RATIONALE

Without knowledge of the absolute dates of Western Zhou, this study analyzes the relative relationship between complete inscription dates. The time interval between two complete inscription dates limits the lunar phase relationship between them. If the specialized terms of the dates satisfy the lunar phase relationship, then the dates are compatible, if not, then they are incompatible. Importantly, without knowledge of the length of each reign, the time interval between two dates can only be calculated under the assumption that they are from the same reign. Therefore, compatibility provides key information about whether dates can be placed in the same reign: dates belonging to the same reign must be compatible, whereas dates that are incompatible cannot be placed in the same reign.

Any number of inscription dates that are mutually compatible can be grouped together, and the resulting compatibility group represents a hypothetical reign containing all dates within the group. The total number of groups required to account for all complete inscription dates depends on how the specialized terms are interpreted. But regardless of how the terms are understood, the total number of compatibility groups cannot exceed the total number of Western Zhou kings, for there cannot be more reigns than there are kings.Footnote ⁵

The total number of Western Zhou kings is known with certainty and is independent of the absolute dates of Western Zhou. Therefore, if certain interpretations of the specialized terms fail to accommodate all complete inscription dates within the permitted number of compatibility groups, these interpretations can be confidently rejected as incorrect.

THE EVIDENCE

Excavated bronze inscriptions are reliable contemporaneous records and serve as the primary evidence for this study. Appendix A lists the inscriptions considered in this study, including all complete inscription dates (nos. 1–76) and incomplete inscription dates recording a regnal year (nos. 77–107), from bronzes published as of July, 2016. Appendix A also includes select inscriptions that provide helpful information (nos. 108–120). Henceforth, inscriptions will be referenced by their number in Appendix A.

Apart from using the ganzhi and lunar phase information of complete inscription dates to compute absolute dates, this study also considers auxiliary information inferred from the vessels and their inscriptions. Vessel shape and decor, calligraphy style, and inscription content provide an estimate of age, setting approximate bounds for the absolute dates of the vessels.Footnote ¹³ Some vessels mention the same individuals in their inscriptions, which limits the chronological distance between them. Certain vessels belong to separate donors from different generations of the same lineage, which defines their chronological order. In rare cases, inscriptions explicitly identify one or more Zhou kings, either as the recipient of sacrifice or as the ruling monarch, thus providing clues to which reigns the vessels may belong to.

Unlike with bronze inscriptions, errors, distortions, or outright forgery might have occurred during the compilation or transmission of texts, making them less reliable in general. Therefore, texts serve as secondary evidence and are only considered when the primary evidence cannot produce unique solutions. Texts that contradict archaeological evidence are disregarded.

The “Wu cheng” 武成, “Shao gao” 召誥, and “Bi ming feng xing” 畢命豐刑 chapters of Shang shu 尚書, as quoted in Han shu 漢書,Footnote ¹⁴ as well as the “Shi fu” 世俘 chapter of Yizhoushu 逸周書 all contain ganzhi and lunar phase information that can be used to compute absolute dates. The quoted chapters in Han shu are widely believed to be authentic Western Zhou texts,Footnote ¹⁵ whereas “Shi fu” is considered the most reliable chapter of Yizhoushu based on textual comparisons with oracle bone and bronze inscriptions.Footnote ¹⁶ Therefore, these texts will be considered, along with the pre-Qin history texts Chun qiu 春秋, Zuo zhuan 左傳, and Xinian 繫年 of the Tsinghua bamboo slips 清華簡.

Zhushu jinian 竹書紀年, or the Bamboo Annals, was recovered from a looted tomb in the third century c.e. The original work has been lost since the Song dynasty. Late Qing and modern scholars have reconstituted portions of the original text by collecting quotations from pre-Song books. This reconstituted text is known as the Ancient Text (guben 古本) version. The Modern Text (jinben 今本) version appeared in the Ming dynasty and contains a complete chronology of Western Zhou. There is longstanding debate over the authenticity of both versions.Footnote ¹⁷ However, even the proponents of the authenticity of the Modern Text version acknowledge that its chronology is inaccurate, therefore the Modern Text Bamboo Annals cannot be used for chronological reconstruction. On the other hand, the Ancient Text Bamboo Annals contains no known explicit conflicts with bronze inscriptions, in part due to its fragmentary nature. Therefore, this study will consider the Ancient Text version to the extent that it agrees with the archaeological evidence. Future mentions of the Bamboo Annals refer to the Ancient Text version unless otherwise specified.

Although Shi ji was completed in the Han dynasty, its various chapters preserve pre-Qin material accessible to Sima Qian 司馬遷. This information will be consulted if necessary. As a matter of principle, all evidence is accepted as is, allowing no modification.

A SIMPLIFIED CRITERION

Considering all possible combinations of the eighty complete inscription dates in Appendix A is prohibitively complex. To simplify the problem, the initial analysis focuses on complete inscription dates from the late stage of Western Zhou with high (>20) regnal years.

Late Western Zhou includes the reigns of Kings Li 厲王, Xuan 宣王, and You 幽王, as well as the Gonghe regency, which may have maintained a separate year count. According to Shi ji, King Li was expelled from the capital in his thirty-seventh year, the Gonghe regency established its own year count which lasted for fourteen years, King Xuan ruled for forty-six years, and King You ruled for eleven years.Footnote ¹⁸ The duration of the Gonghe regency as well as the reigns of Kings Xuan and You are also corroborated by other sources: Xinian states that the Gonghe regency lasted for fourteen years,Footnote ¹⁹ whereas Guo yu 國語 states that King You ruled for eleven years.Footnote ²⁰ The inscription of LaiFootnote ²¹ pan 逨盤 (no. 119) places the forty-second and forty-third year Lai ding 逨鼎 (nos. 75–76) firmly in King Xuan's reign,Footnote ²² showing that King Xuan reigned for at least forty-three years. Therefore, only King Xuan's reign, and possibly King Li's reign, can accommodate late Western Zhou inscription dates with high regnal years. Interpretations of the specialized terms that fail to accommodate these dates within two reigns can thus be rejected with high confidence.

A NEW END POINT

The complete inscription dates of Lai ding are firmly placed in King Xuan's reign, whose absolute dates are given in Shi ji. This offered a rare opportunity to directly probe the meaning of the associated specialized term, jishengba, using the absolute dates of Western Zhou. However, jishengba was found to be a few days before as well as after shuo, which is nonsensical.Footnote ²³ This result shows that Sima Qian's partial chronology of Western Zhou contradicts archaeological evidence and is thus unreliable.

Previous work all focused on reconstructing dates prior to 841 b.c.e., the first year of the Gonghe regency according to Shi ji. The dates of Lai ding now force this study to disregard Sima Qian's partial chronology and find a new end point for chronological reconstruction. Chun qiu records a solar eclipse in the year of King Ping's 平王 death,Footnote ²⁴ which modern astronomical methods date to February 22, 720 b.c.e.Footnote ²⁵ This firmly establishes 720 b.c.e. as the year of King Ping's death, and this year is chosen as the end point for chronological reconstruction, thereby including the entirety of Western Zhou as well as King Ping's reign within the scope of reconstruction.

CHUJI IS UNRELATED TO THE LUNAR PHASE

Although their exact meanings are disputed, there is general agreement that jishengba, jiwang, and jisiba describe the lunar phase. However, whether chuji describes the lunar phase is a subject of much debate. Chuji appears in the poem “Xiao ming” 小明 (Mao 207) from Shi jing 詩經: “From chuji of the second month [二月初吉] / I have passed through cold and heat [載離寒暑].” Both Mao's commentary (Mao zhuan 毛傳) and Zheng's notes (Zheng jian 鄭箋) interpret chuji as the new moon.Footnote ²⁶ However, the Qing scholar Wang Yinzhi 王引之 questioned this interpretation, proposing instead that chuji refers to an auspicious day within the first ten days of the lunar month,Footnote ²⁷ a view shared by some modern scholars.Footnote ²⁸ Under this interpretation, although chuji is semantically unrelated to the lunar phase, it is functionally related—chuji must be no more than nine days after the lunar phase marking the start of a new calendar month. On the other hand, Wang Guowei argued that chuji spanned the seven to eight days from shuo to the first quarter (inclusive).Footnote ²⁹ Shinjō believed that the Western Zhou calendar month began with the first visibility of the waxing crescent, or fei 胐, and thus modified Wang Guowei's interpretations so that chuji began on fei and ended on the first quarter.Footnote ³⁰

Liu Yu 劉雨 analyzed the frequency of the four specialized terms in bronze inscriptions and found that chuji appeared in over 300 inscriptions throughout Western and Eastern Zhou, whereas the remaining three terms totaled only 114 appearances, of which 110 were in Western Zhou. Such stark contrast in distribution strongly suggested that chuji, unlike the remaining three terms, was not restricted to a particular period of the lunar month, and hence was not related, semantically or functionally, to the lunar phase.Footnote ³¹

The first year and third year Shi Dui gui 師兌簋 (nos. 4 & 13) can be confidently placed in the same reign based on their inscriptions, each of which includes a complete date using the term chuji. Ma Chengyuan calculated the relative lunar phase span between these two dates to be fourteen days (inclusive),Footnote ³² which is the minimal range of chuji if it describes the lunar phase. However, interpretations of chuji linking it to the lunar phase, semantically or functionally, only permit a maximum span of ten days, and are thus all rejected. Therefore, chuji is unrelated to the lunar phase and shall be omitted from subsequent analysis.

JISHENGBA, JIWANG, AND JISIBA: FOUR HYPOTHESES

Starting with Liu Xin, pre-modern scholars invariably proposed fixed-point interpretations for jishengba, jiwang, and jisiba, based on analysis of received texts. Wang Guowei was the first to systematically analyze bronze inscription dates, and he pioneered segmental interpretations for the specialized terms. He proposed that jishengba started the day after the first quarter and ended the day before the full moon, jiwang started on the full moon—or wang 望—and ended on the last quarter, and jisiba started the day after the last quarter and ended on the day before shuo—or hui 晦.Footnote ³³ Shinjō modified Wang Guowei's interpretations so that jishengba began on the day after the first quarter and ended on wang, jiwang began the day after wang and ended on the last quarter, and jisiba began the day after the last quarter and ended the day before fei.Footnote ³⁴

Although Wang Guowei's interpretations of the specialized terms became quite influential, alternatives have been proposed. Chen Jiujin proposed that jishengba starts on fei and ends on wang; jiwang is the day after wang; and jisiba starts the day after jiwang and ends the day before fei.Footnote ³⁵ Wang Shengli 王勝利 proposed that jishengba starts the day after fei and ends on wang; jiwang starts the day after wang and ends on the last day the waning crescent remains visible (hui or the day before hui); and jisiba starts on the first invisibility of the waning crescent (hui or shuo) and ends on fei.Footnote ³⁶ Wang Zhankui proposed that jishengba starts on fei and ends the day before wang; jiwang starts on wang and ends one or two days after the last quarter; and jisiba starts the day after jiwang and ends the day before fei.Footnote ³⁷ None of the alternative proposals treat chuji as a lunar phase.

