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Appendix III. Eclipses during the Reign of Emperor Wen
During this period, six eclipses were recorded in the SC and HS. We discuss them in chronological order.
i. In the second year, the eleventh month, on the day kuei-mao, the last day of the month, an eclipse was recorded (4: 8b). P. Hoang gives this date as Jan. 2, 178 B.C., on which Oppolzer calculated his solar eclipse no. 2447. This was a partial eclipse; calculation shows that at Ch'ang-an it reached a magnitude of 0.20 at 2:48 p.m., local time. The longitude of the sun was 279.0° = 278.2° R.A. HS 27 Cb: 13b says that it was one degree in the constellation Wu-nü, of whose stars ε and μ Aquarii were then in 281.7° and 283.0° R.A. respectively.
ii. In the SC, after the record of the above eclipse, there is the following statement (cf. Mh II, 461), "In the twelfth month, on the day of full moon [the fifteenth of the month], there was an eclipse of the sun." This date was, according to Hoang, Jan. 17, 178 B.C.; but eclipses of the sun cannot happen on the day of full moon. They happen only at new moon, whereas eclipses of the moon happen at full moon. Hsü Kuang (352-425) says that the HS does not record this eclipse [it is now neither in chap. 4 nor chap. 27], and tells that one copy [of the SC] says it was an eclipse of the moon, but that the histories do not record eclipses of the moon. The conjectural emenation of that copy is correct ---Oppolzer calculated his lunar eclipse no. 1580 on the evening of Jan. 16, 178 B.C. at Ch'ang-an. If the historian misread in the astronomical records a poorly written 月 as being 日, this mistake could easily occur. This passage seems to show that the court astronomers kept a record of lunar as well as of solar eclipses. The discrepancy in dates indicates that Hoang's calendar is a day in error here.
iii. In the third year, the tenth month, on the day ting-yu, the last day of the month, a third eclipse was recorded (4: 11a). This date was Dec. 22, 178 B.C., for which Oppolzer calculated his solar eclipse no. 2449. He charts the umbra of the moon as passing through the Malay peninsula; calculation shows that the eclipse at Ch'ang-an reached a magnitude of 0.35 at 1:58 p.m., local time. The sun was in long. 267.4° = 267.1° R.A. HS 27 Cb: 13b adds, "It was 23 degrees in [the constellation] Tou," of whose stars µ, λ, φ, σ, γ and ζ Aquarii were then in R.A. 241.1°, 243.5°, 247.2°, 249.8°, 253.3° and 250.6°, respectively.
iv. In the third year, the eleventh month, on the day ting-mao, the last day of the month, a fourth eclipse is listed (4: 11a). P. Hoang gives this date as Jan. 20, 177 B.C., the first day of the twelfth month. HS 27 Cb: 13b adds, "It was 8 degrees in [the constellation] Hsü," whose stars, α Equulei and β Aquarii, were then in R.A. 291.4° and 293.4°. The Han-chi 7: 7b dates this eclipse on "[the day] yi-mao, the last day of the month," 12 days before the HS's date and on the 18th day of that month.
There was no eclipse on that date, for Oppolzer gives none. In the 22 years from the preceding eclipse to the next correctly dated eclipse in 154 B.C., in which period the HS lists 3 eclipses, there occurred 56 eclipses, of which only 10 were visible in China. 1
In this period, 9 umbral eclipses were visible in China: (1) no. 2452, on June 6, 176 B.C., 23 days after a ting-mao day, sun in long. 70.7° = 69.3° R.A.; (2) no. 2459, on Oct. 10, 174 B.C., 39 days after such a day, sun in long. 193.2°; (3) no. 2460, on May 4, 173 B.C., 36 days after such a day, sun in long. 10.6°; (4) no. 2470, on July 17, 169 B.C., 41 days after such a day, sun in long. 110.2°; (5) no. 2475, on May 28, 167 B.C., 1 day after such a day, sun in long. 61.9°; (6) no. 2477, on May 17, 166 B.C., 55 days after such a day, sun in long. 51.4°; (7) no. 2486, on Mar. 5, 162 B.C., 3 days after such a day, sun in long. 340.9°; but the umbral path of this eclipse ran so far south that I calculated it, and found it invisible in the present Ch'ang-an, Pei-p'ing, Shantung, and Ch'ang-sha. In Wu (present Soochow), the eclipse reached a magnitude of only 0.02 at 4:34 p.m. local time, so that it was practically invisible; (8) no. 2489, on Aug. 16, 161 B.C., 53 days after such a day, sun in long. 140.1° = 142.5° R.A.; the umbral path of this eclipse ran so far north that I calculated it and found that in Ch'ang-an it reached a magnitude of 0.17 at 5:16 a.m. local time; (9) no. 2505, on Oct. 10, 155 B.C., 19 days after such a day, sun in long. 193.4°; the umbral path of this eclipse ran so far south that I calculated it and found that in Ch'ang-an the eclipse reached a magnitude of 0.17 at 9:32 a.m., local time. Westwards and southwards its magnitude was greater.
