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at all seasons of the year, the interval from the rising to the setting of the sun, was perpetually changing, passing through a cycle which required exactly one year for its completion. It became manifest that the sun did not prosecute its annual journey among the stars, in a circle parallel with those described by the stars, in their diurnal revolution. His path was oblique to those circles, and while he participated in their diurnal motion, he was sweeping by his annual revolution round the heavens, and was at the same time, by another most extraordinary movement, carried towards the north to a certain distance, then stopping, commenced a return towards the south, reached his southern limit,-again changed his direction, and thus oscillated from one side to the other of his mean position.
These wonderful changes became the objects of earnest investigation. In what curve did the sun travel among the stars ? All diurnal motion was performed in a circle, the first discovered, the simplest and the most beautiful of curves: and in this curve, analogy taught the early astronomers, that all celestial movements must be performed. It became therefore, a matter of deep interest, to trace the sun's path accurately among the stars, to mark his track, and to see whether it would not prove to be a circle. To accomplish this, more accurate means must be adopted, than the mere watching of the stars which attended the rising or setting sun. The increase and decrease of the shadow of some high pointed rock, to whose refreshing shade the shepherd astrono mer had repaired in the heat of noon, and beneath which he had long pondered this important problem first suggested the means of its resolution. As the summer came on, he remarked that the length of the noon shadow of his rock, perpetually decreased from day to day. As the sun became more nearly vertical at noon, the shadow gave him less and less shelter. Watching these noon shadows, from day to day, he found them proportioned to the sun's northern or southern motion, and finally the thought entered his mind, that these shadows would mark with certainty, the limits of the sun's motion north and south,—the character of his orbit or route among the stars,—the changes and duration of the seasons, and the actual length of the year, which thus far had been but roughly determined. To accomplish the observations more accurately, an area on the ground was smoothed and leveled, and in its centre a vertical pole was erected some ten or fifteen feet in length, whose sharp vertex cast a well defined shadow. And here we have the first astronomical instrument, the gnomon, ever devised by the ingenuity of man. Simple as it is, by its aid the most valuable results were obtained.
The great point was to mark with accuracy the length of the noon-day shadow, from month to month, throug’out the entire year. Four remarkable points in the sun's annual track, were very soon detected and marked. One of these occurred in the summer, and was that point occupied by the sun day of the shortest noon shadow. Here the sun had reached his greatest northern point, and for a few days the noon shadow, cast by the gnomon, appeared to remain the same, and the sun stood still. The noon shadows now increased slowly, for six months, as the sun moved south, till a second point was noted, when the noon shadow had reached its greatest length. Again it became stationary, and again the sun paused and stood still, before commencing his return towards the north. These points were called the summer and winter solstices, and occurred at intervals of half a year. At the summer solstice, the longest day occurred, while at the winter solstice, the shortest day was always observed. These extreme differences between the length of the day and night, occasioned the determination of the other two points. From the winter solstice, the noon shadows decreased as the length of the day increased, until finally the day and night were remarked to be of equal length, and the distance to which the shadow of the gnomon was thrown on that day, was accurately fixed. If on this day the diurnal circle described by the sun, could have been marked in the heavens by a circle of light, sweeping from the east to the west, so that the eye might rest upon and retain it, and if at the same time the sun's annual path among the fixed stars could have been equally exhibited in the heavens, by a circle of light, these two circles would have been seen to cross each other, and at their point of crossing, the sun would have been found. The diurnal circle was called the equator, the sun's path the ecliptic, and the point of intersection was called appropriately, the equinox.— As the sun crossed the equator in the spring and autumn, these points received the names of the vernal and autumnal equinoxes, and were marked with all the precision which the rude means then in use rendered practicable.
T'he bright circle already imagined in the heavens to represent the sun's annual track among the stars, passed obliquely across the equator, and the amount by which these circles were inclined to each other was actụally measured in these early ages, with no mean precision by the noon shadows of the gnomon. The ray casting the shortest noon shadow, was inclined to the ray forming the longest noon shadow, under an angle precisely double of the inclination of the ecliptic or sun's path to the equator, and the inclination of these two rays marked exactly the annual motion of the sun from south to north, or from north to south. A close examination of the order of increase and decrease in the length of the noon shadows cast by the gnomon, demonstrated the important truth already suspected, that the sun's path was actually a circle, but inclined, as has already been shown, to the diurnal circles of the stars and to the equator.
By counting the days which elapsed from the summer solstice to the summer solstice again, a knowledge of the length of the year, or period of the sun's revolution, was obtained. But here again a discovery was made which produced an embarrassment to the early astronomer, which all their perseverance and research never succeeded in removing.
In these primitive ages the heavenly bodies were regarded with feelings little less than the reverence we now bestow on the Supreme Creator. The sun especially, as the Lord of life and light, was regarded with feelings nearly approaching to adoration, even by the astronomers themselves. The idea early be came fixed, that the chief of the celestial bodies must move with a uniform velocity in a circular orbit, nevet increasing or decreasing. Change being inconsistent with the supreme and dignified station which was as signed to him—what then must have been the astonishment of the primitive astronomers, who in counting the days from the summer to the winter solstice, and from the winter round to the summer solstice, these intervals were found to be unequal.—This almost incredible result was confirmed, by remarking that the shorter spaces from equinox to solstice, dividing the sun's annual route, into four equal portions, were passed over in unequal times. These results could not be doubted, for each observation, from year to year, confirmed them. They were received and recorded, but the problem was handed down to succeeding generations for solution.
In consequence of the oblique direction of the ecliptic or sun's track, it was found difficult to retain its position in the mind. To assist in the recurrence to this important circle, a brazen circle was at length devised, and fastened permanently to another brazen circle of equal size, under an angle, exactly equal to the inclination of the equator to the ecliptic. Circles, perpendicular to the equator, and passing through the solstices and equinoxes, completed the second astronomical instrument, the sphere. Having constructed this simple piece of machinery, it was mounted on an axis passing through its centre, and perpendicular to its equator, so as to revolve, as did the heavens, whose motions it was intended to represent. Having so placed the axis of rotation, that its prolongation would pass through the north star, this rude sphere came to play a most important part in the future investigations of the heavens. Its brazen equator and ecliptic were