Now we must advance one stage in our conceptions of the movements of the Earth and the Moon, so far as regards the bearing of those movements on the question of eclipses. The Earth moves in a plane which is called the “Plane of the Ecliptic,” and correspondingly, the Sun has an apparent annual motion in the same plane. The Moon moving in a different plane, inclined to the first mentioned one to the extent of rather more than 5°, the Moon’s orbit will evidently intersect the ecliptic in two places. These places of intersection are called “Nodes,” and the line which may be imagined to join these Nodes is called the “Line of Nodes.” When the Moon is crossing the ecliptic from the S. to the N. side thereof, the Moon is said to be passing through its “Ascending Node” (☊); the converse of this will be the Moon passing back again from the N. side of the ecliptic to the S. side, which is the “Descending Node” (☋). Such changes of position, with the terms designating them, apply not only to the Moon in its movement round the Earth, but to all the planets and comets circulating round the Sun; and also to satellites circulating round certain of the planets, but with these matters we have no concern now.
Footnotes:
[1] D. Lardner, Handbook of Astronomy, 3rd ed., p. 288.
[2] But not one of them was visible at Greenwich.
[3] Latin Annulus, a ring.
CHAPTER III.
THE “SAROS” AND THE PERIODICITY OF ECLIPSES.
To bring about an eclipse of the Sun, two things must combine: (1) the Moon must be at or near one of its Nodes; and (2), this must be at a time when the Moon is also in “Conjunction” with the Sun. Now the Moon is in Conjunction with the Sun (= “New Moon”) 12 or 13 times in a year, but the Sun only passes through the Nodes of the Moon’s orbit twice a year. Hence an eclipse of the Sun does not and cannot occur at every New Moon, but only occasionally. An exact coincidence of Earth, Moon, and Sun, in a straight line at a Node is not necessary to ensure an eclipse of the Sun. So long as the Moon is within about 18½° of its Node, with a latitude of not more than 1° 34′, an eclipse may take place. If, however, the distance is less than 15¼° and the latitude less than 1° 23′ an eclipse must take place, though between these limits[4] the occurrence of an eclipse is uncertain and depends on what are called the “horizontal parallaxes” and the “apparent semi-diameters” of the two bodies at the moment of conjunction, in other words, on the nearness or “far-offness” of the bodies in question. Another complication is introduced into these matters by reason of the fact that the Nodes of the Moon’s orbit do not occupy a fixed position, but have an annual retrograde motion of about 19¼°, in virtue of which a complete revolution of the Nodes round the ecliptic is accomplished in 18 years 218⅞ days (= 18.5997 years).
The backward movement of the Moon’s Nodes combined with the apparent motion of the Sun in the ecliptic causes the Moon in its monthly course round the Earth to complete a revolution with respect to its Nodes in a less time (27.2 days) than it takes to get back to Conjunction with the Sun (29.5 days); and a curious consequence, as we shall see directly, flows from these facts and from one other fact. The other fact is to the Sun starting coincident with one of the Moon’s Nodes, returns on the Ecliptic to the same Node in 346.6 days. The first named period of 27.2 days is called the “Nodical Revolution of the Moon” or “Draconic Month,” the other period of 29.5 days is called the “Synodical Revolution of the Moon.” Now the curious consequence of these figures being what they are is that 242 Draconic Months, 223 Lunations, and 19 Returns of the Sun to one and the same Node of the Moon’s orbit, are all accomplished in the same time within 11 hours. Thus (ignoring refinements of decimals):—