EASTM 28 (2008): 36-81

Reforming Astronomy and Compiling Imperial Science in the Post-Kangxi Era: The Social Dimension of the Yuzhi lixia,ng kaocheng houbia,n f{Q1 ~ JI ~ ~ /Jx ~ fM

Shi Yunli*

[Shi Yunli is Professor at the Department of the History of Science and Scientific Archaeology, University of Science and Technology of China. In 2006, he be­ came a Fellow of the Alexander von Humboldt Foundation and Guest Professor at the Jnstitute for Chinese and Korean Studies, Tubingen University. He has published a number of works on the history of astronomy in China and Korea as well as on the early reception of Western astronomy in these two countries]

* * * Introduction

From very early times, the compilation and promulgation of the civil calendar was thought to be both an exclusive privilege and special duty of the central government in China. At the same time, the capability to predict ominous por­ tents, such as )uni-solar eclipses and the occultations of the moon and the five major planets over the fixed stars, was deemed critical to avert potential political upheavals and natural disasters. For these purposes, every Chinese dynasty main­ tained a special establishment of experts who operated a system of calendrical astronomy, or lifa M rt (calendar method), for the calculation of the calendar and any possible portents. Such a system usually bore an eloquent name and became a symbol of the dynasty. When the system was found to be inconsonant with the celestial motions or unfavourable from the point of view of special socio-political interests, an astronomical reform was launched to remedy the problem. The Yuzhi lixiang kaocheng houbian fiflJ ~ /ffi ~ ~ IVG ~ -~ (Later

* This paper was completed during my visit to Germany as an Alexander von Hum­ boldt fellow in 2006. I wish to express my great gratitude to the AvH foundation and Prof. Han Ulrich Vogel for the funding and hosting of my project. My special thanks also go to Prof. Catherine Jami for her comments on the earlier draft, and to two anonymous referees for their valuable comments and suggestions, and to the English language editor of this issue for the clarity he brought to this article. The remaining problems are my own. 36 Downloaded from Brill.com10/10/2021 10:48:59PM via free access Shi Yunli: Reforming Astronomy and Compiling Imperial Science 37

Volumes of the Thorough Investigation of Calendrical Astronomy Imperially Composed, hereafter Houbian), chiefly compiled by Ignaz Kogler (1680-1746) and Andre Pereira (1689-1743), was the result of such a reform between 1730 and 1742. The book includes a lot of new knowledge from Europe, including Kepler's (1571-1630) first two laws of planetary motion, the geometric solutions of Kepler's equation, Isaac Newton's (1642-1727) theory of the motion of the moon, I as well as the new values of some important astronomical constants de­ termined by the leading astronomers of the time, such as Newton, Jean­ Dominique Cassini (1625-1712) and Jean Richer (1620-1682). A series of stud­ ies on the book have been published. 2 They have detailed this new knowledge and its Western sources and other improvements in the book. In this paper, I would like to treat the book from another perspective. Instead of seeing it simply as a self-contained document in isolation, I will try to situate it and its production in the wider context of the whole history of Jesuit astronomy in China, especially the long-running conflict between Jesuit astronomers and their Chinese adversar­ ies, and consider the book as the product of a process. This approach is both necessary and important, because it will reveal a new story about the production and the contents of the book. It will tell us more about how the Jesuit astrono­ mers carried out their technical work within the changing socio-political and intellectual milieu in the post-Kangxi era.

Prelude: The Old Picture and Its Limits

Our previous understanding of the production of the Houbian was based on a group of memorials produced during the reform, which the Qianlong emperor (r. 1736-1795) later ordered to be published together with the book. According to these memorials, on August 11, 1730, Mingtu ajj Ii, the Manchu director3 of the

I By theory here I do not mean Newton's study of the motion of the moon on the ba­ sis of his law of gravitation, but a set of geometrical rules which he published in 1702 for the practical calculation of the moon's motion, though Newton's himself claimed that the rules resulted from his gravitational study of the moon. For Newton's theory of the mo­ tion of the moon and its difference with his gravitational analysis of the motion of the moon, see Cohen (1975). 2 See Hashimoto (1971); Bo Shuren et al. (1981), pp. 238-239; Bo Shuren (1984); Han Qi (1993); Shi Yunli (1995), pp. 34-35; Shi Yunli (1996b); Lu Dalong (1997a); Lu Dalong (1997b ); Han Qi (1999); Kollerstrom (2000); Halsberghe and Hashimoto (200 I); Han Qi (2001); Shi Yunli (2003); Han Qi (2004); Shi Yunli and Xing Gang (2006); Han Qi (2008). 3 After the "Calendar Lawsuit" (1665-1668) during the Kangxi reign, a system of dual directorship was adopted in the Bureau of Astronomy, which brought the Bureau under the leadership of a Manchu and a Han director. While the Manchu directorship was as­ sumed by a real Manchu, the Han directorship was actually filled by Jesuit astronomers.

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Bureau of Astronomy, memorialized to the Yongzheng emperor (r. 1723-1735) that Kogler and Pereira had discovered some "slight errors" of the Yuzhi lixiang kaocheng ffil ~ JI ~ ~ JJx (Thorough Investigation of Calendrical Astronomy Imperially Composed, hereafter Kaocheng), and that this discovery had been confirmed through the observation of a solar eclipse on July 15, 1730. Mingtu also indicated that the two Jesuits actually possessed a set of new methods that had proved to be more exact. He therefore requested the emperor to initiate an investigation and revision. After the Yongzheng emperor granted the petition, the two Jesuits compiled a set of new tables, but they did not provide any explana­ tions for the underlying theory and use. So in mid-1737, at the request of the Minister of Rites Gu Cong • Ii and by order of the Qianlong emperor, a project was launched to remedy this problem, leading to the completion of the Houbian in 1742.4 In the same set of memorials, we can also find the justifications for the neces­ sity of the reform. For example, in his 1730 memorial, Mingtu explains to the throne:

Since the motions of the sun and the moon will gradually re­ veal differences over a long period of time, the calendar method can keep in step with them only if we revise it in time. Your subjects have been solemnly abiding by the Yuzhi lixiang kaocheng in calculating the Shixian ~ ~ (Time Modelling Calendar)5 and the motions of the Seven Gover­ nors (qizheng -t il&),6 which are promulgated across the na­ tion. [ ... ] It turns out that the Yuzhi lixiang kaocheng was composed according to the Xinfa lishu ffi rt. JI 'IF (Treatises on Calendrical Astronomy According to the New Method).7 But the Xinfa lishu has been used for a long time so that the very tiny fractions of the differences in the motions of the sun and the moon have gradually accumulated up to minutes and seconds. If we do not make a revision, I am afraid that the longer the time the worse the errors will become.8

For the "Calendar Lawsuit", see Chu Pingyi (1997) and Zhang Dawei (1998), and for the dual directorship of the Qing Bureau of Astronomy, see Porter (1980), p. 64. 4 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. la-13b. 5 This is the name of the ci vii calendar of the Qing dynasty. 6 Namely, the sun, moon and the five major planets. 7 This is the abridged title of the Xiyang xinfa lishu jffi if ffi rt. JI 'If (Treatises on Calendrical Astronomy According to the New Method from the West), an expanded version of the Chongzhen lishu * ffl. JI 'IF (Treatises on Calendrical Astronomy of the Chongzhen Reign). 8 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. la-b.

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In his memorial concerning the reform, Prince Yunlu ft~. the General Supervi­ sor (Zongli ~ J.11!) of the project, also repeats the same explanation and adds:

Since the Kangxi era, Western astronomers such as Kaxini Ill jffi }e (Cassini) and Falande #";; ffili it\ (Aamsteed) have ap­ peared in great number. They have invented new pendulum clocks to keep time and used telescopes to measure distances. Thus they have revealed three major points that Digu m~ (Tycho) had not thoroughly discussed: first of all, the old value of the diurnal parallax of the sun is three minutes [of arc], but the newly measured value is just ten seconds [of arc]. Secondly, the old value of the refraction of the atmosphere is thirty-four minutes on horizon and only five seconds at the altitude of forty-five degrees, but new measurements indicate that it is thirty-two minutes on the horizon, while it still amounts to fifty-nine seconds at the altitude of forty-five de­ grees. Thirdly, the heavens of the sun, the moon and the five major planets were formerly supposed to be normal circles, but they are now believed to be ellipses. [ ... ] Because of these three points, the longitudes and latitudes [calculated with the old system] tum out to be slightly discrepant.9

From these materials, it seems that the reform was caused solely by technical reasons-errors in the existing system-and that its goal was purely technical, that is to remedy the shortcomings of the existing system by replacing it with a new and better one. This has become the standard picture of the reform, one that is correct inso­ far as it does reveal some key technical factors leading to the implementation of the reform. On the other hand, however it is very incomplete, for it fails to take into account a series of very important socio-political factors that had a critical impact on the reform. In what follows, I will discuss these factors and their ef­ fects. In order to provide a more complete and balanced picture, I will draw on some materials from the Jesuit side.

The Kaocheng and its Aftermath

The first factor to be taken into account is the completion of the Kaocheng and its aftermath. In 1713, the Kangxi emperor established an Office of Mathematics (Suanxueguan 1¥: * fa) within the palace and filled it with a group of native mathematicians and astronomers charged with the compilation of books on cal-

9 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. 4b-5a.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 40 EASTM 28 (2008) endrical astronomy, mathematics and musical hannonics.10 The book on calen­ drical astronomy, i.e. the Kaocheng, was completed in 1722 shortly after the emperor's death and was printed two years later as one part of the magnificent series Yuzhi Uili yuanyuan m~ W I! mil ~ (Origin of Musical Hannonics and Calendrical Astronomy Imperially Composed). Two other books, the Yuzhi shuli jingyun m~ ll(: J!I!. ~ ~ (Delicate Accumulation of Mathematical Principles Imperially Composed) and Yuzhi lulu zhengyi m ~ W § iE ft (Orthodox Meanings of Musical Hannonics), are also the products of the same office. The whole series was compiled in the name of the Kangxi emperor, hence the use of the words "imperially composed" (yuzhi m~) in the titles. During the Qing dynasty, a great number of books were compiled or written by order and in the name of an emperor, but all were designated simply as yuding mJE (imperially determined), qinding ~ 5E (royally determined) or even yu­ zuan 00 • (imperially redacted) rather than "imperially composed". Normally, the term was not used unless a work really was by the hand of an emperor. There­ fore, the adoption of these two words in the title distinguished the Yuzhi liili yuanyuan m~ 1' /! mil ~ from all other books composed in the name of an emperor. Most importantly, these two words were not a posthumous attribution, but a claim made by the Kangxi emperor himself. In his decree inaugurating the establishment of the Office of Mathematics, he makes it clear that the mission of the office was "to compile the books on calendrical astronomy, musical hannon­ ics and mathematics imperially composed by myself (zhen yuzhi lifa liilii suanfa zhushu $c m~ /! ft;., 1' § , • ft;. ~ ff), as well as to manufacture music instruments". 11 While ordering prince Yunzhi ft 111: to preside over the newly founded office, he repeats: "Now I hand down the books on musical hannonics and mathematics composed by myself. You shall lead the Fellow of Royal Acad­ emy He Guozong fiiJ II * and others to open the Office [of Mathematics] to redact and compile them."12 In his preface to the Yuzhi liili yuanyuan m~ 1' /! mil ~, the Y ongzheng emperor not only stresses the imperial authorship of the whole series and each book in it, but also links it explicitly with the glory of the Kangxi emperor when he writes:

My deceased royal father had an inborn enthusiasm for study and was an innate polymath. When he had some spare time in his administration of the myriad affairs, he paid intensive at­ tention to the study of musical harmonics, calendrical astron­ omy and mathematics. For several decades, he conducted erudite research into complex and profound problems, and

10 For the establishment and work of this institution, see Qingshi gao, chap. 45, pp. 1668-1669, and Han Qi (1999). 11 Han Qi (1999), p. 314. 12 Kangxi zhengyao, p. 357.

