1. Harper, , “The Han Cosmic Board (Shih),” Early China 5 (1979):1–10CrossRefGoogle Scholar. In the following comments on Harper's article references are to page, column and paragraph of his text.

1b.2: Neither Needham nor Wang Chen-to suggests that the hypothetical lodestone ladle was mounted on a pin, which would make little sense of Wang Ch'ung's statement that the ‘south-pointing ladle’ was to be ‘thrown onto the earth-(?plate).’ The suggestion is that both ladle and plate were highly polished so as to cut down friction, allowing the former to rotate freely (Science and Civilization in China [hereafter S.C.C.], IV.1, p. 266 ff.Google Scholar). Harper's doubts about the reality of this device are none the less well justified.

2a.1: It is by no means “clear” that the Dipper dial (or ‘lodge dial’ as I would prefer to call it) “served as the prototype for the heaven plate of the cosmic board (shih).” Although Harper repeats this statement later (3b.3) the only justification offered is that of footnote (39), which argues from the hsiu graduations that the dial may have its origin as early as the fourth century B.C. (see my comment below). There is no reason why the shih itself should not be just as early, or earlier. The well-known lacquer box-lid of the Marquis of Tseng (Wenwu 1979.7:40 ff.) dates from ca. 433 B.C. and displays the ungraduated sequence of the hsiu surrounding the Dipper very much as on the shih. Is it not also likely that a graduated device should develop from an ungraduated one rather than vice versa? 2a.3: According to Harper “It has been demonstrated that for observational purposes the north pole during the Han was placed near a small star known as Knot Star (niu hsing) or Pivot of Heaven (t'ien shu ).” Neither of the authorities quoted do in fact demonstrate this, and one (Schafer, E.H., Pacing the Void [Berkeley, 1977], p. 44Google Scholar) is in any case talking about the T'ang and not the Han at all. If the Knot Star is to be identified with Z1694 Camelopardalis, then a simple graphical construction shows that it was within a degree of the pole for most of the T'ang, but was about six degrees away in 200 B.C. (Fig. 6). Needham's statement that “(the Knot Star) was certainly the pole star of the Han” (S.C.C., III, p. 261) lacks solid supporting evidence. As Harper correctly notes, β UMi (Kochab) was the most important star of the polar area in Han times; it had been within 8 degrees of the pole since 1500 B.C. It is the brightest star of the asterism labelled ‘North Pole’ pei chi, and Ssu-ma Ch'ien says that it is T'ai I ch'ang chüthe fixed place of the Great Monad” (Shih chi [Peking, 1962], ch. 27, p. 1289Google ScholarPubMed). He gives no sign of recognizing any other star as the pole star. In contrast, I know of no Western Han references to the Knot Star. 2a.4 note 18: Surely ‘vapor’ (rather than, e.g., Schafer's ‘pneuma’) is a much too reductionist translation of ch'i But to call yüan ch'i ‘the most basic of all life-forms’ leaps to the opposite extreme. 2b.1 note 20: The Dipper cannot point to the twelve Jupiter stations in turn, because it is fixed relative to these on the celestial sphere. What it actually does is to point in a series of directions designated by the same set of cyclical signs used to label the stations. 3a.1: The Dipper is (ignoring precession) fixed relative to the colures on the celestial sphere in the same way that (e.g.) Greenwich is fixed relative to the meridian 0°. Since the Dipper moves relative to them, the Two Cords of Huai nan tzu are obviously not the colures but, rather more straightforwardly, fixed lines defining the directions north-south and east-west for a terrestrial observer. 3a.3: “In Han times the concept of suspending the sky from the Big Dipper was expressed by analogy with the Mainstay (kang) and Filaments (chi ).”

