CHAP. XVIII. Of Eclipses: Their Number and Periods. A large Catalogue of Ancient and Modern Eclipses. (continued 2)

PLATE XI. Fig. IV. Phenomena of the Earth as seen from the Sun or New Moon at different times of the year.

183338. As seen from the Sun or Moon, the Earth’s Axis appears differently inclined every day of the year, on account of keeping its parallelism throughout its annual course. Let E, D, O, N, be the Earth at the two Equinoxes and the two Solstices; N S its Axis, N the North Pole, S the South Pole, Æ Q the Equator, T the Tropic of Cancer, t the Tropick of Capricorn, and ABC the Circumference of the Earth’s enlightened Disc as seen from the Sun or New Moon at these times. The Earth’s Axis has the position NES at the vernal Equinox, lying towards the right hand, as seen from the Sun or New Moon; its Poles N and S being then in the Circumference of the Disc; and the Equator and all its parallels seem to be straight lines, because their planes pass through the observer’s eye looking down upon the Earth from the Sun or Moon directly over E, where the Ecliptic FG intersects the Equator Æ. 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 23¹⁄₂ degrees towards the Sun, falls so many degrees within the Earth’s enlightened Disc, because the Sun is then vertical to D, 23¹⁄₂ degrees north of the Equator ÆQ; and the Equator with all its parallels seem elliptic curves bending downward, or towards the South Pole as seen from the Sun: which Pole, together with 23¹⁄₂ 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 O, where the Ecliptic cuts the Equator ÆQ. 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 23¹⁄₂ degrees toward the Sun falls 23¹⁄₂ degrees within the enlightened Disc, as seen from the Sun or New Moon which are then vertical to the Tropic of Capricorn t, 23¹⁄₂ degrees south of the Equator ÆQ; and the Equator with all its parallels seem elliptic curves bending upward; the North Pole being as far hid 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.

PLATE XI. Various positions of the Earth’s Axis, as seen from the Sun at different times of the year.

184339. Thus it appears, that from the vernal equinox to the autumnal, the North Pole is enlightened; and the Equator and all its parallels appear Semi-ellipses as seen from the Sun, more or less curved as the time is nearer to or farther from the Summer Solstice; and bending downwards or towards the South Pole; the reverse of which happens from the autumnal Equinox to the vernal. A little consideration will be sufficient to convince the reader, that the Earth’s Axis inclines towards the Sun at the Summer Solstice; from the Sun at the Winter Solstice; and sidewise to the Sun at the Equinoxes; but towards the right hand, as seen from the Sun at the vernal Equinox; and towards 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.

How these positions affect solar Eclipses.

340. The different positions of the Earth’s Axis, as seen from the Sun at different times of the year, 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 fell 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 Equinoxes and Solstices.

Fig. IV.

In the same Diagram, let FG be part of the Ecliptic, and IK ik ik ik 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 Node at the above times, when the Earth has the forementioned different positions; and let the spaces included by the Circles P, p, p, p be the Penumbra at these times, as its center is passing over the center of the Earth’s Disc. At the Winter Solstice, when the Earth’s Axis has the position NNS, the center 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 center 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 (iOk being then part of the Moon’s Orbit) and the Penumbra equally includes part of both Tropics T and t 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 185Earth at A, north of the Tropic of Cancer T, and leaves it at m, south of the Tropic of Capricorn t; having gone over the Earth obliquely southward, as its center described the line AOm: whereas in the latter case the Penumbra touches the Earth at n, south of the Equator ÆQ, and describing the line nEq (similar to the former line AOm in open space) goes obliquely northward over the Earth, and leaves it at q, north of the Equator.

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 Phenomena 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 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, considering also how variously the same places are situated on the enlightened Disc of the Earth, with respect to the Penumbra’s motion, at the different hours that Eclipses happen.

How much of the Penumbra falls on the Earth at different distances from the Nodes.

