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pleting their retrograde one: consequently, as the sun and moon meet the nodes at the end of that period, the same solar and lunar aspects, which happened 18 years, 11 days, 7 hours, 43 minutes ago, will return, and produce eclipses of both luminaries, for many ages, the same as before.

Of ancient astronomical observations much has been said, with very little foundation, by many modern writers: the oldest eclipses of the moon that Hipparchus could make any use of, went no higher than the year before Christ 721. Whatever observations, therefore, the Chaldeans had before this, were probably very rude and imperfect*.

OF PARALLAX AND REFRACTION'.

Astronomy is subject to many difficulties, besides those which are obvious to every eye. When we look at any star in the heavens, we do not see it in its real place; the rays coming from it, when they pass out of the purer etbei-eal medium, into our coarser and more dense atmosphere, are refracted, or bent in such a manner, as to shew the star higher than it really is. Hence, we see all the stars before they rise, and after they set; and never, perhaps, see any one in its true place in the heavens. There is another difference in the apparent situation of the heavenly bodies, which arises from the statics m

History of Astroncmv.

which an observer views them. This difference in situation is called the parallax of an object.

OF PARALLAX.

The parallax of any object is the difference between the places that the,object is referred to in the celestial sphere, when seen at the same time from two different places within that sphere. Or, it is the angle under which any two places in the inferior orbits are seen from a superior planet, or even the fixed stars.

The parallaxes principally used by astronomers, are those which arise from considering the object as viewed from the centres of the earth and the sun, from the surface and centre of the earth, and from all three compounded.

The difference between the place of a planet, as seen from the sun, and the same as seen from the earth, is called the parallax of the annual orbit; in other words, the angle at any planet, subtended between the sun and the earth, is called the parallax of the earth's, or annual orbit.

The diurnal parallax is the change of the apparent place of a fixed star, or planet, of any celestial body, arising from its being viewed on the surface, or from the centre of the earth.

The annual parallax of all the planets is very" considerable, but that of the fixed stars is imperceptible.

The fixed stars have no diurnal parallax; the

moon, a considerable one; that of the planets is greater or less, according to their distances.

To explain the parallaxes, with respect to the earth only, let IISW, plate 7, Jzg. 2, represent the earth; T, the centre thereof; ORG, part of the moon's orbit; Prg, part of a planet's orbit; ZaA, part of the starry heavens. Now, to a spectator at S, upon the surface of the earth, let the moon appear in G; that is, in the sensible horizon of S, and it will be referred to A; but if viewed from the centre T, it will be referred to the point D, which is its true place.

The arc, AD, will be the moon's parallax; the angle, SGT, the parallactic angle; or the parallax is expressed by the angle under which the semidiameter TS of the earth is seen from- the moon.

If the parallax be considered with respect to different planets, it will be greater or less as those objects are more or less distant from the earth; thus the parallax AD of G is greater than the parallax Ad of g.

If it be considered with respect to the same planet, it is evident that the horizontal parallax, or the parallax when the object is in the horizon, is greatest of all, and diminishes gradually, as the body rises above the horizon, until it comes to the zenith, where the parallax vanishes, or becomes equal to nothing. Thus AD and Ad, the horizontal parallaxes of G and g, are greater than oB and ab, the parallaxes of R and r ; but the objects O and P, seen from S or T. appear in the same place Z, or the zenith.

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By knowing tVie parallax of any celestial object, its distance i'rom the centre of the earth may be easily obtained by trigonometry. Thus, if the distance of G from T be sought in the triangle STG, ST being known, and the angle SGT determined by observation, the side TG is thence known.

The parallax of the moon may be determined by two persons observing her from different stations at the same time; she being vertical to the one and horizontal to the other. It is generally concluded to be about 57 .

But the parallax most wanted is that of the sun, whereby his absolute distance from the earth is known; and hence the absolute distances of all the other planets would be also known, from the second Keplerian law. But the parallax of the sun, or the angle under which the semidiameter of the earth

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would appear at that distance, is so exceeding small, that a mistake of a second will cause an error of several millions of miles.

OF REFRACTION.

As one of the principal objects of astronomy is to fix the situation of the several heavenly bodies, it Is necessary, as a first step, to understand the causes which occasion a false appearance of the place of those objects, and make us suppose them in a different situation 'from that which they really have. Among these causes, refraction is to be reckoned. By this term is meant the bending of the rays of light, as they pass out of one medium into another.

The earth is every where surrounded by an heterogeneous fluid, a mixture of air, vapour, and terrestrial exhalations, that extend to the regions of the sky. The rays of light from the sun, moon, and stars, in passing to a spectator upon earth, come through this medium, and are so refracted in their passage through it, that their apparent altitude is greater than their true altitude.

Let AC, plate 7, Jig. 3, represent the surface of the earth; T, its centre; BP, a part of the atmosphere; HEK, the sphere of the fixed stars; AF, the sensible horizon; G, planet; GD, a ray of light proceeding from the planet to D, where it enters our atmosphere, and is refracted towards the line I)T, which is perpendicular to the surface of the atmosphere; and as the upper air is rarer than that near the earth, the ray is continually entering a denser medium, and is every moment bent towards T, which causes it to describe a curve, as DA, and to enter a spectators eye at A, as if it came from E, a point above G. And as an object always appears in that line in which it enters the eye, the planet will appear at E, higher than its true place, and frequently above the horizon AF, when its true place is below it, at G.

This refraction is greatest at the horizon, and decreases very fast as the altitude increases, insomuch that the refraction at the horizon differs from the refraction at a very few degrees above the horizon, by

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