The inex 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 , 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 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.
An example partial inex solar eclipse series
The following fourteen eclipses from part of inex series 52, which has been yielding eclipses every 29 years since saros series −115 in 5275 BC and will continue to do so beyond 15,000 AD.
Saros series 130: Solar eclipse of November 9, 1817
Saros series 131: Solar eclipse of October 20, 1846
Saros series 132: Solar eclipse of September 29, 1875
Saros series 133: Solar eclipse of September 9, 1904
Saros series 134: Solar eclipse of August 21, 1933
Saros series 135: Solar eclipse of July 31, 1962
Saros series 136: Solar eclipse of July 11, 1991
Saros series 137: Solar eclipse of June 21, 2020
Saros series 138: Solar eclipse of May 31, 2049
Saros series 139: Solar eclipse of May 11, 2078
Saros series 140: Solar eclipse of April 23, 2107
Saros series 141: Solar eclipse of April 1, 2136
Saros series 142: Solar eclipse of March 12, 2165
Saros series 143: Solar eclipse of February 21, 2194
An example partial inex lunar eclipse series
These eclipses are part of Lunar Inex Series 40.
Lunar Saros 123: Total Lunar Eclipse of 1826 Nov 14 (Micro Full Moon) Lunar Saros 124: Total Lunar Eclipse of 1855 Oct 25 Lunar Saros 125: Total Lunar Eclipse of 1884 Oct 04 Lunar Saros 126: Total Lunar Eclipse of 1913 Sep 15 (Micro Full Moon) Lunar Saros 127: Total Lunar Eclipse of 1942 Aug 26 Lunar Saros 128: Total Lunar Eclipse of 1971 Aug 06 Lunar Saros 129: Total Lunar Eclipse of 2000 Jul 16 (Micro Full Moon) Lunar Saros 130: Total Lunar Eclipse of 2029 Jun 26 Lunar Saros 131: Total Lunar Eclipse of 2058 Jun 06 Lunar Saros 132: Total Lunar Eclipse of 2087 May 17 Lunar Saros 133: Total Lunar Eclipse of 2116 Apr 27 Lunar Saros 134: Total Lunar Eclipse of 2145 Apr 07 Lunar Saros 135: Total Lunar Eclipse of 2174 Mar 18