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sought to expose hidden subtleties. He synthesized diverse theories and unified them into a uniform system. Then he in­ structed Prince Yunlu to organize the scholar-officials to compile books at the Hall of Cultivation (Mengyangzhai ~ ft Jlf) in the inner palace. He personally corrected the drafts presented to him every day, and edited them into a series of one hundredjuan :ft! (chapters) named Liili yuanyuan ~ II ~ ~ (Origin of Musical Harmonics and Calendrical Astron­ omy) .... Since our country enjoys a far-reaching reputation and great cultural harmony, each of the diverse countries from Europe in the extreme West contributes its arts to our court, and their books, graphs and tables are all splendidly presented. My deceased imperial father widely integrated them and judiciously redacted them. He also studied old Chi­ nese arts long lost or carelessly selected [by previous au­ thors], as well as those from the West, which are in stilted language short on clear expressions. He put all these in a dis­ tinct sequence and clarified their ins and outs. The work is so refined and correct, detailed and comprehensive that even the most famous experts would not be able to achieve one thou­ sandth of it. It is said that "only a sage has the capacity". How can it be incredible? [ ... ] The series is not just an ever­ lasting benefice coming from the hands of the deceased em­ peror. The principles in it are really [representing] a grand compendium grounded on the studies of both ancient and present times, which exceed those of past dynasties and will last for thousands and myriads of years without change.13

In our modem understanding, the scientific knowledge contained in the series really belonged to genuine "imperial science". After the formal publication of the Kaocheng in 1724, some measures were taken by the Qing government to mark the special position of the book as impe­ rial science. First of all, its astronomical calculations were formally adopted at the Bureau of Astronomy as canonical. Secondly, it was decided that the title of the Western Director of the Bureau of Astronomy be changed from zhili lifa ~ l1ll. /ff it; (Administrator of Calendar)l4 to jianzheng fKi. iE (Director of the Bu­ reau), now that the Kaocheng "is an imperially composed book and therefore

13 Yuzhi lixiang kaocheng houbian, front matters, imperial preface, pp. 2a-b. 14 When Ferdinand Verbiest (1623-1688) was appointed Director of the Bureau of Astronomy after the "Calendar Lawsuit" in 1668, he declined the appointment, insisting that, as a missionary, he should stay only as an expert who administered the calendar rather than assume any mundane power. From that time on "Administrator of Calendar" became the title of the Jesuit astronomers who actually took over the position of the Han directorship of the Bureau of Astronomy. See Bo Shuren ( 1978).

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 42 EASTM 28 (2008) does not need the Bureau of Astronomy to administer it".15 Thirdly, the emperor also decreed that hereafter the inscription on the cover page of the annually is­ sued civil calendars should be changed from Qintianjian wuzhun yinzao Shixian Li banxing tianxia tx 7e. m_ * m f::P ;ifI ~ ~ JI »Ji tr 7e. r (Approved by the Throne, the Bureau of Astronomy makes and prints the Time Modelling Calendar and issues it across the country) to Qintianjian qinzun Yuzhi Lixiang kaocheng yinzao Shixian Ii banxing tianxia tx 7C. m_ tx it mi ~ JI j!. ~ /J.IG f::P :ifI ~ ~ JI »Ji tr ?C. r (Solemnly abiding by the Thorough Investigation of Calendrical Astronomy Imperially Composed, the Bureau of Astronomy makes and prints the Time Modelling Calendar and issues it across the country).16 Finally, in front of the prediction issued across the country before each visible eclipse of the sun and moon, the words Qinzun Yuzhi lixiang kaocheng tuisuan de ... tx it mi ~ JI j!. ~ /J.IG m• ~ ... (Solemnly abide by the Thorough Investigation of Calendrical Astronomy Imperially Composed to calculate and find that ... ) were added (Fig. 1).

15 Qingshi gao, chap. 45, p. 1669. 16 Interestingly, in 1736 the inscription was ordered to be changed again to Qintian­ jian qinzun Yuzhi shuli jingyun yinzao Shixian li banxing tianxia tt 7c. .fKl. tt ii ffiJ ~ ~ 11 .ffl ii EfJ ;iii lliJ • /! il'Jt tr 7c. r (Solemnly abiding by the Delicate Accumulation of Mathematical Principles Imperially Composed, the Bureau of Astronomy makes and prints the Time Modelling Calendar and issues it across the country), though the Yuzhi shuli jingyun ffiJ ~ ~ 11 .ffl ii is a book on mathematics rather than astronomy. For all these changes, see Qinding da Qing huidian zeli, chap. 158, pp. 9b-l la.

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Fig. 1: The Prediction of the Lunar Eclipse of December 2, 1732

[Courtesy of the Observatory of Paris]

In the Ming and Qing dynasties, the wording qinzun jj( :it (solemnly abiding by) was not used unless the writer wanted to indicate that he did something according to the decree of the emperor. Their appearance in the aforementioned astronomi­ cal documents shows that the Kaocheng was treated as having the power of an imperial decree, not to be lightly challenged or changed. This special situation was observed also by the French Jesuit Dominique Parrenin (1665-1741), who reports in I 730 from Beijing:

The deceased Emperor Kangxi himself did more than all of his predecessors [in astronomy]: It should be necessary to continue what he has so well started; but people suppose that there is no longer anything that has to be done, and what has been reached is perfect. The Great Compendium of Astron­ omy [i.e. the KaochengJ made by the order of this great prince has appeared under the care of his successor [Emperor] Yongzheng; it is prinied and distributed, and thus becomes the unchangeable rule: If the stars do not conform to it in the future, this will be their fault, rather than the fault of the cal­ culators. At least one will never touch it according to the ap-

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pearances [in the sky], unless an obvious disturbance occurs in the [arrangement of] the seasons.I?

As we will see below, Pereira also reports this situation in similar terms in a letter two years later. At first glance, the compilation of the Kaocheng seems to be nothing more than a revision and re-edition of the Xiyang xinfa lishu jffi ~ if $; /! ~ in order to remove the latter's technical defects and obscurities.IS In fact, however, the whole project of the Office of Mathematics had at least two important goals, (a) to enhance the authority and glory of the Manchu emperor, and (b) to break the Jesuit monopoly in mathematical sciences, both through imperial control of mathematical sciences. For this reason, the project was undertaken exclusively by native scholars who were institutionally independent of the Bureau of Astronomy, which was at the time technically dominated by Jesuit astronomers. No Jesuits appear in the long list of compilers preceding the Yuzhi liili yuanyuan :JfflJ ~ ff I! mll ~,19 although most of its content is based on knowledge introduced by the Jesuits from Europe20 and the Jesuit missionaries in Beijing were frequently called upon for advice during compilation.21 Only four Chinese astronomers from the Bureau of Astronomy appear on this list. In fact, the major members of the Office of Mathematics, especially Mei Juecheng #it fl!: IVG (1681-1763) and He Guozong, were adversaries of the Jesuit astronomers,22 and in the aftermath of the completion of the Kaocheng, the situa­ tion became increasingly unfavourable for the Jesuits in Beijing. As soon as the book was published, they began to openly challenge the Jesuit directorship at the Bureau of Astronomy. This challenge put heavy pressure on the Jesuit missionar­ ies in Beijing, as Pereira reports in a letter to the General of the Society of Jesus written in 1732:

After his [i.e. the Kangxi emperor's] death, the academicians [of Kangxi's Office of Mathematics], who arrogantly refused to submit their book to the correction and censorship of the

17 Translation based on Parrenin ( 1730), p. 376. 18 For the relationship and differences between the Xiyang xinfa lishu iffi r-¥: ffi ¥t. II if and the Kaocheng, see Hashimoto (1970), Bo Shuren et al. (1981), p. 232 and Shi Yunli (1996a). 19 Yuzhi lixiang kaocheng houbian, front matters, names of officers, pp. la-4a. Jami (2001), pp. 701-702. 20 While the Kaocheng is based on the Xiyang xinfa lishu, the books on mathematics and musical harmonics in the series incorporate various Jesuit works on-algebra, geometry, music and harmonics. For details see Jami (1989); Engelfriet (1998), pp. 437-438; Jami (2001), pp. 701-702. 21 Han Qi (1999). 22 Han Qi (2002).