The forty-second year and forty-third year Lai ding belong to the same reign. Both bear inscription dates using the term jishengba. Zhang Peiyu calculated their relative lunar phase difference to be eight days (exclusive).Footnote ³⁸ The relative lunar phase span of jishengba is thus nine days (inclusive), which exceeds the maximum range of the interpretations proposed by Wang Guowei or Shinjō (7–8 days). The relative lunar phase spans for jiwang and jisiba could not be analyzed due to the lack of appropriate material. Therefore, although Wang Guowei's and Shinjō's interpretations of chuji and jishengba have been rejected by archaeological evidence, their interpretations for jiwang and jisiba have not.

To summarize, four hypotheses regarding the interpretations of jishengba, jiwang, and jisiba can be formulated (Table 1). They will each be tested using the simplified criterion described in the previous section.

Table 1. Summary of Lunar Phase Hypotheses

KING XUAN

There are a total of ten common solutions for the inscription dates of Huan pan, Lai ding, and Jin Hou Su zhong between 900 and 800 b.c.e. (inclusive). These are candidates for King Xuan's yuan. Considering the rough time period of King Xuan, the most likely candidates are 841, 836, or 831 b.c.e. (the next available options, 867 and 810 b.c.e., are either too early or too late; see Table S4).

According to hypothesis C, determination of jishengba depends on observing the waxing crescent. The previous analysis permitted a lunar phase error of ±1 day for jishengba. However, a lunar phase error of −1 day for jishengba means that the waxing crescent was observed on the day of conjunction, when it should have been invisible—a highly unlikely scenario. Therefore, search results for jishengba dates with a lunar phase error of −1 are excluded, rejecting 831 b.c.e. as King Xuan's yuan.

Under hypothesis C, the range of jisiba is the most restrictive, lasting only three days from hui to the day after shuo, and up to five days allowing for lunar phase errors. Dates using jisiba are thus the most useful for restricting possible solutions. Xi Jia 兮甲 盤 pan (no. 28) is generally accepted as a vessel from King Xuan's reign, and its inscription date uses the term jisiba. If King Xuan's reign accommodates the inscription date of Xi Jia pan, then King Xuan's yuan can only be 836 b.c.e. Fixing King Xuan's yuan at 836 b.c.e. then places Jin Hou Su zhong in 804–803 b.c.e., which is consistent with radiocarbon dating results.Footnote ⁴⁴

KING LI AND THE GONGHE REGENCY

Yi gui and Bo Kuifu xu belong to King Li's reign. The inscription of Bo Kuifu xu records a regnal year of 33. Since King Xuan's yuan is 836 b.c.e., King Li's yuan must be no later than 869 b.c.e. If the Gonghe regency established a separate year count, then its first year would be 850 b.c.e. (fourteen years before King Xuan's yuan), and King Li's yuan must be no later than 883 b.c.e.

If King Li's yuan is before 883 b.c.e., it can be no later than 891 b.c.e. (Table S4). In this scenario, King Li would have ruled for at least forty-one years before the start of the Gonghe regency in 850 b.c.e. The justification for the Gonghe regency was that King Xuan was too young when King Li fled the capital, an unlikely scenario if King Li had already reigned for over four decades by then. Therefore, the Gonghe regency did not establish a separate year count, and King Li's yuan can only be 870, 875, or 880 b.c.e. (Table S4).

If the Gonghe regency is included in King Xuan's reign, it would constitute its first fourteen years. Xi Jia pan has been placed in King Xuan's fifth year. Its inscription states that “Xi Jia followed the king to behead, capture, and interrogate (enemy soldiers)” (兮甲從王折首執訊). The inscription implies that King Xuan personally led an army into battle, which would be unlikely if the king was so young that he required a regent. Therefore, the Gonghe regency should be included in King Li's reign, constituting King Li's final fourteen regnal years, from 850 to 837 b.c.e.

According to “Zhou benji” 周本紀, King Li was driven out of the capital in his thirty-seventh year. In “Wei Kangshu shijia” 衛康叔世家, this event occurred in Marquis Li's 釐侯 thirteenth year. “Wei Kangshu shijia” also states that Marquis Li's father, Marquis Qing 頃侯, bribed King Li's father, King Yi 夷王, to promote Wei's nobility rank from count (bo 伯) to marquis (hou 侯). However, Marquis Qing ruled for only twelve years,Footnote ⁵² which implies that King Li ruled for no more than twenty-four years before fleeing the capital, contradicting “Zhou benji.” King Li's dates in “Wei Kangshu shijia” likely reflect primary material available to Sima Qian that was related to the state of Wei, making this chapter more reliable than “Zhou benji,” whose dates are known to be inaccurate. If the Gonghe regency started in 850 b.c.e. and King Li fled the capital no later than his twenty-fourth year, then King Li's yuan can be no earlier than 874 b.c.e. Therefore, King Li's yuan must be 870 b.c.e.

VALIDATION

Thus far, a total of ten inscription dates have been used, with the help of Xinian, the Bamboo Annals, and Shi ji, to derive the absolute dates of Kings Li, Xuan, You, Ping, and Hui (of Xie). The remaining complete inscription dates from late Western Zhou can be used to validate the results. Due to complications related to intercalation, dates in the thirteenth month will be excluded from this process and analyzed separately. Omitting dates using the term chuji, there remain eleven inscription dates from the late period: those of Shi Xun gui 師訇簋, Ni zhong 逆鍾, Bo Lüfu xu 伯呂父盨, Shi X gui , Shi You pan 師酉盤, fifth year Shi Shi gui , Da gui 大簋, fifteenth year Da ding 大鼎, Bo Ke hu 伯克壺, Ci ding 此鼎, and Ma ding (nos. 2, 3, 8, 9, 22, 29, 43, 47, 49, 52, 55).

All dates can be accommodated by at least one of the reigns of Kings Li, Xuan, and You (Tables 3 and S6). Ni zhong and Shi You pan (nos. 3, 22) can be placed in the reign of King Xuan or You. Da gui, Bo Ke hu, Ci ding, and Ma ding (nos. 43, 49, 52, 55) fit in King Xuan's reign, whereas the fifth year Shi Shi gui and fifteenth year Da ding (nos. 29, 47) fit in King Li's reign.

Table 3. Summarized Chronology of Late Western Zhou

The inscription dates of Shi Xun gui, Bo Lüfu xu, and Shi X gui (nos. 2, 8, 9) are all in the first year and are compatible only with King Li's reign. However, the inscription date of Shi Xun gui requires that King Li's yuan begin in the month of zi (mo. error = 0), whereas the other two dates require King Li's yuan begin in the month before or after zi (mo. error = ±1; see Table S6). Therefore, these three vessels cannot all fit in King Li's yuan.

The inscription of Shi Xun gui quotes the king addressing the donor: “Woe! Shi Xun! Presently the angry terrors and disasters of Heaven have descended upon us. The virtue of the monarch is inadequate to rule. Thus, I did not succeed the deceased king. Previously, you, with a pure heart and anxiously concerned about the Zhou state, peacefully established my humble self” (師訇, 哀哉! 今日天疾威降喪, , 故亡承于先王. 鄉汝彶純卹周邦, 綏立余小子). Although there are alternative interpretations,Footnote ⁵³ this study adopts Peng Yushang's 彭裕商 interpretation of the phrase “wu chengyu xianwang” 亡承于先王 as “did not succeed the deceased king.”Footnote ⁵⁴ He Jingcheng 何景成 believes this phrase describes the succession of King Yi,Footnote ⁵⁵ who did not immediately succeed his father King Yih 懿王 but only became king after the death of King Xiao 孝王, with help from Zhou's vassals.Footnote ⁵⁶ Presumably, Shi Xun was one of the vassals who helped establish King Yi. Shi Xun gui is thus assigned to King Yi's reign, enabling Bo Lüfu xu and Shi X gui to be placed in King Li's yuan (Table 3).

All eleven dates have now been accounted for, validating the derived dates of Kings Li, Xuan, and You. However, since Shi You is associated with many vessels from the middle stage of Western Zhou, the placement of Shi You pan shall be reconsidered in the following section.

INITIAL ESTIMATES

The inscription of the fifteenth year Que Cao ding 趞曹鼎 (no. 48) states that “in the fifth month of the fifteenth year, jishengba, on the day renwu (19), King Gong was in the new palace of Zhou” (唯十又五年五月既生霸壬午, 龏王在周新宮). Therefore, King Gong ruled for at least fifteen years. In the Jun gui 畯簋 (no. 37) inscription, the king mentions his “exalted and illustrious father King Gong” (丕顯考龏王), thus identifying himself as King Yih, King Gong's successor. The inscription date of Jun gui is in the tenth year, meaning that King Yih ruled for at least ten years. The Bamboo Annals implies that Kings Yi, Mu, and Zhao ruled for a minimum of seven, thirty-seven, and nineteen years, respectively.Footnote ⁵⁹ King Xiao is assumed to have reigned for at least one year.

King Li's yuan is 870 b.c.e. Since King Yi's reign lasted at least seven years and must accommodate the inscription date of Shi Xun gui, King Yi's yuan must be no later than 879 b.c.e. (see Table S8). Consequently, the lower estimates of the yuan of Kings Xiao, Yih, Gong, Mu, and Zhao are 880, 890, 905, 942, and 961 b.c.e., respectively.

REFINEMENT

Of the inscription dates listed in Appendix A, four are found on vessels belonging to Qiu Wei 裘衛: Qiu Wei he 裘衛盉, fifth year Wei ding 衛鼎, ninth year Wei ding, and twenty-seventh year Wei gui 衛簋 (nos. 14, 26, 36, 64). The overall timespan of these vessels must be reasonable.

The inscription of the fifth year Wei ding mentions King Gong. Therefore, this vessel cannot precede King Gong's reign. The inscription date of the twenty-seventh year Wei gui is in the twenty-seventh year, and the only king in middle Western Zhou known to have a twenty-seventh year is King Mu. Therefore, the most reasonable placement of this vessel is in King Mu's reign. Taken together, Qiu Wei's four vessels should span the reigns of Kings Mu and Gong,Footnote ⁶⁰ and may possibly extend to King Yih's reign.

