1. Dunjie, Yan 嚴敦傑, “Guanyu Xi-Han chuqi de shipan he zhanpan” 關於西漢初期的式盤和占盤, Kaogu 1978.5, 334–37Google Scholar; Difei, Yin 殷滌非, “Xi-Han Ruyin hou mu chutu de zhanpan he tianwen yiqi” 西漢汝陰侯墓的占盤和天文儀器, Kaogu 1978.5, 338–43Google Scholar; gongzuodui, Anhui sheng wenwu, “Fuyang Shuanggudui Xi-Han Ruyin hou mu fajue jianbao” 阜陽雙古堆西漢汝陰侯墓發掘簡報, Wenwu 1978.8, 12–25 Google Scholar (preliminary report with reproductions of the originals). For more recent photographs of the instruments, see Haichao, Liu 劉海超, “Fuyang bowuguan cangpin jianjie” 阜陽博物館藏品簡介, Wenwu tiandi 文物天地 2000.1, 35–36 Google Scholar.

2. On Liuren calendrical astrology, see n. 12 below.

3. Harper, Donald, “The Han Cosmic Board (shih 式),” Early China 4 (1978–1979), 1–10 CrossRefGoogle Scholar; Cullen, Christopher, “Some Further Points on the shih ,” Early China 6 (1980–1981), 31–46 CrossRefGoogle Scholar; Harper, Donald, “The Han Cosmic Board: A Response to Christopher Cullen,” Early China 6 (1980–1981), 47–56 CrossRefGoogle Scholar; Cullen, Christopher “The Han Cosmic Model: A Rejoinder to Donald Harper,” Early China 7 (1981–1982), 130–33Google Scholar.

4. Zhoubi suanjing 周髀算經. Further evidence on the filiation between the shi and Gaitian 蓋天 cosmography as described in the Gnomon of Zhou is provided in Cullen's translation of the classic: Astronomy and mathematics in ancient China: the jing, Zhou bi suan, Needham Research Institute Studies 1 (Cambridge: Cambridge University Press, 1996), 43–53 Google Scholar.

5. Needham's standard translation for shi is “diviner's board”. He has devoted considerable attention to the study of this instrument from several points of view; see Science and Civilisation in China, vol. IV.1 (Cambridge: Cambridge University Press, 1962), 261–69Google Scholar. As noted by Cullen, the English word “board” is not normally understood as having moving parts (“Some Further Points on the shih,” 41, n. 8). My own translation in this article is “mantic device”, a generic term that matches the Chinese zhanpan 占盤; see n. 29 below.

6. Another rather widespread translation for shi in Western scholarship starting from the 90s is “cosmograph”; see Field, Stephen, “Cosmos, Cosmograph, and the Inquiring Poet: A New Answer to the ‘Heaven Questions’,” Early China 17 (1992), 83–110 CrossRefGoogle Scholar.

7. For a general presentation of the rishu-type manuscripts, see Lexian, Liu 劉樂賢, Jianbo shushu wenxian tanlun 簡帛數術文獻探論 (Wuhan: Hubei jiaoyu, 2003), 27–98 Google Scholar. To this day, the daybooks that have received the greatest scholarly attention are those discovered in 1975 at Shuihudi (Hubei), tomb 11; see Lexian, Liu, Shuihudi Qin jian rishu yanjiu 睡虎地秦簡日書研究 (Taipei: Wenjin, 1994)Google Scholar; 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 Kalinowski, , “Les livres des jours (rishu) des Qin et des Han: la logique éditoriale du recueil A de Shuihudi (217 avant notre ère),” T'oung Pao 94 (2008), 1–48 CrossRefGoogle Scholar.

8. Ling, Li 李零, “‘Shi’ yu Zhongguo gudai de yuzhou moshi” ‘式’ 與中國古代的宇宙模式, Zhongguo wenhua 4 (1991), 1–30 Google Scholar; rpt. with changes, slight in Ling, Li, Zhongguo fangshu zhengkao 中國方術正考 (Beijing: Zhonghua, 2006), 69–140 Google Scholar.

