place is the place where the body actually is at any time.

Illustrations of the above articles.

1. Let APQBH, (see fig., page 239,) be the elliptical orbit of a planet, S the Sun in one of the foci; the planet in revolving round that luminary in the direction of the letters APRQ, &c. cannot be always at the same distance from the focus S, but will be farthest from it at the extremity A of the greater axis, and nearest to it when in B. The point A is named the higher apsis, or the aphelion; and the point B the lower apsis, or perihelion; these two points vary, and their motion in a century is called the secular motion. The distance between the centre C and the sun, or focus S, is the eccentricity of the orbit. The greater axis AB is the line of the apsides. The straight line SQ, drawn from the extremity of the lesser axis QH to the sun, is the mean distance of the planet from the sun.

The mean distance added to the eccentricity is equal to the aphelion distance SA. And the mean distance minus the eccentricity is equal to the perihelion distance SB.

2. A planet does not proceed in its orbit with an equal motion; but in such a manner that the Radius Vector de-scribes an area proportional to the time: for instance, suppose a planet to be in A, when in a certain time it arrives at P, the space, or area, ASPA is equal to the space, or area, PSQP, described in the same time from P.

3. If the angular motion of the planet about the sun were uniform, the angle described by the planet in any interval of time, after leaving the aphelion, might be found by simple proportion, from knowing the periodic time in which it describes 3600; but as the angular motion is slower near aphe lion, and faster near perihelion, to preserve the equable de scription of areas, the true place will be behind the mean place in going from aphelion to perihelion; and from peri helion to aphelion, the true place will be before the mean place. For instance, suppose P be the true place of planet at the end of a certain time after leaving the aphelion A; then, its mean place would be in some part of the orbit between P and B. Now, let R be the mean place of the planet, when P is its true place; then the angle ASR is the mean anomaly; the angle ASP, the true anomaly; and the angle PSR, the difference between the mean anomaly and the true anomaly, is the equation of the centre.

a

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Or, if a planet is supposed to move in a circle, in the centre of which is the sun, the portion RO of the circle bears the same ratio to the whole circumference, that the time since the planet passed its aphelion does to the time of its whole revolution; the arc RO is termed the mean anomaly.

Again, if the elliptical orbit of a planet be so divided that the area ASP shall have the same ratio to the area of the whole ellipse AQBH, which the time since the planet passed its aphelion has to its whole period, then is the angle ASP the measure of the planet's distance from the aphelion, at the time the planet is in P. This angle is also the true anomaly; and the difference between the mean anomaly and the true anomaly, is the equation of the centre, as before.

4. The arc AD of the circle AGBK intercepted between the aphelion A, and the point D, determined by the perpendicular DPE to the line of the apsides, drawn through the true place P of the planet, is called the eccentric anomaly, or of the centre. Or, the angle ACD at the centre of the circle, is usually called the eccentric anomaly.

5. Equations, in Astronomy, are corrections which are applied to the mean place of a body, in order to get its true place; and argument is also a term sometimes used to denote a quantity upon which another quantity or equation depends; or, it is the arc, or angle, by means of which another arc may be found, bearing some proportion to the first: thus, the argument gument of the equation of the centre, is the distance of a planet from the aphelion or apogee, because it is upon that the equation of the centre depends.

15. The Nodes are the two opposite points where the orbit of a primary planet intersects the plane of the ecliptic, or where the orbit of a secondary planet cuts that of its primary. The straight line joining these two points is called the line of the nodes.

Ascending node is that point where the planet ascends from the south to the north side of the ecliptic; liptic: and and the opposite point where the planet descends from the north to the south side of the ecliptic, is called the descending node. The ascending node is denoted by the character U, and the descending node by. The inclinations of the planes of the orbits of all the planets, except Pallas, to the plane of the Earth's orbit are small.

16. Aspect of the stars or planets, is their situation with respect to each other. There are five aspects, viz. o Conjunction, when they have the same longitude, or are in the same sign and degree; * Sextile, when they are two signs, or a sixth part of a circle distant; Quartile, when they are three signs, or a fourth part of a circle, from each other; A Trine, when they are four signs, or a third part of a circle, from each other, and 8 Opposition, when they are six signs, or half a circle, from each other.

The conjunction and opposition, particularly of the moon, are called the Syzegies; and the quartile aspect the Quadrature.

Or, the five principal aspects of the planets, with their characters and distances, are as follows :

These intervals are reckoned according to the longitudes of the planets; so that the aspects are the same, whether the planet be in the ecliptic or out of it.

These terms were introduced by the ancients for the purposes of Astrology, but they are still retained in some cases in astronomical works; in the former case, they are more numerous; but it would be improper to enumerate such foolish distinctions in the present day.

17. An inferior planet is said to be in inferior conjunction, when it comes between the Sun and the Earth. In superior conjunction, the Sun is between the Earth and planet. And a superior planet is in opposition, when the Earth is between the Sun and planet.

18. The apparent motion of the planets is either Direct, Stationary, or Retrograde. The motion of a planet is said to be direct when it appears to a spectator on the earth to perform its motion from west to east, or according to the order of the signs. A planet is said to be stationary when, to an observer on the earth, it appears to have no motion, or, which amounts to the same thing, when it appears in the same point of the heavens for several days. And retrograde is an apparent motion of the planets, by which they seem to move backward in the ecliptic, or contrary to the order of the signs. These terms shall be more fully illustrated in a subse quent part of the work.

19. The 12th part of the sun or moon's apparent diameter is called a digit. Disc is the face of the sun or moon, such as they appear to a spectator on the earth; for though the sun and moon be really spherical bodies, they appear to be circular planes

20. The geocentric place of a planet means its place as seen from the Earth; or it is a point in the ecliptic, to which a planet, seen from the Earth, is referred: and its heliocentric place as seen from the Sun.

Geocentric is said of a planet or its orbit, to denote its having the Earth for its centre. The Moon alone is properly geocentric, and yet the motions of all the planets may be considered in respect to the Earth, or as they would appear from the Earth's centre, as geocentric, and thence called their geocentric motions. The heliocentric motions of the planets are their motions as seen by a spectator situated in the Sun, which is always direct, or in the order of the signs.

21. Geocentric latitudes and longitudes of the planets, are their latitudes and longitudes as seen from the earth.

22. Heliocentric latitudes and longitudes of the planets, are their latitudes and longitudes, as they would appear to a spectator situated in the Sun.

23. Occultation is the obscuration or hiding from our sight any star or planet, by the interposition of the body of the moon, or of some other planet.

24. Transit is the apparent passage of any planet over the face of the sun, or over the face of another planet. Mercury and Venus, in their transits over the sun, appear like dark specks.

25. Aberration is an apparent motion of the celestial bodies, occasioned by the earth's annual motion in its orbit, combined with the progressive motion of light.

26. The Elongation of a planet is its angular distance from the sun, with respect to the earth, or it is the angle formed by two lines drawn from the earth, the one to the sun, and the other to the planet.

27. Eclipse is a privation of the light of one of the luminaries, by the interposition of some opaque body, either between it and the observer, or between it and the sun.

To the first class belong solar eclipses, and occultations of the fixed stars by the moon or planets, and to the second lunar eclipses, and of the other satellites, particularly those of Jupiter.

28. Eclipse of the Moon is a privation of the light of the moon, occasioned by an interposition of the earth directly between the sun and moon, and so intercepting the sun's rays that they cannot arrive at the moon to illuminate her.

Or, the obscuration of the moon may be considered as a section of the earth's conical shadow, by the moon passing through some part of it.