Volume 19 Treatises 14: Astronomy 1

若夫法紫微以居中，擬明堂而布政，依分野而命國，體眾星而效官，動必順時，教不違物，故能成變化之道，合陰陽之妙。爰在庖犧，仰觀俯察，謂以天之七曜、二十八星，周於穹圓之度，以麗十二位也。在天成象，示見吉凶。五緯入房，啓姬王之肇跡，長星孛斗，鑒宋人之首亂，天意人事，同乎影響。自夷王下堂而見諸侯，赧王登臺而避責，《記》曰：「天子微，諸侯僭。」於是師兵吞滅，僵僕原野。秦氏以戰國之餘，怙茲凶暴，小星交鬭，長彗橫天。漢高祖驅駕英雄，墾除災害，五精從歲，七重暈畢，含樞曾緬，道不虛行。自西京創制，多歷年載。世祖中興，當塗馭物，金行水德，祗奉靈命，玄兆著明，天人不遠。昔者榮河獻籙，溫洛呈圖，六爻摛範，三光宛備，則星官之書，自黃帝始。高陽氏使南正重司天，北正黎司地，帝堯乃命羲、和，欽若昊天。夏有昆吾，殷有巫咸，周之史佚，宋之子韋，魯之梓慎，鄭之裨灶，魏有石氏，齊有甘公，皆能言天文、察微變者也。漢之傳天數者，則有唐都、李尋之倫。光武時，則有蘇伯况、郎雅光，並能參伍天文，發揚善道，補益當時，監垂來世。而河、洛圖緯，雖有星占星官之名，未能盡列。

Heaven's order mirrors earthly rule: the Purple Palace stands at the center as the emperor's seat, the Bright Hall models the distribution of government, territorial divisions assign each state its place, and the stars map the hierarchy of offices. When action follows the seasons and instruction respects the nature of things, the Way of transformation is fulfilled and yin and yang work in harmony. As early as Fuxi, through observation above and inquiry below, it was held that Heaven's seven luminaries and twenty-eight asterisms traverse the arc of the celestial vault to mark the twelve terrestrial positions. Heaven forms images that portend good and ill. The five planets entering the Chamber heralded the Zhou dynasty's rise; a long-tailed comet at the Dipper foreshadowed the Song's first revolt. Heaven's will and human affairs mirror each other as closely as shadow and substance. From King Yi of Zhou descending the hall to meet the feudal lords, to King Nan mounting the tower to shirk responsibility, the Record says: "The Son of Heaven wanes and the feudal lords usurp their prerogatives. Armies then devoured one another, and the dead lay strewn across the fields. The Qin, inheritors of the Warring States' violence, leaned on brutal force; lesser stars clashed in the heavens and a long comet swept the sky. Han Gaozu rallied heroes and swept away disaster; the five planets marched with Jupiter, a sevenfold halo encircled the Net, and the celestial Pivot held its place—the Way of Heaven does not act without purpose. Since the Western Capital was established, many years elapsed. When Emperor Guangwu restored the Han, he seized the moment to rule; Metal and Water received the sacred mandate, dark portents appeared plainly, and Heaven and humanity stood in close accord. When the chart was offered at the Glory of the River and the diagram at the Warmth of the Luo, the six lines revealed their pattern and sun, moon, and stars stood complete—the annals of star officials thus begin with the Yellow Emperor. Emperor Zhuanxu appointed the Southern Regulator Chong to govern Heaven and the Northern Regulator Li to govern Earth; Emperor Yao then charged Xi and He to reverently align themselves with the great Heaven. The Xia had Kunwu, the Yin had Wu Xian, the Zhou historiographer Yi, Song's Zi Wei, Lu's Zi Shen, Zheng's Pi Zao, Wei's Shi clan, and Qi's Duke Gan—all masters of astronomy who could read subtle celestial changes. Among Han transmitters of celestial reckoning were Tang Du, Li Xun, and others of their company. Under Guangwu, Su Bo Kuang and Lang Ya Guang could cross-check astronomical data, advance the proper doctrine, serve their own age, and leave a model for posterity. Even the River and Luo charts and apocryphal texts named star diviners and star officials, yet could not enumerate them fully.

後漢張衡為太史令，鑄渾天儀，總序經星，謂之《靈憲》。其大略曰：「星也者，體生於地，精發於天。紫宮為帝皇之居，太微為五帝之坐，在野象物，在朝象官。居其中央，謂之北斗，動系於占，實司王命。四布于方，為二十八星，日月運行，曆示休咎。五緯經次，用彰禍福，則上天之心，於是見矣。中外之官，常明者百有二十，可名者三百二十，為星二千五百；微星之數萬一千五百二十，庶物蠢動，咸得繫命。」而衡所鑄之圖，遇亂堙滅，星官名數，今亦不存。三國時，吳太史令陳卓，始列甘氏、石氏、巫咸三家星官，著於圖錄。并注占贊，總有二百五十四官，一千二百八十三星，並二十八宿及輔官附坐一百八十二星，總二百八十三官，一千五百六十五星。宋元嘉中，太史令錢樂之所鑄渾天銅儀，以硃黑白三色，用殊三家，而合陳卓之數。高祖平陳，得善天官者周墳，並得宋氏渾儀之器。乃命庾季才等，參校周、齊、梁、陳及祖暅、孫僧化官私舊圖，刊其大小，正彼疏密，依准三家星位，以為蓋圖。旁摛始分，甄表常度，並具赤黃二道，內外兩規。懸象著明，纏離攸次，星之隱顯，天漢昭回，宛若穹蒼，將為正範。以墳為太史令。墳博考經書，勤於教習，自此太史觀生，始能識天官。煬帝又遣宮人四十人，就太史局，別詔袁充，教以星氣，業成者進內，以參占驗云。史臣於觀臺訪渾儀，見元魏太史令晁崇所造者，以鐵為之，其規有六。其外四規常定，一象地形，二象赤道，其餘象二極。其內二規，可以運轉，用合八尺之管，以窺星度。周武帝平齊所得。隋開皇三年，新都初成，以置諸觀臺之上。大唐因而用焉。馬遷《天官書》及班氏所載，妖星暈珥，雲氣虹霓，存其大綱，未能備舉。自後史官，更無紀錄。《春秋傳》曰：「公既視朔，遂登觀臺，凡分至啓閉，必書雲物。」神道司存，安可誣也！今略舉其形名占驗，次之經星之末云。