Shi Hu gui 師虎簋 and Hu gui 虎簋 (nos. 6, 67) are also thought to belong to the same person. The inscription date of Hu gui is in the thirtieth year, placing it most reasonably in King Mu's reign.Footnote ⁶¹ The inscription date of Shi Hu gui is in the first year (yuan). Considering its chronological distance from Hu gui, Shi Hu gui should be placed in the reign of King Mu, Gong, or Yih.Footnote ⁶²

The compatibility of the inscription dates of the Qiu Wei vessels, Hu vessels, and fifteenth year Que Cao ding were analyzed for the years between 990 and 890 b.c.e. (inclusive, the inscription dates of the fifth year Wei ding and Hu gui use the term chuji and were thus omitted). The inscription date of twenty-seventh year Wei gui is highly incompatible with that of Qiu Wei he, but highly compatible with that of ninth year Wei ding. On the other hand, ninth year Wei ding and Qiu Wei he share only four common solutions over 101 years, and in each case one or both dates contain a lunar phase error, displaying poor compatibility (Table S7). Therefore, ninth year Wei ding and twenty-seventh year Wei gui were both placed in King Mu's reign. Qiu Wei he was then placed in King Gong's reign, along with fifth year Wei ding, to minimize the total timespan of the Qiu Wei vessels. If King Gong's reign must accommodate both Qiu Wei he and fifteenth year Que Cao ding, then it cannot accommodate Shi Hu gui, which is placed in King Yih's reign instead.

King Mu's yuan is assumed to be no earlier than 970 b.c.e. Between 942 and 970 b.c.e., the inscription dates of ninth year Wei ding and twenty-seventh year Wei gui have five common solutions. If solutions with lunar phase errors are rejected, then possible candidates for King Mu's yuan are 947, 952, and 957 b.c.e.

King Mu reigned for at least thirty-seven years. Therefore, King Gong's yuan can be no earlier than 920 b.c.e. Between 905 and 920 b.c.e., the dates of Qiu Wei he and fifteenth year Que Cao ding have three common solutions: 906, 911, and 917 b.c.e. These are candidates for King Gong's yuan.

King Gong ruled for at least fifteen years. Therefore, King Yih's yuan can be no earlier than 902 b.c.e., and it must also accommodate the inscription date of Shi Hu gui. Possible candidates for King Yih's yuan thus include 899, 898, 894, 893, and 892 b.c.e. King Yih ruled for at least ten years, therefore King Xiao's yuan can be no earlier than 889 b.c.e.

Both dates of Hu ding 舀鼎 (no. 7a–b) are compatible with the inscription date of Shi Hu gui (Table S8). However, the Shi Hu gui inscription states that the king was in the great hall of shela (, 格于大室) on jiaxu 甲戌 (11), and Jing Bo 井伯 was the right-hand convoy who ushers Shi Hu into the king's presence. In contrast, in the Hu ding inscription, the king was in the great hall of King Mu's temple (王在周穆王大室) on yihai 乙亥 (12), and Jing Shu 井叔 was Hu's right-hand convoy. The two vessels are thus most reasonably placed in separate reigns,Footnote ⁶³ excluding Hu ding from King Yih's reign. The inscription dates of Hu ding are incompatible with King Gong's putative yuan of 906, 911, or 917 b.c.e., nor are they compatible with the inscription date of Shi Xun gui (Table S8), thus excluding Hu ding from the reign of King Gong or Yi. King Mu's temple is mentioned in the Hu ding inscription, excluding the vessel from King Mu's reign as well. Therefore, Hu ding is placed in King Xiao's reign.

In the inscription of Shi You gui 師酉簋 (no. 77), the king calls out Scribe Qiang 史牆 to command Shi You in writing. In the inscription of Shi You pan (no. 22), the king calls out Qiang to perform the same function. Zhang Changshou 張長壽 noted a high degree of similarity between the inscriptions of the two vessels, and identified Qiang in the Shi You pan inscription with Scribe Qiang in the Shi You gui inscription.Footnote ⁶⁴ Scribe Qiang is the donor of Scribe Qiang pan 史牆盤 (no. 118). Based on the inscription of this vessel, Scribe Qiang's lifetime spanned the reigns of Kings Gong and Yih.Footnote ⁶⁵ Therefore, Shi You gui and pan are most reasonably placed in the reign of King Gong or Yih. The inscription date of Shi You pan is incompatible with the putative yuan of King Gong (906, 911, or 917 b.c.e.), but highly compatible with the inscription date of Shi Hu gui (Table S8). Therefore, Shi You pan is placed in King Yih's reign, implying that Scribe Qiang lived at least until King Yih's fourth year.

Qiang's son is Xing (see n. 65), the donor of Xing xu (no. 21). The inscription of Xing xu states that the vessel was made for Xing's deceased father (用作文考寶簋), implying that Qiang had died at the time of inscription. Xing xu must therefore be later than Shi You pan. The inscription dates of both vessels are in the fourth year. However, the inscription date of Xing xu is in the second month, whereas that of Shi You pan is in the third month. Therefore, Xing xu cannot be placed in King Yih's reign along with Shi You pan, and must be placed in the reign of King Xiao or Yi.

In the Xing xu inscription, Sima Gong 司馬共 serves as Xing's right-hand convoy. Sima Gong also serves as right-hand convoy in the inscriptions of Shi Chen ding 師晨鼎, Shi Yu gui 師俞簋, and Jian gui 諫簋 (nos. 16, 17, 27). Moreover, in all four inscriptions, the king's reception takes place in Shi Lu palace 師彔宮. These common features strongly suggest that all four vessels are from the same reign.Footnote ⁶⁶ In the Shi Chen ding inscription, Shi Chen is commanded by the king to assist Shi Sufu 師俗父, who is identified with Bo Sufu 伯俗父 from the fifth year Wei ding inscription. Because fifth year Wei ding has been placed in King Gong's reign, the most reasonable placement of Shi Chen ding, Xing xu, Shi Yu gui, and Jian gui is in King Xiao's reign (Table 4).

Table 4. Summary of Individuals Mentioned in Inscriptions

SOLUTION

According to the inscription date of Shi Xun gui, the latest possible yuan for King Yi is 879 b.c.e. Since the inscription date of Jian gui is in King Xiao's fifth year, King Xiao's yuan must be no later than 884 b.c.e. (and also no earlier than 889 b.c.e.). Between 889 and 884 b.c.e., the dates of Hu ding and Xing xu have a unique common solution: 887 b.c.e. This is King Xiao's yuan (Table S8). King Xiao ruled for at least five years, meaning that King Yi's yuan is no earlier than 882 b.c.e. To accommodate the inscription date of Shi Xun gui, King Yi's yuan can only be 881, 880, or 879 b.c.e. (Table S8).

King Yih reigned for at least ten years. Therefore, King Yih's yuan must be no later than 897 b.c.e. (and no earlier than 902 b.c.e.). To accommodate the inscription date of Shi Hu gui, King Yih's yuan can only be 899 or 898 b.c.e. Notably, the Bamboo Annals states that the day dawned twice at Zheng (天再旦于鄭) in King Yih's yuan.Footnote ⁶⁷ Liu Chaoyang first interpreted this entry as a solar eclipse,Footnote ⁶⁸ and Pang Sunjoo 方善柱 further suggested that this eclipse was an annular eclipse occurring at dawn in central China in 899 b.c.e.,Footnote ⁶⁹ although the interpretation of the “double dawn” as the result of a solar eclipse is not universally accepted.Footnote ⁷⁰ However, since the possibility that the “double dawn” resulted from a solar eclipse cannot be completely excluded, this study favors 899 over 898 b.c.e. as King Yih's yuan.

King Gong ruled for at least fifteen years, meaning that his yuan must be no later than 914 b.c.e. Therefore, King Gong's yuan can only be 917 b.c.e. King Mu ruled for at least thirty-seven years, meaning his yuan must be no later than 954 b.c.e. King Mu's yuan thus can only be 957 b.c.e.

VALIDATION

Apart from the ten complete inscription dates used to derive the absolute dates of Kings Mu, Gong, Yih, Xiao, and Yi, Appendix A contains twelve additional dates from the middle period that are neither associated with chuji nor in the thirteenth month: those of Shi Ju gui 師遽簋, Da xu 達盨, Taishi Cuo gui 太師虘簋, Zou gui 走簋, Shi Shan pan 士山盤, Zouma Xiu pan 走馬休盤, Geng Ying ding 庚嬴鼎, Dian gui 典簋, Lu gui 䚄簋, Jin gui , Zuoce Wu he 作冊吳盉, and Xian gui 鮮簋 (nos. 17, 20, 40, 42, 51, 56–59, 65, 68, 73). These additional dates are used to validate the derived dates of middle Western Zhou (Tables 5 and S9).

Table 5. Summarized Chronology of Middle Western Zhou

All the dates except those of Dian gui, Lu gui, and Xian gui (nos. 58, 59, 73) could be accommodated by at least one of the reigns of Kings Mu, Gong, Yih, Xiao, or Yi (Tables 5 and S9). Notably, in the inscription of Xian gui, the king offers sacrifice to King Zhao in the capital (, 禘於昭王). Therefore, King Zhao must have died at the time of inscription. The inscription records a date in the thirty-fourth year, leading many to place the vessel in King Mu's reign.Footnote ⁷¹ However, the inscription date of Xian gui is incompatible with King Mu's derived yuan of 957 b.c.e.

If the thirty-fourth year in the Xian gui inscription is not King Mu's regnal year, then it can only be King Zhao's final year. In this scenario, King Mu had succeeded the throne after King Zhao's death, but had not yet started his own regnal year count. Indeed, the inscription date of Xian gui fits in the year before King Mu's yuan (Table S9), which puts King Zhao's yuan at 991 b.c.e. King Zhao's reign can accommodate the dates of Dian gui and Lu gui as well (Tables 5 and S9).

Thus, all twelve dates have now been accounted for, validating the dates of Kings Zhao, Mu, Gong, Yih, and Xiao. Additionally, 881 b.c.e. is chosen as King Yi's yuan to minimize the error.

ZHOU'S RECEIPT OF THE MANDATE

The Bamboo Annals counts exactly 100 years from Zhou's receipt of the Mandate to King Mu (see n. 58). From the text alone, it is uncertain whether the year count ends in King Mu's yuan or final year. However, the previous section determined that Kings Zhao and Mu reigned for thirty-four and forty years, respectively, whereas the reigns of Kings Cheng 成王 and Kang 康王 combined for at least forty years according to the Bamboo Annals.Footnote ⁷² The sum of these numbers already exceed 100. Therefore, the 100 years cannot include King Mu's reign, and thus must be counted to King Mu's yuan.

