Suàn qīzhèng jiāoshí língfàn fǎ 算七政交食凌犯法
Method for Computing the Syzygies and Conjunctions of the Seven Governors by anonymous
About the work
The Suàn qīzhèng jiāoshí língfàn fǎ 算七政交食凌犯法, in two juàn, is an anonymous Qīng-era computational manual giving step-by-step procedures for predicting syzygies (jiāoshí 交食 — eclipses) and planetary conjunctions/transits (língfàn 凌犯) of the Seven Governors (qīzhèng 七政: sun, moon, and the five visible planets). It is a practitioner’s recipe-book using the Shíxiàn-era tabular apparatus.
Abstract
The work has no preface and opens directly with the seven-step procedure. (1) Niángēn 年根 (year-root): take the year-root, computed from the winter solstice — not from New Year. (2) Rìshù 日數 (day-number): count the days from winter solstice to the target date and look up the corresponding entry in the Tàiyáng zhōusuì píngxíng biǎo 太陽周歲平行表 (“Table of Mean Solar Motion through the Year”), advancing one gōng 宮 per 30°. The reference cited is “juàn 1, sheet 33.” (3) Shíshù 時數 (hour-number): count the hours from midnight and look up the Zhōurì shí duì zhǔn rìxíng biǎo 周日時對準日行表 (“Table for Adjusting Daily Solar Motion to Hours of the Day”) at “juàn 1, sheet 55.” (4) Píngxíng 平行 (mean motion): sum year-root + days + hours into the mean-motion column. (5) Gāochōng 高衝 (apsidal-line): write the apsidal-line value. (6) Yǐnshù 引數 (anomaly): mean motion minus apsidal line, borrowing 12 gōng if needed. (7) Jūnshù 均數 (equation-of-centre): look up the equation in juàn 2, observe the sign, and interpolate linearly using the difference of successive equations multiplied by the residual.
The technical vocabulary (niángēn, gāochōng, jūnshù, yǐnshù) and the tabular references are pure post-1645 Shíxiàn-style, drawing on the multi-juan tables of the Xīyáng xīnfǎ lìshū 西洋新法曆書 lineage. NotBefore is set at 1645 (the Shíxiàn reform); notAfter at 1911 (the fall of the Qīng). The reference apparatus — citing tables of the Xīyáng xīnfǎ lìshū lineage rather than the later Yōngzhèng / Qiánlóng recasts (the Lìxiàng kǎochéng 曆象考成 of 1721 and its Hòubiān 後編 of 1742) — suggests a Kāngxī to early-Qián-lóng date as most plausible, but this cannot be fixed with confidence from the source alone.
The work is silent on attribution and shows no sign of post-Jiā-qìng / Dàoguāng recasting; it appears to have circulated as a working pedagogical manual within or at the margins of the Qīntiānjiān.
Translations and research
No substantial secondary literature located. The method-type belongs with the Shíxiàn 時憲 procedural literature analysed in general by:
- 石云里 Shí Yún-lǐ. Several papers on Qīng Shíxiàn lì practice.
- 徐光台 Xú Guāng-tái. Articles on the Jesuit-mediated computational tradition in late-Míng / early-Qīng China.
- Jami, Catherine. 2012. The Emperor’s New Mathematics. Oxford: Oxford University Press.
- Chang Ping-ying. 2023. The Chinese Astronomical Bureau, 1620–1850. London: Routledge.