Does this mean that anybody actually thought the sky was suspended from the Dipper, or does it simply mean that such language survived as a metaphor left over from defunct schemes of cosmography? The distinction is surely an important one. By the way, it remains to be shown (as opposed to assumed or asserted) that de Santillana and von Dechend's mythographic hypotheses are applicable to China. 3b.1 note 33: The unperson T.T. Som has usurped the rights of the late Indonesian-Chinese scholar Tjan Tjoe-som. 3b.3: “…the Big Dipper formed an axis which could serve to divide heaven into quadrants as it rotated.” For ‘axis,” read ‘radius’? In any case, since (once more) the Dipper is fixed relative to heaven, how can it divide it into quadrants by rotation? 4a.1 note 39: On the question of the antiquity of the hsiu extensions on the graduated disc, it would have been more helpful to the reader if Harper had given a reference to the source of his statements (Tun-chieh, Yen in Kaogu 1978.5:337Google Scholar), where more detailed evidence is presented. It is by no means certain that the hsiu data attributed to Shih Shen and Kan Te (to which Yen claims that the disc graduations conform) actually date to the fourth century B.C., or whenever else these rather shadowy figures lived. Yabuuchi Kiyoshi argues for a date as late as 70 B.C. (Chūgoku no Temmonrekihō [Tokyo, 1969], pp. 46–75Google Scholar. However, in his discussion of the disc graduations, P'an Nai suggests that they may pre-date the Shih Shen data (Wo-kuo tsao-ch'i-ti erh-shih-pa-hsiu kuan-ts'e chi ch'i shih-tai k'ao in Chung-hua wen-shin lun-ts'ung [Shanghai, 1979], pp. 137-182, particularly p. 158ff.). P'an holds to a date of ca. 450 B.C. for part of the Shih Shen data, but if Yabuuchi's date of 70 B.C. is accepted it is not necessary to hold that the disc graduations represent a system much earlier than the second century B.C., as Nathan Si vi n has pointed out (private communication). 4a.2 and note 40: Harper's remarks on the positioning of the Dipper relative to the hsiu on the Dipper/lodge dial are rendered meaningless by the fact that the disc bearing the Dipper is free to rotate relative to that bearing the hsiu. 5a.2 -5b.2: I cannot see the logic of Harper's suggestions here and elsewhere that the shih itself was the source of certain religious beliefs and practices from Han times onwards. The shih was designed as a physical expression of a certain cosmic view, and outside this context it was meaningless and without significance, religious or otherwise. The shih was dependent on the persistence of a given world view, and did not give rise to it. Harper's examination of those aspects of the shih and the Dipper which Chinese scholars tend to dismiss as ‘pseudo-science’ is nevertheless very worthwhile.

2. Loewe, M.A.N., Ways to Paradise: The Chinese Quest for Immortality (London, 1979), chapter 3Google Scholar.

3. Needham, J., S.C.C. IV.1 (Cambridge 1962), pp. 261–273Google Scholar.

4. See Morohashi's Dai Kanwa Jiten no. 9663, sense 1 for examples.

5. Lao tzu (SPTK), 1.14b.

6. Harper, p. 1.

7. Shih chi (Peking 1962), ch. 127, p. 3218Google ScholarPubMed.

8. A further point is that a board is not normally thought of as having moving parts. While I feel that ‘cosmic model’ is the best available translation of the name of the device in question, I continue to use the transliteration shih in most of the subsequent discussion. My reasons for this are two-fold: firstly it avoids the frequent appearance of tautology in the discussion of the role of the shih as a cosmographie model (section 2), and secondly the use of a translation seems superfluous in a technical discussion addressed to a sinologi cal readership.

9. Pei t'ang shu ch'ao , (repr. Taipei, 1962) 149.3bGoogle Scholar.

10. The same comparison is made in Huai nan tzu compiled ca. 120 B.C. (SPTK) 1.4b; see also 7.2a and 15.3a. Near the beginning of the Chou pi suan ching compiled late first century B.C., we are told “the square pertains to earth and the circle pertains to heaven; heaven is round and earth is square” (SPPY) 1.10b. One section of the Ta Tai li chi, compiled after A.D. 100, makes a point of denying that heaven and earth could really be different shapes, which is a clear indication that this idea was fairly widespread, (Han Wei ts'ung shu, ed. Ch'eng Jung 5.7b.).

