1. It was as a conference participant that I was able to see several originals of the manuscripts studied in this article. However, my research relies principally on texts that either have been published or that have been described by those in charge of the conservation and editing of the manuscipts. For a general discussion of Mawangdui manuscripts, see Riegel, Jeffrey K., “A Summary of Some Recent Wenwu and Kaogu Articles on Mawangdui Tombs Two and Three,” Early China 1 (1975), 10–15 CrossRefGoogle Scholar; and Loewe, Michael, “Manuscripts Found Recently in China,” T'oung Pao 63 (1978), 114–25Google Scholar.

2. Juyou, Fu and Songchang, Cheng , Mawangdui Hanmu wenwu (Changsha: Hunan, 1992)Google Scholar. Hanmu wenwu includes three sets of reproductions of Xingde B: a view of the entire manuscript (pp. 132–33), a color enlargement of the sexagenary grid and the diagram of the nine palaces (pp. 134–35), and black and white plates of the text portion of the manuscript (pp. 136–43).

3. “Boshu Xingde lüeshuo,” Jianbo yanjiu 1 (1993), 96–107 Google Scholar; and “Boshu Xingde yiben shiwen jiaodu,” Hunansheng bowuguan sishi zhounian jinian lunwenji (Changsha: Hunan jiaoyu, 1996), 83–87 Google Scholar.

4. Mawangdui boshu yishu (Shanghai: Shanghai shudian, 1996)Google Scholar.

5. In this article I use Xingde to refer to the texts assigned this title in the first reports of the Mawangdui excavations; the term Xing-De is used in a wider sense to refer to the method described in these texts as well as others.

6. The Boshu yishu reproductions of Xingde A include a fragment corresponding to columns 23–38 of Xingde B (except for a gap between columns 28–33 of the latter) and an additional column at the end; and a second fragment corresponding to columns 88–97 of Xingde B (pp. 120–28). A color plate reproduces text corresponding to Xingde B, columns 82–97 (p. 10). For Yinyang wuxing B, seven fragments are reproduced (pp. 129–56), of which three are concerned with the Xing-De method. Fragment 4 (p. 145) is of particular significance because it contains the section of the text studied in this article (Xingde B, columns 2–15).

7. Tsung-I, Jao, “Mawangdui Xingde yiben jiugongtu zhushen shi, jianlun chutu wenxian zhong de Zhuanxu yu Sheti” , Jiang Han kaogu 1993.1, 84–87 Google Scholar.

8. Xueqin, Li, “Ganzhi jinian he shier shengxiao qiyuan xinzheng” , Wenwu tiandi 1984.3, 41–42 Google Scholar; and Xueqin, Li, “Mawangdui boshu Xingde zhong de junli” , Jianbo yanjiu 2 (1996), 156–59Google Scholar.

9. Lexian, Liu , “Mawangdui Hanmu xingzhan shu chutan” , Huaxue 1(1995), 111–21Google Scholar; Kalinowski, Marc, “Mawangdui boshu Xingde shitan” Huaxue 1 (1995), 82–110 Google Scholar.

10. I am also grateful to Hu Wenhui for giving me a copy of his important study of Xingde B, “Mawangdui boshu Xingde yipian yanjiu” (unpublished).

11. The date recorded in the cell yisi (n42) of the sexagenary grid of Xingde A mentions the eleventh year of “the present emperor” (jin huangdi ; see below), a date that can only correspond to the eleventh year of Gaozu (196 b.c.). Since the reign of this emperor came to an end the following year (195 b.c.), it is likely that the manuscript was copied during this time. See Chen Songchang, “Xingde lüeshuo,” 101.

12. The absence of any mention of the reigns of Empress Gao (r. 187–180 b.c.) or Emperor Wen (r. 179–157 b.c.) could indicate that Xingde B was copied during the reign of Emperor Hui himself since he is the last emperor mentioned in the text. However, another astro-calendrical manuscript from Mawangdui, the Wuxingzhan , contains tables of planetary ephemerides for the years from 246 b.c., as in Xingde B, but ending at the third year of Emperor Wen (177 b.c.; see columns 86,100, 135). The calligraphic style of the two manuscripts is the same, suggesting that they were copied at about the same time at the beginning of the reign of Emperor Wen. For the Wuxingzhan I use the edition of Kawahara Hideshiro and Ichihiko, Miyajima , in Shin hastugen Chūgoku kagakushi shiryō no kenkyū Yakuchū-hen , ed. Keiji, Yamada (Kyoto: Kyoto University, Institute for the Humanities, 1985), 1–44 Google Scholar.

13. See Chen Songchang, “Xingde yiben shiwen,” 87, n. 26.

14. For diurnal rotations in Xingde A, see below, nn. 155–156.

15. Chen Songchang, “Xingde lüeshuo,” 96. For new evidence, see the Addendum.

16. Boshu yishu, 145, pl. 4.

17. For a preliminary comparison between the Yinyang wuxing texts from Mawangdui and the rishu, see Songchang, Chen, “Boshu Yinyang wuxing yu Qinjian rishu” , Jianbo yanjiu 2 (1996), 138–47Google Scholar. We now have some ten manuscripts identified by the authors of excavation reports as being rishu (see Lexian, Liu, “Jiudian Chujian Rishu yanjiu” , Huaxue 2 [1996], 61 Google Scholar). The most complete and best studied are Rishu A and B from Shuihudi tomb no. 11, Hubei (discovered in 1975; burial dated ca. 217 b.c.). For discussions in languages other than Chinese, see Kalinowski, Marc, “Les traités de Shuihudi et l'hémérologie chinoise à la fin des Royaumes Combattants,” T'oung-Pao 72 (1986), 175–228 CrossRefGoogle Scholar; and Mu-chou, Poo, “Popular Religion in Pre-Imperial China: Observations on the Almanacs of Shui-hu-ti,” T'oung-Pao 79 (1993), 225–47Google Scholar. The most exhaustive study of these texts is Lexian, Liu, Shuihudi Qinjian Rishu yanjiu (Taipei: Wenjin, 1994)Google Scholar. The spread of the Xing-De method during this period is also confirmed by manuscripts from Fuyang , Anhui (beginning of the Han), that contain a text accurately identified as related to this divination procedure, including a diagram that seems to be a sexagenary grid like that in Xingde B from Mawangdui (see “Fuyang Hanjian jianjie” , Wenwu 1983.2, 21–23 Google Scholar). For other references to the use of Xing and De in manuscripts, see n. 79 below.

18. Chen Songchang, “Xingde yiben shiwen.” Given the many errors in it, the transcription in Hanwu wenwu should not be used. The reproductions of Xingde A and Yinyang wuxing B in Boshu yishu permit us to double-check many of Chen Songchang's emendations.

19. I follow Chen Songchang's numbering of the columns; he adds a supplementary column between columns 84 and 85, giving a total of ninety-seven columns instead of the ninety-six given in Hanwu wenwu (see “Xingde yiben shiwen,” 87, n. 25).

20. See Hanmu wenwu zongshu, 12.

21. The red dot that marks the beginning of the second subsection (above column 14) is barely visible on the manuscript, and the Hanwu wenwu transcription fails to note it.

