some further points on the "shih"

Society for the Study of Early China

SOME FURTHER POINTS ON THE "SHIH"Author(s): Christopher CullenSource: Early China, Vol. 6 (1980–81), pp. 31-46Published by: Society for the Study of Early ChinaStable URL: http://www.jstor.org/stable/23351654 .

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SOME FURTHER POINTS ON THE SHIH

Christopher Cull en

Clare Hall

Cambridge, CB3 9AL England

Donald J. Harper's recent article on the shih

^ gave a useful review of various questions con

nected with this ancient Chinese aid to divination.1 In addition we now have Michael Loewe's thorough discussion, which relates the shih to Han dynasty TLV mirrors and gaming boards and sets it

jn the

context of contemporary religious beliefs. In

this article I would like to raise a few points on

the relation of the shih to the development of Chi

nese astronomy. Further, it is possible that the shih may provide the key to an ancient problem of

classical scholarship.

I. Terminology

First of all, however, how are we to trans

late the word shih 3^ ? Needham and Loewe render

it as 'diviner's board';3 Harper prefers 'cosmic

board.' Both phrases are good descriptions of the

shih, but neither is strictly speaking a trans latitm of its name. If we are faced with a choice between striving to capture the precise nuance of

some Chinese word and making it clear what we are

talking about, the latter is usually preferable. In this case, however, it may be possible to do both.

In both Chou and Han texts the most frequent sense of the word shih is that of a rule, model or

pattern: it is often glossed as fa_-}£: Thus in

Lao tzu we have wei t'ien hsia shih ,. 5

"]C a 'be a model to the empire.' As Harper

notes, the object under discussion is clearly in tended as a model of the cosmos.6 Why not there fore translate the name shih directly as 'model,' or, if this is felt to be too unqualified, as 'cosmic model'? Such a rendering preserves the

meaning and associations of the word shih to a

high degree of accuracy while at the same time

making it quite clear what the object designated shih was meant to be. A T'ang commentator on the

Shih chi says of the shih: 'The heaven

plate is round and images (hsiang ^ ) heaven;

the earth plate is square and patterned on {fa_

~j-Î\ ) earth.'7 The rendering suggested here con

. tinues the parallelism between shih, hsiang and

fa as well as pointing to the view of the shih as a microcosm contained in this and other texts. The word 'board' in the versions of Needham and

Harper is totally lacking in such resonances.8

II. The shih as a cosmographie model

The purpose of the shih is to provide a conveni ent diagrammatic representation of the cosmic influ ences determining human fate: to this extent it is a cosmic model in an abstract sense. It is, how

ever, also a small-scale model of the physical uni

verse, and may thus more particularly be called a

cosmographie model. An early reference to the view of the universe it portrays is found in a fragment

of a poem by Sung Yii rp 3- , written ca. 300 B.C.:

The square earth is a chariot (ch 'eyL ); ' Q

The round heaven is its umbrella (kai ).

Similar expressions were a commonplace of Han

thought.10 At some time during the late Warring States period such ideas had already been developed into a quantitative cosmography of some complexity;

later sources refer to this as the kai t'ien

^ ('umbrella-[like] heaven') theory.11 In the

basic form of this cosmography described in the

late Western Han compilation Chou pi )f] flf. the

round heaven and the square earth are flat and

parallel planes separated by a distance of 80,000

Jj.1^ The width of the square earth (ssu chi chih

chinq ·30 'the diameter of the four limits')

is 810,000 21, and the diameter of heaven is equal to or somewhat less than this.13 Heaven rotates once daily about an imaginary vertical axis passing through the center of the earth, in just the same

way that the heaven plate of the shih cosmic model turns on its pivot. The center of heaven is the north celestial pole, near which is the constella tion of the Northern Dipper which figures promi nently in the center of the heaven-disc of the shih. The point on the earth directly below it

corresponds to the earth's north pole; the Chou pi

gives a realistic description of this location as surrounded by unmelting ice and experiencing a six

monthly alternation of day and night. The Chinese observer is said to be 103,000 lj_ away from the

subpolar point, which explains why the celestial

31



pole is not directly overhead. The sun, moon and stars are attached to heaven and follow it in its

daily rotation; in addition the sun and moon move

slowly relative to heaven, performing a circuit in the course of a year and a sidereal month respec tively. The sun is 119,000 from the pole at the summer solstice and 238,000 ΤΓ from the pole at the winter solstice: this radial shift explains the annual cycle of temperature and solar altitude. The

problem of explaining day and night on the basis of a flat-earth cosmography, which might seem to imply that all heavenly bodies should be continually vis

ible, is ingeniously solved by the postulate that both human vision and the radiance of bodies such as the sun extend outwards no farther than a distance of 167,000 11· Thus when the rotating heaven carries the sun farther than this distance away from the

observer, night falls; sunset is an optical illusion.

The connection between the shih and the kai t'ien cosmography appears clearly in the plan of the

universe drawn by Chao Shuangj^ ^ for his commen

tary on the Chou pi written ca. A.D. 220. Most cur rent versions of the text reproduce a diagram of the form shown in Fig. 1, but comparison with Chao's

commentary suggests strongly that it has become somewhat garbled through repeated copying. An at

tempted restoration of Chao's original figure is shown in Fig. 2. In addition to the inner and outer circles marking the sun's daily path at the summer and winter solstices respectively, Chao has follow ed the text in depicting five further circles re

presenting the solar path at intermediate seasons;

these seven circles are termed heng ffif· by the Chou

pi.^ The eccentric circle marks the limit of

sight for the Chinese observer at the position shown, and the enclosing square is said by Chao to

represent the ssu chi 'four limits,' that is,

the extent of the earth.^

If we compare Chao's diagram with a well-known excavated specimen of a shih from ca. 165 B.C. (Fig. 3), the resemblance is obvious. No one who knew the kai t'ien theory could have seen a shih cosmic model and missed the connection. It would, however, be

misleading to regard the shih as simply a kai t'ien

orrery; it was not made in order to provide a phy sical illustration of a theory, but was constructed

by men who needed an adjustable model of the uni verse for practical purposes. The form of the cosmic model they used is clear evidence that their ideas of the world were in the same tradition as the cosmographie scheme of the Chou pi.

