, over 41 days and 281 parts [it] travels 50 du and 281 parts, going into conjunction (he) with the sun. One conjunction is 292 days 281 parts, its travel through the stars being [also] as such (i.e., it is the same number of du)
, The Documents raises the due-south stars (meridian stars) for rectifying the four directions, [this] being what the former kings used to elucidate the seasons and grant [them] to people, to serve heaven and nurture [the myriad living] things. However, the accounts of former scholars have similarities and differences between them Yu Xi ?? (fl. 307?346 CE) says: 'In the time of Yao, on the winter solstice Q22 ? shortest day ? the star was Mane L18 ; now, after 2700-odd years, Eastern Wall L14 is centred, which [we] know was arrived at by gradual difference every year' ? ???. Moreover, He Chengtian ??? (370?447 CE) says: ? 'By comparison with the centred star of today, the difference is twenty-seven or eight du, i.e. on winter solstice Q22 in the time of Yao the sun was at Maid L10 10 du, ???????????????????????????????? In total, one termination of its double (i.e., inferior and superior) conjunctions is 584 days Thus, when Zu Chongzhi ??? (429?500 CE) made the Grand Enlightenment li, he first established the year difference (suicha ??), [his] lü being forty-five years and nine months per du of retreat, p.27
, The day being at its shortest, and the asterism being Mao, he thereby determined mid-winter'. 28 Extrapolating from this, in [his Tao-]Tang ?? dynasty, the sun at winter solstice was more than 50 du to the left (i.e., westward) of today's lodge. 29 At the beginning of the Han dynasty (206 BCE), they used the Qin li, [which placed] the winter solstice sun at Led Ox L09 6 du. 30 Emperor Wu of Han ?? ? (r. 141?87 BCE) reformed this [in 104 BCE] and established the Grand Inception li (Taichu li ???), [which placed] the winter solstice sun at the beginning of Ox L09 . The Later Han Quarter-remainder model (Sifen fa ???) [placed] the winter solstice sun at Dipper L08 21, 31 In the time of the Jin ? (265?420 CE), Jiang Ji ?? (fl. 384 CE) [figured out how to] check (jian ?) the [position of the] sun via lunar eclipse, and from this he learned that the winter solstice was at Dipper L08 17. 32 Today, [in 462 CE], comparing (can ?) via the centred stars (zhongxing ??, above) and testing (ke) via eclipse opposition, [we know that] the sun on winter solstice is at Dipper L08 11. 33 ??????????????? Accounted for together, [one finds that], in just under a hundred 100 years, the difference (cha ?) is 2 du, pp.429-500
, 34 of the seven luminaries (qi yao ? ?) 35 would gradually diverge from li [predictions] Once egregious mistakes became apparent, it would immediately require institutional reform, and since [such li] could only accord with a single time (shi ?, i.e. 'age' or 'period'), none was able to connect (tong ?) with those more distant ? all the modifications and reforms without end are due to this point. ???????????????????????????????? Today, [let us] have the position of the winter solstice minutely differ from year to year ??? ?, and in going back to investigate (jian) Han [observational] notesThe Book of Documents', Bulletin of the Museum of Far Eastern Antiquities 22 (1950): 3. 29 According to his solar parameters and method for finding meridian stars as preserved in his Great Enlightenment li ???, in the Song shu ?? (Zhonghua shuju edn), 13.291?304, the 'year difference' is 1 du per 45.92 years, requiring 2295.99 years to produce 50 du in precession. This would place the time of Yao in 1834 BCE, and, indeed, according to his solar table, Mao would then be the dusk meridian star at winter solstice. 30 Note that this is an odd claim: most, as with the Grand Inception li in the following line. 31 Actually, it places it at '6 du before Ox L09 ' or 'Dipper L08 21¼ du', as we will see when reading the Quarterremainder li