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漢四分術

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Text ID
KR3fc052
Date
1795–1817
Dynasty
清

Hàn Sìfēn shù 漢四分術

The Hàn-Dynasty Sì-fēn (Quarter-Day) Calendrical System by 李銳 (述并注)

About the work

李銳 Lǐ Ruì’s (1768–1817) evidential-philological reconstruction in 3 juàn of the HòuHàn Sìfēn lì 後漢四分曆, the official calendar of the Later Hàn (DōngHàn 東漢) dynasty from 85 CE through to the end of the Hàn. The Sìfēn system replaced 劉歆 Liú Xīn’s Sāntǒng (cf. KR3fc051) and used the simpler “quarter-day” tropical-year approximation of 365 ¼ days that gives the system its name.

Abstract

The Sìfēn (“quarter”) calendar was promulgated in Yuánhé 元和 2 (85 CE) under the Hàn emperor Zhāngdì 章帝, replacing the Sāntǒng lì whose accumulated error had become embarrassingly visible. The new system reverted to the simpler tropical-year value 365 ¼ days (the same value embedded in the still-earlier Tàichū 太初 of 104 BCE), with revised metonic 19-year intercalation and revised constants for lunar motion. The system remained in use under successive minor revisions for the rest of the Later Hàn period.

The Sìfēn lì is preserved in the calendrical chapter (Lǜlì zhì 律曆志) of the HòuHàn shū 後漢書, in a procedural form somewhat clearer than that of the Sāntǒng in the Hànshū. Lǐ Ruì’s 3-juàn reconstruction extracts the algorithmic content, organises it under the standard headings of a Chinese calendar treatise (fundamental constants, derived constants, new-moon procedure, solar-term procedure, eclipse and planetary procedures), and supplies a critical zhù 注 that emends corrupted figures where the algorithmic logic permits.

The work is the second member of Lǐ Ruì’s quintet of Hàn-and-Sòng calendrical reconstructions (KR3fc051–KR3fc055). The pair Sāntǒng and Sìfēn together represent the foundational Hàn calendrical tradition; the Qiánxiàng 乾象 (KR3fc053) is the immediate SānGuó successor; the two Sòng reconstructions (KR3fc054, KR3fc055) bring the lineage forward to the Northern Sòng. The whole sequence is the principal Qīng evidential-philological recovery of the indigenous Chinese calendrical tradition.

Dating: composed during Lǐ Ruì’s mature productive period in 阮元 Ruǎn Yuán’s patronage circle. notBefore 1795; notAfter 1817 (death year).

Translations and research

  • Cullen, Christopher. 2017. The Foundations of Celestial Reckoning: Three Ancient Chinese Astronomical Systems. London: Routledge. — Critical edition and English translation; cites Lǐ Ruì’s reconstruction throughout.
  • Sivin, Nathan. 1969. Cosmos and Computation in Early Chinese Mathematical Astronomy. Leiden: Brill.
  • Wú Wénjùn 吳文俊, ed. 1985. Zhōng-guó shù-xué shǐ dà-xì 中國數學史大系, vol. 7.

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