335. When the Penumbra first touches the Earth the general Eclipse begins: when it leaves the Earth the general Eclipse ends: from the beginning to the end the Sun appears eclipsed in some part of the Earth or other. When the Penumbra touches any place the Eclipse begins at that place, and ends when the Penumbra leaves it. When the Moon changes in the Node, the Penumbra goes over the center of the Earth’s Disc as seen from the Moon; and consequently, by describing the longest line possible on the Earth, continues the longest upon it; namely, at a mean rate, 5 hours 50 minutes: more, if the Moon be at her greatest distance from the Earth, because she then moves slowest; less, if she be at her least distance, because of her quicker motion.
336. To make the last five articles and several other Phenomena plainer, let S be the Sun, E the Earth, M the Moon, and AMP the Moon’s Orbit. Draw the right line Wc 12 from the western edge of the Sun at W, touching the western edge of the Moon at c and the Earth at 12: draw also the right line Vd 12 from the eastern edge of the Sun at V, touching the eastern edge of the Moon at d and the Earth at 12: the dark space ce 12 d included between those lines is the Moon’s shadow, ending in a point at 12 where it touches the Earth; because in this case the Moon is supposed to change at M in the middle between A the Apogee, or farthest point of her Orbit from the Earth, and P the Perigee, or nearest point to it. For, had the point P been at M, the Moon had been nearer the Earth; and her dark shadow at e would have covered a space upon it about 180 miles broad, and the Sun would have been totally darkened as at A (Fig I) with some continuance: but had the point A (Fig. II) been at M, the Moon would have been farther from the Earth, and her shadow would have ended in a point about e, and therefore the Sun would have appeared as at B (Fig. I) like a luminous ring all around the Moon. Draw the right lines WXdh and VXcg, touching the contrary sides of the Sun and Moon, and ending on the Earth at a and b: draw also the right line SXM 12, from the center of the Sun’s Disc, through the Moon’s center, to the Earth at 12; and suppose the two former lines WXdh and VXcg to revolve on the line SXM 12 as an Axis, and their points a and b will describe the limits of the Penumbra TT on the Earth’s surface, including the large space a0b12a; within which the Sun appears more or less eclipsed as the places are more or less distant from the verge of the Penumbra a0b.
Draw the right line y 12 across the Sun’s Disc, and parallel to the plane of the Moon’s Orbit; divide this line into twelve equal parts, as in the Figure, for the twelve [76]Digits of the Sun’s diameter: and at equal distances from the center of the Penumbra TT to its edge on the Earth, or from 12 to 0, draw twelve concentric Circles, as marked with the numeral Figures 1 2 3 4 &c. and remember that the Moon’s motion in her Orbit AMP is from west to east, as from s to t. Then,
To an observer on the Earth at b, the eastern limb of the Moon at d seems to touch the western limb of the Sun at W, when the Moon is at M; and the Sun’s Eclipse begins at b; appearing as at A in Fig. III at the left hand; but at the same moment of absolute time to an observer at a in Fig. II the western edge of the Moon at c leaves the eastern edge of the Sun at V, and the Eclipse ends, as at the right hand C of Fig. III. At the very same instant, to all those who live on the Circle marked 1 on the Earth E in Fig. II, the Moon M cuts off or darkens a twelfth part of the Sun S, and eclipses him one Digit, as at 1 in Fig. III: to those who live on the Circle marked 2 in Fig. II the Moon cuts off two twelfth parts of the Sun, as at 2 in Fig. III: to those on the Circle 3, three parts; and so on to the center at 12 in Fig. II, where the Sun is centrally eclipsed as at B in the middle of Fig. III: under which Figure there is a scale of hours and minutes, to shew at a mean state how long it is from the beginning to the end of a central Eclipse of the Sun on the parallel of London; and how many Digits are eclipsed at any particular time from the beginning at A to the middle at B, or the end at C. Thus in 16 minutes from the beginning, the Sun is two Digits eclipsed; in an hour and five minutes, 8 Digits; and in an hour and thirty-seven minutes, 12 Digits.
337. By Fig. II it is plain, that the Sun is totally or centrally eclipsed but to a small part of the Earth at any time; because the dark conical shadow e of the Moon M falls but on a small part of the Earth: and that the partial Eclipse is confined at that time to the space included by the Circle a 0 b, of which only one half can be projected in the Figure, the other half being supposed to be hid by the convexity of the Earth E: and likewise, that no part of the Sun is eclipsed to the large space YY of the Earth, because the Moon is not between the Sun and that part of the Earth: and therefore to all that part the Eclipse is invisible. The Earth turns eastward on its Axis, as from g to h, which is the same way that the Moon’s shadow moves; but the Moon’s motion is much swifter in her Orbit from s to t: and therefore, altho’ Eclipses of the Sun are of longer duration on account of the Earth’s motion on its Axis, than they would be if that motion was stopt, yet in 3 minutes and 13 seconds of time, the Moon’s swifter motion carries her dark shadow quite over any place that its center touches at the time of greatest obscuration. The motion of the shadow on the Earth’s Disc is equal to the Moon’s motion from the Sun, which is about 301⁄2 minutes of a degree every hour at a mean rate; but so much of the Moon’s Orbit is equal to 301⁄2 degrees of a great Circle on the Earth, § 320; and therefore the Moon’s shadow goes 301⁄2 degrees or 1830 geographical miles on the Earth in an hour, or 301⁄2 miles in a minute, which is almost four times as swift as the motion of a cannon-ball.
338. 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.
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 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.
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.
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 Earth 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.
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.
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 Eclipse 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.
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.
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.
345. 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.
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.
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.
347. 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.
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.
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.
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.
351. 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.
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.