be seen by us when it is below the horizon? What effect has cold on the refracting power of the air? What curious circumstance is related by Mr. Ferguson? What excess of the day over the night, is it computed, refraction gives in latitude 43°? Of what curious phenomenon is the refraction of the atmosphere sometimes the cause? Why does the disk of the Sun or Moon, when in or near the horizon, appear elliptical?

CHAPTER XIV.

Twilight.

TWILIGHT, or crepusculum, is the light of the morning before sun-rising, and of the evening after sun-setting. It is the result of refraction. The atmosphere of the Earth extends about 45 miles in height; or, at that distance from the Earth's surface, it is sufficiently dense to refract the rays of the Sun. Hence, when the Sun is about 18° below the horizon, the morning twilight begins, and the evening twilight ends. The evening twilight is said, however, to be longer than that of the morning. The elevation of the atmosphere by the heat of the day and the vapor exhaled by rarefaction, may, by affecting the refracting power of the air, prolong the evening twilight.

The continuance of twilight must increase with the distance from the equator, and be very long in high latitudes. At the poles, the Sun is never more than about 23° 28' below the horizon. If there be polar inhabitants, therefore, they must be blessed with a long twilight. To them it must be more than 50 days after the Sun sets, before it will be 18° below the horizon, and, on its return, the same time, after it approaches within 18°, before it will be above the horizon.

The immense benefit of the atmosphere must be contemplated with admiration. Not only, by the chemical operations of air, does it cause our blood to flow, and diffuse warmth through our bodies; but, by its reflecting and refracting powers, it gives beauty to the day. It gives also an easy and pleasing transition from night to day, and from day to night, and enlarges the borders of the day even into the regions of night. Astronomers generally concur with Dr. Keill, "that it is entirely owing to the atmosphere, that the heavens appear bright in the day time. For without it, only that part of the heavens would be luminous in which the Sun is placed; and, if we could live without air, and should turn our backs to the Sun, the whole heavens would appear as dark as in the night. In this case, also, we should have no twilight, but a sudden transition from the brightest sunshine to dark night, immediately upon the setting of the Sun, which would be extremely inconvenient, if not fatal to the eyes of mortals."

What is twilight? How high is the atmosphere? How far below the horizon is the Sun when the morning twilight begins, and the evening twilight ends? Which have the longest twilight, the people near the equator, or those in high latitudes? How long must the twilight be at the poles? Can you name some particular benefits derived to us from the atmosphere? According to Dr. Keill, what would be the consequence of our being without an atmosphere?

CHAPTER XV.

Latitude and Longitude.

SEC. I. LATitude.

LATITUDE, as before stated, is the distance north or south from the equator. It is reckoned on the meridian in degrees; which, like those of all other circles, are subdivided into minutes, and again into sexagesimal parts. The centre of the meridian, like that of the equator, and other great circles of the globe, is considered at the centre of the Earth.

The great circles of the globe, extended into the visible heavens, are considered as celestial circles, always lying in the same plane with those on the Earth. The position of the heavenly bodies, therefore, in regard to these circles, may be used in determining the latitude and longitude of places.

The latitude of a place may be determined by finding the distance of its zenith from the celestial equator. If, therefore, the zenith distance of a heavenly body, and its declination, be known, the latitude of the place of observation may be ascertained.

The declination of a heavenly body, as before defined, is its distance north or south from the celestial equator. The zenith distance of a heavenly body may be obtained by observing its meridian altitude, or by two altitudes. Four corrections are required in finding the altitude of the Sun or Moon; semi-diameter, depression of the horizon, parallax, and refraction. [For tables to find these, see the author's larger work, and other works on astronomy.] The semi-diameter and parallax of a planet can be but a few seconds. They are imperceptible in a star.

Suppose that, on the 4th of July, 1831, the Sun's declination was found to be 22° 55′ 39′′ north, when it passed the meridian of New York; and at that time the Sun's true zenith distance was found to be 17° 46' 21′′ south; what is the latitude of that city?

If Arcturus, the noble star mentioned in the book of Job, be in 20° 20′ north declination, as placed on the British celestial globe, and be observed to pass the meridian of Boston 22° 3′ south of the zenith, what is the latitude of the city?

With a little attention, the student may easily determine, whether he ought to add or subtract in making these calculations. If, in the last example, the declination had been 20° 20′ south, the zenith distance would have been 62° 43′, and the declination must have been subtracted to find the latitude of the place.

The latitude of a place may be determined by observing the altitude of its elevated pole. This altitude is always equal to the latitude of the place of observation. At this time, the north pole of the Earth points nearly to a particular star, well known as the north or pole star. According to Dr. Flint, in his Survey, the declination of this star in 1810 was 88° 17′ 28′′, with an annual increase of 191". Hence its declination on the 1st day of January, 1831, was 88° 24′ 17′′, and its distance from the pole, 1° 35′ 43′′. Let the altitude of this star above and below the pole be taken. Half the sum of these altitudes, added together, is the altitude of the pole, and equal to the latitude of the place.

Semi-diameter and depression of the horizon have

been mentioned, as necessary corrections in determining latitude, and not explained in separate articles.

The semi-diameter of a heavenly body is the angle under which the semi-diameter of the body appears at the Earth. The distance of the limb being taken in ascertaining the altitude of the Sun or Moon, the semi-diameter is necessarily applied, in order to reduce it to the centre of the body.

Depression of the horizon is caused by the eye of the observer being elevated. When a man stands uprightly, he looks down on the horizon, which touches the Earth at his feet. It must be apparent, that, the higher the eye is elevated, the farther below the horizon, touching the surface of the Earth beneath it, may a heavenly body be seen.

SECTION II. Longitude.

Longitude, on the Earth's surface, is the distance east or west from some fixed meridian, assumed as first. Like latitude, it is reckoned in degrees, minutes and sexagesimal parts.

The best method of determining longitude has long been an object of inquiry by the mariner and the geographer, the mechanic, the statesman, and the philosopher.

Philip III. of Spain, we are informed, offered a reward of a hundred thousand crowns for the discovery of longitude. The States of Holland, then the rival of Spain, soon after followed the example. During the minority of Lewis XV., the Regent of France offered a great reward for the discovery of longitude, at sea. About the year 1675, in the time of Charles II. of England, the royal observatory was built at Greenwich. Mr. Flamstead was appointed astronomer royal. Instructions were given to him and his successors, "that they should apply themselves with the utmost care and diligence to rectify the tables of the motions of the