“CESTIAL PATTERNS” introduces readers to astronomy and related subjects, including cosmology, positional astronomy, calendrics, mathematical harmonics, and astrology. Although some passages may strike modern readers as both obscure and highly technical, from the point of view of Han intellectual history this chapter treats its topics in rather general terms, omitting the sorts of technical detail that would be the province of specialists. Readers of this chapter would be able to understand a situation in which these topics arose (such as a discussion at court of astrologically based policy) but not themselves be practicing astrologers. The principal message of the chapter is that all things in the cosmos are interconnected, that human plans and intentions are subject to the influence of various cosmic cycles and correlations, and that such cycles and correlations can be understood and taken into account in the formulation of policy.
The Chapter Title
“Tianwen” 
can be understood as having two complementary meanings, depending on how one construes the grammar of the phrase: “Heaven Adorned,” noun plus past-participle verb, and “Celestial Patterns,” adjective plus noun. Both meanings are valid, and both would have been present to some extent in the mind of a Han-dynasty reader. In English, however, we must choose one or the other, and in our view the second sense is dominant. The modern Chinese word tianwen is translated in English as “astronomy,” but generally with a wider range of meanings than the English term conveys; for example, it includes atmospheric phenomena such as meteorology and auroras.
Summary and Key Themes
The chapter begins with a lyrical account in parallel prose of how the cosmos originated in undifferentiation and evolved into the familiar world of phenomena through the action of yin and yang. This section ends with the battle between the Titan-like deities Gong Gong and Zhuan Xu, which, by knocking the axis of Heaven and Earth askew, brought an end to the primordial age and ushered in the era of human affairs. This section leads into a demonstration (3.2) that all phenomena conform to the cycles of yin and yang and (3.3) that human actions resonate with the cosmos.
These introductory sections are followed by a list of the principal heavenly bodies and the ninefold divisions of Heaven, correlated with the twenty-eight lunar lodges (constellations), and then by Five-Phase correlates of the five planets visible to the naked eye (Jupiter, Mars, Saturn, Venus, and Mercury, in the order in which they are given in chapter 3) and their motions. Sections 3.4 through 3.11 provide, in effect, instructions for drawing a diagram of significant correlations of heavenly bodies, directions, and seasonal time.1 Such a diagram might form the base (the so-called Earth plate) of the cosmological model known as a shi 
, or “cosmograph,” which consisted of a fixed Earth plate engraved with directions, names of months, lunar lodges, and other correlative categorical information, and a pivoted, movable “Heaven plate” depicting the Northern (Big) Dipper constellation. By rotating the Heaven plate in imitation of the stars’ apparent daily and annual motion, astrological predictions could be made on the basis of where the “handle” of the Dipper pointed on any given day.2 The cosmograph was the preeminent astrological instrument of the late Warring States and early Han periods (being replaced thereafter by the armillary sphere). Because it was a comprehensive microcosm, it allowed practitioners to calculate and interpret a wide range of correlations of astrological significance and is a concrete example of the normative natural order outlined so eloquently in chapter 1.
The remainder of the chapter consists largely of directions for reading and understanding the meaning of such correlations, including the sixty-day ganzhi cycle governed by the heavenly stems and earthly branches, the seasons, the twelve-year orbital cycle of Jupiter, a cycle of eight forty-five-day “wind seasons” correlated with the eight cardinal directions, the twelve tones of the chromatic scale and the five of the pentatonic scale, and the lunar lodges. The chapter includes sections on deriving the twelve tones of the chromatic scale by the “ascending and descending thirds” method (3.29) and correlating the twelve tones with the pentatonic scale; a section on weights and measures correlated with the twelve-tone scale (3.31); the names and characteristics of the twelve years of the Jupiter cycle (3.32–3.34, 3.41); correlations of celestial phenomena with the states and territories of the Warring States period (3.35, 3.37, 3.40); and miscellaneous correlations, prognostications, and omens. The chapter ends with a section (3.43) on using gnomons to measure the size of the cosmos.
A shi 
cosmograph from the early Han period, second century B.C.E. The Heaven plate, which can be rotated, is engraved with an image of the Northern Dipper (known in the West as the Big Dipper), allowing its annual movement around the horizon to be tracked so that predictions might be made in accordance with astrological correlative data encoded on the square Earth plate.
The astronomical and astrological correlations and calculations in this chapter are presented only in overview (enabling the ruler to understand what his astrologers were telling him, but not necessarily giving him enough technical information to perform the operations himself), and much of this material appears obscure to modern readers. Both textual problems and the many questions of meaning and interpretation that arise in this chapter are addressed in the very extensive commentary and notes to my earlier translation of this chapter.3 The translation in this book is based on and corrected from (and so is in every case to be preferred to) that in my 1993 work, but that book contains much more scholarly apparatus and commentarial material than has been possible to include here.
Sources
Chapter 3 of the Huainanzi appears to draw on a range of sources, many of which are no longer extant and whose former existence must be inferred from the material in the chapter itself. The most important known source for the chapter is the poetic catechism called the “Tian wen” 
(Questions About Heaven), dating from perhaps the fourth century B.C.E. and included in the anthology of southern poetry entitled the Chuci 
(Elegies of Chu). The “Questions About Heaven” appear designed to prompt a narrative about the cosmos, and some of the material in chapter 3 of the Huainanzi conforms closely to the narrative that might be elicited by those questions. The order is not always the same, and sometimes this chapter is more expansive than we would expect from the “Questions About Heaven.” Nevertheless, sections 3.1, 3.4, 3.13, 3.15, 3.16, and 3.25 generally are direct responses to those questions. Indeed, there can be no doubt of the connection between the “Questions About Heaven” and the Huainanzi.
One important source for this chapter was completely unknown before the 1970s: the Mawangdui text4 Wuxingzhan 
(Prognostications of the Five Planets). That text, lost for many centuries, gives Five-Phase correlates for the five visible planets, along with detailed information about their orbital periods, proper and retrograde motion, conjunctions, occultations, and other technical matters. The discovery of the Wuxingzhan not only supplies a hitherto-unknown source for the Huainanzi but also gives us an important insight into the working methods of Liu An and his court scholars. For this third chapter of the Huainanzi, they quoted verbatim the Five-Phase correlations that begin each of the five sections of the Wuxingzhan, grouping them together in a single section (3.6) that is followed by five sections (3.7–3.11) describing the apparent motions of the planets in terms similar to but much simpler than the text of the Wuxingzhan. In other words, the Huainanzi draws on the Wuxingzhan to give an “executive summary” of the astrology of the five planets but omits entirely the technical details that would have been of interest only to astrological specialists in the monarch’s employ.
We can only guess how many other lost texts are quoted or alluded to in chapter 3 of the Huainanzi. Some of the chapter’s sections look very much like set pieces drawn verbatim from now-lost sources. These include 3.17, on the annual waxing and waning of yin and yang; 3.25, on the daily motion of the sun (related, as noted, to the “Questions About Heaven” but very likely quoted from a now-lost source); 3.27, in which puns are used to explain the correlations between the twelve earthly branches and the twelve chromatic notes; 3.31, on weights and measures; 3.33, on the twelve years of the Jupiter cycle; and 3.42, on the allocation of daily rations to the people on the basis of variations in the Jupiter cycle years. Section 3.44, on the use of gnomons, also was probably an independent text incorporated into this chapter. Many other sections of the chapter may have been derived from now-lost manuals on the use of the cosmograph. It is, in short, impossible to know how much of the Huainanzi’s chapter 3 is original writing by Liu An and his court scholars, but it appears likely that it is in large part an anthology of material quoted from now-unknown sources.
The Chapter in the Context of the Huainanzi as a Whole
Coming early in the Huainanzi, chapter 3 emphasizes the interconnectedness of all phenomena and the influence of cosmic cycles on human affairs. The overview of cosmology, astronomy, astrology, and related subjects presented here is intended to be sufficient for a ruler to understand, if not actively participate in, the techniques by which cosmic cycles and correlations are calculated (particularly by means of the cosmograph) and taken into account in the formulation of policy. The essential point is that acts of state must harmonize with celestial patterns and cycles in order to be successful.
Chapter 21 of the Huainanzi, “An Overview of the Essentials,” says of this chapter that it enables a person to “possess the means to look upward to Heaven and uphold what to follow and thereby avoid disordering Heaven’s regularities” (21.2). The “Overview” also regards this chapter as part of a subunit of text that includes chapters 4 and 5, and says of them, “Had we discussed ends and beginnings and not illuminated Heaven, Earth, and the four seasons, you would not know the taboos to avoid” (21.3). Thus even the seemingly esoteric subject matter of this chapter is presented by Liu An and his editors as an essential component of the art of rulership.
John S. Major
1. For an excellent study of Chinese schematic cosmography, see Mark Edward Lewis, The Construction of Space in Early China (Albany: State University of New York Press, 2006), esp. chap. 5, “World and Cosmos.”
2. David Pankenier (private communication) suggests that these procedures, which involve rather mechanical readings of good and ill fortune on the basis of cyclical and directional phenomena, might better be known as “astromancy” rather than “astrology.” See also the introduction to chap. 5, n. 4.
3. Major 1993.
4. Part of a funerary library of texts on silk found in the tomb of the younger marquis of Dai, at Mawangdui, Changsha, Hunan, dated 168 B.C.E.
When Heaven and Earth were yet unformed, all was
ascending and flying,
diving and delving.
Thus it was called the Grand Inception.
The Grand Inception produced the Nebulous Void.
The Nebulous Void produced space-time;1
space-time produced the original qi.
A boundary [divided] the original qi.
That which was pure and bright spread out to form Heaven;
that which was heavy and turbid congealed to form Earth.
It is easy for that which is pure and subtle to converge
but difficult for the heavy and turbid to congeal.
Therefore
Heaven was completed first;
Earth was fixed afterward.
The conjoined essences of Heaven and Earth produced yin and yang.
The supersessive essences of yin and yang caused the four seasons.
The scattered essences of the four seasons created the myriad things.
The hot qi of accumulated yang produced fire; the essence of fiery qi became the sun.
The cold qi of accumulated yin produced water; the essence of watery qi became the moon.
The overflowing qi of the essences of the sun and the moon made the stars and planets.
To Heaven belong the sun, moon, stars, and planets;
to Earth belong waters and floods, dust and soil. [3/18/18–23]
In ancient times Gong Gong2 and Zhuan Xu3 fought, each seeking to become the thearch. Enraged, they crashed against Mount Buzhou;4
Heaven’s pillars broke;
the cords of Earth snapped.
