6. Concluding remarks
Since knowing the data of the year, n, and Ganzhi calculated by the Shoushi Calendar system, it can thus readily be converted to the Gregorian Calendar. Now how to review this system? What about its accuracy? The makers wanted it to be used forever, but is that possible? Next, by the way of the Shoushi Calendar, we give the detailed precision of syzygys within its publishing period (Table 1 & Fig. 4). In fact, due to Shoushi, we can only compute the apparent solar time. In this paper, the precision is obtained by comparing the difference of apparent solar time of syzygy calculated by Shoushi and mean solar time by the method of contemporary celestial mechanics.
Table 1. The time precision of real new Moon calculated by the method of the Shoushi Calendar
In Table 1, "Mean value" is the mean value of the differences. "Mean value of absolute" is the mean value of the absolute values of the differences, which shows the deviations of the errors more accurately. By the method of the Shoushi Calendar, we computed all real new Moons from AD 1280 to 1645 and give their distributions of the mean values (Fig. 4). The average value of the differences is 0.9 minute and the mean value of the absolute is 21.0 minutes (Li and Zhang 1996a). By Table 1 and Fig. 4, the longer this calendar was used, the lower its precision. This is one of the important reasons why there were more than 100 calendars established in ancient China.
In fact, the real syzygy calculation is about the relationship among three models of T(t), S(t') and V(t'), all periodic functions. The accuracy of the calculations is based upon the corrections and precision of these models. The results computed by us show that the calculations of this calendar were very exact even in those times, but it could not be used forever, as other calendars published before.
Although this calendar was only used for about 350 years because of the problem of precision, many real historical surveying records fall in it. By the method of the Shoushi Calendar, to recover those data of celestial phenomena which were omitted has great potentialities, because it is very difficult to collect them by other ways. The longer the interval of the time, perhaps the more useful this method could be. So perhaps this calendar is of wide application. Now the contemporary research area of making full use of the ancient records of astronomical phenomena is very active. Our work on "secular variation of Earth's rotation: inferred from the Chinese ancient Shoushi Calendar (AD 1281)" belongs to this area (Li and Zhang 1997). Its prerequisite is how to discover those real ones at that time. According to the Shoushi Calendar's calculating methods, we make a try to get the parameter of times. By selecting these calculating data, some of them may be applied to identify or recover the original observing material of Earth's rotation.
© European Southern Observatory (ESO) 1998
Online publication: March 30, 1998