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to designate, with precision their situations, imaginary circles have been considered as drawn in the heavens, most of which correspond to and are in the same plane with similar circles, supposed, for similar purposes, to be drawn on the surface of the Earth.
In order to facilitate the study of it, artificial representations of the heavens, similar to those of the surface of the Earth, have been made. Thus, a Celestial Atlas, composed of several maps, accompanies this work. Before, however, proceeding to explain its use, it is necessary to make the pupil acquainted with the imaginary circles alluded to above.
CIRCLES OF THE SPHERE.-The Axis of the Earth is an imaginary line, passing through its centre, north and south, about which its diurnal revolution is performed.
The Poles of the Earth are the extremities of its axis. The Axis of the Heavens is the axis of the Earth produced both ways to the concave surface of the heavens.
The Poles of the Heavens are the extremities of their axis. The Equator of the Earth is an imaginary great circle passing round the Earth, east and west, everywhere equally distant from the poles, and dividing it into northern and southern hemispheres.
The Equator of the Heavens, or Equinoctial, is the great circle formed on the concave surface of the heavens, by producing the plane of the Earth's equator.
A plane is that which has surface but not thickness. The plane of a circle is that imaginary superficies which is bounded by the circle.
The Rational Horizon is an imaginary great circle, whose plane, passing through the centre of the Earth, divides the heavens into two hemispheres, of which the upper one is called the visible hemisphere, and the lower one, the invisible hemisphere. It is the plane of this circle which deter-` mines the rising and setting of the heavenly bodies.
The Sensible or Apparent Horizon, is the circle which terminates our view, where the Earth and sky appear to meet.
To a person standing on a plain, this circle is but a few miles in diameter. If the eye be elevated five feet, the radius of the sensible horizon will be less than two miles and three quarters; if the eye be elevated six feet, it will be just three miles. The observer being always in the centre of the sensible horizon, it will move as he moves, and enlarge or contract, as his station is elevated or depress
What expedient has been devised for designating, with precision, the situations of the heavenly bodies? What is the axis of the Earth? What are the poles of the Earth? What is the axis of the heavens? What are the poles of the heavens? What is the equator of the Earth? What is the equator of the heavens or the equinoctial? What is a plane? What is the plane of a circle? What is the rational horizon? What is the sensible or apparent horizon? What is the diameter of this circle to a person standing on a plain? What will its radius be if the eye be elevated five feet? If it be cle vated six feet? On what does the place of its centre and its circumference depend?
The Poles of the Horizon are two points, of which the one is directly over head, and is called the Zenith; the other is directly under foot, and is called the Nadir.
Vertical Circles are circles drawn through the Zenith and Nadir of any place, cutting the horizon at right angles.
The Prime Vertical is that which passes through the east --and west points of the horizon.
The Ecliptic is the great circle which the Sun appears to describe annually among the stars. It crosses the Equinoctial, a little obliquely, in two opposite points which are called the Equinoxes. The Sun rises in one of these points on the 21st of March; this point is called the Vernal Equinox. It sets in the opposite point on the 23d of September; this point is called the Autumnal Equinox. One half of the ecliptic lies on the north side of the Equinoctial, the other half on the south side, making an angle with it of 2340. This angle is called the obliquity of the Ecliptic. The axis of the Ecliptic makes the same angle with the axis of the heavens; so that the poles of each are 234o apart.
This angle is perpetually decreasing. At the commencement of the Christian era, it was about 23° 45'. At the beginning of 1836, it was only 23° 27′ 38 show. ing an annual diminution of about half a second, or 45.70 in a hundred years. A time will arrive, however, when this angle, having reached its minimum, will again increase in the same ratio that it had before diminished, and thus it will continue to oscillate at long periods, between certain limits, which are said to be comprised within the space of 20° 42'.
The ecliptic, like every other circle contains 360°, and it is divided into 12 equal arcs of 30° each, called signs, which the ancients distinguished by particular hames. This division commences at the vernal equinox, and is continued eastwardly round to the same point again, in the following order: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricornus, Aquarius, Pisces. The Sun, commencing at the first degree of Aries, about the 21st of March, passes, at a mean rate,(through one sign every month.
The Zodiac is a zone or girdle, about 16 degrees in breadth, extending quite round the heavens, and including all the heavenly bodies within 8° on each side of the ecliptic. It includes, also, the orbits of all the planets, except some of the asteroids, since they are never seen beyond 80 either north or south of the ecliptic.
Parallels of Latitude are small circles imagined to be
What are the poles of the horizon? What are vertical circles? What is the prime vertical? What is the ecliptic? What are the equinoxes? The vernal equinox? The autumnal equinox? How is the ecliptic situated with respect to the equinoctial? What is the obliquity of the ecliptic? Describe the manner in which this angle varies. Describe the division of the ecliptic into signs. How much, at a mean rate, does the Sun advance in the ecliptic every month? What is the zodiac? What are parallels of latitude?
drawn on the Earth's surface, north and south of the equator, and parallel to it.
Parallels of Declination are small circles, imagined to be drawn on the concave surface of the heavens, north and south of the equinoctial, and parallel to it; or they may be considered as circles formed by producing the parallels of latitude to the heavens.
The Tropic of Cancer is a small circle, which lies 2310 north of the equinoctial, and parallel to it. The Tropic of Capricorn is a small circle, which lies 2310 south of the equinoctial, and parallel to it. On the celestial sphere, these two circles mark the limits of the Sun's farthest declination north and south. On the terrestial sphere, they divide the torrid, from the two temperate zones. That point in the ecliptic which touches the tropic of Cancer, is called the Summer Solstice; and that point in the ecliptic which touches the tropic of Capricorn, is called the Winter Solstice.