King Mu's yuan is 957 b.c.e. Counting backward 100 years yields 1056 b.c.e. by inclusive counting, which is the year that Zhou received the Mandate. Western Zhou texts and inscriptions always credit King Wen 文王 with receiving the Mandate, either alone or along with King Wu 武王. Therefore, King Wen must have been in power when Zhou received the Mandate.

KING CHENG

According to the Bamboo Annals, Kings Cheng and Kang maintained a period of prolonged peace totaling at least 40 years (see n. 72). Since King Zhao's reign started in 991 b.c.e., the last military operation in King Cheng's reign must be no later than 1031 b.c.e. “Bi shi” 費誓 records a speech given by the Marquis of Lu 魯侯 prior to a military campaign,Footnote ⁷³ which Shi ji attributes to Boqin 伯禽, the first Marquis of Lu and son of the Duke of Zhou.Footnote ⁷⁴ According to Shang shu, King Cheng was young when King Wu died. The Duke of Zhou thus ruled as regent and returned power to King Cheng in the seventh year. Boqin was established as marquis at the end of that same year.Footnote ⁷⁵ This means that Boqin's campaign, which can be no later than 1031 b.c.e., must also be no earlier than King Cheng's eighth year.Footnote ⁷⁶ Therefore, King Cheng's yuan must be no later than 1038 b.c.e. (and also no earlier than 1056 b.c.e.).

Han shu quotes two dates from “Shao gao”:Footnote ⁷⁷

These dates are presumed to be in the seventh year of the Duke of Zhou's regency, which is also King Cheng's seventh year. The first date uses the lunar phase term jiwang, which also appears in bronze inscriptions. However, whereas in bronze inscriptions jiwang governs nearly the entire second half of the month, in “Shao gao” it is clear from context that jiwang refers to a specific day. The reason for this discrepancy is unknown, and it is unclear which day jiwang refers to in “Shao gao.” Therefore, the first date is not used for calculation. The second date uses the lunar phase term fei, which is the first visibility of the waxing crescent, usually one or two days after conjunction. Since the meaning of fei is better understood, the second date is used to compute King Cheng's yuan. Between 1038 and 1056 b.c.e., King Cheng's yuan has a unique solution: 1042 b.c.e.

JIWANG IN TEXTS AND INSCRIPTIONS

If King Cheng's yuan is 1042 b.c.e., then the dates of “Shao gao” are in 1036 b.c.e., which is calendar year 115 of the reference calendar (Table S1). It is now possible to analyze and compare the lunar phases described by jiwang in “Shao gao” and in bronze inscriptions. The third month of calendar year 115 contains bingwu 丙午 (43) only if the year begins in the month of hai 亥 or chou 丑. In both cases, bingwu is two days after conjunction. The lunar phase of bingwu is fei, which is the day the waxing crescent is first sighted. This also implies that the waxing crescent was not observed the previous day (yisi 乙巳 [42]).

The visibility of the lunar crescent cannot be predicted with complete certainty. Instead, it is evaluated by empirical criteria derived from observational data. To date, multiple criteria have been proposed. This study adopts Odeh's criterion,Footnote ⁷⁸ which has been peer reviewed, and was derived from observations of both the waxing as well as waning crescent (Table S10, see Supplementary Text for details of implementation).Footnote ⁷⁹

If calendar year 115 begins with the month of hai, the visibility of the waxing crescent is uncertain for yisi of the third month (Table S10, Julian day number [JDN] 1343031+1). However, if the year begins with the month of chou, the waxing crescent is definitely visible on yisi (42) of the third month (Table S10, JDN 1343091+1). Therefore, in order for bingwu (43) to be the first visibility of the lunar crescent, the first month of calendar year 115 must be hai.

According to “Shao gao,” jiwang of the second month is gengyin 庚寅 (27). If calendar year 115 begins in the month of hai, then gengyin of the second month is the day after the full moon. Jiwang in “Shao gao” is thus the first day of the time period governed by jiwang in bronze inscriptions.

JISIBA IS AT THE BEGINNING OF THE MONTH

Wang Shengli proposed that the first day of jishengba marked the start of the calendar month, which would make fei the last day of the month (see n. 36). However, the dates of “Shao gao” do not support his hypothesis, as fei is clearly near the beginning of the third month. If the historical Western Zhou calendar was observational, then the calendar month could not have started with shuo. If the calendar day did not start at sunset, then the calendar month could not have started with fei. The only remaining option for the beginning of the month would be the first invisibility of the waning crescent, which is the first day of jisiba in bronze inscriptions.Footnote ⁸⁰

Computation of absolute dates in earlier sections assumed that the calendar month began with jishengba. Adjusting the beginning of the month to jisiba would not affect the results for inscription dates using jishengba or jiwang. For jisiba dates, this adjustment would only change whether the search results in the reference calendar differed from the inscription date by one month or not. Therefore, the previously derived dates remain valid.

KING KANG

Han shu quotes from “Bi ming feng xing” a date presumed to be in King Kang's reign:Footnote ⁸¹ “In the sixth month of the twelfth year, on the day gengwu (7), it was fei” (惟十有二年六月庚午朏). Additionally, the inscription date of the Lesser Yu ding 小盂鼎 (no. 60) is the sole remaining unused complete inscription date not associated with chuji or in the thirteenth month. The Lesser Yu ding inscription records the ruling king offering animal sacrifices to the Zhou Kings Wu and Cheng (用牲禘周王武王成王), which places the inscription date of Lesser Yu ding after King Cheng's death. Therefore, this vessel is believed to belong to the reign of King Kang or Zhao.

However, the dates of “Bi ming feng xing” and the Lesser Yu ding are incompatible (Table S11), therefore they cannot both fit into King Kang's reign. Notably, the inscription date of Lesser Yu ding is compatible with King Cheng's yuan. With the precedent of Xian gui, the possibility that the inscription date of Lesser Yu ding is in King Cheng's final year must be considered. However, if King Cheng ruled for twenty-five years, then King Kang's yuan must be 1017 b.c.e., which is incompatible with the date of “Bi ming feng xing.” Therefore, Lesser Yu ding cannot be placed in King Cheng's reign, and is instead placed in King Zhao's reign.

The Lesser Yu ding inscription records sacrificial and award ceremonies following a successful military campaign. Placement of this vessel in King Zhao's reign is thus consistent with the account in the Bamboo Annals of Kings Cheng and Kang presiding over a prolonged period of peace (see n. 72). Additionally, recent analyses of the style and content of the Lesser Yu ding inscription suggest that the vessel belongs to the middle period rather than the early period.Footnote ⁸² The placement of Lesser Yu ding one year after the middle period vessels Dian gui and Lu gui (nos. 58, 59, both in King Zhao's twenty-fourth year) is consistent with this view.

King Kang's yuan must be earlier than 991 b.c.e. (King Zhao's yuan) and later than 1036 b.c.e. (the end of the Duke of Zhou's regency). Possible candidates include 1000, 1005, 1010, and 1031 b.c.e. (Table S11). 1031 b.c.e. is discarded because it is too early, being only five years after King Cheng regained power. In Zuo zhuan, the Viscount of Chu 楚子 recounts the history of his state: “In the past our former king Xiong Yi, along with Lü Ji, Wangsun Mou, Xiefu, and Qinfu, all served King Kang” (昔我先王熊繹, 與呂彶, 王孫牟, 燮父, 禽父, 並事康王).Footnote ⁸³ Qinfu refers to Boqin, the first Marquis of Lu. Shi ji records the reign length of each ruler of Lu except Boqin.Footnote ⁸⁴ Based on this information, the yuan of Boqin's successor, Lord Kao 考公, is determined to be 1007 b.c.e. (see Table 9, details of derivation can be found below, in “Revising the Chronology of Shi Ji”). If Boqin served King Kang, then King Kang's yuan must be earlier than 1007 b.c.e., which can only be 1010 b.c.e.

ACCORDING TO THE BAMBOO ANNALS

The Bamboo Annals states that “In the eleventh year, gengyin (27), Zhou began its expedition against Shang” (十一年庚寅, 周始伐商).Footnote ⁸⁵ However, the text does not specify the starting point from which the eleventh year is counted. The Bamboo Annals contains three statements related to the total years of Western Zhou:Footnote ⁸⁶

By inclusive counting, King Cheng's yuan to King You's final year already spans 263 years (1042–780 b.c.e.). Therefore, the total duration of Western Zhou exceeds 257 years. However, the 257 years is alternatively described as the total years from King Wu's extermination of Shang (武王滅殷) to King You, which may not be equivalent to the total years of Western Zhou. A similar statement counting 100 years “from Zhou's receipt of the Mandate to King Mu” (see n. 58) was shown to end the year count in King Mu's yuan. If the 257 years are likewise counted to King You's yuan, then the year count would start in 1046 b.c.e. Notably, 1046 b.c.e. is also the eleventh year counting from the year Zhou received the Mandate (1056 b.c.e.).

Therefore, the Bamboo Annals suggests 1046 b.c.e. as the year of the conquest, and supports the traditional view that King Wen established a new yuan upon receiving the Mandate whereas King Wu continued using King Wen's calendar without establishing his own yuan.

ACCORDING TO “WU CHENG” AND “SHI FU”

Han shu quotes three dates from “Wu cheng”:Footnote ⁸⁷

“Shi fu” also contains three similar dates:Footnote ⁸⁸

Between the dates of “Wu cheng” and “Shi fu,” there are four specialized terms: pangsiba, pangshengba, jisiba, and jipangshengba. Among these terms, only the meaning of jisiba is somewhat known: in bronze inscriptions, jisiba governs the two to three days of the lunar cycle when the moon is invisible. However, in the cited texts, it is clear that jisiba refers to a specific day. Therefore, drawing on the example of jiwang in “Shao gao,” jisiba in “Wu cheng” and “Shi fu” is interpreted as the first day of the time period governed by jisiba in bronze inscriptions—the first invisibility of the waning crescent (i.e. hui or shuo). The second date is thus chosen to compute the year of the conquest. However, in order to effectively utilize this information, the dates of “Wu cheng” and “Shi fu” require further analysis.

The first date of “Wu cheng” and “Shi fu” differ significantly (the reason for this discrepancy will be discussed below). The second and third dates of “Wu cheng” and “Shi fu” are identical. However, the two dates seem to be in conflict. In the second date, jisiba of the second month is gengshen 庚申 (57). In the third date, jipangshengba of the fourth month is yisi 乙巳 (42), which is at least forty-five days (about a month and a half) after gengshen. Being jisiba, gengshen is at the beginning of the second month, which means that yisi cannot be in the fourth month (it should be around the middle of the third month). In addition, “Shi fu” documents multiple intervening dates between the second and third date, further complicating matters.