In the Later Han, Zhang Heng as Grand Astrologer cast an armillary sphere, catalogued the fixed stars, and titled the work Ling Xian. Its summary runs: "Stars have bodies born from Earth and essence radiating in Heaven. The Purple Palace is the emperor's residence, the Supreme Palace the seat of the Five Emperors; beyond the court they mirror things, within the court they mirror offices. At their center stands the Northern Dipper; its motion governs divination and truly holds the royal mandate in charge. The twenty-eight asterisms spread across the four quarters; as sun and moon run their paths they reveal fortune and disaster. The five planets move in their ordained sequence, displaying calamity and blessing—and thus the mind of Heaven is revealed. Among the inner and outer star-offices, one hundred and twenty shine constantly, three hundred and twenty bear names, and as individual stars they number two thousand five hundred; faint stars slightly exceed eleven thousand five hundred and twenty—in this way every living thing has its fate bound. Yet the chart Heng cast was buried in the chaos of war, and the names and counts of the star officials no longer survive. During the Three Kingdoms, Wu's Grand Astrologer Chen Zhuo first compiled the star officials of the Gan, Shi, and Wu Xian schools into charts and catalogues. Adding divinatory notes, he recorded two hundred fifty-four offices and one thousand two hundred eighty-three stars, plus the twenty-eight lodges and their attendant seats with one hundred eighty-two stars—two hundred eighty-three offices and one thousand five hundred sixty-five stars in all. Under Liu Song's Yuanjia reign, Grand Astrologer Qian Lezhi cast a bronze armillary sphere, marking the three schools in red, black, and white while conforming to Chen Zhuo's counts. When Gaozu conquered Chen, he gained the adept celestial officer Zhou Fen and recovered the Song dynasty's armillary instruments. He ordered Yu Ji Cai and others to collate old charts from Zhou, Qi, Liang, Chen, Zu Geng, and Sun Seng Hua—public and private—adjusting scale, correcting density, and using the three schools' star positions as the basis for a canopy chart. Initial divisions were laid out at the margins, standard degrees tabulated, and both the red and yellow paths with inner and outer circles were included. Suspended stars stood plain, lodge boundaries fell in order, stars waxed and waned, and the Milky Way wound back like the vault of sky itself—a standard for correct reckoning. Zhou Fen was made Grand Astrologer. Fen studied the classics exhaustively and taught with diligence; from then on the Astrological Bureau's trainees could identify the celestial offices. Emperor Yang dispatched forty palace women to the Astrological Bureau and separately ordered Yuan Chong to instruct them in star qi; graduates entered the inner palace to aid in divination. The historiographer, examining the armillary sphere at the observatory, found the instrument cast by Northern Wei Grand Astrologer Chao Chong—iron, with six rings. Four of the outer six rings were fixed: one representing terrain, one the equator, and the remainder the two celestial poles. The inner two rings rotated, paired with an eight-foot sighting tube to measure stellar degrees. Northern Zhou's Emperor Wu acquired it when he conquered Qi. In Sui Kaihuang year 3, when the new capital was finished, the instrument was installed on the observatory platform. The Tang dynasty continued to employ it. Sima Qian's Treatise on the Celestial Offices and Ban Gu's account give the broad categories of prodigious stars, halos, spurs, cloud vapors, and rainbows, but do not enumerate every form. Later historiographers kept no further records. The Zuo Commentary says: "After performing the new-moon sacrifice, the duke ascended the observatory—for each solstice, equinox, and seasonal commencement, cloud signs were duly written down. The numinous Way has its officers—how could such things be fabricated! Here I briefly list their forms, names, and divinatory tests, appending them after the section on fixed stars.

○天體

The Celestial Body

古之言天者有三家，一曰蓋天，二曰宣夜，三曰渾天。

Ancient cosmologists recognized three schools: Canopy Heaven, Overnight Heaven, and Spherical Heaven.

蓋天之說，即《周髀》是也。其本庖犧氏立周天曆度，其所傳則周公受于殷商，周人志之，故曰《周髀》。髀，股也；股者，表也。其言天似蓋笠，地法覆槃，天地各中高外下。北極之下，為天地之中，其地最高，而滂沲四蕆，三光隱映，以為晝夜。天中高於外衡冬至日之所在六萬里，北極下地高於外衡下地亦六萬里，外衡高於北極下地二萬里。天地隆高相從，日去地恆八萬里。日麗天而平轉，分冬夏之間日所行道為七衡六間。每衡周徑裡數，各依算術，用句股重差，推晷影極遊，以為遠近之數，皆得於表股也，故曰《周髀》。

