Marco Fumagalli - The earthquake of western Sichuan
The life of the eclipses
How long a time does the place of an eclipse remain sensitive to the following reminders? The Ptolemaic theory of the dating of an event , based on the horary distance of the darkened luminary to the oriental angle, gives a maximum of one year, either for the Solar or the Lunar eclipses. Based on experience, this interval of time seems to match much better the Lunar eclipses than the Solar ones, the smaller frequency of which suggests to consider a decidedly greater temporal space, either when we consider the relation between the date of the event and the horary distance of the Sun to the Horoscope, or when we search, in the successive times, the returns of the places activated by the eclipse.
As for the lunar eclipses, let’s observe all the visible ones for Sichuan, in a period of 15 months, so as to consider also those that go lightly over the Ptolemaic limit of one year:
Both these eclipses were not visible from the beginning to the end of the totality, but the eclipsed Moon was visible at the setting eclipse of March 2007, and at the rising one of August.
As for the Solar eclipses, since we are lacking of a sure criterion of choice, a more extensive inquiry is needed. It seems reasonable to suppose, in a theoretical line, that a very big darkening of the solar disk gives a greater strength to the zodiacal degrees of the eclipses which will remain sensitive to the following figures for a longer time. On the contrary, a very small darkness seems to indicate that the strength vanishes very quickly and that the potential reminders which still may occur lose their meaning.
Now, if we observe all the visible solar eclipses of the Sichuan region, the first eclipse we find with a darkness of over 90% is the one of June 6 1872, 136 years before the earthquake . Obviously too much, even for ‘Alî ibn Ridwân who, while accepting a temporal arc of 12 years , would have observed these four eclipses:
This limit of 12 years seems too large at first sight because of the number of solar eclipses occurring in such an interval of time. A more reasonable limit seems to be 4 years which was recently suggested by Rosalba Signorello , according to whom only the eclipse of 2007 would be accepted. A single example cannot be used for solving the question about the maximum life of the eclipse according to the successive reminders; however, the idea of considering the darkness as a limiting factor  of the maximum life of an eclipse can be used in these eclipses to confirm that the only one to be retained is the one of 2007. To consider the darkness would mean saying that, if an eclipse of 100 % lived a certain number of years, an eclipse of 50 % would live half of it, one of 25 % a quarter of it, and so on.
Now, if we take the limit of 4 years, we see that the eclipse of 2007, although it does not present a very big darkness (33,2%), is still “alive” because quite near: its duration is 1,3 years (33,2: 25), which means it remains effective up to July 2008. If instead we were applying the criterion of the limit of 12 years, the relationship would become 100% = 12 years, 50 % = 6 years and so on.
By following the diagram, we see that the eclipses of 2002 and 1998, with a darkness under 8,3%, would have had a very short span of life, less than one year; the one of 1997, with a darkness of 63%, would have had a span of life comprised between 7 and 8 years and would then have been too distant from the earthquake; on the contrary, the eclipse of 2007, closer, would still be very "young", since the darkening of 32,2% would allow it a span of life of almost four years. Therefore, the criterion of darkness applied to this single case, on the one hand does not allow us any step ahead as for the general problem of the maximum span of life of a solar eclipse, on the other hand it allows us to conclude that the eclipse of 2007 is certainly alive the day of the earthquake. The checking of all the four eclipses confirms besides that the one of 2007 is the only one that can be effectively compared with the two lunar eclipses and with the earthquake, because of the part played by the planets, by the angles and by the stars (9). We therefore accept this eclipse, with the other two lunar ones.
 Tetr. 2.6:« And with regard either to the beginnings or to the more important intensifications of the event, we’ll deduce them from the position of the place of the eclipse relative to the angles. For, if the place of the eclipse falls on the eastern horizon, this signifies that the first symptoms of the event will start during the first period of four months from the time of the eclipse, and that its biggest strength will lie in the first third of the entire period of its duration; if it falls on the mid heaven, in the second four months and the middle third; if upon the western horizon, in the third four months and in the final third (of its duration)».
 Let me point out, as a pure curiosity, that an eclipse with a darkening of 100 %, will be visible at Chengdu on July 22 2009, a little more than one year after the earthquake, with Mars culminating at the Mid Heaven with Aldebaran, at 1h12 m48s UT.
 The fact that the limit of one year seems to be too strict for the solar eclipses was the opinion of the egyptian physician ‘Alî ibn Ridwân (XI century): in his commentary of the Ptolemy’s chapter (Tetr. 2.6), he says that «the Sun is making a rotation of the heavens in one year and it would be better to consider that the events of the solar eclipses last for years, the Moon makes its journey in one month, and it is better to consider that its effects last for months». Therefore, considering that the times of the Sun are measured in years, and accepting the ptolemaic theory of the horary distance of the Sun to the horoscope, he concluded that a maximal distance of 12 hours, equaling the diurnal arc, corresponds to 12 years.
 Cfr. Rosalba Signorello, Le eclissi di sole e il tempo degli eventi, «Phôs» 16, June 2008, p. 1ss. (The solar eclipse and the time of the events). The study wants to confirm the possibility of finding a date for the event from the ptolemaic principle of the horary distance of the Sun, on a different temporal base, and suggests the limit of 4 years, basing her argument on the quarterly seasonal cycle. This boundary, in my opinion, could be taken as the “maximum life” of an eclipse independently of the possibility of dating the event through the position of the Sun in its horary circle, but by considering it as an extreme limit for the “successive reminders”. The figures shown are indeed rich of “reminders”: we can see, for example, the New Moon of 8/28/1973 (op.cit. p. 17) preceding the military coup in Chile, where the arising degree is the one where Saturn was located in the solar eclipse of 1969.
 Considering, as I suggest, the darkening of a luminary as a prevailing factor with regard to the life of an eclipse, it follows that, for "maximal life" we must understand the life of an eclipse at 100%, and that a minor darkening reduces the duration proportionally. Instead, according to the ptolemaic method based on one year (Ptolemy) or more (4 years Signorello, 12 years Ridwân) the maximal life of an eclipse must be measured at the Western horizon, regardless of the quantity of darkening.
 The comparison between the solar eclipse of 2002 and the figures of 2007-2008 shows a few connections between the degrees (in the eclipse 1 the MC of the solar eclipse is rising and the degrees of the luminaries and of Saturn transit on the IC) and, above all, shows the total absence of correspondences between the stars, which are numerous instead in the figures of 2007-2008. In the eclipse of 1998 the “reminders” on the degrees are more important (Mars of the earthquake is coming back on its own degree, the MC of the previous New Moon is near the degree of the eclipse, Saturn of the eclipse 2 is on the degree of the eclipse), but in this eclipse also, the stars are completely lacking. In the eclipse of 1997 the only reminder (which would be most important if the eclipse were still “alive”) is with regard to the solar eclipse of 2007, where the luminaries were opposing the degree of Mars 1997. Again, in this eclipse of 1997, the stars are absent.