Analysis of interval constants in calendars affiliated with the Shoushili

We study interval constants that are related to motions of the Sun and Moon,i.e., the Qi, Intercalation, Revolution and Crossing interval, in calendars affiliated with the Shoushi calendar(Shoushili), such as Datongli and Chiljeongsannaepyeon. It is known that these interval constants were newly introduced in the Shoushili calendar and revised afterward, except for the Qi interval constant, and the revised values were adopted in later calendars affiliated with the Shoushili. We first investigate the accuracy of these interval constants and then the accuracy of calendars affiliated with the Shoushili in terms of these constants by comparing times for the new moon and the maximum solar eclipse calculated by each calendar with modern methods of calculation. During our study, we found that the Qi and Intercalation interval constants used in the early Shoushili were well determined, whereas the Revolution and Crossing interval constants were relatively poorly measured. We also found that the interval constants used by the early Shoushili were better than those of the later one, and hence better than those of Datongli and Chiljeongsannaepyeon. On the other hand, we found that the early Shoushili is, in general, a worse calendar than Datongli for use in China but a better one than Chiljeongsannaepyeon for use in Korea in terms of times for the new moon and when a solar eclipse occurs, at least for the period 1281 – 1644.Finally, we verified that the times for sunrise and sunset in the Shoushili-Li-Cheng and Mingshi are those at Beijing and Nanjing, respectively.