Plate XI. distance from the earth, and once at her greatest, Fig. I. in every lunation. When the Moon changes at her least distance from the Earth, and so near the node that her dark shadow falls upon the Earth, she ap pears big enough to cover the whole disc of the Sun from that part on which her shadow falls; and Total and the Sun appears totally eclipsed there, as at A, for eclipses of some minutes: but when the Moon changes at her the Sun. greatest distance from the Earth, and so near the annular The long node that her dark shadow is directed toward the earth, her diameter subtends a less angle than the Sun's; and therefore she cannot hide his whole dise from any part of the Earth, nor does her shadow reach it at that time; and to the place over which the point of her shadow hangs, the eclipse is annular, as at B; the Sun's edge appearing like a luminous ring all around the body of the Moon. When the change happens within 17 degrees of the node, and the Moon at her mean distance from the Earth, the point of her shadow just touches the Earth, and she eclipses the Sun totally to that small spot whereon her shadow falls; but the darkness is not of a moment's continuance. 333. The Moon's apparent diameter, when largest, est dura exceeds the Sun's when least, only 1 minute 38 tion of to- seconds of a degree: and in the greatest eclipse of tal eclipses of the the Sun that can happen at any time and place, the Sun To how much of the Earth the Sun may be to tally or partially eclipsed at once. total darkness continues no longer than while the Moon is going 1 minute 38 seconds from the Sun in her orbit; which is about 3 minutes and 13 seconds of an hour. 334. The Moon's dark shadow covers only a spot on the Earth's surface, about 180 English miles broad, when the Moon's diameter appears largest, * Although the Sun and Moon are spherical bodies, as seen from the Earth they appear to be circular planes; and so would the Earth do, if it were seen from the Moon. The apparently flat surfaces of the Sun and Moon are called their discs by astronomers. Yet and the Sun's least; and the total darkness can ex- Plate XI. tend no farther than the dark shadow covers. the Moon's partial shadow or penumbra may then cover a circular space 4900 miles diameter, within all which the Sun is more or less eclipsed, as the places are less or more distant from the centre of the penumbra. When the Moon changes exactly in the node, the penumbra is circular on the Earth at the middle of the general eclipse; because at that time it falls perpendicularly on the Earth's surface: but, at every other moment it falls obliquely, and will therefore be elliptical, and the more so, as the time is longer before or after the middle of the general eclipse; and then, much greater portions of the Earth's surface are involved in the penumbra. and parti 335. When the penumbra first touches the Earth, Duration the general eclipse begins: when it leaves the Earth, of general the general eclipse ends: from the beginning to the cular eclpend the Sun appears eclipsed in some part of the ses. 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 centre 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 Fig. II. 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 side of the Sun at IV, touching the western side of the Moon at c, and the Earth at 12: draw also the right line Vd 12 from the eastern side of the Sun at V, touching the eastern side of the Moon at d, and the The dark sha- Earth at 12: the dark space ce 12 d included be tween those lines in 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 and pe. appeared, as at B (Fig. I.), like a luminous ring all numbra. around the Moon. Draw the right lines IV Xdh and VXeg, touching the contrary sides of the Sun and Moon, and ending on the Earth at a and 6: draw also the right line S X M 12, from the centre of the Sun's disc, through the Moon's centre, 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 a 0 b 12 a, within which the Sun appears more or less eclipsed, as the places are more or less distant from the verge of the penumbra a 0 b. Digits, what. Draw the right line y 12 across the Sun's disc, perpendicular to SXM, the axis of the penumbra: then divide the line y 12 into twelve equal parts, as in the figure, for the twelve digits of the Sun's diameter and at equal distances from the centre of the penumbra at 12 (on the Earth's surface YY) to its edge a 0 b, draw twelve concentric circles, as marked with the numeral figures 1, 2, 3, 4, &c. and A digit is a twelfth part of the diameter of the Sun or Moon. remember that the Moon's motion in her orbit Plate XI. AMP is from west to east, as from s to t. Then, To an observer on the Earth at b, the eastern Thediffer limb of the Moon at d seems to touch the western ent phases of a solar limb of the Sun at W, when the Moon is at M; eclipse. 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 centre 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 rate, 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, eight digits; and in an hour and thirty-seven minutes, 12 digits. Fig. 111. 337. By Fig. II, it is plain, that the Sun is total- Fig. 14 ly 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 a 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 The velo the Earth. Plate XI. of the Sun is eclipsed to the large space rr of the Earth, because the Moon is not between the Sun and city of the any of that part of the Earth: and therefore to all that Moon's part the eclipse is invisible. The Earth turns eastshadow on ward on its axis, as from g to b, 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 : and therefore, although 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 four minutes of time at most the Moon's swifter motion carries her dark shadow quite over any place that its centre 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 30 minutes of a degree every hour at a mean rate; but so much of the Moon's orbit is equal to 30 degrees of a great circle on the Earth, § $20; and therefore the Moon's shadow goes 30 degrees or 1830 geographical miles on the Earth in an hour, or 30 miles in a minute, which is almost four times as swift as the motion of a cannon ball. Fig. IV. 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, NS its axis, N the north pole, S the south pole, Q the equator, T the tropic of Cancer, t the tropic of Capricorn, and A B C the circumference of the Earth's enlightened disc as seen from the Sun or new Moon at these Phonome- times. The Earth's axis has the position NES at na of the the vernal equinox, lying toward the right hand, as seen from seen from the Sun or new Moon; its poles N and S the Sun or being then in the circumference of the disc; and the atdifferent equator and all its parallels seem to be straight lines, times of 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 Earth as new Moon the year. |