22. On this manuscript, see Loewe, Michael, “The Han View of Comets,” in Loewe, , Divination, Mythology and Monarchy in Han China (Cambridge: Cambridge University Press, 1994), 61–84 Google Scholar. In this regard, the title assigned to the Xingde texts does not correspond to their actual contents. A title that indicates the dual nature of their contents would be preferable.

23. Liu Lexian, “Xingzhan shu chutan.”

24. Except where indicated, the Chinese text given below is based on Chen Songchang, “Xingde yiben shiwen.” I have modified Chen's punctuation where it seems to me to be incorrect. I have also consistently added codes identifying the sexagenary signs so as to make the hemerological concepts that underlie the Xing-De method more understandable. The “s” stands for stem, “b” for branch, and “n” for binom (the combined stem and branch). The numbers accompanying the codes indicate the position of the sign in question in the series to which it belongs. These codes are used throughout the article, and are summarized in Table 1.

25. The term gongzhong in the text is clearly an error for zhonggong “Central palace.” Yinyang wuxing B (Boshu yishu, 145) has zhonggong in place of gongzhong.

26. The character transcribed as xun “accordingly” appears in the manuscript with the element chuan to the left of the element ma . This is obviously a simple variant of the character xun , the expression xunxing “conduct oneself in conformity to the rules” being common in Han texts. Since xun is interchangeable with xun “conform to” and xun “follow,” the term xunxing means here that the sixty binoms are divided up among the cells of the nine palaces layout according to their progressive order.

27. The characters in brackets (and English words), here and below, are restored based on Yinyang wuxing B.

28. Honshu (Beijing: Zhonghua, 1962)Google Scholar, “Yiwenzhi” , 30.1768–69.

29. Hanshu, 30.1760. The connection between the Mawangdui Xingde texts and the bing yinyang specialists has long been noted (see the comments of Lan, Tang in “Zuotan Changsha Mawangdui Hanmu boshu” , Wenwu 1974.9,50)Google Scholar. For a classification of all the Mawangdui manuscripts according to the Hanshu bibliographic categories, see Xueqin, Li, “Ji zai Meiguo juxing de Mawangdui boshu gongzuo huiyi” , Wenwu 1979.11, 71–73 Google Scholar.

30. In Kalinowski, “Xingde shitan,” 84, I give examples from works such as the Wei Liaozi and the Huainanzi . For the use of Xing-De in the military texts from Yinqueshan , see Yates, Robin, “The Yin-Yang Texts from Yinqueshan: An Introduction and Partial Reconstruction, with Notes on their Significance in Relation to Huang-Lao Taoism,” Early China 19 (1994), 82–84, 88–90CrossRefGoogle Scholar.

31. Liutao (Bingjia baojian ed.; Shijiazhuang: Heibei renwu, 1991)Google Scholar, “Long-tao” , 740–41 (the “Wangyi” chapter).

32. See above, n. 12, for the Wuxingzhan.

33. Yinyang wuxing B contains several examples of the square cells (see Chen Songchang, “Xingde lüeshuo,” 97–98), but this is the only one that is inscribed (it is not, however, directly tied to the Xing-De method).

34. For this diagram, see the important study by Jianmin, Li , “Mawangdui Hanmu boshu Yuzang maibao tu jianzheng” , Bulletin of the Institute of History and Philology, Academia Sínica 65.4 (1994), 725–832 Google Scholar. See also, Harper, Donald, Early Chinese Medical Literature: The Mawangdui Medical Manuscripts (London: Kegan Paul, 1998), 374–77Google Scholar.

35. The classic reference is in the Huainanzi astrological treatise: “Zi (bl), wu (b7), mao (b4), and you (blO) are the two cords; chou (b2) and yin (b3), chen (b5) and si (b6), wei (b8) and shen (b9), xu (bll) and hai (bl2) are the four hooks.” See Qian Tang , Huainan lianwen xun buzhu (hereafter, Tianwenxun buzhu), in Wendian, Liu , Huainan honglie jijie (Taipei: Shangwu, 1974), 33bGoogle Scholar. See also, Major, John, Heaven and Earth in Early Han Thought: Chapters Three, Four, and Five of the Huainanzi (Albany: State University of New York Press, 1993), 84–85 Google Scholar. The expression “two cords and four hooks” also occurs in the manuscripts from Yinqueshan, accompanied by mention of the solstices (Yates, “The Yin-Yang Texts from Yinqueshan,” 133).

36. See Difei, Yin , “Xi-Han Ruyinhou mu chutu de zhanpan he tianwen yiqi” Kaogu 1978.5, 338–43Google Scholar; and Dunjie, Yan , “Guanyu Xi-Han chuqi de shipan he zhanpan” Kaogu 1978.5,334–37Google Scholar. On the front of the instrument is a diagram with the oldest known occurrence of the numbers one to nine arranged in the magic square of three. The instrument was used in the method of the motion of Taiyi in the nine palaces (Taiyi xing jiugong ) recounted in the Huangdi neijing lingshu jing (see Yamada Keiji, “Kyuku hachifū setsu to Shoshisha no tachiba” , Tōhō gakuhō 52 [1980], 199–242). We may note that a date inscribed on the back of the instrument (seventh year of Emperor Wen, 173 b.c.) shows that it is contemporaneous with the Mawangdui Xingde B manuscript.

37. See n. 36 for the references. For specialized studies of the liuren astrolabes, see Kalinowski, Marc, “Les instruments astro-calendériques des Han et la méthode Liuren,” Bulletin de l'Ecole française d'Extrême-Orient 72 (1983), 309–419 CrossRefGoogle Scholar; and Dunjie, Yan, “Shipan zongshu” , Kaogu xuebao 1985.4, 445–64Google Scholar. We should note also the 1993 discovery at Wangjiatai , Hubei, of a similar object in a tomb dated to the second half of the third century b.c. According to the excavation report, the object is a square wooden board with the twenty-eight celestial lodges and the twelve branches on one side and a cord-hook diagram on the other (see “Jiangling Wangjiatai 15 hao Qinmu” Wenwu 1995.1, 37–43)Google Scholar.

38. See the unpublished study by Guosheng, Liu , “Shashi chutu shizhan zhujian jiqi xiangguan wenti yanjiu” (gradua te degree thesis, Wuhan University, 1995)Google Scholar.

39. A liubo playing board was found in Mawangdui tomb no. 3, the same tomb as the Xingde texts (Hanmu wenwu, 76). For a study, see Chuanxin, Xiong , “Lun Mawangdui sanhao Xi–Han mu chutu de liubo” , Wenwu 1979.4, 35–39 Google Scholar. The fourth century b.c. examples of the liubo board are from Yutaishan , Hubei (see jiangling Yutaishan Chumu [Beijing: Wenwu, 1984], 103–5Google Scholar), and from the royal burial at Zhongshan (see guanlichu, Hebeisheng wenwu, “Hebeisheng Pingshanxian Zhanguo shiqi Zhongshanguo muzang fajue jianbao” , Wenwu 1979.1, 26 Google Scholar, figs. 32–33). The sundial in Fig. 7:c was found in Inner Mongolia in 1897. See Maspero's, Henri study, “Les instruments astronomiques des Chinois au temps des Han,” Mélanges chinois et bouddhiques 6 (1939), 281–93Google Scholar. A similar sundial also dating from the Han is reported by Jiandeng, Li , “Guiyi: woguo xiancun zui gulao de tianwen yiqi” , in Zhongguo gudai tianwen wenwu lunji (Beijing: Wenwu, 1989), 145–53Google Scholar. The TLV mirror in Fig. 7:d dates from the period of Wang Mang . It is noteworthy for its inscription which shows that the TLV marks on the mirrors were seen as a borrowing from the liubo playing board: “The [liu]bo playing board was engraved to ward off bad luck” (ke ju boju qu buxiang ). See Zheng, Zhou , “Guiju jing yinggai cheng boju jing” , Kaogu 1987.12, 1116–18Google Scholar.

