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and projected on the lunar disk in a right line; and then measuring the arc of the heavens comprised between the Moon and the Sun; and lastly, in conceiving a rectangled triangle, the right angle of which terminates at the Moon, while it's three sides are formed by the three lines which join the Earth, the Moon, and the Sun. In this triangle, it is obvious, the three angles are known, from which the ratio of it's three sides to each other may consequently be deduced. In this manner Aristarchus found, that the Sun is eighteen or twenty times as far from the Earth as the Moon; which is not very accurate, for it's distance is three or four hundred times greater: but to have attempted the solution of a problem at that time so difficult, and so complicated, was no trifling matter. By the strong probabilities, derived from observations, with which he supported the pythagorean system of the Earth's revolution round the Sun, Aristarchus acquired more real and permanent glory as a geometrician and astronomer. Accordingly this grand truth was matured by degrees in minds capable of conceiving it, till at length it acquired strength enough to appear in open day, like Minerva issuing armed from the brain of Jupiter.

The emulation of the philosophers who addicted themselves to astronomy was not the sole cause of it's progress: but for this it was partly indebted to the invention of some new instruments, with which it was gradually enriched, and by means of which observations were rendered more easy, more accurate and more numerous. Among others of these are mentioned the rings, which Eratosthenes caused to

be constructed in the museum of Alexandria. These, according to the description given by Ptolemy, were an assemblage of different circles, not much unlike our armillary sphere, which probably derived it's origin from them. First there was a great circle performing the office of a meridian: the equator, ecliptic, and two colures, formed an interiour assemblage, turning on the poles of the equator. There was likewise a circle turning on the poles of the ecliptic, and furnished with vanes diametrically opposite to each other, it's concave side nearly touching the ecliptic, or carrying an index, to point out the division at which it stopped. Such was the general form of the instrument. It was applied to several uses: the following, for instance, is the manner, in which it was employed to determine the equinoxes.

The equator of the instrument being placed with great care, as it always ought to be, in the plane of the celestial equator, the observer watched the moment, when the upper and lower surfaces were no longer illumined by the Sun; or rather, which was less liable to errour, when the shadow of the anteriour convex portion of the circle completely covered the concave part, on which it was projected. It is evident, that this point of time was that of the equinox. When this did not take place, which indicated that the equinox occurred during the night, two observations were selected, in which the shadow was projected on the concave part of the circle in opposite directions, and the mean of the interval between these observations was considered as the instant of the equinox.

Not contented with having rendered it easier for others to take observations, Eratosthenes made a great number himself. He likewise wrote several books on astronomy, which are quoted by the ancients, but of which one alone, a description of the constellations, has escaped the ravages of time. of time. His genius led him to things out of the common track, one proof of which is his measure of the Earth.

Of all the ancient astronomers, no one has so much enriched the science, or acquired so great a name, as Hipparchus, a native of Nice in Bithynia. A. c. 142. Among these he holds nearly the same rank, as Archimedes among the geometricians. He began by making observations at Rhodes, and afterward settled at Alexandria, where he executed all those labours, which established ancient astronomy on certain foundations, and furnished the moderns with points of comparison for a multitude of astronomical theories.

One of his first cares was to rectify the duration of the year, which before his time was made to consist of 365 days, 6 hours, and which he found to be a little too long. By comparing an observation of his own at the summer-solstice with a similar one made a hundred and forty five years before by Aristarchus of Samos, he shortened it about seven minutes; which however was insufficient. But that Hipparchus did not come nearer the truth must unquestionably be ascribed to some inaccuracy in the observation of the samian astronomer for those of Hipparchus himself, being compared with modern observations, give 365 days, 5 hours, 49 seconds, for the duration of the year; a result

a result differing scarcely a second from what is found. on comparing the best observations of our own day with those of Tycho Brahe. In general, modern observations, in which the assistance of glasses is employed, are much more accurate than those of the ancient astronomers, who observed the stars merely through vanes by means of the naked eye. But in questions, where the inevitable errours of observations are diffused over a long interval of time, as on the present occasion, the comparison of ancient with modern observations may afford a result nearly as accurate, as that which is derived from a comparison of the latter alone.

The ancient astronomers supposed, that the Sun, in it's annual motion, proceeded uniformly in a circular orbit but this uniformity, believed to be real, was altered, in appearance at least, with respect to the Earth. The general effect was known: but Hipparchus investigated and assigned it's cause. He observed, that the Sun was about 94 days 12 hours in proceeding from the vernal equinox to the summer solstice, and only 92 days 12 hours in it's progress from the summer solstice to the autumnal equinox; which gave 187 days, nearly, for the time spent by the Sun in traversing the northern part of the ecliptic, and 178 days only for it's progress in the southern portion. Of course the Sun must either move, or appear to move, with greater velocity in the southern part of the ecliptic, than in the northern. Without relinquishing the hypothesis of the real uniformity of the Sun's motion, Hipparchus explained the inequality of the motion with respect to the Earth by

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placing the Earth at a certain distance from the centre of the ecliptic. This distance, which he termed the eccentricity of the solar orbit, gave rise to an equation between the real and apparent motions, sometimes additive, at others subductive, by means of which the two motions were made to correspond in every instant. He determined the quantity of the eccentricity with respect to the radius of the ecliptic, as well as the position of the line of the apses, or the line which joins the diametrically opposite points, in which the Sun is at it's greatest and least distance from the Earth. He made similar remarks and calculations for the lunar orbit. From these data he constructed tables of the motions of the Sun and Moon, which are the first of the kind that are mentioned. All these determinations were offered as attempts, which time and farther observations were to bring to perfection. Hipparchus had formed the project of constructing similar tables for the motions. of the five planets Mercury, Venus, Mars, Jupiter, and Saturn but judging, that the observations then known were insufficient, to furnish elements sufficiently accurate, he relinquished this task.

Though the eccentricities of the orbits of the Sun and Moon, as determined by Hipparchus, differed not widely from the truth, it must be remarked, that they were affected by a radical errour: they supposed these orbits to be perfect circles. The ancients never suspected, that the planets in reality described ellipses: much less did they imagine, that these ellipses themselves are continually varied and altered in their

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