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Europeans, turned to his son [i.e. the Yongzheng emperor] immediately, and appealed to the successor in throne, so that the new reform of astronomy [i.e. the Kaocheng] on which they had worked for so long could be published. At first the new emperor did not accept their demands, but ordered the book to be returned to them again, hoping in vain for further polish and certainty. Finally, however, in the third year of his enthronement, [the Yongzheng emperor] was persuaded and issued a decree, and the hidden thus came to light [i.e. the Kaocheng was published] and hereafter became a fixed rule. The Bureau of Astronomy was forced to conform to its norm in their calculation and composition of ephemerides. Even a tiny deviation was not permitted. And therefore the Chinese academicians became completely intoxicated by their wishes, as if they had already evaded the mentors of their mentor. 23 At that time, [the situation] was terribly feared by us, and rumour was spread by the Chinese in order that Europeans would no longer take the chair of mathematics, and therefore the only root of the diffusion of the faith of God in this em­ pire, the dependence on European mathematics as we know, would have been thoroughly pulled out. At that time this was no empty fear. Having obtained this opportunity, the manda­ rin from the same academy named He [Guozong], an enemy of the name of Christ and a descendant of another with the same surname who also had stirred up fierce persecution on us in Father Adam Schall's time, submitted an appealing memorial to the new emperor. He said-among other things-that since the reform of astronomy had already been released by Chinese academicians, the Bureau of Astronomy, the observation of the planets and the [compilation of] ephemerides of the eclipses should no longer be directed ac­ cording to the work of the Europeans; and a certain mandarin, named Mei [Juecheng], of the academy itself should be just appointed to this office. He proposed Mei in place of the Europeans.24

Although the Yongzheng emperor was said to have dismissed this proposal, it was definitely a very dangerous and frightening signal to the Jesuits. As Catherine Jami has argued, the compilation of the Yuzhi liili yuanyuan fiQI ~ ff M mil ~ "represented the imperial appropriation of W estem learning, which integrated some elements of it into a recreated Chinese leaming".25 Taking such an appropriation at face value, it seems that Western learning had by then

23 Most of the members of the Office of Mathematics claimed to be students of the Kangxi emperor, who was actually a student of Jesuit missionaries in the sciences. 24 Rodriges (1925), pp. 88-89. English translation from the Latin by myself. 25 Jami (2001), pp. 701-702.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 46 EASTM 28 (2008) taken much deeper root in the soil of Chinese learning, and thus secured its per­ manent existence in China. From our analysis above, however, it is clear that the appropriation did not bring an end to the conflict between indigenous and Jesuit astronomers, but only strengthened Chinese astronomers' claims to real control of the Bureau of Astronomy,26 hence directly endangering the existence of Jesuit astronomers in China. In addition, as a result of the stand-off between the Qing sovereign and the Holy See caused by the Rites Controversy,27 the situation in China became even worse for Jesuit missionaries, especially after the death of the Kangxi emperor in December 1722. In January 1724, a decree was signed by the Yongzheng em­ peror and issued through the Ministry of Rites, forbidding the acceptance of Christianity in all Chinese provinces and ordering the expulsion of all missionar­ ies from the country, except for Jesuit astronomers, painters and technicians serving at the court in Beijing on account of the usefulness of their arts.28 Under such circumstances it became even more urgent for the Jesuit astrono­ mers to act and to demonstrate that, despite the completion of the Kaocheng, the actual authority on astronomical matters still resided in their hands. In other words, they had to prove that Jesuit service at the Bureau of Astronomy was still indispensable for the maintenance of a reliable system of calendrical astronomy in China. As I am going to show later, when Kogler and Pereira completed the new tables in 1732, they at first did not make them immediately intelligible and usable to most indigenous astronomers at the Bureau of Astronomy for a period of more than five years. This means that, as a consequence of the establishment of Kangxi's imperial science, the Jesuit missionaries in China had to re-establish their authority through the introduction of new knowledge from the West.

The Hidden Defect in the Old Jesuit System and its Implications

Another equally important factor to be taken into consideration is the defect existing in the old Jesuit system of calendrical astronomy. The defect itself was a purely technical matter, but it gave rise to some socio-political issues that might also have endangered Jesuit existence in China. This old system had been chiefly constructed between 1629 and 1644 by Jo­ hann Terrenz Schreck (1576-1630), Johann Adam Schall von Bell (1592-1666) and Giacomo Rho (1592-1638) in the Chongzhen lishu * ffl M a:. The system

26 After the "Calendar Lawsuit", the Han directorship of the Bureau of Astronomy was actually taken by Jesuit astronomers. Needless to say, this must have been a great annoyance to such Han Chinese astronomers as He Guozong and Mei Juecheng. 27 For a brief description of this long lasting event, see Standaert (2001), pp. 680-688. For its significance and consequences, see Mungello (ed.) (1994). 28 Allan (1935), p. 267.

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was based primarily on the Tychonic system as presented in Christian Severin Longomontanus' (1562-1647) Astronomia Danica (1622)29 and underwent no substantial changes in both the Xiyang xinfa lishu illi ~ ffi rt, M if, Schall von Bell's re-edition of the Chongzhen lishu, and the Kaocheng. Although it turned out to be better than any existing Chinese system of calendrical astronomy, it was still far from perfect in the predictive calculation of such celestial phenomena as eclipses of the sun and moon. In traditional Chinese portent astrology, solar and lunar eclipses were be­ lieved to be the most disastrous omens. Whenever an eclipse occurred, a special ceremony was held to "rescue the sun and the moon from loss", and thus to ease the ill fortune presaged by such portents. As a very important formality in the traditional Chinese system of imperial rituals, this ceremony was strictly codified. It was complied with by every ruling regime, and the duties of the imperial Bu­ reau of Astronomy were clearly regulated. For example, the stipulation of the Qing dynasty runs as follows:

[The Bureau of Astronomy] must make a prediction five months in advance whenever a !uni-solar eclipse is going to occur. An illustrated report regarding the times, magnitude and the initiating and ending directions of the eclipse as seen from Beijing and other provinces must be submitted to the throne and subsequently issued to the provinces concerned through the Ministry of Rites, so that the rescuing ceremony can be held in due time. A few days before the eclipse, an­ other memorial [concerning the eclipse] must be submitted. On the day [of the eclipse], all Manchu and Han officials of the Bureau must go to the observatory to make an observa­ tion together with officials from the Ministry of Rites. Meanwhile, astronomical students from the Bureau must be sent to every yamen (seat of local government) to join the ceremony held there. Keeping time by burning joss sticks, they must announce the initial, maximum and final phases. After the ceremony, the Bureau must present to the throne an illustrated report based on the true [observed] process of the eclipse, and must attach to it an astrological interpretation. 30

The strictness of this ceremonial operation in the early Qing dynasty was verified by Verbiest, who added information about how, during the ceremony, the astro­ nomical officers had to observe the eclipse attentively, record all important data and compare them with those predicted. He also stressed that, the day after an eclipse, the director of the Bureau had to "report to the emperor whether the calculation, according to the observation, corresponds to the Heavens or not,

29 Hashimoto (1988). 30 Qinding da Qing huidian, chap. 246, pp. 5a-6a.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 48 EASTM 28 (2008) presenting a petition to the emperor on this very topic, which is certified with their signature and the seal of the Bureau. "31 Being aware of the extreme importance of correct eclipse prediction in the Chinese astronomical and ritual system, Jesuit astronomers and their Chinese supporters always claimed the superiority of Western astronomy in this respect. For example, at the beginning the astronomical reform launched in 1629, Xu Guangqi ~ -Yt l'lll ( 1562-1633 ), the organizer of the reform, tried to convince the Ming emperor that "the [temporal] errors [in the eclipse prediction] can be counted in days before the Han [206 BC-224 AD] period, in double-hours before the Tang [618-907) period and in ke32 ever since the Song [960-1279) and Yuan [ 1207-1367) periods, whereas it can now be counted in [less than 14.4] minutes" and "could be around half a ke" at worst, due to the application of the new system based on Western astronomy.33 Afterwards, this claim was further exaggerated by the Jesuits and their Chinese followers. They made the Shunzhi emperor (r. 1644-1661), the first emperor of the Qing dynasty, believe that "the new method [composed by the Jesuits] exactly conforms to the heavenly motions and is ex­ tremely perfect", and therefore "the officers and students of the Bureau of As­ tronomy must study it carefully and abide by it forever".34 In 1672, Verbiest also conveyed a similar message to the Kangxi emperor and claimed that the new system "will be abided by and passed down [to later generations] forever", be­ cause "no discrepancy and mistake has appeared in the first twenty years of its formal application" and its exactitude was reconfirmed during the counter charge of Yang Guangxian m-Yt 5'e (1597-1669).35 But these claims are definitely not true, because, according to recent analysis, the time errors for eclipse prediction of the systems contained in both the Xiyang xinfa lishu jffi rf if rJ;. I! ~ and the Kaocheng typically amounted to a quarter of an hour. In many cases, the timing errors were more than half an hour.36 In fact, even before the beginning of the astronomical reform at the end of the Ming dynasty, Jesuit astronomers in China were quite clear that the Tychonic system was far from perfect in practical calculations. In 1621, Johann Terrenz

31 Golvers (1993), p. 81. 32 In traditional Chinese measurement of time before the early Qing dynasty, l ke = 14.4 minutes. 33 Xu Guangqi wenji, chap. 8, pp. 395, 415. 34 Xichao ding 'an, pp. 9 la-b. 35 Xichao ding'an, p. 91 b. 36 Cf. Stephenson and Fatoohi (1995), and Fatoohi and Stephenson (1996). Since the majority of the "observational" data analyzed by Stephenson and Fatoohi come from eclipse predictions, rather than observations, made by the Qing Bureau of Astronomy, their analysis more or less reflects the error pattern of these predictions. For a detailed discussion of Stephenson and Fatoohi's work, see Shi Yunli (2000a). Our new analysis on the basis of more complete prediction data yields the same results. See Lil Lingfeng and Shi Yunli (2003), and Lil Lingfeng (2007).

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wrote from China to a friend in Europe that ''Tycho has something good, but at times he errs by a quarter of an hour". Therefore, he turned to Galileo and Kepler for better methods.37 Up to 1669 and 1670, two other Jesuit Fathers in China, Adrien Grelon (1618-1696) and Christian W. Herdtrich (1625-1684), also ex­ pressed the same concern.JS In his famous book Astronomia Europaea, Verbiest openly complains how, on the one hand, mandarin authorities "expect our calcu­ lations to correspond very precisely to the Heavens", whereas on the other hand even famous astronomers in Europe "differ between themselves half an hour or more" in predictive calculations.39 But before the compilation of Kaocheng, none of these Jesuits ever allowed this secret to leak out to their Chinese patrons. The Chinese authorities had no knowledge of the practical discrepancy of the "West­ ern method" in predictive calculations, something Verbiest states with much satisfaction and religious confidence:

When I consider more closely the fact that often a great dis­ crepancy has been found between the tables and calculations of even the most prominent astronomers in Europe and the observed heavenly movements, then I do not doubt that it was due to God's extraordinary Providence that, in the course of so many years that (Chinese) have been comparing our astronomy and our calculations with heavenly move­ ments, not one conspicuous deviation has been found! This is, I insist, because the Divine Clemency has concealed the er­ rors, if there were any: by carelessness of observers, by clouds, or by some similar favour from the indulgent Heaven, and because it leads all things to the good of our Religion.40

In fact, as our recent analysis shows, at least since the restoration of the "Western Method" in the Bureau of Astronomy after the "Calendar Lawsuit", all data in the routine reports of observations submitted to the throne after each eclipse were direct transcriptions from the predictions, rather than the results of real observa­ tions as prescribed in the aforementioned stipulation of the Qing dynasty, giving the impression that the calculations of the Bureau of Astronomy really corre­ sponded to the Heavens perfectly.41 This is apparently the real reason why the secret was able to be kept for so long. At first, the truth was very successfully concealed. Even the Kangxi emperor did not realize the problem, retaining for quite some time confidence in the sys-

37 D'Elia (1960), pp. 28-33. 38 Golvers (1993), pp. 221 and 245-246. 39 Golvers (1993), p. 81. · 40 Golvers (1993), p. 75. 41 For the unreliability of the data in the observational reports of the Qing Bureau of Astronomy, See Shi Yunli (2000a), and Shi Yunli and Lii Lingfeng (2002), and Lii Ling­ feng (2007).