If the intervening dates in “Shi fu” are assumed to appear in temporal order, this results in a long interval of 105 days between the second and third date (Table 6; ganzhi dates are grouped by ten-day xun 旬 for convenience). It might have been this same information that prompted Liu Xin to insert an intercalary month between the second and third month in his attempt to reconcile the second and third date of “Wu cheng”: The insertion of an intercalary month results in a 105-day interval between gengshen and yisi. If gengshen is near the start of the second month, then yisi is in the fourth month.Footnote ⁹⁰ However, excavated bronze inscriptions indicate that the intercalary month was inserted at the end of the calendar year throughout Western Zhou, thus refuting Liu Xin's proposal.

Table 6. The Intervening Dates of “Shi Fu”: Long Interval Arrangement

Gu Jiegang 顧頡剛 and Zhou Fagao (Chou Fa-kao) 周法高 proposed that the fourth month in “Shi fu” is a mistranscription of the sixth month, caused by the similarity between the archaic forms of four () and six ().Footnote ⁹¹ However, if yisi (42) is in the sixth month and gengshen (57) is in the second month, then gengshen must be in the second half of the month, inconsistent with jisiba being at the beginning of the calendar month. Therefore, this proposal is rejected.

Chen Yigang 陳以綱 proposed that the first and second months of “Shi fu” and “Wu cheng” followed an ad hoc calendar that began when King Wu started his military campaign, whereas the fourth month followed the Zhou calendar with the calendar year beginning in the month of zi. Shaughnessy proposed a similar solution, assuming that King Wu established a new calendar and proclaimed the beginning of a new year in the month following his victory over the Shang.Footnote ⁹² Chen Yigang and Shaughnessy differ chiefly in their interpretation of jisiba: Chen Yigang follows Liu Xin's interpretation equating jisiba with shuo, whereas Shaughnessy uses Wang Guowei's interpretation. Shaughnessy's proposal is incompatible with the meaning of jisiba deduced by this study, and is thus rejected. On the other hand, Chen Yigang's proposal is compatible with this study.

Kong Guangsen 孔廣森 noticed that “Shi fu” separately documents two sets of sacrificial ceremonies occurring on xinhai 辛亥 (48) and yimao 乙卯 (52) (see Table 6, xun 6–7 and xun 12–13). He believed that, rather than document two sets of sacrifices sixty days apart, “Shi fu” recorded the same set of activities twice. Therefore, he combined these two sets of events, resulting in a short interval of forty-five days between gengshen (57) of the second month and yisi (42) of the fourth month (Table 7; the combined dates are shown in bold, and dates that are moved up compared to Table 6 are underlined).Footnote ⁹³

Table 7. The Intervening Dates of “Shi Fu”: Short Interval Arrangement

Kong Guangsen then proposed that gengshen was in the second month of the Shang calendar, whereas yisi was in the fourth month of the Zhou calendar. Tradition holds that the Shang calendar year began in the month of chou 丑 (containing the solar term dahan 大寒), whereas the Zhou calendar year began one month earlier in the month of zi. Gengshen in the second month of the Shang calendar is thus in the third month of the Zhou calendar, which is consistent with yisi being in the fourth month of the Zhou calendar, thereby resolving the conflict.

Alternatively, Huang Zhangjian 黃彰健 believed that the fourth month was simply a mistranscription of the third month, because the archaic character for four (亖) is very similar to the character for three (三).Footnote ⁹⁴ This proposal is disregarded to avoid altering the evidence.

So far, only the solutions proposed by Chen Yigang and Kong Guangsen are compatible with this study. Chen Yigang allows a long interval of 105 days, whereas Kong Guangsen permits only a short interval of forty-five days. A long interval assumes that the dates in “Shi fu” appear in chronological order. However, this premise is highly dubious. The first ganzhi date in “Shi fu” is yiwei (32) of the fourth month (四月乙未日). The last ganzhi date of the text is jiazi (1), the same day that King Wu defeated the Shang, which is in the second month according to the preceding text. These are clear examples of dates in “Shi fu” appearing out of chronological order. Therefore, the intervening ganzhi dates between the second and fourth month in “Shi fu” may be out of chronological order as well.

Shaughnessy argues that King Wu inspected the defeated troops of Shang at Muye 牧野 on jiayin 甲寅 (51) (in xun 7), implying that the first set of sacrifices on xinhai (48) and yimao (52) (Table 6, xun 6–7) occurred near the Shang capital and are therefore distinct from the second set of activities (Table 6, xun 12–13) that happened after King Wu returned to Zhou, precluding a short interval.Footnote ⁹⁵

However, the activity on jiayin was originally written as 謁我殷于牧野. The character 我 is believed to be the result of textual corruption. Lu Wenchao 盧文弨 changed this line to 謁戎殷于牧野, whereas Zhuang Shuzu 莊述祖 changed it to 謁伐殷于牧野.Footnote ⁹⁶ Regardless of the character chosen to replace 我, this line is commonly seen as documenting a sacrificial ceremony in which King Wu reports to his ancestors and Heaven that “the Shang were defeated at Muye.” In this context, the phrase “at Muye” (于牧野) describes the site of Shang's defeat, not King Wu's whereabouts on jiayin.

In fact, Li Xueqin argues that the first set of sacrifices must have happened in the Zhou temple. He points out that on the first xinhai (48) day (Table 6, xun 6), King Wu goes to the temple (格于廟), and reports the crimes of Shang (告殷罪) to his ancestors Tai Wang 太王, Tai Bo 太伯, Wang Ji 王季, Yu Zhong 虞仲, King Wen, and Yi Kao 邑考. Li Xueqin argues that the Shang temple is ill-equipped to host such a ceremony, because it would not have the required spirit tablets of the Zhou ancestors, and it is highly unlikely that King Wu would have brought the tablets with him on the campaign. Therefore, a ceremony involving so many ancestors could only be performed in the Zhou temple.Footnote ⁹⁷

Considering the overall evidence, this study adopts Kong Guangsen's proposal in favor of a short interval. In doing so, this study makes the additional assumption that the Shang calendar year began one month after the Zhou calendar year. Analysis of oracle bone inscriptions has been inconclusive regarding the beginning of the historical Shang calendar year.Footnote ⁹⁸ If future research demonstrates that the historical Shang calendar year did not begin one month after the historical Western Zhou calendar year, then Kong Guangsen's proposal should be rejected in favor of Huang Zhangjian's proposal.

According to “Wu cheng” and “Shi fu,” in the year of the conquest, jisiba of the second month of the Shang calendar year was gengshen (57). Therefore, shuo of the third month of the Zhou calendar year must be gengshen or xinyou 辛酉 (58). Between 1056 b.c.e. (Zhou's receipt of the Mandate) and 1042 b.c.e. (King Cheng's yuan), the reference calendar contains a unique solution: 1044 b.c.e.

RECONCILING “WU CHENG,” “SHI FU,” AND THE BAMBOO ANNALS

“Wu cheng,” “Shi fu,” and the Bamboo Annals appear to disagree on the year of the conquest. The Bamboo Annals suggests the conquest occurred in 1046 b.c.e., whereas the dates of “Wu cheng” and “Shi fu” suggest the conquest happened two years later, in 1044 b.c.e. Notably, according to Shi ji, King Wu led an initial campaign against Shang, but stopped short at Mengjin 盟津, where he met with 800 vassal lords (會八百諸侯) and held a military display (guan bing 觀兵) before returning to Zhou. Two years later, King Wu led a second expedition that overthrew the Shang.Footnote ⁹⁹ Could the Bamboo Annals be referring to King Wu's initial expedition?

The Bamboo Annals counts 257 years from King Wu's extermination of Shang to King You, arguing against 1046 b.c.e. as the year of the initial expedition (see n. 86). However, the statements related to the total years of Western Zhou in the Bamboo Annals are indirect quotes. This study showed previously that later authors mistook the end point of the 257-year count as King You's final year instead of his yuan. The starting point of the 257-year count may also have been misinterpreted.

Notably, the Bamboo Annals states that “Zhou began its expedition against Shang” (周始伐商; emphasis added) in the eleventh year (see n. 85), supporting 1046 b.c.e. as the year of the initial expedition. Therefore, to reconcile the Bamboo Annals with “Wu cheng” and “Shi fu,” and imitating the statement counting 100 years “from Zhou's receipt of the Mandate to King Mu” (see n. 58), the original statement related to the total years of Western Zhou is reconstructed as: “From Zhou's campaign against Shang to King You there were 257 years” (自周伐商至幽王二百五十七年).

Later scholars likely equated the “campaign against Shang” (fa Shang 伐商) with the “extermination of Shang” (mie Yin 滅殷), and thus expressed the starting point of the 257-year count as “King Wu's extermination of Shang.” Later scholars also likely further assumed that King Wu established yuan in the year of the conquest and further simplified the expression to “King Wu.” The year count was then assumed to end in King You's final year, leading to the belief that Western Zhou had a total of 257 years.

Therefore, this study concludes that 1046 b.c.e. is the year of King Wu's initial expedition, and 1044 b.c.e. is the year of the conquest. This conclusion supports the traditional narrative of King Wu holding a military display at Mengjin (觀兵孟津) two years before defeating Shang.

FURTHER ANALYSIS OF THE DATES OF “WU CHENG” AND “SHI FU”

According to the second date of “Wu cheng” and “Shi fu,” gengshen (57) of the third month (in the Zhou calendar) of the conquest year (1044 b.c.e., calendar year 107) is the first invisibility of the waning crescent, implying that the crescent was observed the day before, on jiwei 己未 (56). To accommodate the dates of “Wu cheng” and “Shi fu,” calendar year 107 must begin with the month of hai or chou (Table S1). In either case, the waning crescent is invisible on gengshen (57) (Table S10, JDN 1340108−1 and 1340167). On jiwei (56), the waning crescent is certainly visible if the year begins with the month of hai (Table S10, JDN 1340108−2), but may be invisible if the year begins with the month of chou (Table S10, JDN 1340167−1).

Therefore, the year of the conquest began with the month of hai. In this case, renchen (29) of the first month (in the Shang calendar, the second month in the Zhou calendar) was the day after the new moon, which is pangsiba according to “Wu cheng”; yisi (42) of the fourth month (in the Zhou calendar) was the day of the full moon, which is jipangshengba according to “Wu cheng” and “Shi fu” (Table S1).