Heaven tilted in the northwest, and thus the sun and moon, stars and planets shifted in that direction.
Earth became unfull in the southeast, and thus the watery floods and mounding soils subsided in that direction. [3/18/25–26]
The Way of Heaven is called the Round;
the Way of Earth is called the Square.
The square governs the obscure;
the circular governs the bright.
The bright emits qi, and for this reason fire is the external brilliance of the sun.
The obscure sucks in qi, and for this reason water is the internal luminosity of the moon.
Emitted qi endows;
retained qi transforms.
Thus yang endows and yin transforms. [3/18/28–30]
The unbalanced qi of Heaven and Earth, becoming perturbed, causes wind;
the harmonious qi of Heaven and Earth, becoming calm, causes rain.
When yin and yang rub against each other,5 their interaction produces thunder.
Aroused, they produce thunderclaps;
disordered, they produce mist.
When the yang qi prevails, it scatters to make rain and dew;
when the yin qi prevails, it freezes to make frost and snow. [3/19/1–2]
Hairy and feathered creatures make up the class of flying and walking things and are subject to yang.
Creatures with scales and shells make up the class of creeping and hiding things and are subject to yin.
The sun is the ruler of yang. Therefore, in spring and summer animals shed their fur; at the summer solstice, stags’ antlers drop off.
The moon is the fundament of yin. Therefore when the moon wanes, the brains of fish shrink; when the moon dies, wasps and crabs shrivel up.
Fire flies upward;
water flows downward.
Thus,
the flight of birds is aloft;
the movement of fishes is downward.6 [3/19/4–7]
Things within the same class mutually move one another;
root and twig mutually respond to each other.
Therefore,
when the burning mirror sees the sun, it ignites tinder and produces fire.
When the square receptacle7 sees the moon, it moistens and produces water.
When the tiger roars, the valley winds rush;
when the dragon arises, the bright clouds accumulate.
When qilins wrangle, the sun or moon is eclipsed;
when the leviathan dies, comets appear.
When silkworms secrete fragmented silk,8 the shang string [of a stringed instrument] snaps.
When meteors fall, the Bohai9 surges upward. [3/19/9–11]
The feelings of the rulers of men penetrate to Heaven on high.
Thus,
if there are punishments and cruelty, there will be whirlwinds.
If there are wrongful ordinances, there will be plagues of devouring insects.
If there are unjust executions, the land will redden with drought.
If there are unseasonable ordinances,10 there will be great excess of rain. [3/19/13–14]
The four seasons are the officers of Heaven.
The sun and moon are the agents of Heaven.
The stars and planets mark the appointed times of Heaven.
Rainbows and comets are the portents of Heaven. [3/19/16–17]
Heaven has nine fields and 9,999 junctures. It is 150,000 li distant from the earth. There are five planets, eight winds, and twenty-eight lunar lodges. There are five offices and six departments. The [six departments] are called the Purple Palace, the Great Enclosure, the Chariot Frame,11 the Pool of Xian,12 the Four Guardians, and the Heavenly Slope. [3/19/19–20]
What are the nine fields?
The central one is called Balanced Heaven. Its asterisms are Horn, Neck, and Root.13
The eastern one is called Azure Heaven. Its asterisms are Room, Heart, and Tail.
The northeastern one is called Variable Heaven. Its asterisms are Winnowing Basket, Dipper, and Ox Leader.
The northern one is called Umbral Heaven. Its asterisms are Serving Maid, Emptiness, Rooftop, and Encampment.
The northwestern one is called Secluded Heaven. Its asterisms are Eastern Wall, Stride, and Bond.
The western one is called Luminous Heaven. Its asterisms are Stomach, Pleiades, and Net.
The southwestern one is called Vermilion Heaven. Its asterisms are Turtle Beak, Triad, and Eastern Well.
The southern one is called Fiery Heaven. Its asterisms are Ghost Bearer, Willow, and Seven Stars.
The southeastern one is called Yang Heaven. Its asterisms are Extension, Wings, and Chariot Platform. [3/19/22–26]
What are the five planets?
The East is Wood. Its god is Tai Hao.14 His assistant is Gou Mang. He grasps the compass and governs spring. His spirit is Year Star [Jupiter]. His animal is the Blue-green Dragon. His musical note is jue; his days are jia and yi.15
The South is Fire. Its god is Yan Di.16 His assistant is Zhu Ming. He grasps the balance beam and governs summer. His spirit is Sparkling Deluder [Mars]. His animal is the Vermilion Bird. His musical note is zhi; his days are bing and ding.
The Center is Earth. Its god is the Yellow Emperor. His assistant is Hou Tu. He grasps the marking cord and governs the four quarters. His spirit is Quelling Star [Saturn]. His animal is the Yellow Dragon. His musical note is gong; his days are wu and ji.
The West is Metal. Its god is Shao Hao. His assistant is Ru Shou. He grasps the T-square and governs autumn. His spirit is Great White [Venus]. His animal is the White Tiger. His musical note is shang; his days are geng and xin.
The North is Water. Its god is Zhuan Xu. His assistant is Xuan Ming. He grasps the weight and governs winter. His spirit is Chronograph Star [Mercury]. His animal is the Dark Warrior. His musical note is yu; his days are ren and gui. [3/20/1–6]
When taiyin 
is in any of the four midpoints, the planet Jupiter passes through three of the lunar lodges.
When taiyin is in any of the four hooks, the planet Jupiter passes through two of the lunar lodges.
Two times eight is sixteen;17 three times four is twelve. [16 + 12 = 28] Therefore, in twelve years [Jupiter] traverses [all] twenty-eight lunar lodges. The [average] daily motion [of Jupiter] is [approximately] one-twelfth of a [Chinese] degree. In one year, [Jupiter traverses] 307/16d. In twelve years, [Jupiter] completes a circuit [of the heavens]. [3/20/8–10]
Mars normally enters the asterism Grand Enclosure in the tenth month. [The corresponding state thereupon] comes under its control. Then it emerges, passing through the lunar lodges in turn. [Mars] is in charge of states that lack the Way. It
causes disorder, causes violence;
causes sickness, causes death;
causes famine, and causes warfare.
Its leavings and enterings [of lunar lodges] are irregular. Its color perceptibly varies. [Its color] is sometimes visible and sometimes unnoticeable. [3/20/12–13]
On the day jiayin [no. 51], in the first year of the Epoch, Saturn is in [the lunar lodge] Dipper. Each year Saturn moves through one lunar lodge. If Saturn should be [in a particular lunar lodge] but is not there, the state [corresponding to that lodge] will lose its land. If Saturn ought not yet to be [in a particular lunar lodge] but [already] occupies it, the state corresponding to that lodge] will increase its land and [its] crops will ripen. The [average] daily motion [of Saturn] is one-twenty-eighth of a [Chinese] degree. Its annual motion is 135/112d. In twenty-eight years it completes a circuit [of the heavens]. [3/20/13–15]
In the first month, on the day jiayin, in the first year of the Epoch, Venus rises at dawn in the east in [the lunar lodge] Encampment. After 240 days, it disappears. It remains hidden for 120 days and then appears in the evening in the west. After 240 days, it disappears. After thirty-five days, it once again appears in the east. It appears in chen or xu and disappears in chou or wei. When [Venus] should appear but does not appear, or should not yet disappear but does disappear, throughout the world armies will be withdrawn. When [Venus] should disappear but does not disappear, or should not yet appear but does appear, throughout the world armies will set forth [on campaigns]. [3/20/15–18]
[The movements of] Mercury correspond exactly to the four seasons. Normally in the second month, at the spring equinox, it appears in [the lunar lodges] Stride and Bond. In the fifth month, at the summer solstice, it appears in [the lunar lodges] Eastern Well and Ghost Bearer. In the eighth month, at the autumn equinox, it appears in [the lunar lodges] Horn and Neck. In the eleventh month, at the winter solstice, it appears in [the lunar lodges] Dipper and Ox Leader. [Mercury] appears in [the chronograms] chen or xu and disappears in chou or wei. It appears for twenty days and then disappears.
At dawn it attends [the sun] in the east;
in the evening it attends [the sun] in the west.
If in any season it does not appear, that season will be unfortunate. If it does not appear for four seasons, throughout the world there will be famine. [3/20/20–23]
What are the eight winds?
Forty-five days after the winter solstice arrives, the Regular [northeast] Wind arrives.18
Forty-five days after the Regular Wind arrives, the Brightly Abundant [east] Wind arrives.
Forty-five days after the Brightly Abundant Wind arrives, the Clear Bright [southeast] Wind arrives.
Forty-five days after the Clear Bright Wind arrives, the Sunshine [south] Wind arrives.
Forty-five days after the Sunshine Wind arrives, the Cooling [southwest] Wind arrives.
Forty-five days after the Cooling Wind arrives, the Changhe [west] Wind19 arrives.
Forty-five days after the Changhe wind arrives, the Buzhou [northwest] Wind20 arrives.
Forty-five days after the Buzhou wind arrives, the Broadly Expansive [north] wind arrives.
When the Regular Wind arrives, release those imprisoned for minor crimes and send away those [foreign intruders] who had been detained.
When the Brightly Abundant Wind arrives, rectify boundaries of fiefs and repair the fields.
When the Clear Bright Wind arrives, issue presents of silk cloth and send embassies to the Lords of the Land.
When the Sunshine Wind arrives, confer honors on men of position and reward the meritorious.
When the Cooling Wind arrives, report on the Potency of the earth and sacrifice at the four suburbs.
When the Changhe wind arrives, store away the suspended [bells] and hanging [chimestones]; qin and se [stringed instruments] [must be] unstrung.
When the Buzhou wind arrives, repair palaces and dwellings and improve dikes and walls.
When the Broadly Extensive Wind arrives, close up gates and bridges and execute punishments. [3/20/25–30]
What are the five offices?
That of the east is Agriculture.
That of the south is the Military Command.
That of the west is Public Order.
That of the north is Public Works.
That of the center is Metropolitan Affairs. [3/21/1]
What are the six departments? They are ziwu, chouwei, yinshen, maoyu, chenxu, and sihai.21 [3/21/3]
The Grand Enclosure is the hall of the Grand One.22
The Purple Palace is the dwelling place of the Grand One.
Chariot Frame is the residence of the imperial concubine.
The Pool of Xian is a park of water and fishes.
The Heavenly Slope is the gate tower of the assembled spirits.