11. The earliest firm evidence for the existence of this theory in a systematic form is found in the Lü shih ch'un ch'iu compiled 239 B.C. (SPTK) 13.3a-b. At present the most reliable account of this and other Chinese cosmographies in a Western language is that given by Shigeru, Nakayama in his A History of Japanese Astronomy (Harvard, 1969), pp. 24–43Google Scholar. While the survey of Needham (S.C.C. III, pp. 210-218) is essential reading, it may be supplemented by the comments in C. Cull en “Joseph Needham on Chinese Astronomy,” forthcoming in Past and Present, 1980.

12. It should be noted that the original name of this text had the words suan ching added to it under the T'ang. For details of the reasoning behind the dimensions given, see in the first instance Nakayama, op. cit. A detailed discussion of this work will be found in Chūryō, NōdaShūhi sankei no kenkyū (Kyoto, 1933)Google Scholar. A full translation and study of the Chou pi is at present (1980) in preparation by the present writer.

13. See below, note 14.

14. During the course of a tropical year the sun is located on a heng on twelve occasions as it moves from the outer heng to the inner one and back again. Beginning with the winter solstice, the tropical year was divided into twenty-four equal periods alternately designated as chieh ch'i ‘nodal ch'i’ and chung ch'i ‘medial ch'i’; the heng marked the position of the sun at the inception of the nodal ch'i. The text mentions an eighth circle beyond the seventh heng, marking the extreme limit of solar illumination at the winter solstice. Its diameter is 810,000 li, the same as that of the square earth, and it seems possible that the author of this section of the Chou pi understood it to mark the size of the heavenly disc. It is omitted by Chao.

15. Chou pi suan ching (SPPY) 1.32b.

16. For its time the Chou pi is notable for giving an account of the universe almost completely free from references to the numinous.

17. Similarly, discussions of the fact that the earth is round do not usually make an explicit reference to a modern terrestrial globe as an illustration.

18. One motive for including this method in the Chou pi may have been an attempt to show that Kai t'ien methods could compete with the newly developed armi Hary sphere, which was associated with a rival cosmography. See section 3, and note 36.

19. Chou pi suan ching (SPPY) 2.8a-b. The horizon is to be thought of as divided into twelve equal portions, each 30° (30 tu 7/16) in extent. These sectors are arranged so that (e.g.) the northernmost one extends 15° on either side of the direction due north. Beginning with this sector and running clockwise, these divisions are labelled with the twelve cyclical signs tzu, ch'ou, etc. One of the bands on the earth-plate of the shih shown in Fig. 3 is marked out in accordance with this scheme. Another section of the Chou pi (2.23b) also uses the eight trigrams as horizon divisions. These likewise appear round the earth-plate of at least one shih; see Loewe, , Ways to Paradise, p. 205Google Scholar.

20. The Chou pi is particularly concerned with the hsiu Tung Ching and Ch'ien Niu because it takes these as marking the solar positions at the summer and winter solstices respectively. It is, however, clear from the month markings on the shih heaven-plate that the sun at the winter solstice was not thought to be in Ch'ien Niu but in the adjacent hsiu Tou ; this accords with the scheme of the Yueh ling (see note 21). Since Tou and Tung Ching are fourteen hsiu apart, equidistant hsiu spacing would lead to exact opposition of the corresponding markings on the heaven-plate. Near the time of manufacture of the shih in the second century B.C., the right ascension of the determinative star of Tou (ϕ Sagittarii) was near 248°, and that of Tung Ching was 64°; alignment was missed by only 4°. For the makers of the shih (and also the lodge dial, see below and Fig. 4), it was therefore a reasonable approximation to show their solsticial hsiu in precise opposition. For both the shih and the Chou pi, however, it seems probable that the real motive for showing the solsticial hsiu determinants in opposition was less empirical than theoretical: the fact that the solsticial solar positions are in opposition has led to the idealized view that the determinants of the relevant hsiu must themselves be opposed in right ascension.