40. Ling, Li, “Shi yu Zhongguo gudai de yuzhou moshi” , Zhongguo wenhua 4 (1991), 1–30 Google Scholar. The term “astrolabe diagram” seems too narrow to me since it imposes the idea that the cord-hook diagram is inseparable from the production of these instruments. Even if the hypothesis of the astro- calendrical origin of the diagram seems to be the most plausible one, we have no evidence that the liuren astrolabes of the Han period existed in the same form during more ancient periods, yet cord-hook motifs are already found in the fifth century b.c., closely followed by the TLV motif on the liubo playing boards.

41. mu, Zenghou Yi (Beijing: Wenwu, 1989), vol. 2, pi. 126:3Google Scholar. It is possible that the cord-hook motifs reflect an astro-calendrical symbolism since the cover of another chest found in the same tomb has a representation of the sky with the twenty-eight celestial lodges (pi. 121). Although very stylized, the four hooks are clearly visible at the four corners of the cover. The two cords are missing and are replaced by the four elongations of the character dou (representing the constellation Northern Dipper) which divides the plan of the sky into four sectors corresponding to the four seasons.

42. The drawings in Fig. 8:c are based on the coffin lining boards from three Chu tombs: at Zidanku , Hunan, (bowuguan, Hunansheng, “Changsha Zidanku Zhanguo muguo mu” , Wenwu 1974.2, 37, fig. 2)Google Scholar; at Wangshan , Hubei, (Jiangling Wangshan Shazhong Chumu [Beijing: Wenwu, 1996], 18)Google Scholar; and at Baoshan , Hubei, (Baoshan Chumu [Beijing: Wenwu, 1991], 19)Google Scholar. A motif identical to the one from Baoshan is found on a lining board from a tomb at Jiudian , Hubei, (Jiangling Jiudian Dong-Zhou mu [Beijing: Kexue, 1995], 47)Google Scholar. It should be noted that cord-hook motifs appear in Chu Kingdom tombs only from the middle to the end of the Warring States period. I thank Alain Thôte for pointing this fact out to me.

43. See Allan, Sarah (Lan, Ai ), “Yaxing yu Yinren de yuzhou guan” , Zhongguo wenhua 4 (1991), 31–47 Google Scholar; and Allan, , The Shape of the Turtle: Myth, Art, and Cosmos in Early China (Albany: State University of New York Press, 1991), 75–111 Google Scholar. On the connections between the TLV motif and the archaic form of the character wu , see Zonghao, Chang , “Jiaguwen wu zi de zai kaocha” in Dierjie guoji Zhongguo guwenzixue yantaohui lunwenji (Hong Kong: Chinese University of Hong Kong Press, 1993), 161–68Google Scholar.

44. Studies in this area have dealt mostly with the three types of objects belonging to the TLV group (Fig. 7:b–d). Following the line of the research of Schuyler Camman, Michael Loewe developed the hypothesis that the origin of the TLV motif on Han mirrors and liubo boards was to be found among liuren astrolabes ( Loewe, , Ways to Paradise: The Chinese Quest for Immortality [London: George Allen and Unwin, 1979], 60–85)Google Scholar. More recently, Jianmin, Li leans towards sundials as a source; see “Handai juxi de qiyuan yu yanbian” , Dalu zazhi 77.3 (1988), 1–20 (part 1)Google Scholar; 77.4 (1988), 27–47 (part 2). Li draws on earlier studies, such as Minao, Hayashi , “Kankyō no zuhyō ni san ni tsuite” , Tōhō gakuhō 44 (1973), 1–65 Google Scholar. The problem with these arguments is that the first liubo playing boards are more than two centuries older than the most ancient known examples of the TLV sundial and the liuren astrolabe. A hypothesis concerning the functional origin of the TLV motif in one of these instruments must presuppose the existence of these instruments as early as the fourth century b.c. But we see nothing equivalent to the liubo board at that period except in motifs bearing the cord- hook form and in symbolic representations of space divided into sectors.

45. See Yinwan Hanmu jiandu (Beijing: Zhonghua, 1997), 125–26Google Scholar. The predictions inscribed on the back of the planchette indicate that the basis of this fortune-telling procedure lay in the game of liubo; see Xueqin, Li, “Boju zhan yu guiju wen” , Wenwu 1997.1, 49–51 Google Scholar.

46. See Wen, Gao , Sichuan Handai huaxiang zhuan (Shanghai: Renmin meishu, 1987), pl. 116 Google Scholar.

47. On the relations between astro-calendrical divination and games of chance, see Jianmin, Li, “Handai juxi de qiyuan yu yanbian” (part 2); and Needham, Joseph, Science and Civilisation in China (Cambridge: Cambridge University Press, 1954-), vol. 4.1, 318–34Google Scholar.

48. On the idea of schematic cosmography, see Major, John, “The Five Phases, Magic Squares, and Schematic Cosmography,” in Explorations in Early Chinese Cosmology (Journal of the American Academy of Religion, Thematic Studies, 50/2), ed. Rosemont, Henry Jr., (Chico: Scholar Press, 1984), 133–66Google Scholar.

49. For the dates mentioned in Xingde A, see Chen Songchang, “Xingde lüeshuo,” 102. The Qin period is defined by the accession of the future First Emperor to the Qin throne in 246 b.c. and not by the formation of the Qin kingdom into an empire in 221. On the ephemeral kingdom of Zhang Chu, arising from Chen Sheng's revolt in 209 b.c., see Naihe, Liu , “Boshu suoji Zhang Chu guohao yu Xi-Han fajia zheng-zhi” , Wenwu 1975.5, 35–37 Google Scholar.

50. See Xueqin, Li, “Ganzhi jinian he shier shengxiao qiyuan xinzheng”; and Moruo, Guo , “Shi zhigan” , in Guo Moruo, Jiagu wenzi yanjiu (Hong Kong: Zhonghua, 1976), 288–89Google Scholar.

51. Chen Songchang, “Xingde lüeshuo,” 101. For other details, see the Addendum.

52. According to the Quarter-day system (sifen li), which underlies the calculation of luni-solar conjunctions in calendars before the development of the Taichu calendar (104 b.c.), the base unit is the zhang (nineteen years), the period at the end of which the new moon (first day of the month in the civil calendar) returns to the same day in the solar year (usually the winter solstice). For such a conjunction to occur at the same hour of the day, four zhang must pass, producing a bu (seventy-six years). For the day to have the same binom in the sexagenary sequence requires twenty bu (one ji , or 1520 years). Finally, for the year also to have the same binom in the sexagenary sequence requires three ji, which make up the Epoch cycle (yuan) mentioned here. The ji and the yuan are essentially calendrical units associated with the application of the sexagenary norms to the calculation of astronomical periods. See Cullen, Christopher, Astronomy and Mathematics in Ancient China: The Zhoubi suanjing (Cambridge: Cambridge University Press, 1996), 24–27 CrossRefGoogle Scholar.

