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figure by the universal and reciprocal gravitation of the celestial bodies.

Hipparchus, however, made another discovery, which, having been confirmed and brought to perfection by time, is become one of the principal foundations of astronomy. On comparing his observations with those of Aristillus and Timocharis, made a hundred and fifty years before, he found that the stars constantly preserved the same positions with respect to each other, but that they all had, or appeared to have, a trifling motion in the order of the signs of the Zodiac, or from west to east, the quantity of which was two degrees in a hundred and fifty years, or 48 seconds in a year. This motion having been since studied and observed with persevering attention, has been found to be a little more than 50 seconds a year. Hence it follows, that the Sun and a given star, setting out together from the same point of the ecliptic, and proceeding from west to east with velocities, which should be in the ratio of 360 degrees to 50 seconds of a degree, the Sun would return to the point of departure in a shorter time than it would to the star by a quantity corresponding to 50 seconds of a degree. By calculation we find, that, the former period of time, which constitutes the tropical year, being 365 days, 5 hours, 48 minutes, 48 seconds, the latter, or sidereal year, is 365 days, 6 hours, 9 minutes, 10 seconds. The tropical revolution, we see, brings back the solstices and equinoxes before the sidereal revolution is finished, or the equinoctial points appear to recede with respect to the stars. Hence is derived the term of precession of the equino.res, given to this motion

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motion by which the equinoxes are found to anticipate. the sidereal revolution. The physical cause of this precession of the equinoxes, with that of the variations to which it is subject, will appear hereafter. The quantity and cause of the third kind of anomalistic, will likewise be pointed out.

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The method given by Aristarchus of Samos for determining the ratio of the distances of the Sun and Moon from the Earth was very imperfect, as has been already observed: and besides it was incapable of making known the absolute quantities of these distances. To this method Hipparchus substituted others more complete, in which he made use chiefly of the parallaxes.

The reader is not to be informed, that the parallax of a star is the angular quantity comprised between the point in the heavens to which a star is referred, when seen from a given point on the surface of the Earth, and the point to which it would be referred, were it observed from the centre of the Earth. This is equal to nothing, when the star is in the zenith of the observer, and greatest when it is in his horizon, The parallaxes of the common planets, as the Moon, Mars, Jupiter, &c. are easily ascertained, and thence the distance of these planets from the Earth are afterward deduced. The distance of the Sun from the Earth is a subject of more delicate investigation, and more liable to errour. To discover it, Hipparchus began with calculating the distance of the Moon from the Earth, taking the Earth's radius for a basis, or by means of the horizontal parallax of the Moon. In this there was no difficulty, since the sine of the horizontal

horizontal parallax of a star is as the sine of the angle under which it's horizontal semidiameter is seen, and in the case before us, we have a right angled triangle, of which the three angles are known, and also one of the sides, namely the radius of the Earth, by the measure of Eratosthenes: whence the hypothenuse, or the distance of the Moon from the centre of the Earth, may be obtained. Having then measured the apparent diameter of the Sun, as he had measured that of the Moon; and having calculated, by the duration of a lunar eclipse, the breadth of the cone of the shadow traversed by the Moon; from all these data he formed triangles and analogies, which led him to conclude, that the distance of the Sun from the Earth was equal to about twelve or thirteen hundred times the length of the Earth's radius, or that the horizontal parallax of the Sun was about three minutes. This conclusion is very remote from the truth: but it will not be a matter of wonder, when we consider, that Hipparchus has employed in his calculations a multitude of elements, which could not be determined with sufficient precision in his time. In fact the moderns, enriched by all the knowledge of their predecessors, and furnished with the best instruments, were long before they had determined with accuracy the horizontal parallax of the Sun. It is but little more than a century ago, that la Hire and the Cassinis made it fifteen seconds; while in reality, according to the best observations of our days, it is about eight seconds only: which carries the Sun to a prodigious distance in celestial space,

An extraordinary phenomenon, the almost sudden disappearance of a large star, in the time of Hipparchus, excited that indefatigable astronomer to number the stars, and to note down their configurations, respective situations, &c.; in order to enable posterity to know, whether they were permanent bodies, invariably fixed in the vault of Heaven, and preserving always the same position with regard to each other; or whether, exclusive of the motion that produces the precession of the equinoxes, they be not subject to other irregular and unknown motions, in which case the motions of the planets could no longer be referred to them as points of comparison. This immense labour laid the foundation, on which the whole superstructure of astronomy was to be raised. He was admired and celebrated in all nations, where learning was pursued. Pliny speaks of him with enthusiasm. Hipparchus,' says

he, has never been sufficiently praised: no one has given proofs like him, that man is allied to Heaven, and that his mind is a portion of the Deity...... He has braved the anger of the gods, in making known to man the number of the stars....... thus bestowing the heavens as a portion on those who are capable of making use of it.' Hist. Nat. lib. 11, chap. 26.

To so many important researches, immediately connected with the progress of astronomy, Hipparchus added the merit of applying this science to familiar purposes of the greatest utility to geography and the promotion of commerce. He reduced to certain and invariable principles the method of de

termining

termining the situation of terrestrial objects by their latitude and longitude, of which men had some notion as early as the time of Alexander. The principal points being once directly fixed by astronomical observations, the topographical details, by which they are connected together, are nothing but easy operations, which may be executed and abridged by means of various instruments, as the graphometer, the plane table, &c.

The limits of this sketch oblige me to pass over in silence the rest of the works of Hipparchus, such as his researches respecting the calendar, astronomical calculation, &c. He likewise undertook to correct the measure, which Eratosthenes had given of the circumference of the Earth, but we know not what he made it.

In these discoveries he was followed by several astronomers, who, without equalling him in genius and learning, contributed notwithstanding to the progress of the science, by the new observations with which they enriched it, or the works in which they displayed it's theory.

In the number of these benefactors of astronomy posterity reckons the philosopher Posidonius, whom I have already mentioned on the subject of measuring the Earth. He lived in the island of Rhodes, A. c. 60, where he made many observations. To represent the state of the heavens he constructed a movable sphere, of which Cicero speaks with admiration. Tusc. 1, de Nat. Deo. I.

If Posidonius were not an astronomer of the first order, he deserves our attention for a moment by his

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