Before we can solve the logic of the 56-year cycle and its implications, we must see eclipses as a phenomena occurring regularly during the year. They can occur only at certain specified times. Solar eclipses occur only at the very moment of the new moon (the molad or conjunction), lunar eclipses 14.765 days (on the average) later, at the time of the full moon (or opposition). A people following a lunar calendar would soon be aware of occasional solar eclipses on the final day of the month, and lunar eclipses in mid-month. They would hardly become frightened at this expected "sign in the heavens."
Saros Related to Metonic Cycle
The Saros cycle was supposedly known by early Chinese and Egyptians. Did they also know of the Metonic cycle? It is but a single eclipse year longer. The goal of an astronomer dealing with time would be to find a cycle where the year, the month and the day come out even. The Saros cycle would likely have been discovered first because it produces very similar solar eclipses slightly over 18 years apart. It would have been a simple step to note another eclipse 346.62 days later at the completion of a Metonic cycle. The unusual fact that 19 tropical years (almost exactly) were then complete, would make this latter eclipse stand out as being of great importance to calendar makers. From this time forward both Saros and Metonic cycles could have been used to predict eclipses. Cycles might have been added together. Take three Metonic cycles for example. The total would be 57 years. Subtracting a single eclipse year would bring us close but slightly short of the 56-year (less four days) Stonehenge cycle. It would require but half a synodic month more.
Eclipses in Sequence
Are eclipses so infrequent that 18-, 19- and 56-year cycles are needed to keep track of them? Not at all. Eight have been known to occur in just over a year We might have three eclipses in less than, a month's time! Consider the sequence that started with an eclipse of the sun on January 5, 1935:
This series of eight eclipses in a 369-day period shows a startling frequency in a phenomenon that we are apt to think of as occurring only at widely spaced intervals. Five are eclipses of the moon, most valuable to Stonehenge astronomers in noting the exact relative positions of moon and stars at the central moment of the eclipse with the sun exactly 180 away at that moment. The hour of the day would give the fraction of the earth's revolution.
Conditions for an Eclipse
Let's consider lunar eclipses first because they are of greatest value in timekeeping, A lunar eclipse will occur only at the time of full moon, but not at every full moon. It must be a full moon during an "eclipse season." For lunar eclipses this is only a 25-day period of time, centered on the crossing place of the moon's orbit and the ecliptic, called a node. These 25-day eclipse seasons (there are two of them, 173.31 days apart, one at the ascending and one at the descending node) for lunar eclipses drift slowly backwards through the calendar year. They come about 18.6 days earlier each year because the "eclipse year" (346.62) is that much shorter than the tropical year. Will there be a lunar eclipse during each of these "eclipse seasons" each year? No, because the 29.53-day synodic month is longer than the 25-day season. We might have a full moon three days before the season began and thus no eclipse; then the following full moon would arrive one day after the season ended and again no lunar eclipse. In most cases, however, the 25-day season would contain one lunar (and one solar) eclipse, and that lunar eclipse could be seen by more than half the people on earth. At the next eclipse season six lunar months later another lunar eclipse would usually occur, again visible to over half the earth's population. The new moon half way between these two full moons would produce a central solar eclipse in that the new moon crossed the sun's path (the ecliptic) about in the center of the season.
Years Without Lunar Eclipses
There is however the possibility that the full moons might "straddle the eclipse season at consecutive seasons (173.31 days apart) and thus we might go an entire calendar year without a lunar eclipse. Examples are 1929, '40, '51, '62, '66, '69 and '80. The synodic month is only 2.32 days longer than the 27.21-day nodical month and thus at the second season, the full moon would arrive just before the eclipse season and the following full moon about three days after. In this case also the intervening new moon would produce a central solar eclipse with its track near the equator. Years without lunar eclipses would, make it urgent for calendar makers to be aware of impending (not menacing) eclipses, hence the building of Stonehenge.
Solar Eclipse Frequency
Solar eclipses are more frequent than lunar eclipses because the eclipse seasons for them is 37 days long, again centered on the ascending and descending nodes. These eclipses of the sun will occur at the very moment of the molad, or conjunction of the moon and the sun in the sky. This is the astronomer's new moon and will also (normally) precede the "new moon" day of the Sacred Calendar by six hours to several days. Five solar eclipses might occur in a single calendar year. How is this possible? Each 37-day eclipse season must contain at least one solar eclipse, and may contain two. The synodic month is only 29.53 days long; thus two new moons could occur during the season and both would produce solar eclipses. Both however would be partial eclipses, the shadow cone crossing above the north pole in one, and below the south pole in the other. How many seasons might occur in a single calendar year? Three; if one began early in January, the next would begin 173.31 days later in July, and a third season late in December. With conditions just right we can have 3 eclipses in the first season, 3 in the second and 2 in the third, all in a single calendar year. Despite the abundance of eclipses the value to calendar makers is in the lunar eclipse for two reasons. First it is much more widely visible being seen from over half the earth. Second because it marks the very midpoint of the synodic month whereas a solar eclipse would mark the moment of the conjunction (the new moon) for that longitude only. This moment would sweep eastward over the earth just as the moon's shadow (umbra) would follow an easterly track. The observation of the lunar eclipse does not suffer from this variable. It points out midmonth to all observers. A similar situation exists with regard to observing the sun at the equinox. It rises due east (and sets due west) for every observer on earth on the day of the equinox. Selection of the solstice as a beginning point has advantages but requires a different azimuth at different latitudes.