1. See below, I.3.

2. See below, n.18.

3. See below, I.4.

4. See below, I.1–2.

5. See below, n.19.

6. See below, I.5.

7. See below, II–III.

8. I indicate the reign years according to the dukes of Lu, the months by a slash after the year (“Yin 1/5”: the first year of duke Yin’s rule, fifth month), the intercalary months by the letter R (“6R”: 6 run 閏, an intercalary month after the sixth month), and days in the sexagesimal cycle jiazi, yichou … renxu, guihai (ganzhi, Gassmann, 26) by figures in square brackets (“[1]”: jiazi; “[52]”: yimao, etc.). In conversions of dates into the Western calendar, the years are counted historically (without the year 0: “722 B.C.E.”), not astronomically (with the year 0: “–721”), and the days are counted according to the Julian calendar (see below, III 5). The Chun qiu and Zuo zhuan sections are indicated according to Bojun, Yang 楊伯峻, Chun qiu Zuo zhuan zhu 春秋左傳注, 2d ed., 4 vols. (Beijing: Zhonghua, 1990)Google Scholar. Yu, Du 杜預 is cited according to Shisan jing zhushu 十三經注疏, ed. Yuan, Ruan 阮元 (1815; reprint, Beijing: Zhonghua, 1980)Google Scholar.

9. Useful is Hoang, Pierre, Concordance des chrononologies néoméniques, 2d. ed. (Taichung: Kuangchi, 1968)Google Scholar, though he uses the Gregorian calendar for pre-Christian times (106, 305; cf. n.72 below). Hoang’s conversions of the cyclical day dates into Western dates are reliable, but his reconstructions of the month beginnings are not. The important article by Eberhard, Wolfram, Müller, Rolf, and Henseling, Robert, “Beiträge zur Astronomie der Han-Zeit I/II,” in Sitzungsberichte der preußischen Akademie der Wissenschaften, philosophisch-historische Klasse 1933 (1933), 209–29, 937–79Google Scholar (reprinted in Eberhard, Wolfram, Sternkunde und Weltbild im alten China, Gesammelte Aufsätze [Taipei 1970], 115–80Google Scholar) unfortunately relies at page 955 on Hoang’s month beginnings.

10. List at Legge, James, The Chinese Classics (1893–1895; reprint, Taipei: Southern Materials Center, 1985)Google Scholar III prol. 103f., V prol. 86f. (not all dates are correct). Not identifiable: Chun qiu, Xi 15.4: “Fifth month,” 645 B.C.E.; Chun qiu, Xuan 17.5: “Sixth month, [40],” May 15, 592 (see n.40 below); Chun qiu, Xiang 21.6: “Tenth month, [17], shuo,” September 19, 552 (see n.39 below); Chun qiu, Xiang 24.7: “Eighth month, [30], shuo,” July 18, 549; Chun qiu, Zhao 17.2: “Sixth month, [11], shuo,” June 23, 525. The records of the solstices (Zuo, Zhuang 29.4; Zuo, Xi 5.1; Zuo, Zhao 20.1) are worthless for calendar reconstruction as the Spring and Autumn astronomers were not able to establish precise days for them; for example, they recorded the winter solstice in Zuo, Xi 5.1 for the day [48] (December 25, 656), when in fact the solstice fell on December 27, 656.

11. See below, II.2.

12. Zuo, Xi 7.5 (Xi 7/12R); Zuo, Wen 1.2 n.f at Table 2; Chun qiu, Wen 6.9 (Wen 6/11R); Zuo, Cheng 17.12 (Cheng 17/12R); Zuo, Zhao 20.4 (Zhao 20/8R); Zuo, Zhao 22.5 (Zhao 22/12R); Chun qiu, Ai 5.6 (Ai 5/12R); Zuo, Ai 15.5 (Ai 16/12R, cf. Gassmann 84, 145 n.1218); Zuo, Ai 24.4 (Ai 24/12R). The text of Zuo, Xiang 9.6 (“Xiang 9/12R”) has been corrupted; see Legge V 440b–441a; Yang Bojun I.969; Gassmann, Antikchinesisches Kalenderwesen, 122n707.

13. See Gassmann, Antikchinesisches Kalenderwesen, 110n445.

14. See below II.1.

15. Of course, the new moon is not observable, but the first observation of the new moon’s crescent may indicate the month beginning; this was the method of the Romans before Caesar’s calendar reform. The Chinese probably only sometimes observed the full moon to calibrate their calendars; cf. Zuo, Wen 1.2 (see below, n.55).