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 the North Pole N; and, as seen from that place the Moon appears to touch the Sun, but hides no part 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 of 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 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, the Penumbra PN takes the longest course possible on the Earth’s Disc; its center falling on the middle thereof, 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 portion of the Disc, as is evident by the Figure.

The Earth’s diurnal motion lengthens the duration of solar Eclipses, which fall without the polar Circles.

342. The nearer that the Penumbra’s center is to the Equator at the middle of the general Eclipse, the longer is the duration of the 186Eclipse at all those places where it is central; because, the nearer that any place is to the Equator, the greater is the Circle it describes by the Earth’s motion on its Axis: and so, the place moving quicker keeps longer in the Penumbra whose motion is the same way with that of the place, tho’ faster as has been already mentioned § 337. Thus, (see the Earth at D and the Penumbra at 12) whilst the point b in the polar Circle abcd is carried from b to c by the Earth’s diurnal motion, the point d on the Tropick of Cancer T is carried a much greater length from d to D: and therefore, if the Penumbra’s center goes 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.

And shortens the duration of some which fall within these Circles.

343. In the middle of Summer the whole frigid Zone included by the polar Circle abcd is enlightened; and if it then happens that the Penumbra’s center goes over the north Pole, the Sun will be eclipsed much the same number of Digits at a as at c; but whilst 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 towards d, but a moves the contrary way towards 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 in the Horizon.

The Moon has no Atmosphere.

344. If the Moon were surrounded by an Atmosphere of any considerable Density, it would seem to touch 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 were eclipsed by the Moon: But as no such faintness has been observed, at least so far as I 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 total Eclipses, called by Cassini la Chevelure du Soleil, seems to be the Atmosphere of the Sun; because it has been observed to move equally with the Sun, not with the Moon.

PLATE XI.

187345. Having been so prolix concerning Eclipses of the Sun, we shall drop that subject at present, and proceed to the doctrine of lunar Eclipses; which, being more simple, may be explained in less time.

Eclipses of the Moon. Fig. II.

That the Moon can never be eclipsed but at the time of her being Full, and the reason why she is not eclipsed at every Full, have been shewn already § 316, 317. Let S be the Sun, E the Earth, RR the Earth’s shadow, and B the Moon in opposition to the Sun: in this situation the Earth intercepts the Sun’s light in its way to the Moon; and when the Moon touches the Earth’s shadow at v she begins to be eclipsed on her eastern limb x, and continues eclipsed until her western limb y leaves the shadow at w: at B she is in the middle of the shadow, and consequently in the middle of the Eclipse.

Why the Moon is visible in a total Eclipse.

346. The Moon when totally eclipsed, is not invisible if she be above the Horizon and the Sky be clear; but appears generally of a dusky colour like tarnished copper, which some have thought to be the Moon’s native light. But the true cause of her being visible is the scattered beams of the Sun, bent into the Earth’s shadow by going through the Atmosphere; which, being more dense near the Earth than at considerable heights above it, refracts or bends the Sun’s rays more inward § 179, the nearer they are passing by the Earth’s surface, than those rays which go through higher parts of the Atmosphere, where it is less dense according to its height, until it be so thin or rare as to lose its refractive power. Let the Circle fghi, concentric to the Earth, include the Atmosphere whose refractive power vanishes at the heights f and i; so that the rays Wfw and Viv go on straight without suffering the least refraction: But all those rays which enter the Atmosphere between f and k, and between i and l, on opposite sides of the Earth, are gradually more bent inward as they go through a greater portion of the Atmosphere, until the rays Wk and Vl, touching the Earth at m and n, are bent so as to meet at q, a little short of the Moon; and therefore the dark shadow of the Earth is contained in the space moqpn where none of the Sun’s rays can enter: all the rest RR, being mixed by the scattered rays which are refracted as above, is in some measure enlightened by them; and some of those rays falling on the Moon give her the colour of tarnished copper, or of iron almost red hot. So that if the Earth had no Atmosphere, the Moon would be as invisible in total Eclipses as she is when New. If the Moon were so near the Earth as to go into its dark shadow, suppose about po, she would be invisible during her stay in it; but visible before and after in the fainter shadow RR.