21. On the importance of the meridian transits of stars for Chinese astronomy, see note 50. One datum that can be obtained directly from the shih is the hsiu in which the sun lies in a given month of the year; this is indicated by the numbers (with cheng, for the first month) marked against twelve of the hsiu on the heaven-disc (see also Kaogu 1978.5: 334Google Scholar). The data on the shih differ in three cases from those in the Yueh ling chapter of the Li chi: Chang (not I ), 7th. month; Ti (not Fang ), 9th. month; Hsin (not Wei ), 10th month. As a practical guide to the actual position of the sun, the information on the shih is quite crude, rather less accurate than the guides to zodiac birthsigns found in modern newspaper astrology columns. In the first place no indication is given as to the day of the month on which a particular hsiu is entered, and in the second place the nature of the Chinese luni-solar calendar meant in any case that the day of the solar year on which a particular month began could shift by up to thirty days. Harper (“The Han Cosmic Board,” note 44) has suggested that the shih was “an accurately constructed model of the rotation of the Dipper,” but I do not think that the markings on the heaven-disc bear this out. According to Harper, the direction indicated by the handle of the Dipper at any date and hour could be ascertained by setting the hsiu marked for that month on the heaven-disc against the appropriate one of the twelve cyclical signs marking the double-hours on the earth-plate. The handle then indicates the cyclical sign corresponding to the required direction. This will certainly give a rough indication of the configuration of the Dipper, but the word ‘accurate’ is hardly justified, and there is good reason to doubt whether the maker of the shih was attempting to provide for quantitative matching with the celestial phenomena. The equidistant spacing of the hsiu allots (e.g.) the same width to Kuei (5 tu) as to Ching (26 tu), despite the fact that these measurements are given explicitly on the pair of graduated discs found in the same tomb. As a result it is implied that the position of the Dipper at some fixed hour changes by 2/28 of a revolution (26 tu) during some months and 3/28 of a revolution (39 tu) during others, since a month's change in solar position can be represented by two long hsiu or three shorter ones. This is in clear contradiction with observation, as well as with the Chinese tradition (mentioned by Harper) that the Dipper shifts by 1/12 revolution per month. What seems to have happened on the shih is that the real celestial phenomena have been replaced for purposes of divination by an idealized scheme; the shifting of the Dipper to the center of the disc (which represents the celestial pole) is an instance of this. See also note 25 on the position of the Dipper.

22. See the excavation report in Wenwu 1978.8:12ffGoogle Scholar. and the discussions in Kaogu 1978.5:334-337 and 338–343Google Scholar.

23. On the basis of the correlation heaven/round earth/square one might expect that unlike the shih both elements of this object would be concerned with the heavens; a similar indication is given by the fact that one disc bears the stars of the Dipper and the other is marked with the hsiu.

24. On the date indicated by these see note 1.

25. On the lower disc the function of these lines is apparently to mark out the sequence of the hsiu into the usual seasonal quadrants, each beginning with the position of the sun at a solstice or equinox. Some idealization and distortion has occurred. Thus the initial points of the solsticial hsiu Tou and Ching are shown as diametrically opposite each other, although according to the extensions marked the angle from the first to the second is only 178 tu (175°) counted anticlockwise. Following the month markings on the shih, one might have expected that the equinoctial hsiu K'uei and Chüeh would have appeared on the perpendicular diameter; the problem is, however, that the obtuse angle between them is only 173 tu (170½°; two hsiu extensions restored on the basis of data given in P'an Nai 1979, p. 163 table 8). It was evidently felt to be important that the quadrantal points should be marked by the initial point of a hsiu, and rather than distort the graduation by the amount required to position Chüeh opposite K'uei, it was found preferable to replace Chüeh by the adjacent hsiu Chen (lost by breakage of the edge of the disc). This involves approximating 180° by 189 tu (186°). An error of one tu represents one day's solar motion. The two perpendicular lines on the upper disc obviously serve to divide the graduated circumference into quadrants as on the lower disc, but their relation to the Dipper marked on it is unclear. As Harper notes, the diagrams given in Wenwu 1978.8:19 and Kaogu 1978.5:342 are somewhat different; apart from the lengths of the lines shown, the straightened Dipper handle is at about 15° to one diameter in the first drawing, and parallel to it in the second. As can be seen from Fig. 6, neither position approximates very well to the relation of the Dipper to the quadrantal lines of right ascension in about 200 B. C, leaving aside the shifting of the Dipper to the center of the disc. The same can be said of the position of the Dipper on the shih of Fig. 3; in this case the general line of the Dipper is shown as close to the direction 0° to 180° right ascension, whereas in reality it is closer to the line 45° to 225°. This can perhaps be understood as follows. Astronomical references to the handle of the Dipper pointing in a certain direction are not made on the basis of the general line indicated by the stars ε to η UMa, but rather on the basis of the line between the celestial pole (or perhaps the pole star β UMi) and the last star of the handle (η UMa). The direction thus indicated at (e.g.) 6 p.m. on the summer solstice would indeed be due south as stated in Huai nan tzu and discussed in Harper's note 44, since at that instant the line from the pole to the solar position would run due west. The line of the Dipper handle itself would be well off bearing. What seems to have happened on the disc in question is that the Dipper has been pivoted about the end of its handle to make it lie along the line of 0° to 180° right ascension, so that it now indicates as a whole the direction previously given by one of its stars. It has also been enlarged so that it lies centered around the pole.

