Mathematic Al Geography

meridian, body, equinoctial, ecliptic, circle, passing and arch

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The meridian of the place, or the twelve o'clock hour cir cle, is the meridian that cuts the horizon in the north and south points.

The six o'clock hour circle, is the meridian at right angles to the meridian of the place.

An azimuth or vertical circle, is a great circle perpendicu lar to the horizon, and consequently passing through the zenith and nadir.

The prime vertical, is a vertical circle passing through the east and west points of the horizon, and consequently cutting the meridian of the place at right angles.

The ecliptic is a great circle representing the sun's an nual path, and cutting the equinoctial at an angle of about 23° 28'. hence the poles of the ecliptic are about 2S° 28' distant from the corresponding poles of the world.

The signs are the twelve equal parts into which the eclip tic is divided, each consisting of 30°. They are written and named as follows : The cardinal points of the ecliptic are the two equinoc tial and two solstitial points.

The equinoctial points or equinoxes, are those points of the ecliptic where it intercepts the equinoctial, viz. the be ginning of Aries and the beginning of Libra, 180° distant from each other. The sun enters Aries about the middle of spring, and Libra about the middle of autumn ; hence the former is called the vernal, and the latter the autumnal equinox.

The solstitial points or solstices, are those points of the ecliptic that are at the greatest distance from the equinoc tial, viz. the beginning of Cancer and the beginning of Capri corn, also 180° distant from each other. The sun enters the former about the middle of summer, and the latter at the middle of winter ; hence the one is called the summer, and the other the winter solstice.

The equinoctial colure is a meridian passing through the equinoctial points.

The solstitial colure is a meridian passing through the solstitial points.

Circles of celestial longitude are great circles perpen dicular to the ecliptic, and consequently passing through its poles.

Parallels of declination are small circles parallel to the equinoctial.

Every point in the celestial sphere between the equinoc tial and the poles appears to describe a parallel of declina tion in 24 hours. When part of this parallel is above, and part below the horizon, the former is called the diurnal, and the latter the nocturnal arch.

The tropics of Cancer and Capricorn are parallels of de clination, passing, the one through the summer solstice 23° 28' to the north, and the other through the winter solstice 23" 28' to the south of the equinoctial. They are so call ed from a Greek word signifying to turn, because the sun in his annual course appears to recede from the equinoc tial till he reaches the tropics, after which he returns to wards it. • The arctic and antarctic polar circles are parallels of de clination, 23° 28' from their corresponding poles.

Parallels of celestial latitude are small circles parallel to the ecliptic.

The declination of a heavenly body is its distance from the equinoctial measured on a meridian ; or it is the arch of a meridian intercepted between the equinoctial, and a parallel of declination passing through the body. It is called north or south, according as it is to the north or south of the equinoctial.

The declination of a hc.ly cannot exceed 90°.

The right ascension of a heavenly body is its distance from the vernal equinox measured on the equinoctial ; or it is the arch of the equinoctial intercepted between the ver nal equinox and a meridian passing through the body, reckoning in the order of the signs.

The latitude of a heavenly body is its distance north or south from the ecliptic, measured on a circle of longitude; or it is the arch of a circle of longitude intercepted between the ecliptic and a parallel of latitude passing through the body.

The longitude of a heavenly body is its distance from the vernal equinox measured on the ecliptic ; or it is the arch of the ecliptic intercepted between the vernal equinox, and a circle of longitude passing through the body.

The altitude of a heavenly body is its height above the horizon measured on a vertical circle ; or it is the arch of a vertical circle intercepted between the horizon and the body. The arch of the same circle between the body and the zenith, is called its zenith distance. The altitude and zenith distance are together equal to 90". The former is greatest when the body is on the meridian of the place, which is then called its meridian altitude, and at equal dis tances on either side of the meridian, the altitude is the same.

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