“Wu cheng” states that King Wu left Zhou on guisi (30) and arrived in the outskirts of Shang on jiazi (1). But according to “Shi fu,” King Wu left on dingsi (54) and arrived seven days later on jiazi. Considering the distance from Zhou to Shang, the dates of “Wu cheng” are much more realistic. Therefore, the ganzhi and lunar phase of the first date of “Shi fu” are generally seen as erroneous. However, now that King Wu is shown to have led two expeditions against Shang, is it possible that the first date of “Shi fu” is in the year of the initial expedition instead of the conquest year?

If the first date of “Shi fu” was two years earlier than the dates of “Wu cheng,” it must have also used the Shang calendar. Since the first date of “Shi fu” and “Wu cheng” are both in the first month of the Shang calendar, they must be twenty-four or twenty-five months apart, assuming no consecutive intercalary years. The twenty-fourth month before the first date of “Wu cheng” (by exclusive counting) contains bingchen (53), which is the day before the full moon (Table S1). According to “Shi fu,” this day is pangshengba, which is one day before jipangshengba in the lunar cycle. The lunar phase relationship between pangshengba and jipangshengba thus agrees with the literal interpretation of jipangshengba as “after pangshengba,” supporting the placement of the first date of “Shi fu” in the year of the initial expedition, and showing that it is compatible with the dates of “Wu cheng.”

THE PLACEMENT OF MU GUI

The inscription date of Mu gui is seventh year, thirteenth month, jishengba, jiayin (51). The vessel is dated to the middle period of Western Zhou. In the inscription, the king calls out Interior Scribe Wu 内史吳, who also appears in Shi Hu gui inscription. Since Shi Hu gui has been placed in King Yih's reign, the most suitable placement for Mu gui is in the reign of King Gong or Yih.

King Gong's seventh year (911 b.c.e., calendar year 240) is an intercalary year in the reference calendar (Table S1). If that year begins with the month of hai or chou, the thirteenth month will contain jiayin, but it is five or six days after the full moon, far beyond the range of jishengba.

King Yih's seventh year (893 b.c.e., calendar year 258) is not an intercalary year in the reference calendar. However, if the seventh year begins with the month of zi and the eighth year begins with the month of chou, then the seventh year will have a thirteenth month containing jiayin, which is six days after the new moon, within the range of jishengba. Mu gui is therefore placed in King Yih's reign.

THE PLACEMENT OF WU HU DING

The inscription date of Wu Hu ding is eighteenth year, thirteenth month, jishengba, bingxu 丙戌 (23). The vessel is dated to late Western Zhou. In this time period, only Kings Li and Xuan have an eighteenth year. In the Wu Hu ding inscription, the king reiterates King Li's command () when enfeoffing Wu Hu with lands previously held by Wu Ying . Therefore, Wu Hu ding should be placed in King Xuan's reign.Footnote ¹⁰⁰

King Xuan's eighteenth year (819 b.c.e., calendar year 332) is an intercalary year in the reference calendar. If that year began with the month of zi, then the thirteenth month contains bingxu (23), which is two days after the full moon and slightly beyond the range of jishengba. The lunar phase error of the inscription date of Wu Hu ding thus exceeds the one-day limit imposed by this study. However, given the overall success of the derived chronology in accommodating complete dates from inscriptions and texts, it is highly unlikely that the interpretations of the specialized terms or the derived yuan of the Zhou kings are wrong. The lunar phase error of the inscription date of Wu Hu ding thus suggests that the Western Zhou calendar was not as accurate as assumed.

The stringent one-day limit for the lunar phase error is based on the belief that the Western Zhou calendar was observational.Footnote ¹⁰¹ The lunar phase error of the inscription date of Wu Hu ding is thus taken as evidence that the Western Zhou calendar no longer relied purely on observation by King Xuan's eighteenth year. The Lu 魯 calendar documented in Chun qiu used shuo as the start of the month, and it must therefore be computational. The inscription date of Wu Hu ding suggests that the transition from an observational calendar to a computational one was under way in the late stage of Western Zhou. In conclusion, Wu Hu ding is placed in King Xuan's reign despite the two-day error.

THE PROBLEM WITH CHUJI DATES

Liu Yu proposed that chuji was related to divination and could apply to any day of the month (see n. 31). However, this interpretation of chuji runs into problems upon further examination. The third and fourth dates of Jin Hou Su zhong (nos. 71c–d) are both in King Xuan's thirty-fourth year (803 b.c.e., calendar year 348). The third date is second month, jisiba, renyin 壬寅 (39), and the fourth date is sixth month, chuji, wuyin 戊寅 (15). If renyin is in the second month and wuyin is in the sixth month, then wuyin must be ninety-six days—about three months and seven days—after renyin. This means that wuyin must be near the beginning of the sixth month, whereas renyin must be near the end of the second month. The inscription dates of Jin Hou Su zhong thus appear to imply that jisiba is at the end of the month, contradicting “Shao gao,” which shows that fei—the last day of jisiba in bronze inscriptions—is near the beginning of the month.

The inscription dates of Hu gui and Zuoce Wu he (nos. 67–68) are both in the fourth month of King Mu's thirtieth year (928 b.c.e., calendar year 223).Footnote ¹⁰² To accommodate the inscription date of Zuoce Wu he (renwu 壬午 [19]), King Mu's thirtieth year must begin with the month of zi. As a result, the new moon of the fourth month is bingzi 丙子 (13), two days after the ganzhi of Hu gui's inscription date (jiaxu 甲戌 [11]). This means that, regardless of the position of jisiba in the calendar month, the fourth month of King Mu's thirtieth year does not contain jiaxu. The inscription date of Hu gui thus cannot fit in King Mu's reign. Therefore, the interpretation of chuji must be reconsidered.

CHUJI, DIVINATION, AND THEORETICAL DATES

If chuji can describe any day of the month, the same day can always be alternatively described by jisiba, jishengba, or jiwang. Why, then, are some dates described by chuji, while others are described by their lunar phase? Chuji literally means “initially auspicious.” Is it possible that chuji indicates auspicious dates, whereas the other terms do not?

Complete inscription dates are frequently associated with formal ceremonies in which the king bestows prestigious titles and valuable gifts on the donor of the vessel. Received texts show that auspicious days for holding such events were selected with great care by divination. If chuji exclusively describes auspicious dates, then the dates of these formal ceremonies in bronze inscriptions should all use chuji. However, all four specialized terms appear in inscription dates associated with these ceremonies, suggesting that the terms can all describe auspicious dates. Therefore, auspiciousness does not explain the distinction between chuji and the other three specialized terms.

Yi li 儀禮 documents the process for selecting by divination an auspicious date for the minister's ancestral sacrificial ceremony (shaolao kuisi li 少牢饋食禮). Curiously, although this ceremony prefers days on ding 丁 or ji 己, the incantation invokes “the coming day (of) dinghai (24)” (來日丁亥). According to Zheng Xuan's 鄭玄 commentary, the ceremony is not always held on a dinghai 丁亥 day: If the coming dinghai day is not auspicious, then a subsequent auspicious day on ding will be chosen by divination.Footnote ¹⁰³ Pang Pu 龐朴 believed that, regardless of the true ganzhi of the day of the ceremony, the incantation invariably invoked the coming day of dinghai. Therefore, he argued that dinghai in the incantation is best understood as a general indication of auspiciousness rather than the actual ganzhi date of the ceremony, and he proposed that dinghai functioned as a theoretical date in this situation (i.e. the invoked ganzhi is not necessarily the true ganzhi).Footnote ¹⁰⁴

A high occurrence of dinghai in bronze inscription dates was first noticed by Wang GuoweiFootnote ¹⁰⁵ and later confirmed by systematic analysis of Shang and Zhou bronzes.Footnote ¹⁰⁶ The clear preference for dinghai prompted Pang Pu to propose that dinghai in bronze inscription dates may also function as a theoretical date, similar to its role in the incantation of the minister's ancestral sacrificial ceremony (see n. 104).

Five of the complete inscription dates used previously for chronological reconstruction are on dinghai (Shi X gui, Da gui, fifteenth year Da ding, Yi gui, and forty-third year Lai ding; nos. 9, 43, 47, 63, 76). All are true dates, suggesting that dinghai is not a theoretical date when associated with jishengba or jiwang (or, presumably, jisiba). This implies that, if dinghai can function as a theoretical date, it can only be associated with chuji. Chuji would thus appear to specifically indicate situations where dinghai functioned as a theoretical date.

Dinghai was likely not the only ganzhi that could function as a theoretical date, since different ceremonies had different ganzhi preferences: The king's ancestral sacrificial ceremony (di yu taimiao li 禘於太廟禮) preferred dinghai, the minister's ancestral sacrificial ceremony preferred days on ding or ji, the sacrificial ceremony to the god of soil (she 社) preferred days on jia 甲, and the suburban offerings (jiao 郊) preferred days on xin 辛.Footnote ¹⁰⁷ Presumably, the various ceremonies in the bronze inscriptions also had specific preferences for ganzhi. In principle, these preferred ganzhi could all function as theoretical dates in a manner similar to dinghai, and chuji may have specifically indicated this type of usage.

The inscription dates of Fan you 緐卣 (nos. 114a–b) offer a rare opportunity to analyze the true ganzhi of a chuji date. The Fan you inscription records two sacrificial ceremonies: “In the ninth month, chuji, on the day guichou (50), the lord performed the rong ceremony. Eleven days later, on xinhai (48), the lord performed the di and rong ceremonies in honor of Lord Xin” (唯九月初吉癸丑, 公肜祀. , 公禘肜辛公祀).

According to the inscription, the ceremony on xinhai occurred eleven days (inclusive) after the ceremony on guichou, which contradicts the ganzhi sequence. Chen Peifen 陳佩芬 suggested that the eleven days were counted from a hypothetical ceremony not mentioned in the inscription.Footnote ¹⁰⁸ However, this interpretation lacks supporting evidence. Li Xueqin points out that the true ganzhi of the first ceremony is xinchou 辛丑 (38) (calculated by counting eleven days [inclusive] back from xinhai [48]), and viewed guichou (50) as an inscription error.Footnote ¹⁰⁹ However, this mismatch between the true ganzhi and the inscribed ganzhi should be seen as evidence that the date in question is a theoretical date. Therefore, the inscription of Fan you shows that guichou can function as a theoretical date, just like what has been proposed for dinghai. Moreover, Fan you provides direct evidence that chuji can indicate theoretical dates.

Interpreting chuji as an exclusive indicator for theoretical dates resolves the difficulties related to the chuji dates of Jin Hou Su zhong and Hu gui, since the inscribed ganzhi is not the true ganzhi. The distinction between chuji and the other three specialized terms also becomes obvious: theoretical dates are indicated by chuji, whereas real dates are described by their lunar phase. Therefore, this new interpretation of chuji is accepted as the proper meaning of this term.