Canopy Heaven theory is set forth in the Zhou Bi. Fuxi first established the degrees of Heaven's circuit; the tradition passed from Shang to the Duke of Zhou, and the Zhou recorded it—hence Zhou Bi, "Zhou Gnomon." Bi means thigh— the thigh serves as the measuring post. Heaven resembles an inverted bowl, Earth an upturned dish—each highest at the center and sloping downward at the rim. Beneath the North Pole lies the center of Heaven and Earth, where the land stands highest; waters spill outward on all sides, and the three luminaries alternately hide and shine to create day and night. At the center Heaven rises sixty thousand li above the outer ring where the winter solstice sun stands; land under the North Pole stands sixty thousand li above land under the outer ring, while the outer ring itself stands twenty thousand li above the land beneath the North Pole. Heaven and Earth rise together in parallel, and the sun always stands eighty thousand li from Earth. The sun rides Heaven and revolves evenly; between winter and summer its path forms seven rings and six intervals. Each ring's circumference and diameter follow arithmetical calculation; by gnomon shadows and double-difference triangulation one derives distances of extreme motion—all from the measuring post—hence the name Zhou Bi.

又《周髀》家云：「天圓如張蓋，地方如棋局。天旁轉如推磨而左行，日月右行，天左轉，故日月實東行，而天牽之以西沒。譬之於蟻行磨石之上，磨左旋而蟻右去，磨疾而蟻遲，故不得不隨磨以左回焉。天形南高而北下，日出高故見，日入下故不見。天之居如倚蓋，故極在人北，是其證也。極在天之中，而今在人北，所以知天之形如倚蓋也。日朝出陰中，暮入陰中，陰氣暗冥，故從沒不見也。夏時陽氣多，陰氣少，陽氣光明，與日同暉，故日出即見，無蔽之者，故夏日長也。冬時陰氣多，陽氣少，陰氣暗冥，掩日之光，雖出猶隱不見，故冬日短也。」

The Zhou Bi school also holds: "Heaven is round like an opened canopy; Earth is square like a chessboard. Heaven rotates sideways like a millstone turning left; sun and moon move rightward. Heaven turns left, so though sun and moon truly travel east, Heaven pulls them westward to set. Like an ant on a turning millstone: the stone spins left while the ant crawls right; the stone outpaces the ant, so the ant is carried leftward with it. Heaven slopes high in the south and low in the north; the sun rises from the heights and becomes visible, and sets in the depths and disappears. Heaven rests like a tilted canopy, placing the pole north of the observer—this is the evidence. The pole stands at Heaven's center, yet appears north of us—whence we know Heaven's shape resembles a tilted canopy. At dawn the sun rises from yin; at dusk it enters yin again. Yin qi is dark, so once it sets the sun vanishes from sight. In summer yang prevails and yin is sparse; yang shines bright and shares the sun's light, so at sunrise nothing obscures it—hence long summer days. In winter yin prevails and yang is sparse; dark yin shrouds the sun's light, so even after rising it stays concealed—hence short winter days."

漢末，揚子雲難蓋天八事，以通渾天。其一云：「日之東行，循黃道。晝夜中規，牽牛距北極南百一十度，東井距北極南七十度，並百八十度。週三徑一，二十八宿周天當五百四十度，今三百六十度，何也？」其二曰：「春秋分之日正出在卯，入在酉，而晝漏五十刻。即天蓋轉，夜當倍晝。今夜亦五十刻，何也？」其三曰：「日入而星見，日出而不見，即斗下見日六月，不見日六月。北斗亦當見六月，不見六月。今夜常見，何也？」其四曰：「以蓋圖視天河，起斗而東入狼弧間，曲如輪。今視天河直如繩，何也？」其五曰：「周天二十八宿，以蓋圖視天，星見者當少，不見者當多。今見與不見等，何出入無冬夏，而兩宿十四星當見，不以日長短故見有多少，何也？」其六曰：「天至高也，地至卑也。日托天而旋，可謂至高矣。縱人目可奪，水與影不可奪也。今從高山上，以水望日，日出水下，影上行，何也？」其七曰：「視物近則大，遠則小。今日與北斗，近我而小，遠我而大，何也？」其八曰：「視蓋橑與車輻間，近杠轂即密，益遠益疏。今北極為天杠轂，二十八宿為天橑輻。以星度度天，南方次地星間當數倍。今交密，何也？」其後桓譚、鄭玄、蔡邕、陸績，各陳《周髀》考驗天狀，多有所違。逮梁武帝于長春殿講義，另擬天體，全同《周髀》之文，蓋立新意，以排渾天之論而已。

Late in the Han, Yang Xiong posed eight objections to Canopy Heaven theory in favor of Spherical Heaven. The first objection: "The sun moves east along the Yellow Path. At noon it bisects the horizon; Oxherd lies one hundred ten degrees south of the North Pole, Well seventy degrees south—one hundred eighty degrees together. With circumference thrice the diameter, the twenty-eight lodges should span five hundred forty degrees, yet they span only three hundred sixty—why? The second: "At the equinoxes the sun rises at mao due east and sets at you due west, with fifty marks of daylight. If Heaven's canopy rotates, night should be twice as long as day. Yet tonight too runs fifty marks—why? The third: "Stars appear at sunset and vanish at sunrise—below the Dipper the sun is visible six months and hidden six months. The Northern Dipper should likewise be visible six months and hidden six months. Yet it is always visible at night—why? The fourth: "On the canopy chart the Milky Way rises from the Dipper and runs east between Wolf and Arc, curved like a wheel. Yet viewed directly it runs straight as a cord—why? The fifth: "The twenty-eight lodges circle Heaven—on the canopy chart, visible stars should be fewer and invisible stars more numerous. Yet seen and unseen are equal—why, with no seasonal change in rising and setting, are fourteen stars of two lodges always visible, unaffected by day length—why? The sixth: "Heaven is supremely high and Earth supremely low. The sun rides Heaven and revolves—surely this is the highest reach. The eye may err, but water and shadow cannot. Yet from a high mountain, sighting the sun in water, at sunrise the sun appears below the water while the shadow rises above—why? The seventh: "Near objects look large; distant ones look small. Yet the sun and Northern Dipper look small when near and large when far—why? The eighth: "Between canopy ribs and chariot spokes, spacing is tight near the hub and grows wider with distance. The North Pole is Heaven's hub; the twenty-eight lodges are its rafters and spokes. By stellar degrees, star intervals in the south near Earth should be several times wider. Yet they crowd together—why? Later Huan Tan, Zheng Xuan, Cai Yong, and Lu Ji each examined the Zhou Bi against Heaven's actual state and found much amiss. When Liang Wudi lectured in the Everlasting Spring Hall, he proposed a celestial model identical to the Zhou Bi—chiefly a new formulation meant to overturn Spherical Heaven.

