宋《統元曆日出入辰刻立成》考

The Study of The Record of Sunrise and Sunset in The Tong Yuan Calendar in the Song Dynasty

本文秉持科際整合之理念，採數學研究法，將《宋史．藝文志》所載亡佚已久的《統元曆日出入辰刻立成》一書，在拙著〈宋統元曆盈縮朏朒立成考〉一文日躔研究成果的基礎上，根據統元曆步晷漏中所載相關法數、步術，考釋其術文，設立其公式，試圖還原《統元曆日出入辰刻立成》一書概貌。文分二部，首以全年每日升降差及盈縮分，依次求出每日午中日行積度及分秒等。再就此等數值，依所立公式求出全年每日黃道去赤道內外度，先為統元曆日出入辰刻之數值推算預作張本。次則據全年每日黃道去赤道內外度，亦依公式，推算出日出入分、晨昏分、半晝分、晝夜刻、日出入辰刻，並表列其數值，施之以網底，還原出《統元曆日出入辰刻立成》一書之概貌。使亡佚之文獻得以重現，提供宋曆研究之參考。

The aim of this paper is to apply interdisciplinary ideas and mathematical methods to restore the long lost book-The Record of Sunrise and Sunset in The Tong Yuan Calendar. According to The Song Dynasty History-The Record of Art and Literature, this book records the methods such as the uses of the constant, dial and water dropping to calculate the times for sunrise and sunset, which regulate everyday life during that time. However, the book is long lost. Therefore, this paper, with an ambition, attempts to restore the similar record in the book by re-setting up its formula with modern mathematical methods. By doing so, we can make the long lost timetables an accountable source for the study of the Song's Calendar.