9. Major, John, “The Five Phases, Magic Squares and Schematic Cosmography,” in Explorations in Early Chinese Cosmology, ed. Rosemont, Henry Jr., JAAR Thematic Studies 50/2 (Chico: Scholar Press, 1984), 133–66Google Scholar.

10. 爲了敍述的方便, 本書把式所代表的圖式簡稱為 ‘式圖’ (Zhongguo fangshu zhengkao, 69). Li Ling's focus on the term shitu was somehow in the air since it is incidentally used by Yan Dunjie when considering the possible filiation between the shi-devices from the early Han and the famous design appearing on one of the lacquered chests found in the tomb of the Marquis Yi of Zeng 曾侯乙 at Leigudun (Hubei, 433 B.C.E.); see Dunjie, Yan, “Shipan zongshu” 式盤綜述, Kaogu xuebao 1985.4, 448 Google Scholar.

11. 式占是以式，即一種模仿宇宙結構的工具進行占卜 (Zhongguo fangshu zhengkao, 30).

12. The locus classicus for shizhan being used to designate the three systems practiced by Tang court astrologers is Tang liudian 唐六典 (Siku quanshu 四庫全書 ed.), 14.30b–32a. On earlier evidence, see Dunjie, Yan, “Shipan zongshu,” 445–64Google Scholar. On the three classical systems of calendrical astrology, see Yoke, Ho Peng, Chinese Mathematical Astrology: Reaching out to the Stars (London: RoutledgeCurzon, 2003)Google Scholar. For evidence on shi-divination drawn from titles appearing in Sui and Tang bibliographical treatises, see Ling, Li, Zhongguo fangshu zhengkao, 87–92 Google Scholar.

13. The term “calendrical astrology” parallels that of “calendrical astronomy” used by specialists as a characterization of Chinese astronomical systems; see Sivin, Nathan, “Cosmos and Computation in Early Chinese Mathematical Astronomy,” T'oung Pao 55 (1969), 1–73 CrossRefGoogle Scholar; Cullen, , Astronomy and mathematics in ancient China, 92–101 Google Scholar.

14. Han shu (Beijing: Zhonghua, 1968), 30.1769Google Scholar. Xianmen could refer to Xianmen Gao 高, an obscure character from the Warring States. Relying on an anecdote quoted in the Tang dynasty encyclopedia Yiwen leiju 藝文類聚 (Shanghai: Shanghai guji, 1985), 75.1286Google Scholar, Yan Dunjie speculates that the Xianmen shi could represent an early form of the Taiyi system (“Shipan zongshu,” 446).

15. 式占在本質上是一種形式化了的星占術，或許是由於用了栻盤而稱為式占. Yang, Lu 盧央, Zhongguo gudai xingzhanxue 中國古代星占學 (Beijing: Zhongguo kexue jishu, 2008), 302 Google Scholar. The long section of Lu Yang's book devoted to shi-divination (298–523) includes, in addition to the three classical systems mentioned above, a description of the so-called Wind-Angle divination (fengjiao 風角).

16. Quoted in Cullen, , “Some Further Points on the shih,” 34 Google Scholar. The following list is a first attempt to define the basic features of calendrical (or “mathematical” according to Ho Peng-Yoke) astrology. The formalistic dimension of this kind of astrology lies in the fact that it has less to do with the position of celestial bodies in the sky than with the abstract time cycles and correlated space orientations that determine the periodic revolutions of the mobile entities proper to each system. For example, in the Dunjia system, the series of wandering spirits called the “Nine Stars” (jiuxing 九星) are not related to any particular celestial body.

