penumbra, as towards d, e, or f, the greater portion of the sun may be seen.

4. Out of the penumbra, the entire disc of the sun is visible.

OF THE LIMITS OF SOLAR AND LUNAR

ECLIPSES.

The distance of the moon, in degrees and minutes, above or below the ecliptic line, is called her latitude. If she be above the ecliptic, she is said to have north; if below it, south latitude.

If the latitude at any time exceed the sum of the semidiameter of the moon, equal to 16 min. and the earth's shadow equal to 45 minutes, the moon at that time cannot be eclipsed; but will either pass under or over the shadow, according as she happens to be above or below the ecliptic line.

The distance from the node, either before or after it, corresponding to the above extent, is about 12 degrees, which is consequently the limit of lunar eclipses for when a full-moon happens within 12 degrees of the nodes, she will be eclipsed; and the nearer to the nodes, the greater will the eclipse be.

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If at the new-moon, the latitude exceeds the sum of the semidiameters of the sun 16 minutes, and of the moon 163 minutes, we should see no eclipse of the sun from the centre of the earth. But as we view the luminaries from the surface, which is much

higher, we are obliged to take in the semidiameter of the earth as seen from the moon. Then, if the latitude of the moon be greater than the sum of these three numbers, 942 minutes, the sun will not be eclipsed; for the moon will pass either over or under his disc, according as she is above or below the ecliptic line. The distance from the node on either side agreeing to the above-mentioned extent, is the 18 degrees, which is the utmost limit of solar eclipses, whence it follows, that if the sun and moon, at the time of new-moon, happen to be within 18 degrees of the node, the sun will be eclipsed.

OF THE PERIOD OF ECLIPSES.

If the places of the moon's nodes were fixed, eclipses would always happen nearly at the same time of the year; but as they have a motion of about 3 min. 11 sec. every day backwards, or contrary to the order of the signs, the succeeding eclipse must recede likewise; and in one revolution of the nodes, which is completed in 18 years, 224 days, 3 hours, they will revolve in a retrograde manner through the year, and return to the same places again.

But there is a more correct period, called the Chaldean Saros, which is 18 years, 11 days, 7 hours, 43 min. ; for, in that time, the sun and moon advance just as far beyond a complete direct revolution in the ecliptic, as the nodes want of com

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 ethereal 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 stations in

*Costard's History of Astronomy.

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 HSW, plate 7, fig. 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 aB 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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