宣夜之書，絕無師法。唯漢秘書郎郗萌記先師相傳云：「天了無質，仰而瞻之，高遠無極，眼瞀精絕，故蒼蒼然也。譬之旁望遠道之黃山而皆青，俯察千仞之深谷而窈黑，夫青非真色，而黑非有體也。日月眾星，自然浮生虛空之中，其行其止，皆須氣焉。是以七曜或逝或住，或順或逆，伏見無常，進退不同，由乎無所根系，故各異也。故辰極常居其所，而北斗不與眾星西沒也。」

No master lineage survives for Overnight Heaven texts. Only Han Secretariat officer Xi Meng recorded the oral tradition: "Heaven has no solid body; gazing upward it extends without limit, the eyes dazzled and spirit spent—hence the blue expanse. Like seeing distant Yellow Mountains all blue from the side, or a thousand-ren gorge black from above—blue is not true color, black is not solid form. Sun, moon, and stars naturally float in the void; their motion and rest depend entirely on qi. Hence the seven luminaries now hurry, now pause, now advance, now retreat; their visibility shifts without rule because nothing anchors them—each moves on its own. Thus the pole star holds its station, and the Northern Dipper does not sink westward with the other stars."

晉成帝咸康中，會稽虞喜因宣夜之說，作《安天論》，以為「天高窮於無窮，地深測於不測。天確乎在上，有常安之形，地魄焉在下，有居靜之體，當相覆冒，方則俱方，圓則俱圓，無方圓不同之義也。其光曜布列，各自運行，猶江海之有潮汐，萬品之有行藏也。」葛洪聞而譏之曰：「苟辰宿不麗於天，天為無用，便可言無。何必復云有之而不動乎？」由此而談，葛洪可謂知言之選也。喜族祖河間相聳，又立《穹天論》云：「天形穹隆如雞子幕，其際周接四海之表，浮乎元氣之上。譬如覆奩以抑水而不沒者，氣充其中故也。日繞辰極，沒西還東，而不出入地中。天之有極，猶蓋之有斗也。天北下於地三十度，極之傾在地卯酉之北亦三十度。人在卯酉之南十餘萬里，故斗極之下，不為地中，當對天地卯酉之位耳。日行黃道繞極。極北去黃道百一十五度，南去黃道六十七度，二至之所舍，以為長短也。」吳太常姚信，造《昕天論》云：「人為靈蟲，形最似天。今人頤前侈臨胸，而項不能覆背。近取諸身，故知天之體，南低入地，北則偏高也。又冬至極低，而天運近南，故日去人遠，而斗去人近，北天氣至，故水寒也。夏至極起，而天運近北，而斗去人遠，日去人近，南天氣至，故蒸熱也。極之高時，日行地中淺，故夜短；天去地高，故晝長也。極之低時，日行地中深，故夜長；天去地下，故晝短也。」自虞喜、虞聳、姚信，皆好奇徇異之說，非極數談天者也。

During Jin Chengdi's Xian Kang reign, Yu Xi of Kuaiji, drawing on Overnight Heaven theory, wrote the An Tian Lun, arguing that Heaven stretches endlessly upward and Earth measures immeasurably downward. Heaven stands firmly above in fixed form; Earth's essence rests below in settled body—they mutually cover and enclose, alike in shape whether square or round, with no asymmetry between them. Their lights are arrayed and each runs its own path, like ocean tides and the appearing and hiding of all creatures. Ge Hong scoffed: "If the lodges do not attach to Heaven, Heaven is useless—one might as well deny it exists. Why insist it exists yet never moves? On this point Ge Hong showed himself a master of critical judgment. Yu Xi's kinsman Song, Chancellor of Hejian, proposed the Qiong Tian Lun: "Heaven arches like an egg-shell canopy, its rim joining the outer edge of the four seas, floating on primordial qi. Like a lid pressed on water that does not sink—because qi fills the space within. The sun orbits the pole, sets west and returns east, never passing beneath Earth. Heaven's pole is like the hub of a canopy. Heaven dips thirty degrees below Earth to the north; the pole tilts thirty degrees north of the mao-you line. Humanity stands over one hundred thousand li south of mao-you, so beneath the Dipper's pole is not Earth's center but the mao-you axis between Heaven and Earth. The sun follows the Yellow Path around the pole. The pole stands one hundred fifteen degrees north of the Yellow Path and sixty-seven south; the solstices mark its lodging and fix day length. Wu Grand Steward Yao Xin wrote the Xin Tian Lun: "Humanity is the numinous creature whose form most resembles Heaven. The human chin juts forward over the chest, yet the neck cannot cover the back. From our own bodies we infer Heaven's form: low where it enters Earth in the south, higher in the north. At the winter solstice the pole stands lowest and Heaven's motion nears the south; the sun recedes and the Dipper draws near—northern qi arrives and water turns cold. At the summer solstice the pole rises and Heaven nears the north; the Dipper recedes and the sun draws near—southern qi arrives and heat steams upward. When the pole stands high, the sun's path through Earth's center is shallow, so nights are short; Heaven stands far above Earth, so days are long. When the pole is low, the sun's path through Earth's center runs deep, so nights are long; Heaven sits lower above Earth, so days are short. Yu Xi, Yu Song, and Yao Xin all offered curious, eccentric theories—not the definitive reckoning of Heaven.

