  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.