In this period, 11 partial eclipses occurred in the northern hemisphere, of which only one was visible in ancient China: no. 2481, on Mar. 26, 164 B.C., 13 days after a ting-mao day, sun in long. 165.7°. At Ch'ang-an the eclipse reached a magnitude of only 0.02 at 7:12 a.m., with visibility better at places north and west. On the longitude of Ch'ang-an, at latitude 40°, in the Ordos region, the magnitude of the eclipse reached 0.14. 2
It is probable that the eclipse intended by the text was the first umbral eclipse listed above, on June 6, 176 B.C. Then the ting 丁- mao of the text is an error for hsin 辛- mao (a natural mistake) and Hoang's calendar is two days in error; this date was the first day of the fifth month, in the fourth year. The heavenly location given for this eclipse is then greatly in error.
v. In the latter part of the reign, the fourth year, the fourth month, on the day ping-yin, the last day of the month, a fifth eclipse is listed (4: 17b). The Han-chi 8: 15a has the same reading. But there was no ping-yin day in that month. HS 27 Cb: 13b dates it on the day ping-ch'en, and adds, "It was 13 degrees in [the constellation] Tung-ching." This latter date was June 9, 160 B.C., according to P. Hoang. The first star in Tung-ching, μ Gemini, was then in 63.4° R.A. But Oppolzer lists no eclipse on this date.
For the eclipses occurring about this time, cf. the discussion under the preceding eclipse. As to their cyclical days, ping-yin is the day before ting-mao, and ping-ch'en is 11 days before ting-mao.
Very possibly the eighth umbral eclipse mentioned previously, on Aug. 16, 161 B.C., is the eclipse referred to in the text. It occurred on a keng-shen day, in the third year, the sixth month, the day before the last day of the month, according to Hoang's calendar. This identification would require no alteration in the order of events of HS ch. 4, merely a redating of one event; the cyclical day is already in doubt because of the difference between the two recordings. The location of the eclipse in the heavens is about 60° in error.
vi. HS 27 Cb: 13b adds, "In the seventh year, the first month, on [the day] hsin-wei, the first day of the month, there was an eclipse of the sun." The Han-chi has the same recording. P. Hoang gives this date as Feb. 9, 157 B.C. But no eclipse occurred on that date.
For eclipses occurring about this time, cf. sub eclipse iv. Hsin-wei is 4 days after ting-mao. There was no eclipse visible in China in Emperor Wen's reign after the date we adopted for the preceding eclipse. It seems that Pan Ku considered this eclipse doubtful, for he did not put it into his "Annals," although it got into his chapter on the "Five Elements," and was copied by the Han-chi in its chronological account. It looks as though someone considered that an eclipse was due at this time in order to predict the death of Emperor Wen, so placed an eclipse five months (about an eclipse season) before his death. Pan Ku's rejection of this eclipse in his Annals is a good testimony to his historical judgment.
But the solar eclipse of Oct. 10, 155 B.C., which Hoang dates in Emperor Ching's second year, the ninth month, the day yi-yu, the last day of the month, was the only eclipse visible in China after the one identified for the preceding eclipse and before the next and correctly dated eclipse. Since Hoang's calendar may be a day in error, this date may have been the tenth month, the first day, the day ping-hsü. It seems stretching things to identify this eclipse with the one listed in ch. 27, yet it is peculiar that, in a period during which only one eclipse was listed, there should have been only one eclipse visible.
1. Besides those located in Oppolzer, the following 9 partial eclipses were invisible in China because they belonged to initial (i.) or terminal (t.) runs in exeligmos series whose nearest umbral eclipses was located near the south pole: no. 2454 (t.); no. 2457 (i.), no. 2464 (i.), no. 2473 (t.), no. 2498 (t.), no. 2474 (t.), no. 2482 (i.), no. 2483 (t.), and no. 2501 (i.).
2. The other ten eclipses were all calculated approximately and found to be invisible in China. They were: no. 2455, on May 26, 175 B.C.; no. 2456, on Oct. 20, 175 B.C.; no. 2465, on Mar. 14, 171 B.C.; no. 2466, on Aug. 8, 171 B.C.; no. 2471, on Jan. 10, 168 B.C.; no. 2472, on June 7, 168 B.C.; no. 2490, on Jan. 12, 160 B.C.; no. 2492, on Aug. 6, 160 B.C.; 2499, on June 5, 157 B.C.; and no. 2500, on Oct. 31, 157 B.C.
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