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 50 EASTM 28 (2008) tern introduced by the Jesuits, which he had restored to official endorsement after the "Calendar Lawsuit". On December 27, 1704, he observed a solar eclipse from within the palace and noted a marked discrepancy with the prediction made by the Bureau of Astronomy. 42 Eventually, however, he attributed the errors to miscalculation by the astronomical officers rather than suspecting the reliability of the astronomical system used by them, believing that "there is no possibility that the new method can result in any mistakes".43 In 1711, however, while observing the summer solstice, he again discovered an obvious discrepancy in the predictive calculation provided by the Bureau of Astronomy.44 In the wake of this discovery, he ordered the Bureau to investigate the source of the discrepancy thus igniting a fierce dispute among Jesuit astrono­ mers in China, which culminated in 1716. On one side, the French Jesuit Jean­ Fran~ois Fouquet (1665-1741 ), who was not a member of the Bureau of Astron­ omy but who had been recommended to the emperor as an advisor on the issue, pressed the Jesuit astronomers of the Bureau of Astronomy to admit at least that the Bureau of Astronomy "had erred slightly". On the other side, however, Killian Stumpf (1655-1720) and other Jesuits subject to the Portuguese vice­ province of the Society of Jesus opposed any such admission, retorting that "such an admission would be more harmful than all the objections the Chinese and the Muslims had raised against European astronomy",45 for it could endanger the mission by throwing doubt on their illustrious predecessors, especially on Verbi­ est.46 In the meantime, Fouquet also advocated that the outdated system of calen­ drical astronomy used by the Bureau of Astronomy should be reformed by adopt-

42 According to the prediction of the Bureau, the first, maximum and last phases should have happened at 12h.93, J4h_25 and J5h_37 (Beijing local time with 24 hours a day and midnight as 0h.00). Kangxi, however, obtained 12h.43, 13h.78 and 15h.25 from his observation. The theoretical results tum out to be 12h.24, 13h_62 and 14h.94, which are much closer to Kangxi's observation. The theoretical results are deduced from the data provided in Tables 2 and 3 in Stephenson and Fatoohi (1995). 43 For a detailed report of this event, see Shi Yunli (2000a), p. 140. 44 Shengzu renhuangdi shengxun, chap. 5, p. 23b, and Qingshi gao, chap. 45, p. 1668. According to the algorithms provided in the Xiyang xifa lishu, chap. 25, pp. 8a-b, the calculation given by the Bureau of Astronomy is the true solstice. Ironically, however, the so-called "observed result" of Emperor Kangxi (11 :52) is actually much worse than this calculation (12:45) as compared to the value calculated with David Eagle's NEWCOM (13:22). It would be very interesting to investigate whether Kangxi really discovered the discrepancy or simply used such an "accident" as a pretext to launch his project for the indigenization of European astronomy. Maybe this is the reason why Kil­ liam Stumpf (1655-1720), the Jesuit director of the Bureau of Astronomy at the time, refused to admit to the miscalculation of this solstice. For Stumpfs refusal, see Jami (1994), p. 538. 45 Witek (1982), p. 183, n. 87. 46 Jami (1994), p. 539.

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ing new tables composed by Philip de La Hire (1677-1719).47But Stumpf in­ sisted that he would accept La Hire's tables only if the calculations were based on the past fifty eclipses and agreed with astronomical observations.48 Although the astronomical reform suggested by Fouquet was not carried out and the compilation of the Kaocheng (started in 1713) was still based on the Xiyang xinfa lishu fill if fr r! I! 3,49 his argument that "if the Chinese found out by themselves the shortcomings of a theory, the Jesuits, by supporting it, would throw discredit on the mission"50 may have been a very important factor in causing the Jesuit astronomers at the Bureau of Astronomy to begin to take the issue more seriously. Yet, Fouquet himself does not appear to have been too insistent, as he accepted that the issue should be subject to further observations.SI

Kogler's Actions

It seems that the task of further study and observation was put on the shoulders of Kogler (1680-1746), who arrived in China on August 30, 1716, during the cli­ max of the controversy. He was immediately summoned to the Bureau of Astron­ omy as an assistant of calendrical astronomy and arrived in Beijing on January 2, 1717. 52 Soon he began a systematic observation of eclipses, during which he checked the calculations based on the tables of de la Hire and John Flamsteed (1646-1719) against the observed results. 53 Most of these observations were "secretly" undertaken in the observatory within his church, which was equipped with instruments more advanced than those installed in the official observatory of the Bureau of Astronomy. From these observations, it should not have been diffi­ cult for Kogler to acquire a good knowledge of the errors in eclipse prediction of

47 Fouquet translated La Hire's tables into Chinese and attached them to a treatise ti­ tled Lifa wenda lf!f #i. r"~ ~ (Dialogue on Calendar Method). The treatise introduces some new developments in Western astronomy since Kepler and openly attacks the pit­ falls of Tychonic astronomy in a number of respects. For recent studies of the Lifa wenda, see Martzloff (1994); Jami (1994); Hashimoto and Jami (1997); and Hashimoto (1999). 48 Witek ( 1982), p. 183, n. 87. 49 A few minor changes concerning the inclination of the ecliptic to the equator and the format of some tables were adopted in the Kaocheng. For details, see Hashimoto (1970) and Shi Yunli (1996a). 50 Jami (1994), p. 539. 51 Witek (1982), p. 183, n. 87. 52 On Kogler's arrival in China a,nd his work at the Bureau of Astronomy, see Stilcken (2003), pp. 175-209 and 358-368; Sun Xi (2005), pp. 61-68, 86-120, 207, 177- 207, and 224-244. 53 See Hallerstein (1768), Part I, pp. 3-15. In addition to the calculations based on the tables of la Hire and Flarnsteed, he also checked the predictions made by Eustachio Man­ fredi (1674-1739) in his ephemeredes.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 52 EASTM 28 (2008) the old Jesuit system and hence the necessity for the introduction of more exact tables. The differences between the predictions of the Bureau of Astronomy and his own observations became very obvious, as shown in Table l, in which the "Predicted Times" are taken from the extant predictions of the Bureau of Astron­ omy,54 whereas the "Observed Times" are from Kogler's observations.55 Ac­ cording to V erbiest, "in China, it is considered more disgraceful [than in Europe] to deviate half a quarter of an hour [0.125 hours]" in astronomical predictions.56 However, among the twenty-six eclipse phases observed by Kogler and listed in Table 1, fifteen show deviations greater than this limit and are marked with aster­ isks.

Table 1: Kogler's Observations of Loni-solar Eclipses

Predicted Observed Prediction- No. Date Phases Times Times Observa- (hours) (hours) tions Lunar Eclipses First Contact 0.133 0.417 -0.284* 1717/ 1 Middle 1.750 1.842 -0.092 9/21 Last Contact 3.367 3.267 0.1 First Contact 21.717 21.785 -0.068 1718/ 2 Middle 23.633 23.557 0.076 3/16 Last Contact 1.567 1.328 0.239* First Contact 1.600 1.708 -0.108 1718/ 3 Middle 3.683 - - 9/10 Last Contact 5.767 - - First Contact 21.183 21.200 -0.017 1721/ 5 Middle 22.850 22.683 0.167* 1/13 Last Contact 0.500 0.167 0.333* First Contact 20.367 20.317 0.05 1722/ 6 Middle 22.450 22.283 0.167* 1/2 Last Contact 0.533 0.250 0.283* First Contact 0.012 0.725 -0.713* 1725/ 8 Middle 0.355 - - 10/22 Last Contact 4.950 4.358 0.592*

54 These predictions are obtained from two sources. The first is the astronomical ar­ chives of the Qing dynasty published in Cui Zhenhua and Zhang Shucai (eds.) (1997). The second is the China-related archives of the Choson dynasty, which have been dis­ cussed by Shi Yunli, Lil Lingfeng and Zhang Binglun (2000). 55 Hallerstein (1768), Part I. 56 Golvers (1993), p. 81.

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Predicted Observed Prediction- No. Date Phases Times Times Observa- (hours) (hours) tioos Solar Eclipses First Contact 15.117 14.642 0.475* 1719/ l Middle 16.033 - - 2/19 Last Contact 17.180 -- First Contact 10.567 10.717 -0.15* 1720/ 2 8/4 Middle 12.200 12.217 -0.017 Last Contact 13.750 13.700 0.05 First Contact 17.117 17.350 -0.233* 1721/ 3 Middle 17.983 - - 7/24 Last Contact 18.783 - - First Contact 10.950 - - 1730/ 4 Middle - 12.850 7/15 - Last Contact 14.433 14.453 -0.02 First Contact 19.417 -- 1726/ 9 Middle - 4/16 -- Last Contact 22.487 22.258 0.229* First Contact 23.117 23.033 0.084 1728/ 10 Middle - 0.517 8/19 - Last Contact 2.483 2.000 0.483* First Contact 2.450 2.642 -0.192* 1729/ 11 Middle - - - 2/14 Last Contact 6.583 6.294 0.289*

In the meantime, Kogler probably also started to look for more reliable tables suitable for use in China. In so doing, he did not leave out England, another im­ portant centre of predictive astronomy.57 The tables based on Newton's theory of the motion of the moon were soon brought to his attention by the Jesuit astrono­ mer Nicasius Grammatici ( 1864-1736) at Ingolstadt, with whom Kogler kept up regular correspondence.58 According to Gaubil, Grammatici was in touch with many astronomers in Europe and was eager to share with Kogler everything he learned, while also forwarding what he received from Kogler to other astrono-

57 In a letter by Antoine Gaubil (1689- 1657) in August of 1720, Kogler is said to have calculated an eclipse with the tables that "came to him from England", which gave a result different from the calculation conducted by Gaubil based on La Hire's tables. See Gaubil (1970), p. 61. 58 For the communication between Grammatici and Kogler, see Stiicken (2003), pp. 362-364. For Grammatici' s astronomical work at Ingolstadt, see Grass (1994 ).

