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NUMBER OF ECLIPSES.

327

sion of the node, find the sun again within the ecliptic limits.

It is easy to perceive that, under such circumstances, the first full moon, and the seventh also, must have been involved in the earth's shadow, and that very near the node for the sun, after the first new moon for instance, would just have had time to get from a little less than 17° to within 2° of the node, and consequently be casting the earth's shadow within 2° of the opposite one, when the moon arrived to receive it. We see, then, that there might be seven eclipses within the year, five of them being solar.

w The sun and moon are, during the year, as much below the horizon as they are above it; and, hence, taking the average number of eclipses to be four-two of the sun and two of the moon-the average of visible eclipses will be one solar and one lunar. We know that, in consequence of parallax, the sun may be appearing clear of the moon's disk from many parts of the earth even whilst entirely eclipsed by her as viewed from another part. A lunar eclipse, however, is visible from half the earth's surface at once; for, when shadowed by the earth, the moon is seen thus from all places to which she is above the horizon.

X The duration of a lunar eclipse depends upon the distance of the sun from the earth at the time, as well as upon the moon's distance; for upon these circumstances depend the dimensions of the earth's shadow where it is crossing the moon's path, and the rate of her passage through it. But the earth's shadow extends three times and a half as far as the average distance of the moon, and its dimensions there are, at least, equal to 23 of her diameters; so that (partially and wholly) she may continue as long as 3 hours eclipsed by it. For nearly an hour, also, before she enters the umbra, and after she leaves it, the penumbra may be perceived obscuring a part of her disk.

The moon is not invisible even whilst totally in the earth's shadow. The atmosphere all around the disk of our planet, as beheld from the moon, refracts some of the light of the hidden sun into our shadow; and a portion of this reaches the moon. It would seem that the light thus

refracted is decomposed (V 2, p. 187), and the other parts of it becoming absorbed, the red rays principally reach the moon. In the total eclipse of 2nd September, 1830, she appeared of adeep blood-colour when most obscured.

z The duration of a solar eclipse, even if total, depends upon the distances of the sun and moon from the earth's centre; for upon their relative distances depend the relative sizes of their disks; the moon's disk sometimes being less and sometimes greater than the sun's disk. Her passage across him, too, is performed in a less or in a longer time, according as she is near her apogee or her perigee.

B When the new moon is nearest to us and the sun at his greatest distance beyond her, her shadow, although then the longest possible, does not much outreach the earth's surface: we are so near its apex or termination, that it obscures an area of not more than 180 miles broad, and this, at the utmost, is the whole extent* of a total eclipse at any one instant. But the moon's penumbra (see F, p. 194-5,) is at the same time extending over a circular space of 4,900 miles in breadth; and from all stations within this space, various portions of the sun's disk are occulted.

C When the moon is at more than her average distance from the earth, no total eclipse of the sun can take place; for her shadow is shorter than her average distance, and if the centre of her disk be then seen to coincide with that of the sun's, his circumference appears all around her, and we have an annular eclipse (lat. annulus, a ring).

A solar eclipse cannot continue annular longer than twelve and a half minutes, nor total longer than eight minutes.

* This darkened area of 180 miles' diameter, if viewed telescopically from the distance of Mars or Venus, would be seen like a round blot traversing the wider or narrower part of the earth's disk, like the shadow of a satellite of Jupiter as it moves across him (see 4 of D, on p. 192).

RECURRENCE OF ECLIPSES.

The remarkable correspondence (note on p. 307) of the time of a complete revolution of the moon's node with 223 of her synodic periods or "lunations," causes a perpetual recurrence of the eclipses which take place during that time.

The following extracts from an extended table of eclipses, calculated by a French astronomer as visible from Europe, Asia, and Northern Africa, will serve to exhibit a few remarkable instances of the return of such eclipses.

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D During eighteen years and eleven days, the time of this revolution of the moon's node, there are about sixty eclipses-twenty-one of the moon and forty-one of the sun-and since the sun, moon, and earth, at each termination of this period, are nearly in the same relative positions, the series of eclipses recommences in nearly the same order.

PROBLEM H.

CELESTIAL GLOBE.

Having the time of new or full moon, to find whether an eclipse be possible.

1. For the time of new moon :

RULE. Find the place of the node, and adjust the cord as in Prob. C-If the sun's place in the ecliptic for the given day be within 17° of either node, there will be a solar eclipse.

Whether places to the north of the sun, or to the south of him, may view this eclipse, will depend upon the situation of the moon as north or south of him.

2. For the time of full moon:

Find the place of the node, and adjust the cord as in Prob. C-If the sun's place be within 12° of either node, the moon will be eclipsed at the same distance on the corresponding side of the opposite one.

Ex. 1. There was a new moon on the 25th of March, 1838, at which time the longitude of her ascending node was 14°, (or 14°):—was the sun then eclipsed; and if eclipsed, could it have been viewed from places in the northern hemisphere?

Here, having adjusted the cord, I find that the sun was within 9° of the moon's ascending node, and consequently was eclipsed. As the longitude of the new moon coincides with the sun's, like him she was west of her ascending node, and had not yet arrived at it; she must therefore have been to the south of the sun, and projected on his disk by parallax only from some southern places.

Ex. 2. There was a full moon on the 9th of April, 1838, at which time her ascending node was 13 r :—did she escape eclipse?

Here, having adjusted the cord, I find that the sun, by this time,

POSSIBILITY OF SOLAR OR LUNAR ECLIPSE. 331

had advanced only 6° to the east of the moon's ascending node; the moon, therefore, was eclipsed 6° on the corresponding side of her descending node, or in 190.

Ex. 3. The moon was full on the 1st of May, 1836; her ascending node was then 20° Ŏ 34:-shew her longitude, and state whether she escaped the earth's shadow?

Ex. 4. Fourteen days after this, (or May 15,) did the new moon eclipse the sun; the moon's node having regressed to 19° 50:-and give reasons for supposing, that if eclipsed, the sun was not visibly eclipsed to certain latitudes ?

Ex. 5. Did the new moon of the 8th of November, in the same year, (1836,) eclipse the sun: the moon's ascending node having, by that time, become 10° 30:--and if eclipsed, from which hemisphere could he not have been seen eclipsed, although above the horizon?

Ex. 6. Was the full moon of the 7th of March, 1841, eclipsed, her node being 16° 47'?

Ex. 7. Was she eclipsed when full, on the 2d of August, her node having then become 9° m 0?

Ex. 8, Could she have been eclipsed at the next time of being full? Why, or why not? (S, on p. 326.)

Ex. 9. Was the sun eclipsed on either of the two following occasions of his conjunction with the moon, viz. ?

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Ex. 10. Find what eclipses took place under the several

circumstances given below :

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