前儒舊說，天地之體，狀如鳥卵，天包地外，猶殼之裹黃，周旋無端，其形渾渾然，故曰渾天。又曰：「天表裡有水，兩儀轉運，各乘氣而浮，載水而行。」漢王仲任，據蓋天之說以駁渾儀，云：「舊說，天轉從地下過。今掘地一丈輒有水，天何得從水中行乎？甚不然也。日隨天而轉，非入地。夫人目所望，不過十裡，天地合矣。實非合也，遠使然耳。今視日入，非入也，亦遠耳。當日入西方之時，其下之人亦將謂之為中也。四方之人，各以其近者為出，遠者為入矣。何以明之？今試使一人把大炬火，夜行於平地，去人十裡，火光滅矣。非火滅也，遠使然耳。今日西轉不復見，是火滅之類也。日月不圓也，望視之所以圓者，去人遠也。夫日，火之精也；月，水之精也。水火在地不圓，在天何故圓？」丹陽葛洪釋之曰：

Earlier scholars taught that Heaven and Earth resemble a bird's egg—Heaven wraps Earth as a shell enfolds the yolk, revolving endlessly in perfect roundness—hence Spherical Heaven. It also holds: "Water lies inside and outside Heaven; the two principles rotate, each borne on qi, carrying water as they move. Han's Wang Chong, using Canopy Heaven to refute the armillary sphere, argued: "Old doctrine says Heaven rotates beneath Earth. Dig one zhang down and water appears—how can Heaven travel through water? This cannot be right. The sun turns with Heaven—it does not plunge into Earth. Human sight reaches only ten li—then Heaven and Earth seem to meet. They do not truly meet; distance creates the illusion. When we see the sun set, it does not enter Earth—it merely recedes. When the sun sets in the west, observers there likewise call it the center. Each quarter of the world takes the near as sunrise and the far as sunset. How may this be demonstrated? Suppose a man carries a great torch across level ground at night—ten li away, its light disappears. The fire is not out; distance only makes it seem so. When the sun wheels west and vanishes, the principle is the same. Sun and moon are not inherently round; distance makes them appear so. The sun is fire's essence; the moon is water's essence. Fire and water on Earth are not round—why round in Heaven? Ge Hong of Danyang replied:

《渾天儀注》云：「天如雞子，地如中黃，孤居於天內，天大而地小。天表裡有水，天地各乘氣而立，載水而行。周天三百六十五度四分度之一，又中分之，則半覆地上，半繞地下，故二十八宿半見半隱。天轉如車轂之運也。」諸論天者雖多，然精於陰陽者少。張平子、陸公紀之徒，咸以為推步七曜之道，以度曆象昏明之證候，校以四八之氣，考以漏刻之分，占咎影之往來，求形驗于事情，莫密於渾象也。張平子既作銅渾天儀，於密室中，以漏水轉之，與天皆合如符契也。崔子玉為其碑銘曰：「數術窮天地，製作侔造化。高才偉藝，與神合契。」蓋由於平子渾儀及地動儀之有驗故也。若天果如渾者，則天之出入，行于水中，為必然矣。故《黃帝書》曰：「天在地外，水在天外。水浮天而載地者也。」又《易》曰：「時乘六龍。」夫陽爻稱龍，龍者居水之物，以喻天。天陽物也，又出入水中，與龍相似，故比以龍也。聖人仰觀俯察，審其如此。故《晉》卦坤下離上，以證日出於地也。又《明夷》之卦離下坤上，以證日入於地也。又《需》卦乾下坎上，此亦天入水中之象也。天為金，金水相生之物也。天出入水中，當有何損，而謂為不可乎？然則天之出入水中，無複疑矣。

The Armillary Sphere Commentary says: "Heaven is like an egg, Earth like the yolk within, alone inside Heaven—Heaven vast, Earth small. Water surrounds Heaven within and without; Heaven and Earth ride qi, carrying water as they turn. Heaven's circuit is three hundred sixty-five and a quarter degrees; halved, half covers Earth above and half runs beneath—so half the twenty-eight lodges appear and half hide. Heaven rotates like a chariot hub. Many have theorized about Heaven, yet few master yin and yang. Zhang Heng, Lu Tongji, and others held that tracking the seven luminaries, calibrating dusk and dawn by degrees, comparing the four-eight qi, testing clepsydra marks, reading shadow motion, and verifying by observation—nothing matches the spherical model. Zhang Heng's bronze armillary sphere, water-driven in a sealed chamber, matched Heaven like a tally. Cui Ziyu wrote its inscription: "Calculation exhausts Heaven and Earth; craftsmanship rivals creation itself. Supreme talent and art accord with the divine. This praise rested on the verified performance of Heng's armillary sphere and seismoscope. If Heaven is truly spherical, its passage through water is necessarily so. The Yellow Emperor's Book says: "Heaven lies outside Earth; water lies outside Heaven. Water floats Heaven and carries Earth. The Book of Changes says: "Timely riding the six dragons." Yang lines are called dragons; dragons dwell in water, imaging Heaven. Heaven is yang, and passing through water like a dragon, it is likened to one. The sage observed above and below and confirmed this. The Jin hexagram—Kun below, Li above—shows the sun rising from Earth. The Ming Yi hexagram—Li below, Kun above—shows the sun entering Earth. The Xu hexagram—Qian below, Kan above—likewise images Heaven entering water. Heaven is metal; metal and water mutually generate. What harm if Heaven passes through water—why call it impossible? Heaven's passage through water need no longer be doubted.