PLATE XI. Why the Sun and Moon are sometimes visible when the Moon is totally eclipsed.

188347. When the Moon goes through the center of the Earth’s shadow she is directly opposite to the Sun: yet the Moon has been often seen totally eclipsed in the Horizon when the Sun was also visible in the opposite part of it: for, the horizontal refraction being almost 34 minutes of a degree § 181, and the diameter of the Sun and Moon being each at a mean state but 32 minutes, the refraction causes both Luminaries to appear above the Horizon when they are really below it § 179.

Fig. V. Duration of central Eclipses of the Moon.

348. When the Moon is Full at 12 degrees from either of her Nodes, she just touches the Earth’s shadow but enters not into it. Let GH be the Ecliptic, ef the Moon’s Orbit where she is 12 degrees from the Node at her Full; cd her Orbit where she is 6 degrees from the Node, ab her Orbit where she is Full in the Node, AB the Earth’s shadow, and M the Moon. When the Moon describes the line ef she just touches the shadow but does not enter into it; when she describes the line cd she is totally though not centrally immersed in the shadow; and when she describes the line ab she passes by the Node at M in the center of the shadow, and takes the longest line possible, which is a diameter, through it: and such an Eclipse being both total and central is of the longest duration, namely, 3 hours 57 minutes 6 seconds from the beginning to the end, if the Moon be at her greatest distance from the Earth: and 3 hours 37 minutes 26 seconds, if she be at her least distance. The reason of this difference is, that when the Moon is farthest from the Earth she moves slowest; and when nearest to it, quickest.

Digits.

349. The Moon’s diameter, as well as the Sun’s, is supposed to be divided into twelve equal parts called Digits; and so many of these parts as are darkened by the Earth’s shadow, so many Digits is the Moon eclipsed. All that the Moon is eclipsed above 12 Digits, shew how far the shadow of the Earth is over the body of the Moon, on that edge to which she is nearest at the middle of the Eclipse.

Why the beginning and end of a lunar Eclipse is so difficult to be determined by observation.

350. It is difficult to observe exactly either the beginning or ending of a lunar Eclipse, even with a good Telescope; because the Earth’s shadow is so faint, and ill defined about the edges, that when the Moon is either just touching or leaving it, the obscuration of her limb is scarce sensible; and therefore the nicest observers can hardly be certain to four or five seconds of time. But both the beginning and ending of solar Eclipses are visibly instantaneous; for the moment that the edge of the Moon’s Disc touches the Sun’s, his roundness seems a little broke on that part; and the moment she leaves it he appears perfectly round again.

The use of Eclipses in Astronomy, Geography, and Chronology.

189351. In Astronomy, Eclipses of the Moon are of great use for ascertaining the periods of her motions; especially such Eclipses as are observed to be alike in all circumstances, and have long intervals of time between them. In Geography, the Longitudes of places are found by Eclipses, as already shewn in the eleventh chapter: but for this purpose Eclipses of the Moon are more useful than those of the Sun, because they are more frequently visible, and the same lunar Eclipse is of equal largeness and duration at all places where it is seen. In Chronology, both solar and lunar Eclipses serve to determine exactly the time of any past event: for there are so many particulars observable in every Eclipse, with respect to its quantity, the places where it is visible (if of the Sun) and the time of the day or night; that ’tis impossible there can be two Eclipses in the course of many ages which are alike in all circumstances.

The darkness at our Saviour’s crucifixion supernatural.

352. From the above explanation of the doctrine of Eclipses it is evident, that the darkness at our Saviour’s crucifixion was supernatural. For he suffered on the next day after eating his last Passover-Supper, on which day it was impossible that the Moon’s shadow could fall on the Earth, for the Jews kept the Passover at the time of Full Moon: nor does the darkness in total Eclipses of the Sun last four minutes in any place § 333, whereas the darkness at the crucifixion lasted three hours, Matt. xxviii. 15. and overspread at least all the land of Judea.