Neither the Chou pi nor any other description of the kai t'ien theory mentions the shih explicit

ly. The connection of the shih with divination may have meant that it was not thought of as a complete ly respectable association to invoke.16 It is, however, more likely that its existence as a model of the universe was so much taken for granted that

it was felt that no explicit discussion was re

quired J ? Despite the lack of direct references, there is evidence that kai t'ien theorists were influenced by the abstract divinatory sequences used on the shih in the same way that diviners drew on physical cosmography in the construction of

their instruments. Thus the Chou pi describes a

procedure which involves the marking out of a 120 feet diameter circle on level ground and the gradu

ation of its circumference into 365% t£ ^

gnomon is erected at its center, and with the aid of a movable gnomon on the circumference a series of sightings are taken on the standard stars of the

28 hsiu îffj , with the object of determining the

width of each hsiu in right ascension. The method

given involves a crude approximation of differences in right ascension to changes in azimuth; it could

not have yielded useful results and was probably never tried in practice J° A section of the text reads:

When Tung Ching -tf is centered (chung

, i.e., on the meridian) at midnight,

then the beginning of Ch'ien Niu ^ 'ή

falls over the middle of (the horizon div

ision) tzu . When Tung Ching is 30 tij

and 7/16 to the west of the central fixed

gnomon and falls over the middle of (the

horizon division) wei ^ , then the begin

ning of Ch'ien Niu falls over the middle of

(the horizon division) ch'ou jg. . At that

moment, heaven is matched with earth

(t'ien .yu ti hsieh ^ i-C. +$>) J 9

These statements bear no more than a rough correspondence to reality. The text assumes that

the standard stars marking the initial points of

the hsiu Tung Ching ( μ Geminorum) and Ch'ien Niu

( β Capricornis) are diametrically opposite in

right ascension, so that when the first is cross

ing the meridian due south of the observer the

second is due north of him (although out of sight over the northern horizon). In the first century B.C., the right ascensions of these stars were close to 65° and 276° respectively, so that align ment was missed by over 30°. On the heaven-disc of the shih shown in Fig. 3, however, the hsiu are laid out at equal intervals round the circumfer ence and the alignment is very close to that speci fied by the Chou pi. Thus, when the dot marking the position of Tung Ching on the disc falls over

the cyclical sign w ip

in the center of the

south side of the earth-plate (and is thus 'cen

tered'), the dot marking Ch'ien Niu is within a

few degrees of tzu in the middle of the north side.

When Tung Ching has moved through 30 tu 7/16 (i.e., 30°) to wei, Ch'ien Niu has shifted through an

equal angle and falls near ch'ou.20 Most signifi cant, however, is the statement that when this has occurred heaven and earth are 'matched,' hsieh.

It is precisely under these circumstances that the

28 hsiu marked on the heaven-disc are arranged in

correspondence with their names round the edge of

the earth-plate. It is clear that the author of

this section of the Chou pi was strongly condi

tioned by the schematic view of the universe em

bodied in the shih cosmic model.

32



Fig. 1. The kai t'ien universe as described in the Chou pi (first century B.C.), from the diagram of Chao

Shuang (ca. A.D. 220), as reproduced in a Ming dynasty printing of the Chou pi (SPTK ed.) 1.55b.

s

X 100,000 LI

Fig. 2. Reconstruction of Chao Shuang's original diagram in accordance

with his commentary to th<: Chou pi.

33



III. The shih and early astronomical instruments

The shih of Fig. 3 is of very little direct astronomical use. Thus, for instance, the depic tion of the hsiu as spaced round the heaven-disc at

equal intervals rather than with their true and

widely varying widths in right ascension makes it

impossible to predict which of them is on the mer idian at a given moment. The shih is an instru ment graduated with ordinal scales rather than ratio scales: its purpose is to relate sequences rather than register quantities, and that was

probably all that a diviner required of it. A different principle seems to lie behind another

object excavated from the same tomb as the shih discussed here (see Fig. 4).2

2 It resembles the classic form of the shih to some extent; like the shih it has a round heaven-disc marked with the stars of the Northern Dipper and mounted on a base

plate by means of a pivot. An obvious difference, however, is that the base-plate is circular rather than square. It is further evident that the

markings on both discs are rather different from those on the shih. Apart from the Northern Dipper and the pair of perpendicular lines through its

center, the upper disc appears to have been divided round its circumference into 365 tiK The lower disc bears the names of the 28 hsiu in anti clockwise sequence; these are spaced at realistic

intervals, and the number of tu occupied by each hsiu is marked below its nameT2^ Like the upper disc it is marked with a pair of perpendicular lines through its center.25

Unlike the shih, it seems likely that this instrument was intended as a source of quantitative astronomical data rather than as a framework for

setting up symbolic correlations. In the absence of literary evidence as to how it was used, the nature of early Chinese astronomical practice sug gests a number of possible applications for such an

object:

(a) Finding the position of the sun on any given day of the year. The crossed lines on the lower disc indicate the hsiu in which the sun lies at the solstices and equinoxes; to find its

position η days after one of these dates, one uses the circumferential markings of the upper disc to count η tu anti-clockwise from the initial posi tion. 2°

(b) Finding the position of the moon at a

given time of a given month. At the beginning of

a month, shuo , the sun and moon are in con

junction and lie in the same hsiu. Thereafter the moon's position may be found by counting off increments of its mean daily motion of 13 tu anti clockwise. A more convenient method for locating the moon at its main phases would be to count off the motion of the sun (close to lh tu/quarter month), and use the perpendicular lines on the

upper disc to locate the positions of quadrature and opposition as appropriate.2'

(c) Finding the hsiu on the meridian at any given date and time. First locate the sun as in

(a), and set the upper disc so that one of its lines marks this position. The hsiu diametrically opposite is the one which will culminate at mid

night, and the two ends of the perpendicular line indicate those which will culminate at 6 a.m. and 6 p.m. Data for intermediate times can easily be found by interpolation.