17. The term youshen is not attested to in Han sources that commonly refer to this type of calendar spirits by using the generic term shen (spirits), though in the Huainanzi one finds the expression xi zhu shen 徙諸神 with a similar meaning; Huainan honglie jijie 淮南鴻烈集解, ed. Wendian, Liu 劉文典 (Taipei: Shangwu, 1974), 3.26bGoogle Scholar (“Tianwen xun” 天文訓).

18. A Tang dynasty occurrence of shipan is found in the Zhitian lu 芝天錄 quoted in Taiping guangji 太平廣記 (Beijing: Zhonghua, 1995), 78.495–96Google Scholar, in an anecdote showing Jia Dan 賈耽 (730–805) divining with a shi-device; see Dunjie, Yan, “Shipan zongshu,” 446 Google Scholar, for an attempt to identify the type of device used by the famous Tang statesman and geographer.

19. 佈式的工具叫式盤 (“Shipan zongshu,” 445).

20. Jingyou Taiyi fuying jing 景佑太乙福應經, Jingyou Dunjia fuying jing 景佑遁甲符應經, and Jingyou Liuren shending jing 景佑六壬神定經. On Yang Weide, see Yoke, Ho Peng, Chinese Mathematical Astrology, 6–8 Google Scholar. For an easy access edition to Yang's treatises, see Ling, Li and Lexian, Liu, Zhongguo fangshu gaiguan: Shifa juan 中國方術概觀: 式法卷 (Beijing: Renmin Zhongguo, 1993), 223–342 Google Scholar.

21. Jingyou Liuren shending jing (Zhongguo fangshu gaiguan ed.), 337–38. It may be added that the section on the manufacture of the device (“Shi zao shi” 釋造式), is placed near the end of the treatise (section 30 of 39 sections).

22. Jingyou Dunjia fuying jing (Zhongguo fangshu gaiguan ed.), 276. For the Taiyi system, we are told a similar story, in the Jingyou Taiyi fuying jing (Zhongguo fangshu gai guan ed.), 233, as well as in the earlier Taiyi jinjing shijing 太乙金鏡式經 (Zhongguo fangshu gaiguan ed.), 172 (attributed to Wang Ximing 王希明 of the eighth century).

23. The device is composed of (1) an inner ring with the compass needle, the eight trigram names and the eight gates (ba men 八門); (2) a middle ring with the trigram symbols, the eight gates, and the nine stars (jiu xing 九星); and (3) a square base divided into eight parts representing the eight directions (ba fang 八方) as well as the eight solar nodes (ba jie 八節). On those basic features of the Dunjia system, see Jingyou dunjia fuying jing, 276–77. For a modern Dunjia device with at least five rings made for generating all the specific configurations of the system, see Yoke, Ho Peng, Chinese Mathematical Astrology, 104 Google Scholar.

24. Yoke, Ho Peng, Chinese Mathematical Astrology, 45 Google Scholar. In his presentation of the Taiyi system, Yan Dunjie shows a diagram similar to the one reproduced by Yoke, Ho Peng, calling it perhaps more accurately “Taiyi shi-diagram” 太乙式圖; “Shipan zongshu,” 458 Google Scholar. It should be noted however that Ho cautiously avoids being too definite in his understanding of the term shi and refers to it by using indifferently such words as “board”, “system”, “cosmic board”, and “cosmic board system”.

25. Tang liudian, 14.32a.

26. There are presently six such devices; see Kalinowski, Marc, “Les instruments astrocalendériques des Han et la méthode Liuren,” Bulletin de l'École française d'Extrême-Orient 72 (1983), 309–419 CrossRefGoogle Scholar; Yan Dunjie, “Shipan zongshu”; and Ling, Li, Zhongguo fangshu zhengkao, 69–85 Google Scholar, for a general survey and a commented bibliography of previous studies. Reproduced in Fig. 2 are: on the right side, the lacquered Liuren device (square base: 9 cm) dating from the Wang Mang period, discovered at Mozuizi 磨咀子 (Wuwei, Gansu) in 1972, presently at the Gansu Provincial Museum; and on the left side, the bronze Liuren device (square base: 11.3 cm) of unknown provenance from the late Six Dynasties, presently at the Shanghai Museum.

