The Astronomical Bureau and the Calendar Case

For most of two thousand years, computing the calendar in China was an office of the state, and issuing it was an act of sovereignty. That single fact reorganises almost everything a European reader expects about the subject. The astronomer was a civil servant, the almanac was a government publication, and interpreting the sky was a licensed activity.

This entry follows the institution that held the office, and then one episode inside it: the prosecution of 1664 to 1669, in which the European director of the bureau was imprisoned, several of his Chinese colleagues were executed, and the affair ended with a measurement of the length of a shadow. That episode belongs to the history of European astronomy at least as much as to the history of Chinese astronomy, which is why it sits on this site.

Granting the seasons

The office grew out of the ritualist-scribe of the first millennium BCE, who both recorded and divined. With the formation of a single empire in the late third century BCE the title became Grand Scribe, its holder became the head of a bureau of experts, and within a millennium the primary sense of the title had shifted to Grand Astrologer ^{1 pp. 36-37}.

The reason was doctrinal. Imperial legitimacy was argued on the Mandate of Heaven: a ruling house held its mandate by the correct performance of ritual, and neglect drew warnings in the form of unpredictable and baleful events in the sky and on the earth. A reigning emperor could never be certain his conduct met the requirement, and the doctrine therefore generated anxiety that specialists were employed to manage ^{1 pp. 36-37}.

From that follows the standing of the almanac. Sivin records that any group seeking imperial dominion learned that calculating and issuing the annual almanac was a ritual without which the claim did not stand, and that granting the seasons was one of the ways a new regime asserted legitimate succession ^{1 p. 140}. A better computational system in the hands of a potential rebel was therefore a symbol of legitimacy, and rulers were periodically tempted to forbid the private study of astronomy ^{1 pp. 58-59}.

One consequence cuts against a common assumption about premodern astronomy anywhere. Observational testing of a computational system was old and routine. As early as 78 BCE a dispute over the validity of a system was settled by imperial order for a systematic programme of solar and lunar observation running two years and involving more than twenty people, and the practice of testing by observation continued through every subsequent century of official astronomical work ^{2 p. 453 n. 4}.

Inside the bureau

The bureau’s internal shape can be read off a surviving regulation. The Yuan bureau, closely modelled on its Jin predecessor and in turn the model for the late imperial Bureau of Astronomy, the Qīntiānjiān 欽天監 of the Ming and Qing, was divided into five sections which Qiao Yang lists in their order of privilege: Omen Astrology, tiānwén 天文; Mathematical Astronomy, lìsuàn 曆算; Three Boards Divination, sānshì 三式; Quantitative Observation, cèyàn 測驗; and Time Keeping, lòukè 漏刻 ^{3 pp. 252-53}.

Interpretation ranked above computation, and the observers, who did the measuring, ranked fourth of five.

The asymmetry was enforced. Imperial courts commonly prohibited the practice of omen astrology outside the astronomical bureaus, and inside the bureau not everyone held permission to interpret. Under the Tang, students in the Quantitative Observation Section were allowed to report any unusual celestial observation but were forbidden to interpret it or to read books of omen astrology, and the Yuan regulation of 1275 shows the same one-way arrangement: the Omen Astrology Section studied the Quantitative Observation curriculum, and not the reverse ^{3 p. 261}.

Europeans in the bureau

In September 1629 the Chongzhen emperor commissioned Xu Guangqi (1562-1633), a member of the Confucian elite who had converted to Christianity in 1603 through his friendship with Matteo Ricci, to reform the calendar by western methods. The occasion was a contest of prediction. The partial solar eclipse of 21 June 1629 at Beijing had been forecast by the established Chinese method, the Dàtǒng lì 大統曆; by the Islamic method maintained at the same court, the Huíhuí lì 回回曆; and by the Jesuits ^{4 pp. 327-29}.

None of the three did well. Compared against a modern reconstruction, the timing errors were often larger than a quarter of an hour, which di Serego Alighieri and Corsi note is not much worse than the Jesuits’ own eclipse forecasts between 1644 and 1750, where errors run up to forty-one minutes ^{4 pp. 330-31}.

The Ming fell before the reformed system came into official use: Sivin’s list of systems in official use gives the Great Concordance system of 1384 as current until 1644, and the Temporal Pattern system from 1644 ^{1 pp. 52-53}. When the Qing took Beijing in 1644 the resulting system was adopted, and Johann Adam Schall von Bell (1592-1666, Tāng Ruòwàng 湯若望 in Chinese) was appointed to the bureau, beginning a Jesuit tenure in a leading position there that lasted a century and a half ^{4 p. 327}. Sivin dates the official use of the resulting Temporal Pattern system, Shíxiàn lì 時憲曆, from 1644 to 1742, and describes its treatise as a hybrid of Chinese content with European content that was already becoming obsolete in Europe ^{1 pp. 52-53, 234}. What that system changed about the calendar itself is the subject of The Chinese Lunisolar Calendar.

A small detail shows how deep the substitution went. The day had been divided into one hundred marks, a number that does not divide by twelve and that occasionally provoked edicts to change it, without the change ever sticking. One hundred held until the Jesuits took over palace astronomy in 1644, at which point the count became ninety-six, so that one mark equalled a European quarter of an hour ^{1 p. 88}.

