The graph below shows the actual number of solar eclipse per
century, and a plot of a sine shape function with a period of 585.1 years.
This period also seems to determine the frequency of lunar tetrads (4 total
lunar eclipse each separated by 6 lunations, the the frequency of so-called
duo eclipses and double duos. See below. IIt should be noted that 586 year
is a reasonable average approximation. In reality the period is decreasing.
This is described in Morsels III, chapter 21.
A duo eclipse is a set of two solar eclipse separated by one lunation (of 29.5 days). The last time this happened were the partial eclipses of 1 and 31 July 2000. The next duo pair will be on 1 June 2011 and 1 July 2011.
A double duo consists of two duo pairs separated by 5 lunations. The sequence for a double duo is: eclipse - 1 lunation - eclipse - 5 lunations - eclipse - one lunation - eclipse. In this case there are 4 eclipse within 7 months. The last double duo was in 1935 (5 January / 3 February / 30 June / 30 July), and the next one will be in 2134 (24 April / 23 May / 17 October / 16 November) [a separate page on duos and double duos will be developed]
The graph below shows the total number of solar eclipses per century, as well as number of duos and double duo eclipses. Again the 586 year period can be seen. It also shows that in some centuries (including the current one) there is no double duo at all. The double duos in the 26th and 27th century are taking place in 2150 and 2691, leaving 181 years without a double duo.
TRIVIAL FACT: the number of solar
eclipses that are part of a double duos happens to be multiple of 4 for each
century considered. The number of eclipses that a are part of duo was odd in
the 12th and 13th century. The duo of 8 December 1200
and 6 January 1201 was divided between the two centuries.