16. Gassmann, , Antikchinesisches Kalenderwesen, 437, 441 Google Scholar.

17. Gassmann, , Antikchinesisches Kalenderwesen, 441 Google Scholar. To be precise, 235 synodic months add up to 6939^d 16^h 31^m 45^s or 6939.6887^d and are therefore longer than 19 tropic years (6939^d 14^h 26^m 34^s or 6939.6018^d) by 2^h 5^m 11^s or 0.0869^d. The small difference of 0.0869^d between lunar and solar cycle adds up to one full day only after 218 years and to one synodic month only after 6457 years and may be neglected for the time being (but see below, II.5).

18. Month intercalation has already been proved for the Yin, when intercalary months occurred during the year and at the end of the year. See Zungui, Chen 陳遵媯, Zhongguo tianwenxue shi 中國天文學史 (Shanghai: Shanghai renmin, 1980), I.203–04nn5, 9Google Scholar. The cycle 235:19 was known during the Han; cf. Eberhard et al., “Beiträge” (above n.9) I.217. Practically speaking, it existed as early as the Spring and Autumn period; see Zhongguo da baike quanshu 中國大百科全書, Tianwenxue 天文學 (Beijing: Zhongguo da baike quanshu, 1980), 277 “Runzhou” 閏周. Since Taichu 太初 1 (104 B.C.E.), the rule has been that the intercalary months of the 19-year-cycle are precisely those seven months during which the sun does not pass a zhongqi 中氣 point: “When the new moon day does not reach the zhongqi point [i.e., when shuo does not happen before the zhongqi transit], this is called ‘intercalary month’” 朔不得中， 是謂閏月 (Han shu 漢書 [Beijing: Zhonghua, 1962], 21a.984). The solar year is divided into 24 jieqi 節氣 “solar terms” ( Mathews, R.H., Chinese-English Dictionary, rev. American ed. [reprint, Cambridge/Ma.: Harvard University, 1966], 1178)Google Scholar, which are determined by the sun’s entry into the 24 points of ecliptic latitude λ = 0°, 15°, … , 345°. It is chunfen 春分 when the apparent course of the sun reaches the vernal point (λ = 0°), i.e., when it enters Aries, it is qingming 清明 when the sun reaches λ = 15°, and so on. Because the ecliptic points depend only on the sun’s course, their Western calendar dates are almost the same each year. The even points (0°, 30°, … , 330°) are called zhongqi 中氣 (they are identical with the beginnings of the zodiacal signs Aries, Gemini etc.), while the odd points (15°, 45°, … , 345°) are called jieqi 節氣. As each year has only 12 zhongqi-transits, during 19 years (235 lunar months, but only 228 zhongqi) there are seven lunar months lacking zhongqi-transits. Since 104 B.C.E., these months have been intercalary. Cf. Ginzel, F.K., Handbuch der mathematischen und technischen Chronologie I (Leipzig: Hinrichs, 1906), 474 Google Scholar; Zhongguo da baike quanshu, Tianwenxue, 69 “Ershisi jieqi” 二十四節氣, 223 “Luoxia Hong” 落下閎). This rule, requiring as it does a most precise knowledge of the ecliptic course, cannot have existed during the Spring and Autumn period; the intercalary months were inserted as occasion demanded and not always precisely.

19. See the outstanding work of Gu Donggao, originally published in 1748, Chun qiu dashi biao 春秋大事表 (Beijing: Zhonghua, 1993), 46–395 Google Scholar; James Legge (1815–1897), The Chinese Classics V prol. 93–97; Tao, Wang, Chun qiu lixue san zhong 春秋歷學三種 (Beijing: Zhonghua, 1959), 3–100, 139–54Google Scholar (on Wang’s life see Bauer, Wolfgang, Das Antlitz Chinas [München: Beck, 1990], 544ff.)Google Scholar; Hoang, , Concordance, 16–48 Google Scholar; Havret, H., Chambeau, , Hoang, Pierre, Mélanges sur la chronologie chinoise (Chang-Hai: Mission Catholique, 1920), 61–66 Google Scholar; Yang Bojun, Chun qiu Zuo zhuan zhu, passim. The reconstruction of Mo Feisi 莫 非斯, “Chunqiu Zhou Yin lifa kao” 春秋周殷歷法考, Yanjing xuebao 20 (1936), 263–329 Google Scholar, is useless; he presumed the intercalary months to have varied in length from 10 to 20 or 30 days.

20. According to the Julian calendar (see below, III.5). If the Gregorian calendar is extended backward, the dates of the transits were about November 21, December 21, and January 20.

