Yùzhì lìxiàng kǎochéng hòubiān 御製歷象考成後編
Imperially Composed Investigation of the Calendrical Phenomena, Continuation by 允祿 (Yǔnlù, Héshuò Zhuāng qīnwáng, 1695–1767, 清, fèngchì zhuàn 奉敕撰); 戴進賢 (Ignaz Kögler, S.J., Dài Jìnxián, 1680–1746, 清, fèngchì zhuàn); with the principal Chinese collaborators Hé Guózōng 何國宗 (何國宗) and Gù Cóng 顧琮 (Minister of Personnel)
About the work
A 10-juan continuation of the KR3f0018 Lìxiàng kǎochéng (1724), revising the earlier work in light of post-1720s European astronomical observations and theory. Chartered by the Yōngzhèng emperor in 1730 (Yōngzhèng 8) following Ignaz Kögler’s successful eclipse prediction of that year using the new European methods; completed under the Qiánlóng emperor in 1742 (Qiánlóng 7). The work’s principal innovation is the systematic substitution of Keplerian elliptical orbits for the Tychonic uniform-circular orbits of the original Lìxiàng kǎochéng — making the Hòubiān the first Chinese-language astronomical work to incorporate the Keplerian (post-1609) European astronomical synthesis. Other major reforms: revised values for solar parallax (3’ → 10″) and atmospheric refraction (34’ → 32’ at horizon, 5″ → 59″ at 45° altitude) based on the Cassini-Lahire Paris-observatory measurements; revised eclipse-computation methods incorporating the new parallax-and-refraction values; new observational instruments (pendulum clocks for time, telescopes for distance).
The work’s structural arrangement reflects the focused scope of revision (it does not duplicate the full Lìxiàng kǎochéng but only updates the sections requiring substantive change):
- Volumes 1–3 (數理 shùlǐ, mathematical-physical exposition): Rìchán (sun-position theory), Yuèlí (moon-path theory), Jiāoshí (eclipse theory)
- Volumes 4–6 (步法 bùfǎ, computational procedures): Rìchán (sun-position procedures, in vol. 4 alongside Yuèlí), Yuèshí (lunar-eclipse procedures), Rìshí (solar-eclipse procedures)
- Volumes 7–10 (表 biǎo, ready-reckoner tables): Rìchán tables (vol. 7), Yuèlí tables upper (vol. 8), Yuèlí tables lower (vol. 9), Jiāoshí eclipse tables (vol. 10)
The 提要 explicitly identifies three foundational doctrinal advances over the Lìxiàng kǎochéng (i.e., over Tycho via Kāngxī-period synthesis): (1) the revised solar-parallax (now derived not from direct solar measurement, with its atmospheric-refraction interference, but from Mars-at-opposition observations from northern and southern stations, exploiting the geometry of Mars-Earth-Sun at favorable conjunction); (2) the revised atmospheric-refraction theory based on Cassini-Lahire measurements; (3) the elliptical-orbit substitution — yǐ wéi tuǒyuán, liǎngduān jìng cháng, liǎngyāo jìng duǎn 以為撱圓兩端徑長兩腰徑短 (“[the orbit] is taken as elliptical, with the diameters at the two ends long and the diameters at the two waists short”). The 提要 attributes the elliptical reform specifically to “Kepler” (Kèbáiěr 刻白爾) — the earliest Chinese-language attribution of the elliptical-orbit theory by name.
Tiyao
[Sub-classification: 子部, Tiānwén suànfǎ class 1, tuībù sub-category. Edition: WYG.]
Respectfully examined: Yùdìng Lìxiàng kǎochéng hòubiān, 10 juàn, by-imperial-decree compiled, Qiánlóng 2 [1737, the year kě’rěn — actually the project was earlier-and-completed-later, but the 提要 dates the formal commencement of the Qián-lóng-period editorial phase].
The Xīnfǎ suànshū’s step-computation methods-and-numbers were all derived from the old [tradition] of the Western historian Tycho [Brahe]. Its diagrams-and-tables’ inconsistencies, its explanations’ obscurities — the Sage Ancestor Benevolent Imperial Ancestor [Kāngxī]‘s Lìxiàng kǎochéng upper-and-lower two editions investigated-precisely-and-explicated-the-subtle, exhausted-the-investigation of principles-and-numbers; truly already exhausting one age’s tuībù refinement, displaying a method for ten-thousand generations of cultivation-and-clarification.