It seems quite likely, therefore, that the device before us is a variety of astronomical ready-reck oner. All the procedures outlined above can equally well be performed by simple arithmetic alone, but it cannot be denied that the use of the device enables results to be obtained with much greater ease. One

particular difficulty of calculating in the Chinese

system is that the hsiu sequence divides the heavens into a number of discrete and independently gradu ated sections rather than into a continuous sequence of degrees; with the use of the discs this obstacle

disappears. While this device is not in itself intended for divination, it would clearly be a valuable auxiliary in the manipulation of the shih for that purpose. There is good literary evidence that the positions of the sun and moon were neces

sary data in setting up the shih, and it would indeed be somewhat surprising if this was not the case.28 The inclusion of the graduated discs in a set of divination equipment is therefore unlikely to be a mere coincidence.

The question arises as to what we are to call this previously unknown device. Since it does not

appear to correspond to any object described by ancient writers, a new term must be coined. The excavation report refers to this object as an

erh-shih-pa hsiu yûan p'an j— ]|3 90

"disc of the twenty-eight hsiu.' Harper on the other hand suggests "Dipper dial."30 "Dial" is

certainly better than "disc" for an adjustable ob

ject, but one may question the implication that the Dipper is really more important than the hsiu on this device. Perhaps the best of both terms can be combined if, adopting the translation of hsiu as "lodge," we call the object in question a

"lodge dial."31

It has been suggested that the lodge dial may have served as an instrument for making astronomi cal observations.32 There are a number of reasons for doubting that this was the case. In the first

place the lodge dial device was found in close assocation with objects whose purpose was clearly divinatory rather than observational, and it is similar to them in construction; as we have seen it is not unlikely that it served as an auxiliary reckoning device. Secondly, the suggestion that a diviner might need to make astronomical observations in the normal course of his work ignores the level of development that had been attained by contem

porary Chinese calendrical astronomy. As Nathan Sivin has said, calendrical astronomy was the art of not having to look at the heavens, and by the late Warring States period a number of systems had been developed which were capable of yielding mean values for the positions of the sun and moon

by the use of simple arithmetic.33 One of these

systems, the Chuan hsii li , was offici

ally approved under the Ch'in and early Western Han and seems to have been the system underlying the design of one of the shih found with the lodge dial. 4 Not to have used the official system might well have been taken as a treasonous act.

Thirdly, and perhaps most significantly, the

lodge dial as represented in this specimen is ill

adapted to serve as an observational instrument. No sighting aid of any kind is apparent, and the size of the graduations on the upper disc (approx.

34



(a) f

(b)

Fig. 3. Shih cosmic model, early second century B.C., from Kaoqu 1 978.5:340; (a) line drawing of original object, (b) schematic drawing. Note the incorrect placing of some of the twelve

cyclical characters on the middle band of the earth-plate in (b). The actual width of the

earth-plate is 13.5 cm.

Fig. 4. Two early second century B.C. graduated discs, components of the "lodge dial" (F?rper:

"Dipper dial"), drawing from Menwu 1978.8:19; actual diameter approximately 25 cm. Modern

characters for some hsiu have been added.

35



2mm/ltu) is so small that naked-eye estimation might yield comparable accuracy. Further, the presence of the 28 hsiu representing divisions of the sky in

right ascension argues that as an observational de vice the lodge dial would have had to be fixed in the plane of the celestial equator; in the approxi mate latitude of Lo-yang this is inclined at an

angle of 55° to the horizon. No provision for this is apparent. Supposing the necessary arrangements made, a further problem arises: the sun and moon do not move along the equator, but follow the eclip tic, which is inclined to it at an angle of 23^°; the moon may be up to 5° from the ecliptic. It is

very hard to see how the lodge dial alone could have been of much use in determining the position of bodies 1yiog so far above or below its plane of

operation.·"

Although the lodge dial itself was probably not an observational device, it nevertheless has con siderable significance as the earliest known example of a graduated circle in the history of Chinese

astronomy. One must therefore consider the possi bility that it is an ancestor of the graduated rings which made up the main instrument of Chinese astron omers from the Han dynasty onwards, the armillary

sphere, hun t'ien i -*ψ ^ -jj^ .3® A simple form of

this instrument, such as seems to have been in of ficial use in the first century A.D., is sketched in Fig. 5. It is in effect a dissected model of the celestial sphere, provided with sights, and so

arranged that the hour angle and north polar dis tance of any visible celestial body can be deter mined at will. As its name implies, this instrument

was closely connected with the hun t'ien ^

'continuous heaven' cosmography, according to which heaven was a continuous sphere surrounding the flat

earth, rather than a covering umbrella-shape as held by kai t'ien theorists."

The early history of both instrument and

cosmography are somewhat obscure; the earliest

explicit references occur near the beginning of the Eastern Han. Yabuuchi's analysis of early obser vational data suggests that armillary instruments

may have been in use in the early first century B.C.;38 such a date accords well with the tradition

recorded by Yang Hsiung Ίφ (53 B.C. - A.D. 18),

who recounts the following dialogue between himself and a questioner:

Someone asked about the hun t'ien. He replied

'Lo-hsia Hung |Ίτ f ^ (fl. 110 B.C.) thought it out (.ying chih ) ; Hsien-yu Wang-jen

$2^ ^ jg. (fl- 80 B.C.) gave it dimen

jions (tu chih sL); Keng (Shou-ch'ang <§ ) the palace assistant (fl. 50 B.C.) made

a representation of it (hsiang chih è~).

How exact it is! No one can contradict it.'

