Print TENG Yan-hui1, TANG Quan2,3
(1. Research Center for the History of Mathematics and Science, Northwest University, Xi′an 710127, China;
2. School of Mathematics and Information Science, Xianyang Normal University, Xianyang 712000, China;
3. Institute of Chinese Ideology and Culture, Northwest University, Xi′an 710069, China)
Abstract: The arrangement of intercalary months in the calendars of the Song Dynasty using the method of the level Qi and the real new moon is discussed. According to the corrections of the non-uniform motions of the sun and moon, the numerical model of the lunation length is established. Through comparing and analyzing the lunation length and the interval between one Qi and the following Qi, it is pointed out that since the Qi and the new moon were on the same day, the intercalary month was arranged a month earlier in 4 cases and it was rare to arrange the intercalary month two months ahead of schedule. The direct basis for the restoration and textual research on the ancient Chinese almanac is provided.
Key words: algorithm of intercalary months arrangement; synodic month; jinshuo; almanac