English: Comparison of length variation for three eclipse periods of exceptionally small length variability. The x-axis gives the date of the second eclipse, between 2001 and 2050. The y-axis shows the fraction of a day left after subtracting 539848, 132592, and 126007 days respectively from the 1478-, 363-, and 345-year periods. The axis on the right shows more or less the same thing, expressed as hours and minutes.

The red points are for intervals going from an eclipse at the descending node to an eclipse at the ascending node, and blue points are for intervals going from ascending to descending node. The groups of points linked by green lines represent groups in which the starting eclipses (and the ending eclipses) are separated by six months. In all three cases the variation is quite small, because of the fact that the numbers of anomalistic months and anomalistic years in each period are close to whole numbers:

4573.002 and 344.979 for the 345-year Hipparchic period

4811.994 and 363.008 for the 363-year period (a Hipparchic period plus a saros)

19591.999 and 1477.982 for the 1478-year period (33 inex plus 29 saros)

Some eclipse periods have much greater variation in length, plus or minus more than a day for the "semester" (six lunar months) for example (see File:Length of semester.png).

Both the red points and the blue points are made up of waves of periods 6 years and 18.6 years. The 18.6-year wave for the Hipparchic period peaks when the two eclipses are near the time when the earth is at aphelion (early July). For the Hipparchic period the 6-year component (based on the interval between alignments of a node and the perigee) is very small because the Hipparchic period is so close to a whole number of anomalistic months. The component of period 6 years peaks either when the two eclipses occur when the moon is near apogee (for the Hipparchic period, having more than a whole number of anomalistic months) or when the moon is near perigee (for the other two, having a bit less than a whole number of anomalistic months).

The combination of the 363-year period and the 1478-year period is the so-called "Accuratissima" eclipse cycle of 1841 years, which also, as its name suggests, has a length that is quite constant. Like the Hipparchic period, it is also close to a whole number of days.