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 65 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 inost 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, accordirg 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,

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Mean Duration
of the Synodic

Mercury, Venus, Mars, Jupiter, Saturn, Uranus,


Angular Distances be

Mean Duration tween the Planet and the Mean Arc of

of the RetroSun, at the instant of Retrogradation. being stationary.

grade Motion.

is oo
13 30

28 48

16 12

42 136 48

16 12

73 115 12

9 54

121 108 54

6 18

139 103 30

3 36



[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 is 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 systerns 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 workınanship, too, is here perfect at once; the law of every body is not only irnplanted 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 from 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 form the second class. They are solid bodies, and not luminous in themselves, but shine merely by reflectiug the light of the

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 uniforin 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 roon 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 eye; 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 labours of that illustrious man, may eonsult Dr. Robert Smsll's work on Kepler's discoveries, published in 1804.

In the early ages, the planets were held to have certain influences upon individuals and nations. The comets, which are more singular in their form, and more varied in the times of their appearance, were still better adapted for superstitious purposes; and accordingly we find that their visits have been attempted to be connected with the great, more especially the calamitous, events of nations. They were favorite themes with the poets ; and they are thus introduced by Shakspeare, in the lamentation which the Duke of Bedford makes over the bier of Henry V.

• Comets, importing change of times and states,
Brandish your crystal tresses in the sky;
And with them scourge the bad revolting stars,

That have consented unto Henry's death.' Milton, too, though he lived after the days of Galileo and Kepler ; though he was imbued with all the learning and philosophy of his time; and though he shows that he was well acquainted with the labors of those philosophers, does not scruple to call in the aid of the malign power of comets, in order to heighten his picture of Satan when preparing for combat.

i On the other side,
Incensed with indignation, Satan stood,
Unterrified, and like a comet burned,
That fires the length of Ophiuchus huge
I'the Arctic sky, and from its horrid hair

Shakes pestilence and war.' When such a man alludes to the subject, even for the purpose of illustration, it may well be supposed that the visits of comets were regarded with great apprehensions by the illiterate and unphilosophical.

The appearance of a comet is, however, no more a prodigy, and has no more influence upon the fate of men or of nations, than the appearance of the moon, or of a leaf upon a deciduous tree in spring. Indeed it has not nearly so much; for the moon, by causing tides, affects the atmosphere and the weather, and must thence, to some extent or other, affect the human body; and the leaf is an indication of the season ; but the comets are so distant, and either their motions are so rapid, or their substance is so rare, that none of them have been found to have any material action upon such of the planets as they have come near, although the planets have had a considerable influence upon them.

What the comets are, or what purposes they serve in the economy of creation, we do not know; and they are subjects upon which conjecture would be quite useless. As far as observation has gone - and beyond that one word need not be said — they are subject to the same laws as the planets, revolving about the sun in orbits or paths, with this difference, that they are much more eccentric, or differ much more from circles, than the

orbits of the planets; and thus, while they approach much nearer to the sun at one time of their revolutions, they recede correspondingly farther from it at another. The time since men had rational opinions on the subject has, however, been too short for verifying, by observation, the theory as applicable to the whole, or even the greater number of these bodies that have from time to time made their appearance.

Tycho Brahe, who was an astronomer of Nature's own making, who could not be driven from the pursuit of it by all the influence of his guardian and preceptor, and to whose twenty-one years of close and regular observation at Uranibourg, in the little Danish isle of Huena, the science is more indebted than to the observations of any other individual, was the first who expressed a decidedly rational opinion on the subject of comets. Finding, by careful observation, that the comet of 1577 had no diurnal parallax, which he could detect, – that is, that its place, when viewed from the surface of the earth, was not different from what it would have been if viewed from the centre, - he properly concluded that its distance from the earth must be greater than that of the moon, in which this parallax was apparent to him. This was one step; and it was an important one; it removed comets to such a distance from the earth, that their use could not well be supposed to be for it, or their influence upon it very great.

Kepler, a pupil every way worthy of his illustrious inaster Brahe, turned the observations on this comet to account in determining (or, at all events guessing at) the motions and paths of comets, just as he did the observations of the planets to the determining of the laws of their motions. His first conjecfure was that the comets moved in straight lines; but as that did not agree with the observations, he again concluded that they were parabolic curves, having the sun near the vertex, and running indefinitely into the regions of space at both extremities. Though sixteen comets had been mentioned in history previous to the time (about 1636) when Kepler attempted to determine the form of their paths, there was nothing to fix their identity, so as to lead him to conclude that any one was the reappearance of a former; and thus there was nothing to suggest to him the necessity of a comet’s moving in an orbit, so as to return and re-appear at a future period. To do that was reserved for one of the most industrious as well as sagacious of astronomers, Dr. Halley, the contemporary and friend of Newton. The discovery of the law of gravitation by the latter, its being a confirmation of the doctrine of Kepler, and its being found constant and universal, in every situation, whether on the earth or in the solar system, in which it could be traced, gave to the physical sciences generally, and to that of astronomy in particular, a generalization and harmony which had not previously been known. The general law of the motion of bodies in free space, as well as his own particular observations on the comet of 1680, led Newton to conclude that the orbits of the comets must, like those of the planets, be ellipses, having the sun in one

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