affected, an inextricable confusion of changes of position, apparent and real, results, which involves the observer in obscurity and difficulty, if his purpose be to ascertain the actual motions and relative distances and arrangement of the objects around him.

262. Peculiar difficulties presented by the solar system. -All these difficulties are presented in their most aggravated form to the observer, who, being placed upon the earth, desires to ascertain the motions and positions of the bodies composing the solar system. These bodies all move nearly in one plane, and from that plane the observer never departs: he is, therefore, deprived altogether of the facilities and advantages which a bird's eye view of the system would afford. He is like the commander who can find no station from which to view the evolutions of the army against which he has to contend, except one upon a dead level with it, but with this great addition to his embarrassment, that his own station is itself subject to various changes of position, of which he is altogether unconscious, and which he can only ascertain by the apparent changes of position which they produce among the objects of his observation and inquiry.

The difficulties arising out of these circumstances obstructed for

ages the progress of astronomical science. The persuasion so universally entertained of the absolute immobility of the earth, was not only a vast error itself, but the cause of numerous other errors. It misled inquirers by compelling them to ascribe motions to bodies which are stationary, and to ascribe to bodies not stationary, motions altogether different from those with which they are really affected.

263. General arrangement of bodies composing the solar system.—The solar system is an assemblage of great bodies, globular in their form, and analogous in many respects to the earth. Like the earth, they revolve round the sun as a common centre, in orbits which do not differ much from circles: all these orbits are very nearly, though not exactly, in the same plane with the annual orbit of the earth, and the orbital motions all take place in the same direction as that of the earth.

Several of these bodies are the centres of secondary systems, another order of smaller globes revolving round them respectively in the same manner, and according to the same dynamical laws as govern their own motion round the sun.

264. Planets primary and secondary. This assemblage of globes which thus revolve round the sun as a common centre, of which the earth itself is one, are called PLANETS; and the secondary globes, which revolve round several of them, are called SECONDARY PLANETS, SATELLITES, or MOONS, one of them being our

moon, which revolves round the earth as the earth itself revolves round the sun.

265. Primary carry with them the secondary round the sun. — The primary planets which are thus attended by satellites, carry the satellites with them in their orbital course; the common orbital motion, thus shared by the primary planet with its secondaries, not preventing the harmonious motion of the secondaries round the primary as a common centre.

266. Planetary motions to be first regarded as circular, uniform, and in a common plane. It will be conducive to the more easy and clear comprehension of the phenomena to consider, in the first instance, the planets as moving round the sun as their common centre in exactly the same plane, in exactly circular orbits, and with motions exactly uniform. None of these suppositions correspond precisely with their actual motions; but they represent them so very nearly, that nothing short of very precise means of observation and measurement is capable of detecting their departure from them. The motions of the system thus understood will form a first and very close approximation to the truth. The modifications to which the conclusions thus established must be submitted, so as to allow for the departures of the several planets from the plane of the ecliptic, of their orbits from exact circles, and of their motions from perfect uniformity, will be easily introduced and comprehended. But even these will supply only a second approximation. Further investigation will show series after series of corrections, more and more minute in their quantities, and requiring longer and longer periods of time to manifest the effects to which they are directed.

267. Inferior and superior planets.-The concentric orbits of the planets then are included one within another, augmenting successively in their distances from the centre, so as in general to leave a great space between orbit and orbit.

Those planets which are included within the orbit of the earth are called INFERIOR PLANETS, and all the others are called SUPE

RIOR PLANETS.

268. Periods. The PERIODIC TIME of a planet is the interval between two successive returns to the same point of its orbit, or, in short, the time it takes to make a complete revolution round the sun. It is found by observation, as might be naturally expected, that the periodic time increases with the orbit, being much longer for the more distant planets; but, as will appear hereafter, this increase of the periodic time is not in the same proportion as the increase of the orbit.

269. Synodic motion. -The motion of a planet considered merely in relation to that of the earth, without reference to its actual position in its orbit, is called its SYNODIC MOTION.

270. Geocentric and heliocentric motions. -The position and motion of a planet as they appear to an observer on the earth are called GEOCENTRIC *; and as they would appear if the observer were transferred to the sun, are called HELIOCENTRIC.

271. Heliocentric motion deducible from geocentric.— Although the apparent motions cannot be directly observed from the sun as a station, it is a simple problem of elementary geometry to deduce them from the geocentric motions, combined with the relative distances of the earth and planet from the sun; so that we are in a condition to state with perfect clearness, precision, and certainty, all the phenomena which the motions of the planetary system would present, if, instead of being seen from the movable station of the earth, they were witnessed from the fixed central station of the

sun.

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272. Elongation. The geocentric position of a planet in relation to the sun, or the angle formed by lines drawn from the earth to the sun and planet, is called the ELONGATION of the planet, and is EAST or WEST, according as the planet is at the one side or the other of the sun.

273. Conjunction.-When the elongation of a planet is nothing, it is said to be in CONJUNCTION, being then in the same direction as the sun when seen from the earth.

274. Opposition.

When the elongation of a planet is 180°, it is said to be in OPPOSITION, being then in the quarter of the heavens directly opposite to the sun.

