Hence, the period of Eclipses and revolution of the Nodes are completed in different times. [Sidenote: 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 2-1/2 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 2-1/2 minutes of declination from the Ecliptic in the Moon’s Orbit, is equal to 150 such miles, or 2-1/2 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. [Sidenote: From Mr. G. SMITH’s dissertation on Eclipses, printed at _London_, by E. CAVE, in the year 1748.]