Owing to the inclination of the moon's orbit to the plane of the ecliptic, an eclipse of the sun can occur only when the conjunction of the sun and moon takes place within about 16° of one of the nodes of the moon's orbit. The eclipse can be total only within about 11° of the node. An eclipse of the moon can occur only when the line sun-moon-earth makes an angle less than about 11° with the line of nodes; and the eclipse can be total only within about 8° of the node, the average limiting distances varying 1° or 2° according to the circumstances. These conditions being understood, the cycles of recurrence of eclipses of either kind can be worked out geometrically from the mean motions of the sun, moon, node and perigee by the aid of geometric conceptions shown in their simplest form in fig. 4. Here E is the earth, at the centre of a circle representing the mean orbit of the moon around it. MN is the line of nodes which is moving in the retrograde direction from N towards S1, at a rate of about 19.3° in a year, making a complete revolution in 18.6 years. Let the sun at the moment of some new moon be in the line ES1, continued. If the angle NES1 is less than 16° there will probably be an eclipse of the sun, which may be central if the angle is less than 11°. Let the next new moon take place in the line ES2 a month later. The mean value of the angle S1ES2 is about 29°; but as the node N has moved towards S1 about 1.4° during the interval, the sum of the angles NES1 and NES2 will be somewhat greater than S1ES2 by about 1.6°. The result is that if these two angles are nearly equal there may be two small partial eclipses of the sun, after which no more can occur until, by the annual revolution of the earth, the direction of the sun approaches the opposite line of nodes EM, nearly six months later. The result is that there are in the course of any one year two "eclipse seasons" each of about one month in duration, in which at least one eclipse of the sun, or possibly two small partial eclipses, may occur. One eclipse of the moon will generally, but not always, occur during a season.
Owing to the retrograde motion of the node the direction ES of the sun returns to the node at the end of about 347 days, so that a third eclipse season may commence before the end of a year. In this way there is a possible but very rare maximum of five eclipses of the sun in a year. Owing to the motion of the line of nodes each eclipse season occurs about 19 days earlier in the year than it did the year before. Another conclusion from the greater eclipse limit for the sun than for the moon is that in the long run eclipses of the sun, as regards the earth generally, occur oftener than those of the moon. But as any eclipse of the sun is visible only from a limited region of the earth's surface, while one of the moon may be seen from an entire hemisphere, more eclipses of the moon are visible at any one place than of the sun.