They asked about the kai t'ien. He said 'The kai! The kai i It leads to difficulties and is inaccurate.'39

In isolation the phrase hun t'ien can refer to the

cosmographie theory or the instrument embodying it, but in the present context it seems clear that the

theory is intended. In the first place, the hun t'ien is contrasted with the kai t'ien, and there are no known instances of the latter referring to an

instrument; we are also told that the hun t'ien can

not be contradicted (wei ), which is obviously

more appropriate for a theory. On this interpreta tion Lo-hsia Hung conceived of the heavens as a ro

tating sphere, Hsien-yu Wang-jen put the theory on an exact basis by working out the quantitative de

tails, and Keng Shou-ch'ang made a physical repre sentation, possibly a prototype armillary sphere.4°

The limited amount of independent data on the activities of these three men is not inconsistent with Yang Hsiung's account, and to some extent con firms it. The use of the armillary sphere for pur poses of calendrical astronomy is discussed in part of a memorial submitted to the throne by Chia K'uei

in A.D. 92; as an early example he quotes

from a report submitted by Keng Shou-ch'ang in 52 B.C., in which Keng stated that he had 'measured the motions

of the sun and moon with a t'u i gjj , and checked

the phenomena of the celestial rotation.Keng's t'u i (charting instrument?) sounds very much as if it might have been the object mentioned by Yang Hsiung as the first physical embodiment of the hun t'ien theory. Of Hsien-yu Wang-jen we know only that he led the defense of the official T'ai ch'u

7$χ) ('Grand Inception') calendrical system 42

against an attack on it made in 78 B.C. Hsien-yu headed a team of over twenty men who carried out a

program of observation extending over two years, but there is no record of what instruments they used.

Despite this he was clearly in an excellent position to gather data for the new hun t'ien theory as Yang Hsiung says that he did.

Lo-hsia Hung himself, to whom Yang Hsiung as cribes the invention of the hun t'ien, played a

major part in the great calendar reform which cre ated the Grand Inception system defended by Hsien-yu Wang-jen. The necessity for this reform had been

urged by Ssu-ma Ch'ien £] fa and others in a

memorial of 116 B.C.^ On receipt of the imperial commission these men

fixed east and west, erected gnomons (kuei i

) and set water-clocks working, in

order to investigate the spacing of the twenty eight hsiu in the four quarters (of the heavens), their aim being to determine (the instants of) the beginnings and ends of lunations and of the equinoxes and solstices, and follow the succession of crescent and full moons.44

Other calendrical experts were also recruited,

more than twenty men in all, amongst whom

were the mage (fang shih -jç ± ) T'ang Tu

M , and Lo-hsia Hung from Pa 2L

prefecture (in Szechuan). Tu divided heaven into its sectors (i.e., the hsiu), and Hung carried out calculations to revise the

calendar (yun suan chuan 1i v!L ) ·45

36



Fig. 6. Bright stars in the region of the north celestial pole, 200 B.C. The positions of stars have been calculated for this epoch and plotted in^olar coordinates. The dotted curved line represents the path taken by the celestial pole in the slow movement caused by precession; it has been approximated by an arc of a circle centered on the pole of the

ecliptic. The right ascension of the sun is 0° at the spring equinox, 90° at the summer solstice, 180° at the autumn equinox and 270° at the winter solstice. The approximate mag nitudes of stars are shown as: © 2nd., A 3rd., X 4th. Constellations are shown ac

cording to the traditional Chinese 'ball-and link' convention.

NORTH

Fig. 5. Simple form of armillary sphere, cap able of measuring declination and differences in right ascension.

SOUTH PIVOT

A % Boo.

Fig. 5. Simple form of armillary sphere, cap able of measuring declination and differences in right ascension.

Fig. 6. Bright stars in the region of the north celestial pole, 200 B.C. The positions of stars have been calculated for this epoch and plotted in^olar coordinates. The dotted curved line represents the path taken by the celestial pole in the slow movement caused by precession; it has been approximated by an arc of a circle centered on the pole of the

ecliptic. The right ascension of the sun is 0° at the spring equinox, 90° at the summer solstice, 180° at the autumn equinox and 270° at the winter solstice. The approximate mag nitudes of stars are shown as: Ο 2nd., Δ 3rd., X 4th. Constellations are shown ac

cording to the traditional Chinese 'ball-and link' convention.

37



The completed system was finally promulgated in

104 B.C.

If Lo-hsia Hung made use of a hun t'ien i

armillary instrument there is no sign of it here or in any other early document.46 in any case, the

gnomons and water-clocks mentioned in the above account were quite adequate to the observational

requirements of those who set up the Grand Incep tion system, which limited itself to considering the mean motion of the sun and moon in right as cension. 47 For such purposes, as well as for

checking the widths of the hsiu, simple transit

timings were all that were required in addition to determination of the solstices by gnomon shadow observations.48 Further, the role allotted to Lo hsia Hung in the text is that of a theoretician rather than a practical observer. It does not therefore seem unlikely that, as Yang Hsiung seems to suggest, Lo-hsia Hung was the originator of an idea rather than the inventor of an instrument.

What role might have been played by a device such as the lodge dial in the development of the hun t'ien theory and instrument as outlined above? I conjecture that it may have fulfilled an impor tant function in forming the concept of the heavens as a framework of great circles, all of which can be graduated in the same units. This

concept, absent from the kai t'ien, was an essen tial ingredient of the hun t'ien system. In early

Han sources the astronomical unit tij , common

ly translated as 'degree,' was strictly limited to

measuring what we would now call right ascension; in terms of the kai t'ien cosmography embodied in the shih cosmic model, a certain number of ti[ corresponded to a certain amount of rotation of the heavenly disc. Other astronomical measurements

were expressed in feet ( ch ' i h ) or decimal

inches (ts'un ~^r ); the interpretation of such - 49

measures is still somewhat problematic. This distinction can be traced back to the overwhelming concentration of early Chinese stellar astronomy on the meridian transit; some of the earliest ex tant Chinese astronomical data consist of lists of asterisms which would lie on the observer's merid

ian (literally 'be centered' chung φ ) at vari 50

ous seasons of the year. When the system of the

twenty-eight hsiu was set up, the northerly or

southerly position of the defining asterisms does not seem to have been of much importance: any celestial body that crossed the meridian simultan

eously with the relevant asterism was said to be 'in' the hsiu in question. The 'width' of a hsiu in tu^ amounted to no more than a count of the

number of days the sun spent in it. A relative

ly crude estimate could be obtained with the help of nothing more than a pair of gnomons set up on

a north-south line for sighting purposes, but the

use of a water-clock to time intervals between

transits in the diurnal rotation of the heavens

would add both convenience and accuracy; this was

evidently standard practice in the time of Ssu-ma Ch'ien and Lo-hsia Hung.52 The tjj was basically a measure of time rather than of angle, and there would obviously have been a considerable concep tual barrier against using it as a measure for north-south distances where no timeable rotation

53 was involved. This was nevertheless what was done in the hun t'ien scheme.