53. Tianwen xun buzhu, 82a–b; Major, Heaven and Earth in Early Han Thought, 118—19. Qian Tang has established the connection of the Quarter-day system with the calculation of the Epoch cycle; Major does not follow Qian, and translates the beginning of the passage (Taiyin yuanshi ) as “the beginning of the Jovian cycle.” Besides being far from the original, this translation implies that the passage in question deals only with the Jovian cycle, which is far from being the case (see below, n. 125). The years that mark the beginning of the three cycles of completion (sanzhong ) are the year 1 (jiayin), the year 1521 (jiaxu), and the year 3041 (jiawu).

54. This is why the sexagenary year count is sometimes called the Taiyin year count (Taiyin jinian ); see, for example, Qian Tang's commentary at Tianwen xun buzhu, 82a.

55. On the twenty-four solar periods, see Needham, Science and Civilisation, vol. 3, 405. The Beginning of Spring (lichun ) is the day chosen as the start of the epoch cycle in the Zhuanxu calendar (Zhuanxu li ) which was in use in the Qin and at the beginning of the Han.

56. For the hemerological uses of Taiyin in the Huainanzi, see Kalinowski, “Xingde shitan,” 86.

57. This system is idealized because the sidereal revolution of Jupiter actually takes 11.86 years and its synodic revolution 399 days (or 33.75 days more than the solar year of 365.25 days). The system lags by one celestial division every eighty-three years, a lag to which the Han astro-calendrists gave the name of chaochen “division overlap.” Pre-imperial sources like the Zuozhuan and the Guoyu attest to the existence of a notation of the sidereal positions of Jupiter well before the first evidence of the application of the sexagenary cycle to the recording of years. The evolution leading from the system of sidereal positions to that of Jovian year names and to the sexagenary year count that underlies the annual revolution of Taiyin is little known. Here I shall limit myself to stressing how the role played by Taiyin in the Mawangdui Xingde texts can help us to understand better its relationship with Jupiter. For a general and somewhat dated presentation of the Jovian cycle, see Saussure, Léopold de, Les origines de l'astronomie chinoise (Leiden: Brill, 1909; reprinted, Taipei: Chengwen, 1967), 315–406 Google Scholar.

58. Wuxingzhan, columns 41–43. Dots of elision indicate lacunae in the text. The terms wei “corner” and zhong “middle” refer to the distribution of the twelve branches and the twenty-eight celestial lodges on the twelve line-ends of the cord-hook diagram (zhong denotes the line-ends forming the two cords and wei the line-ends forming the four hooks; see Fig. 6). Jupiter and Taiyin move in opposite directions, as can be seen in Table 2. Their points of intersection are located between the branches chou (b2) and yin (b3) and between the branches wei (b8) and shen (b9)—that is, at the borders on the cord-hook diagram separating the yin seasons (autumn and winter) from the yang seasons (spring and summer), the “borderline between yin and yang” in the text.

59. Tianwen xun buzhu, 18a–19a; Major, Heaven and Earth in Early Han Thought, 73.

60. Tianwen xun buzhu, 83b–;87b; Major, Heaven and Earth in Early Han Thought, 120–21. For details concerning Table 2, see Major's commentary to his translation (pp. 122–23). The heliacal risings mark the starting point for the synodic revolutions of Jupiter. The passage from one month to the next is determined by the theoretical lag of one month for each complete revolution (see above, n. 57). In the Jovian year- count proper, the binoms for the years are indicated with particular terms for the twelve branches and the ten stems. Shetige is the name given to the first year of the cycle of twelve, which corresponds in the ancient form of nomenclature to the branch yin (b3).

61. The layout turns out to be even more idealized in that the width of the celestial lodges varies from two degrees for the smallest to more than thirty degrees for the largest. For a table of the width of the lodges and correspondences with Western stellar terminology, see Cullen, Astronomy and Mathematics in Ancient China, 18.

62. The Jupiter cycle turns up in two places in the text: first in a general account mentioning the Jovian year names but without any connection to historical chronology (columns 1–4); and later, in the section on ephemerides, which does not mention the exact Jovian year names (columns 77–88). There are two variants in the lodges used to indicate the sidereal position of the planet, but I have not taken them into account here.

63. Tianwen xun buzhu, 84a–b; Major, Heaven and Earth in Early Han Thought, 1201–21. The passage corresponds to the first row in Table 2.

64. Wuxingzhan, column 1. There is a lacuna in the original text. The passage in brackets was added by the editors on the basis of the rubrics for the following months.

65. Hanshu, “Tianwen zhi” , 26.1289.

66. See Tianwen xun buzhu, 43b, 83b, 101b. The Shuihudi Rishu mention a similar cycle, but using Sui (Year) instead of Taisui; see Kalinowski, “Les traités de Shuihudi,” 216–19.

67. On the problems associated with the indication of the Jupiter cycle in the Wuxingzhan, see Jiujin, Chen , “Cong Mawangdui boshu Wuxingzhan de chutu shitan woguo gudai de suixing jinian wenti” Zhongguo tianwenxue shi wenji 1 (1978), 48–65 Google Scholar; Jiujin, Chen and Meidong, Chen , “Cong Yuanguang lipu ji Mawangdui boshu Wuxingzhan de chutu zaitan Zhuanxu li wenti” , Xueshu yanjiu 1980.6, 82–87 Google Scholar; Youqi, He , “Guanyu Wuxingzhan wenti da kenan” , Xueshu yanjiu 1981.3, 97–103 Google Scholar; Keizō, Hashimoto , “Sengyoku rekigen to saisei kinenhō” , Tōhō gakuhō 59 (1987), 323–43Google Scholar.

68. Existing studies on the reconstruction of the Jovian year count during the Qin and at the beginning of the Han generally take as a departure point the hypothesis that the sexagenary recording of years had not yet become fixed at that time, which leads to the idea that the phenomenon of Jupiter's “division overlap” (chaochen) must automatically bring an equivalent jump in the annual binom that fixes the position of Taiyin. 1 find it difficult to agree with Chen Jiujin and Chen Meidong when they say that “according to the indications in the Wuxingzhan, the first year of the First Emperor was a jiayin (n51) year” (“Cong Yuangguang lipu ji Mawangdui boshu Wuxingzhan,” 110) because the sexagenary grid in Xingde B clearly proves that this year was considered at the time to be a yimao (n52) year.

69. This does not exclude the possibility, supported by a number of ancient texts, that the Taiyin cycle was originally conceived on the model of the revolutions of Jupiter to give the sexagenary year count astronomical legitimacy. We shall see that this was also true of the De and Xing revolutions, which are symbolically associated with those of the sun and moon. Nevertheless, the new evidence provided by the Mawangdui texts demonstrates the need for caution in considering the relationship between Taiyin and Jupiter in the context of calendrical astrology at the end of the Warring States and beginning of the Han. When we read the Huainanzi in the light of these texts we also see the leading role given at that time to Taiyin in the Jupiter cycle as well as the other cycles based on the sexagenary calendrical norm. If not completely false, the term “counter-Jupiter” applied to Taiyin is nonetheless a misleading characterization at this stage in the evolution of techniques of counting years.