The Four Guardians are those who bestow rewards and punishments.
The Grand Enclosure governs the Vermilion Bird. [3/21/5–7]
The Purple Palace controls the Dipper and turns to the left. The sun moves 1d [in relation to the fixed stars] each time it makes a revolution across the heavens. At the winter solstice, the sun is in [the constellation] Lofty Wolf Mountain. The sun shifts 1d per day. Therefore, after it has traveled 
, at the summer solstice the sun is in [the constellation] Ox Head Mountain. Then it turns back and, [after traveling through] 
, completes one year. [3/21/7–9]
At the beginning of a Heavenly Singularity Epoch, the first [civil] month being established in yin, the sun and moon together enter the fifth degree of [the lunar lodge] Encampment. Seventy-six years after the beginning of the Heavenly Singularity Epoch, the sun and moon again enter the fifth degree of Encampment, without any remainder fraction. This is called an Era. Twenty Eras make 1,520 years, called a Grand Conclusion. [After three Grand Conclusions], the sun, moon, and asterisms all recommence in jiayin. [3/21/9–11]
The daily motion of the sun is 1d. Thus in a year there will be a surplus of ¼d. Thus after four years, there will be an accumulation of 1,461 days, and [the fractional days] will come together again [to make a full day]. Thus after eighty years, [the days of the sixty-day cycle] will be repeated [on the same days of the year]. [3/21/11–13] Thus it is said23 that
ziwu and maoyu are the two diametral chords;
chouyin, chensi, weishen, and xuhai are the Four Hooks.
Northeast is the binding cord24 of Returning Accretion;
Southwest is the binding cord of Reverting Yang;
Southeast is the binding cord of Perpetual Ocean;
Northwest is the binding cord of Penetrating Cleft. [3/21/15–16]
When the sun is at the winter solstice, the Dipper [points] north, exactly on the [north–south] marking-cord line. The yin qi is at its maximum, and the yang qi begins to grow. Thus it is said that the winter solstice produces accretion.25
When the sun is at the summer solstice, the Dipper [points] south, exactly on the [north–south] marking-cord line. The yang qi is at its maximum, and the yin qi begins to grow. Thus it is said that the summer solstice produces recision.
When the yin qi is at its maximum, north is at its farthest extent [from the sun]. The Northern Limit penetrates down to the Yellow Springs. Hence one must not cut into the earth or bore wells. The myriad creatures are shut up in hibernation, and insects are head down in their burrows. Thus it is said that accretion is in the Room.
When the yang qi is at its maximum, south is at its farthest extent [from the sun]. The Southern Limit penetrates upward to the Vermilion Heaven. Hence one must not level hills or raise roof beams. The myriad creatures flourish and increase, and the five grains grow abundantly. Thus it is said that accretion is in the Field. [3/21/18–21]
When the sun is at the winter solstice, fire follows it.
When the sun is at the summer solstice, water follows it.
Thus,
in the fifth month, fire is at its maximum and water begins to seep out.
In the eleventh month, water is at its maximum and fire arises.26
Yang qi produces fire; yin qi produces water.
[Because] water [begins to be] dominant, the summer solstice is damp.
[Because] fire is [begins to be] dominant, the winter solstice is parched.
When [the weather] is parched, charcoal is light.
When [the weather] is damp, charcoal is heavy. [3/21/23–25]
When the sun is at the winter solstice, wells are full of water and basins overflow. Goats shed their hair, deer’s antlers fall away, and magpies nest. An eight-foot gnomon27 casts a shadow thirteen feet long [at noon].
When the sun is at the summer solstice, the yellow floods enrich the fields, and mineral essences emerge from the soil. Cicadas begin to sing, and the half-summer herb grows; flying insects do not bite foals and calves, and birds of prey do not seize nestlings. An eight-foot gnomon casts a shadow one foot and five inches [i.e., 1½ feet] long [at noon].
When the gnomon shadow is long, yin qi is dominant.
When the gnomon shadow is short, yang qi is dominant.
When the yin qi is dominant, there is water.
When the yang qi is dominant, there is drought. [3/22/1–4]
Yin and yang, recision and accretion, have seven habitations. What are these seven habitations? They are the Room, the Hall, the Court, the Gate, the Lane, the Road, and the Field. In the eleventh month, accretion dwells in the Room for thirty days, fifteen days before the winter solstice and fifteen days after. Thereafter it shifts its place every thirty days.
When accretion is in the Room, recision is in the Field.
When accretion is in the Hall, recision is in the Road.
When accretion is in the Court, recision is in the Lane.
When yin and yang are of equal power, then recision and accretion are together in the Gate. In the eighth month and the second month, the qi of yin and yang is equal, and day and night are of equal length. Thus it is said that recision and accretion are together in the Gate.
When accretion is in the south, there is birth;
When recision is in the south, there is death.
Thus,
at the meeting [in the Gate] at the second month, the myriad creatures come to life.
At the meeting [in the Gate] in the eighth month, the herbs and trees begin to die. [3/22/6–9]
Between the two binding cords is a span of 
. The sun’s daily motion being 1d, fifteen days makes one node [jie 
]. Thus are produced twenty-four seasonal alterations.
When the [handle of the] Dipper points to zi [at midnight], it is the Winter Solstice [node]. Its sound is like [the pitch pipe] Yellow Bell.28
After fifteen days, [the handle of the Dipper at midnight] points to gui. This is the Lesser Cold node. Its sound is like [the pitch pipe] Responsive Bell.
After fifteen more days, [the handle of the Dipper at midnight] points to chou. This is the Greater Cold node. Its sound is like [the pitch pipe] Tireless.
After fifteen more days, [the handle of the Dipper at midnight] points to the binding cord of Returning Accretion, and there is a surplus of yin in the land. Thus it is said that the forty-sixth day from the winter solstice marks the Beginning of Spring [node], when the yang qi dispels the cold. Its sound is like [the pitch pipe] Southern Regulator.
After fifteen more days, [the handle of the Dipper at midnight] points to yin. This is the Rain node. Its sound is like [the pitch pipe] Tranquil Pattern.
After fifteen more days, [the handle of the Dipper at midnight] points to jia. This is the Awakening of Insects node. Its sound is like [the pitch pipe] Forest Bell.
After fifteen more days, [the handle of the Dipper at midnight] points to mao. Thus it [is said that the forty-sixth day after the Beginning of Spring]29 is called the Spring Equinox [node]. Thunder is abroad. Its sound is like [the pitch pipe] Luxuriant.
After fifteen more days, [the handle of the Dipper at midnight] points to yi. This is the node of the Clear Bright wind-maximum. Its sound is like [the pitch pipe] Median Regulator.
After fifteen more days, [the handle of the Dipper at midnight] points to chen. This is the Grain Rain node. Its sound is like [the pitch pipe] Maiden Cleanliness.
After fifteen more days [the handle of the Dipper at midnight] points to the binding cord of Perpetual Ocean, and the portion [of the year allotted to] spring reaches its limit. Thus it is said that that the forty-sixth day [after the spring equinox] is the Beginning of Summer [node]. The great winds end. Its sound is like [the pitch pipe] Pinched Bell.
After fifteen more days, [the handle of the Dipper at midnight] points to si. This is the Lesser Fullness node. Its sound is like [the pitch pipe] Great Budding.
After fifteen more days, [the handle of the Dipper at midnight] points to bing. This is the Grain in Ear node. Its sound is like [the pitch pipe] Great Regulator.
After fifteen more days, [the handle of the Dipper at midnight] points to wu. Yang qi reaches its maximum. Thus it is said that the forty-sixth day [after the beginning of summer] marks the Summer Solstice [node]. Its sound is like [the pitch pipe] Yellow Bell.
After fifteen more days, [the handle of the Dipper at midnight] points to ding. This is the Lesser Heat node. Its sound is like [the pitch pipe] Great Regulator.
After fifteen more days [the handle of the Dipper at midnight] points to wei. This is the Great Heat node. Its sound is like [the pitch pipe] Great Budding.
After fifteen more days [the handle of the Dipper at midnight] points to the binding cord of Reverting Yang. Thus it is said that forty-six days after [the summer solstice] is the Beginning of Autumn [node]. This is the node of the Cool Wind wind-maximum. Its sound is like [the pitch pipe] Pinched Bell.
After fifteen more days [the handle of the Dipper at midnight] points to shen. This is the End of Heat node. Its sound is like [the pitch pipe] Maiden Cleanliness.
After fifteen more days [the handle of the Dipper at midnight] points to geng. This is the Descent of White Dew node. Its sound is like [the pitch pipe] Median Regulator.
After fifteen more days, [the handle of the Dipper at midnight] points to you, on the central marking line. Thus it is called the Autumn Equinox [node]. Thunder ceases, and swarming insects turn toward the north. Its sound is like [the pitch pipe] Luxuriant.
After fifteen more days, [the handle of the Dipper at midnight] points to xin. This is the Cold Dew node. Its sound is like [the pitch pipe] Forest Bell.
After fifteen more days, [the handle of the Dipper at midnight] points to xu. This is the Descent of Hoarfrost node. Its sound is like [the pitch pipe] Tranquil Pattern.
After fifteen more days, [the handle of the Dipper at midnight] points to the binding cord of Perpetual Cleft. Thus the portion [of the year allotted to] autumn comes to its end. Thus it is said that the forty-sixth day [after the autumn equinox] is the Beginning of Winter [node]. Herbs, trees, and flowers die. Its sound is like [the pitch pipe] Southern Regulator.
After fifteen more days, [the handle of the Dipper at midnight] points to hai. This is the Lesser Snow node. Its sound is like [the pitch pipe] Tireless.
After fifteen more days, [the handle of the Dipper at midnight] points to ren. This is the Great Snow node. Its sound is like [the pitch pipe] Responsive Bell.
After fifteen more days, [the handle of the Dipper at midnight again] points to zi.
Therefore it is said that
yang is born in zi;
yin is born in wu.
Yang is born in zi. Therefore in the eleventh month, the sun is at the winter solstice; magpies begin to nest; and human qi accumulates in the head.
Yin is born in wu. Therefore in the fifth month lesser punishments are carried out. Shepherd’s purse and wheat stop growing and wither. The herbs and trees that sprouted in the winter must die. [3/22/11–29]
The handle of the Dipper makes the Lesser Year. In the first [civil] month [the Dipper] is established in yin. The months move from the left through the twelve chronograms.30
The Pool of Xian makes the Greater Year. The second month is established in mao. The moon moves from the right through the four quadrants. When it finishes, it begins again.