又今視諸星出於東者，初但去地小許耳。漸而西行，先經人上，後遂轉西而下焉，不旁旋也。其先在西之星，亦稍下而沒，無北轉者。日之出入亦然。若謂天磨石轉者，眾星日月，宜隨天而回，初在於東，次經于南，次到於西，次及於北，而複還於東，不應橫過去也。今日出於東，冉冉轉上，及其入西，亦複漸漸稍下，都不繞邊北去。了了如此，王生必固謂為不然者，疏矣。今日徑千里，其中足以當小星之數十也。若日以轉遠之故，但當光曜不能複來照及人耳，宜猶望見其體，不應都失其所在也。日光既盛，其體又大於星。今見極北之星，而不見日之在北者，明其不北行也。若日以轉遠之故，不復可見，其比入之間，應當稍小。而日方入之時，反乃更大，此非轉遠之徵也。王生以火炬喻日，吾亦將借子之矛，以刺子之盾焉。把火之人，去人轉遠，其光轉微，而日月自出至入，不漸小也。王生以火喻之，謬矣。又日之入西方，視之稍稍去，初尚有半，如橫破鏡之狀，須臾淪沒矣。若如王生之言，日轉北去者，其北都沒之頃，宜先如豎破鏡之狀，不應如橫破鏡也。如此言之，日入北方，不亦孤孑乎？又月之光微，不及日遠矣。月盛之時，雖有重雲蔽之，不見月體，而夕猶朗然，是月光猶從雲中而照外也。日若繞西及北者，其光故應如月在雲中之狀，不得夜便大暗也。又日入則星月出焉。明知天以日月分主晝夜，相代而照也。若日常出者，不應日亦入而星月出也。

Watch stars rise in the east: at first they stand barely above Earth. They drift west, pass overhead, then wheel down to set—never circling sideways. Stars in the west likewise sink gradually at setting—none wheel northward. The sun rises and sets the same way. If Heaven turned like a millstone, sun, moon, and stars would wheel with it—east, south, west, north, and back—not cut horizontally across the sky. The sun rises east and mounts gradually; setting west it sinks gradually—never circling north along the rim. The evidence is plain—Wang Chong's stubborn denial misses the mark. The sun's diameter spans a thousand li—room enough for dozens of lesser stars. If distance alone hid the sun, its body should still be visible—it should not vanish entirely. Sunlight is brilliant and the sun larger than any star. We see polar stars yet never the sun in the north—proof it does not travel north. If distance hid the sun, it should shrink slightly between transit and setting. Yet at setting the sun grows larger—not a sign of receding distance. Wang Chong's torch analogy invites the retort: your spear against your own shield. A torch-bearer's light fades with distance—yet sun and moon do not shrink from rise to set. Wang Chong's fire analogy fails. At western setting the sun recedes gradually; half remains like a horizontally split mirror, then sinks in an instant. If the sun wheeled north as Wang Chong claims, it would vanish like a vertically split mirror—not a horizontal one. Thus the sun setting northward stands alone and implausible. Moonlight is faint, far dimmer than sunlight. At full moon, heavy clouds may hide the disk yet evening stays bright—moonlight penetrates the clouds. If the sun circled west and north, its light would diffuse like moonlight in clouds—not plunge the night into darkness. When the sun sets, stars and moon appear. Clearly Heaven assigns sun and moon to alternate in governing day and night. If the sun always rose, it would not set while stars and moon emerge.

又案河、洛之文，皆云水火者，陰陽之餘氣也。夫言餘氣，則不能生日月可知也，顧當言日精生火者可耳。若水火是日月所生，則亦何得盡如日月之圓乎？今火出於陽燧，陽燧圓而火不圓也。水出於方諸，方諸方而水不方也。又陽燧可以取火於日，而無取日於火之理，此則日精之生火明矣。方諸可以取水於月，無取月于水之道，此則月精之生水了矣。王生又云：「遠故視之圓。」若審然者，月初生之時及既虧之後，何以視之不圓乎？而日食，或上或下，從側而起，或如鉤至盡。若遠視見圓，不宜見其殘缺左右所起也。此則渾天之體，信而有徵矣。

River and Luo texts call fire and water surplus qi of yin and yang. As surplus qi they cannot generate sun and moon—rather the sun's essence generates fire. If sun and moon generated fire and water, why would both be round like sun and moon? Fire from the yang mirror: the mirror is round, the flame is not. Water from the square vessel: the vessel is square, the water is not. The yang mirror draws fire from the sun, not the sun from fire—proof the sun's essence begets fire. The square vessel draws water from the moon, not the moon from water—proof the moon's essence begets water. Wang Chong also argued: "Distance makes them look round. If distance alone made things round, why does the crescent moon not look round at first rise or after waning? Solar eclipses show the sun clipped above or below, or hooked from the side until fully covered. If distance made it round, eclipses should not show partial loss from left or right. Spherical Heaven is thus verified by evidence.