The distance of these two points from the equinoctial, is always equal to the obliquity of the ecliptic, which, in round numbers, is 23c°; but as we have seen the obliquity of the ecliptic is continually changing; therefore the position of the tropics must make a correspondent change.
The Colures are two great circles which pass through the poles of the heavens, dividing the ecliptic into four equal parts, and mark the seasons of the year. One of them passes through the equinoxes at Aries and Libra, and is thence called the Equinoctial Colure; the other passes through the solstitial points or the points of the Sun's greatest declination north and south, and is thence called the Solstitial Colure.
The Sun is in the equinoctial points the 21st of March and the 23d of Septem ber. He is in the solstitial points the 22d of June and the 22d of December.
The Polar Circles are two small circles, each about 6610 from the equator, being always at the same distance from the poles that the tropics are from the equator. The northern is called the Arctic circle, and the southern the Antarctic circle.
Meridians are imaginary great circles drawn through the poles of the world, cutting the equator and the equinoctial at right angles.
Every place on the Earth, and every corresponding point in the heavens, is considered as having a meridian passing through it; although astronomers apply
What are parallels of declination? What is the tropic of cancer? What is the tropic of capricorn? What is the summer solstice? What is the winter solstice? What is their distance from the equator, compared with the obliquity of the ecliptic? Is this distance always the same? What are the colures? What is the equinoctial colure? What is the solstitial colure? On what days of the year is the sun in the equinoctial points? On what days, is he in the solstitial points? What are the polar circles? By what names, are they distinguished? What are meridians? How many meridians are there? How many, do astronomers apply to the heavens?
bnt 24 to the heavens, thus dividing the whole concave surface into 24 sections, each 150 in width. These meridians mark the space which the heavenly bodies appear to describe, every hour, for the 24 hours of the day. They are thence sometimes denominated Hour Circles.
In measuring distances and determining positions on the Earth, the equator, and some fixed meridian, as that of Greenwich, contain the primary starting points; in the heavens, these points are in the ecliptic, the equinoctial, and that great meridian which passes through the first point of Aries, called the equinoctial colure.
Latitude on the Earth, is distance north or south of the equator, and is measured on a meridian.
Latitude in the Heavens, is distance north or south of the ecliptic, and at right angles with it.
Longitude on the Earth, is distance either east or west from some fixed meridian, measured on the equator.
Longitude in the Heavens, is distance east from the first point of Aries, measured on the ecliptic.
Declination is the distance of a heavenly body either north or south of the equinoctial, measured on a meridian.
Right Ascension is the distance of a heavenly body east from the first point of Aries, measured on the equinoctial.
It is more convenient to describe the situation of the heavenly bodies by their declination and right ascension, than by their latitude and longitude, since the former correspond to terrestrial latitude and longitude.
Latitude and declination may extend 90° and no more. Terrestrial longitude may extend 180° either east or west; but celestial longitude and right ascension, being reckoned in only one direction, extend entirely round the circle, or 360°.
In consequence of the Earth's motion eastward in its orbit, the stars seem to have a motion westward, besides their apparent diurnal motion caused by the Earth's revolution on its axis; so that they rise and set sooner every succeeding day by about four minutes, than they did on the preceding. This is called their daily acceleration. It amounts to just two hours a month.
EXAMPLE.-Those stars and constellations which do not rise until 10 o'clock this ning, will, at the same hour, on month hence, be 30° above the horizon; and, for the same reason, those stars which we see directly over head this evening, will at the same hour, three months hence, be seen setting in the west; having in this time, performed one fourth of their apparent annual revolution.
The following table of sidereal revolutions, shows the difference between sclar and sidereal time. The first column contains the numbers of complete revolu tions of the stars, or of the Earth's rotation on its axis; the second exhibits the
Into how many sections, do these meridians divide the concave surface of the heavens? Of what width are these sections? Why are these meridians sometimes called hour circles? In measuring distances on the Earth, what circles contain the primary starting points? Where are these points in measuring distances in the heavens? What is latitude on the Earth? What is latitude in the heavens? What is longitude on the Earth? What is longitude in the heavens? What is declination? What is right ascension? Why is it more convenient to describe the situation of the heavenly bodies by their de clination and right ascension, than by their latitude and longitude? How many degrees may latitude and declination extend? How many terrestrial longitude? Hoo Το many celestial longitude? What is meant by the daily acceleration of the stars? how many minutes does it amount? Illustrate this subject with an example.
times in which these revolutions are made; and the third, shows how much the Stars gain on the Sun every day-that is, how much sooner they rise and come to the meridian every succeeding day, than they did on the preceding
On this account, we have not always the same constellations visible to us throughout the year. While some, that were not visible before, are successively rising to view in the east, and ascending to the meridian, others sink beneath the western horizon, and are seen no more, until, having passed through the lower hemisphere, they again reappear in the east.
It is easy to convert right ascension into time, or time into right ascension; for if a heavenly body is one hour in passing over 150, it will be one fifteenth of an hour, or 4 minutes, in passing over 10.
If the first point of Aries be on the meridian at 12 o'clock, the next hour line, which is 150 E. of it, will come to the meridian at 1 o'clock; the second hour line at 2 o'clock; the third at 3, &c. Of any two bodies whose right ascensions are given, that one will pass the meridian first which has the least right ascension.
The first map of the atlas represents, upon a large scale, a general view of the solar system.
This will be more fully described in the Second Part of the work.
Do we always see the same constellations? Explain the manner of converting right ascension into time, and time into right ascension.