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Source: Inex

The inex (plural inexes) is an eclipse cycle of 10,571.95 days (about 29 years minus 20 days). The cycle was first described in modern times by Crommelin in 1901, but was named by George van den Bergh who studied it in detail half a century later. It has been suggested that the cycle was known to Hipparchos. One inex after an eclipse of a particular saros series there will be an eclipse in the next saros series, unless the latter saros series has come to an end.
It corresponds to:

358 lunations (synodic months)
388.50011 draconic months
30.50011 eclipse years (61 eclipse seasons)
383.67351 anomalistic months.
8 eclipse sets
The 30.5 eclipse years means that if there is a solar eclipse (or lunar eclipse), then after one inex a New Moon (resp. Full Moon) will take place at the opposite node of the orbit of the Moon, and under these circumstances another eclipse can occur.
Unlike the saros, the inex is not close to an integer number of anomalistic months so successive eclipses are not very similar in their appearance and characteristics. From the remainder of 0.67351, being near 2⁄3, every third eclipse will have a similar position in the moon's elliptical orbit and apparent diameter, so the quality of the solar eclipse (total versus annular) will repeat in these groupings of 3 cycles (87 years minus 2 months), called triads.
Inex series last much longer than saros series. For example, inex series 30 started in saros series −245 in 9435 BC and will continue well beyond 15,000 AD. But inex series are not unbroken: at the beginning and end of a series, eclipses may fail to occur. However once settled down, inex series are very stable and run for many thousands of years. For example, series 30 has produced eclipses every 29 years since saros series −197 in 8045 BC, including most recently the solar eclipse of February 5, 2000.
An inex also is close to an integer number of days (10,571.95) so solar eclipses on average take place at about the same geographical longitude at successive events, although variations of the moon's speed at different points of its orbit mask this relation. In addition sequential events occur at opposite geographical latitudes because the eclipses occur at opposite nodes. This is in contrast to the better known saros, which has a period of about 6,585+1⁄3 days, so successive solar eclipses tend to take place about 120° in longitude apart on the globe (although at the same node and hence at about the same geographical latitude).
The significance of the inex cycle is not in the prediction, but in the organization of eclipses: any eclipse cycle, and indeed the interval between any two eclipses, can be expressed as a combination of saros and inex intervals.