THE CHRONOLOGY OF LU

“Lu Zhougong shijia” 魯周公世家 states that King You died in Lord Xiao's 孝公 twenty-fifth year, and Lord Xiao ruled for twenty-seven years. However, in “Shi'er zhuhou nianbiao,” King You dies in Lord Xiao's thirty-sixth year and Lord Xiao dies in his thirty-eighth year.Footnote ¹¹³ This discrepancy is due to the inclusion of Boyu's 伯御 eleven-year reign in Lord Xiao's regnal year count, which seems unnecessary.

Why would Sima Qian include Boyu's reign in Lord Xiao's reign at the expense of consistency? The most likely explanation is that Sima Qian saw material that clearly documented King You's death in Lord Xiao's twenty-fifth year, but also explicitly recorded Lord Xiao's regnal year beyond thirty. Since Sima Qian was unaware of the seven-year gap between King You's final year and King Ping's yuan, he likely thought the material was contradictory, and “resolved” the issue by including Boyu's reign in Lord Xiao's reign.

Therefore, the chronology of Lu is revised by separating the eleven years of Boyu from Lord Xiao's reign, while maintaining the first year of the Gonghe regency as Lord Zhen's 真公 fifteenth year and preserving the reign lengths of Lords Zhen, Wu 武公, Yi 懿公, and Boyu as documented in “Shi'er zhuhou nianbiao.”

This study determined the first year of the Gonghe regency to be 850 b.c.e., now equated with Lord Zhen's fifteenth year. Lord Zhen died in his thirtieth year and was succeeded by Lord Wu in 834 b.c.e. Lord Wu ruled for ten years, thus placing Lord Yi's yuan in 824 b.c.e. Lord Yi ruled for nine years and was succeeded by Boyu in 815 b.c.e. Boyu ruled for eleven years, thus making Lord Xiao's yuan 804 b.c.e. King You perished in 780 b.c.e., which was indeed Lord Xiao's twenty-fifth year, as stated in “Lu Zhougong shijia.”

Lord Yin's 隱公 yuan is fixed at 722 b.c.e. by the solar eclipse of 720 b.c.e. If the reign length of Lord Hui 惠公 is maintained at forty-six years, then Lord Hui's yuan remains in 768 b.c.e. and Lord Xiao reigned for thirty-six years (Table 8; see Table S12 for complete chronology).

Table 8. Summary of Proposed Adjustments to the Chronology of Lu

Shi ji documents the reign lengths of all rulers of Lu with the sole exception of Boqin.Footnote ¹¹⁴ Based on this information, the yuan of Lord Zhen's predecessors (Lords Xian 獻公, Li 厲公, Wei 魏公, You 幽公, Yang 煬公, and Kao 考公) can all be derived (Table 9). The yuan of Lord Kao, Boqin's immediate successor, is 1007 b.c.e. This study has determined that Boqin was established as the first ruler of Lu in 1036 b.c.e. Assuming that his year count started the following year, Boqin ruled for twenty-eight years. The chronology of Lu is thus reconciled with the derived chronology of Western Zhou.

Table 9. The Derived Yuan of the Lords of Lu

THE CHRONOLOGY OF QI

According to “Qi Taigong shijia” 齊太公世家, the Gonghe regency started in the tenth year of Lord Wu's 武公 (of Qi) and Lord Yin of Lu was established in Lord Lí's 釐公 ninth year. Between Lords Wu and Lí there are Lords Lì 厲公, Wen 文公, Cheng 成公, and Zhuang 莊公. “Qi Taigong shijia” states that Lords Wu, Wen, Cheng, Zhuang, and Lí reigned for 26, 12, 9, 64, and 33 years, respectively, but curiously omits Lord Lì, who reigned for nine years according to “Shi'er zhuhou nianbiao.”Footnote ¹¹⁵ This suggests that Sima Qian altered Lord Lì's reign length.

Therefore, the chronology of Qi is simply revised by maintaining the first year of the Gonghe regency (850 b.c.e.) as Lord Wu's tenth year, and Lord Yin of Lu's yuan (722 b.c.e.) as Lord Lí's ninth year, while preserving the reign lengths of Lords Wu, Wen, Cheng, Zhuang, and Lí (Table 10; see Table S12 for complete chronology). Lord Lì's reign is thus lengthened to eighteen years in the revised chronology of Qi, which is now reconciled with the derived chronology.

Table 10. Summary of Proposed Adjustments to the Chronology of Qi

THE CHRONOLOGY OF WEI

According to “Wei Kangshu shijia,” King Li fled the capital in Marquis Li's 釐侯 thirteenth year.Footnote ¹¹⁶ Both Chun qiu and Zuo zhuan record Lord Huan's 桓公 death in Lord Yin of Lu's fourth year,Footnote ¹¹⁷ thus fixing Lord Huan's final year in 719 b.c.e. Between Marquis Li and Lord Huan there are Lords Wu 武公 and Zhuang 莊公. According to “Wei Kangshu shijia,” Marquis Li and Lords Wu, Zhuang, and Huan ruled for 42, 55, 23, and 16 years, respectively.Footnote ¹¹⁸ If the first year of the Gonghe regency is maintained as Marquis Li's fourteenth year, then then total years of these four rulers must be increased by nine. Since Marquis Li and Lord Wu ruled for 42 and 55 years, respectively, the extra nine years should be inserted in the reign of Lord Zhuang or Huan.

In “Wei Kangshu shijia,” Lord Zhuang took as wife a lady from Qi in his fifth year. He later took as wife a lady from Chen 陳, whose younger sister bore Lord Zhuang a son—the future Lord Huan. Afterwards, Lord Zhuang's concubine gave birth to Lord Huan's younger brother Zhouxu 州吁. In Lord Zhuang's eighteenth year, Zhouxu had come of age (zhang 長) and showed an interest in military affairs. Lord Zhuang thus put Zhouxu in command of an army.Footnote ¹¹⁹

The transmitted tradition suggests that adulthood for men began at the age of twenty in pre-Qin times.Footnote ¹²⁰ However, according to the narrative above, Zhouxu was less than thirteen years old in Lord Zhuang's eighteenth year. This inconsistency suggests that the extra nine years should be inserted in Lord Zhuang's reign.

To revise the chronology of Wei, the first year of the Gonghe regency (850 b.c.e.) is maintained as Marquis Li's fourteenth year, and the final year of Lord Huan is kept as Lord Yin of Lu's fourth year (719 b.c.e.), maintaining Lord Huan's yuan at 734 b.c.e. The reign lengths of Marquis Li as well as Lords Wu and Huan are preserved. This adjustment lengthens Lord Zhuang's reign to thirty-two years (Table 11; see Table S12 for complete chronology). Lord Zhuang's marriage to the lady of Qi is maintained in his fifth year (762 b.c.e.), and Zhouxu's coming of age remains six years before Lord Huan's yuan, now in Lord Zhuang's twenty-seventh year (740 b.c.e.). Zhouxu can thus be twenty years old when he comes of age, consistent with tradition.

Table 11. Summary of Proposed Adjustments to the Chronology of Wei

THE CHRONOLOGY OF QIN

According to “Qin benji” 秦本紀, when King You was attacked by the Quan Rong 犬戎 in his final year, Lord Xiang 襄公 came to Zhou's aid. However, in “Shi'er zhuhou nianbiao,” Lord Xiang's yuan is 777 b.c.e.,Footnote ¹²¹ which is three years after King You's death in the chronology derived in this study (780 b.c.e.). Lord Xiang's dates in Shi ji are thus clearly inaccurate.

“Qin Benji” states that Lord Ning's 寧公 fourth year was the final (eleventh) year of Lord Yin of Lu, thus fixing Lord Ning's yuan in 715 b.c.e. Lord Ning's predecessor was Lord Wen 文公, who succeeded Lord Xiang and ruled for fifty years. It is unlikely that Lord Wen's reign can be lengthened. Moreover, “Qin benji” states that Lord Xiang was the first ruler of Qin to be conferred a nobility title, in return for providing protection for King Ping's eastward move in 770 b.c.e.Footnote ¹²² Therefore, Lord Wen's yuan cannot predate 770 b.c.e., and is maintained at 765 b.c.e.

According to fragments of the original Bamboo Annals preserved in “Xi qiang zhuan” 西羌傳, Qinzhong 秦仲 was killed in King Xuan's fourth year, and Lord Xiang's elder brother was captured forty-five years later (in King You's third year) at Quanqiu 犬丘.Footnote ¹²³ Based on the derived chronology, Qinzhong died in 833 b.c.e. and Lord Xiang's brother was captured in 788 b.c.e.

Shi ji states that Lord Xiang's brother was captured in Lord Xiang's second year. If Lord Xiang's yuan is in 789 b.c.e., then Qinzhong's successor, Lord Zhuang 莊公, reigned for forty-three years (832–790 b.c.e.) before being succeeded by Lord Xiang. However, Lord Zhuang ruled for forty-four years according to Shi ji.Footnote ¹²⁴

This one-year discrepancy can be explained by differences in the calendar used by the texts. According to Du Yu 杜預, the Bamboo Annals used the Xia calendar, which starts the calendar year in the month of yin 寅 (containing the solar term yushui 雨水).Footnote ¹²⁵ On the other hand, “Qin benji” preserves primary sources from Qin, and presumably follows the Qin calendar, which begins the calendar year with the month of hai (containing the solar term xiaoxue 小雪).Footnote ¹²⁶ The Qin calendar year thus starts three months earlier than the Xia calendar year. Therefore, Lord Xiang's brother may have been captured near the end of the year in the Xia calendar, which was already in the next year in the Qin calendar, resulting in a one-year difference.

Lord Zhuang's reign length of forty-four years is thus preserved in the revised chronology, placing Lord Xiang's yuan in 788 b.c.e. Since Lord Wen's yuan is maintained at 765 b.c.e., Lord Xiang's reign is lengthened to twenty-three years. The reign lengths of Lord Zhuang's predecessors recorded in “Qin benji” are also assumed to be accurate and preserved in the revised chronology, thus completing the revision process (Table 12; see Table S12 for complete chronology).

Table 12. Summary of Proposed Adjustments to the Chronology of Qin

THE CHRONOLOGY OF JIN

Xinian, Guo yu, and “Zhou benji” all state that King Xuan was defeated at the Battle of Qianmu 千畝之戰 in his thirty-ninth year. However, “Jin shijia” 晉世家 states that this battle occurred in Marquis Mu's 穆侯 tenth year, which “Shi'er zhuhou nianbiao” places in King Xuan's twenty-sixth year.Footnote ¹²⁷ This discrepancy shows that the chronology of Jin in Shi ji is significantly distorted.

