sun, moves just so much faster, as to make the space passed over by the revolving radius, in a day, for instance, always the same.

3. If we take the times in which any two planets complete their revolution, and multiply each by itself; and then the ther mean distances from the sun, a d multiply each by itself twice; the two first results will have the same proportion to each other, as the two last; in other words, the squares of the times are as the cubes of the distances.

There are several particulars respecting a planet, given in the following tables, which being known, we are able to calculate its position or place at any time. These are termed the elements of a planet's orbit, and are as follows.

1. The time employed in making a complete circuit of the heavens, which is called the sidereal revolution.

2. The average distance of the planet from the sun, which is half the greatest diameter of the elliptical orbit. This is called the mean distance. 3. The eccentricity, or the proportion which the distance from the focus to the centre bears to the mean distance. This is subject to a slight change, the amount of which, for a century, is put down under the title of secular variation.

4. The position or mean longitude of the planet, for any given time, as the beginning of the century. This longitude is reckoned from the vernal equinox, or the 1st of Aries, as longitude on the earth is reckoned from any assumed meridian, as that of Greenwich. But celestial longitude is counted on the ecliptic, and only in one direction, namely, from west to east, in the direction of the planetary motions.

5. The position of the point of nearest approach of the planet to the sun, is called the perihelion (from two Greek words, which signify about the sun). This point is referred, also, to the 1st of Aries, and its position is determined, like that of the planet itself, by its distance from the vernal equinox, reckoned on the ecliptic. This distance is denominated the longitude of the perihelion. As the perihelion has a slow motion, its position is given for a particular time, or epoch, and also its change of position in a century, termed the secular variation.

6. The orbits of the planets not being coincident with, or parallel to the ecliptic, their oblique position with respect to the ecliptic, is of great importance in calculating their places. This is called the inclination of the orbit. Like the other elements, it is subject to a slight change; hence the inclination is given for a particular epoch, together with the alteration in a century.

7. The two points in which the orbit of a planet cuts the ecliptic are called its nodes. That node, through which the planet passes in coming from the south to the north, is distinguished as the ascending node. The position of this point is determined, like that of other points, by its distance

from Aries. It is called the longitude of the ascending node. The node, in like manner, has a slight motion; accordingly its position is given for à particular epoch, together with the sidereal and secular variation, or change with respect to a star in a century.

(2.) Mean Distance, or Half the Major Axis of the Orbit.

(3.) Ratio of the Eccentricity to the Mean distance, at the Beginning of 1801, with the Secular Variation. The Sign indicates a

(4.) Mean Longitude, for the Minute which separates the 31st of December, 1800, from the 1st of January, 1801, Mean Time at Paris.

(5.) Mean Longitude of the Perihelion, for the same Epoch, with the Sidereal and Secular Variation. The Sign-indicates a Retrograde Motion.

(6.) Inclination of the Orbit to the Ecliptic, at the Beginning of 1801, with the Secular Variation of the Inclination to the true Ecliptic.

(7.) Longitude of the Ascending Node, at the Beginning of 1801, with

(3.) Ratio of the Eccentricity to the Mean Distance.

(5.) Longitude of the Perihelion at the same Epoch.

(7.) Longitude of the Ascending Node, at the Beginning of 1810.

XII. SYNODIC REVOLUTIONS OF THE PLANETS.

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 3o 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,