As for the Greater Year:
one who faces is it humiliated;
one who turns away from it is strong;
one who is on its left is in decline;
one who is on its right attains glory.
When the Lesser Year is in the southeast, there is birth;
when it is in the northwest, there is death.
This is what is meant by the saying
It must not be met, but it may be turned away from;
it must not be to the left, but it may be to the right.31 [3/23/1–4]
The Great Season is [governed by] the Pool of Xian. The Lesser Season is that of the month establishments. The binding cords of Heaven establish the Epoch, which always begins with yin. Arising, [taisui] moves to the right for one year and then shifts. After twelve years, it [completes] a heavenly circuit and then begins again. [3/23/6–7]
In the winter of the first year of [the King of] Huainan, the Grand One32 was in [the cyclical year] bingzi. The winter solstice was on [the cyclical day] jiawu; [the node] Beginning of Spring [began] on [the cyclical day] bingzi. [3/23/9]
One yin and one yang make two qi.
Two yang and one yin make three qi.
Combining these qi makes the [pentatonic] notes.
Combining the yin makes yang.
Combining [this number with] the yang makes the pitch pipes.
Thus there are five notes and six pitch pipes.
The notes double to produce the number of the days.
The pitch pipes double to produce the earthly branches.
Thus there are ten days and twelve branches. [3/23/11–12]
The moon’s daily motion is 
A lunar month is twenty-nine and 499/940 days. Twelve months make a year. The [tropic] year is ten and 827/940 days longer [than the lunar year]. Hence in nineteen years there are seven intercalary months. [3/23/12–14]
The days of the winter solstice take the branches zi and wu.
The days of the summer solstice take the branches mao and you.
Adding three days to the [branches of] the winter solstice yields the days of the summer solstice. The whole year shifts by six days and begins again with renwu.
At the winter solstice, [the cyclical day] jiazi receives control. [The phase] wood is used in all affairs, and the smoke of fires is bluegreen.
After seventy-two days, bingzi receives control. [The phase] fire is used in all affairs, and the smoke of fires is vermilion.
After seventy-two days, wuzi receives control. [The phase] earth is used in all affairs, and the smoke of fires is yellow.
After seventy-two days, gengzi receives control. [The phase] metal is used in all affairs, and the smoke of fires is white.
After seventy-two days, renzi receives control. [The phase] water is used in all affairs, and the smoke of fires is black.
After seventy-two [more] days, the year comes to an end, and gengwu takes control. The year shifts by six days so that the number may extend [to the full count of 366]. After ten years, [the sequence] begins again with jiazi.
When jiazi is in control, act gently and graciously, and relax the many prohibitions. Open doors and covers, and penetrate barriers. It is prohibited to cut down trees.
When bingzi is in control, promote the worthy and the good, and reward the meritorious. Enfeoff nobles and distribute wealth. When wuzi is in control, nourish the old and the widowed, distribute food alms, and bestow grace and favor.
When gengzi is in control, improve walls and enclosures, strengthen city walls and fortifications, scrutinize prohibitions [with a view toward strengthening them], refurbish the armor of the troops, admonish officials, and punish the lawless.
When renzi is in control, shut doors and gates, investigate strangers, execute punishments, kill the condemned, [command the people to] rest within their gates and under the beams of their roofs, and prohibit wandering outside [the city walls]. [3/23/16–23]
The qi of jiazi is dry and turbid.
The qi of bingzi is dry and bright.
The qi of wuzi is damp and turbid.
The qi of gengzi is dry and cold.
The qi of renzi is clear and cold. [3/23/25]
When [the day designated] bingzi opposes [the “season” governed by] jiazi, hibernating insects hatch forth prematurely, and there is [unseasonably] early thunder.
When wuzi opposes jiazi, the pregnant suffer calamities, eggs are infertile, and birds and insects suffer great injuries.
When gengzi opposes jiazi, there will be military operations.
When renzi opposes jiazi, there will be spring frosts.
When wuzi opposes bingzi, there will be claps of thunder.
When gengzi opposes bingzi, there will be bolts of lightning.
When renzi opposes bingzi, there will be hail.
When jiazi opposes bingzi, there will be earthquakes.
When gengzi opposes wuzi, the five grains will suffer calamities.
When renzi opposes wuzi, there will be cold spells in summer, with rain and frost.
When jiazi opposes wuzi, silkworms will not mature.
When bingzi opposes wuzi, there will be great drought; aquatic grasses will dry out entirely.
When renzi opposes gengzi, fish will not grow.
When jiazi opposes gengzi, herbaceous plants and trees die and then sprout again.
When bingzi opposes gengzi, herbaceous plants and trees bloom for a second time [out of season].
When wuzi opposes gengzi, some of the annual harvest will preserved and some lost.
When jiazi opposes renzi, [creatures] will not hibernate [as they should].
When bingzi opposes renzi, there will be meteors.
When wuzi opposes renzi, in winter insects depart from their places.
When gengzi opposes renzi, there will be thunder in winter. [3/23/25–3/24/5]
In the third [and final] month of spring, abundant thunder sounds forth, bringing in the rains.
In the third [and final] month of autumn, the qi of Earth has not yet become [completely] quiescent, and one gathers in the killed things.33 All crawling things become torpid and hide away, and country dwellers shut their gates. Gray Woman34 comes out and brings down frost and snow.
Thus the qi of the twelve times of the year progress until they reach an end [again] in the second month of spring, when what has been stored away is received forth [again] and the cold is shut away. Then Tranquil Woman drums and sings to regulate the harmony of Heaven and to make grow the hundred kinds of cereals, the beasts and birds, and the herbs and trees.
In the first month of summer the crops ripen; the cries of pheasants and pigeons become prolonged, causing the emperor to look forward to the annual harvest.
Thus,
if Heaven does not give forth yin, the myriad things cannot be born;
if Earth does not give forth yang, the myriad things cannot grow to maturity.
Heaven is round;
Earth is square;
the Way is exactly in the middle.
The sun [produces] accretion;
the moon [produces] paring away.
When the moon reverts [in its course], the myriad creatures die.
When the sun attains its apogee, the myriad creatures are born.
Separated from mountains, the qi of mountains is hidden away.
Separated from water, aquatic insects become dormant.
Separated from trees, leaves wither.
When the sun is not seen for five days, [the ruler] will lose his throne. Even a [ruler who is a] sage cannot withstand this. [3/24/7–12]
The sun rises up from the Bright Valley, bathes in the Pool of Xian, and rests in the Fusang Tree. This is called Dawn Light.
Ascending the Fusang Tree, it thereupon commences its journey. This is called Emergent Brightness.
[When the sun] reaches the Bent Slope, this is called Dawn Brilliance.
[When the sun] reaches the Steaming Spring, this is called the Morning Meal.
[When the sun] reaches the Mulberry Field, this is called the Late-Morning Meal.
[When the sun] reaches the Balance Beam of Yang, this is called Within the Angle.
[When the sun] reaches Kun Wu, this is called the Exact Center.
[When the sun] reaches the Bird Roost, this is called the Lesser Return.
[When the sun] reaches the Valley of Grief, this is called the Dinner Hour.
[When the sun] reaches Woman’s Sequence, this is called the Great Return.
[When the sun] reaches the Angle of the Abyss, this is called the Raised Pestle.
[When the sun] reaches Carriage Stone, this is called the Descending Pestle.
[When the sun] reaches the Fountain of Grief, it halts; its female attendant rests her horses. This is called the Suspended Chariot.
[When the sun] reaches the Abyss of Anxiety, this is called Yellow Dusk.
[When the sun] reaches the Vale of Obscurity, this is called Definite Dusk.
The sun enters the floodwaters of the Abyss of Anxiety; sunrise emerges from the drainage stream of the Vale of Obscurity. [The sun] travels over the nine continents, [passing through] seven resting places, [covering a distance of] 507,309 li. The divisions [of its journey] make dawn, daylight, dusk, and night. [3/24/14–22]
At the summer solstice, yin [begins to be] ascendant over yang. For this reason, the myriad creatures come to an end and die.
At the winter solstice, yang [begins to be] ascendant over yin. For this reason, the myriad creatures lift up their heads and come to life.
Daylight is the portion of yang;
night is the portion of yin.
Thus when the yang qi dominates, days are long and nights are short.
When the yin qi dominates, days are short and nights are long.
Appearing in mao and you [at the equinoxes], yin and yang divide day and night equally. [3/24/24–3/25/2]
Thus it is said that
when the compass is born, the square dies;
when the balance beam35 is [being] set up, the weight36 is hidden away;
when the marking cord occupies the center, it [marks out] the foundation of the four seasons.37 ([3/25/14–15])
The Celestial Thearch stretches out the four binding cords of Heaven, and employs the Dipper to revolve [through] them. In a month it shifts by one chronogram, its location being successively displaced. In the first [civil] month, it points to yin; in the eleventh month it points to zi. It completes a circle in one year; finishing, it begins again.
[In the first civil month, the Dipper] points to yin. The myriad creatures stir like earthworms underground. The pitch pipes take the note Great Budding. Great Budding means that there are buds but they have not yet emerged.38
[In the second civil month, the Dipper] points to mao. Mao means “burgeoning,” thus [living things] burgeon forth. The pitch pipes take the note Pinched Bell. Pinched Bell means that seeds first begin to swell.
[In the third civil month the Dipper] points to chen. Chen means “to stir up.” The pitch pipes take the note Maiden Cleanliness. Maiden Cleanliness means that what is withered is done away with and the new comes forth.
[In the fourth civil month the Dipper] points to si [fetus]. There being a fetus, there is sure to be birth in consequence. The pitch pipes take the note Median Regulator. Median Regulator means that the center grows large.
[In the fifth civil month the Dipper] points to wu. Wu means “to oppose.” The pitch pipes take the note Luxuriant. Luxuriant means that all is tranquil and fitting.
[In the sixth civil month the Dipper] points to wei. Wei means “flavor.” The pitch pipes take the note Forest Bell. Forest Bell means to extend forth and then stop.
[In the seventh civil month the Dipper] points to shen. Shen means “chanting.” The pitch pipes take the note Tranquil Pattern. Tranquil Pattern means that the pattern is changed. The [force of] accretion is expunged [from the annual cycle].
[In the eighth civil month the Dipper] points to you. You means “satiety.” The pitch pipes take the note Southern Regulator. Southern Regulator means that it is recognized that the satiety is great.
