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漢乾象術

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Text ID
KR3fc053
Date
1795–1817
Dynasty
清

Hàn Qiánxiàng shù 漢乾象術

The Hàn-Dynasty Qián-xiàng Calendrical System by 李銳 (述并注)

About the work

李銳 Lǐ Ruì’s (1768–1817) evidential-philological reconstruction in 2 juàn of the Qiánxiàng lì 乾象曆 designed by 劉洪 Liú Hóng (c. 130 – c. 210 CE) at the close of the Eastern Hàn and promulgated as the official calendar of the state of Wú 吳 in 223 CE. The Qiánxiàng is a foundational document in the history of Chinese mathematical astronomy: it is the first Chinese calendar to model the inequality of lunar motion (the variation in apparent lunar velocity between perigee and apogee) and the first to incorporate a non-zero inclination of the lunar orbit relative to the ecliptic.

Abstract

劉洪 Liú Hóng was Grand Astrologer (Tàishǐlìng 太史令) under Hàn Língdì 漢靈帝 and the senior astronomical authority of the closing decades of the Eastern Hàn. His Qiánxiàng lì introduced two technical innovations of fundamental importance: (1) the huíchà 回差 “return-difference” — a tabular correction to lunar mean motion that captures the variation in lunar apparent velocity over the anomalistic month, the earliest non-uniform lunar model in Chinese astronomy; and (2) an explicit non-zero value for the inclination of the lunar orbit, permitting more accurate eclipse prediction. The system also revised the fundamental constants of lunar and solar mean motion to give a better fit to current observations than the older Sìfēn 四分 system (cf. KR3fc052).

Because the Wèi 魏 court retained the older Sìfēn lì, the Qiánxiàng was not adopted as the official calendar of the Hàn successor regime in the north. It was adopted in 223 CE as the official calendar of the Wú state under Sūn Quán 孫權, and remained in use there until the Wú surrender to Jìn in 280 CE. Its technical innovations were absorbed into all subsequent Chinese calendrical work.

The Qiánxiàng lì survives in the calendrical chapter of the Jìnshū Lǜlì zhì 晉書律曆志 (the chapter compiled under 李淳風 Lǐ Chúnfēng), with the procedural prescriptions reasonably well-preserved. Lǐ Ruì’s reconstruction extracts the algorithmic content into the standard treatise format and supplies a critical zhù 注 emending and explaining the technical procedures. The shorter length (2 juàn compared to 3 for Sāntǒng and Sìfēn) reflects the better preservation of the source material and the somewhat narrower technical scope.

This is the third of Lǐ Ruì’s five Hàn-and-Sòng calendrical reconstructions (KR3fc051–KR3fc055).

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

Translations and research

  • Cullen, Christopher. 2017. The Foundations of Celestial Reckoning: Three Ancient Chinese Astronomical Systems. London: Routledge. — Critical edition and English translation of the Sān-tǒng, Sì-fēn and Qián-xiàng; principal modern reference for the Qián-xiàng.
  • Sivin, Nathan. 1969. Cosmos and Computation in Early Chinese Mathematical Astronomy. Leiden: Brill.
  • Sivin, Nathan. 2009. Granting the Seasons. New York: Springer.
  • 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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