Inex


The inex is an eclipse cycle of 10,571.95 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. 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:
  • 10,571.95 solar days
  • 28.95 years
  • 358 synodic months
  • 388.50011 draconic months
  • 30.50011 eclipse years
  • 383.67351 anomalistic months
  • 386.94 sidereal months
  • 8 eclipse sets
The 30.5 eclipse years means that if there is a solar eclipse, then after one inex a New 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 will repeat in these groupings of 3 cycles, 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 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.
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 form 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.
These eclipses are part of Lunar Inex Series 40.
A saros-inex panorama has been produced by Luca Quaglia and John Tilley. It shows 61775 solar eclipses from −11000 to +15000.
Each column of the graph is a complete Saros series which progresses smoothly from partial eclipses into total or annular eclipses and back into partials. Each graph row represents an inex series.
The lifetime of each inex series is not simple due to long-term period variations in the synodic and draconic month lengths. One can see from the data file that in the future the graph is horizontal, whereas at the beginning of the panorama around 11,000 BC for the moon to come back to the same latitude at another eclipse required about one saros for every ten inex. This implies that back then 3580+223 or 3803 synodic months equaled 3885+242 or 4127 draconic months. So a synodic month was about 1.0851959 draconic months, as compared to about 1.0851958 today. This decrease by about 0.1 ppm can be compared to the decrease in the length of a tropical year by about 1 ppm in the last 10,000 years. One source states that the draconic month is increasing by about 0.4 seconds per millennium whereas the synodic month is increasing by about 0.2 seconds per millennium, but doesn't explain why the draconic month is increasing faster.
From the data file we can see that eclipses recur with a period of a combination of 15 inex and 1 saros throughout the whole panorama, for example from the eclipse of saros series −290, inex series 2 to the eclipse of saros series 580, inex series 60 on the right-side edge of the panorama. Similar cycles with more or less than 15 inex per saros also cover the whole panorama.

Lunar Saros-Inex panorama

Lunar eclipses can also be plotted in a similar diagram, this diagram covering 1000 AD to 2500 AD. The yellow diagonal band represents all the eclipses from 1900 to 2100. This graph immediately illuminates that this 1900–2100 period contains an above average number of total lunar eclipses compared to other adjacent centuries.