[In the ninth civil month the Dipper] points to xu. Xu means “destruction.” The pitch pipes take the note Tireless. Tireless means that there is bringing in without satisfaction.
[In the tenth civil month the Dipper] points to hai. Hai means “hindrance.” The pitch pipes take the note Responsive Bell. Responsive Bell means to respond to the bell.
[In the eleventh civil month the Dipper] points to zi. Zi means “black.” The pitch pipes take the note Yellow Bell. Yellow Bell means that the bell is beginning to be yellow.
[In the twelfth civil month the Dipper] points to chou. Chou means “to tie.” The pitch pipes take the note Great Regulator. Great Regulator means to go out one after the other. [3/25/4–13]
Thus it is said, “The Way begins with one.” One [alone], however, does not give birth. Therefore it divided into yin and yang. From the harmonious union of yin and yang, the myriad things were produced. Thus it is said,
“One produced two,
two produced three,
three produced the myriad things.”39
[With regard to] Heaven and Earth, three months make one season. Thus a sacrifice of three [types or portions of] cooked grains are used in mourning rites. The year continues for three shifts [of seasons] to make the seasonal nodes [complete their cycle]. Armies emphasize three signal flags in order to maintain control.40
Using three to examine matters: 3 × 3 = 9. Thus the Yellow Bell pitch pipe is nine inches long and harmonizes with the note gong. Furthermore, 9 × 9 = 81. Thus the number of the Yellow Bell is established therein. Yellow is the color of the Potency of Earth; the bell is that by which the [seeds of] qi are sown. At the winter solstice the qi of accretion produces Earth; the color of Earth is yellow. Thus the [note of the winter solstice] is called Yellow Bell.
The number of pitch pipes is six, classified as female and male [for a total of twelve]. Thus it is said there are twelve bells to act as adjuncts to the twelve months. Each of the twelve is based on three. Thus if one sets up [the number] one and triples it eleven times [i.e., 311], the total is 177,147. The Great Number of the Yellow Bell is thereby revealed. [3/25/17–23]
There are twelve pitch pipes.
Yellow Bell makes the note gong.
Great Budding makes the note shang.
Maiden Cleanliness makes the note jue.
Forest Bell makes the note zhi.
Southern Regulator makes the note yu.
Matters are brought to completion by means of three;
Notes are established as [all together] five.
3 + 5 = 8. Creatures born from eggs have eight bodily orifices. This was the beginning of the pitch pipes. [The ancients] recorded the sounds of the phoenix; therefore the notes are born from eight. [3/25/23–25]
Yellow Bell makes the note gong; gong is the sovereign of the notes. Thus Yellow Bell is established in zi; its number is 81, and it governs the eleventh month.
Descending, [Yellow Bell] produces Forest Bell. The number of Forest Bell is 54 [81 × 2/3]; it governs the sixth month.
Ascending, Great Budding is produced. Its number is 72 [54 × 4/3]; it governs the first month.
Descending, Southern Regulator is produced. Its number is 48 [72 × 2/3]; it governs the eighth month.
Ascending, Maiden Cleanliness is produced. Its number is 64 [48 × 4/3]; it governs the third month.
Descending, Responsive Bell is produced. Its number is 42 [64 × 2/3]; it governs the tenth month.
Ascending, Luxuriant is produced. Its number is 57 [42 × 4/3 + 1]; it governs the fifth month.
Ascending, Great Regulator is produced. Its number is 76 [57 × 4/3]; it governs the twelfth month.
Descending, Tranquil Pattern is produced. Its number is 51 [76 × 2/3]; it governs the seventh month.
Ascending, Pinched Bell is produced. Its number is 68 [51 × 4/3]; it governs the second month.
Descending, Tireless is produced. Its number is 45 [68 × 2/3]; it governs the ninth month.
Ascending, Median Regulator is produced. Its number is 60 [45 × 4/3]; it governs the fourth month.
[Beyond this] limit, nothing [further] is produced. [3/26/1–7]
Those pipes that descend are [created by multiplying the previous pipe’s number] by 2/3.
Those pipes that ascend are [created by multiplying the previous pipe’s number] by 4/3.41 [3/26/24]
Gong produces zhi; zhi produces shang; shang produces yu; yu produces jue. Jue produces Maiden Cleanliness.
Maiden Cleanliness produces42 Responsive Bell. Responsive Bell is comparable43 to the fundamental note [i.e., Yellow Bell] and thus produces harmony.
Responsive Bell produces Luxuriant. Luxuriant is not comparable to the fundamental note and thus produces discord.
At the winter solstice, the note is like Forest Bell in a flattened tone;
At the summer solstice, the note is like Yellow Bell in a clear tone.44
The twelve pitch pipes respond to the alterations of the twenty-four seasonal nodes.
At jiazi, Median Regulator moves to zhi.
At bingzi, Pinched Bell moves to yu.
At wuzi, Yellow Bell moves to gong.
At gengzi, Tireless moves to shang.
At renzi, Tranquil Pattern moves to jue. [3/26/7–11]
In ancient times, weights and measures were created; lightness and heaviness were born from the Way of Heaven.
The length of the Yellow Bell pitch pipe is nine inches. All things are produced by [virtue of] three. [3 × 3 = 9.] 3 × 9 = 27. Thus the width of a standard bolt of cloth is two feet, seven inches.45 This is the ancient standard.
There are shapes; thus there are [also musical] sounds. The musical notes are mutually produced by [means of] the number eight. Thus the span of a man’s arms measures four feet.
A xun is double [this length]; thus eight feet make one xun. A xun is the height of an average man.46
The number of the notes is five. Using five to calculate in terms of eight, 5 × 8 = 40. Thus four zhang make one pi.47 Therefore, one pi is used as [the standard unit in the cloth tax] administration.
At the autumn equinox, the beards of grain husks are fully grown. When the beards of the husks are fully grown, the grain ripens. The number of the pitch pipes is twelve. Thus [the width of] twelve husk beards [laid side by side] equals one fen.48
The pitch pipes correspond to the chronograms. The [pentatonic] notes correspond to the sun. The number of the sun is ten. Thus ten fen make one inch; ten inches make one foot; and ten feet make one zhang.
For those units used to measure weight, twelve millet grains make one fen. Twelve fen make one zhu. Twelve zhu make one half-ounce [ban liang].49 The balance beam has a left side and a right side. Therefore, doubling the weight, twenty-four zhu make one ounce.
Heaven has four seasons, completing one year. Therefore, reckoning by fours, 4 × 4 = 16. Therefore sixteen ounces make one catty. Three months make a season, and thirty days, a month. Therefore thirty catties make one jun. Four seasons make one year; therefore four jun make one dan.50
For [units of] musical measurement: One pitch pipe produces five tones; twelve pitch pipes produce sixty tones. Therefore, reckoning by sixes, 6 × 6 = 36. Therefore, 360 tones correspond to the days of one year. Thus the number of [notes of] the pitch pipes and [days of] the calendar are in accord with the Way of Heaven and Earth. [3/26/13–24]
The beginning of the Jovian cycle is established in jiayin.
After one completion, it [begins again,] established in jiaxu.
After two completions, it [begins again,] established in jiawu.
After three completions, it returns to its beginning in jiayin.
The year’s annual shift is one chronogram. After the [seasonal node] Beginning of Spring, it attains its [proper annual] location by shifting its position [away from the previous one]. When it has moved forward three places and back five, then all matters may be taken in hand. [3/26/26–27]
Where taiyin is established, insects lie head down in their burrows and stay quietly [in them]; magpies nest in the countryside and make their homes.
[When] taiyin is in yin, the vermilion bird is in mao; the Hooked Array is in zi; the Dark Warrior is in xu; the White Tiger is in you; the Bluegreen Dragon is in chen.
If yin is the establishing chronogram, then mao is Removal; chen is Fullness; si is Evenness, governing birth; wu is Fixedness; wei is Holding Firm, governing pitfalls; shen is Breaking, governing the balance beam; you is Danger, governing the ladle; xu is Completion, governing minor Potency; hai is Receiving, governing great Potency; zi is Opening, governing taisui; chou is Closing, governing [. . .].51 [3/27/1–4]
When taiyin 
is in yin, the year is called Shetige.52 The male [mate] of taiyin is Jupiter. It dwells in the [lunar lodges] Dipper and Ox Leader. In the eleventh53 month, it rises with them in the east at dawn. [The lodges] Eastern Well and Ghost Bearer are opposite [i.e., setting in the west at dawn].
When taiyin is in mao, the year is called Ming’e.54 Jupiter dwells in Serving Maid, Emptiness, and Rooftop. In the twelfth month, it rises with them in the east at dawn. Willow, Seven Stars, and Extension are opposite.
When taiyin is in chen, the year is called Zhixu. Jupiter dwells in Encampment and Eastern Wall. In the first month, it rises with them in the east at dawn. Wings and Chariot Platform are opposite.
When taiyin dwells in si, the year is called Dahuangluo. Jupiter dwells in Stride and Bond. In the second month, it rises with them in the east at dawn. Horn and Neck are opposite.
When taiyin is in wu, the year is called Dunzang. Jupiter dwells in Stomach, Pleiades, and Net. In the third month, it rises with them in the east at dawn. Root, Room, and Heart are opposite.
When taiyin is in wei, the year is called Xiexia. Jupiter dwells in Turtle Beak and Alignment. In the fourth month, it rises with them in the east at dawn. Tail and Winnowing Basket are opposite.
When taiyin is in shen, the year is called Tuntan. Jupiter dwells in Eastern Well and Ghost Bearer. In the fifth month, it rises with them in the east at dawn. Dipper and Ox Leader are opposite.
When taiyin is in you, the year is called Zuo’e. Jupiter dwells in Willow, Seven Stars, and Extension. In the sixth month, it rises with them in the east at dawn. Serving Maid, Emptiness, and Rooftop are opposite.
When taiyin is in xu, the year is called Yanmao. Jupiter dwells in Wings and Chariot Platform. In the seventh month, it rises with them in the east at dawn. Encampment and Eastern Wall are opposite.
When taiyin is in hai, the year is called Dayuanxian. Jupiter dwells in Horn and Neck. In the eighth month, it rises with them in the east at dawn. Stride and Bond are opposite.
When taiyin is in zi, the year is called Kundun. Jupiter dwells in Root, Room, and Heart. In the ninth month, it rises with them in the east at dawn. Stomach, Pleiades, and Net are opposite.