The function of the lodge dial in this process may have been as follows. The graduation of a disc into tu may not at once have created an observa tional instrument, but it did provide a physical model of a concept that had previously been under stood in terms of counting or timing. The way was then open for someone to pick up the device and

attempt to arrange it in correspondence with the

rotating night sky by holding it at an appropriate angle to the horizon for it to be parallel to the

paths of the celestial bodies; this would natural

ly place it in the plane of the celestial equator. Such a manipulation could have pointed the way to wards two important insights:

(a) The concept of the celestial equator as

a great circle running round the heavens and divided

into tu^, the macrocosmic counterpart of the gradu ated disc of the lodge dial.^^

(b) The realization that this great circle was

at any instant divided into two equal halves, one visible above the horizon and the other symmetrical ly positioned below the earth.

The second of these in particular, with its obvious

implication that the heavens lay below the earth as

well as above it, is in clear contradiction with the kai t'ien cosmography and leads directly to the hun t'ien concept of the heavens as a rotating

sphere surrounding the earth. If we follow the tradition passed on by Yang Hsiung, it is possible that Lo-hsia Hung gained such an insight in the context of the detailed review of astronomical data

in which he took part around 110 B.C. Since we

are told that the widths of the hsiu were re-mea

sured at that time, renewed interest in the use of

the lodae dial would have been by no means un

1i kely.55

As Yang Hsiung's account suggests, the crea

tion of the hun t'ien theory does not entail the

simultaneous development of the hun t'ien i armil

lary sphere. Measurements of right ascension, the celestial coordinate of most interest to Western Han calendrical astronomy, were already fairly adequately dealt with by traditional methods of

transit timing. While the concept of the heavens as a sphere certainly led to the extension of the

application of the ti[ to measurements of such

quantities as north polar distance in planes per pendicular to the equator, a complete armillary

sphere was not necessary for this. All that was

required was a single graduated circle, possibly a modified lodge dial provided with sights; at first it may even have been fixed in the meridian

plane. The stimulus to combine an equatorial and a polar ring into a single instrument, capable of

giving an immediate determination of the coor dinates of any celestial body, may have come from a wish to investigate the phenomena in more detail

than traditional calendrical astronomy had pre

viously demanded. It is therefore striking that

Keng Shou-ch'ang, to whom Yang Hsiung ascribes

the first physical representation of the hun

t'ien, should be on record as having conducted researches into the inequality of lunar motion. 6

Whatever the true story of the development of

the hun t'ien theory and instrument, both were

38



certainly widely known by the end of the Western Han. Indirect evidence of this may be found in the Chou pi, which was compiled around this time.

Although this work is firmly committed to the kai .

t'ien, one section of it consists of a highly dubious attempt to fudge the calculations so that the traditional methods may be made to yield values for the sun's north polar distance in tu at the solstices and equinoxes, a clear attempt to com

pete with the hun t'ien.5^ If as has been sug gested here the hun t'ien may have been inspired by an object that was originally a kai t'ien cos mic model, this seems a little ironic.

IV. The shih and the hsiian chi yii heng

The Yao tien ^

J®· chapter of the Shang shu

V% Ί|" is generally held to have been compiled at

some time during the fifth or fourth centuries B.C. After describing the reign of the mythical

emperor Yao ^ , the text records the accession

of the virtuous commoner Shun whom he chose as

his successor. Shun's first act after receiving Yao's abdication is given in the words

it- 3, tiq »A If ^ tsai hsiian chi .yu heng i ch'i ch'i cheng

Or, in Karlgren's reconstruction of archaic Chi

nese: *dzag dzjwan kjar ngiuk g'Sng ζjag dz'iar

ts'jët tjëng.59 I have discussed the exegesis of

this passage at length elsewhere, and for the

present purpose it would not be relevant to give more than a brief outline of my conclusions.50 A

partial translation of the sentence may be given as

(Shun) attended to the hsiian chi yii heng so as to set in order the seven (concerns

of) government.61

What, however, is meant by the phrase hsiian chi .yii

heng which designates the object of Shun's atten

tion? There appear to be no instances of its use

which are independent of the Yao tien, and the

context does not provide any obvious clues. One

fairly straightforward possibility, based on pre Ch'in evidence for the meanings of the words in

volved, is that hsiian chi and .yii heng refer to

objects made of jade or some other precious mate

rial, perhaps forming part of the royal insignia assumed by Shun on his accession. It is not, how

ever, clear why Shun should have found attention to

such objects helpful in ordering state affairs. Another possibility is suggested by the existence

of early quotations from the Yao tien in which

ί§- hsûan chi/*dziwan kjar is replaced by

homophones which suggest that the text may origi

nally have been understood as^j-o^;^ 'rotating

device.' All ancient explanations of the passage in question do in fact involve rotation of some

kind, even when the reading of the current text

is retained. None of these glosses is earlier

than the Western Han, but the oldest of them may

tpreserve a link with pre-Ch'in traditions. Accord

ing to Ssu-ma Ch'ien, the scholar Fu Sheng ^j^

ifc hid his copy of the Shang shu during the

Ch'in censorship, and lived to recover part of it

shortly after the beginning of the Han dynasty in

206 B.C.62 One of the surviving fragments of Fu

Sheng's exposition of the ancient text deals with

the events of Shun1 s accession; a quotation from

the text is followed by an exegesis:6^

"On' the first day of the first month (Shun)

accepted the abdication (of Yao) in the

(temple of) Accomplished Ancestors. He

attended to the hsiian chi γ'ϋ heng 5^

?.. so as to set in order the

seven (concerns of) government." What is --Λ'

the hsuan chi? The commentary says:

hsiian/*dziwan means hsLian/*dz1 iwan

('rotate'); chi/*kjar64 means

chi/*kjar ('incipient') or 45^ wei/*miwar

('subtle').65 The thing which changes infinitesimally but moves something great

is called the hsuan chi ; therefore

the hsiian chi (may be) said to be the dfc.

