Plate XI. tal 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. Eclipses of the Moon. Fig. II. Why the Moon Man is total 345. Having said so much about 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, has 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 bygoing through the atmoseclipse. phere; which, being more dense near the Earth than at considerable heights above it, refracts or bends the Sun's rays more inward, § 179; and those which pass nearest the Earth's surface, are bent more than those rays which go through higher parts of the atmosphere, where it is less dense, until it be so thin or rare as to lose its refractive power. Let the circle f g h i, concentric to the Earth, include the atmosphere, whose refractive power vanishes at the heights fand i; so that the rays Wƒw and Vio go on straight without suffering the least refraction. Plate XI." But all those rays which enter the atmosphere, between f and k, and between i and 7, 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 VI touching the Earth at m and n, are bent so much as to meet at q, a little short of the Moon; and therefore the dark shadow of the Earth is contained in the space mo q pn, 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 R R. Moon are when the 347. When the Moon goes through the centre of why the the Earth's shadow, she is directly opposite to the Sun and Sun: yet the Moon has been often seen totally eclips- sometimes ed in the horizon when the Sun was also visible in visible the opposite part of it: for, the horizontal refraction Moon is being almost 34 minutes of a degree, § 181, and the totally eclipsed. 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 Fig. v.. either of her nodes, she just touches the Earth's shadow, but enters not into it. Let G H be the ecliptic, ef the Moon's orbit where she is 12 degrees from the node at her full; c d her orbit where she is 6 degrees from the node; a b her orbit where she is full in the node; A B the Earth's shadow, and M Duration the Moon. When the Moon describes the line ef, of central she just touches the shadow, but does not enter into eclipses of the Moon. it; when she describes the line cd, she is totally, Digits. Why the a lunar though not centrally immersed in the shadow; and when she describes the line a b, she passes by the node at M in the centre 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 the slowest; and when nearest to it, the 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 beginning or ending of a lunar eclipse, even with a good telescope; because the Earth's shadow is so eclipse faint and ill-defined about the edges, that when the cult to be Moon is either just touching or leaving it, the obdetermin- scuration of her limb is scarce sensible; and thereed by observation. fore the nicest observers can hardly be certain to se is so diffi The use of veral 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 broken on that part; and the moment she leaves it, he appears perfectly round again. 351. In astronomy, eclipses of the Moon are of in astro- great use for ascertaining the periods of her motions; eclipses nomy, chro especially such eclipses as are observed to be alike in geograall circumstances, and have long intervals of time Phy, and between them. In geography, the longitudes of nology. places are found by eclipses, as already shewn in the eleventh chapter. 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 it is impossible there can be two solar eclipses in the course of many ages which are alike in all circumstances. ness at crucifixion 352. From the above explanation of the doctrine The darkof eclipses, it is evident that the darkness at our SA- our SAVIOUR's crucifixion was supernatural. For he suf- VIOUR'S fered on the day on which the passover was eaten by supernathe Jews, on which day it was impossible that the tural.. 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 above 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. CHAP. XIX. Sherving the Principles on which the following Astronomical Tables are constructed, and the Method of calculating the Times of New and Full Moons and Eclipses by them. eye of THE nearer that any object is to the THE 353. an observer, the greater is the angle under which it appears: the farther from the eye, the less. The diameters of the Sun and Moon subtend different angles at different times. And at equal intervals of time, these angles are once at the greatest, and once at the least, in somewhat more than a complete revolution of the luminary through the ecliptic, from any given fixed star to the same star again. This proves that 'the Sun and Moon are constantly changing their distances from the Earth; and that they are once at their greatest distance and once at their least, in little more than a complete revolution. The gradual differences of these angles are not what they would be, if the luminaries moved in circular orbits, the Earth being supposed to be placed at some distance from the centre: but they agree perfectly with elliptic orbits, supposing the lower focus of each orbit to be at the centre of the Earth.* The farthest point of each orbit from the Earth's centre is called the apogee, and the nearest point is called the perigee.-These points are directly oppo site to each other. Astronomers divide each orbit into 12 equal parts called signs; each sign into 30 equal parts, called degrees; each degree into 60 equal parts, called minutes; and every minute into 60 equal parts, called seconds. The distance of the Sun or Moon from * The Sun is in the focus of the Earth's orbit, and the Earth in or near that of the Moon's orbit. |