When taiyin is in chou, the year is called Chifenruo. Jupiter dwells in Tail and Winnowing Basket. In the tenth month, it rises with them in the east at dawn. Turtle Beak and Alignment are opposite. [3/27/4–18]
When taiyin is in jiazi,55 recision and accretion are harmoniously together in the Eastern [Celestial] Palace. In their normal movements, which cannot be overcome, they are together for four years and then part. They remain parted for sixteen years and then come together again. As for the reason why they part, recision cannot enter the Central Palace but moves into Wood.
In the place where taiyin dwells
the day causes accretion.
The chronograms cause recision.
With accretion, [the number of] unyielding days naturally doubles because pliant days cannot overcome them.
With recision,
the chronograms [associated with] water move to wood.
The chronograms [associated with] wood move to water.
Metal and fire stay in their [designated] places.
Generally, [taiyin] moves through the directional gods [as follows]:
The Vermilion Bird is one place ahead of taiyin.
The Hooked Array is three places behind.
The Dark Warrior is five places ahead.
The White Tiger is six places behind.
The Empty Star carries the Hooked Array, and Heaven and Earth are in accord with this. [3/27/18–22]
Of the days [i.e., the heavenly stems], jia is unyielding, yi is pliant, bing is unyielding, ding is pliant, and so on to gui.
Wood is born in hai, matures in mao, and dies in wei. These three chronograms together are Wood.
Fire is born in yin, matures in wu, and dies in xu. These three chronograms together are Fire.
Earth is born in wu, matures in xu, and dies in yin. These three chronograms together are Earth.
Metal is born in si, matures in yu, and dies in chou. These three chronograms together are Metal.
Water is born in shen, matures in zi, and dies in chen. These three chronograms together are Water.
Thus [as for] the five overcomings, if birth [occurs in step] 1, then maturity [occurs in step] 5, and death [occurs in step] 9 [in any sequence of the earthly branches]: 5 × 9 = 45. Thus the [directional] gods shift one place every forty-five days. Taking three and responding with five, there are thus eight [such] shifts, and the year comes to an end.
In using taiyin [for prognostication], as a rule
whatever is to its left, that is, ahead of it, suffers cutting away;
whatever is to its right, that is, behind it, obtains increase.56
[As for] the chronogram that suspends the Hooked Array in the balance beam,
if there is war, [the state associated with that chronogram] certainly will be victorious;
if there is an assault, it must succeed. [3/27/24–29]
If one wishes to know the Way of Heaven, one takes the sun as the ruling factor. In the sixth month, it matches [the lunar lodge] Heart. Rotating leftward, it moves, dividing [the celestial circle] and making the twelve months. When they accord with [the movements of] the sun, Heaven and Earth are doubly in accord. Thereafter, there can be no calamitous asterisms. [3/27/29–30]
The first month is established in Encampment and Eastern Wall.57
The second month is established in Stride and Bond.
The third month is established in Stomach and Pleiades.
The fourth month is established in Net, Turtle Beak, and Alignment.
The fifth month is established in [Eastern] Well and Ghost Bearer.
The sixth month is established in Willow, Seven Stars, and Extension.
The seventh month is established in Wings and Chariot Platform.
The eighth month is established in Horn, Neck, and Root.
The ninth month is established in Room and Heart.
The tenth month is established in Tail and Winnowing Basket.
The eleventh month is established in Dipper and Ox Leader.
The twelfth month is established in Emptiness and Rooftop. [3/28/1–4]
The angular extensions of [the stars in the lunar lodges are as follows]:
| Horn: 12d | Serving Maid: 12d | Turtle Beak: 12d |
| Neck: 9d | Emptiness: 10d | Alignment: 9d |
| Root: 15d | Rooftop: 17d | [Eastern] Well: 30d |
| Room: 5d | Encampment: 16d | Ghost Bearer: 4d |
| Heart: 5d | Eastern Wall: 9d | Willow: 15d |
| Tail: 18d | Stride: 16d | [Seven] Stars: 7d |
| Winnowing Basket: 11.25d | Bond: 12d | Extension: 18d |
| Dipper: 26d | Stomach: 14d | Wings: 18d |
| Ox Leader: 8d | Pleiades: 11d | Chariot Platform: 17d |
| Net: 16d | [3/28/6–9] |
The stars [= lunar lodges] are apportioned to territories, namely,
Horn and Neck to Zheng
Root, Room, and Heart to Song
Tail and Winnowing Basket to Yan
Dipper and Ox Leader to Yue
Serving Maid to Wu
Emptiness and Rooftop to Qi
Encampment and Eastern Wall to Wey
Stride and Root to Lu
Stomach, Pleiades, and Net to Wei
Turtle Beak and Alignment to Zhao
[Eastern] Well and Ghost Bearer to Qin
Willow, Seven Stars, and Extension to Zhou
Wings and Chariot Platform to Chu. [3/28/11–13]
When Jupiter dwells [in a lodge corresponding to a state, in that state,] the five grains will be bountiful. [The situation of the state corresponding to the lodge] opposite will be the reverse; the harvest will suffer calamity. If Jupiter should dwell [in a lodge] and does not dwell there, if it skips over and enters another place, the ruler of the country [governed by that lodge] will die and his state will be extinguished. [3/28/15–16]
When taiyin controls the ordinances of spring, [the ruler] should act [in a way that is] pliant, kind, mild, and good.
When taiyin controls the ordinances of summer, [the ruler] should publish, bestow, proclaim, and make clear.
When taiyin controls the ordinances of autumn, [the ruler] should repair, put in order, and make ready his troops.
When taiyin controls the ordinances of winter, [the ruler] should be fiercely brave and resolute and harden the frontier defenses.
In every three-year period, there is an alteration of what is usual.
In every six-year period, there are changes from what is normal.
Thus,
within three years, there is a year of famine;
within six years, there is a year of depression;
once in twelve years, there is abundance. [3/28/18–20]
[The territorial allotments of the celestial stems are as follows:] |
|
| jia with Qi | ji with Hann |
| yi with Eastern Yi | keng with Qin |
| bing with Chu | xin with Western Yi |
| ding with Southern Yi | ren with Wey |
| wu with Wei | gui with Yue |
[The territorial allotments of the earthly branches are as follows:] |
|
| zi with Zhou | wu with Qin |
| chou with Di | wei with Song |
| yin with Chu | shen with Qi |
| mao with Zheng | you with Lu |
| chen with Jin | xu with Zhao |
| si with Wey | hai with Yan [3/28/22–24] |
[The stem and branch correlations of the Five Phases are as follows:] |
||
| [stems] | [branches] | [phases] |
| jia and yi | yin and mao | Wood |
| bing and ding | si and wu | Fire |
| wu and chi | the four seasons | Earth |
| geng and xin | shen and you | Metal |
| ren and gui | hai and zi | Water [3/28/26–27] |
Water produces Wood; Wood produces Fire; Fire produces Earth; Earth produces Metal; Metal produces Water.
If the child gives birth to the mother, this is called Rightness.
If the mother gives birth to the child, this is called fostering.
If the mother and child each give rise to the other, this is called concentration.
If the mother vanquishes the child, this is called control.
If the child vanquishes the mother, this is called obstruction.
If one employs victory to smite and kill, the victory will be without recompense.
If one employs concentration to pursue affairs, there will be achievement.
If one employs Rightness to carry out fixed principles, one’s fame will be established and it will not diminish.
If one employs fostering to nurture the myriad creatures, there will be luxuriant growth and prosperity.
If one employs obstruction to pursue affairs, there will be destruction, extermination, death, and extinction [of the state]. [3/28/26–29]
The gods of the Northern Dipper are both female and male. In the eleventh month, at the beginning [of the year], they are established [together] in zi. Every month they shift by one chronogram. The male goes leftward, the female rightward. In the fifth month they coincide in wu and devise recision. In the eleventh month they coincide in zi and devise accretion. [3/29/1–2]
The chronogram in which taiyin is located58 is called an “oppressive day.” On oppressive days it is not possible to pursue the hundred [normal] affairs. Earth and Heaven59 move with slow dignity; the male knows the female by the sound [of her singing]. Thus [the chronogram in which taiyin is located] is known as the “extraordinary chronogram.” [3/29/2–3]
The numbers [of the sexagenary cycle] begin with jiazi. Offspring and mother seek each other out. The place where they come together is called a concurrence. Ten stems and twelve branches make a sexagenary cycle.
In all there are eight concurrences. If the concurrence is [at a point in the cycle] before [the stem–branch combination in which taiyin is located], there will be death and destruction; if the concurrence is later [in the cycle], there will be no calamity. [3/29/5–6]
[The territorial allocations of the “eight concurrences” are as follows:]
| jiaxu is Yan | gengchen is Qin |
| yiyou is Qi | xinmao is the Rong tribes |
| bingwu is Yue | renzi is the Dai tribes |
| dingsi is Chu | guihai is the Hu tribes |
[The territorial allocations of the “lesser conjunction” cyclical pairs are as follows:]60 |
|
| [wuchen is . . .] | yiyou is . . . |
| wuxu is . . . | yimao is Wei |
| [yisi is . . .] | wuwu is . . . |
| yihai is Hann | wuzi is . . . |
The eight concurrences [together with the eight lesser conjunctions] [thus correspond to] the world. [3/29/8–10]
When taiyin, the Lesser Year, the asterisms [= lunar lodges], the branches, the stems, and the five [directional] gods all coincide on the same day, there will be clouds, vapors, and rain. The state and ruler match [the prognostication]. [3/29/12]
Of those prized by the heavenly spirits, none is more prized than the Bluegreen Dragon. The Bluegreen Dragon is otherwise called the Heavenly Unity, or otherwise taiyin. [The country corresponding to] the place where taiyin dwells cannot retreat but can advance. [The country corresponding to] the place beaten against by the Northern Dipper cannot withstand attack. [3/29/14–15] When Heaven and Earth were founded, they divided to make yin and yang.
Yang is born from yin;
yin is born from yang;
they are in a state of mutual alternation. The four binding cords [of Heaven] communicate with them.
Sometimes there is death;
sometimes there is birth.
Thus are the myriad things brought to completion.
[Of all creatures that] move and breathe, none is more prized than humans. [The bodily] orifices, limbs, and trunk all communicate with Heaven.
Heaven has nine layers; man also has nine orifices.
Heaven has four seasons, to regulate the twelve months;
Man also has four limbs, to control the twelve joints.
This diagram of the stems, branches, lunar lodges, and Five Phases is in the form of the Earth plate of a shi 
cosmograph, showing significant alignments with the “pointer” of the Northern Dipper engraved on the rotating Heaven plate (not depicted here).