70. See, for example, Shangshu zhengyi (Sibu beiyao ed. of Shisanjing zhushu “Lüxing” , 19.18b, recording words traditionally attributed to King Mu of the Zhou : “The King said … ‘I respect Punishment; those with Virtue are in charge of Punishment’” . Compare Legge, James, The Chinese Classics (Hong Kong: Hong Kong University Press, 1960), vol. 3 (The Shooting), 609 Google Scholar.

71. Bojun, Yang , Chunqiu Zuozhuan zhu (Beijing: Zhonghua, 1990), 880 (Cheng 16)Google Scholar.

72. On the evolution of the ideas of De and Xing-De during the Shang and Zhou periods, see Tsung-I, Jao, “Tianshen guan yu daode sixiang” , Bulletin of the Institute of History and Philology, Academia Sinica 49.1 (1978), 77–100 Google Scholar; and Nivison, David, The Ways of Confucianism (LaSalle and Chicago: Open Court, 1996), 17–43 Google Scholar.

73. See Major, John, “The Meaning of Hsing-te,” in Chinese Ideas about Nature and Society, ed. Blanc, Charles Le and Blader, Susan (Hong Kong: Hong Kong University Press, 1987), 281–91Google Scholar. Major distinguishes between two interpretations of Xing-De in ancient texts: one “refers to an overt action of human agency” and the usual translation of Virtue and Punishment fits it perfectly; the other “refers to a cosmological principle” and he finds it more appropriate to translate Xing and De in these cases with naturalistic terms like “recision” and “accretion” (p. 291). For further discussion, see n. 75 below.

74. Guanzi (Xin zhuzi jicheng ed.), “Sishi” , 298. For additional citations, see Kalinowski, “Xingde shitan,” 88. There is ample attestation of the cosmological use of Xing-De in excavated Qin and Han manuscripts. See Yates, “The Yin-Yang Texts from Yinqueshan,” 93, for Mawangdui manuscripts; and 89, for those from Yinqueshan. For Zhangjiashan manuscripts, see “Jiangling Zhangjiashan Hanjian gaishu” Wenwu 1985.1, 13 Google Scholar. The cosmological and astrological symbolism of Xing and De is mainly luni-solar. Many texts associate them with the moon and the sun. Other antonyms often share the same symbolism: yin/yang, darkness/light, lunar eclipse/solar eclipse, summer solstice/winter solstice, autumn-winter/spring-summer. The Mawangdui Wuxingzhan associates Xing and De with appearances of Venus in the western and eastern parts of the sky (column 20).

75. In this regard, Major's translation of Xing and De as “recision” and “accretion” (in “The Meaning of Hsing-te”) when they refer to a cosmological principle seems mis-leading to me. First of all, this translation ignores the religious context in which these notions developed, a context in which the distinction between personal and impersonal action by a divine agency is not sharply distinguished (see Vandermeersch, Léon, “Une tradition réfractaire à la théologie: la tradition confucianiste,” Extrême-Orient Extrême-Occident 6 [1985], 9–21)CrossRefGoogle Scholar. An expression like tianxing “the punishment of heaven” can have a personal or an impersonal meaning depending on the situation and the individuals concerned, without going back to any choice between cosmological principle and human action. Finally, Chinese cosmology is constructed on the basis of ideas and categories that, by incorporating human morality into the natural order, meant that “the threatening gulf between Heaven and man was closed before man had time to rethink himself as a solitary exception in a morally neutral universe” ( Graham, Angus, Disputers of the Tao: Philosophical Argument in Ancient China [LaSalle: Open Court, 1989], 313)Google Scholar. Major himself gives an example in which Xing and De appear “in a context that implies a middle ground between, or a combination of, cosmological principles and human governmental actions” (“The Meaning of Hsing-te,” 290). In the sphere of correlative cosmology and calendrical astrology, the “middle ground” uses of Xing and De seem to me the most common, and the translation of “harm” and “benefit” adopted by Major in this example is doubtless better than the translation he proposes for general use. Finally, on the level of techniques, the terms “recision” and “accretion” pose certain problems. Major's entire argument rests on the analysis of the method of the “seven dwellings of Xing-De” in the Huainanzi (see below, nn. 80–81). But Qian Tang already noted that the Huainanzi astrological treatise contains two distinct Xing-De methods (Tianwen xun buzhu, 88a-b; also see below, n. 79), and the second is precisely the one described in the Mawangdui Xingde texts. Here the shifts of Xing and De are not ruled by a natural process of the growth and shrinking of the yin and yang energies of the year but rest on arithmetic principles that underlie sexagenary hemerology. In addition, their functions are no different from those of other calendrical spirits such as the Bloody Branch (xuezhi ), the Day Spell (rhjan ), and the multitude of Yearly Miasmas (niansha ) which were attached to calendars from as early as the Han. The oldest example of a calendar including calendrical spirits—including the Punishments of the Month (yuexing )— was discovered in 1993 at Yinwan; see Yinwan Hanmu jiandu, 128. The endeavor to translate all these terms by giving them a naturalistic meaning that does not “give rise to a certain feeling of intellectual unease” (Major, “The Meaning of Hsing-te,” 282) seems to me overdone. While the attempt is worth making, especially when dealing with terms that have elsewhere entered philosophical vocabulary, care must be taken not to generalize and not to systematize a new usage that is basically only a makeshift.

76. See Qinding xieji bianfang shu (Siku quanshu ed.), chapters 3–5.

77. Wuxing dayi (Zhibuzu zhai ed.), “Lun De” , 2.17a–b; Kalinowski, Marc, Cosmologie et divination dans la Chine ancienne: Le Compendium des cinq agents (Wuxing dayi, 6e siècle) (Paris: Ecole française d'Extrême-Orient, 1991), 233 Google Scholar.

78. Wuxing dayi, “Lun Xing” , 2.28b; Kalinowski, Cosmologie et divination, 252.

79. In the excavated manuscripts the differentiation is harder to make because of gaps in the texts or lack of precision in excavation reports. The Fuyang Xingde manuscript is probably of the same type as that from Mawangdui (see above, n. 17). A text on a wooden board from Yinwan describes a hemerological procedure based on the ten stems and also is related to the second category of the Wuxing dayi (Yinwan Hanmu jiandu, 145). The method of the seven dwellings is attested in the manuscripts from Juyan , Gansu; see juyan xinjian (Beijing: Wenwu, 1990)Google Scholar, EPT 43: 185; EPT 65:48; and EPS4.T2:80. We also find divinatory uses of Xing-De in the yin-yang texts from Yinqueshan (nos. 0473, 3311, and 0430), but it is difficult to decide which category they belong in (see Yates, “The Yin-Yang Texts from Yinqueshan,” 87 and 132).

80. Tianwen xun buzhu, 38a–39b; Major, Heaven and Earth in Early Han Thought, 86–88. Ming, Wang , Taiping jing hejiao (Beijing: Zhonghua, 1976)Google Scholar, “Anshu ming Xing-De fa” , l104–11.

81. The passage dealing with the gnomon comes immediately before the one that describes the seven dwellings of Xing-De (Tianwen xun buzhu, 37b). At the Winter Solstice, when the shadow of the gnomon is longest, Xing is in the open countryside (ye ; that is, farthest from the gnomon) while De is inside the house (shi ; that is, close to the gnomon). At the Summer Solstice the situation is reversed: De is in the open countryside while Xing is inside the house. On the connections among the seven dwellings, the system of the sixteen hour-divisions in the Shuihudi manuscripts, and the seven heng in the Zhoubi cosmography, see the analyses by Xiantong, Zeng in Tsung-I, Jao and Xiantong, Zeng, Yunmeng Qinjian Rishu yanjiu (Hong Kong: Chinese University of Hong Kong Press, 1982), 81–95 Google Scholar.

