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equator EQ. At the summer solstice, the Earth's axis has the position NDS; and that part of the ecliptic FG, in which the Moon is then new, touches the tropic of Cancer T at D. The north pole N at that time inclining 23 degrees toward the Sun, falls so many degrees within the Earth's enlightened disc, because the Sun is then vertical to D, 23 degrees north of the equator EQ; and the equator, with all its parallels seem elliptic curves bending downward, or toward the south pole, as seen from the Sun: which pole, together with 23 degrees all round it, is hid behind the disc in the dark hemisphere of the Earth. At the autumnal equinox, the Earth's axis has the position NOS, lying to the left hand as seen from the Sun or new Moon, which are then vertical to 0, where the ecliptic cuts the equator EQ. Both poles now lie in the circumference of the disc, the north pole just going to disappear behind it, and the south pole just entering into it; and the equator with all its parallels seem to be straight lines, because their planes pass through the observer's eye, as seen from the Sun, and very nearly so as seen from the Moon. At the winter solstice, the Earth's axis has the position NNS; when its south pole S inclining 23 degrees towards the Sun, falls 23 degrees within the enlightened disc, as seen from the Sun or new Moon, which are then vertical to the tropic of Capricorn t, 23 degrees south of the equator EQ; and the equator with all its parallels seem elliptic curves bending upward; the north pole being as far behind the disc in the dark hemisphere, as the south pole is come into the light. The nearer that any time of the year is to the equinoxes or solstices, the more it partakes of the phenomena relating to them.

339. Thus it appears, that from the vernal equinox to the autumnal, the north pole is enlightened; and the equator and all its parallels appear elliptical as seen from the Sun, more or less curved as the time is nearer to or farther from the summer sol

of the

Earth's

Plate XI. stice; and bending downward, or toward the south Various pole; the reverse of which happens from the aupositions tumnal equinox to the vernal. A little consideration will be sufficient to convince the reader, that the Earth's axis inclines toward the Sun at the summer the Sun at solstice; from the 'Sun at the winter solstice; and different sidewise to the Sun at the equinoxes; but toward the year. the right hand, as seen from the Sun at the vernal

axis are

seen from

times of

How these

affect solar

equinox; and toward the left hand at the autumnal. From the winter to the summer solstice, the Earth's axis inclines more or less to the right hand, as seen from the Sun; and the contrary from the summer to the winter solstice.

340. The different positions of the Earth's axis, positions as seen from the Sun at different times of the year, eclipses. affect solar eclipses greatly with regard to particular places; yea so far as would make central eclipses which fall at one time of the year, invisible if they had fallen at another; even though the Moon should always change in the nodes, and at the same hour of the day of which indefinitely various affections, we shall only give examples for the times of the equi noxes and solstices.

Fig. IV.

In the same diagram, let FG be part of the ecliptic, and IK, ik, ik, i k, part of the Moon's orbit; both seen edgewise, and therefore projected into right lines; and let the intersections N, O, D, E, be one and the same nodes at the above times, when the Earth has the forementioned different positions; and let the space included by the circles, P, p, p, p, be the penumbra at these times, as its centre is passing over the centre of the Earth's disc. At the winter solstice, when the Earth's axis has the position NN S, the centre of the penumbra P touches the tropic of Capricorn t in N at the middle of the general eclipse; but no part of the penumbra touches the tropic of Cancer T. At the summer solstice, when the Earth's axis has the position NDS (iDk

being then part of the Moon's orbit, whose node is at D), the penumbra p has its centre at D, on the tropic of Cancer T, at the middle of the general eclipse, and then no part of it touches the tropic of Capricorn t. At the autumnal equinox, the Earth's axis has the position NOS (i Ok being then part of the Moon's orbit), and the penumbra equally includes part of both tropics Tandt at the middle of the general eclipse: at the vernal equinox it does the same, because the Earth's axis has the position NES: but in the former of these two last cases, the penumbra enters the Earth at A, north of the tropic of Cancer T, and leaves it at m, south of the tropic of Capricorn ; having gone over the Earth obliquely southward, as its centre described the line AOm: whereas, in the latter case, the penumbra touches the Earth at n, south of the equator EQ, and describing the line n E q (similar to the former line A 0 m in open space) goes obliquely northward over the earth, and leaves it at q, north of the equa

tor.

