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396. The amplitude of a body is an arc of the horizon, intercepted between the east or west point, and a vertical circle passing through the body.*

397. The declination of a body is its distance from the equinoctial, measured by the arc of the meridian passing through it, which is intercepted between the body and the equinoctial.

398. The latitude of a body is its distance from the ecliptic, measured by the arc of a circle of longitude passing through it, which is intercepted between the body and the ecliptic.

399. The altitude of a body is its distance above the horizon, measured by the arc of a vertical circle passing through the body, which is intercepted between the body and the

true horizon.

400. The dip, or depression of the horizon, is the angle of depression of the visible horizon, in consequence of the eye of the observer being situated above the surface of the earth.

401. The observed altitude is the altitude indicated by the instrument; the apparent altitude is the result, after correcting the observed altitude for the error of the instrument and the dip; and the true altitude is the result, after correcting the apparent altitude for refraction and parallax. The meridian altitude of a body is its altitude when on the meridian. When a body is on the meridian, it is said to culminate; and its culmination is said to be upper or lower, according as it is then in its highest or lowest position.

402. The polar distance or codeclination of a body is its distance from the pole of the equinoctial, measured by the arc of a meridian, intercepted between the body and the pole.

403. The zenith distance or coaltitude of a body is its distance from the zenith, measured by the arc of a vertical circle, intercepted between the body and the zenith.

404. The obliquity of the ecliptic is the inclination of the ecliptic to the equator. This inclination is nearly 23° 28'.

*Amplitudes may be named also according to the quadrants in which they lie, as the azimuths are named,

405. The horary angle of a body at any instant is an angle at the pole of the equator, contained by the meridian of the body and the meridian of the place of observation.

This angle measures the time between the instant of observation and the instant of the body's passage over the meridian of the observer.

406. The oblique ascension of a heavenly body is an arc of the equinoctial, intercepted between the vernal equinox and the eastern or western point of the horizon respectively, when the body is rising or setting.

407. The ascensional difference is the difference between the right and oblique ascension.

This difference, in reference to the sun, is the time he rises or sets before or after six o'clock.

408. The rising or setting of a body is the time when its centre is apparently in the horizon when rising or setting.

409. The diurnal arc of any body is that portion of its parallel of declination that is situated above the horizon, and its nocturnal arc that portion of the same parallel which is below the horizon.

The semidiurnal and seminocturnal arcs are the halves of the preceding. The diurnal arc, reckoned at the rate of 15° to 1 hour, will express the interval of continuance of a body above the horizon, for a star in sidereal time, for the sun in solar time, for the moon in lunar time, and for a planet in planetary time (420.) There are also similar planetary arcs.

410. The precession of the equinoxes is a small motion of the equinoxes towards the west.*

411. A tropical year is the time in which the sun moves from the vernal equinox to that point again.

412. A sidereal year is the time in which the sun moves from a fixed star to the same star again; or the time in which it performs an absolute revolution.

413. An anomalistic year is the time in which the sun moves from any point in its orbit to the same point again.†

* This retrograde motion is about 1° in 72 years, or 50"-2 annually; and in consequence of it, the sun returns to the vernal equinox sooner than it would do were this point at rest; and hence the origin of the term. The tropical year, in consequence of the precession of the equinoxes, is shorter than the sidereal year, by the time the sun takes to move

414. Apparent time is that which depends on the position of the sun, and is also called solar time. This is the time shown by a sun-dial, the days of which are unequal.

415. Mean time is the time shown by a well-regulated clock, the days of which are equal.

416. An apparent solar day is the time between two successive transits of the sun's centre over the meridian, and is of variable length.*

417. A mean solar day is a constant interval of time, and is the mean of all the apparent solar days in a year; or it is what an apparent solar day would be were the sun's motion referred to the equinoctial uniform.

418. The equation of time is the difference between mean and apparent time.

It is just the difference between the time shown by a regulated time-piece and a sun-dial; at mean noon, it is the difference between 12 o'clock mean time, and the time of the sun's passing the meridian.

419. A sidereal day is the interval between two successive transits of the same star over the meridian.

This interval is just the time in which the earth performs an absolute rotation on its axis; and as this motion is uniform, the sidereal day is always of the same length.

The sidereal day begins when the vernal equinox, that is, the first point of Aries, arrives at the meridian; and its length is 23h 56m 4s-09 in mean solar time, or 24 sidereal hours.