21. See Zuo, Zhuang 29.4; Shi ji 史記 (Beijing: Zhonghua, 1959), 26.1258; Gassmann, , Antikchinesisches Kalenderwesen, 440 (not quite correct)Google Scholar.

22. A star rises four minutes earlier each day; if Antares is still seen rising after sunset on April 23 and is visible already risen at sunset on the evening of April 24, then it has “come out” (chu 出). This calculation of the last evening rising of Antares is based on Baehr, Ulrich, Tafeln zur Behandlung chronologischer Probleme (Karlsruhe: Braun, 1955)Google Scholar.

23. Gassmann, , Antikchinesisches Kalenderwesen, 440 et seq.Google Scholar; Legge V prol. 91.

24. Cf. Gassmann, Antikchinesisches Kalenderwesen, 105n336. Of course, we must acknowledge that various feudal domains used different calendars. For clues to these differences, see Tao, Wang, Chun qiu lixue san zhong, 102ff.Google Scholar; Zhongguo da baike quanshu, Tianwenxue, 283 “San zheng”. Cf. Gassmann, Antikchinesisches Kalenderwesen, 104n332; 112n490 (Jin calendar); 117n594 (Chu calendar); 90n41; 91n53; 98n211; 99n217 (Zheng calendar); 121n680 (Chen calendar). Zuo, Yin 3.3 (“In the fourth month, Zhaizu of Zheng … harvested the wheat at Wen” 四月, 鄭祭足 … 取溫之麥) suggests that the calendar of Zheng had a later year beginning than the calendar of Lu, since in the month Yin 3/4 (April 21–May 19, 719) the wheat was not yet ripe. Cf. Bojun, Yang, Chun qiu Zuo zhuan zhu, 27 Google Scholar; Shuye, Tong 童書業, Chun qiu Zuo zhuan yanjiu 春秋左傳研究 (Shanghai: Shanghai renmin, 1980), 267 Google Scholar.

25. Did the Yin calendar really exist? In my view, the sanzheng hypothesis is a result of Han scholasticism and a misunderstanding of the reference in Shang shu 尚書, “Gan shi” 甘誓 to sanzheng 三正, “three governing forces [Heaven, Earth and Man]”; see Karlgren, Bernhard, “Glosses on the Book of Documents,” Bulletin of the Museum of Far Eastern Antiquities 20 (1948), 168 Google Scholar; “The Book of Documents,” Bulletin of the Museum of Far Eastern Antiquities 22 (1950), 18 Google Scholar; and see Legge, Chinese Classics, V prol. 91.

26. See Donggao, Gu, Chun qiu dashi biao, 3f.Google Scholar; Bojun, Yang, Chun qiu Zuo zhuan zhu, 51 Google Scholar.

27. See above, n.26.

28. With only one exception; see below, II.5.

29. See above, I.3.

30. E.g., Gassmann, Antikchinesisches Kalenderwesen, 104n325: in Chun qiu, Xi 20.3, 乙巳 yisi [42] is a scribal error for 己巳 jisi [6].

31. Cf. below, n.55.

32. Gassmann, , Antikchinesisches Kalenderwesen, 437 Google Scholar.

33. See above, n.17.

34. Gassmann, , Antikchinesisches Kalenderwesen, 66 Google Scholar.

35. Gassmann, , Antikchinesisches Kalenderwesen, 445fGoogle Scholar.

36. Gassmann, Antikchinesisches Kalenderwesen, 125n769.

37. Eberhard, Wolfram, “Beiträge zur kosmologischen Spekulation in der Han-Zeit,” Baessler-Archiv 16 (Berlin 1933), 1ffGoogle Scholar. (reprinted in Eberhard, Sternkunde [above n.9], 11ff.), 93, thought that the non-existent solar eclipses were recorded deliberately to criticise the government in an indirect way; a solar eclipse was (according to Eberhard) Heaven’s warning in times of bad government. This might have been credible during the Han. But if Confucius really was the author of the Chun qiu, then to judge from everything we know about him, he would not have used eclipse records in this way, as he was more interested in earthly things (cf. Lun yu 11.12, Bojun, Yang 楊伯峻, Lun yu yizhu 論語譯注 [Beijing: Zhonghua, 1980], 113 Google Scholar “While you are not able to serve men, how can you serve the spirits? … While you do not understand life, how can you understand death?” 未能事人, 焉能事鬼? … 未知生, 焉知死?). And Zuo Qiuming 左丘明 showed sympathy for enlightened and rationalistic men: Han Jian 韓簡 opposed the view that Heaven influenced human fate (Zuo, Xi 15.4; 645 B.C.E.), citing the verses of Shi jing 詩經, “Shi yue zhi jiao” 十月之交 (Mao 193), in which the ominous effect of a solar eclipse was rejected (stanza 7): “The calamities of the inferior people do not descend from Heaven” 下民之孽, 匪降自天. Or read the words of Shen Xu 申繻 in Zuo, Zhuang 14.2: “Only when men abandon the constant path do portents arise; that is why there are portents” 人棄常, 則妖興, 故有妖.