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 54 EASTM 28 (2008) mers in Europe.59 In 1726, Grammatici published his Tabulae Lunares,60 which turned out to be the first Newtonian tables of the sun and moon ever published in Europe. These tables were immediately sent to Jesuit astronomers in China from Germany and reached Beijing in 1727. During the lunar eclipse on August 19, 1728, predictive calculations made with the tables of La Hire and Grarnmatici were compared against actual observation. In a letter from Beijing dated Novem­ ber 19 of the same year, Gaubil reports the result of the comparison: "The obser­ vation was very different from the calculation of la Hire's tables, but extremely close to the calculation made with the papers sent here from Germany last year. They are luni-solar tables according to Newton's system."61 Finally, the Jesuit astronomers at Beijing decided to initiate a reform to rem­ edy the shortcomings of the old system. Needless to say, this was also intended as a counter-strike against anti-Catholic astronomers like He Guozong and Mei Juecheng, as can be seen from Pereira's 1732 letter to the General of the Society of Jesus, which we have quoted above. In the letter, Pereira reports how they began to examine the Kaocheng in light of new theories and practical observa­ tions to reveal its errors. He also describes how the Yongzheng emperor, after having become aware of the errors of the Kaocheng, reprimanded the Chinese academicians for their ignorance and praised the Jesuit astronomers for their work. Pereira simply interprets these developments and the success of the Jesuit reform of astronomy as a triumph over their Chinese adversaries. 62 The solar eclipse of July 15, 1730, provided the Jesuit astronomers with a very good opening, because, as Pereira reports in his 1732 letter, this was the first eclipse visible from Beijing since the publication of Kaocheng. Before the eclipse, Kogler and Pereira submitted their prediction made with the new method to Mingtu and reported to him the error of the prediction made with the Kaocheng. After their report had been verified by observation of the solar eclipse, Mingtu presented a petition to the Yongzheng emperor, as I have described at the beginning of this paper, confessing tactically that "slight errors" of the Kaocheng had been detected through the observation. He then proposed that a decree be issued to the two Jesuits permitting them to organize skilled personnel to conduct a thorough investigation and revision.63

59 Gaubil (1970), p. 246. 60 Grammatici ( 1726). 61 Gaubil (1970), p. 213. 62 For details see Rodriges ( 1925), pp. 91-97. 63 See Pereira' s letter in Rodriges (1925), pp. 91-93, and Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. la-2a. In his letter, Pereira describes in details how prediction and observation were conducted and finally reported to the emperor. Accord­ ing to him, the correctness of their new theory was proved again in the same way with a lunar and a solar eclipse occurring on November 9 and December 29, 1731, respectively.

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After this proposal was granted by the emperor, Kogler and Pereira compiled a set of new luni-solar tables. The tables were completed by 1632,64 but they came with "neither any explanations on the underlying principles, nor any in­ structions for computational procedures", so that "no one at the Bureau of As­ tronomy could understand and apply these new tables except the two Jesuits and Ming'antu ll~ ti. Ii (1692-1765)",65 an astronomical officer of Mongolian na­ tionality. Dissatisfied with this situation, the Minister of Rites, Gu Cong, formerly a member of Kangxi's Office of Mathematics,66 petitioned the Qianlong emperor in May 1737, urging that future astronomers would find no place to learn and to follow up the underlying principles and computational procedures of these tables unless a textual explanation was compiled and documented.67 It seems that this time both the minister and the emperor had no choice other than to commission the two Jesuit astronomers to conduct the work and permit the project to be car­ ried out under the jurisdiction of the Bureau of Astronomy. Therefore, at first, Gu Cong suggested to the Qianlong emperor to appoint Kogler as the general super­ visor, and Pereira and Ming'antu as the associate supervisors of the project. He also indicated that the "supporting personnel for calculation and transcription could be mobilized from within the Bureau of Astronomy". But in less than a month he had changed his mind. While repeating in a new memorial that "all the personnel will be recruited from the Bureau of Astronomy and the compiling office will be opened within the Bureau", he now asked the emperor to appoint Mei Juecheng as the general supervisor and He Guozong as the associate, under the pretext that "people both expert in mathematics and good at writing are re­ quired to modify and polish the compiled texts so that the implicit meanings become clear and explicit". 68 About six months later, however, the emperor

64 According to Pereira, the new tables were presented to the throne a few days after the 1731 eclipses. This also indicates that the tables were completed in late 1731 or early 1732. See Rodriges (1925), p. 95. These tables are not a simple translation of those of Grammatici, but a new construction of the two Jesuit astronomers. For a detailed discus­ sion of the relationship between the 1732 tables and the tables in the Houbian and Gram­ matici' s Tabulae Lunares, see Shi Yunli and Xing Gang (2006). 65 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. 4b-5a. 66 His name appears in the list of authors in front of the Yuzhi liili yuan yuan 1!111 ~ W I! ml! ~- See Yuzhi lixiang kaocheng houbian, front matters, names of officials, p. 1b. 67 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. 4b-5a. Since the as­ tronomical reform of the late Ming dynasty, the ability to explain underlying principle, i.e. to demonstrate the motion of the heavenly bodies with geometrical models, had been thought to be one of the most important superiorities of Western astronomy over tradi­ tional Chinese calendrical astronomy. Accordingly, a "theoretical" part devoted to these principles, which Xu Guangqi called fayuan rt. ~ (underlying principles), had been deemed an indispensable part of a system of calendrical astronomy. See Xiyang xinfa lishu, chap. 1, pp. 17a-19b. 68 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. 4b-6a.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 56 EASTM 28 (2008) reappointed Prince Yunlu ft li, former chief compiler of the Kaocheng, as the General Supervisor of the new project.69 The Houbian was completed five years later in May 1742. In the long list of compilers preceding the book, the Chinese names of Kogler and Pereira, i.e. Dai Jinxian • ~ If and Xu Maode {t- ~ tl, appear as two of the eight General Compilers (Chart 2 below). When compared with the list of compilers of the Yuzhi tali yuanyuan til=l1 ~ ~ }ff mM ~. this con­ stituted a major victory for the Jesuit astronomers in China, although their names were still put after those of five indigenous officials, including Gu Cong, He Guozong and Mei Juecheng.70

A Reform or a Continuation of Imperial Science?

Through the adoption of the new astronomical achievements since Kepler's time, especially of Newton's theory of the motion of the moon, the Houbian actually provided the Qing government with a new system of calendrical astronomy for the calculation of the sun, moon and luni-solar eclipses, a system totally different from the Tychonic one contained in the Kaocheng. Compared with the latter, the solar theory in the Houbian was more than ten times more accurate, the lunar theory more than four times more accurate in longitudinal calculation and nearly ten times in latitudinal calculation.71 It was only from this time onward that the Jesuit astronomers in China were really able to control the standard error of the predictive times of luni-solar eclipses within half a quarter, the limit of tolerance in astronomical predictions as reported by Verbiest. 72 The new tables even adopted a new epoch, that is the first year of the Y ongzheng reign ( 1723 ), rather than the twenty-third year of the Kangxi reign, as used in the Kaocheng. What this means is that the adoption of the new system was in fact a very important reform of astronomy in the Qing period. However, this appraisal only represents our own retrospective evaluation from a pure technical point of view. Looking at the particular socio-political context of the compilation of the book, however, when one takes into account the rhetoric of the actors involved the reform was not treated as a reform at all. In ancient China, an astronomical reform simply implied that the existing sys­ tem of calendrical astronomy was in error and or out-dated. Therefore, the actors participating in the reform in question were faced with a difficult situation. Since the existing system under reform was "imperially composed" by a recently de­ ceased emperor who was considered the greatest sovereign of the age, they had to consider how to carry out the reform without it reflecting badly on both his glory

69 Yuzhi lixiang kaocheng houbian, front mattes, memorials, pp. 5b-6b and p. 8b. 70 Yuzhi lixiang kaocheng houbian, front matters, names of officials, pp. la-4b. 71 See Shi Yunli (2003). 72 Li.i Lingfeng and Shi Yunli (2003).

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and authority. Their solution was not to treat it as a reform, but just as a revision of, or even a supplement to, the "imperially composed" system. Therefore, when Kogler and Pereira completed the new tables in 1732, the Yongzheng emperor simply decreed that they be printed as an appendix to the Kaocheng,73 rather than an independent book. As a result, the new tables were published under the title Yuzhi lixiang kaocheng biao ffiJ ~ JI ~ :;;I§- .IVG ~ (Tables of the Thorough Investigation of Calendrical Astronomy Imperially Composed, Fig. 2), without any indication who the actual authors were, notwithstanding that the Kaocheng already contained a part with the same title and the new tables themselves actu­ ally had nothing to do with the book at all.74

Fig.2: The Yuzhi lixiang kaocheng biao

. i= ~

o, 111-1111>-w- 1tt 1l!i.ltJ11- £11.(tfN.e"""". -=, 11-.::1!1 0 -'Q._u . -i• -,G ~:~ _:.~_- . l!I. ~- "'_li:;J! -,o, - ~-11 1'1-':.'-Jl -.o \~i ~ l i -

------

[Courtesy of the Observatory of Paris]

The same strategy was applied to the compilation of the Houbian, though this time with explicit justifications. In this case, the significance of the Kaocheng as

73 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. 8a-b. 74 See Yuzhi lixiang kaocheng biao. These tables are quite rare today. I have checked two complete copies preserved in the Observatory of Paris and the Library of the Univer­ sity of Munich respectively. There may be a few more copies in Britain, Japan and even Korea.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 58 EASTM 28 (2008) an "imperially composed" science was reinterpreted. Instead of claiming that it represented an "unchangeable rule" in calendrical astronomy, it was now empha­ sized that what the book revealed was the essential principles, or the "Way" (dao ii!), of calendrical astronomy, by the use of which later astronomers could carry out necessary revisions. This point is made clear by Prince Yunlu in his 1738 memorial concerning the compilation of the Houbian. He argues:

Our dynasty adopted the new method from the West. Its data are all based on practical measurements, and its method of eight trigonometric lines is especially precise. But all its cal­ culations are made by using the ready tables, and, not being the theory of one school, most of its explanations are inco­ herent and obscure. Therefore only a few scholars know the meaning of the method. Our Sage Sovereign and Merciful Emperor's75 scholarship penetrated the three domains,76 and he profoundly investigated the nine numbers. 77 The Kaocheng still follows the old system of Tycho in the Xinfa suanshu fir ~ JI: if (Treatises on Calendrical Astronomy according to the New Method).78 Its theory has profoundly and exhaustively made use of the observation of the heavens, the arrangement of the calendar, as well as the longitudes and latitudes of the Seven Govemors,79 while its method is able to reveal the past and foresee the future, so that one can sim­ ply obtain any date in a thousand years from one's seat. Therefore, one can now exhaustively make use of the princi­ ples from the numbers and then determine the method from the principles. It integrates the Chinese and the Western into one system and unifies the beginning and the end into a whole. Not only does it reach the extreme of wisdom of one era, but also inaugurates the incipient enlightenment of all ages. Even though over a long time there will be discrepan­ cies, one can carry out additions or reductions whenever nec­ essary, and all its Way does not go beyond this (huo jiu er you cha, yin shi sun yi, qi dao ju bu yue hu ci yi BJt )... ffiJ ~ ~. ~ 8'J ffl ~. ::l'UtH\Lf ~ 3¥ Jlt ~)_so

75 Shengzu renhuangdi ~ tll f= §!. ,W, the posthumous title of the Kangxi emperor. 76 Sancai-= ;t, i.e. the domains of Heaven, Earth and Human Beings. 77 Jiushu :tL fix:, i.e. mathematics and mathematical sciences. 78 This is the version of the Treatises incorporated in the Qinding siku quanshu ~ 5E llY /$' it 3 (Complete Book in Four Treasuries). Apparently, the new title was adopted to avoid the use of the character li II, which was used in the Qianlong emperor's given name and thus became a taboo in his reign period. 79 Qizheng -t j!jl{, i.e. the sun, the moon and the five planets, which can be seen with the naked eye. 80 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. 7a-b.