It is evident that a planet which is in conjunction, passes the meridian at or very near noon, and is therefore above the horizon during the day, and below it during the night.

On the other hand, a planet which is in opposition, passes the meridian at or very near midnight, and therefore is above the horizon during the night, and below it during the day.

275. Quadrature.

its elongation is 90°.

A planet is said to be in quadrature when

In this position it passes the meridian at about six o'clock in the morning, when it has western quadrature, and six o'clock in the evening, when it has eastern quadrature. It is, therefore, above the horizon on the eastern side of the firmament during the latter part of the night in the former case, and on the western side during the first part of the night in the latter case. It is a morning star in the one case, and an evening star in the other.

276. Synodic period. The interval which elapses between two similar elongations of a planet is called the SYNODIC PERIOD of

From the Greek words yn (gē) and λtos (helios), signifying the earth and the sun.

the planet. Thus, the interval between two successive oppositions or two successive eastern or western quadraturés, is the synodic period.

277. Inferior and superior conjunction. —A superior planet can never be in conjunction except when it is placed on the side of the sun opposite to the earth, so that a line drawn from the earth through the sun would, if continued beyond the sun, be directed to the planet. An inferior planet is, however, also in conjunction when it crosses the line drawn from the earth to the sun, between the earth and sun. The former is distinguished as SUPERIOR and the latter as INFERIOR conjunction.

As inferior conjunction necessarily supposes the planet to be nearer to the sun than the earth, and opposition supposes it to be more distant, it follows that inferior planets alone can be in inferior conjunction, and superior planets alone in opposition.

278. Direct and retrograde motion. When a planet appears to move in the direction in which the sun appears to move, its apparent motion is said to be DIRECT; and when it appears to move in the contrary direction, it is said to be RETROGRADE.

The apparent motion of an inferior planet is always direct, except within a certain elongation east and west of inferior conjunction, when it is retrograde.

279. Conditions under which a planet is visible in the absence of the sun. — -It is evident that to be visible in the absence of the sun, a celestial object must be so far elongated from that luminary as to be above the horizon before the commencement of the morning twilight, or after the end of the evening twilight. One or two of the planets have, nevertheless, an apparent magnitude so considerable, and a lustre so intense, that they are sometimes seen with the naked eye, even before sunset or after sunrise, and may, in general, be seen with a telescope when the sun has a considerable altitude. In most cases, however, to be visible without a telescope, a planet must have an elongation greater than 30° to 35°.

As an instance of the visibility of a planet to the naked eye during the day time, it may be mentioned that Venus has frequently been seen at Greenwich, between one and two o'clock in the afternoon, when the planet was near the meridian, and under favourable circumstances with a brilliant sky.

280. Evening and morning star.-Since the inferior planets can never attain so great an elongation as 90°, they must always pass the meridian at an interval considerably less than six hours before or after the sun. If they have eastern elongation they pass the meridian in the afternoon, and are visible above the horizon after sunset, and are then called EVENING STARS. If they have

western elongation they pass the meridian in the forenoon, and are visible above the eastern horizon before sunrise, and are then called

MORNING STARS.

281. Appearance of superior planets at various elongations.—A superior planet, having every degree of elongation east and west of the sun from 0 to 180°, passes the meridian during its synodic period at all hours of the day and night. Between conjunction and quadrature, its elongation east or west of the sun being less than ço°, it passes the meridian earlier than six o'clock in the afternoon in the former case, and later than six o'clock in the forenoon in the latter case, being, like an inferior planet, an evening star in the former, and a morning star in the latter case.

At eastern quadrature it passes the meridian at six in the evening, and at western quadrature at six in the morning, appearing still as an evening star in the former, and as a morning star in the latter case.

Between the eastern quadrature and opposition, the elongation being more than 90° east of the sun, the planet must pass the meridian between six o'clock in the evening and midnight, and is therefore visible from sunset until some hours before sunrise. Between western quadrature and opposition, the elongation being more than 90° west of the sun, the planet must pass the meridian at some time between midnight and six o'clock in the morning, and it is therefore visible from some hours after sunset until sunrise.

At opposition the planet passes the meridian at midnight, and is therefore visible from sunset to sunrise.

282. Phases of a planet. While a planet revolves, that hemisphere which is presented to the sun is illuminated, and the other dark. But since the same hemisphere is not presented generally to the earth, it follows that the visible hemisphere of the planet will consist of a part of the dark and a part of the enlightened hemisphere, and, consequently, the planet will exhibit PHASES, the varieties and limits of which will depend upon the relative directions of the lines drawn from the earth and sun to the planet. It is evident that the section of the planet at right angles to a line drawn from the sun to its centre is the base of its enlightened hemisphere, while the section at right angles to a line drawn from the earth to its centre, is the base of its visible hemisphere. The less the angle included between these lines is, the greater will be the portion of the visible hemisphere which is enlightened.

283. Perihelion, aphelion, mean distance.—That point of the elliptic orbit at which a planet is nearest to the sun is called PERIHELION, and that point at which it is most remote is called

APHELION.