The Calendar Case, 1664 to 1669

In autumn 1664 the Jesuits at court were imprisoned as the result of a prosecution launched by Yáng Guāngxiān 楊光先 (1597-1669), a Chinese literatus opposed to the Jesuit presence. Initial sentences of death or banishment on those principally concerned were commuted to house arrest in May 1665, and their colleagues elsewhere in China were removed to Canton. Several Chinese Christian officials holding posts in the Astronomical Bureau were executed ^{2 pp. 423-24}. Sivin, writing about the campaign against the Temporal Pattern system as a whole, dates it 1657 to 1668 and records the same outcome: imprisonment for the Europeans, execution for some of their Chinese supporters ^{1 p. 58}.

The asymmetry matters more than anything else on this page: the European defendants were reprieved and their Chinese colleagues were executed. A summary that treats the affair as the trial of a Jesuit has dropped the people who died in it.

Schall von Bell, formerly Director of the bureau, died in 1666 without being restored. By late 1668 three Jesuits were left in Beijing: Ferdinand Verbiest (1623-1688, Nán Huáirén 南懷仁), who had been Schall’s assistant and was the only one of them competent in astronomy; Lodovico Buglio (1606-1682), the superior of the group; and Gabriel de Magalhães (1609-1677), who was skilled with his hands and who wrote the detailed account of what followed in a letter of 2 January 1669 ^{2 pp. 423-24}.

The shadow of a gnomon

In December 1668 the presence of the three remaining Jesuits came to the notice of the young Kangxi emperor, who had formally assumed personal rule the year before. They were summoned, and in the audience of 26 December the emperor asked what clear evidence there was that Verbiest’s astronomical system was in conformity with the heavens ^{2 pp. 424-25}.

Verbiest’s answer, in the translation of Cullen and Jami, proposed a test:

In checking whether an astronomical system is or is not in conformity with the heavens, in all [cases] from antiquity onwards the proof has come from observation.

For checking the day, hour and degree at which the sun reaches a given solar season, he continued, nothing served better than the method applying right-angled triangles to gnomon shadows. He asked that a gnomon of any length be fixed, that both parties predict the length of its shadow at a stated instant to hundredths of an inch, and that the result be read off in company: all eyes would see it, and no dispute would be needed because the answer would be self-evident ^{2 p. 425}.

Verbiest’s appeal to antiquity was accurate, as the 78 BCE observation programme shows ^{2 p. 453 n. 4}. And the quantity he offered to be judged on is exactly the object described at The Chinese Lunisolar Calendar: the moment at which the sun reaches a given solar term. The trial of the Jesuit mission in China turned on a solar term.

The measurement was made at noon on three successive days, 27, 28 and 29 December. Yang Guangxian, by then Director of the bureau, and the Deputy Director Wú Míngxuān 吳明烜 at first claimed to be able to make such predictions and, when tested, had to admit that they could not. Verbiest was judged to have succeeded, the Jesuits were released from confinement, further tests were set and passed, Yang and Wu were deprived of office in 1669, and Verbiest was given most of the functions Schall had exercised ^{2 pp. 423-24}.

What the first day was really about

What happened on day one matters more than the verdict, and it is a problem about definitions.

Verbiest predicted 16.66 chi. The officials’ report to the emperor agreed that the shadow fell on the line he had drawn in advance, but recorded that his two adversaries refused to concede the value: Yang Guangxian said the shadow was 0.09 chi longer, Wu Mingxuan that it was 0.06 chi longer ^{2 p. 449}.

Both were looking at something Verbiest had not predicted. He had computed the umbral shadow, cast by the sun’s upper limb, as was standard practice in the Europe where he learned astronomy. His rivals saw a fainter shadow continuing past his line, and took the shadow to extend into the visible part of the penumbra. Cullen and Jami are explicit that this was a difference of convention about where a shadow ends ^{2 pp. 449-51}.

What Verbiest then did is documented by its arithmetic. Cullen and Jami reproduce his day-one figure by three separate methods available to him, and none of the three reproduces his figures for days two and three; the change implied by his stated values runs in the wrong direction for the sun’s actual motion after the solstice, so whatever he did on the first day, he did not do it again on the second ^{2 pp. 449-50}. Their reading is that he adapted the calculation to predict the shadow as he now knew his opponents would recognise it, and that he was open about the change: on 28 December he explained the difference between umbra and penumbra to the supervising officials with a diagram, drawing an exclamation of admiration from one Manchu official, and after the trial closed on 29 December he showed the same diagram to the emperor, who kept it ^{2 p. 451}.

Cullen and Jami consider and reject the reading in which this is Jesuit accommodation shading into unreliability: his techniques were as accurate as the astronomy of the period allowed ^{2 p. 451}.

Why this page belongs here

A European Jesuit directed an East Asian state observatory, was prosecuted and imprisoned, died in 1666 without being restored, and was succeeded by a colleague whose restoration turned on a public measurement whose outcome depended on which edge of a shadow counted as the shadow. The instruments were a gnomon and a set of tables; the tables were the ones seventeenth-century Europe had; the audience was a Manchu court; and the quantity in dispute was a solar term.

A site that covers Renaissance and modern European astronomy and stops at the edge of Europe is telling half of its own subject. For the eastern end of the same traffic six centuries earlier, when the same bureau was directed first by an Indian and then by a Persian astronomer, see Eastward Transmission of Hellenistic Astral Material.