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In other words, any future revision could still be conducted within the theoretical framework of imperial science and therefore would still be a continuation of it. Though the praise lavished on the Kaocheng in this memorial may seem verbose, it reflects precisely Prince Yunlu's efforts to vindicate the everlasting authority of the book. When submitting the complete draft of the Houbian to the throne for scrutiny in 1742, he reiterates this view almost verbatim in his memorial and emphasizes again that "the principles [of the new book] do not transcend the scope of the Upper and Lower Volumes" of the Kaocheng, although he also points out that the new book contains "refined and precise ideas which have not been achieved by previous scholars".81

The New Book and the Standards of Imperial Science

According to Prince Yunlu's interpretation, the newly compiled book was simply a natural continuation of imperial science. In his own words, "what is presently being added and compiled actually belongs to the same sequence" as the Kaocheng.82 This was not empty rhetoric, but was realized in the actions of the compilers of the new book, who took the Kaocheng and the manner of its pro­ duction as a model. First of all, the institutional establishment for the compilation was organized in accordance with that of the Kaocheng, despite the death of the Kangxi em­ peror. The project was put under the supervision of two princes. Subordinate to them, but above a great number of assistant personnel were, in both cases, a number of General Compilers and Individual Correctors, who were apparently in charge of the actual compilation of the book (Chart 1 and 2). Understandably, the most symbolic figures in this setting were the two princes, which explains why the candidate for the post of the general supervisor of the compilation changed from Kogler to Mei Juecheng and finally to Prince Yunlu, and why in the end another prince, Prince Hongzhou * ft, was also appointed as associate supervi­ sor. The purpose is quite obvious, that is to conform to the original institutional setting for the compilation of imperial science. In addition, the first and final drafts of the new book were submitted to the throne in 1738 and 17 42 respec­ tively so that the new book could be "imperially determined" (qinding ~ Ji:) by the Qianlong emperor.83

81 See Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. l la-12b. As I am going to show soon below, the Upper and Lower Volumes are two major parts of the Kaocheng. 82 Yuzhi lixiang kaocheng houbian, front matters, memorials, p. 9b. 83 Yuzhi lixiang kaocheng houbian, front matters, memorials, p. lOb. The Houbian is said to be "imperially determined" (yuding ~ 5:E) by the Qianlong emperor also in the Huangchao wenxian tongkao, chap. 229, p. 11 b.

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Chart 1. The Compilation Group of the Kaocheng

I Emperor Kangxi I

Compliers by the Decree ( fengzhi zuanxiu $ ~ •~): Princes Yunlu ft,$ and Yunzhi fttl:

General Compilers (huibian •Mil): He Guozong foJli* and Mei Juecheng tfjf2:Jjji;

Individual Correctors (fenjiao ,H~): WeiTingzhen l!lif~. Fang Bao Jjfi. and Wanglansheng .:EiW1:.

I Assistant Personnel I

Chart 2. The Compilation Group of the Houbian

Qianlong Emperor

I General Supervisor (zong/i AIJ!): Prince Yunlu ft-$ I Associate Supervisor Uianli 11:i.J!): Prince Hongzhou *ff General Compilers (huibian •fail): Gu Zong lliijl, Zhang Zhao '.IJ!lt He Guozong foJli*• Mei Juecheng tlftt/£, Jin'ai i!Ut Dai Jinxian aU&'lf, Xu Maode ~IH9 and Ming'antu HJl'ti:il Individual Correctors (fenjiao :5ttl): Gao Ze illliiJ, Meng Taiyin ~lU!t. He Junhui fort!"~. Fang Jue Jitt, He Guodong foJlil!k and Pan Ruying ffi~~

I Assistant Personnel I

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Secondly, the new book was named after the Kaocheng. In his 1738 memorial, Prince Yunlu states:

The Kaocheng is originally divided into two parts subtitled shangbian J: ~ (Upper Volumes) and xiabian r tlli9 (Lower Volumes),84 and what is presently being added and compiled actually belongs to the same sequence. [ ... ] As to what is presently being added and compiled, [we] humbly request [Your Majesty's] personal judgment and endorsement to en­ title it Yuzhi lixiang kaocheng houbian and to merge it into one book with the former one.85

In other words, the new book should be treated only as a sequel to the Upper and Lower Volumes of the Kaocheng and thus should logically be named as the Houbian 1f ~ (literally "Later Volumes") of the same book. Thirdly, the structure of the new book was designed similarly to that of the Kaocheng. While the Kaocheng contains three major parts, i.e. Upper Volumes, Lower Volumes and Tables, devoted respectively to Lili M W (principles of calendrical astronomy), lifa M rt;, (methods of calendrical astronomy)86 and biao ~ (tables), the contents of the Houbian also fall into three parts, although the subtitles shangbian, xiabian and biao were not explicitly used. The Houbian's three chapters were devoted to shuli fx l:!I! (mathematical principles), shufa fx rt;, (mathematical methods) and biao in this order. From their contents it is very clear that the so-called Lili M W and shuli fx l:!I! volumes both refer to the theo­ retical aspect of calendrical astronomy, including the cosmological scheme, the explanation of the basic astronomical constants, the special mathematical theories to be adopted, and the geometric demonstrations and analyses of the motions of the heavenly bodies, whereas the so-called lifa M rt;, and shufa fx rt;, volumes both deal with the method of practical calculations. Similar also to the Kaocheng, in the shufa fx rt;, part of the Houbian two sets of computational procedures are provided, the first of which can be used directly without consulting the pre­ calculated tables contained in the third part of the book, while the second is based on the pre-calculated tables. The reason why the compilers of the Houbian used the word shu fl<: rather than Ii M in this context was obviously because the latter

84 The structure of the Kaocheng is actually divided into three parts. Apart from the Upper and Lower Volumes, there is a very voluminous part entitled biao :,& (Tables), which contains the pre-calculated tables.• 85 Yuzhi lixiang kaocheng houbian, front matters, memorials, pp. 9b-10b. 86 Two elegant titles were given to the Upper and Lower Volumes as well, i.e. Kui tian cha ji ~ 'Ji;:. ~ £ (Measuring the Heaven and Understanding the Essentials) and Ming shi zheng du aJI ~ iE Ji (Being Aware of the Seasons and Making Right Calcula­ tions), respectively. See Yuzhi lixiang kaocheng, front matters, imperial preface, pp. 2b-3a.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 62 EASTM 28 (2008) word appeared in the Qianlong emperor's given name Hongli * I! and therefore in accordance with ritual prescriptions was taboo. 87 Fourthly, the new book was printed in exactly the same block-carving style as that of the Kaocheng, which was printed twenty years earlier (Fig. 3). To be noted here is that the caption columns in the middle of each sheet, which bear the title Yuzhi lixiang kaocheng ffii ~ J! ~ ~ fflG are in big characters, while the subtitles shangbian J: ~. xiabian r ~ and houbian ~ ~ are in small fonts, giving the impression that the Houbian is not an independent book, but only a part of a book called Yuzhi lixiang kaocheng ffii ~ J! ~ ~ fflG, just like the shangbian J: ~ and xiabian r ~-

87 This taboo could be lifted in some special circumstances. For example, in the first year of the Qianlong reign (1736), when Mei Juecheng petitioned the throne for permis­ sion to allow local publishers across the country to re-carve the woodblocks for the Yuzhi luli yuanyuan ffiJ ~ tf !ff mM ~. he suggested that the title in the re-carving be changed to Xiangshu yuanyuan ~ fl{ mM ~ (Origin of Diagrams and Numbers) in order to avoid the use of the character Ii !ff. This request was, however, declined by the Qianlong em­ peror, who decreed that: 'These books were determined by the royal grandfather and the deceased royal father. How can we change the titles just because of my name? It is proper to still use the title Luli yuanyuan tf 11/f mM ~ in the re-carved version, but let officials and the people orally call it Lushu yuanyuan tf ff mM ~ (Origin of the Book on Musical Harmonics)." The character Ii also remains in the title of the Houbian, but with the lower part of the character cut off to mark it as taboo, as can be seen in the central caption col­ umn of the page in Fig. 3 (b) below.

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Chart 3. Content Structure of the Kaocheng and Houbian

The Kaocheng The Houb/an Upper volumes (shangblan .1:•): Matherratlcal principles (Shu/I ltll) - Calendncal Pnnc,ples (Uli Jlf) - Chapt.1, of the Sun (Richan shuli ll ■ fll!f); Chapt.1, General discussion (Lili zonglun Jlflll:a), Chapt.2, of the Moon (Yueli shuli Jllll!!Jlf); Chapt 2-3, Spherical trigonometry (Hu sanjiaoxing Chapl.3, of the Eclipses (Jiaosh1 shuli l't:t:l!!l!). fl /!Ill>) Chapl.4, of the Sun (Richan /iii I l •t'll'I'); Chapl.5, of lhe Moon (Yueli /iii JI 11111'1'); Chapl.6-8, of the Eclipses (Jiaoshi /iii 'i: tr Jlf), Chapt.9-15, of the live planets ( Wuxmg illi ft~ Jlf), Chapl.16, of the fixed stars (Hengxinglili~il'. JII!). Lower volumes (xlanbian r•) Con1)Utatlonal methods (Bufa /li#i)­ Calendncal methods (Ufa IW.) - Chapl.4, of the Sun (Richanbufa ll ■ WIJ.); Chapl.1, of the Sun (Richan hfa 11 • it.); Chapt.5, of the Moon (Yueli bu/a /llf!J;/t.); Chapl.2, of the Moon (Yueli lifa Jlll ,J.); Chapt.6, of Lunar, and Solar Eclipses ( Yueshi Chapl.3, of lhe lunar eclipse ( Yuesh, lifa Jl tr 1!;); bufa II tt:.H.t, R1shi buls II ttWl.t). Chapl.4, of the solar eclipse (Rish, lifa JI tr it); Chapt.5, of Salum (Tuxing lifa 1 !fflil.); Chapt.6, of Jup,ter (Muxing lifa .+ell.Mil.); Chapt.7, of Mars (Huoxing Ii/a :k~ 1t); Chapt.8, of Venus (Jinxmg hfa $- ' i.t); Chapt.9, of Mercury (Shuixinglifa 1M! iJ.); Chapl;10, of the fixed stars (Hengxinglifal!i · IJ.) • Tables(bilo •)- Tables (b/ao •)- Chapt.1, of the Sun (Richan biao 111,U); Chapt. 7, ol the Sun (Richan biao 11 ■ .&); Chapt.2-4, of the Moon (Yuelibiao JIii«); Chapl.8, ollhe Moon (a) (Yueli biao shang WIU l:); Chapt.5-8, of the Eclipses (J1aoshi biao 'i:tl" U); Chapl.9, olthe Moon (b) (Yuelibiao shang illl:U n Chapt.9. of Salum (Tuxmgb,ao Ul.U), Chapt.10, of the Eclipses (Jiaoshibiao 'i:tt~).