27. The series of Monthly Generals are displayed on the disk in a clockwise direction, following the twelve branches: Shenhou 神后/zi-b1 子, Daji 大吉/chou-b2 丑, Gongcao 功曹/yin-b3 寅, and so on; see n. 34 below. For reports on the Fuyang findings, see n. 1 above.

28. This round lodge dial (yuanpan 圓盤) is commonly seen as being used in connection with the Dipper device; see Harper, , “The Han Cosmic Board,” 3 Google Scholar; Cullen, , “Some Further Points on the Shih,” 34 Google Scholar.

29. See Dunjie, Yan, “Guanyu Xi-Han chuqi de shipan he zhanpan,” 335–37Google Scholar; “Shipan zongshu,” 451–52.

30. For a reproduction and study of the diagram, see Kalinowski, Marc, “The Xingde 刑德 Texts from Mawangdui,” Early China 23–24 (1998–1999), 178 CrossRefGoogle Scholar. On the magic square of three in relation to the Fuyang Nine Palaces device, see Wen, Xing 邢文, Boshu Zhouyi yanjiu 帛書周易研究 (Beijing: Renmin, 1997), 103–10Google Scholar.

31. The diagram on the right side of Fig. 4 shows the elements inscribed on the surface of the Dipper device: x1, x2, x3 for the stellar lodges; I, II, III for the months (Monthly Lodges); s1, s2, s3 for the ten stems (gan 干); b1, b2, b3 for the twelve branches (zhi 支). The stems and branches run in a clockwise direction, whereas lodges and months are arranged counterclockwise.

32. For example, Southern Dipper (x8 nandou 南斗) is connected to the eleventh month (XI) because this is the month when the sun reaches the winter solstice according to the lunar-solar calendar current in those days. Similarly, Eastern Well (x22 dongjing 東井) represents the Monthly Lodge of the fifth month (V), the period of the year when the sun is in the summer solstice position. The same applies to the spring equinox (second month, II) when the sun dwells in Stride (x15 kui 奎), and to the autumn equinox (eight month, VIII) when the sun dwells in Horn (x1 jiao 角).

33. See Kalinowski, Marc, “The Use of the Twenty-Eight xiu 宿 as a Day-Count in Early China,” Chinese Science 13 (1996), 55–81 Google Scholar.

34. In the Liuren system, the Generals and the lunar months are both identified by the twelve branches (see n. 27 above); therefore the celestial position of the sun for a given month is understood as a branch-to-branch relationship. For example, if the divination concerns the eleventh month of the calendar year, the diviner will adjust his device in order to connect General Daji (celestial mansion chou-b2 which in theory includes not only the Monthly Lodge Southern Dipper [see n. 32 above] but also lodge x9 niu 牛, Ox) on the mobile disk to branch zi-b1 (monthly indicator, doujian, of the eleventh month) on the square base.

35. See yanjiusuo, Hubei sheng wenwu kaogu, “Yuanling Huxishan yihao mu fajue jianbao” 沅陵虎溪山一號墓發掘簡報, Wenwu 2003.1, 48–49 Google Scholar. The signs still visible in one of the boxes are bingzi 丙子 to gengchen 庚辰.

36. It is not excluded that the Huxishan device was used to play some sort of a game. Archaeological findings have provided several game boards bearing sexagenary signs or designs similar to those found on mantic devices; see n. 55 below, and Xueqin, Li 李學勤, “‘Boju zhan’ yu guiju wen” ‘博局占’ 與規矩紋, Wenwu 1997.1, 49–51 Google Scholar; Ling, Li, Zhongguo fangshu zhengkao, 132–39Google Scholar; Loewe, Michael, Ways to Paradise: The Chinese Quest for Immortality (London: George Allen and Unwin, 1979), 75–85 Google Scholar. For a fascinating recent discovery, see Fengchun, Huang 黃風春 and Guosheng, Liu 劉國勝, “Zuozhong sanhao Chu mu chutu de qiju wenzi ji yongtu chukao” 左冢三號楚墓出土的棋局文字及用途初考, in yanjiusuo, Hubei sheng wenwu kaogu, Jingmen Zuozhong Chu mu 荊門左冢楚墓 (Beijing: Wenwu, 2006), 227–32Google Scholar.

