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曆象誌中○閏考
Celestial Phenomena, Part Two — Intercalation
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月度不足，是生朔虛； 天行有餘，是為氣盈。 盈虛相懸，歲月乃牉，積牉而差，寒暑互易，百谷不成，庶政不明。 聖人驗以斗柄，準以歲星，爰立閏法，信治百官。 是故閏正而月正，月正而歲正。 歲月既正，頒令考績，無有不時。 國史正歲年以敘事，莫重於此。 遼始征歷梁、唐。 入晉之後，奄有帝制，《乙未》、《大明》，曆法再變。 穆宗應歷六年，周用顯德《欽天曆》； 十年，宋用建隆《應天曆》。 景宗乾亨四年，宋用《乾元曆》。 聖宗統和十九年，宋用《儀天曆》； 太平元年，宋用《崇天曆》。 道宗清寧十年，宋用《明天曆》； 大康元年，宋用《奉元曆》； 大安七年，宋用《觀天曆》。 天祚皇帝乾統六年，宋用《紀元曆》。 五代歷三變，宋凡八變，遼終始再變。 曆法不齊，故定朔置閏，時有不同，覽者惑焉。 作《閏考》。 〈（書540－564頁有表）〉
When a lunar month runs short of a full cycle, a "new-moon deficit" arises; when the sun's annual course runs long, the result is "qi surplus." Surplus and deficit pull against each other until year and month can be brought back into alignment; let misalignment accumulate and the seasons swap places, crops fail, and government loses its rhythm. The sages checked the seasons against the Dipper's handle and Jupiter's station, established intercalation on that basis, and thereby kept the civil calendar trustworthy for every office. Correct intercalation makes the months right; correct months make the year right. With the calendar set right, orders go out and performance is reviewed on schedule. The court historians align the annual record to narrate events—nothing in statecraft weighs more. At first the Liao turned to the Liang and Tang for calendrical systems. Once they held the imperial mantle after entering Jin territory, they adopted the 《Yiwei》 and 《Daming》 systems in succession—two great calendar reforms. In Muzong's sixth Yingli year the Later Zhou used the Xiande-era 《Qintian Calendar》; in his tenth Yingli year the Song adopted the Jianlong 《Yingtian Calendar》. In Jingzong's fourth Qianheng year the Song used the 《Qianyuan Calendar》. In Shengzong's nineteenth Tonghe year the Song used the 《Yitian Calendar》; in the first Taiping year the Song used the 《Chongtian Calendar》. In Daozong's tenth Qingning year the Song used the 《Mingtian Calendar》; in the first Dakang year the Song used the 《Fengyuan Calendar》; in the seventh Da'an year the Song used the 《Guantian Calendar》. In Tianzuo's sixth Qiantong year the Song used the 《Jiyuan Calendar》. The Five Dynasties saw three calendar reforms, the Song eight, and the Liao only two from start to finish. Because their systems did not match, intercalary months and new-moon dates diverged, leaving readers baffled. Hence this 《Study of Intercalation》. (Tables occupy pages 540–564 of the printed edition.)〉