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Analysis of interval constants of Shoushili-affiliated calendars

We study the interval constants that are related to the motions of the Sun and the Moon, i.e., the Qi, Intercalation, Revolution, and Crossing interval constants, in calendars affiliated with the Shoushi calendar(Shoushili), such as Datongli and Chiljeongsannaepyeon. It is known that those interval constants were newly introduced in Shoushili and revised afterward, except for the Qi interval constant, and the revised values were adopted in the Shoushili-affiliated calendars. In this paper, we investigate first the accuracy of the interval constants and then the accuracy of the Shoushili-affilated calendars in terms of the interval constants by comparing the times of the new moon and the solar eclipse maximum calculated by each calendar with modern calculations. 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 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 the new moon and the solar eclipse times, at least for the period 1281 - 1644. Finally, we verified that the sunrise and sunset times recorded in Shoushili-Li-Cheng and Mingshi are those at Beijing and Nanjing, respectively.