Jfâx pei chi/*p?k g'igk north pole (star).66

As for the 'seven (concerns of) government,' another fragment of Fu Sheng's commentary explains these as 'spring, autumn, winter, summer, the signs of heaven, the pattern of earth and the way of

man.'67 The clear implication of Fu's gloss of

the Yao tien is that Shun began his reign with an

act of stellar divination, his object being to en

sure the regularity of the cosmic order for which

he had assumed responsibility. The hsiian chi is

taken to be the pole star, which as we have seen

was probably eUMi at this epoch. There is no

record of Fu Sheng's interpretation of the words

,yii heng, but if the hsiian chi is the pole star, both the context and the literal sense of the term

'jade crosspiece' suggest that .yii heng could be a

reference to the Dipper itself. Supporting evi

dence is given by the fact that Ssu-ma Ch'ien uses

heng as the normal name for the fifth star of the

Dipper, "eUMa, as distinct from k'uei 'the

bowl' (-a to SUMa) and piao 'the handle'

(ζ and riUMa).68 His view of Shun's actions differs

somewhat from that of Fu Sheng. According to his

T'ien kuan shu:

The seven stars of the Northern Dipper are

what are called 'the hsiian chi .yii heng

f°r setting in order the

seven (concerns of) government.'6®

The encomium on the cosmic importance of the Dip

per which follows this statement makes it plain

why Ssu-ma Ch'ien thought that Shun would have

been likely to seek guidance from it.70 Except in

the case of heng already mentioned, it does not

seem that the terms hsiian chi yii heng were ever

the usual names for stars under the early Western

39



Han. One strong argument that the usage was un common is the fact that Fu Sheng and Ssu-ma Ch'ien both felt that the words of the Yao tien required some explanation. On the basis of the literary evidence alone all that can be said with certainty is that in the second century B.C. there was a tradition that the obscure expressions of the ancient text referred to an act of divination by Shun, evidently involving stars near the pole such as the Dipper.

It may however be possible to reach a more definite conclusion as to precisely what the com

pilers of the Yao tien had in mind. A key to the

difficulty may be to recall a fact that would have been so obvious to Fu Sheng and his contemporaries as to seem not worth mentioning: anybody who wanted to use the Dipper for divinatory purposes would naturally have done so by means of a shih cosmic model. To mention the Dipper was auto

matically to call the shih to mind, in the same

way that a statement of a ship's course makes one think of a compass dial. Thus the tradition that Shun consulted the configuration of circumpolar stars at the beginning of his reign should alert us to the strong possibility that the Yao tien is

describing the use of the shih, although quite possibly in terms which had become obsolete by the

beginning of the Han dynasty.

The scheme of thought on which the shih was based can be traced back into the period of the

Warring States, and there is one story of its use as early as the sixth century B.C.'2 It is there fore not impossible that the shih (or at least a

prototype or predecessor of the device later so

called) was known to the compilers of the Yao tien in the fifth or fourth centuries B.C., and it cer

tainly presents itself as a plausible candidate for the object from which Shun sought guidance in his

handling of state affairs. The heaven-disc of the

shih is definitely a rotating device hsiian chi

; the figure of the Dipper lying along one

of its diameters could easily have been the yii heng 'jade cross-(?marking).''3 On this basis, a free rendering of the Yao tien passage might be as fol 1ows:

(Shun) attended to the rotating (divination) device and the Dipper (marked on it), so as to set in order the seven (concerns of) government.

If this was indeed the original meaning of the ancient text, it is not difficult to imagine how

the traditions of exegesis represented by Fu

Sheng and Ssu-ma Ch'ien could have arisen. In the

case of the former, a name once applied to the heaven-disc as a whole has been affixed to its

pivot, the microcosmic equivalent of the celestial

pole. In the latter instance the importance of the Dipper has allowed it to take over the entire

expression hsiian chi .yii heng, no reference being made to the disc on which it is marked, or to the

celestial pole represented by the central pivot. This shift seems to be reflected on the shih it

self, where the Dipper has been displaced so that

it occupies the center of the heaven-disc and

usurps the astronomical position of the pole star.'4 On the lodge dial in particular it is

noteworthy that ε UMa, whose name was heng as we

have seen, is placed in the polar position where one would normally have expected to find g UMi, one of whose names was hsiian chi. Thus, perhaps, the pole and the centered Dipper become a single entity, the hsiian chi yii heng as described by Ssu ma Ch'ien.

The hypothesis outlined above may be plausible, but its evidential basis is as yet decidedly slim. As one might have expected, given the fact that the words of the Yao tien were already obsolete enough to require exegesis, no Han writer gives any explicit sign of using the terms hsiian chi yU heng as names for the shih.75 Apart from the Yao tien

itself, no pre-Han examples of this phrase are known. The lack of pre-Han specimens of the shih

might conceivably be supplied by new archaeological discoveries, but even then it seems unlikely that we shall ever know what the early name for such devices was. Until such evidence becomes available, the hypothesis that the story of Shun describes the use of a shih can be regarded as little more than an interesting speculation.76

FOOTNOTES

1. Harper, "The Han Cosmic Board (Shih)Early China 5 (1979): 1-10. In the following comments on

Harper's article references are to page, column and paragraph of his text. lb.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).1 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.). 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 (E.H. Schafer, Pacing the Void [Berkeley, 1977], p. 44) is in any case talking about the

