The 38year

The saros is a wonderful cycle: not only do eclipses recur with 18.03-year spacings, because 223S is very close to 242N, but their character also repeats owing to the fact that 239A is also near to the magic number of days, 6,585 and a bit. Just what I mean by their character we will discuss later, but if we relax that added constraint, and look only for repeating occurrences of any sort, then we need to find only an agreement between S (the synodic month) and N (the nodical month).

Again a few strokes on the pocket calculator should satisfy you that

The difference amounts to about three hours.

This implies that an eclipse will likely take place 47 synodic months after a previous event. In terms of solar years that is a 3.8-year gap, almost exactly (I could have written 3.80005). Rather than convert the decimal to months and days it's easier just to count off the 1,388 days making up 3.8 years.

Again one can pore over tables of eclipses and check whether this is the case. I will not bore you with a whole string of examples, but take just one. Adding 3.8 years onto the July 6, 1982, total lunar eclipse invoked above, one expects a following eclipse about a week before the end of April in 1986. Sure enough, there was one on April 24.

There is an obvious relationship with the Metonic cycle here. Five multiplied by 3.8 equals 19 solar years, and 5 times 47 makes 235 synodic months. The 3.8-year cycle is a submultiple of the Metonic cycle. Not only do short sequences of eclipses occur with regular intervals of 19 years, but also that period is split up into five interleaving but distinct eclipse series.

The 3.8-year gap provides yet another regularity, then, which would allow investigators of eclipse records to make prognoses about future events once the pattern was recognized.

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