38. Han shu 27c2.1491.

39. Cf. Theodor Ritter von Oppolzer, Canon der Finsternisse, Denkschriften der kaiserlichen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse, Band 52 (Wien, 1887), nr. 1588, plate 32.

40. Legge, Chinese Classics, V prol. 89; V.332.

41. See Oppolzer, Canon, nr. 1445; see the electronic program by Lohr, Alfred, Mikro-Planetarium 6.0 (Schallstadt: Lohr 1993)Google Scholar.

42. Gassmann, , Antikchinesisches Kalenderwesen, 241 Google Scholar.

43. Tao, Wang, Chun qiu lixue san zhong, 165, 177 Google Scholar; Bojun, Yang, Chun qiu Zuo zhuan zhu, 771 Google Scholar.

44. Gassmann, , Antikchinesisches Kalenderwesen, 56 Google Scholar.

45. There are only a few exceptions; see n.56.

46. See above, II.1; only Lu Huan 2 and Huan 10 have the notation.

47. 29.5^d; see above, I.3.

48. Gassmann, , Antikchinesisches Kalenderwesen, 448 Google Scholar.

49. Donggao, Gu, Chun qiu dashi biao, 83ffGoogle Scholar.

50. Tao, Wang, Chun qiu lixue san zhong, 8–9, 139, 162 Google Scholar.

51. Legge, Chinese Classics, III prol. 103, V prol. 86f.

52. Hoang, , Concordance, 18 Google Scholar.

53. Havret, , Chambeau, , and Hoang, , Mélanges sur la chronologie chinoise, 61 Google Scholar.

54. Bojun, Yang, Chun qiu Zuo zhuan zhu, 96f., 102 Google Scholar.

55. In my view, Wei Zhao 韋昭, cited by Pei Yin 裴駰 (Shi ji jijie 史記集解 at Shi ji 26.1259n5) hit the mark: “When at full moon the solar term is zhongqi, then the seasons and days, dusks and dawns are all corrected” 氣在望中, 則時日昏明皆正也. Thus the full moon (wang 望) gave the opportunity to calibrate. See also Chavannes, Édouard, Les mémoires historiques de Se-ma Ts’ien (Leiden: Brill, 1967), III.327n3Google Scholar; by way of contrast, see, e.g., Bojun, Yang, Chun qiu Zuo zhuan zhu, 510fGoogle Scholar. who thinks ju zheng yu zhong 舉正於中 refers to the equinoxes and solstices, not to the full moon.

56. See Gassmann, Antikchinesisches Kalenderwesen, 107n394. Elsewhere he has no scruples: Yin 10/6R; Wen 6/11R; Wen 9/9R; Xuan 2/6R; Cheng 14/6R; Xiang 2/5R; Zhao 20/8R; Zhao 28/6R; Zhao 30/6R; Ding 7/11R; cf. Tao, Wang, Chun qiu lixue san zhong, 108 Google Scholar.

57. Thus Zuo and Guliang 穀梁, Wen 1.2 (Shisan jing zhushu, 2404b); Gongyang 公羊, Wen 1.2 (Shisan jing zhushu, 2266a) additionally marks the day [60] as shuo (二月癸亥朔, 日有食之).

58. Shi ji, 26.1259.

59. Yu, Du, Shisan jing zhushu, 1832a Google Scholar; Donggao, Gu, Chun qiu dashi biao, 189 Google Scholar; Tao, Wang, Chun qiu lixue san zhong, 109 Google Scholar.

60. Antikchinesisches Kalenderwesen, 106n353.

61. The very few misprints are easily correctable and hardly worth mentioning. For instance, in note 267 on page 101, instead of [45] JD 1482175, the correct figure would be [48] JD 1482178; in column 10 on page 151 (June 9, –718) and elsewhere, the new moon time has not been printed completely.

62. Like Schram, Robert, Kalendariographische und Chronologische Tafeln (Leipzig: Hinrichs, 1908)CrossRefGoogle Scholar. Scaliger (1540–1609) had established a period that began on January 1, 4713 B.C.E. (= –4712; for the form of this notation, see below, III.5) at 12:00 noon Greenwich Time (Universal Time, UT; up to 1925 the astronomers reckoned the days from noon to noon UT to avoid changing dates during nightly observations). From this date, the time is reckoned without interruption; JD 0 lasts from January 1, 4713 B.C.E., 12:00 noon until January 2, 4713, 12:00 noon; January 2, 4713, 12:00 noon is JD 1.0.