37. The basic applications of the Fuyang “lodge dial” suggested by Cullen in his Early China 7 article (“Some Further Points on the Shih,” 34–36) may also account for those of the Dipper device.

38. See n. 32 above for the connection in Han times between the Monthly Lodges and the four critical periods of the year (solstices and equinoxes). As a result, when the sun dwells in Stride (x15) in the early evenings of the second month (spring equinox), Dipper's handle will point towards east (branch mao-b4); by the same token, it will point towards south during the summer solstice evenings (fifth month, branch wu-b7), towards west at the autumn equinox (eight month, branch you-b10), and north at the winter solstice (eleventh month, branch zi-b1).

39. 斗柄東指天下皆春, 斗柄南指天下皆夏, 斗柄西指天下皆秋, 斗柄北指天下皆冬; Heguanzi huijiao jizhu 鶡冠子彙校集注, ed. Huaixin, Huang 黃懷信 (Beijing: Zhonghua, 2004), 5.76Google Scholar (“Huan liu” 環流).

40. Harper, , “The Han Cosmic Board,” 2–5 Google Scholar; “A Response to Christopher Cullen,” 52–56.

41. See bowuguan, Hubei sheng Jingzhoushi Zhouliangyuqiao yizhi, Guanju Qin Han mu jiandu 關沮秦漢墓簡牘 (Beijing: Zhonghua, 2001), 104–17Google Scholar. The slips can be divided into five sections: (a) the twelve months and the twenty-eight stellar lodges arranged according to the Monthly Lodge system, (b) a list of the stems and branches as orientation marks (c) a diagram (Fig. 7) showing a Day Court diagram in the centerand a division of the day into twenty-eight units corresponding to the twenty-eight lodges, (d) prognostications for the twenty-eight lodges, (e) a method for finding the orientation of the Dipper (qiu dou shu 求斗術). For an interpretation of this group of slips, see Jinhua, Peng 彭錦華 and Guosheng, Liu, “Shashi Zhoujiatai Qin mu chutu xiantu chutan” 沙市周家臺秦墓出土線圖初探, Jianbo yanjiu 簡帛研究 2001, 241–50Google Scholar.

42. This is usually formulated as: yi yuejiang jia zhengshi 以月將加正時 (connect the Monthly General to the proper time of the day).

43. These expressions appear in the qiu dou shu section of the manuscript (slip 243); see n. 41 above.

44. yanjiusuo, Hubei sheng wenwu kaogu, Suizhou Kongjiapo Han mu jiandu 隨州孔家坡漢墓簡牘 (Beijing: Wenwu, 2006), 133–36Google Scholar (slips 49–77) for the list of predictions, and 136–37 (slips 78–89) for the double-entry table. Even though the text refers to the same basic elements as those in the Zhoujiatai manuscripts (stellar lodges, Monthly Lodges, hours of the day, the Dipper as a monthly indicator), the way they were used in prognosticating might have been quite different.

45. See Nianzu, Dai 戴念祖, “Qin jian ‘Lü shu’ de yuelü yu zhanbu” 秦簡 《律書》 的樂律與占卜, Wenwu 2002.1, 79–83 Google Scholar. For further references and debates, see Kalinowski, Marc, “Théorie musicale et harmonie calendaire à la fin des Royaumes combattants,” Études chinoises 30 (2011), 99–138 Google Scholar.

