An Inex corresponds to:
358 lunations (synodic months) = 28.94444 years
388.50011 draconic months
30.50011 eclipse years
This means two Inex = 716 synodic months (358×2) and 777 draconic months (388.5×2).
This period will also be 61 eclipse or draconic years (777 – 716 or 30.5 x 2).
Each number in the diagram (below the top line) is derived from the numbers above it. Note that 18 Inex is the same period as 28 lunar nodal cycles. Both periods end at the lunar node they started at.
We can build on this, first by looking at data from a well-known science paper by Keeling & Whorf titled:
‘The 1,800-year oceanic tidal cycle: A possible cause of rapid climate change’
By adding these two periods together, plus one year, we get 7 sets of 18 Inex cycles (3647 years = 521y x 7).
Returning briefly to Wikipedia it says re Inex cycles:
‘Their appearance and longitude are irregular due to a lack of synchronization with the anomalistic month (period of perigee). However, groupings of 3 inex cycles (˜87 years minus 2 months) comes close (˜1,151.02 anomalistic months), so eclipses are similar in these groupings.’
So we can re-define the 7 sets of 18 Inex as 21 sets of 3, x 2 (= 126 Inex).
We shall return to the 21 Inex figure shortly.
Turning to a new paper (H/T Talkshop contributor ren) by Zhao and Feng:
‘Correlation between solar activity and the local temperature of Antarctica during the past 11,000 years’ (2015)
we note a possible link between the long Inex period and sunspot numbers.
‘It is found that SSN and temperature have some common periodicities, such as the 208 (204) yr, 441 yr, 488 (483) yr, 521 (516) yr, 562 (568) yr and 962 yr cycles, during the interval of interest.’
The abstract of the paper notes:
‘We find that the variations of SSN and T have some common periodicities, such as the 208 year (yr), 521 yr, and ~1000 yr cycles. The correlations between SSN and T are strong for some intermittent periodicities.’ [T = local temperature at Vostok].
The 208 year period is approximately the well-known de Vries cycle.
With all this information we can put forward for discussion possible ratios between certain data items:
21 Inex = 55 average solar cycles (a ratio of 1:Phi² as 21 and 55 are Fibonacci numbers), or 1 Inex = Phi² solar cycles
5 de Vries = 2 Inex long periods of 521 years each
Since 35 Inex cycles = almost 51 Jupiter-Saturn(J-S) conjunctions:
210 Inex (35×6) = 306 J-S (51×6), or
21 x 10 Inex = 34 x 9 J-S, or
1 Inex = Phi x 0.9 J-S
That would also mean: 1 solar cycle = 0.9 J-S / Phi
That would make the Jose cycle of 9 (= 3²) J-S equal to (5 x 2 x Phi) solar cycles.
A post at the Talkshop by Roy Martin noted:
‘As a footnote: In the work on the tidal theory there is a very significant cycle of 110.3 years. It is interesting to note that 110.3 x 1.61803(phi) = 178.48 years, within 0.31 years of the nominal José cycle period as derived above from the Jupiter – Saturn synodic.’
So here we have several interesting relationships between the Inex eclipse cycle, tides, Jupiter-Saturn synodics, sunspots, solar cycles and Fibonacci/Phi related harmonics.