63. Cf. Ginzel, , Handbuch (above, n.18), 99f.Google Scholar; Schram, , Tafeln, xiii Google Scholar; Neugebauer, Otto, A History of Ancient Mathematical Astronomy (Berlin: Springer, 1975), 1061, 1063fCrossRefGoogle Scholar.

64. Cf. von Oppolzer, Canon, nr. 1582 and plate 32; see the electronic program by Lohr, Mikro-Planetarium (above, n.41).

65. Antikchinesisches Kalenderwesen, 282.

66. Gassmann, , Antikchinesisches Kalenderwesen, 149–347, column 11Google Scholar.

67. Antikchinesisches Kalenderwesen, 101n267.

68. Shisan jing zhushu, 1794b.

69. On shi shuo 視朔, see Zhufeng, Luo 羅竹風 et al. ed., Hanyu da cidian 漢語大辭典 (Shanghai: Hanyu Da Cidian, 1992), 10.334f.Google Scholar; Bojun, Yang, Chun qiu Zuo zhuan zhu, 302 Google Scholar; and most modern translators: Yucheng, Shen 沈玉成, Zuo zhuan yiwen 左傳譯文 (Beijing: Zhonghua, 1981), 74 Google Scholar; Shouqian, Wang 王守謙 et al., Zuo zhuan quanyi 左傳全譯 (Guiyang: Guizhou renmin, 1990), 211 Google Scholar; Bojun, Yang et al., Baihua Zuo zhuan 白話左傳 (Changsha: Yuelu, 1993), 61 Google Scholar; Weiqi, Li 李維琦 et al., Shisan jing jinzhu jinyi 十三經今注今譯 (Changsha: Yuelu, 1994), 1092 Google Scholar; the English translation of Hu Zhihui 胡志揮 in Zhihui, Hu and Kejiong, Chen 陳克炯, Zuo’s Commentary/Zuo zhuan 左傳 (Changsha: Hunan renmin, 1996), 179 Google Scholar. But Chen Kejiong in the Chinese translation (Zuo’s Commentary, 178), Legge, Chinese Classics, V.144a, Couvreur, Séraphim, La chronique de la principauté de Lòu (Paris: Cathasia, 1951), 248 Google Scholar, and Yanjin, Zhang 張燕瑾, Wenbai duizhao quanyi Zuo zhuan 文白對照全譯左傳 (Beijing: Guoji wenhua, 1993), 185 Google Scholar, all understand the text as Du Yu did. The Manchu translation ( Bauer, Wolfgang, Tsch’un–ts’iu mit den drei Kommentaren Tso-Tschuan, Kung-yang-tschuan und Ku-liang-tschuan in Mandschuischer Übersetzung [Wiesbaden: Steiner, 1959], 175)Google Scholar, gung ice doroi wecehe manggi (“the duke, after having sacrificed according to the rites on the shuo-day”), hints at the sheep sacrifice during the gu-shuo-ceremony (cf. Lun yu 3.17 [ Bojun, Yang, Lun yu yi zhu, 29 Google Scholar] “the sacrifice of a living sheep at the inauguration of the first day of the month” 告朔之餼羊); here, too, gu shuo and shi shuo are confused.

70. See below, III.5a.

71. Antikchinesisches Kalenderwesen, 8; 148 No. 8; 349; and in the column heads, 350–429.

72. Because the Gregorian calendar has no February 29 for the years 901, 701, 601, 501, 301 B.C.E., etc., it was increasingly making up the difference, until it caught up with the Julian calendar on March 1, 200 C.E. (February 29, 200 C.E. jul. was still February 28, 200 C.E. greg.) and overtook it by March 1, 300 c.e. greg. (February 29, 300 C.E. jul.). So the solar eclipse of 720 B.C.E. (Chun qiu, Yin 3.1) occurred on February 14 according to Gregorian day counting (Legge V.12, Tao, Wang, Chun qiu lixue san zhong, 175 Google Scholar, Hoang, , Concordance, 16 Google Scholar, Eberhard, “Beiträge” [see above, n.37], 87ff.), and on February 22 according to Julian day counting ( Bojun, Yang, Chun qiu Zuo zhuan zhu, 23 Google Scholar).

73. Antikchinesisches Kalenderwesen, 450n9.

74. The German text, Antikchinesisches Kalenderwesen, 27n9, adds: “without the year o.”]