46. See Fig. 2; the thirty-six animals are placed in the outer cases of the square base, nine on each side. On this series of animals and their relation to the Six Dynasties Liuren device, see Loewe, , Ways to Paradise, 207 Google Scholar; Kalinowski, Marc, Cosmologie et divination dans la Chine ancienne: Le Compendium des cinq agents (Wuxing dayi 五行大義, VIe siècle) (Paris: École française d'Extrême-Orient, 1991), 107–8, 437–447 Google Scholar; Hiroko, Shimizu 清水浩子, “Sanjūroku kin shōkō” 三十六禽小考, in Yinyō gogyō no saiensi: Shisōhen 陰陽五行のサィエンス. 思想編, ed. Tokimasa, Takada 武田時昌 (Kyoto: Kyoto daigaku jinbun kagaku kenkyūjo, 2011), 87–99 Google Scholar.

47. Fig. 8 shows the Eastern quadrate of the Six Dynasties Liuren device reproduced in Fig. 2 (bottom part). In the column on the left, I have added the division of the day as indicated in the Six Dynasties Wuxing dayi, chapter 40 (“Lun sanshiliu qin” 論三十六禽): “The reason why there are three animals for each branch is that the day is divided into three parts, morning, afternoon, and evening.” (see Kalinowski, , Cosmologie et divination dans la Chine ancienne, 437)Google Scholar. In the Fangmatan daybooks, Tiger, Hare and Dragon are all morning animals; see yanjiusuo, Gansu sheng wenwu kaogu, Tianshui Fangmatan Qin jian 天水放馬灘秦簡 (Beijing: Zhonghua, 2009), 97–98 (slips 212, 215 and 218)Google Scholar.

48. The text is based on the new transcription of the Fangmatan Daybook B by Changgui, Yan 晏昌貴, “Tianshui Fangmatan Qin jian yizhong ‘Rishu’ fenpian shiwen (gao)” 天水放馬灘秦簡乙種 ‘日書’ 分篇釋文 (稿), Jianbo 5 (2010), 39 (slip 322)Google Scholar. As suggested by Prof. Yan (private communication), yi ri chen wei shi 以日辰為式 has been amended to yi wang chen wei shi 以亡辰為式.

49. If the term shi had to be translated, something like “basic pattern” or “configuration” in the sense of ju 局 would probably be the most suitable. Heguanzi, 5.154–55 (“Du wan” 度萬), has: “Five fives is twenty-five, thus is arranged the sub-celestial realm (yi li tian xia 以理天下); six sixes is thirty-six, thus is conceived the year pattern (yi wei sui shi 以為歲式).”

50. See Fig. 3 for the Nine Palace device; and “Yuanling Huxishan yihao mu fajue jianbao,” 49, for the reverse side of the Huxishan device where several small cord-hook diagrams are still visible. For other occurrences, see Kalinowski, , “The Xingde 刑德 Texts from Mawangdui,” 135–47Google Scholar.

51. “Formant un complexe de conditions emblématiques à la fois déterminantes et déterminées, le Temps et l'Espace sont toujours imaginés comme un ensemble de groupements, concrets et divers, de sites [fang 方] et d'occasions [shi 時].” (La pensée chinoise, Paris 1934 Google Scholar; rpt. Paris: Albin Michel, 1968), 79.

52. See n. 1 above for references concerning the Nine Palaces device. The Greek horoscope shows planetary positions among the zodiacal signs on 497 October 28; the different sectors of the diagram correspond to the twelve loci of classical Ptolemean astrology; reproduced and studied in Neugebauer, O. and Hoesen, H.B. Van, Greek Horoscopes (Philadelphia: The American Philosophical Society, 1987), 152–57 (and illustration #20)Google Scholar.