26. During the Western Han it was assumed that the sun moved through a constant one tu of right ascension daily. The effect of the sun's ecliptic motion was not considered until the Eastern Han, and its inequality of motion in longitude was not discovered until the sixth century A.D.; see Yabu-uchi, , Chūgoku no Temmonrekihō, pp. 307–309Google Scholar.

27. The first signs of systematic interest in the inequalities of lunar motion come with the work of Keng Shou-ch'ang in 52 B.C.; see below and note 41.

28. See Loewe, , Ways to Paradise, pp. 77–78Google Scholar. The marking of the monthly solar positions on the shih of Fig. 6 confirms this view.

29. Wenwu 1978.8:14Google Scholar.

30. Harper, “The Han Cosmic Board,” p. 1.

31. See Major, J., “A Note on the Translation of Two Technical Terms in Chinese Science: wu-hsing and hsiu,” Early China 2 (1976), p. 1CrossRefGoogle Scholar.

32. Ti-fei, Yin in Kaogu 1978.5:339Google Scholar.

33. For a characterization of such systems, see vin, N. Si, “Cosmos and Computation in Early Chinese Mathematical Astronomy,” T'oung Pao iv (1969), pp. 1–73Google Scholar.

34. See Tun-chieh, Yȩn in Kaogu 1978.5:336Google Scholar.

35. As mentioned below, early measurements of right ascension relied on gnomon observations of meridian transits.

36. A general survey of the history of this instrument in China is given in Needham, S.C.C. III, pp. 339-381.

37. See Nakayama, , A History of Japanese Astronomy, pp. 24–43Google Scholar.

38. Yabuuchi, , Chūgoku no Temmonrekihō, pp. 64–71Google Scholar. Yabuuchi puts forward the view that the idea of the armi Hary sphere may have reached China via India (op. cit., pp. 72-74). While this is by no means impossible, the present discussion is based on the hypothesis of an indigenous invention.

39. Fa yen (SPPY), 10.1b. Needham (S.C.C. III, 354) would prefer to take ying as a verb referring to the construction of some object, but it can equally well bear an abstract sense, and the context strongly suggests this.

40. At this stage it is unlikely that there was a definite distinction between an observational instrument and a demonstrational model; see Needham, S.C.C. III, p. 383f.

41. Hou Han shu (Peking, 1963), chin 2, p. 3029Google Scholar. Keng claimed to have discovered that the moon moved more rapidly in right ascension when in certain hsiu and more slowly in others. Chia K'uei contested this, giving the earliest Chinese description of the motion of the lunar nodes (p. 3030).

42. Han shu (Peking, 1962), 21A, p. 978Google ScholarPubMed.

43. Han shu, ch. 21A, p. 974.

44. Han shu, ch. 21A, p. 975.

45. Han shu, ch. 21A, p. 975. The statement of these men's duties is presumably drawn from the parallel passage in Shih chi 25, p. 1260, written by Ssu-ma Ch'ien as a first-hand account of the business of the calendar reform.