宋何承天論渾天象體曰：「詳尋前說，因觀渾儀，研求其意，有悟天形正圓，而水居其半，地中高外卑，水周其下。言四方者，東曰暘穀，日之所出，西曰濛汜，日之所入。《莊子》又云：'北溟有魚，化而為鳥，將徙于南溟。 '斯亦古之遺記，四方皆水證也。四方皆水，謂之四海。凡五行相生，水生於金。是故百川發源，皆自山出，由高趣下，歸注於海。日為陽精，光曜炎熾，一夜入水，所經焦竭。百川歸注，足以相補，故旱不為減，浸不為益。」又云：「周天三百六十五度、三百四分之七十五。天常西轉，一日一夜，過周一度。南北二極，相去一百一十六度、三百四分度之六十五強，即天經也。黃道袤帶赤道，春分交於奎七度，秋分交於軫十五度，冬至斗十四度半強，夏至井十六度半。從北極扶天而南五十五度強，則居天四維之中，最高處也，即天頂也。其下則地中也。」自外與王蕃大同。王蕃《渾天說》，具于《晉史》。

He Chengtian of Song wrote on the spherical model: "Studying prior doctrine and the armillary sphere, I grasp its meaning: Heaven is truly round, water fills half; Earth rises at center and falls at the rim, water encircling below. The four directions: east is Yang Valley of sunrise; west is Meng Si of sunset. Zhuangzi says: "In the Northern Sea a fish becomes a bird and migrates to the Southern Sea." This ancient record too proves all four directions are water. Water on all four sides constitutes the four seas. In the five phases, water generates from metal. All rivers spring from mountains, run downhill, and pour into the sea. The sun is yang essence, fiercely bright. One night's passage through water scorches all it touches. Rivers returning to the sea replenish it—drought does not shrink it, floods do not swell it. It also states: "Heaven's full circuit is three hundred sixty-five and seventy-five quarter-degrees. It also states: "Heaven's circuit is three hundred sixty-five and seventy-five quarter-degrees. Heaven turns constantly westward; one day-night cycle advances one degree. North and south poles stand one hundred sixteen and sixty-five quarter-degrees apart—Heaven's axis. The Yellow Path belts the equator: spring equinox at Kui 7°, autumn at Zhen 15°, winter solstice at Dipper 14.5°, summer at Well 16.5°. Fifty-five and a half degrees south from the North Pole marks Heaven's zenith—the highest point at the center of the four quarters. Below lies Earth's center." Beyond this it largely matches Wang Fan. Wang Fan's Spherical Heaven Discourse appears in the Jin History.

舊說渾天者，以日月星辰，不問春秋冬夏，晝夜晨昏，上下去地中皆同，無遠近。《列子》曰：「孔子東遊，見兩小兒鬭。問其故，一小兒曰：'我以日始出去人近，而日中時遠也。 '一小兒曰：'我以為日初出遠，而日中時近也。 '言初出近者曰：'日初出，大如車蓋，及其日中，裁如盤蓋。此不為遠者小，近者大乎？ '言日初出遠者曰：'日初出時，滄滄涼涼，及其中時，熱如探湯。此不為近者熱，遠者涼乎？'」

Old Spherical Heaven doctrine holds sun, moon, and stars stay equidistant from Earth's center in all seasons and hours—no variation in distance. The Liezi says: "Confucius traveling east saw two boys arguing. One said: "The sun at dawn is near; at noon it is far." The other said: "At dawn it is far; at noon it is near." The "near at dawn" boy said: "At sunrise the sun is chariot-canopy large; at noon only plate-sized. Are not distant things small and near things large? The "far at dawn" boy said: "At sunrise it is cool; at noon hot as boiling water. Are not near things hot and far things cool?

桓譚《新論》云：「漢長水校尉平陵關子陽，以為日之去人，上方遠而四傍近。何以知之？星宿昏時出東方，其間甚疏，相離丈餘。及夜半在上方，視之甚數，相離一二尺。以准度望之，逾益明白，故知天上之遠於傍也。日為天陽，火為地陽。地陽上升，天陽下降。今置火於地，從傍與上，診其熱，遠近殊不同焉。日中正在上，覆蓋人，人當天陽之沖，故熱于始出時。又新從太陰中來，故複涼於其西在桑榆間也。桓君山曰：子陽之言，豈其然乎？」

Huan Tan's New Discourses records Guan Ziyang of Pingling: "The sun is far overhead and near at the sides. How know this? At dusk eastern stars stand widely spaced—over a zhang apart. At midnight overhead they crowd together—one or two chi apart. By degree measure, overhead stars appear denser—proving Heaven is farther above than at the sides. The sun is Heaven's yang; fire is Earth's yang. Earth's yang rises upward; Heaven's yang descends. Place fire on Earth and test heat from the side versus overhead—the difference is great. At noon the sun stands directly overhead—yang strikes full force, hence hotter than at dawn. Also newly emerging from lunar shadow, hence cooler when west among mulberry and elm. Huan Tan asked: Can Ziyang's theory be correct?"

張衡《靈臺》曰：「日之薄地，暗其明也。由暗視明，明無所屈，是以望之若大。方其中，天地同明，明還自奪，故望之若小。火當夜而揚光，在晝則不明也。月之於夜，與日同而差微。」

Zhang Heng's Ling Tai says: "Near Earth the sun dims its brilliance. Seen from darkness, brightness shows unobstructed—hence it looks large. At zenith Heaven and Earth share equal light; brightness cancels itself—hence it looks small. Fire shines at night; by day it is invisible. The moon at night resembles the sun but dimmer."

