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the plane of which passes directly through the centre of the earth; this is a great circle. So is A E for the same reason, for if the globe were to be divided through these circles it would be exactly halved, but a circle passing through H B, or FD, is called a small circle, since the plane of the circle does not pass through the centre of the sphere on which the circle is drawn. From this definition it will be perceived that the circle A I E K, (the part behind the sphere being shown by the dotted line) is a great circle, because the plane of this circle passes through the centre of the sphere. Every great circle, has what is called a pole, that is, a point ninety degrees, or one quarter of a circle, distant from it in every direction, thus—A is the pole of the circle G C, for from whatever point on the circle G C, the distance is measured up to A, it will be found 90°. For instance the arcs AG, AI, AO, A K, AC, are all # of their respective circles. Now suppose the circle G C, to represent the equator, then A will be the north pole of the earth, and Ethe south pole. Suppose now this great circle which we have called the equator to be actually traced around the earth and divided into 360 parts called degrees, marked (9), and suppose these degrees subdivided into minutes marked ('), and call these minutes miles, how many miles would the earth be in circumference? Evidently sixty times 360, or 21,600 miles. This is not so much as the circumference is usually stated to be; viz, 24,000 miles, and for this reason; the mile at the equator, is longer than the English statute mile. Referring to the preceding figure, it will be readily perceived that if the circle H B was divided into 360 parts and these again subdivided into 60 parts each, called miles, these miles would be much smaller than the equatorial miles, indeed it would require 69% English statute miles to constitute 19, or 60 equatorial, or geographical miles. Now if we take 694 miles for the length of a degree, it is evident the circumference of the earth will be 360 times this, or 25,020 miles, and as the diameter is a little less than the circumference, the diameter is called in round numbers 8000 miles. When therefore we assert that the earth is 8000 miles in diameter, we mean simply this, if the equator, or any great circle drawn upon the


earth, is divided into 360 parts, and these subdivided into sixty parts each, and their length ascertained, that it would take 8000 of them to measure the diameter of the earth. The length of a mile therefore, instead of determining the diameter of the earth, or its circumference, is itself determined by that diameter or circumference. The circle might have been divided into 1000 parts, and these subdivided into 100 each, this would give 10,000 minutes or miles for the circumference, but the mile in this case would be shorter. Having assumed the earth’s circumference 24,000 miles, we next desire to know when we have passed over a mile on its surface. This would seem a difficultundertaking at first thought, for how can we determine when we have passed over a degree upon the earth 7 A diagram will explain the manner this is

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accomplished. Let A B C D represent the earth, A C being the equator. A spectator at the pole B, would see the pole star directly overhead, but a spectator at A, on the equator, would see the pole star in the horizon. Hence, in travelling from the north pole to the equator, the elevation of the pole star changes from directly overhead, or in the zenith as it is called, to the horizon, or 909, changing its altitude 19 for every degree traveled over the earth's surface, either north or south. The astronomer is furnished with the means of measuring the altitude of the pole star, or its distance above the horizon by means of the quadrant, or the astronomical circle which we shall describe, together with some other astronomical instruments in the next chapter. We have now learned three important facts in regard to our earth, and the celestial bodies, viz: The ceaseless and uniform motion, the rotundity of the earth, and the actual length of a degree upon its surface, and this is no small progress, supposing we commeneed entirely unacquainted with the subject. Fortunately, as we proceed to show the gradual improvement in astronomical knowledge, we can also give a history of the science, and briefly notice those eminent men, and their discoveries, whose labors have brought astronomical science to its present state of perfection. Supposing that we are ignorant of the nature of the motion perceived in the heavenly bodies, we will lay aside further observation for the present, and notice some of the instruments employed in astronomical discoveries.

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“ He sat and read. A book with silver clasps,

All gorgeous with illuminated lines
Of gold and crimson, lay upon a frame
Before him. 'Twas a volume of old time;
And in it were fine mysteries of the stars,
Solved with a cunning wisdom.” - Willis.

The imperfect historical records of the nations of antiquity prevent us from determining with certainty when, and with whom, astronomical science had its origin. It is certain however, that it was cultivated at a very early age by the Egyptians, the Chaldeans, the Bramins of India, and the Chinese. In a fine climate, and fertile country, inhabited by nomadic tribes, we can well imagine the sublime spectacle of the heavens to have arrested early attention. At a later period, when the motion of the sun among the stars began to be noticed, and consequently the helical rising and setting of certain stars, i. e., their rising or setting just before or after the sun, became the signs of approach of certain seasons, the stars were grouped into constellations, and fanciful names given to them. Thus we find Hesiod alludes to the helical rising of Arcturus, and Thales mentions the number of days after the vernal equinox, when the Pleiades set just as the sun arose, by means of which we are now enabled to tell the age in which he lived, as will be explained hereafter.

The constellations being located and named, and the sun's apparent path determined in the heavens, astronomers began to observe more carefully the motions of the sun, moon, and planets, among the stars, and endeavored to frame a system of the world which would explain all the apparently irregular motions. It was

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very early observed that the sun and moon moved around the earth with different velocities from the stars, and that there were certain bodies, five in number, which also appeared to be wandering in the heavens, these were called planets, from a Latin word meaning to wander, and were named in order, according to their supposed distance from the earth, Mercury, Venus, Mars, Jupiter, and Saturn. As soon as these wandering bodies were closely observed, certain irregularities in their motion attracted attention, instead of moving uniformly in a circle in the heavens, like the sun, their paths were often broken, and even turned back, as represented by the lines below, moving from u to b direct, i. e.,

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in the order of the signs, from b to c, retrograde, or contrary to their previous motion, at b and c, apparently still, or stationary for a short time, and from c to d moving again direct. In addition to these irregular movements, two of them were observed to always remain in the neighborhood of the sun, viz. Mercury and Venus, while Mars, Jupiter, and Saturn were often seen directly opposite, rising when the sun was setting. Hence, in framing any theory, it was necessary to account for these motions.

All the early astronomers supposed that the earth was the centre of the system, and that all the celestial bodies were revolving around it. The only system of the world which attracted much notice, was that of Ptolemy the great Egyptian king and philosopher, called, from him, the Ptolemaic system. This is the system which we would naturally adopt upon casual thought. Here is the earth occupying the centre, and around it the moon is supposed to be revolving not quite as fast as the sun, next comes Mercury, then Venus, the Sun, Mars, Jupiter, and Saturn, beyondthe whole was supposed to be the grand primum mobile, a sphere

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