In all these circumstances, the Moon has been supposed to change at noon in her descending node: had she changed in her ascending node, the pheno mena would have been as various the contrary way, with respect to the penumbra's going northward or southward over the Earth. But because the Moon changes at all hours, as often in one node as in the other, and at all distances from them both at different times as it happens, the variety of the phases of eclipses are almost innumerable, even at the same places; especially considering how variously the same places are situate on the enlightened disc of the Earth, with respect to the penumbra's motion, at the different hours when eclipses happen.

How

much of

341. When the Moon changes 17 degrees short of her descending node, the penumbra P 18 just touches the northern part of the Earth's disc, near umbra

Rr

e pe

falls on the

different

godes.

Earth at the north pole N; and as seen from that place the distances Moon appears to touch the Sun, but hides no part from the of him from sight. Had the change been as far short of the ascending node; the penumbra would have touched the southern part of the disc near the south pole S. When the Moon changes 12 degrees short of the descending node, more than a third part of the penumbra P 12 falls on the northern parts of the Earth at the middle of the general eclipse: had she changed as far past the same node, as much on the other side of the penumbra about P would have fallen on the southern part of the Earth; all the rest in the expansum or open space. When the Moon

The

Earth's

diurnal

lar eclip

changes 6 degrees from the node, almost the whole penumbra P6 falls on the Earth at the middle of the general eclipse. And lastly, when the Moon changes in the node at N, the penumbra P N takes the longest course possible on the Earth's disc; its centre falling on the middle of it, at the middle of the general eclipse. The farther the Moon changes from either node, within 17 degrees of it, the shorter is the penumbra's continuance on the Earth, because it goes over a less proportion of the disc, as is evident by the figure.

342. The nearer that the penumbra's centre is to the equator at the middle of the general eclipse, the motion longer is the duration of the eclipse at all those lengthens the dura places where it is central; because, the nearer that tion of so- any place is to the equator, the greater is the circle ses, which it describes by the Earth's motion on its axis; and fall with so, the place moving quicker, keeps longer in the lar circles. penumbra, whose motion is the same way with that of the place, though faster, as has been already mentioned, § 337. Thus (see the Earth at D and the penumbra at 12) while the point b in the polar circle a b c d is carried from b to c by the Earth's diurnal motion, the point d on the tropic of Cancer Tis carried a much greater length from d to D:

out the po

and therefore, if the penumbra's centre should go one time over c, and another time over D, the penumbra will be longer in passing over the moving-place d, than it was in passing over the moving-place b. Consequently, central eclipses about the poles are of the shortest duration; and about the equator of the longest.

ens the du

which fall

cles.

343. In the middle of summer, the whole frigid and shortzone, included by the polar circle a b c d, is enlight-ration of ened; and if it then happens that the penumbra's some centre passes over the north pole, the Sun will be within eclipsed much the same number of digits at a as at these cir. c; but while the penumbra moves eastward over c, it moves westward over a, because, with respect to the penumbra, the motions of a and c are contrary: for c moves the same way with the penumbra toward d, but a moves the contrary way toward b; and therefore the eclipse will be of longer duration at c than at a. At a, the eclipse begins on the Sun's eastern limb, but at c, on his western: at all places lying without the polar circles, the Sun's eclipses begin on his western limb, or near it, and end on or near his eastern. At those places where the penumbra touches the earth, the eclipse begins with the rising Sun, on the top of his western or uppermost edge; and at those places where the penumbra leaves the Earth, the eclipse ends with the setting Sun, on the ' top of his eastern edge, which is then the uppermost, just at its disappearing on the horizon.

mosphere.

344.If the Moon were surrounded by an atmosphere The Moon of any considerable density, it would seem to touch has no at. the Sun a little before the Moon made her appulse to his edge, and we should see a little faintness on that edge before it was eclipsed by the Moon: but as no such faintness has been observed, at least so far as I have ever heard, it seems plain, that the Moon has no such atmosphere as that of the Earth. The faint ring of light surrounding the Sun in to

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