Updated: 14 October 2007
A lunation is the period between 2 successive New Moons. On average the
length of a lunation is 29.53 day. Two subsequent solar eclipses are
separated by 1, 5 or 6 lunations. A duo eclipse is a set of two solar eclipse separated by one lunation. The last time this
occurred 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 of solar eclipses is: eclipse  1 lunation  eclipse  5 lunations  eclipse  1 lunation  eclipse In this case there are 4 eclipses within a 7 lunation period. 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). It is extremely rare that one of the eclipses of a double duo is total. During the 5 millennia (2000 / +3000) this has happened only three times.
The graph below shows the total number of solar eclipses per century, as
well as number of eclipses that belong to a duo and double duo of eclipses. Again the
585 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. 

A Saros series consist of 69 to 86 solar eclipse, each separated by 18 year and 10 or 11 and 1/3 days. (10 or 11 depending on the number of leap year in the 18 year period) A Saros series lasts therefore 1226 to 1550 years. Saros series are numbered. Currently eclipses belong to Saros 117 to 155. A new Saros series 156 will begin on 1 July 2011. The graph below shows the total number of eclipses for Saros series 31  144, as well as the number of eclipses of that series that belong to a duo, and the number of eclipses per series that belong to doubleduo. Please note that the other eclipse (or three eclipse in case of a double duo) will always belong to different Saros series. As stated, eclipses in the same Saros series are separated by 18 year and 11 days. The graph also indicates that Saros series with more eclipse seem to have
more eclipse that are part of a duo pair or doubleduo quartet, and it is
remarkable that some Saros series (4145, 6063, 7984, 97101, 117120,
135138) do not have any eclipses at all that a part of a double duo. 

Looking at the graph above we see that some Saros series have just as many eclipses belonging to a duo as to a double duo. The doubleduo to duo ratio per Saros series is plotted below. For Saros series 37, 49, 57, 67, 95, 104, 122 and 142 this ratio is 100%, meaning that if an eclipse of this series is part of a duo it is also part of a double duo. For series that have no eclipses at all being part of a double duo, this ratio off course will be zero. 





Currently the duo Saros 117155 is "active". It started with the a rare duo
where on of the two eclipses is total (19 May 1928) and the other partial
(17 June 1928) and will end 126 years later in 2054.
The next duoSaros series will start with the eclipse on 1 June (Saros 118)
and 1 July 2011 (first of Saros 156). It has 4 duo members and will end 72 years later with a solar
eclipse duo on 15 July (last of Saros 118) and 13 August 2083. A Saros
series begins and ends with a minimum of 6 and maximum of 22 partial
eclipses. This means that a duoSaros series with less than 6 members cannot
have PT or TP pairs. 

One lunation in Van der Bergh's formula that 1 = 38I  61S. On page 124 of Morsels IV, Jean Meeus refers to work that shows that the average number of eclipses per Saros will decrease to just over 61, as compared to more than 73 currently . It is for the reader to argue that this means that the duoSaros series will become shorter, and that duos in general will happen less frequently. Will this lead to a situation where PePb duos are possible, or even een situation that some Pb or Pe eclipses are not part of a duo?  
The DoubleDuoSaros seriesDouble duos are often followed by an other double duo one Saros period later. If the Saros number of the first eclipse of a double duo is n, then the Saros numbers of the subsequent eclipses are n+38, n+5 and n+43. Currently (2007), the active Saros numbers range from 117 to 155, which excludes the possibility of double duos. Saros 160 (117+43) will only start after Saros 117 has ended. However, on 24 October 2098 Saros 164 begins, and on 23 May 2134 Saros 159 will begin, while Saros 121 will end 7 Jun 2206. This leads to a series of 5 double duos with Saros numbers 121159126164 in the period 2134 up to 2206. The last double duo Saros series 111149116154 only had two double duo members in 1916/17 and 1935. The longest double duo Saros (142180147185) will have 9 members and last from 2760 until 2904. The chart belows shows that the double duo Saros series are grouped. Many combinations, such as above 117155122160 consist of Saros series that do not overlap in time. The graph shows the number of double duos per series. 