A meridian of the earth returns to the same star in a shorter interval than it does to the sun; the difference, expressed in mean time, is called the retardation of mean on sidereal time; and, when expressed in sidereal time, it is called the acceleration of sidereal on mean time.†

over 50"-2, or 20m 1989. The length of the former is 365d 5h 48m 5186, and that of the latter is 365d 6h 9m 11s-5. The length of the anomalistic year is 365d 6h 14m 2s, which is longer than the other years, as the earth's elliptic orbit has a very slow direct revolution in its own plane.

* In consequence of the obliquity of the ecliptic, and the sun's unequal motion in its orbit, its motion referred to the equinoctial is not uniform, and consequently the intervals between its successive transits are variable.

+ The retardation for 24 hours of mean time is sidereal hours 23h 56m 4s-0906 of mean time.

= 3m 55s 9094, or 24 The acceleration for

420. Generally, the interval of time between the departure of a given meridian from a celestial body, and its return to that body, is called a day in reference to the body. If the body is a star, the interval is called a sidereal day; if the sun, a solar day; if the moon, a lunar day; each day consisting of 24 hours, the hours for these days being of course of different magnitudes. Were the moon supposed to move with its mean motion, the day in reference to the mean moon might be called the mean lunar day. The sidereal day is the shortest, the solar is next in regard to length, and the lunar is the longest; there may similarly be planetary days, as a martial day. The arc described by the meridian of a place, from any given time till the culmination of a body, may be named in reference to that body; for a star, it may be called the horary sidereal arc; for the sun, the horary solar arc; for the moon, the horary lunar arc; and for a planet, the horary planetary arc.

The astronomical day begins at noon, and is reckoned till next noon; and it is thus twelve hours later than the civil day.

421. As the moon's right ascension increases at a greater rate than that of the sun, there is a retardation of mean lunar on mean solar time; just as there is an acceleration of sidereal on solar time.

An equation of time may also be said to exist between apparent and mean lunar time.

422. The refraction of the atmosphere causes the altitude of a celestial body to appear greater than it would be were there no atmosphere; the increase of altitude from this cause is the refraction of the body (see art. 436.)

When the body is in the horizon, its refraction is greatest;

24 hours of sidereal time is 3m 568-5554, or 24 hours of mean solar time are = 24h 3m 568-5554 of sidereal time. These equivalents are obtained from the fact that the sun's mean increase of right ascension in a mean solar day is 59′ 8′′-3, or 3m 55s-9 of mean time; so that a meridian of the earth moves over 360° in a sidereal day and 360° 59' 8"-3 in a mean solar day; the former motion, which is just the time of the earth's rotation on its axis, is performed in 24 sidereal hours, and the latter in 24h 3m 56s-5554 of sidereal time; or the former is performed in 23h 56m 4s-09 mean time, and the latter in 24 hours of mean

and when in the zenith, it is nothing; at other altitudes, the refraction is intermediate.

423. The parallax of a celestial body is the quantity by which its altitude, when seen from the surface of the earth, is diminished, compared with its altitude seen from the earth's centre.

The parallax, like the refraction, is greatest when the body is in the horizon, and is nothing when it is in the zenith.

When the body is in the horizon, its parallax is called horizontal parallax; its parallax at any altitude is called its parallax in altitude; and its parallax, supposed to be subtended by the greatest or equatorial radius of the earth, is called its equatorial parallax.

424. Most of these definitions will be readily understood from the two following diagrams :


Let PQM be a meridian passing through the pole of the ecliptic; MQ the equator, N and S its north and south poles; CC' the ecliptic, P and p its north and south poles. Then A is the first point of Aries; C that of Cancer, and C' that of Capricornus; and angle CAQ, measured by CQ, M is the obliquity of the ecliptic. The parallels of declination CB, C'T, are the tropical circles, the former being the tropic of Cancer, and the latter that of Capricorn; and PR, Ep, are the polar circles, the former being the arctic, and the latter the antarctic circle. Also, if POp and NOS are respectively a circle of celestial longitude, and a meridian passing through any celestial body O, then AL is its longitude, OL its latitude, AH its right ascension, and OH its declination. The meridian NQSM is the solstitial colure, and NAS the equinoctial colure.


Again, let RH be the horizon, Z and N its poles, the former being the zenith and H the south point; EQ the equator, P and p its north and south poles; also, let B be any celestial body, and ZBN a vertical circle through it; then BL is its altitude, HL its azimuth, and if O is its








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