Jiāoshí tōngguǐ / Rìshí tōngguǐ / Yuèshí tōngguǐ / Sìyú tōngguǐ / Wǔxīng tōngguǐ 交食通軌/日食通軌/月食通軌/四余通軌/五星通軌
Running-Track Computational Manuals for Eclipses (general), Solar Eclipses, Lunar Eclipses, the Four Supplementary Terms, and the Five Planets by 元統 (撰)
About the work
This catalog entry is a single bound set of five short tōngguǐ 通軌 (“running-track” or “step-procedure”) computational manuals from the early Míng imperial Astronomical Bureau, all composed by 元統 Yuán Tǒng around the time of the Míng adoption of the Dàtǒng lì 大統曆 (1384). The five manuals together exhaust the principal calculation procedures of the calendar: (1) Jiāoshí tōngguǐ 交食通軌, the general framework for eclipse prediction; (2) Rìshí tōngguǐ 日食通軌, solar-eclipse-specific reductions; (3) Yuèshí tōngguǐ 月食通軌, lunar-eclipse-specific reductions; (4) Sìyú tōngguǐ 四余通軌, the four shadow-planet supplementary terms (紫氣 zǐqì, 月孛 yuèbó, 羅睺 Rāhu 羅睺, and 計都 Ketu 計都 — the lunar node and apogee corrections imported from Indian astronomy into the YuánMíng tradition); (5) Wǔxīng tōngguǐ 五星通軌, the five visible planets. Each manual is one juǎn.
Abstract
The catalog field gives the author as “正元统”, which is a corruption of the standard form 元統 Yuán Tǒng. He was the first Tàishǐ lìng 太史令 of the Míng dynasty under Hóngwǔ, charged with the re-promulgation of the Yuán Shòushí lì 授時曆 — Guō Shǒujìng’s 1281 calendar — under the Míng-dynastic name Dàtǒng lì 大統曆 in 1384 (Hóngwǔ 17). The tōngguǐ manuals are the operational handbook by which the Shòushí’s computational machinery was put to daily use by the Astronomical Bureau staff. They are organised as sequenced “step-procedures” (lǐguǐ 立軌) running from the input data (epoch, observed positions) through the chain of intermediate quantities to the final ephemeris output, with worked numerical examples.
Sivin (2009) treats the Shòushí lì mathematical apparatus at book length; the tōngguǐ texts are the principal evidence for the calendar’s practical, as opposed to its theoretical, operation. They form one of the indispensable corpora for understanding why the Dàtǒng / Shòushí system held its place at the Míng court for two and a half centuries before the Jesuit reform of the Chóngzhēn lìshū 崇禎曆書 (1635) finally displaced it. The composition window 1384–1390 brackets the Hóngwǔ-era promulgation and the early operational years.
The five tōngguǐ survive in Míng manuscript copies and in the Sìkù wèishōu shū jíkān; they are reprinted as a set in the Zhōngguó kēxué jìshù diǎnjí tōnghuì (refid KX03-07-015).
Translations and research
- Sivin, Nathan. 2009. Granting the Seasons: The Chinese Astronomical Reform of 1280, with a Study of its Many Dimensions and an Annotated Translation of its Records. New York: Springer. — the standard English-language treatment of the Shòu-shí lì; sets out the computational apparatus that the tōngguǐ manuals implement.
- 陳美東 Chén Měidōng. 1995. Guō Shǒujìng píng-zhuàn 郭守敬評傳. Nanjing: Nán-jīng dàxué chūbǎnshè. — Chinese-language biography with technical detail.
- 陳遵媯 Chén Zūnguī. 1980–84. Zhōngguó tiānwénxué shǐ 中國天文學史. — the Dà-tǒng lì chapter discusses Yuán Tǒng’s role.
Other points of interest
This is the principal early-Míng evidence for the operational continuation of Guō Shǒujìng’s Shòushí lì under the new dynasty. The four-supplementary-term apparatus (Sìyú) is also a particularly interesting witness to the assimilation of Indian-astronomical concepts (Rāhu, Ketu, and the yuèbó 月孛 apogee) into the imperial Chinese calendar tradition via the Yuán court’s Huíhuí lì 回回曆 office.