331. Eclipses of the Sun are more frequent than of the Moon, because the Sun’s ecliptic limits are greater than the Moon’s § [317]: yet we have more visible Eclipses of the Moon than of the Sun, because Eclipses of the Moon are seen from all parts of that Hemisphere of the Earth which is next her, and equally great to each of these parts; but the Sun’s Eclipses are visible only to that small portion of the Hemisphere next him whereon the Moon’s shadow falls; as shall be explained by and by at large.
Fig. I.
Total and annular Eclipses of the Sun.
[PLATE XI].
332. The Moon’s Orbit being elliptical, and the Earth in one of its focuses, she is once at her least distance from the Earth, and once at her greatest in every Lunation. When the Moon changes at her least distance from the Earth, and so near the Node that her dark shadow falls on the Earth, she appears big enough to cover the whole [[75]]Disc of the Sun from that part on which her shadow falls; and the Sun appears totally eclipsed there, as at A, for some minutes: But when the Moon changes at her greatest distance from the Earth, and so near the Node that her dark shadow is directed towards the Earth, her diameter subtends a less angle than the Sun’s; and therefore she cannot hide his whole Disc 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 eclipseth the Sun totally to that small spot whereon her shadow falls; but the darkness is not of a moment’s continuance.
The longest duration of total Eclipses of the Sun.
333. The Moon’s apparent diameter when largest exceeds the Sun’s when least only 1 minute 38 seconds of a degree: And in the greatest Eclipse of the Sun that can happen at any time and place, the total darkness continues no longer than whilst 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.
To how much of the Earth the Sun may be totally or partially eclipsed at once.
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 and the Sun’s least; and the total darkness can extend no farther than the dark shadow covers. Yet the Moon’s partial Shadow or Penumbra may then cover a circular space 4900 miles in diameter, within all which the Sun is more or less eclipsed as the places are less or more distant from the Center 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.
Duration of general and particular Eclipses.
The Moon’s dark shadow.
And Penumbra.
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.
Fig. II.