1. I adapt this homely example from Salmon, Wesley C., Scientific Explanation and the Causal Structure of the World (Princeton, N.J.: Princeton U. Press, 1984), 220Google Scholar, and I recommend that our critics study Salmon's discussion, which should lay to rest the misconception sometimes expressed (it has been said, in print, about my own work) that such “arguments to the best explanation” are circular. The credibility in the case at hand of any one of the four unreliable witnesses is established for the investigator by what each of the other three says; yet the investigator's confidence of the truth of what they all tell him depends, it seems, on his having concluded that in this case he can believe them. But the investigator's reasoning is not circular; quite the contrary: it is the agreement of the testimony that convinces him. (I am indebted to Professor Nancy Cartwright of the Stanford Philosophy Department for calling my attention to Professor Salmon's book.)

2. Even if the precise meaning is not agreed on, a lunar phase date can still serve to invalidate a proposed scheme of chronology; and sometimes, together with other evidence, it will show that a hypothesis cannot be avoided. E.g., the Shanfu Shan ding has a thirty-seventh year date, and in style must be a late King Xuan vessel. The rest of the date is “first month, chuji, day gengxu (47)”, Chuji must include at least the first quarter; but Xuan 37, if Xuan 1 = 827, is 791 B.C., whose first month must begin, approximately, either day 28 or 59; but if the calendar began with Xuan 1 = 825, then the date is 789, whose solstice month does begin with gengxu (47). This with much similar evidence makes the double-calendar (two-year calendar-break) hypothesis inescapable. Pankenier has made an epistemologically incorrect a priori decision that permits him to ignore this, and as a result his chronological reconstruction of Western Zhou before 841 does not have a single correct date.

3. For the meaning of the verb-phrase “cuo xing” 錯行, see Zhongyong 中庸 30, “pi ru si shi zhi cuo xing, ru ri yue zhi dai ming” 譬如四時之行, 如日月之代明, “like the alternating progress of the four seasons, like the successive shining of the sun and moon.”

4. The three of us agree that the lunar eclipse in 1065 (Yi Zhou shu, “Xiao kai”) and the conjunction of 1059 limit possible dates for the Conquest to the decade 1050–1040. Pankenier dated it 1046, rejecting lunar phase evidence and relying on the position of Jupiter as given in the Guoyu, “Zhou yu” 3.7. I have published an argument that that Guoyu paragraph was faked and interpolated in the first century B.C. (Ni Dewei 悅德 衛),” Guoyu ‘Wu Wang fa Yin’ tian xiang bian wei” 《國語》 “武王伐殷”天象辨僞, tr. K'e-wen, Wang 王竞文, Giwenzi yanjiu 古文字硏究 12 (10, 1985), 445–461)Google Scholar, and Shaughnessy and I both insist on the validity of lunar phase evidence, which limits possibilities to 1045 and 1040 (1040 fitting lunar phase dates slightly better).

5. Pang, Sunjoo (Shanzhu, Fang 方善柱), “Xi Zhou niandaixue shang di jige wenti”西周年代學上的幾個問題, Dalu zazhi 大陸雜誌 51.1 (1975), 1–9Google Scholar. Pang, K. D. (“Extraordinary Floods in Early Chinese History and their Absolute Dates”, Journal of Hydrology 96 (1987), 139–155)CrossRefGoogle Scholar has studied the problem independently, arriving at the same date, achieving an important advance in precision.

6. The end-of-Xia summary does not suffice to date interregnums, which are indicated in the “present text” only by implication from the ganzhi names of the first years of rulers. The summary gives the total of years “when there were kings and when there were not” (you wangyu wu wang 有王與無王); this suggests that the tomb text simply said at the end of a reign, wu wang ‥ nian,“ no king, so many years.”

