When the line of the nodes coincides with the line or the syzigies, or when the moon has no latitude at the time of new moon, the sun will be centrally eclipsed, as at A, PLATE XL. Fig. 1. This eclipse will be total, as in PLATE XXXIX. Fig. 11, if the diameter of the moon, as seen from the earth, is equal to that of the sun, or greater ; but if the moon's diameter is less, the eclipse will be annular, as in Fig. 12., or a ring of the sun's disc will appear round the moon at the time of apparent con junction. When the moon is about 14 degrees distant from her node at the time of new moon, and her latitude north, she will eclipse about 11 digits of the sun's north limb, as at B ; a digit being equal to a twelfth part of the sun's diameter. When the moon's distance from her node is about :3 degrees at the time of conjunction, she will obscure only 10 digits of the sun's northern limb, as at C, and so on, as is represented in the figure. But when the distance of the moon from her node is about 18 degrees, the moon will just touch the sun's northern limb, as at 0, without producing an eclipse. When the moon has south latitude, the same phenomena will be ob served in the sun's southern limb, as is represented in Fig. 1. between A and 0'.
While the moon is thus eclipsing the sun, the shadow of the moon will pass over the surface of the earth, and all those places over which the shadow passes, will per ceive the sun under an eclipse. Those who are under the centre of the shadow, will see the sun either totally or annularly eclipsed ; and those who are not under the centre, will see so many digits eclipsed proportional to their proximity to the centre of the shadow. This will be understood from Plate XL. Fig. 2. where S is the sun, E the earth, and NI the moon, moving in its orbit in the direction AMB. The dark space cel2d, comprehended between the lines Ce12, De12, will be the real shadow of the moon, within which none of the direct rays of the sun can fall ; and the lighter space c a b d, contained be tween the lines c a, d b, will be the penumbraof the moon, none of which is illuminated by the whole of the sun, but only by parts of his disc ; the parts near c12, d12 be ing enlightened only by a small portion of the sun's limb, and the parts near c a, (I b by nearly the whole of the sun. In this figure, the moon's shadow just ends in a point when it falls on the earth, as the moon is sup posed to be at her mean distance from the earth. Had the moon been in her apogee, or in the point of her orbit nearest the earth, her shadow would have covered a space upon its surface about 180 miles broad ; and to all places within this circle of 180 miles the eclipse would have been total. Had the moon been in her perigee, or
in that point of her orbit where she is nearest the earth, her shadow would have terminated in a point about e, and the sun would have been annularly eclipsed. The pe numbra cadbwill evidently be part of a cone whose ver tex is X, arid will cover the circular space aOb on the carth's surface. Divide the sun's diameter CD into 12 digits, and the space 120 into 12 equal parts, and from 12 as a centre describe 11 concentric circles, marked 11, 10, 9, 8, &c. in the figure. Then to a spectator on the earth at b, the western limb d of the moon will seem to touch the eastern limb of the sun C, and the eclipse will begin at the place b, and appear as at 0, Fig. 1. An observer at a will at the same instant see the western limb of the moon at c, leaving the eastern limb of the sun at D, and the sun and moon will appear as at 0', Fig. 1. To the inhabitants of the earth under the circle marked 1, the sun will appear eclipsed 1 digit, as at N, Fig, 1.: those who live under the circle marked 2, will have the sun eclipsed 2 digits, as at 'Al, Fig. 1. and so on with the rest. Those who live at the centre 12 of the pe numbra, will have the sun centrally eclipsed, as at A, Fig. 1.
Since the dark shadow of the moon covers such a small portion of the earth, the central eclipse is visible to few places, while the partial eclipse, or that in which only a part of the sun is obscured, is visible to all places within the circle a0b, about 4900 miles in diameter. All the places of the earth without the circle aOb have no eclipse of the sun ; and therefore when the moon's shadow does fall upon the earth at the time of new moon, the eclipse is only visible to those parts of the earth over which the earth's shadow happens to pass, When the moon is in her nodes at the time of new moon, the centre 12 of the moon's shadow will pass over the centre of the earth, and therefore the whole penumbra will fall upon the earth. When the moon is about 6 degrees from the node at the time of her con junction, almost the whole penumbra will fall upon the northern hemisphere of the earth, if the moon has north latitude ; but upon the southern hemisphere, if she is south of the ecliptic. If the moon changes 12 degrees from the node, a little more than a third part of the penumbra will fall upon the northern part of the earth when the moon has north latitude, and on the southern part if she has south latitude. When the conjunction happens at 17 or 18 degrees from the nodes, thc penum bra will just touch the earth.