The reader may upon this subject consult also Bartholinus De Cometis, 4to.Copenhagen, 1665; Hooke's Lectures and Collections, 4to. 1678; Cometa,-Figures, p. 2, 3; Heinsius, Ueber den Cometen, 4to. Petersb. 1743; Dionis du Séjour, Essai sur les Cometes, Paris, 1775; Deguignes, S. E. X. 1785. App. 39; Young's Nat. Phil.Vol. I. p. 513.

CHAP. XVI.

SYNOPSIS OF THE PRINCIPAL ELEMENTS OF ASTRONOMY, DEDUCED FROM M. LA PLACE'S EXPOSITION DU SYSTEME

DU MONDE.

THE following article is drawn from the third edition of M. La Place's very excellent Exposition (1808) in which the author has given the elements of the planets in a more correct manner than in either of the preceding editions; and wherein he has revised and amended all his former calculations by more recent and exact observations.

The arrangement of the present memoir is somewhat new; but many persons have frequently found the want of a manual of this kind, where all the different facts, relative to astronomy, might be brought under their respective heads, without the necessity of turning to a variety of works for information. Much time is often lost in a research of that kind, which it is the object of the present abstract to prevent.

In the original work, the author has universally adopted the decimal division of the day, and of the quadrant. This method is here preserved in the Tables of the Elements of the Planets; but, in subsequent parts, the common sexagesimal notation is adopted, as being more easily understood in this country..

Some other facts, not mentioned by M. La Place, are inserted in this tract, in order to enlarge the view of the subject: but these passages are always kept separate, by being inclosed within brackets.

The Sun.

"

The Sun, which is the source of light and heat to our system, is the most considerable of all the heavenly bodies, and governs all the planetary motions.

Its diameter is 111:454 times the mean diameter of the earth; whence its volume is 1384472 times greater than that of the earth; but its mass is only 337086 times greater. Whence we conclude that its density is, or about that of our globe,...

It is surrounded by an atmosphere; and it is oftentimes covered with spots. Some of these spots have been observed so large as to exceed the earth four or five times in magnitude.

The observation of these spots shows that the Sun moves on its axis, which is nearly perpendicular to the ecliptic; and the duration of an entire sidereal rotation of the sun is about 251 days.

Whence we conclude that the sun is flattened at the poles. The solar equator is inclined 7° 30' to the plane of the ecliptic.: A body, which weighs one pound at the surface of the earth, would, if removed to the surface of the sun, weigh 27.933 pounds. And bodies would fall there with a velocity of 334-65 feet in the first second of time.

The sun, together with the planets, moves round the common centre of gravity of the system; which centre is nearly in the centre of the sun.

This motion changes into epicycloids the ellipses of the planets and comets, which revolve round the sun.

The sun appears to have a particular motion, which carries our system towards the constellation of Hercules.

The apparent diameter of the sun, as seen from the earth, undergoes a periodical variation. It is greatest when the earth is in its perihelion; at which time it is 32′ 35′′,6: and it is least when the earth is in its aphelion; at which time it is 31′ 31′′,0. Its mean apparent diameter is therefore 32′ 5′′,3..

His horizontal parallax is 83".

The greatest equation of his centre is 1° 55′ 27,7; which diminishes at the rate of 16",9 in a century.

The diurnal motion of the sun from east to west, and his annual

motion in the ecliptic, are optical deceptions; arising from the real

motion of the earth on its axis, and in its orbit..

The Planets.

The number of planets belonging to our system is eleven. Six of these have been known and recognised from time immemorial: namely, Mercury, Venus, the Earth, Mars, Jupiter and Saturn. But the remaining five, which are not visible to the naked eye, have lately been discovered by the help of the telescope and are therefore called telescopic planets: namely,

Uranus, discovered by Dr. Herschel, March 13, 1781.

Ceres

Pallas,

Juno, ...
Vesta,

M. Piazzi,.. January 1, 1801.

M. Olbers,... March 28, 1802.

M. Harding,.. Septem. 1, 1803.

M. Olbers,.. March 29, 1807.

All these planets revolve round the sun, as the centre of motion: and in performing their revolutions they follow the fundamental laws of the planetary motion so happily discovered by Kepler; and which have been fully confirmed by subsequent observations. These laws are,

I. The orbit of each planet is an ellipse; of which the sun occupies one of the foci.

The extremity of the major axis of this ellipse, nearest the sun, is called the perihelion; the opposite extremity of the same axis is called the aphelion. The line, which joins these two points, is called the line of the apsides. The radius vector is an imaginary line drawn from the centre of the sun to the centre of the planet, in any part of its orbit.

The velosity of a planet in its orbit is always greatest at its perihelion. This velosity diminishes as the radius vector increases; till the planet arrives at its aphelion, when its motion is the slowest. It then increases, in an inverse manner, till the planet arrives again at its perihelion.

JI. The areas, described about the sun by the radius vector of the planet, are proportional to the times employed in describing them.

These laws are sufficient for determining the motion of the planets round the sun; but it is necessary to know, for each of these planets, seven quantities; which are called the elements of their elliptical motion. The first five of these elements relate to the motion in an ellipse; the last two relate to the position of the orbit; since the planets do not all move in the same plane.

1. The duration of a sidereal revolution of the planet.

2. Half the major axis of the orbit ; or the mean distance of the planet from the sun.

3. The eccentricity of the orbit; whence we deduce, the greatest equation of the centre.

4. The mean longitude of the planet at a given epoch.

5. The longitude of the perihelion at a given epoch. 6. The longitude of the nodes at a given epoch.

7. The inclination of the orbit to the ecliptic.

The following Tables present all these elements for the first mo ment of the present century; namely, for that point of time at midnight which separates the 31st of December. 1800, and. the Ist of January 1801; mean time at Paris.-[The observatory at Paris is in north latitude 48° 50′ 14′′, and in longitude 9′ 21′′ east from Greenwich observatory.]

1. Duration of a Sidereal Revolution.

3. Ratio of the Eccentricity to half the Major Axis.

The examination of the first two tables here given will show us that the duration of the revolutions of the planets increases with their mean distance from the sun, Whence Kepler, discovered his third fundamental law; namely,

III. The squares of the times of the revolutions of the planets are to each other as the cubes of their mean distances.

The ellipses, which the planets describe, however, are not unalterable. Their major axes appear to be always the same; but their eccentricities, the positions of their perihelion and nodes, together with the inclination of their orbits to the ecliptic, seem to vary in a