T'ang and not the Han at all. If the Knot Star is

to be identified with Σΐ694 Camelopardalis, then

a simple graphical construction shows that it was

within a degree of the pole for most of the T'ang,

40



but was about six degrees away in 200 B.C. (Fig. 6). Needham's statement that "(the Knot Star) was cer

tainly 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 impor tant 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 jfo. » and Ssu-ma Ch'ien says

that it is T'ai I ch'ang chu ^ ^"the fixed

place of the Great Monad" (Shih chi [Peking, 1962], ch. 27, p. 1289). 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 yuan ch'i

7t. ^ '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 celes tial 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 dis tinction 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 (Yen Tun-chieh in Kaogu 1978.5:337), 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. (Chugoku no ·

Temmonrekihô ̂ I[Tokyo, 1969],

pp. 46-75. However, in his discussion of the disc

graduations, P'an Nai ^ suggests that they may

pre-date the Shi h Shen data (Wo-kuo tsao-ch'i-ti erh-shih-pa-hsiu kuan-ts'e chi ch'i shih-tai k'ao

in Chunq-hua wen-shih lun-ts'ung

[Shanghai, 1979], pp. 137-182, particularly

p. 158ff.). Ρ'an holds to a date of ca. 450 B.C. for part of the Shi h 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 Sivin has pointed out (private coitmunication). 4a.2 and note 40: Harper's remarks on the position ing 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. M.A.N. Loewe, Ways to Paradise: The Chinese

Quest for Immortality (London, 1979), chapter 3.

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

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. 3218.

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 subse

quent discussion. My reasons for this are two-fold:

firstly it avoids the frequent appearance of tautol

ogy 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 tech nical discussion addressed to a sinological reader

ship.

9. Pei t'ang shu ch'ao Jfc,(repr. Taipei, 1962) 149.3b". 7

10. The same comparison is made in Huai nan tzu

")jt , compiled ca. 120 B.C. (SPTK) 1.4b; see

also 7.2a and 15.3a. Near the beginning of the

Chou pi suan ching Jp|- 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

41



of the Ta Tai 1i 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 wide

spread, (Han Wei ts'ung shu > ec'·

Ch'eng Jung5.7b.).

11. The earliest firm evidence for the existence of this theory in a systematic form is found in the

LU shih ch'un ch'iu g "fK.' compi 1 ed 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 Nakayama Shigeru in his A History of Japanese Astronomy (Harvard, 1969), pp. 24-43. While the survey of Needham

(S.C.C. Ill, 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 ins tance Nakayama, op. cit. A detailed discussion of

this work will be found in Nôda Churyô © jfe,

Shûhi sankei no kenk.yu ^

(Kyoto, 1933). 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 21, 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 il lustration.

18. One motive for including this method in the Chou pi may have been an attempt to show that kji

t'ien methods could compete with the newly developed armTTlary 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 northern most 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 jjj. , 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. 205.

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 j\- ; this accords with the scheme of the Yueh

1ing (see note 21). Since Tou and Tung Ching are fourteen hsiu apart, equidistant hsiu spacing would lead to exact opposition of the corresponding mark

ings on the heaven-plate. Near the time of manufac ture of the shih in the second century B.C., the

right ascension of the determinative star of Tou

(ψ 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 be low and Fig. 4), it was therefore a reasonable ap proximation 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 opposi tion was less empirical than theoretical: the fact that the solsticial solar positions are in opposi tion has led to the idealized view that the determin ants 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

SL for the first month) marked against twelve of

the hsiu on the heaven-disc (see also Kaogu 1978.5:

334). The data on the shih differ in three cases

from those in the Yueh ling ^chapter of the

Li chi /jffi gf. : Chang (not I ]pL ), 7th.

month; Ti fa (not Fang ), 9th. month; Hsin

(not Wei ), 10th month. As a practical

guide to the actual position of the sun, the infor mation 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

42



4n 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 rota tion of the Dipper," but I do not think that the

markings on the heaven-disc bear this out. Accord

ing 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 Dip per, 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 phenom ena. The equidistant spacing of the hsiu allots

(e.g.) the same width to Kuei ^ (5 tu) as to

Ching jf (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 Dip per at some fixed hour changes by 2/28 of a revo lution (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 1978.8:12ff. and the discussions in Kaogu 1978.5:334-337 and 338-343.

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 Dip per 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 oc curred. Thus the initial points of the solsticial

hsiu Tou j5j- and Ching 4f" are shown as diametri

cally opposite each other, although according to the extensions marked the angle from the first to the second is only 178 tu (175°) counted anti clockwise. Following the month markings on the

shih, one might have expected that the equinoctial

hsiu K'ueiJ^" and Chiieh fê\ would have appeared oij) the perpendicular diameter; the problem is, however, that the obtuse angle between them is only 173 tu

(170%°; 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 gradu ation by the amount required to position Chiieh op posite K'uei, it was found preferable to replace

Chiieh by the adjacent hsiu Chen (lost by break

age of the edge of the disc). This involves ap

proximating 180° by 189 tu (186°). An error of one

tu represents one day's solar motion. The two per

pendicular 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 be

tween the celestial pole (or perhaps the pole star

β UMi) and the last star of the handle (n 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 en

larged 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 ascen sion daily. The effect of the surfs 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, Chûgoku no Temmonrekihô, pp. 307-309.

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. 77-78. The

marking of the monthly solar positions on the shih of Fig. 6 confirms this view.

43



29. Wenwu 1978.8:14.

30. Harper, "The Han Cosmic Board," p. 1.

31. See J. Major, "A Note on the Translation of

Two Technical Terms in Chinese Science: wu-hsing and hsiu," Earl.y China 2 (1976), p. 1.

32. Yin Ti-fei in Kaoqu 1978.5:339.

33. For a characterization of such systems, see

N. Sivin, "Cosmos and Computation in Early Chinese

Mathematical Astronomy," T'oung Pao Iv (1969),

pp. 1-73.

34. See Yen Tun-chieh in Kaoqu 1978.5:336.

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 instru

ment in China is given in Needham, S.C.C. Ill, pp. 339-381.