53. A valuable survey of all diagrammatic representations appearing in the excavated texts may be found in Ruxuan, Huang 黃儒宣, “Patterns of the Almanacs (Ri-shu)” 日書圖像研究 (Ph.D. dissertation, adviser Zhou Fengwu 周鳳五, National Taiwan University, 2010)Google Scholar. Even though the author deals with all types of diagrams and designs, cosmo grams (shitu) and their relation to the mantic devices are given special attention.

54. See Suizhou Kongjiapo Han mu jiandu, 144–46, for a reconstructed transcription of the original slips. In the first diagram explicitly named Riting 日廷 (Day Court), there are terms that appear to describe a kind of hemerological cycle otherwise unknown. For the second, the inscriptions are the twelve months arranged according to the “monthly indicator” (doujian) function of the Dipper; a short text inserted next to it (slips 129³–131³) specify the way to make auspicious or inauspicious predictions in relation to the orientations of the handle of the constellation (douxi 斗擊). Lastly, the third diagram shows the triangular relations between the twelve branches known as the “three unions” (sanhe 三合) pattern.

55. Preliminary report in bowuguan, Jingzhou diqu, “Jiangling Wangjiatai 15hao Qin mu” 江陵王家臺 15 號秦墓, Wenwu 1995.1, 42 Google Scholar. The diagram shown in Fig. 11 is based on a unpublished conference paper by Wang Mingqin 王明欽, “Wangjiatai Qin mu chutu de mushi” 王家臺秦墓出土的木式, plate 1. The coding for the stems, branches, stellar lodges and months is identical to that used for the Fuyang Dipper device (see n. 31 above). According to Wang Mingqin, a Liubo game pattern (boju wen 博局紋) appears on the reverse side of the board with badly damaged inscriptions identified as sexagenary signs (16cm × 14cm for the rectangle part, 6.5cm × 3.8cm for the handle), just as the wooden tablet of late Western Han found at Yinwan 尹灣; see Li Xueqin, “‘Boju zhan’ yu guiju wen” and n. 36 above.

56. See xiaozu, Mawangdui Han mu boshu zhengli, “Mawangdui boshu ‘Shifa’ shi wen zhaiyao” 馬王堆帛書《式法》釋文摘要, Wenwu 2000.7, 93 Google Scholar, for the “Shifa” cosmogram (plate 6, “Shitu” 式圖). The name originally given to the manuscript was “Zhuan shu yinyang wuxing” 篆書陰陽五行 (Seal script Yin-Yang and Five-Agents). For a color reproduction of the Yizheng board (square base: 21cm), see the inside front cover of bowuguan, Yizheng, “Jiangsu Yizheng Liuji Lianying Xi-Han mu chutu zhanbu qipan” 江蘇儀征劉集聯營西漢墓出土占卜漆盤, Dongnan wenhua 2007.6, and 19–22 Google Scholar for details. There are some minor variations between the two cosmograms.

57. When arranged clockwise (north-east-south-west), the branches are connected to the twelve lunar months according to the monthly indicator function of the Dipper (doujian). On the “Shifa” and Yizheng cosmograms, the first branch (zi-b1 子) is also connected to the eleventh lunar month (in the middle of the northern quadrate; see the lower part of Fig. 12), but the following branches move counterclockwise (north-west-south-east), in a “rightward” direction; see Wen, Xing, “Hexagram Pictures and Early Yi Schools. Reconsidering the Book of Changes in Light of Excavated Yi Texts,” Monumenta Serica 51 (2003), 595 CrossRefGoogle Scholar. It has been suggested that this counterclockwise arrangement could be related to the twelve Monthly Lodges on the Dipper device. This remains highly speculative because, if it was the case, branch zi-b1 (month XI) should have been connected to the preceding position which corresponds to its Monthly Lodge (Southern Dipper, x8, branch chou-b2); see Fig. 4.

58. Han shu, 30.1768; see n. 14 above.

59. 與 ‘式’ 的運作有關 (“Mawangdui boshu ‘Shifa’ shiwen zhaiyao,” 85).