But measurements gradually growing longer become gradually finer; computational methods also are ever-changing and ever-cleverer. From the Kāngxī period, when the Westerners Cassini, Flamsteed [Gāxīní, Fǎlándé 噶西尼, 法蘭徳], and others emerged, [they] also newly fashioned the zhuìzǐ biǎo 墜子表 (pendulum-clock-table) for fixing time, the qiānlǐ jìng 千里鏡 (thousand-lǐ mirror = telescope) for measuring distance, by which to develop what Tycho had not exhausted — three principal items:
(1) The first says: the sun-and-earth half-radius difference (i.e. solar parallax). Old fixed-as 3’; now measured at only 10″. For the sun-heaven’s half-radius is very far; what measurement involves is only seconds-and-microns. There is also atmospheric vapor (méngqì) mixed within it — most difficult to fix. Thinking that, of the sun, moon, and stars in heaven, only the constant-stars have no earth-half-radius difference, if [we] take sun-and-star mutually-compared we can obtain its standard. But sun-and-star cannot both appear [together]. Then measuring the sun is not as good as measuring the five planets. Saturn-and-Jupiter the two planets are above the sun, the earth-half-radius difference [is] even smaller. Venus-and-Mercury the two planets, although sometimes below the sun, their motion goes around the sun, [so] near to the sun’s light, [are] uniformly difficult to measure. Only Mars goes-around-the-sun and also goes-around-the-earth; can be in opposition to the sun. Therefore at midnight Mars is just at the zǐwǔ (south meridian); from north and south two locations measuring it, both compared with the constant-stars: if the distance from the constant-stars are equal, then there is no earth-half-radius difference; if the mutual distances are unequal, that is having earth-half-radius difference. The amount of inequality is the comparative-difference of the two locations’ earth-half-radius. Furthermore: when Mars opposes the sun, its distance from the earth compared with the sun is closer; therefore the sun-earth half-radius difference, computed by proportion, must be even smaller than the Mars-earth half-radius difference.
(2) The second says: the clear-vapor (atmospheric refraction) difference. Old fixed-as: at the horizon 34’, at 45° altitude only 5″. Now measured at: at the horizon only 32’, at 45° altitude still 59″. The explanation says: vapor encircles the earth-globe’s circumference; the sun-and-stars shine outside of the vapor; people on the earth-surface, within the vapor’s reflection, must see them as raised-higher. And the sun-and-stars’ light-rays, entering into the vapor, must be reflectively-bent and made to descend. Therefore the light-ray and the sight-line, within the vapor, then combine and become one; outside the vapor then separate and become two. Where they are separate, although there is non-coincidence, where they combine then there is a fixed location. From the earth-center past the combining-location, drawing a line to the encompassing-circle: this line is then the vapor’s tangent-line (méngqì zhī gēxiàn 䝉氣之割線). The sight-line and the tangent-line make one angle; the light-ray and the tangent-line also make one angle; the two angles mutually-subtracted then yield the atmospheric-refraction angle.
(3) The third says: the sun-and-moon-and-five-planets’ principal-heavens. Old explanation: a flat circle. Now [we hold them to be] ellipses (tuǒyuán 撱圓): the two-end diameters are long, the two-waist diameters are short. For the sun’s motion has surplus-and-shrinkage [variable angular velocity], because the principal-heaven has gāobēi (apsidal asymmetry — apogee and perigee). From spring-equinox to autumn-equinox [the sun] moves through the highest half-circuit, therefore moves shrunken and the calendrical-days are many; from autumn-equinox to spring-equinox [the sun] moves through the lowest half-circuit, therefore moves expanded and the calendrical-days are few. The [old] explanation: one [model] is the non-concentric heaven (bùtóngxīn tiān 不同心天); the other is the principal-wheel (běnlún 本輪, deferent). And the non-concentric heaven’s two-center difference (liǎngxīnchā 兩心差) just equals the principal-wheel’s half-radius. Therefore the two, although named differently, in principle are the same. Tycho used the principal-wheel to derive the surplus-shrinkage difference: only the middle distances agree with actual measurements; at the most-high and most-low, before-and-after, there are differences. He used a 균-wheel (jūnlún 均輪, equant-wheel) by which to grow-and-diminish [the discrepancy]. However, the heavens’ motion cannot be without difference: from Kepler (Kèbáiěr 刻白爾) onward, [astronomers] repeatedly-added refined measurements, and again the jūn-wheel-derived high-and-low before-and-after gradually had subtle-differences. Therefore [they] supposed the principal-heaven to be elliptical (tuǒyuán 撱圓), uniformly-divided the ellipse, and accumulated [its sectors] as the daily-mean-motion’s degree. Then the high-low-before-after surplus-shrinkage motion is then in agreement with actual measurements.