Heaven has twelve months, to regulate the 360 days;
Man also has twelve joints, to regulate the 360 nodes.61
A person who undertakes affairs while not obeying Heaven is someone who deviates from what gave birth to him. [3/29/17–20]
Take the arrival of the winter solstice and count to the first day of the first month of the coming year. [If] there are a full fifty days, the people’s food supply will be sufficient. [If] there are fewer [than fifty days], [the people’s rations] will be reduced by one pint per day. [If] there is a surplus [above fifty], [the people’s rations] will be increased by one pint per day. This is what controls the harvest. [3/29/22–23]
Translation of the diagram of the stems, branches, lunar lodges, and Five Phases.
The year Shetige: A year of early moisture and late drought. Rice plants are sickly and silkworms do not mature. Legumes and wheat flourish. The people’s food ration is four pints [of grain per day]. Yin in jia is called “impeded seedlings.”
The year Ming’e: The year is harmonious. Rice, legumes, wheat, and silkworms flourish. The people’s food ration is five pints. Mao in yi is called “flag sprouts.”
The year Zhixu: A year of early drought and late moisture. There is minor famine. Silkworms are obstructed, and wheat ripens. The people’s food ration is three pints. Chen in bing is called “pliant omen.”
The year Dahuangluo: A year of minor warfare. Silkworms mature in small numbers, wheat flourishes, and legumes are sickly. The people’s food ration is two pints. Si in ding is called “strengthen the frontier.”
The year Dunzang: A year of great drought. Silkworms mature, rice is sickly, and wheat flourishes, but the crops do not yield. The people’s food ration is two pints. Wu in wu is called “manifestly harmonious.”
The year Xiexia: A year of minor warfare. Silkworms mature, rice flourishes, and legumes and wheat do not yield. The people’s food ration is three pints. Wei in ji is called “differentiate and separate.”
The year Tuntan: The year is harmonious. The lesser rains fall in season. Silkworms mature; legumes and wheat flourish. The people’s food ration is three pints. Shen in geng is called “elevate and make manifest.”
The year Zuo’e: A year of great war. People suffer illness, silkworms do not mature, legumes and wheat do not yield, and crops suffer insect damage. The people’s food ration is five pints. You in xin is called “redoubled brightness.”
The year Yanmao: A year of minor famine and warfare. Silkworms do not mature, wheat does not yield, but legumes flourish. The people’s food ration is seven pints. Xu in ren is called “umbral blackness.”
The year Dayuanxian: A year of great warfare and great famine. Silkworms rupture their cocoons; legumes and wheat do not yield; crops suffer insect damage. The people’s food ration is three pints. [Hai in gui is called . . .]62
The year Kundun: A year of great fogs rising up and great waters issuing forth. Silkworms, rice, and wheat flourish. The people’s food ration is three bushels. Zi in jia is called “dawning brilliance.”
The year Chifenruo: A year of minor warfare and early moisture. Silkworms do not hatch. Rice plants are sickly, legumes do not yield, but wheat flourishes. The people’s food ration is one pint. [Chou in yi is called. . . .]63 [3/29/25–3/31/8]
To establish the directions of sunrise and sunset, first set up a gnomon in the east. Take one [other] gnomon, and step back ten paces from the first gnomon. Use it to sight in alignment toward the sun when it first emerges at the northern edge [of its position on the eastern horizon?] When the sun is just setting, again plant one gnomon to the east [of the second gnomon], and use the gnomon to the west of it to sight in alignment toward the sun when it sets at the northern edge. Then establish the midpoint of the two eastern gnomons; this along with the western gnomon fixes a true east–west line. At the winter solstice, the sun rises at the southeastern binding cord and sets at the southwestern binding cord. At the spring and autumn equinoxes, it rises exactly in the east and sets exactly in the west. At the summer solstice, the sun rises at the northeastern binding cord and sets at the northwestern binding cord. At the zenith it is exactly in the south. [3/31/10–14]
If you wish to know the numerical values for the east–west and north–south breadth and length [of the earth], set up four gnomons to form a square one li on each side. Ten or a few more days before the spring or autumn equinox, use the two gnomons on the northern edge of the square to sight in alignment on the rising sun when it first appears [above the horizon]. Wait until [the day when the gnomons] coincide [with the rising sun]. When they coincide, then this corresponds to the true [east] position of the sun. Then immediately also use the south[west]ern gnomon to sight on the sun in alignment. Take the amount by which [this sighting] is within the forward gnomons as the standard. Divide the width and length [between the gnomons [i.e., one li]] by this, and from this you will know the numerical value of [the width of the earth] from east to west. For example, observe the [alignment of the southwestern gnomon with] the rising sun to be one inch within the forward gnomons, and let one inch equate to one li. One li equals 18,000 inches, so the distance from [the point of observation] eastward to the sun is 18,000 li. Or [on the same day] observe the setting sun; [the alignment of the sun with the southeastern gnomon] lies one-half inch within the forward gnomons. For one-half inch, one obtains one li. Divide the number of inches in one li by one-half inch; one obtains the answer of 36,000 li. Thus one obtains the numerical value of the distance from [the point of observation] westward to the sun. Add [the two figures] together for the numerical value of the distance from east to west. This number represents the span between the extreme end points [of the earth].
If the alignment [of the gnomons on the northern edge of the square] occurs before the spring equinox or after the autumn equinox, you are to the south [of the midline of the earth]. If the alignment occurs before the autumn equinox or after the spring equinox, you are to the north. If the alignment occurs exactly on the equinox, then you are midway between north and south.
If you wish to know true south from a position in the exact center, [observe that] if the alignment [of the gnomons on the northern edge of the square] does not occur before the autumn equinox, the position is exactly between north and south. If you wish to know the distance to the extreme limits of south and north from a position in the center, use the southwestern gnomon to sight in alignment on the sun. When the sun at the summer solstice first rises, sight on the north[west]ern gnomon, and [you will see that] the sun is an equal distance to the east, [aligned with] the northeastern gnomon. The distance to the east is 18,000 li, so the distance from the center to the north is also 18,000 li. Double this to obtain the numerical value of the distance from south to north.
The amount by which [a position] departs from the center is larger or smaller, [proportional to the] amount by which [the sight line] is within or outside the forward gnomons. If [that line] is one inch inside the gnomons, the sun is closer by one li. If [the line] is one inch outside the gnomons, the sun is more distant by one li. [3/31/15–24]
If you wish to know the height of heaven, plant a gnomon one zhang [i.e., ten feet] tall in the south [and another] in the north, at a distance of a thousand li. Measure their shadows [at noon] on the same day. [Suppose that] the northern gnomon [casts a shadow of] two feet, and the southern gnomon [casts a shadow of] one foot, nine inches. Thus by going a thousand li to the south, the shadow is shortened by one inch.64 Going twenty thousand li [to the south], there would be no shadow. That would be directly beneath the sun. A shadow two feet long results from a height of ten feet, so going south one [li] [increases] the height by five [li] Thus if one measures the li from [the northern gnomon] to a point directly beneath the sun and then multiplies that by five, it makes 100,000 li, and that is the height of heaven. Or if you suppose that the [length of] the shadow is equal to [the height of] the gnomon, then the height [of heaven] would be equal to the distance [southward to a point directly beneath the sun].65 [3/32/1–4]
Translated by John S. Major
1. Conventionally translated as “cosmos” or “universe,” yuzhou 
more precisely means, as Angus C. Graham put it, “process enduring in time” and “matter extending in space” (“Reflections and Replies: Major,” in Chinese Texts and Philosophical Contexts: Essays Dedicated to Angus C. Graham, ed. Henry Rosemont [La Salle, Ill.: Open Court Press, 1990], 279). “Space-time,” a term borrowed from modern physics, captures the idea very well.
2. Gong Gong 
is a mythical figure of high antiquity, sometimes described as the “minister of works” to the ancient thearchs but also depicted as a rebel and fomenter of disorder.
3. Zhuan Xu 
is a divine thearch and god of the north, from whom many aristocratic lineages of the Bronze Age claimed descent. See also chap. 5, n. 46.
4. Mount Buzhou, conceptualized as the central peak of Mount Kunlun and therefore located to the northwest of China (see the introduction to chap. 4 and fig. 4.1), is the pivot of Heaven and Earth. Zhou 
means “to circle” in the sense of “to circumambulate” or “to orbit”; it does not mean “to revolve on its own axis.” Thus the common translation of “Unrotating Mountain” for Buzhou 
is not correct. The sense of the term is that the mountain rests unmoving at the very center of the universe, which rotates around it.
5. The same phrase, yin yang xiang bo 
, occurs five times in 4.19 and once in 17.174. The context of 17.174 requires a slightly different translation: “yin and yang erode each other.”
6. See 10.27: “When an eagle hovers above the river, fish and turtles plunge and flying birds scatter. By necessity they distance themselves from harm.”
7. A device intended to collect dew by condensation.
8. Reading er 
as er 
. Essentially the same statement appears in 6.2. See chap. 6, n. 18.
9. That is, the Gulf of Bohai, a shallow body of water located off northeastern China and partly enclosed by the Liaodong and Shandong peninsulas.
10. Reading ling bu shi 
as in the Yiwen, in place of the ling bu shou 
of the Huainanzi text. My thanks to Michael Loewe (private communication) for suggesting this emendation. For the concept of “unseasonable ordinances,” see chap. 5.
11. “Chariot Frame,” Xuanyuan 
, is the personal name of the Yellow Emperor, after the name of his supposed birthplace in Henan. The compound word means “axle and shafts”—that is, the basic frame of a chariot.
12. The Pool of Xian is a constellation. The word xian 
is open to various interpretations, but in this compound it seems to be the name of the legendary figure Shaman Xian, Wuxian 
. For further discussion, see Major 1993, 199. See also chap. 11, n. 35.
13. The “asterisms” (xing 
) of this passage are the lunar lodges (xiu 
). For the lunar lodges and the English translations of their names used in this work, see app. B.
14. Tai Hao, Gou Mang, and the other planetary gods and “assistants” are mythical figures; many also appear in the poems of the Chuci. For further identifications, see the “Glossary of Names” in Hawkes 1985, 322–45.