Xinian states that King Hui of Xie was killed in his twenty-first year.Footnote ¹²⁸ The Bamboo Annals also states that Marquis Wen of Jin 晉文侯 killed the Xie King 攜王 in the twenty-first year,Footnote ¹²⁹ but does not indicate whose calendar the “twenty-first year” belongs to. Du Yu suggests that the focus of the Bamboo Annals shifted to the Jin state following King You's death.Footnote ¹³⁰ According to Xinian, Marquis Wen was an early supporter of King Ping. As a text documenting history from the perspective of Jin, the Bamboo Annals was thus unlikely to use the Xie King's regnal years. Therefore, the twenty-first year in the Bamboo Annals can only belong to Marquis Wen's calendar, placing Marquis Wen's yuan in the same year as King Hui of Xie's yuan (779 b.c.e.), only one year after Marquis Wen's yuan given in Shi ji (780 b.c.e.).

According to Du Yu, throughout Xia, Shang, and (Western) Zhou, the Bamboo Annals only recorded events pertaining to the kings. Events in the Bamboo Annals unrelated to the kings all pertain to Jin, or Wei 魏 after Jin's dissolution. The events pertaining to Jin begin with events of Shangshu 殤叔, followed by those of Marquises Wen and Zhao 昭侯, followed by the events of Quwo Zhuangbo 曲沃莊伯 (see n. 125). Presumably, the focus of the Bamboo Annals shifted from the Zhou kings to the Jin marquises following the death of King You, implying that Shangshu reigned past King You's eleventh year.

However, if Marquis Wen's yuan is in the same year as King Hui of Xie's yuan, then Shangshu's final year is also the same year as King You's final year, suggesting that Shangshu did not reign past King You's eleventh year. This apparent conflict may reflect the difference between the Zhou and Xia calendars. The Zhou calendar year begins with the month of zi, whereas the Xia calendar year starts two months later in the month of yin. Therefore, if King You died early in his eleventh year, then it would have been before the start of Shangshu's final year, allowing Shangshu to reign past King You's death.

“Jin shijia” states that King Xuan died in Shangshu's third year,Footnote ¹³¹ suggesting that Sima Qian saw source material from Jin that documented the death of a king in Shangshu's third year. From the analysis above, this king must be King You. Shangshu's final year was thus his fourth year, in agreement with the length of Shangshu's reign given in “Jin shijia” (see n. 131). Shangshu's yuan is thus 783 b.c.e.

The inscription of Jin Hou Su zhong documents events spanning King Xuan's thirty-third and thirty-fourth year (804 and 803 b.c.e.). There is broad consensus identifying Jin Hou Su with Marquis Xian 獻侯,Footnote ¹³² based on the text of Shiben 世本 quoted in the Suoyin 索隱 commentary to Shi ji.Footnote ¹³³ Since Shangshu's yuan is 783 b.c.e., the yuan of Marquis Mu 穆侯, Shangshu's predecessor and Jin Hou Su's successor, must be between 802 and 784 b.c.e. (inclusive).

Which year between 802 and 784 b.c.e. is Marquis Mu's yuan? Of all the material accessible to Sima Qian, the chronological data of Lu were the most extensive. Sima Qian likely used the chronology of Lu as a reference frame to assemble “Shi'er zhuhou nianbiao.” Therefore, the correspondence between the regnal years of Jin and Lu may offer important clues for revising the chronology of Jin. In “Shi'er zhuhou nianbiao,” Marquis Mu's yuan is Lord Yi of Lu's fifth year (811 b.c.e.). This suggests that Sima Qian may have seen material that placed Marquis Mu's yuan in the fifth year of a certain lord of Lu. According to the revised chronology of Lu, 802 and 784 b.c.e. correspond to Lord Xiao of Lu's third and twenty-first year, respectively. Therefore, Marquis Mu's yuan is set to Lord Xiao of Lu's fifth year: 800 b.c.e.

The first year of the Gonghe regency (850 b.c.e.) is maintained as Marquis Jing's 靖侯 eighteenth year, and the reign lengths of Marquises Jing and Li 釐侯 are kept at eighteen years each. Consequently, the yuan of Marquises Jing, Li, and Xian are 867, 849, and 831 b.c.e., respectively. Marquis Xian's reign is lengthened from eleven to thirty-one years, whereas Marquis Mu's reign is shortened from twenty-seven to seventeen years. Marquis Xiao's 孝侯 yuan is maintained as Lord Hui of Lu's thirtieth year (739 b.c.e.), as documented in Zuo zhuan.Footnote ¹³⁴ The reign length of Marquis Zhao (Marquis Xiao's predecessor) is kept at six years, maintaining his yuan at 745 b.c.e. (Table 13; see Table S12 for complete chronology).

Table 13. Summary of Proposed Adjustments to the Chronology of Jin

THE CHRONOLOGY OF ZHENG

Shuijing zhu 水經注 cites the Bamboo Annals stating that Lord Huan of Zheng 鄭桓公 defeated Kuai 鄶 in Marquis Wen of Jin's second year. Fang Shiming and Wang Xiuling also noted that the commentary to Han shu quotes Zan 瓚 stating that Lord Huan defeated Kuai two years after King You's demise. Zan is believed to have taken part in editing the original excavated slips of the Bamboo Annals, thus his statement was likely based on the Bamboo Annals as well.Footnote ¹³⁵ However, in “Shi'er zhuhou nianbiao,” Marquis Wen's second year is King You's third year. Therefore, Zan's statement apparently conflicts with the Bamboo Annals as quoted in Shuijing zhu. Moreover, “Zheng shijia” 鄭世家 states that Lord Huan perished alongside King You,Footnote ¹³⁶ which is incompatible with both the quotation from Shuijing zhu and Zan's statement.

However, in the revised chronology of Jin, Marquis Wen's second year is indeed two years after King You's death (Table S12), showing that Zan's statement and the quotation from Shuijing zhu are in fact compatible with each other. This result justifies the proposed revisions to the chronology of Jin, and further bolsters the reliability of the Bamboo Annals. The statement in “Zheng shijia” that Lord Huan perished alongside King You is rejected as inaccurate.

To revise the chronology of Zheng, Lord Huan's yuan is simply maintained at King Xuan's twenty-second year (815 b.c.e.), while the yuan of Lords Wu 武公 and Zhuang 莊公 are maintained at 770 and 743 b.c.e., respectively (Table 14; see Table S12 for complete chronology). Lord Huan's reign is lengthened to forty-five years.

Table 14. Summary of Proposed Adjustments to the Chronology of Zheng

The chronologies of Lu, Qi, Wei, Qin, Jin, and Zheng have now all been reconciled with the chronology of Zhou derived in this study.

UTILITY FOR CHRONOLOGICAL STUDIES

As this study demonstrates, the Ancient Text Bamboo Annals is fully compatible with bronze inscription dates. Moreover, in the process of derivation, apparent inconsistencies were all successfully resolved. Although these results cannot rigorously prove the reliability or authenticity of the Ancient Text Bamboo Annals, they nonetheless highlight the exceptional value of this text for chronological studies.

As even the proponents of the authenticity of the Modern Text Bamboo Annals acknowledge, the chronology contained in the Modern Text Bamboo Annals is inaccurate.Footnote ¹⁵¹ The absolute dates of Kings Xuan and You given in the text are identical to those given in Shi ji, which means that the Modern Text Bamboo Annals also contradicts the inscription dates of Lai ding (see n. 23). In addition, the Modern Text Bamboo Annals states that King Gong reigned for only twelve years, clearly contradicting the inscription of the fifteenth year Que Cao ding.Footnote ¹⁵² Moreover, the Modern Text Bamboo Annals documents a solar eclipse on the xinmao day of the tenth month of King You's sixth year,Footnote ¹⁵³ which is a clear reference to the solar eclipse of 776 b.c.e. Modern calculations show that this eclipse is invisible from Xi'an (see n. 142), therefore this entry in the Modern Text Bamboo Annals can only reflect calculations done by a later author, presumably based on the poem “Shiyue zhi jiao.” This entry must postdate Wang Ji of the Three Kingdoms period (220–280 c.e.), and likely postdates Yu Kuo of the Southern Liang dynasty (502–557 c.e.). Furthermore, this study shows that 776 b.c.e. is not even King You's sixth year.

It thus becomes apparent that the author or editor who produced the Modern Text Bamboo Annals was ignorant of the true dates of Western Zhou. The simplest explanation is that the Modern Text Bamboo Annals is a forgery, although the possibility that it contains authentic but distorted information cannot be strictly excluded. However, this possibility cannot be investigated in a reliable way without concrete knowledge of the true dates of Western Zhou. Therefore, the Modern Text Bamboo Annals cannot be used for chronological reconstruction.

THE ACCURACY OF INDIRECT QUOTES

The Ancient Text Bamboo Annals contains indirect quotes which must be treated with caution. It has long been assumed that the Bamboo Annals gave the total duration of Western Zhou as 257 years (see n. 86). However, this study shows that statements in the Bamboo Annals related to the total years of Western Zhou are indirect quotes that most likely misrepresent the original text. The 257 years should be counted from Zhou's initial expedition against Shang to King You's yuan (inclusive), whereas Western Zhou totaled 265 years (1044–780 b.c.e.).

The Bamboo Annals also contains a statement related to the total years of Xia: “From Yu to Jie there were seventeen generations, with and without kings, taking up 471 years” (自禹至桀十七世, 有王與無王, 用歲四百七十一年). Another statement is related to the total years of Shang: “From Tang's extermination of Xia to Shou (i.e. Zhòu), there were twenty-nine kings, taking up 496 years” (湯滅夏以至于受, 二十九王, 用歲四百九十六年). Other statements in the Bamboo Annals simply describe the 471 and 496 years as the total years of Xia and Shang, respectively,Footnote ¹⁵⁴ which is inconsistent with the Bamboo Annals also stating that Xia lasted longer than Shang.Footnote ¹⁵⁵ This inconsistency can be resolved by counting the 471 and 496 years to the yuan of Jie and Zhòu, respectively: If Jie's reign was at least 25 years longer than Zhòu's reign, then the Xia dynasty would be longer than the Shang dynasty.

Therefore, in the Bamboo Annals, the number of years “from time point A to King B” is always counted to King B's yuan. Notably, the Bamboo Annals also counts the number of years “from Pan Geng's relocation to Yin, to Zhòu's demise” (自盤庚遷殷, 至紂之滅).Footnote ¹⁵⁶ Although the text is unambiguous about the ending point of the year count, whether it accurately reflects the original text is unclear—considering other similar statements, the year count likely ends in Zhòu's yuan.