Finding the beginning or end direction of an occultation is important in the descriptions of eclipses in Chinese calendar-making systems, and it is used as one standard to verify the quality of a calendar. However, there are still some deficiencies in our understanding and textual editing of this. Through an examination of the original texts and analysis of the principle of the rules, we summarize the evolution of the rules pertaining of the beginning or end direction of occultation in calendric systems. The Jingchu li (景初历, Jingchu Calendar) of the Cao Wei period first introduced the rule that gives the direction of the occultation in the cases of “the moon on the inner and outer paths” and the sequence of jiao (交, sun passing the node) and hui (会, occultation), but is wrong, perhaps due of the rough calculations of the paths of the sun and the moon that lie behind it; the calendars of the Sui and Tang dynasties and later no longer considered jiao and hui, developing a rule on the base of the Daye li (大业历, Daye Calendar) and the Wuyinyuan li (戊寅元历, Wuyinyuan Calendar), which is perfected in the Dayan li (大衍历, Dayan Calendar); later rules up to the Ming's Datong li (大统历, Datong Calendar) and Huihui lifa (回回历法, Muslim Calendar) are basically no different from that of the Dayan li. On the other hand, the rule in the Huangji li (皇极历, Huangji Calendar) is probably based on observation, while that in the later Qintian li (钦天历, Qintian Calendar) involving the consideration of the ecliptic's change, is on an elaborate model theory of the paths of the sun and the moon.
XIN et al. (2024) studied this question.