82. Wuxing dayi, 2.17b–19b and 28a–29b; Kalinowski, Cosmologie et divination, 233–35 and 252–54.

83. The mutual production order is Wood-Fire-Earth-Metal-Water. The mutual conquest order is Water-Fire-Metal-Wood-Earth.

84. The correlations appear in the Xieji bianfang shu, 3.11a–12a, where they have the name suizhi he “union of the year-branch.”

85. The correlations between the sectors and the Five Agents are not indicated in the cord-hook diagrams but they are mentioned in the text and in the diagram of the nine palaces.

86. See below, p. 163, for the occurrence of the phrase suo bu sheng “non-conquest position” in Xingde B.

87. Qiyou, Chen , Lüshi chunqiu jiaoshi (Shanghai: Xuelin, 1984)Google Scholar, “Yingtong” , 13.677. On the doctrine of the Five Virtues and dynastic changes, see the classic study by Jiegang, Gu , Wude zhongshi shuo xiade zhengzhi he lishi (Hong Kong: Longmen, 1970)Google Scholar.

88. A caption in the border of the sexagenary grid in Xingde A also refers to Xing as well as to De; see details in the Addendum.

89. In the Huainanzi this is the beginning of the passage cited in the next paragraph.

90. The Wuxingzhan parallel is from the end of the passage concerning the relation between Taiyin and Jupiter translated above, pp. 148–49 (citation in n. 58).

91. Tianwen xun buzhu, 80a; Major, Heaven and Earth in Early Han Thought, 123.

92. An unfortunately fragmentary passage in the yin-yang texts from Yinqueshan sets Xing and De in relation to the two solstices (Yates, “The Yin-Yang Texts from Yinqueshan,” 132), but it is difficult to say whether this refers to the annual rotation of Xing-De.

93. Tianwen xun buzhu, 82.a–b; Major, Heaven and Earth in Early Han Thought, 118–19. See also the discussion of this passage above, p. 147.

94. See above, pp. 146–47, and nn. 52–53.

95. The parallel is an extract from the passage cited above, p. 164, n. 91.

96. Notice that the branch elements of the binoms have the same agent as the sector in which the conjunction takes place: mao (b4), East; you (b10), West; wu (b7), South; zi (bl), North.

97. Tianwen xun buzhu, 88b–91b; Major,Heaven and Earth in Early Han Thought, 123–24.

98. The yin-yang texts from Yinqueshan contain a passage that attributes to Xing a movement in the opposite direction to that of De: “Five Agents: De moves to the non-conquered position, Xing moves to the conquered position” . See Jiulong, Wu , Yinqueshan Hanjian shiwen (Beijing: Wenwu, 1985), 85 Google Scholar.

99. Wangeng, Zheng , Taixuan jing jiaoshi (Beijing: Shifan daxue, 1989), 297–98Google Scholar; Nylan, Michael, The Canon of Supreme Mystery (Albany: State University of New York Press, 1993), 446 Google Scholar. On the five unions, see Kalinowski, Cosmologie et divination, 482–83, n. 9; 492, nn. 3–4. See also, Xieji bianfang shu, 1.45a–47b.

100. The stems corresponding to Metal are geng (s7) and xin (s8). Since the stem and branch elements of the binoms are always of the same class (odd or even), the binom in question must be gengwu (s7–b7).

101. See above, pp. 166–67; Tianwen xun buzhu, 88b–91b; Major, Heaven and Earth in Early Han Thought, 123–24.

102. See Kalinowski, “Les traités de Shuihidi,” 222–23; Lexian, Liu, “Wuxing sanhe ju yu nayin shuo” , Jiang Han kaogu 1992.1,89–91 Google Scholar. For the three unions, see Xieji bianfang shu, 1.39a–40b.

103. See Kalinowski, “Boshu Xingde shitan,” 94 and fig. 12; Liu Lexian, Shuihudi Qinjian Rishu yanjiu, 101–2 and 286–88.

104. For this formulation of the three unions in the Wuxing dayi, see Kalinowski, Cosmologie et divination, 90–91 and 231–32.

105. See the Huainanzi passage cited in n. 97, which serves as the basis for the discussion of the three unions just above.

106. Hanshu, 75.3168. In other words, Wood moves to Water and Water to Wood, while Metal and Fire remain in their places.

107. Shangqing huangshu guodu yi (Daozang , S1294; S designates the number assigned to the Daoist scriptures in Schipper, K.M., Concordance du Tao-tsang [Paris: Ecole française d'Extrême-Orient, 1975]), 8aGoogle Scholar. I have extracted the relevant phrases from the detailed record of this seminal Daoist sexual rite. For a full study of the rite, see Kalinowski, Marc, “La transmission du dispositif des neuf palais sous les Six Dynasties,” in Tantric and Taoist Studies in Honour of R. A. Stein, vol. 3, ed. Strickmann, Michel (Brussels: Institut des hautes études chinoises, 1985), 773–811 Google Scholar.

108. Wuxing dayi, 1.23a–b; Kalinowski,Cosmologie et divination, 183.

109. For details, see Kalinowski, “La transmission du dispositif des neuf palais.”

110. See the list of “Stem Virtues” from the Wuxing dayi on p. 35 above.

111. See the list of “Branch Punishments” from the Wuxing dayi on p. 35 above.

112. The sequence reflects the reversing of Wood and Water as explained in the Huainanzi rule for determining the position of Xing.

113. Hanshu, 99. 4120.

114. Hanshu, 99.4131.

115. Hou Hanshu (Beijing: Zhongua, 1965), 35.1197Google Scholar.

116. Hou Hanshu, 30A.1045; 43.1462.

117. A Dunhuang manuscript: Pelliot 2765.

118. A Dunhuang manuscript: Stein 95.

119. See Peiyu, Zhang, “Chutu Hanjian boshu shang de lizhu” , in Chutu wenxian yanjiu xuji (Beijing: Wenwu, 1989), 135–47Google Scholar.

120. Zhang Peiyu, “Chutu Hanjian boshu shang de lizhu.”

121. On these hemerological functions, see Xieji bianfang shu, 3.6a–7b (suide) and 3.53a–54a (suixing). The use of the term suide is recorded in the Chu Silk Manuscript (see below, n. 175). The Yuejue shu mentions it in opposition to Taiyin: “When Taiyin is in yang, suide is in yin.” See Yuejue shu (Sibu beiyao ed.), 4.3a (“Ji Ni neijing” ); and the fragments collected by Guohan, Ma under the title Fanzi Jiran (Yuhan shanfang jiyi shu [Taipei: Wenhai, 1967], vol. 5, 2557)Google Scholar.