15. This and the following four paragraphs are quoted verbatim from the Mawangdui manuscript text known as “Wuxingzhan.” See Xi Zezong 
, “Zhongguo tianwenxue shi de yige zhongyao faxian—Mawangdui Hanmu boshu zhong de ‘Wuxingzhan’” 
— 
(An important discovery for the history of Chinese astronomy—the Mawangdui silk manuscript “Prognostications of the Five Planets”), in Zhongguo tianwenxue shi wenji 
(Beijing: Science Press, 1978), 14–33. On the motions of the five planets, 3.7 through 3.11 are similar to but less detailed than the corresponding sections of the “Wuxingzhan.”
16. Yan Di 
, the “Flame Emperor,” is a semidivine figure who figures variously in different myths. In some stories he is credited with having invented the use of fire for humankind, and in others he is depicted as a rebel against the legitimate authority of the Yellow Emperor, who is sometimes identified as his half brother.
17. Each of the “four hooks” defines two points on the horizon, and Jupiter passes through two lunar lodges for each of those points. Thus four hooks equal eight points and therefore the “two times eight is sixteen” of the text. See Major 1993, 34, fig. 2.2.
18. These wind names are repeated in 4.18. A different list of wind names, perhaps representing an alternative tradition, is found in 4.1.
19. Changhe 
is the name of the Gate of Heaven, the portal through which communication between Heaven and Earth is possible. See 4.3.
20. Mount Buzhou 
is the pivot of Heaven, around which the cosmos rotates. See 4.3 and chap. 4, n. 10.
21. Six imaginary diametral lines that span the celestial circle.
22. Yu Yan suggests that here taiyi 
should read tianzi 
, “Son of Heaven.” Wang Yinzhi suggests wudi 
, “five emperors” or “five thearchs.” The suggested emendations are plausible but not compelling. Taiyi, the “Grand One,” is a philosophical/cosmological concept, a star, and a god. All the places mentioned here (Grand Enclosure, etc.) are constellations; thus the location of Taiyi among them is reasonable within the framework of the cosmology presented here. See Zhang Shuangdi 1997, 1:290n.78.
23. Rejecting Lau’s (HNZ 3/21/12–13) suggestion in the concordance text that gu yue 
be emended to gu ri 
and attached to the end of the preceding paragraph.
24. The four “corner” directions (northeast, southeast, southwest, and northwest) are conceived of as cords (wei 
) binding the cosmos together and restraining the movements of yin and yang. See 1.1.
25. The terms “accretion” and “recision,” de 
and xing 
, in this passage and after refer to the accumulation and paring away of the yang qi throughout the year. For an extended discussion of this idea, see John S. Major, “The Meaning of Hsing-te,” in Chinese Ideas About Nature and Society: Studies in Honour of Derk Bodde, ed. Charles Le Blanc and Susan Blader (Hong Kong: Hong Kong University Press, 1987), 281–91.
26. Reading sheng 
as sheng 
, as suggested by Yu Yue. See Lau, HNZ, 21n.13.
27. A biao 
, “gnomon,” is a straight stick or rod designed to cast a solar shadow. Gnomons used in sundials are aimed at the celestial north pole. Gnomons used to find direction (e.g., finding a true north–south line by bisecting the angle of shadows cast at sunrise and sunset) or to track the seasons (by measuring the length of the noon shadow) are usually exactly vertical.
28. Lau (HNZ 3/22/12–29) emends the text here and throughout the passage relating to the twenty-four solar nodes to shift the pitch-pipe notes by one unit in each case. For example, in this line he emends Yellow Bell to read Responsive Bell and similarly throughout the passage. We believe that those emendations are not soundly based, and so we follow the original, unemended text in this translation.
29. Adding this line of text to maintain the pattern of the passage overall.
30. The “chronograms” (chen 
) are the twelve earthly branches considered as markers of calendrical time: the twelve months distributed around the horizon circle (and around the Earth plate of the astronomical/astrological instrument known as the shi 
, “cosmograph”). See Major 1993, 34, fig. 2.2.
31. Although the details are obscure, this whole passage is an example of Han “military astrology” dealing in the vulnerability of states to attack, depending on their geographical location in relation to certain heavenly bodies and calendrical periods.
32. Rejecting Lau’s (HNZ 3/23/9) emendation of taiyi 
to tianyi 
.
33. Nai shou qi sha 
. It is not clear what is meant by this unusual phrase; perhaps it is a reference to bringing in game that has been killed in the hunt. Another possible interpretation would be “[the authorities] take charge of those who are to be executed.”
34. Qing Nü 
. The color word qing embraces a range of colors from blue to green; our usual translation is “bluegreen.” But with respect to horses, dogs, and other mammals, it means “gray,” a color that also would be appropriate for what is apparently a mythical winter goddess or fairy.
35. The heng 
, “balance beam,” is the horizontal member in a hand scale. The heng works in conjunction with a quan 
, “weight.”
36. Quan 
means a “weight.” When using a hand scale, the object to be weighed is suspended from one arm of the balance, and a weight or combination of weights is suspended from the other arm. The weights are equal when the balance beam achieves a stable horizontal position. In the type of scale known as a steelyard, the object to be weighed is suspended from one arm of the beam, while a weight is moved along the other arm of the balance beam until the latter achieves a stable horizontal position. The weight of the object being weighed then can be read on a scale inscribed onto the surface of the beam. Recent scholarship suggests that the steelyard became common in China only from the Latter Han dynasty onward. See Griet Vankeerberghen, “Choosing Balance: Weighing (quan) as a Metaphor for Action in Early Chinese Texts,” Early China 30 (2005): 47–89, esp. 48–53.
Quan also sometimes refers to the plumb bob of a plumb line, rather than a weight for weighing things. The word also has a number of extended meanings, such as “heft” and “expediency,” beyond its basic meaning of a “weight” as a physical object. See app. A.
37. This line has been transposed to here from 3/25/14–15, where it is clearly out of place. For textual notes relating to this and the following section, see also Major 1993, 299.
38. For the numerous puns, both phonetic and logographic, that give this section its meaning and make it very difficult to translate, see Major 1993, 299–300.
39. Laozi 42.
40. Following the original wording of the text, rather than the emendation suggested by Lau.
41. This and the previous line have been moved here from 3/26/24, where they are out of place.
42. Rejecting Lau’s proposed emendation of sheng 
to zhu 
.
43. Rejecting Lau’s insertion of bu 
, “not,” in this line.
44. In early Chinese musical terminology, notes could be designated as “turbid” or “muddy” (zhuo 
) or “clear” (qing 
). The former were lower in pitch than the latter; so here we might speak of Forest Bell, flat. But the precise meaning of ruo and qing in ancient musical terminology is uncertain. See app. B.
45. That is, 2.7 chi 
; one Chinese foot is equal to ten inches (cun 
).
46. Xun 
. The Han “foot” (chi 
) was about nine modern inches long; thus eight Han feet equals approximately seventy-two inches, or six feet, probably in fact somewhat taller than the height of an “average man” in Han times. In 7.5, the height of a person is given as seven feet (chi)—that is, about five feet, three inches, in today’s terms.
47. One zhang 
is ten feet; one pi 
is forty feet.
48. Note that fen 
, a generic term meaning “portion,” is used in 3.31 as both a unit of length (1/10 Han inch) and a unit of weight (1/12 zhu 
, i.e., 1/144 of a half ounce, ban liang 
). It seems unlikely in fact that twelve husk beards side by side would add up to a breadth as small as 1/10 inch, and it also seems unlikely that the weight of 1/12 zhu (in modern terms, equal to about 0.05 gram) could have been measured accurately.
49. A half ounce, ban liang, was the weight of a standard Han coin.
50. A “catty” is a jin 
; thirty catties make one jun 
; four jun make one dan 
. (The character for dan is normally pronounced shi, meaning “stone”; it has the unusual pronunciation dan when used as a unit of weight.)
51. A character is evidently missing here.
52. Yin is the third of the earthly branches and thus the third astronomical month (after zi, the month in which the winter solstice occurs, and chou). In the so-called Xia calendar, the third astronomical month is, by convention, the first civil month; hence yin is associated with the first Jovian year, Shetige.
53. In the received text this passage reads “in the eleventh month,” and subsequent passages read “twelfth month,” “first month,” and so on. Lau (HNZ 3/27/5–18) emends this to “first month,” “second month,” “third month,” and so on, on the grounds that the civil year begins with yin. But part of the point of this passage is to correlate the civil months of the lunar year with the astronomical months of the solar year: the first astronomical month, zi, in which the winter solstice occurs, is the eleventh month of the civil year that begins with yin. It is important to remember that this passage, like much of the astronomical information in this chapter, refers primarily to manipulations of the shi 
chronograph rather than to observations of the sky.
54. The character 
is normally pronounced dan. For the name of the second Jovian year, it has the nonstandard pronunciation ming; hence, Ming’e.
55. On this passage, see Donald Harper, “Warring States Natural Philosophy and Occult Thought,” in The Cambridge History of Ancient China: From the Origins of Civilization to 221 b.c., ed. Michael Loewe and Edward L. Shaughnessy (Cambridge: Cambridge University Press, 1999), 849–50.
56. Rejecting Lau’s (HNZ 3/27/28–29) emendations of these two lines.
57. In almost all cases, the received text gives only one lunar lodge for each of the twelve months in this list. We follow Lau in giving the full allotment of lunar lodges to each month, but with some misgivings, as it is not clear to us that the abbreviated list in the received text was not what the author intended. For a translation of the list in its original form, see Major 1993, 127.
58. Rejecting Lau’s (HNZ 3/29/2) suggestion that taiyin be replaced by ci 
, “female [deity].” The context of this passage pertains to the celestial location of taiyin.
59. Not the usual phrase tiandi 
“Heaven and Earth” but kanyu 
, literally “support and canopy,” a poetic term for Earth and Heaven.
60. The text here is obviously defective; most of the names of states to which these “lesser conjunctions” refer are missing; and it is not possible to reconstruct them with confidence. For what I have called the “lesser conjunctions,” see Major 1993, 134.
61. In this instance, “nodes” (jie 
) refers to any place in the body where two bones meet.
62. This phrase, expected from parallelism with the other years of the Jovian cycle, is missing from the text.
63. This phrase, expected from parallelism with the other years of the Jovian cycle, is also missing from the text.
64. Note that in Chinese linear measure, one foot equals ten inches (not twelve, as in the English system); thus two feet minus one inch equals one foot, nine inches, as stated here.
65. For a highly detailed analysis of 3/31/10 to 3/32/4, see Christopher Cullen’s annotated translation, “A Chinese Eratosthenes of the Flat Earth,” in Major 1993, 269–90.