7. Readers unused to mental exercise may wish to turn to Joseph Needham for assistance: Science and Civilization in China, vol. 3, Mathematics and the Sciences of the Heavens and the Earth (Cambridge: Cambridge U. Press, 1959), 247Google Scholar, where a method is shown from a Han text so simple that it could be thousands of years older. For an argument that some such methods were used as early as the third millennium B.C., see my “The Origin of the Chinese Lunar Lodge System,” in World Archaeoastronomy, ed. Aveni, A.F. (Cambridge: Cambridge U. Press, 1989), 203–218, esp. p. 210Google Scholar. My analysis implies that the Chinese as early as the third millennium B.C. must have had the working equivalent of a (perhaps crude) map of the zodiac band of stars, divided into both 28ths and 24ths (and 12ths). Pankenier would challenge this, as he shows in his n. 26: “Even in Babylonia where astronomical observation and accurate record-keeping in the second millennium B.C. were well in advance of the Chinese, the notion of a zodiac … did not make its appearance until about 700 B.C.”, citing B. L. van der Waerden. Actually, (1) no one knows whether the Chinese or the Babylonians were ahead in the second millennium B.C. and earlier; (2) Van der Waerden does not mention the Chinese in the article cited; (3) he actually says that the Babylonians had a zodiac no later than 700 B.C.; and (4) he also shows that the Greeks got their astronomy from the Babylonians, and adds that Eudoxus, middle fourth century B.C., used a zodiac with solstices and equinoxes located correctly for about 1000 B.C. Thus the Babylonians would seem to have had a zodiac at least as early as 1000 B.C.

8. Positions of Jupiter at certain dates mentioned in the Zuo zhuan can be used to estimate a terminus for the date of compilation, by finding a date an exact multiple of twelve years later, when Jupiter actually was at the location given. For example, at Xiang 28.1 (545 B.C.), the Zwo quotes a man as saying that “Jupiter is in Xing Ji, but is sneaking into Xuan Xiao.” This describes Jupiter's actual movement (12×17=) 204 years later, in 341. Other examples in the Zuo are consistent with this. Zhang Peiyu is mistaken, incidentally, in supposing that the ancients would have been unable to distinguish the stars in an asterism as narrow as the Fang asterism; it is a string of four stars more than ten degrees long (when declination is considered).

9. Zhang Peiyu (his #2, first paragraph) asserts that the Zhong Kang eclipse data in the (Jinben) Annals “obviously were based on” statements in the Dayan liyi by Yixing in the Tang dynasty. His argument provides no reason for not supposing that the reverse is the actual fact: i.e., that the “new calendar” picks up this information from the Annals. Yixing's not referring to the Annals proves nothing; he believed the “Yin zheng” chapter of the Shangshu to be authentic, and for him it was, of course, the important text to cite. (My interpretation of the Zuo for Zhao 17, sixth month, is designed for the Zuo text as it now stands. For a much fuller discussion of this complex problem, see Kevin Pang's response.)

10. Among other reasons for suspecting the Di Gui chronicle to be an early interpolation, notice that of the seventeen Xia kings, the first, ninth and seventeenth are spaced as follows: Yu 1 = 1989; Mang 1 = 1789; Di Gui 1 = 1589. The numeroiogist who arranged the chronology this way probably saw the whole dynasty as four-hundred years, the first two-hundred for the first eight kings, the second two-hundred for the second eight, the next year (which became Di Gui 1) being the beginning of Shang.

11. Shinzō, Shinjō 新城新藏, “Shu-sho no Nendai” 周初の年代, Shinagaku 支那學 4 (1928), 542–43Google Scholar.

12. Pei Yin in the fifth century A.D. commentary on the Shij, Shiji jijie, says at the death of Wei king Xiang in the “Wei shijia” that “Xun Xu says that He Qiao said that the Annals begins with Huang Di, Xun and He were both editors in the Jin court. Du Yu, returning from his service as a general in the South, and about to return to his work on the Zuo zhuan, inspected the recently discovered texts and said that the Annals began with Xia. It is possible (as has been suggested) that there was a chronicle starting with Huang Di that was attached to the Annals but not a part of it. The crucial question is whether this earlier chronicle was part of the tomb's contents, and had a chronological system that was continuous with that in the Annals. Only the analysis of the contents of the pre-Xia parts of the Annals can determine this.

13. In my paper for the Xia Symposium, I have worked out corrected dates before Yu (taking Shun 14 as 1953, making Yao's last year his fifty-eighth [i.e., 1969] when his son was banished, and as before, assuming two-year breaks after deaths of rulers). It turns out that at this stage of the text (before 427 B.C.) the first year of Huang Di corresponded to 2287. Later, when the Di Gui chronicle was inserted and other changes were made pushing dates back, 2287 became Zhuanxu 13. (This is probably why the calendar came to be called the “Zhuanxu calendar.”) Thus, the Zhuanxu 13 entry has to be a very early interpolation, dictated by the requirement that the shangyuan year-date 2287 be kept fixed in absolute time (see 5.6). If my calculation in 5.5.3 is right, the shangyuan first day calculated at the time the interpolation was done (probably before 350 B.C.) would have been gengwu (7) rather than jisi (6); but the chronicle does not specify the day.