122. See above, pp. 158–59, nn. 80–81.

123. See above, pp. 146–47.

124. See above, n. 74.

125. Tianiuen xun buzhu, 82a–87b. Major, Heaven and Earth in Early Han Thought, 118–24, does not make these distinctions since he puts the entire passage under the aegis of Jupiter, translating Taiyin consistently as “Jovian cycle” (see above, n. 53). The subdivisions of the Huainanzi text are as follows (I use the line numbering established by Major in his translation): Taiyin and the sexagenary Epoch cycle (section 32.1–9); the five seasonal emblems (section 32.10–15); the jianchu system (section 32.16–27); the Jovian year count (section 33.1–49); the annual rotation of Xing-De (section 34.1–13); technical descriptions on the keying of Xing-De and on the five seasonal emblems (section 34.14–33). The jianchu system was widespread during the Qin and the Han periods, and constitutes the most prominent feature of the Shuihudi, Fangmatan, and Jiudian rishu manuscripts (see Liu Lexian, “Jiudian Chujian Rishu yanjiu,” 64–66; and Kalinowski, “Les traités hémérologiques de Shuihudi,” 197–99). We know for sure that the jianchu system is based on the cycle of twenty-four solar periods and that it has nothing to do with Jupiter (see Zhang Peiyu, “Chutu Hanjian boshu de lizhu,” 136–37). The five seasonal emblems do not appear in the Xingde texts from Mawangdui, but they are found in those from Fuyang (see above, n. 17; and Pingsheng, Hu , “Fuyang Hanjian mulu” [unpublished paper presented at the Ecole Pratique des Hautes Etudes, Paris, May 1994])Google Scholar.

126. See above, p. 162 and n. 87.

127. See above, pp. 170–71.

128. This is why the passages about the Taiyin/Xing-De method in the Huainanzi cannot be understood without having before one the diagrams that controlled their movements. Major understood well the role played by such diagrams when he wrote: “Nevertheless the overall import of this section is clear enough; it has to do with day prognostication based on the movement of taiyin (counter-Jupiter) through the celestial circle represented by the cosmograph [that is, the liuren astrolabe] or some analogous instrument with the stem-branch designation of days being the controlling factor” (Heaven and Earth in Early Han Thought, 125).

129. Hanmu wenwu, 135.

130. The concepts of zheng and ji are as widespread in ancient texts as are those of Xing and De. There is, for example, the famous passage from Laozi , paragraph 57: “Use the regular to govern the state; use the odd to employ weapons” . It is worth noting that paragraph 57 also contains the only attack on the observance of taboos and prohibitions (jihui, ) in the Laozi. When zheng and ji are applied to spatial divisions as is the case in Xingde B, zheng designates a frontal position and ji a sideways position; see Ling, Li, Wu Sunzi fawei (Beijing: Zhonghua, 1997), 64, n. 4Google Scholar.

131. See the text of paragraph 3.4 below. For the nine palace system on other excavated artifacts, see above, n. 36.

132. See Chen Songchang, “Xingde lüeshuo,” 97. The use of colors to indicate orientations on a diagram is still common in the astro-calendrical tradition. The Chu Silk Manuscript is another ancient example; see Ling, Li, “Chu boshu yu shitu” , Jiang Han kaogu 1991.1, 60 Google Scholar.

133. The regular palaces in Xingde A only mention De; see Chen Songchang, “Xingde lüeshuo,” 103. For further references, see the Addendum.

134. Fengbo and Yushi are also seen to the right and the left of the god Taiyi in one of ihe Mawangdui banners; see Ling, Li, “An Archaeological Study of Taiyi (Grand One) Worship,” Early Medieval China 2 (1995–96), 1–39 Google Scholar.

135. Chuci jizhu (Shanghai: Guji, 1979), 109–10Google Scholar; Hawkes, David, The Songs of the South (Harmondsworth: Penguin, 1985), 196–97Google Scholar.

136. Hanfeizi (Xin zhuzijicheng ed.), “Shixie ,” 88–89. For the events mentioned in the text, see Chavannes, Edouard, Les mémoires historiques de Se-Ma Ts'ien (Paris: Adrien-Maisonneuve, 1967), vol. 5, 170–95Google Scholar; for the territories of Wei and Tao, see vol. 5,139, n. 3. Han Fei is critical of hemerological procedures based on the presence or absence of calendrical spirits and atmospheric phenomena in one direction or another. Defining the positions of the spirits by using the terms in front of/behind (xianhou ) and left/right (zuoyou ) is also characteristic of Xingde B, which devotes a whole section to prognostications derived from fifteen different locations of Xing and De in relation to a strategic position (columns 23–28). For example: “When Xing and De are on the right, the battle will be won; when they are on the left, it will be half lost” .

137. See Jao-Tsung-I, “Xingde yiben jiugongtu.”

138. For an analysis of this passage, see Li Xueqin, “Ganzhi jinian he shier sheng- xiao.”

139. See Major, Heaven and Earth in Early Han Thought, 217–68, for translation and analysis of Huainanzi 5, which treats of the “monthly ordinances.”

140. The transcriptions from Xingde A and Xingde B are taken from Chen Songchang, “Xingde liieshuo,” 99–100. For possible variants, see Jao Tsung-I, “Xingde yiben jiugongtu,” 86. For the Wuxingzhan, see columns 1,17, 45, and 54.

141. For the development of the yueling tradition, which was the basis for ideas about the cosmological organization of the state, see the recent study by Yitian, Xing , “Yueling yu Xi-Han zhengzhi: cong Yinwan jibu zhong de ‘yi chun ling cheng hu’ shuoqi” , Xin shixue 9.1 (1998), 1–54 Google Scholar.

142. Xingde B, columns 19–20.1 have corrected xinmao to xinyou based on the context.

143. The transcription qingze is dubious, and restoration of the character qiang in yuqiang is based on Xingde A; see Chen Songchang, “Xingde lüeshuo,” 101. For other interpretations, see Jao Tsung-I, “Xingde yiben jiugongtu,” 86–87.

144. Jao Tsung-I, “Xingde yiben jiugongtu,” 86–87.

145. Xingde B, column 21. The other two four-pole binoms are yimao (n52) and xinyou (n58) which, curiously, are also among the root binoms associated with the sovereigns of the four sectors (see above).

146. See above, p. 14 and n. 36. On the Taiyi board the term associated with the Winter Solstice is yezhi . The expression shangtian is also associated with the Summer Solstice in the Erya , “Shitian .” See Yan Dunjie, “Guanyu Xi-Han chuqi de shipan he zhanpan,” 385; and Jao Tsung-I, “Xingde yiben jiugongtu,” 86.

147. See above, p. 138, n. 36; and pp. 163–64. The Huainanzi mentions the two solstices along with Xing and De in the description of the yin and yang cycle of the year (Tianwen xun buzhu, 48a; Major, Heaven and Earth in Early Han Thought, 84).

148. For yunqi in Xingde A, see Chen Songchang, “Xingde lüeshuo,” 101. For sidou, see ”Xingde lüeshuo,” 100–101; and Jao Tsung-I, ”Xingde yiben jiugongtu,” 87.

149. Xing and De are visible, however, in the inner circle. Each of the ten surrounding cells contains the name of a spirit and a sexagenary binom.

150. See Chen Songchang, “Xingde l¨eshuo,” 96. Chen Songchang mentions only the inscriptions. For their actual distribution in the Central palace, see the article by Chen, in Wenwu 2000.3, 78 Google Scholar, which is discussed in the Addendum.