46. Two ancient texts have been adduced as evidence that Lo-hsia Hung actually used an armi Hary sphere. The first of these is a fragment of a book entitled Hsin lun, by Yang Hsiung's friend and conteroporary Huan T'an (40 B.C. A.D. 30). One version records a conversation between Yang and an old artisan who had made a hun t'l'en (T'ai p'ing yü lan [SPTK], 2.11a). Another version (Pei l'ang shu ch'ao 130.12a) has the heading “Lo-hsia Hung (and the) hun t'ien,” and somewhat awkwardly gives the old artisan the ming Hung. This is clearly impossible: Lo-hsia Hung (fl. 110 B.C.) could never have spoken to Yang Hsiung, who was not born until 53 B.C., and he was certainly not an artisan (kung ). The second text is a fragment of a work written by Ch'en Shu ca. 240 A.D., entitled I pu chi chiu chuan “Old stories of the elders of Ssu-ch'uan.” The longest version is found in the T'ang So yin commentary to the Shih chi, ch. 26, p. 1261, and states:

(Lo-hsia) Hung's tzu was Ch'ang Kung. He was a brilliant astronomer and went into retirement at Lo-hsia. He held the office of consultant scholar under Wu Ti, and rotated a hun t'ien at the center of the earth. He reformed the Chuan Hsü calendar and made the Grand Inception calendar. The rank of councillor was conferred on him but he would not accept it.

All versions contain the clause yü ti chung chuan hun t'ien; ‘the center of the earth’ is of course the Chinese capital, or more precisely the ancient observatory site of Yang-ch'eng. Ch'en Shu was writing over three centuries after the event, at a time when it was hard to imagine an astronomer not using an armi Hary sphere, and it seems unlikely that he had an independent source of data on Lo-hsia Hung. I suggest that the most likely explanation is that he was inspired by Ssu-ma Ch'ien's statement that Lo-hsia Hung yun suan chuan li carried out calculations to revise the calendar.’ With the benefit of hindsight and on the basis of Yang Hsiung's story, yun could well suggest hun, and chuan is already present.

47. See notes 26 and 27.

48. An additional source of data, and one which required no instruments at all, would naturally be a long sequence of records of the dates of solstices and new moons. For the important metaphysical assumptions behind the Grand Inception system, see Sivin, “Cosmos and Computation,” and Yabuuchi, Chūgoku no Temmonrekihō, pp. 21-30.

49. The ten-foot measure chang is also used. A highly relevant example is the T'ien kuan shu astronomical monograph by Ssu-ma Ch'ien, which forms chapter 27 of his Shih chi. The motion of e.g., Jupiter in right ascension is given in tu (p. 1313), while such data as the length of comets are given in chang (p. 1316). It seems a reasonable assumption that Ssu-ma's co-worker Lo-hsia Hung would have used a similar scheme at least initially.

50. The standard time for such observations seems to have been the instant of first stellar visibility after sunset; dawn observations were also made. A. given star crosses the meridian four minutes earlier each day, and it is not a difficult matter to fix the date of its dusk transit to within a few days using simple gnomon sightings. A report of experiments on this topic is now in preparation. Such procedures do not require timing devices of any kind and may well be of great antiquity. The oldest list of seasonal stars was traditionally taken to be the four asterisms mentioned in the Yao tien; these and similar data are discussed in Needham, S.C.C. III, p. 245ff. The obvious connection between meridian transit observations and the extremely ancient tradition of the southwards ceremonial orientation of the Chinese ruler (at least as old as the Shang) is made explicitly by Liu Hsiang (77 B.C. - A.D. 6); see his Shuo yuan (Han-wei ts'ung-shu), 18.10b.

51. It is therefore misleading, although not uncommon, to speak of the hsiu as if they were marked out as divisions of the celestial equator; in any case there is no evidence that the concept of this particular great circle had developed before the middle Western Han - see below and note 54. Attempts to date the hsiu system by finding a date when its defining asterisms lay nearest to the equator are similarly ill-based: cf. Needham, S.C.C. III, p. 248.

52. Without a timing device it is possible to obtain estimates of the width of a hsiu by counting the number of days between the dusk transit of its standard star and that of the succeeding hsiu. The position of the full moon could serve as an indicator of the sun's hsiu six months away from the present.