60. See Fig. 12 and n. 56 above for references. Due to the ambivalence of the term shi, we don't really know if the authors meant that the use of this shitu cosmogram was somehow related to the operation of a specific device; see Wen, Xing, “Hexagram Pictures and Early Yi Schools,” 593–95Google Scholar. The change of the original title of the manu-script to Shifa has been questioned by several scholars; see Ling, Li, “Canjia “Xinchu jianbo guoji xueshu yantaohui” de jidian ganxiang” 參加 ‘新出簡帛國際學術研討會’ 的幾點感想 (http://www.jianbo.org; accessed on 12 30, 2000)Google Scholar; Changgui, Yan, Jianbo shushu yu lishidili lunji 簡帛數術輿歷史地理論集 (Beijing: Shangwu, 2010), 116 Google Scholar.

61. See Kalinowski, , “The Xingde 刑德 Texts from Mawangdui,” 193–95Google Scholar.

62. The diagram was first published in Juyou, Fu 傅擧有 and Songchang, Chen 陳松長, Mawangdui Han mu wenwu 馬王堆漢墓文物 (Changsha: Hunan chubanshe, 1992), 145 Google Scholar; for the reconstruction shown in Fig. 13 and identifications of the calendrical functions and wandering spirits inscribed in the thirty-six cases of the diagram, see Ling, Li, Zhongguo fangshu xukao 中國方術續考 (Beijing: Zhonghua, 2006), 250–52Google Scholar; see also Lexian, Liu, Jianbo shushu wenxian tanlun, 130–43Google Scholar.

63. In the middle section of the rectangle on the right-hand side of the diagram as reconstructed by Li Ling (Fig. 13). Next to it is xiaosui 小歲 which is another name for the Dipper as a monthly indicator (doujian).

64. Huainanzi 3.30a (“Tianwen xun”).

65. Han shu, 30.1768. For the competition between different hemerological methods in Western Han, see the famous anecdote preserved in Shi ji (Beijing: Zhonghua, 1959), 127.3222Google Scholar (“Rizhe liezhuan” 日者列傳); and Lexian, Liu, “Cong chutu wenxian kan ‘Shi ji—Rizhe liezhuan’” 從出土文獻看 ‘史記–––日者列傳’, Guwenzi yu gudaishi 古文字與古代史 1 (Taipei: Academia Sinica, 2007), 435–52Google Scholar.

66. For an attempt to classify the methods described in the Shuihudi daybooks according to their technical features, see Kalinowski, , “Les traités de Shuihudi et l'hémérologie chinoise,” 224–27Google Scholar.

67. Use of the word “hemerology” in Western scholarship has been mainly in Near Eastern studies where it designates the calendar based techniques of selecting auspicious time periods, and therefore is a ready-made translation for the Chinese art of selecting days (zeri or xuanze 選擇); see Labat, René, Hémérologies et ménologies d'Assur (Paris: Adrien-Maisonneuve, 1939)Google Scholar.

68. On the activities of the hemerologists (rizhe) in Qin and Han, see Lexian, Liu, “Cong chutu wenxian kan ‘Shi ji–Rizhe liezhuan’,” 436–41Google Scholar.

69. However, as pointed out by Cullen in his Early China article (“Some Further Points on the shih,” 46, n. 74), when Sima Qian writes that the Northern Dipper “turns in the center” (yun yu zhong yang 運于中央), he might have had in mind the idealized scheme of the shi.

70. On evidence for uses of sexagenary hemerology in the Shang oracle bones, see Keightley, David, The Ancestral Landscape: Time, Space, and Community in Late Shang China (ca. 1200–1045 B.C.) (Berkeley: University of California, Institute of East Asian Studies, 2000), 29–43 Google Scholar. Yang, Lu, Zhongguo gudai xingzhanxue, 298–99Google Scholar, describes the formation of calendrical astrology as a continuous process of change between observational astrology in early times to formalistic astrology in the Han.