into a line of conjunction with the sun, will return to the same position, after it has gained one revolution, or 360°; just as the hour and minute hands of a watch, after being together at 12 o'clock, will come together again when the minute hand has gained one revolution of the hour hand. We find the daily motion of Mercury, by dividing 360° by 88, the number of days in a sidereal revolution. The daily motion of the sun, in like manner, is 36 or 1 degree nearly. Mercury, therefore, gains of the sun nearly 3° in a day. Whence, as 3° : 1 day :: 360° : 120 days. By taking the daily motions more accurately, we should obtain a more accurate result. It is thus found that the mean synodic revolution of Mercury is 116 days; that is, after being in any particular position with respect to the sun, as that of a morning or evening star, Mercury returns to the same position again, at a mean, in 116 days. We say at a mean, since this period is subject to some variation, according as the time happens to embrace more or less of that part of the orbit in which the motion is most rapid.
It will be seen by the tables, that the planets move round the sun in less time according as they are nearer or move in less orbits; and while one planet is thus passing another, the slower planet, when referred to the stars, seems to have a motion in the opposite direction. Thus when the earth is passing Mars, that is, when Mars is on the side of the earth opposite to the sun, rising when the sun sets, and crossing the meridian at midnight, Mars seems to move among the stars in a direction opposite to its real motion. Mars is then said to be retrograde ; and this retrograde motion becomes slower and slower, according as the planet deviates more from the point opposite to the sun, till at length it reaches a position in which it appears for a short time to have no motion among the stars. It is then said to be stationary. When Mars thus seems stationary, as viewed from the earth, the earth will seem stationary as seen from Mars. Moreover, when Mars appears retrograde to an inhabitant of the earth, the earth will seem to have a retrograde motion to a spectator in Mars. Thus all the planets, whether nearer the sun than we are, or more remote, are sometimes apparently stationary, sometimes retrograde, and sometimes direct in their motions.
It will be readily perceived, that those planets will have the longest arcs of retrogradation which are nearest to us, while those will appear retrograde for the longest time, that are most distant, and slowest in their motions, as will be manifest from the following table.
Mean Duration | Angular Distances be Mean Arc of Mean Duration
[The following account of Comets is taken from the Companion to the British Almanac.]
OBJECTS and phenomena, which are remote in their situations, apparently' irregular in the time, or singular in the mode of their appearance, have, in the uninstructed ages of the world, been taken hold of by the cunning, and, being invested with superstitious and supernatural powers, have been made the means of enslaving the human mind. In this way, many pages of the volume of nature have been read as evil, long before the investigations of philosophy taught men to read them for good. Nor is it easy, even with all the intellectual improvement of modern times, to guard completely against abuses of this kind; wherever there is ignorance, there is sure to be credulity; and where credulity exists, there is always found some one ready to impose on it. Hence it becomes the duty of every one who is anxious, in matters of knowledge and action, to separate the wheat of belief from the chaff, to advert to, and, as far as is possible, to explain, those subjects upon which the popular or partially-informed mind is in greatest danger of being abused.
With respect to the several bodies that compose the material universe, and their several appearances and changes, be they ever so distant, ever so singular, or ever so contrary to the current of one's own past experience, there is a general philosophy of common sense, which if we could keep it constantly in mind, would remove, at once, all superstition, and change what have been objects of apprehension to the ignorant, into subjects of instruction and delight. That philosophy is this :-The universe, with every thing of which it is made up, from the smallest animalcule that the microscope can discover-haply not equal to the millionth part of a grain of sand,—to planets and suns, and systems more extended and magnificent than the telescope, or even the imagination of man can reach, is the workmanship of One Almighty Artist, who sees all its parts, and its movements, infinitely better than any human being can discern the working of the simplest tool that he takes in his hand. The workmanship, too, is here perfect at once ; the law of every body is not only implanted in itself, but
is the constituent principle of its existence; and, therefore, every appearance which is put on by nature, throughout all its variety, depends upon a cause, as inscrutable in its origin, but as certain and uniform in its operation, as the alternation of day and night, or the succession of the seasons.
Of natural appearances there are few that have been regarded with more superstitious apprehensions than those bodies which occasionally appear in the sky, luminous like the stars, but generally distinguished froin these by a tail, or train of fainter light, bearing some resemblance to a tuft or lock of hair. Of this the Latin name is coma, and in consequence these bodies are called comets, to distinguish them from the other luminaries, which, whether near or remote, apparently fixed or movable, have not this trainlike accompaniment.
Comets are one of the three classes into which astronomers divide those celestial bodies that adorn the sky during the night. The stars, which retain their relative positions with regard to each other, and are at so great distances from the earth, that no means or instruments hitherto invented can measure them, are one class, -and a class not apparently connected with our sun, or deriving light or heat from that luminary. The planets, which change their relative positions among the stars, and of which our earth is one, form the second class. They are solid bodies, and not luminous in themselves, but shine merely by reflecting the light of the sun. The masses of the planets, their magnitudes, and their motions, have been all determined with the greatest accuracy; and the place that any one of them will occupy at any proposed point of time, can be calculated with the greatest ease, by any one acquainted with practical astronomy. The planets are, in their motions, governed by one uniform law. [This law we have already stated, page 83. It is usually expressed in the following terms; “ The squares of the periodic times are to each other as the cubes of the mean distances.”] This is the grand law of planetary motion; and it is proved by the most careful, and, therefore, the most satisfactory observations, through a period of time that leaves not the least room for mistake or error. Indeed, the theory of this part of astronomy has been found to agree so well with the facts, that, as it is one of the most splendid, so it is one of the most perfect departments of science. The improvements of telescopes, and the watchfulness of observers, have added to the list of the planets a few small ones, which are not visible to the naked eyė; but from the time (about the beginning of the seventeenth century) that Kepler* deduced the law of the planetary motions from the observations made on the planet Mars, that law has remained unshaken and undoubted.
* Those who wish to appreciate the great and successful labors of that illustrious man, may consult Dr. Robert Small's work on Kepler's discoveries, published in 1804,