53. Traces of this distinction are still visible in modern astronomy: both right ascension and declination can be measured in degrees, but right ascension can also be expressed in hours.

54. It is significant that Ssu-ma Ch'i en's T'ien kuan shu makes no reference at all either to the celestial equator, ch'in tao, or to the ecliptic, huang tao. The fact that Ssu-ma does not mention the latter does not of course imply that he was ignorant of the general path followed by the moon and planets against the background of the stars (possible references to this are found at pp. 1299 and 1330). The fact was, however, that neither ecliptic nor equator formed part of his basic set of astronomical concepts. Measurements of right ascension were dealt with by the hsiu system, and the north-south motion of the sun (the only celestial body for which this was important) was adequately dealt with by gnomon noon shadow observations. This is exactly the situation met with in the Chou pi, the classic exposition of the kai t'ien theory in the Western Han. The recognition of the ecliptic and equator was an essential part of the hun t'ien cosmography, and it is interesting that the offical astronomy of Lo-hsia Hung's time had not yet taken this step.

55. Han shu ch. 21A, p. 975 (translated above) and p. 976.

56. See above and note 41.

57. Chou pi suan ching (SPPY), 2.9a-12a.

58. Shang shu (SPTK), 1.6b.

59. Karlgren, B., “Grammata Serica Recensa,” BMFEA no. 20 (1948), pp. 1–332Google Scholar. My reasons for not following Karlgen's suggestion that should be read as rather than as are set out in the reference given in note 60.

60. Christopher Cullen and Anne S.L. Farrer, “On the Term Hsüan Chi and the Flanged Trilobate Jade Discs,” submitted to BMFEA (Sept., 1980). One of the objects of this paper is to disprove the theory of H. Michel (reviewed by Needham in S.C.C. III, pp. 332-339), which identifies the hsüan chi with a serrated variety of the jade disc pi, and the yü heng with the tubular jade form ts'ung. Michel suggests that the two objects were used in combination as an astronomical instrument.

61. Karlgren's version of this passage is “He examined the sün-stone apparatus and the jade traverse and thereby (adjusted ) verified (the movements of) the seven directors (i.e., sun, moon and planets)”: see his “Glosses on the Book of Documents,” BMFEA no. 20 (1948), pp. 77-79. For points of dissent from this see the reference in note 60. The version given in Legge, J., The Chinese Classics (Hongkong, 1865), iii, p. 33Google Scholar follows the Eastern Han commentators who interpreted hsüan chi yü heng as an armi Hary sphere, an anachronism before the middle Western Han.

62. Shih chi ch. 121, p. 3124.

63. T'ai p'ing yu lan 29.3a. Fu Sheng's commentary was known as the Shang shu ta chuan.

64. The use of this character suggests that the T'ai p'ing yu lan editors may have altered to in the rest of the quotation to bring it closer to the received text. A T'ang quotation of an Eastern Han commentary on the Shang shu ta chuan reads , and there seems some possibility that this was Fu Sheng's original reading: see Shih chi ch. 27, p. 1292 (comm.). The same reading is found in Han shu ch. 21A, p. 969, although not in a quotation from Fu Sheng.

65. For the connection between chiand wei compare the appendix to the I ching (SPTK), 8.5b “chi means the subtlety (wei) of movement, the first visible signs of fortune.” To perceive the chi clearly is the object of divination; for Fu Sheng there is evidently a resonance between the idea of the celestial pole as the unmoved pivot of the turning sky and the infinitesimal chi conceived as the beginning of all events.