Fig. 3: The Printing Style of the Kaocheng (a) and Houbian (b)

(a) [From Kaocheng , j. 5, pp. 68a-b]

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(b) [From Houbian, j. 2, pp. 93a-b]

Finally, the organizer of the project even tried to make the writing style of the new book consonant with that of the Kaocheng. Therefore, as soon as the draft of the "Mathematical Principles" and the "Tables of the Sun" were completed in June 1738, Prince Yunlu submitted a sample copy of them to the throne for impe­ rial inspection and petitioned for the following:

As to all matters concerning the writing style and the diction which should be made to meet the standards, I humbly beg [Your Majesty] to hand back [the submitted manuscript] so that it can be corrected and re-submitted for your sagely in­ spection in order for it to be imperially endorsed.88

Apparently, the so-called "standards" (tizhi ff ~) here refer to the standards of compiling imperial science, or imperial astronomy more specifically, as illus­ trated by the Kaocheng.

Newton's Astronomy in the Given Framework

It is very clear from the facts listed above that what the organizer of the project wanted to "be made to meet the standards" (yihe tizhi lU il- ffl ~) were not limited solely to the writing style of the book. For the Qing government, espe­ cially for the opponents of the Jesuit astronomers, the integration of the new book

88 Yumi lixiang kaocheng houbian, front matters, memorials, p. lOb.

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into the framework of imperial science obviously had another function, that is to reduce the apparent importance of the Jesuit astronomers in the reform and thus to regain control of the whole project, both in the name of imperial science. This function was realized quite successfully, as can be judged from at least two events. Firstly, when the 1732 tables were published, the names of the two Jesuit authors were not explicitly indicated; and secondly, when the Houbian was com­ pleted, their names were put, apparently according to their official ranks, in a not so eye-catching position in the long list of the compilers at the front of the book, despite the key role that they had played in the introduction of the new knowl­ edge contained in it. As a result, the two Jesuits were placed in a paradoxical situation in the entire process of the reform. On the one hand, they possessed and controlled the new knowledge necessary for the reform. On the other, however, they were obviously not the real decision-makers and therefore had no right to decide how the new knowledge should be presented. In other words, they had to fit the new knowledge into the framework set up by Chinese officials and as­ tronomers. The most interesting example of this can be found in their treatment of Newton's theory of the motion of the moon. When the compilation of the Houbian started, Newton's theory of the motion of the moon was available from Europe in three published versions; (I) Newton's Theory of the Moon's Motion, which provided the necessary constants and a set of pure mathematical rules for the positional calculation of the sun and moon;89 (2) the Scholium of Prop. 38 in Book 3 of the second and third editions of New­ ton's Principia, which provided an explanation of the computational rules con­ tained in the Theory of the Moon's Motion;90 and (3) J. Machin's ''The Laws of the Moon's Motion According to Gravitation" in Andrew Motte's English trans­ lation of the Principia published in 1729, which served "to explain and demon­ strate the truth of the rules in Sir Isaac Newton's Theory of the Moon".91 Version (I) furnished an indispensable basis for the shufa fx: it (mathematical methods) part of the Houbian. The real question was which version could be taken as the basis for the shuli fx: 3:11!. (mathematical principles) part? It was not only required by the "standards" of the imperial science that prescribed the three-fold structure of the book, but also its inclusion was one of Gu Cong's main objectives in carry­ ing out the compilation .

89 Newton's Theory of the Moon's Motion was first published in 1702 in English and Latin. The English version is an independent pamphlet, while the Latin version is actually a part in David Gregory's astronomical textbook. At least 14 editions and reprints of the essay followed before 1730. See Cohen (1975). Some table makers in Europe also pub­ lished their explanations and developments of Newton's essay. See, for example, Leadbet­ ter (1729). 90 For the explanatory feature of the Principia version of Newton's theory of the mo­ tion of the moon, see Kollerstrom (2000), pp. 165-166. 91 Newton (1729), vol. 2, Appendix.

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From Kogler's correspondence with the Jesuit theologian and philosopher Eusebius Amort (1692-1775) it is clear that he accepted neither Copernicus' heliocentric system nor Newton's gravitational philosophy.92 Therefore, it was not possible for him to ground the theory of the moon in the Houbian on versions (2) and (3). The only choice was to compile a new version, and this gave rise to Chapter 2 of the Houbian, that is. the chapter on the "Mathematical Principles of the Lunar Motion" (Yueli shuli ~ ~ fx :JI). A detailed comparison shows that this chapter is totally different from either versions (2) and (3), or any other elucidation of Newton's theory of the motion of the moon ever published in Europe before the compilation of the Houbian, with only one exception, the application of the Horrox-wheel93 in the demonstration of both the fluctuation of the eccentricity of the orbit of the moon and the produc­ tion of the second equation of the lunar apogee,94 which was available from both versions (1) and (2). As a whole, however, this chapter can be justifiably called the "Chinese version of Newton's theory of the motion of the moon", not only because it was written in Chinese, but also because it was apparently an invention of the two Jesuit astronomers for Chinese use. There are at least two features in this version that cannot be found in the works of any other astronomers in contemporary Europe. Firstly, all eight equa­ tions contained in Newton's Theory of the Moon's Motion for the correction of the motion of the moon,95 including the five newly discovered by Newton,96 are said to be results of "repeated measurements and test" (janfu ceyan & ~ m~ ~) and the so-called "methods of measurement and test" (ceyan zhifa m1J ~ Z. it:)

92 In his Systema Planetarium ( 1723 ), Amort established a new mechanical model of the planetary system, in which Mercury and Venus revolved around the sun, while the sun, the moon and the three major superior planets moved on elliptic orbits around the earth, all being driven by the "atmosphere" within each specific orbit. On the basis of this model, he refuted not only Copernicus' heliocentricism, but also Newton's gravitational philosophy. In about 1724, he wrote to Kogler for his opinion on the issue. In his reply, Kogler said that he accepted Amort's planetary system "with reverence and without any doubt". In fact, Amort's system might have been a direct inspiration for Kogler to adopt elliptic orbits in the geocentric model. For Amort's planetary system, see Amort (1723). For Kogler's reply to Amort see Kogler (1726). 93 For the discussion of Newton's application of the Horrox-wheel, see Kollerstrom (2000), pp. 81-95. 94 Yuzhi lixiang kaocheng houbian, chap. 2, pp. 19a-21a. 95 For a detailed discussion of these equations and their practical application, see Kollerstrom (2000), pp. 97-104 and 111, 113-128. 96 These five equations are the Yi pingjun -~ -if :15] (first mean equation, i.e. New­ ton's annual equation of the lunar apogee and node), Er pingjun = -if :isJ (second mean equation, i.e. Newton's equation depending on the situation of the lunar apogee in respect to the sun), San pingjun -= -if :l:,;J (third mean equation, i.e. Newton's equation depending on the aspect of the nodes with the sun), San jun = :15] (third equation, i.e. Newton's sixth equation), and Mo jun* :15] (last equation, i.e. Newton's seventh equation).

Downloaded from Brill.com10/10/2021 10:48:59PM via free access Shi Yunli: Reforming Astronomy and Compiling Imperial Science 67 are explained at length and in detail. According to Newton himself, however, most of the five new equations resulted from his theoretical analysis on the basis on his law of gravitation, rather than observation.97 Secondly, wherever possible Newton's rules are explained using principles and geometrical models from the Kaocheng, which are totally different from Newton's own explanations.98 For example, according to Newton, the annual equations of the moon and its apogee and node (Yi pingjun - 51'- it}) resulted from the action of gravitation between the sun, the moon and the earth. However, this explanation is not adopted in the Houbian. Since the annual equation of the moon had already been considered in the Kaocheng, where it was explained as an effect of the equation of time, Kogler and Pereira continued to apply this expla­ nation not only to the annual equation of the moon, but also to the annual equa­ tions of its apogee and node. Another example concerns the explanation of the cause of Newton's second equation of the lunar node (Zhengjiao jun iE 3( it], i.e. the equation of the lunar node). While Newton applies another Horrox-wheel directly to the node in describing this fluctuation, Kogler and Pereira return again to the Kaocheng and adopt the model used there, which is equivalent to Newton's own model but much more complicated and indirect. A more convincing example is that Kogler and Pereira even correlate Newton's equation depending on the situation of the lunar apogee in respect of the sun (San pingjun = 51'- it}) to the second equation of the lunar node on account of the fact that both of them depend on the angular distance between the sun and lunar node. For this reason, they also use the same model to demonstrate the rise of the San pingjun = 51'- it}, while Newton himself did not give any explicit explanation for the cause of this equa­ tion at all.

Epilogue: Imperial Science or Western Science?