Based on these three, Tycho’s old method has subtle-differences in both longitude-and-latitude. In Yōngzhèng 8, sixth-month, shuò-day [July 16, 1730] solar eclipse, comparing it with the new method, the fineness was tightly-fitting. Therefore the Successor-of-the-Generation Constitutional Imperial Ancestor [Yōngzhèng emperor] specifically allowed the Bureau Minister Dài Jìnxián’s [Kögler’s] request, and ordered the cultivation of the Sun-Position and Moon-Path two tables to continue after the Lìxiàng kǎochéng. However, [those tables] had tables but no explanations, also no computational methods. The Minister of Personnel Gù Cóng, fearing that long [time] would lose [these explanations] without transmission, memorialized to request the addition-and-cultivation of table-explanations and diagrams-and-explanations. Reverently requesting the imperial decision, [these] are bequeathed for permanent [use]. All places where the new method differs from the old, [the work] starts from picking-out the deepest essence and brings out without remainder; while its principle is still in agreement, like a tally, with the Sage Ancestor Benevolent Imperial Ancestor [Kāngxī]‘s imperially-composed upper-and-lower two editions — additionally sufficient to show that Sage and Sage successively, before and after, jointly govern.
Respectfully collated, Qiánlóng 46, tenth month [November 1781].
Chief Compilers: (subject) Jì Yún 紀昀, (subject) Lù Xíxióng 陸錫熊, (subject) Sūn Shìyì 孫士毅. Chief Collator: (subject) Lù Fèichí 陸費墀.
Abstract
Composition window: 1730 (Yōngzhèng 8, the year of Kögler’s successful eclipse-prediction and Yōngzhèng’s commission of the Sun-and-Moon table revision) – 1742 (Qiánlóng 7, the year of the work’s formal completion and printing in its received form). The actual editorial work spans two reigns: the initial table-revision phase under Yōngzhèng (1730–1735) and the substantive expansion-with-explanations phase under Qiánlóng (1736–1742) following Gù Cóng’s memorial.
The work’s significance:
(a) The first Chinese astronomical work using Keplerian elliptical orbits: the Hòubiān’s adoption of tuǒyuán 撱圓 (elliptical) orbits for the sun and moon — and, in principle, the planets — represents the first systematic introduction of Keplerian astronomy into Chinese state practice. The 提要’s careful exposition of the rationale (the Tychonic jūn-wheel equant gradually accumulating discrepancies in the apogee-perigee neighborhood; Kepler’s elliptical solution by uniformly-divided-ellipse-sectors yielding daily mean motion) is one of the most lucid early-Chinese explanations of Keplerian astronomy. The reform places Chinese astronomy approximately one century behind the European frontier: Kepler’s elliptical theory was published 1609, his Tabulae Rudolphinae 1627, but the systematic Chinese adoption is 1742. The lag is partly attributable to the Jesuit theological-political reluctance to embrace post-Copernican developments before the 1690s, partly to the institutional inertia of the Qīntiānjiān between successive reforms.
(b) The Mars-parallax method for solar parallax: the 提要’s exposition of why the solar parallax cannot be directly measured (atmospheric refraction interference) and how Mars-opposition observations from north-south stations can be triangulated to yield the corrected solar parallax of 10″ (vs. the old 3’) is one of the great moments of late-Qīng-period mathematical-astronomical sophistication. The technique was developed by Cassini and others at the Paris Observatory in the 1670s-1690s; its incorporation here represents the high-Qīng catching-up with the European observational frontier of the previous century.
(c) The Cassini-Lahire atmospheric refraction: the new refraction values (32’ at horizon vs. old 34’, 59″ at 45° vs. old 5″) reflect Cassini-Lahire’s late-17th-century measurements at the Paris Observatory. The corrected values were not merely empirical adjustments but were grounded in the new theoretical understanding of atmospheric refraction as the bending of light through a continuously-varying medium — anticipating the more rigorous formulation that would come with the optical work of Huygens, Bradley, and Newton.
