The longitude of the earth for January 1st. for that year, was 100 degrees and 6 minutes, to the earth's longitude, add 120 degrees, (the given aspect,) and the sum is 220 degrees and 6 minutes.

The longitude of Venus on the first day of January, 1824, was 150 degrees and two minutes; the difference was 70 degrees and 4 minutes; Then 1,6021 degrees,9856,6165 difference of daily motion. Then,6165: 1 day :: 70 d. 4 minutes: 113 days, or the 22d. of April. 2. On what day were the earth and Jupiter in conjunction in the year 1826?

3. When in 1835, will the earth and Venus be in conjunction?

NOTE.—The preceding PROBLEMS would be correct, if the Planets moved in perfect circular orbits, which however is not the fact, yet they approach so near to circles, that deductions founded upon their figure as circles, are sufficiently accurate for ordinary calculations.

SECTION TWELFTH.

ON ECLIPSES.

In the Solar System, the Sun is the great fountain of Light, and every planet and satellite is illuminated by him, receive the distribution of his rays, and are irradiated by his beams. The rays of light are seen in direct lines, and consequently are frequently intercepted by the dark and opaque body of the Moon, passing directly between the earth and the Sun; and hiding a portion, or the whole of his disk from the view of those parts of the earth where the penumbra, or the shadow of the Moon happens to fall. This is called an ECLIPSE OF THE SUN.

It is only at the time of new Moon, that an Eclipse of this kind can possibly take place, and then only when the Sun is within seventeen degrees of either the ascending or descending nodes; for if his distance at the time of new Moon be greater than seventeen degrees from either node, no part of the Moon's shadow will touch the earth, and consequently there will be no Eclipse.

The orbit in which the Moon really moves, is different from the ecliptic, one half being elevated five and

one-third degrees above it, and the other half as much depressed below. The Moon's orbit therefore intersects the ecliptic in two points diametrically opposite to each other, and these intersections are called the · Moon's nodes. The Moon, therefore can never be in the ecliptic, but when she is in either of her nodes; which is at least twice in every lunation, or course from change to change, and sometimes thrice. That node from which the Moon begins to ascend northward, or above the ecliptic in northern latitudes is called the ascending node; and the other the descending node; because the Moon when she passes by it descends below the ECLIPTIC Southward. The ECLIPTIC is the great circle which the earth describes in its annual revolution around the Sun, and is divided into twelve equal parts, of thirty degrees each called signs. Six of these, namely, Aries, Taurus, Gemini, Cancer, Leo and Virgo are north; and the other six, to wit, Libra, Scorpio, Sagitarius, Capricornus, Aquarius and Pisces, south of the equotor.*

When the earth comes between the Sun and Moon, the Moon passes through the earth's shadow, and having no light of her own, she suffers a real Eclipse; the rays of the Sun being intercepted by the earth. This can only happen at the time of full Moon; and, when the Sun is within twelve degrees of the Moon's ascending or descending nodes. Should the Sun's distance

* The Equator is an imaginary circle passing round the earth from east to west, dividing it into two equal parts, called Hemispheres.

from the node exceed twelve degrees, the shadow of the earth would no where touch the surface of the Moon, and consequently she could not suffer an Eclipse.

When the Sun is Eclipsed to us, the inhabitants of the Moon on the side next the earth, see her shadow like a dark spot travelling over the earth about twice as fast as its equatorial parts move, and the same way.

When the earth passes between the Sun and Moon, the Sun appears in every part of the Moon where the earth's shadow falls totally Eclipsed; and the duration is as long as she remains in the earth's shadow.

If the earth and Sun were of equal sizes, the shadow of the earth would be infinitely extended, and wholly of the same breadth, and the planet Mars when in either of her nodes, and in opposition to the Sun, (although forty-two millions of miles from the earth,) would be Eclipsed by the shadow. If the earth were larger than the Sun, her shadow would be sufficient to Eclipse the larger planets, Jupiter and Saturn with all their satellites, when they were opposite to him; but the shadow of the earth terminates in a point long before it reaches any of the primary planets. It is therefore evident, that the earth is much less than the Sun, or its shadow could not end in a point at so short a distance.

If the Sun and Moon were of equal sizes, she would cast a shadow on the earth's surface of more than two thousand miles in breadth, even if it fell directly against its centre. But the shadow of the Moon is seldom more than one hundred and fifty miles in breadth at

the earth, unless in total Eclipses of the Sun, her shadow strikes on the earth in a very oblique direction.

In annular Eclipses, the Moon's shadow terminates in a point at some distance before it reaches the earth; and consequently the Moon is much less than the Sun. If the Moon were actually thrice its present size, it would still in many instances, be totally Eclipsed. A sufficient proof of this, is given by her long continuance in the earth's shadow, during any of her total Eclipses. Therefore the diameter of the earth is more than three times the diameter of the Moon.

Though all opaque bodies, on which the Sun shines, have their shadows; yet such is the magnitude of the Sun, and the distances of the planets, that the primaries can never Eclipse each other. A primary can only Eclipse its secondary, or be Eclipsed by it, and never by those except when they are in opposition or conjunction with the Sun, as before stated. The primary planets are very seldom in such positions, but the Sun and Moon are, in every month.

If the Moon's orbit were coincident with the plane of the ecliptic, in which the earth wheels its stated courses, the Moon's shadow would fall on the earth at every change, and the Sun be eclipsed to every part of the earth where the penumbra happened to fall. In the same manner, the Moon would have to travel through the middle of the earth's shadow, and be totally Eclipsed at every full. The duration of total darkness in every instance, exceeding an hour and a half.