37. See Nakayama, A History of Japanese Astronomy,

pp. 24-43.

38. Yabuuchi, ChOgoku no Temmonrekihô, pp. 64-71.

Yabuuchi puts forward the view that the idea of the

armillary 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 -A % (SPPY), 10.1b. Needham (S.C.C.

Ill, 354) would prefer to take ying as a verb re

ferring 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 instru

ment and a demonstrational model; see Needham, S.C.C.

Ill, p. 383f.

41. Hou Han shu (Peking, 1963), chih 2, p. 3029.

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 con

tested this, giving the earliest Chinese description of the motion of the lunar nodes (p. 3030).

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

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

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

45. Han shu, ch. 21 A, p. 975. The statement of

these men's duties is presumably drawn from the

parallel passage in Shi h 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 armillary sphere. The first of these is a fragment of a book entitled

Hsin lun jffj· ̂ , by Yang Hsiung's friend and con

(40 B.C. - A.D. 30). One

version records a conversation between Yang and an . old artisan who had made a hun t'ien (T'ai p'ing y'J

lan ^ #f^[SPTK], 2.11a). Another version

(Pei t'ang shu ch'ao 130.12a) has the heading "Lo

hsia Hung (and the) hun t'ien," and somewhat awk

wardly gives the old artisan the minq 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 j. ). The second text is a fragment

of a work written by Ch'en Shu iff ca. 240 A.D.,

entitled I pu chi chiu chuan "01d

stories of the elders of Ssu-ch'uan." The longest version is found in the T'ang So yin commentary to

the Shi h 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 Hsu 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 ,yû 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 im

agine an astronomer not using an armillary 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 jÛf 'carried out calculations to

revise the calendar.' With the benefit of hindsight

and on the basis of Yang Hsiung's story, ^uji

could well suggest hun , and chuan is already

present.

47. See notes 26 and 27.

48. An additional source of data, and one which re

quired no instruments at all, would naturally be a

long sequence of records of the dates of solstices

and new moons. For the important metaphysical as

sumptions behind the Grand Inception system, see

Sivin, "Cosmos and Computation," and Yabuuchi,

Chugoku no Temmonrekihô, pp. 21-30.

49. The ten-foot measure chang 5^. is also used.

A highly relevant example is the T'ien kuan shu

A. %. 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

44



after sunset; dawn observations were also made. A,

given star crosses the meridian four minutes ear lier 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. Ill, p. 245ff. The obvious connec tion between meridian transit observations and the

extremely ancient tradition of the southwards cere monial 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 w (Han-wei ts'ung-shu), 18.10b.

51. It is therefore misleading, although not un

common, 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. At

tempts 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. Ill, p. 248.

52. Without a timing device it is possible to ob tain 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 indi cator 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'ien's T'ien kuan shu makes no reference at all either to the

celestial equator, ch'ih tap τΪί>£|_, or to the

ecliptic, huang tao ^ . The fact that Ssu-ma

does not mention the latter does not of course im

ply that he was ignorant of the general path fol lowed by the moon and planets against the back

ground 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 ex

position 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 chinq (SPPY), 2.9a-12a.

58. Shang shu (SPTK), 1.6b.

59. B. Karlgren, "Grammata Serica Recensa," BMFEA no. 20 (1948), pp. 1-332. My reasons for not fol

lowing Karlgen's suggestion that should be read

as hsûn/*dziwan rather than as hsûan/*dziwan are set λ r\

out in the reference given in note 60.

60. Christopher Cullen and Anne S.L. Farrer, "On the Term Hsiian 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. Ill,

pp. 332-339), which identifies the hsiian chi with

a serrated variety of the jade disc 21 » and

the yii heng with the tubular jade form ts'ung fjf; .

Michel suggests that the two objects were used in combination as an astronomical instrument.

61. Karlgren's version of this passage is "He ex amined the sun-stone apparatus and the jade trav erse and thereby (adjusted = ) verified (the move ments of) the seven directors (i.e., sun, moon and

planets)": see his "Glosses on the Book of Docu

ments," 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. 33 follows the Eastern Han commentators who interpreted hsiian chi yii heng as an armillary sphere, an anachronism before the middle Western Han.

62. Shi h chi ch. 121, p. 3124.

63. T'ai p'ing yu lan 29.3a. Fu Sheng's commen

tary 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 Shi h 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 chi and 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 con ceived as the beginning of all events.

66. The asterism pei chi 'north pole' is called

45



t'ien chi 'celestial pole' by Ssu-ma Ch'ien,

Shih chi ch. 27, p. 1289, and contains the five stars γ, 0, 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 identifi cations of the hsuan chi with e 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

fZ. of Liu Hsiang ^'] fsj (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 aster

isms pei ch'en ;)fc (i.e., pei chi) and kou ch'en

('the hooked array': principal stars ζ, η, &, and aUMi). It is not unusual for these two

polar groups to be referred to jointly; see K'ai

.yuan chan ching gjsj fj- ̂ (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 mis

leading 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 Σ1694

Cam., the pole star under the T'ang. (The use of t'ien shu as an esoteric name for α 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 Yii hai ?. -J&- (repr. Taipei,

1964), 2.50a, notes in addition an obviously spuri ous 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 hsiian 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 yli 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 hsuan chi. In his discussion of the phrase hsiian chi .yii heng in the Shang shu, Liu Hsiang (Shuo yuan 18.1b) says that the hstian chi is the pole star (see note

65), but follows this immediately by a reference to the divinatory significance of the direction indi

cated by ch'i k'uei piaoJ^-^4~^ 'its bowl and

handle.' It looks as if the sentence "The .yii heng is the Dipper" has dropped from the text, particu

larly as Liu gives no other explanation of this term. The Han shu, 21A.969 uses .yii 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, Ma.ys to Paradise, p. 77. The lac

quer 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 them selves. The yu 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 de

fining 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

.yûn .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 explain ing that the hsUan chi is the pole star (? and that the yii 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 conversa tion with Dr. Michael Loewe in early 1977.

46



some further points on the "shih"

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