(d) The Yōngzhèng 8 eclipse: the 提要’s specific reference to the July 16, 1730 solar eclipse — predicted with greater accuracy by Kögler’s new method than by the Lìxiàng kǎochéng — is one of the few cases in the Sìkù tíyào of a specific eclipse-event being cited as the empirical basis of an editorial reform. The successful prediction was the proximate cause of Yōngzhèng’s commission; the historical-mathematical-astronomical event marks the institutional transition from Tychonic to Keplerian astronomy in Qīng practice.
The work’s institutional significance: the Hòubiān was the Qīntiānjiān’s working handbook from 1742 until the late-Qīng telegraph-and-Western-astronomical-revolution period (essentially until the institutional reorganization of the late 19th century). For 150 years it was the official Chinese state-astronomical method.
Note: Ignaz Kögler (戴進賢) is the principal Western Jesuit author; the 提要 records his proposal as the proximate origin of the project. The catalog meta lists only Yǔnlù as primary author, following the conventional pattern by which imperial-prince directors are credited with works actually composed by mixed Chinese-Jesuit teams. The full collaborative team is documented in the work’s personnel section.
For the precursor work, see KR3f0018 Lìxiàng kǎochéng. For the contemporary instrument-and-star catalog, see KR3f0020. For broader context of the imperial mathematical-astronomical synthesis, see 允祿, 戴進賢, 何國宗.
Translations and research
- Jami, Catherine. The Emperor’s New Mathematics: Western Learning and Imperial Authority during the Kangxi Reign (1662–1722), Oxford: Oxford University Press, 2012 (essential context for the precursor Lì-xiàng kǎo-chéng project).
- Han Qi 韓琦, Tōng-tiān zhī xué: Yēsū-huì shì hé tiānwén-xué zài Zhōng-guó de chuán-bō 通天之學, Beijing: Sānlián, 2018 (treats Kögler and the Keplerian transition in detail).
- Hashimoto Keizō 橋本敬造. “The Hòu-biān and the Adoption of Keplerian Astronomy in 18th-Century China”, in Historia Scientiarum (Tōkyō) 13.3 (2004).
- Standaert, Nicolas (ed.). Handbook of Christianity in China, vol. 1: 635–1800, Leiden: Brill, 2001 (Kögler entry).
- Sivin, Nathan. “Copernicus in China”, Studia Copernicana 6 (1973): 63–122.
- Cullen, Christopher. Heavenly Numbers: Astronomy and Authority in Early Imperial China, Oxford: Oxford University Press, 2017.
- Pingyi Chu 祝平一, “Tian li zhi yi: Yōng-Qián zhi ji de tiānwén-suàn-fǎ” 天理之異: 雍乾之際的天文算法, in his Wǎn-Qīng tiān-xué shǐ lùn 晚清天學史論, Tài-běi: Lián-jīng, 2017.
Other points of interest
The 提要’s careful use of the Chinese transcription Kèbáiěr 刻白爾 for “Kepler” — together with Gāxīní 噶西尼 for Cassini and Fǎlándé 法蘭徳 for Flamsteed — represents one of the earliest explicit Chinese-language references to specific named European astronomers (rather than the generic “Westerner” of the late-Wànlì period). The naming reflects the Qián-lóng-period editorial concern to give credit-by-attribution within the European tradition.
The 提要’s framing of the institutional sequence — Yōngzhèng’s specific commission of “Sun-and-Moon two tables”, followed by Gù Cóng’s memorial requesting the addition of explanations, followed by Qiánlóng’s approval — documents the bureaucratic process by which Qīng imperial astronomy adapted to new theoretical input. The pattern is characteristic: a Western-Jesuit input identifies a specific empirical-or-theoretical advance, an imperial commission authorizes table-revision, a Chinese mathematical-staff intervention extends the table-revision into a substantive theoretical exposition. The Hòubiān is the paradigmatic example of this Qīng synthetic process.
The Yōngzhèng-Qián-lóng-period translation conventions for European astronomical terminology — tuǒyuán 撱圓 for “ellipse” (literally “leaning circle”), jūnlún 均輪 for “equant” (literally “even wheel”), zhuìzǐ biǎo 墜子表 for “pendulum clock” (literally “hanging-thing table”), qiānlǐ jìng 千里鏡 for “telescope” (literally “thousand-lǐ mirror”) — established the Chinese astronomical vocabulary that would remain standard through the late-Qīng period.