66. The asterism pei chi ‘north pole’ is called t'ien chi ‘celestial pole’ by Ssu-ma Ch'ien, Shih chi ch. 27, p. 1289, and contains the five stars γ, β 4 and 5 UMi and Σ1694 Cam. The second of these was the Western Han pole star (see note 1); by T'ang times precession had forced a change to the fifth and much fainter star. Other identifications of the hsuan chi with β UMi are found in the Chou pi (first century B.C.) which uses this name for “the great star in the middle of the north pole (asterism),” 2.3a, and in the Shuo yuan of Liu Hsiang (Han-wei ts'ung-shu) 18.1b (ca. 10 B.C.). Liu says that the hsuan chi is the ‘pivot star’ shu hsing in the asterisms pei ch'en (i.e., pei chi) and kou ch'en (‘the hooked array’: principal stars ζ, η, δ, ana αUMi). It is not unusual for these two polar groups to be referred to jointly; see K'ai yuan chan ching (Ssu-k'u chen-pen edn.), 67.23b-25a. Shu hsing is simply an obvious descriptive term for the pole star of the writer's epoch, and it is somewhat misleading to think of it as the name of a particular star, despite the fact that t'ien shu eventually became fossilized as a name for Σl694 Cam., the pole star under the T'ang. (The use of t'ien shu as an esoteric name for a UMa in the Western Han “weft books” is irrelevant here.)

67. Quoted in a T'ang commentary on the Shih chi, ch. 1, p. 24 and ch. 27, p. 1292. The thirteenth-century encyclopaedia Yü hai (repr. Taipei, 1964), 2.50a, notes in addition an obviously spurious version making the ch'i cheng the sun, moon and five planets; this is borrowed from Eastern Han commentators.

68. Shih chi ch. 27, p. 1291; this looks as if it might have been a genuine survival of an ancient usage rather than an archaizing coinage as in e.g., the use of the names hsüan and chi separately for stars of the Dipper in the “weft books,” see K'ai yuan chan ching 67.9a ff. A further argument for Fu Sheng having identified the yü heng with the Dipper in the lost section of his commentary is that the circumpolar region has no other object of comparable importance apart from the pole star, and this he has already identified with the hsüan chi. In his discussion of the phrase hsüan chi yü heng in the Shang shu, Liu Hsiang (Shuo yuan 18.1b) says that the hsüan chi is the pole star (see note 65), but follows this immediately by a reference to the divinatory significance of the direction indicated by ch'i k'uei piao ‘its bowl and handle.’ It looks as if the sentence “The yü heng is the Dipper” has dropped from the text, particularly as Liu gives no other explanation of this term. The Han shu, 21A.969 uses yü heng in a clear reference to the Dipper as a whole; it is possible that both Han shu and Liu Hsiang were influenced by Fu Sheng.

69. Shih chi ch. 27, p. 1291.

70. Translated in Harper “The Han Cosmic Board,” p. 2a.

71. Under the late Western Han the “weft books” indulged in various permutations of these terms, and others, as names for the stars of the Dipper: see the reference in note 68. There is no evidence that these names were ever more than literary conceits.

72. See Loewe, , Ways to Paradise, p. 77Google Scholar. The lacquer box-lid of the Marquis of Tseng (ca. 433 B.C.) is marked out very similarly to the heaven-plate of a shih, see note 1.

73. Other less likely possibilities present themselves. The yü heng could be the earth-plate of the shih, or taking another meaning of heng it could be a balance of some sort; in the story cited by Loewe (note 72) a balance heng and weights are used in setting up the shih. It is noteworthy, although the connection is unclear, that the Chou pi uses the word heng as a name for the seven circles defining the solar path: see above and note 14. There may be a correlation with the seven stars of the Dipper behind this choice.

74. Ssu-ma Ch'ien actually says that the Dipper yün yu chung yang “turns in the center,” although he was obviously aware that it is well off center in the night sky (Shih chi ch. 27, p. 1291). This seems to be another instance of the reality of celestial phenomena being replaced by the idealized scheme of the shih.

75. Liu Hsiang (Shuo yuan 18.1b) does, however, drop what may be a revealing hint. After explaining that the hsüan chi is the pole star (? and that the yü heng is the Dipper, see note 68), he refers to the divinatory significance of the hsiu indicated by the Dipper at any moment. On the celestial sphere the Dipper is of course fixed in relation to the hsiu, but on a shih such as that illustrated in Fig. 3 the hsiu are marked round the earth-plate as well as on the heaven-disc, so that it is possible for the Dipper on the rotating disc to point to each of them in turn. Could Liu, like Ssu-ma Ch'ien (note 74) be thinking of the shih?

76. I owe the suggestion of following the line of thought set out in the above section to a conversation with Dr. Michael Loewe in early 1977.