151. See paragraph 3.1, pp. 165–66.

152. See Liu Lexian, Shuihudi Qittjian Rishu yanjiu, 282–83.

153. Starting with paragraph 3.3. See pp. 163–66, for the detailed treatment of the text preceding 3.3.

154. Recall, however, that in the Xingde A diagram only De is mentioned in the regular palaces (see above, n. 133).

155. This is, at least, the situation in theory. Yet we have evidence that things were different in practice. In Xingde A, the table of the daily cycle of Xing-De for the eleventh year of Gaozu always places De in the west when it moves independently of Xing; that is, from nl to n6, from nl3 to nl8, and so on (see the discussion below and n. 156). This variation seems to be connected to the fact that the annual position of De for the year in question, yisi (n42; 196 b.c.) was to be found in the West (see the sexagenary grid in Fig. 3). For a reference to a recent transcription, see the Addendum.

156. See also, n. 155. The table is drawn beneath the sexagenary grid at the beginning of Xingde A (see Kalinowski, “Xingde shitan,” 97 and fig. 20). Because Xingde A has not been published, I limit myself to reproducing only the first column, which gives the exact date of the beginning of the cycle for the eleventh year of Gaozu.

157. According to the chronological tables of Peiyu, Zhang, Sanqian wubai nian liri tianxiang (n.p.: Henan jiaoyu, 1990)Google Scholar, the first day of the twelfth month of the eleventh year of Gaozu was wuzi (n25; January 21).The shangshuo day, jihai (n36; February 1), was the twelfth day of this month. The daily cycle of Xing-De began the next day, on gengzi (n37; February 2), seven days before the Beginning of Spring on the nineteenth day, bingwu (n43; February 8).

158. Lunheng (Xin zhuzi jicheng ed.), “Biansui” , 239.

159. Weishu (Beijing: Zhonghua, 1974), 107B.2718Google Scholar. For the calculation of the shangshuo day, see Zhang Peiyu, “Chutu Hanjian boshu shangde lizhu,” 138–39.

160. Hanmu wenwu,144. For transcription and discussion, see Kalinowski, ”Xingde shitan,” 98; and Chen Songchang, “Boshu Yinyang wuxing yu Qinjian Rishu,”144–45.

161. Hanmu wenwu, 144, last column of the fragment.

162. The original passage reads: “Among the venerable celestial spirits, none is more so than Qinglong (Green Dragon); some say it is Tianyi (Celestial One) while some say it is Taiyi (Grand One).” Tianwen xun buzhu, 101b; Major, Heaven and Earth in Early Han Thought, 135.

163. Hanmu wenwu, 145.

164. On this method, with mostly military applications, see Li Chunfeng , Yisizhan Congshu jicheng ed.), 10.169-217. See also, Xuyet, Ngo Van, Divination, magie et politique dans la Chine ancienne (Paris: Presses universitaires de France, 1976), 186–90Google Scholar.

165. See above, p. 171.

166. See the fragments of Yi Feng's work in his Hanshu biography and commentaries, Hanshu, 75.3168-71. On the liuqing, see Kalinowski, Cosmologie et divination, 363–66.

167. Xingde B, columns 34–35.

168. Yisi zhan, 10.186.

169. See above, nn. 36–37.

170. The most ancient account of the dunjia method is in the Taibo yinjing attributed to Li Quan (mid eighth century). See Taibo yinjing (Mohai jinhu ed.), 9.1a-15b. The dunjia method is mentioned by Ge Hong (ca. 280–340) in the Baopuzi (Xin zhuzijicheng ed.), “Dengshe” , 78. See also, Yan Dunjie, “Shi-pan zongshu,” 453–57; and Ngo Van Xuyet, Divination, magie et politique, 190–95.

171. See Tang liudian (Siku quanshu ed.), 14.31b–33a; and Chisongzi zhangli (Daozang, S615), 4.22b.

172. Taibo yinjing, 9.1a.

173. Xingde B, column 18; Taibo yinjing, 9.3b. In both cases, the anomalies are divided into the anomalies of the day (riqi ), month (yueqi ), and year (suiqi ).

174. See, for example, Sunzi bingfa (Xin zhuzi jicheng ed.), “Xushi” , 103. Many examples of calendrical divination in a military context are reported in the Yuejue shu and the Wu Yue chutiqiu ; see Harper, Donald, “The Han Cosmic Board: A Response to Christopher Cullen,” Early China 6 (1980–1981), 53–54 Google Scholar.

175. The term suide (Virtue of the year) occurs several times in the text; see Ling, Li, Changsha Zidanku Zhanguo Chu boshu yanjiu (Beijing: Zhonghua, 1985), 57 Google Scholar. De also appears in combination with ni “concealed.” Li Ling interprets ni as an antonym of De that prefigures the idea of Xing (Punishment; Chu boshu yanjiu, 57–58). For opposing opinions, see Tsung-I, Jao, Chu boshu (Hong Kong: Zhonghua, 1985), 52–53 Google Scholar; and Gang, Zheng, “Chu boshu zhong de suixing jinian he suixing zhan” , lianbo yanjiu 2 (1996), 59–68 Google Scholar. On the connection between the structure of the Chu Silk Manuscript and the cord-hook diagram, see Li Ling, “Chu boshu yu shitu,” 59–62.

176. This cycle of ten six-day periods also reminds us of the cycle of thirty periods of twelve days described in the yin-yang texts from Yinqueshan. There each twelve-day period is divided into two nodes (jie ) of six days: “twelve days is a period; six days is a node” (; slip 3258). In addition, the hemerological functions associated with the nodes are sheng “vitality” and xing “punishment.” See Yates, “The Yin-Yang Texts from Yinqueshan,” 106.

177. Various dates for the formulation of the Zhuanxu system have been proposed, from 246 to 238b.c. Since, in this system, the beginning of the Epoch cycle is set at the Beginning of Spring of 366b.c. (a yimao year), it is thought that it was during the 120 years between this date and the first year of the First Emperor (246 b.c., also a yimao year)—that is, two complete sexagenary cycles—that Jovian astrology was progressively blended with the sexagenary year-count. I think that the Mawangdui Xingde texts correspond to an already well-advanced stage in the process of assimilation (see the discussion of Taiyin and the Jovian year count on pp. 148–54 above). For studies on the formulation of the Zhuanxu calendar in relation to recent discoveries, see the references cited in n. 67. See also Cullen, Astronomy and Mathematics in Ancient China, 27-28.

178. On the basis of the territorial and administrative divisions mentioned in the meteoromantic part of Xingde B, Liu Lexian sees the compilation of this part of the manuscript as dating to sometime between 304 and 284 b.c. (“Mawangdui Hanmu xingzhan shu chutan,”120). Since we do not know when the two parts of Xingde B were first joined as a single compilation, this dating is not decisive for the part devoted to the Xing-De method.

179. On the concept of position in early Chinese calendrical astrology, see Kalinowski, Marc, “Astrologie calendaire et calcul de position dans la Chine ancienne: Les mutations de l'hémérologie sexagésimale entre le IVe et le Ile siècle avant notre ère,” Extrême-Orient Extrême-Occident 18 (1996), 71–113 CrossRefGoogle Scholar.

180. See above, p. 141 and n. 41.

181. See above, p. 14 and n. 36.

182. See the well-documented study by Frank, Bernard on hemerological practices in Japan, Kata-imi et Kata-tagae: Etude sur les interdits de direction à l'époque Heian (Tokyo: Maison Franco-Japonaise, 1958)Google Scholar.

183. See above, n. 170.