As with many previous reforms of astronomy in China, technical concerns played an important role in the reform beginning in 1730 and the subsequent compila­ tion of the Houbian. Nonetheless, from my discussions above, it is clear that the reform and compilation was not just a matter of technicalities, but involved a number of socio-political variables that largely shaped the whole process. These variables derived from a seesaw battle between Jesuit missionaries and anti­ Christian officials and astronomers in the Qing government. While the Kangxi emperor had tried to break the Jesuit monopoly of official astronomy through the incorporation of Western astronomy into the system of imperial science, the anti­ Jesuit astronomers attempted to take back control of official astronomy in the

97 See Cohen (1975), pp. 57-58; Kollerstrom (2000), pp. I 13 and 115-118; and Nauenberg (2001a). 98 For a more detailed discussion of the next three examples, see the Appendix below.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 68 EASTM 28 (2008) name of imperial science. In the face of these challenges, the Jesuit missionaries had to use new Western astronomical knowledge to defend their existence in China. Like many other fields of knowledge in imperial China, astronomy centred on the emperor. But it was only in the early Qing period that official astronomy was put directly under the authorship of the emperor and thus became a real imperial science. This had a profound impact on science in the subsequent period. The imposition of tighter control over and restrictions on the further transmission of W estem astronomy into China and the future development of astronomy in the Qing dynasty can hardly be seen as a positive step. In the eyes of official-scholars of the Qing dynasty, however, the successive completion of the Kaocheng, Yuzhi lixiang kaocheng biao ffiJ ~ /! ~ ~ IVG ~ and the Houbian was a great event in the history of the dynasty and an emblem of imperial glory. In his 1738 memo­ rial, Prince Yunlu celebrates the series as a work by "one sage sovereign after another, which concentrates the efforts of the three reign periods, reflects their brilliance, and manifests the grand feats of the dynasty."99 Similar eulogies can also be seen in a number of other officially compiled works in the Qianlong reign period. For example, in the Huangchao wenxian tongkao .lit ~ )( ~ :ii "'.& (Comprehensive Studies in the Administration of the Present Dynasty), the Houbian is attributed explicitly to the Qianlong emperor and commented on thus:

The longer the time that passes, the more refined the studies of the observational science [i.e. astronomy] become. Its method has prevailed since the Western astronomer Tycho. Our Sage Sovereign and Merciful Emperor (Shengzu ren­ huangdi ~ ffl. 1= .~ '/ff) created both the Upper and Lower Volumes of the Lixiang kaocheng !ff ~ ~/£,which eluci­ date its subtleties and expose its mathematical principles. The book has truly integrated Chinese and Western methods and achieved a grand unification, and will be handed down for myriads of years. Then, the Westerners such as Cassini and Flarnsteed further investigated meanings that Tycho had not exhausted, and explored down to the extremely tiny details. [ ... ] Therefore the Erudite and Potent Emperor Xianzong (Shizong xianhuangdi tit * '.« .!i!. '/ff) [i.e. the Yongzheng emperor] specially ordered the compilation of the two tables of the sun and moon and to attach them to the Lixiang kaocheng. But there were no detailed explanations and the calculative methods were not discussed. Our emperor [i.e. the Qianlong emperor] has continued the previous cause and diligently explores it day and night. The explanations of the tables and diagrams have been compiled again. All the differ­ ent points in the new method have been explicated eloquently and in great detail, and the old and new methods have been

99 Yuzhi lixiang kaocheng houbian, front matters, memorials, p. 10b.

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merged with each other without distinction, which reverently manifests the profoundness of the Emperor's scholarship and the conformity of the source of mind. I 00

Similar comments can found in the Qinding siku quanshu wngmu tiyao i;X J1:'. [!l µI[ ~ :If • § tJl ~ (General Catalogue and Abstracts of the Complete Book in Four Treasuries Imperially Determined).101 Ironically, however, the incorporation of Western astronomy into imperial science did not prevent this new type of astronomy from arousing criticism from Chinese scholars, especially after the French Jesuit Michel Benoist (1715-1774) introduced the concept of heliocentricism into the Qing palace around 1761. 102 This stirred up strong dissatisfaction among Chinese literati toward the incoher­ ence of Western astronomy in its adoption of cosmological models, especially the change from Tycho's deferent-epicycle scheme to Kepler's elliptic orbit and finally to Copernicus' heliocentric system. The most famous criticism was by Ruan Yuan (jljc Ji:;, 1764-1849), one of the most influential writers within scien­ tific circles in China after the mid-eighteenth century, who argued:

Since the Europeans, attracted by the Emperor's civilizing virtue, came from afar and translated their techniques for pac­ ing the heavens, we have had the mathematics of deferents and epicycles. [ ... ] And then, not very long after, there was a change. For what all along has been called circles they have replaced by ellipses, and they hold that the earth moves and the sun is static. This means that the Westerners were unable to firmly maintain their previous arguments. [ ... ] From Ty­ cho's time to the present it has been only somewhat over a century, but how many times have they changed their meth­ ods! I cannot imagine how much further they will go. They are certain to surpass these beginnings, boasting of knowl­ edge that only they have and inventing absurd theories.103

The only problem is that Ruan Yuan, while firing off this tirade, did not make it clear to his readers what kind of science the Tychonic Kaocheng and the Kepler­ Newtonian Houbian belonged to: Were they imperial science or just simply Western science?

100 Huanchao wenxian tongkao, chap. 229, pp. 12a-b. IOI Qinding siku quanshu wngmu tiyao, chap. 106, pp. 3la-34a. 102 For Benoist' s introduction of Copemicanism in China, see Sivin ( 1995). 103 See Chouren zhuan, pp. 609-610. The English translation is based on Sivin (1995).

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Appendix: Three Examples concerning the Representation of Newton's Theory in the Houbia.n

1. The Demonstration of the Yi pingjun - 3fl ~

At the beginning of the Scholium to Prop. 35 of Book 3, Newton explains the rise of the annual equations (Yi pingjun) of the moon and its apogee and node in the following way:

By the same theory [of gravity] I found, in addition, that the annual equation of the mean motion of the moon produced by the force of the sun, according to book I, Prop. 66, Corol. 6. When the sun is in perigee, this force is greater and dilates the orbit of the moon; when the sun is in apogee, the force is smaller and permits the orbit to be contracted. The moon re­ volves more slowly in the dilated orbit, more swiftly in the contracted one. . .. I found also that the apogee and nodes of the moon move more swiftly in the perihelion of the earth (because of the greater force of the sun) than in its aphelion, [and this] inversely as the cube of the distance of the earth from the sun. And from this there arise annual equations of these motions proportional to the equation of the sun's cen­ tre.104

Since the annual equation of the moon appears in the Kaocheng, where it is ex­ plained as an effect of the equation of time as suggested by Tycho and Kepler,105 Kogler and Pereira continue to apply this explanation not only to the annual equation of the moon, but also to the annual equations of lunar apogee and node. Therefore, the readers are told that, since mean motions of the moon as well as the lunar apogee and node are all measured with respect to the motion of the sun, they will manifest differences in response to the variation of the speed of the sun. As a result, the equation of the mean motion of the moon becomes a consequence of the equation of time stemming from this variation, whereas the equations of the apogee and node resulted partially from the equation of time thus produced and partially from the variation itself. After an obscure sequence of reasoning, they even provide three algorithms to derive the amplitudes of these three equa­ tions simply from the amplitude of the solar equation of centre and the speeds of the mean sun, mean moon, lunar apogee and node.106

I 04 Newton ( 1999), pp. 869-870. 105 For Tycho and Kepler's explanation of the annual equation of the moon's mean motion, see Taton and Wilson (1989), pp. 195-200, and Stephenson (1987), pp. 197-201. 106 Yuzhi lixiang kaocheng, chap. 2, pp. 37a-39b.

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Fig. 4: The Horrox-wheel adopted by Newton

[From Cohen ( 1975), p. 115]

2. The demonstration of the Zhengjiao jun iE 3(: :1$

In the Theory of the Moon's Motion, Newton directly uses a Horrox-wheel to describe the cause of the second equation of the lunar node (Zhengjiao jun). His demonstration can be represented as Fig. 4, wherein T denotes the earth, TS is a line joining the earth and the sun, TAB points to the mean position of the ascend­ ing node, whereas the true node is moving on the circle BFA counter clockwise in such a way that angle BCF equals the double of angle ATS, the angular distance between the sun and mean node. Given that TC to CB is as 57.5 to 1.5, the angle ATF can be obtained through trigonometric operations, which provides the equa­ tion of node. This model is very simple and clear, but Kogler and Pereira show little interest in it.107 Instead, they prefer to go back to the Kaocheng again, wherein the same equation is also applied and demonstrated (Fig. 3 illustrates the corresponding models from the two books)_108 The geometrical model borrowed by them from the Kaocheng can be reproduced as Fig. 5,109 wherein A is the pole of the ecliptic CGFK, whereas circle DGMF is the lunar orbit. The pole of the lunar orbit sets out from H to move counter clockwise on circlet HBJI with a speed of double the angular distance between the sun and the node,110 while N,

I 07 In the Scholium to Prop. 33 in Book 3 of the Principia, J. Machin devised another model to demonstrate and calculate the second equation of the lunar nodes, but it exerted no influence on Kogler and Pereira's work. 108 Yuzhi lixiang kaocheng, chap. 5, pp. 67a-72b. 109 For the original models used in the Kaocheng and Houbian, see Fig. 3 and 4 above. · 110 In the Kaocheng, this speed is double the angular distance between the sun and the moon.

Downloaded from Brill.com10/10/2021 10:48:59PM via free access 72 EASTM 28 (2008) the centre of the circlet, revolves on circle NOPQ with the same speed as that of the mean node moving along the ecliptic. The proportion of arc AN to arc NH comes as 18507.5 to 482.5, or approximately as 57.5 to 1,5,111 When the pole of the lunar orbit moves to B, angle CAB corresponds to the second equation of lunar nodes. Since the spherical triangle ABN is not very big, it is eventually treated as a plane triangle in the Houbian,112 and hence becomes an equivalent of Newton's model.

3. The demonstration of the San pingjun ~ ljl- ~

Kogler and Pereira correlate the San pingjun = f :l$;J to the Zhengjiao jun iE 3e: :l$;J on account of the fact that both of them depend on the angular distance be­ tween the sun and lunar node. For this reason, they also use the same model to demonstrate the rise of the San pingjun, which is now believed to be one of the "new inequalities discovered by Newton from his gravitational theory" .I 13 Ac­ cording to the two Jesuit astronomers, since the pole of the lunar orbit is revolv­ ing on the epicycle, as shown in Fig. 5, the lunar orbit is involved in another vibration with respect to the ecliptic, hence an additional discrepancy in the lon­ gitude of the moon. For instance, if the north pole of the lunar orbit is at B and the moon located at R on its own orbit, then the arc RS corresponds to the dis­ crepancy thus produced in its ecliptic longitude, which is actually the San ping­ jun. After an ordinary operation of spherical trigonometry has been carried out, the amount of this equation can be found, whose peak value turns out to be "ex­ actly the same as that ofNai Duan (Newton)".114

111 This proportion is derived from the maximum and minimum inclinations of the moon's orbit to the ecliptic, which comes as 18480 to 570 in the Kaocheng. For the deri­ vation of this proportion, see Yuzhi lixiang kaocheng, chap. 5, p. 67b-68a. 112 Yuzhi lixiang kaocheng, chap. 2, pp. 91 b-95a. 113 Nauenberg (2001b). 114 Yuzhi lixiang kaocheng, chap. 2, pp. 61a-66a.

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Fig. 5: The Model for the Zhengjiao jun in the Kaocheng

K

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