318. The point X where the Moon’s Orbit crosses the Ecliptic is called the Ascending Node, because the Moon ascends from it above the Ecliptic: and the opposite point of intersection V is called the Descending Node, because the Moon descends from it below the Ecliptic. When the Moon is at Y in the highest point of her Orbit, she is in her greatest North Latitude; and when she is at W in the lowest point of her Orbit, she is in her greatest South Latitude.
The Nodes have a retrograde motion.
Fig. I.
Which brings on the Eclipses sooner every year than they would
be if the Nodes had not such a motion.
319. If the line of the Nodes, like the Earth’s Axis, was carried parallel to itself round the Sun, there would be just half a year between the conjunctions of the Sun and Nodes. But the Nodes shift backward, or contrary to the Earth’s annual motion, 191⁄3 degrees every year; and therefore the same Node comes round to the Sun 19 days sooner every year than on the year before. Consequently, from the time that the ascending Node X (when the Earth is at E) passes by the Sun as seen from the Earth, it is only 173 days (not half a year) till the descending Node V passes by him. Therefore, in whatever time of the year we have Eclipses of the Luminaries about either Node, we may be sure that in 173 days afterward we shall have Eclipses about the other Node. And when at any time of the year the line of the Nodes is in the situation VGX, at the same time next year it will be in the situation rGs; the ascending Node having gone backward, that is, contrary to the order of Signs from X to s, and the descending Node from V to r; each 191⁄3 degrees. At this rate the Nodes shift through all the Signs and degrees of the Ecliptic in 18 years and 225 days; in which time there would always be a regular period of Eclipses, if any compleat number of Lunations were finished without a fraction. But this never happens, for if the Sun and Moon should start from a conjunction with either of the Nodes in any point of the Ecliptic, whilst the same Node is going round to that point again the Earth performs 18 annual revolutions about the Sun and 222 Degrees (or 7 Signs 12 Degrees) over; and the Moon 230 Lunations or Courses from Change to Change and 85 Degrees (or 2 Signs 25 Degrees) over; so that the Sun will be 138 Degrees from the same Node when it comes round, and the Moon 85 Degrees from the Sun. Hence, the period of Eclipses and revolution of the Nodes are completed in different times.
A period of Eclipses.
The defects of it.
320. In 18 years 10 days 7 hours 43 minutes after the Sun Moon and Nodes have been in a line of conjunction, they come very near to a conjunction again: only, if the conjunction from which you reckon falls in a leap-year, the return of the conjunction will be one day later. Therefore, if to the [[65]]mean time of any Eclipse of the Sun or Moon in leap-year, you add 18 years 11 days 7 hours 43 minutes; or in a common year a day less, you will have the mean time of that Eclipse returned again for some ages; though not always visible, because the 7 hours 43 minutes may shift a solar Eclipse into the night, and a lunar Eclipse into the day. In this period there are just 223 Lunations, and the Sun is again within half a degree of the same Node, but short of it. Therefore, although this period will serve tolerably well for some ages to examine Eclipses by, it cannot hold long; because half a degree from the Node sets the Moon 21⁄2 minutes of a degree from the Ecliptic. And as the Moon’s mean distance from the Earth is equal to 60 Semidiameters of the Earth, every minute of a degree at that distance is equal to 60 geographical miles, or one degree on the Earth; consequently 21⁄2 minutes of declination from the Ecliptic in the Moon’s Orbit, is equal to 150 such miles, or 21⁄2 degrees on the Earth. Consequently, if the Moon be passing by her ascending Node at the end of this period, her shadow will go 150 miles more southward on the Earth than it did at the beginning thereof. If the Moon be passing by her descending Node, her shadow will go 150 miles more northward: and in either case, in 500 years the shadow will have too great a Latitude to touch the Earth. So that any Eclipse of the Sun, which begins (for example) to touch the Earth at the south Pole (and that must be when the Moon is 17 degrees past her descending Node) will advance gradually northward in every return for about a thousand years, and then go off at the north Pole; and cannot take such another course again in less than 11,683 years.
This falling back of the Sun and Moon in every period, with respect to the Nodes, will occasion those Eclipses which happen about the ascending Node to go more southerly in each return; and those which happen about the descending Node to go more northerly: for the farther the Moon is short of the ascending Node, within the limits of Eclipses, the farther she is south of the Ecliptic; and on the contrary, the more she is short of the descending Node, the farther she is northward of the Ecliptic.
From Mr. G. Smith’s dissertation on Eclipses, printed at London, by E. Cave, in the year 1748.
321. “To illustrate this a little farther, we shall examine some of the most remarkable circumstances of the returns of the Eclipse which happened July 14, 1748, about noon: This Eclipse, after traversing the voids of space from the Creation, at last began to enter the Terra Australis Incognita, about 88 years after the Conquest, which was the last of King Stephen’s reign; every [[66]]Chaldean period it has crept more northerly, but was still invisible in Britain before the year 1622; when on the 30th of April it began to touch the south parts of England about 2 in the afternoon; its central appearance rising in the American South Seas, and traversing Peru and the Amazon’s country, through the Atlantic ocean into Africa, and setting in the Æthiopian continent, not far from the beginning of the Red Sea.
“Its next visible period was after three Chaldean revolutions in 1676, on the first of June, rising central in the Atlantic ocean, passing us about 9 in the morning, with four [[67]]Digits eclipsed on the under limb; and setting in the gulf of Cochinchina in the East-Indies.
“It being now near the Solstice, this Eclipse was visible the very next return in 1694, in the evening; and in two periods more, which was in 1730, on the 4th of July, was seen above half eclipsed just after Sun-rise, and observed both at Wirtemberg in Germany, and Pekin in China, soon after which it went off.