晉著作郎陽平束皙，字廣微，以為傍方與上方等。傍視則天體存於側，故日出時視日大也。日無小大，而所存者有伸厭。厭而形小，伸而體大，蓋其理也。又日始出時色白者，雖大不甚，始出時色赤者，其大則甚，此終以人目之惑，無遠近也。且夫置器廣庭，則函牛之鼎如釜，堂崇十仞，則八尺之人猶短，物有陵之，非形異也。夫物有惑心，形有亂目，誠非斷疑定理之主。故仰遊雲以觀月，月常動而雲不移；乘船以涉水，水去而船不徙矣。

Jin compiler Shu Xi of Yangping held side and overhead equal in distance. Viewed sideways Heaven's body lies to the side—hence the sun looks large at rising. The sun has no intrinsic size—what varies is compression and extension of its image. Compressed it looks small; extended it looks large—such is the principle. A white dawn sun looks large but not greatly so; a red dawn sun looks very large—all eye illusion, not distance. In a broad courtyard an ox cauldron looks like a pot; in a ten-ren hall an eight-chi man looks short—context alters appearance, not the thing itself. Things confuse the mind and forms confuse the eye—they cannot settle definitive principle. Watch the moon through moving clouds—the moon moves, clouds do not; board a boat—the water flows past while the boat stays still.

姜岌云：「余以為子陽言天陽下降，日下熱，束皙言天體存於目，則日大，頗近之矣。渾天之體，圓周之徑，詳之於天度，驗之於晷影，而紛然之說，由人目也。參伐初出，在旁則其間疏，在上則其間數。以渾檢之，度則均也。旁之與上，理無有殊也。夫日者純陽之精也，光明外曜，以眩人目，故人視日如小。及其初出，地有遊氣，以厭日光，不眩人目，即日赤而大也。無游氣則色白，大不甚矣。地氣不及天，故一日之中，晨夕日色赤，而中時日色白。地氣上升，濛濛四合，與天連者，雖中時亦赤矣。日與火相類，火則體赤而炎黃，日赤宜矣。然日色赤者，猶火無炎也。光衰失常，則為異矣。」

Jiang Kui wrote: "Ziyang's descending yang explains midday heat; Shu Xi's stored-in-the-eye explains dawn size—both near the mark. Spherical Heaven's body and circuit—investigated by degrees, verified by shadows—the tangled theories stem from human sight. Shen and Wei at first rising stand sparse at the horizon, dense overhead. On the sphere their degrees are equal. Side and overhead differ in appearance, not principle. The sun is pure yang; outward radiance dazzles the eye—hence it looks small. At dawn earthly vapors filter sunlight, sparing the eye—the sun looks red and large. Without vapors it looks white and not greatly large. Earthly qi does not reach Heaven—hence red sun at dawn and dusk, white at noon. When earthly qi rises in haze joining Heaven, even noon shows red. The sun resembles fire; fire is red and blazing yellow—the sun's redness fits. Yet a red sun is like fire without flame. Fading light breaking norm signals anomaly."

梁奉朝請祖暅曰：

Liang court gentleman Zu Geng wrote:

自古論天者多矣，而群氏糾紛，至相非毀。竊覽同異，稽之典經，仰觀辰極，傍矚四維，睹日月之升降，察五星之見伏，校之以儀象，覆之以晷漏，則渾天之理，信而有徵。輒遺眾說，附渾儀云。《考靈曜》先儒求得天地相去十七萬八千五百里，以晷影驗之，失於過多。既不顯求之術，而虛設其數，蓋誇誕之辭，宜非聖人之旨也。學者多固其說而未之革，豈不知尋其理歟，抑未能求其數故也？王蕃所考，校之前說，不啻減半。雖非揆格所知，而求之以理，誠未能遙趣其實，蓋近密乎？輒因王蕃天高數，以求冬至、春分日高及南戴日下去地中數。法，令表高八尺與冬至影長一丈三尺，各自乘，並而開方除之為法。天高乘表高為實，實如法，得四萬二千六百五十八裡有奇，即冬至日高也。以天高乘冬至影長為實，實如法，得六萬九千三百二十裡有奇，即冬至南戴日下去地中數也。求春秋分數法，令表高及春秋分影長五尺三寸九分，各自乘，並而開方除之為法。因冬至日高實，而以法除之，得六萬七千五百二裡有奇，即春秋分日高也。以天高乘春秋分影長實，實如法而一，得四萬五千四百七十九裡有奇，即春秋分南戴日下去地中數也。南戴日下，所謂丹穴也。推北極裡數法，夜于地中表南，傅地遙望北辰紐星之末，令與表端參合。以人目去表數及表高各自乘，並而開方除之為法。天高乘表高數為實，實如法而一，即北辰紐星高地數也。天高乘人目去表為實，實如法，即去北戴極下之數也。北戴斗極為空桐。

Since antiquity many theorized Heaven, yet schools quarreled and reviled each other. I compared schools against the classics, observed pole, quarters, sun, moon, and planets, tested with instruments, gnomon, and clepsydra—Spherical Heaven stands verified. I set aside rival theories and append this to the armillary sphere. Kao Ling Yao placed Heaven and Earth one hundred seventy-eight thousand five hundred li apart—gnomon tests prove this too great. With no shown method and empty numbers, it is boastful—not the sages' intent. Scholars cling to unreformed doctrine—unable to seek principle, or unable to seek numbers? Wang Fan's reckoning cuts prior estimates by more than half. Though calipers cannot reach it, by principle it approaches reality more closely. Using Wang Fan's Heaven height I derive solstice and equinox sun heights and southern nadir distances. Method: gnomon eight chi, winter solstice shadow one zhang three chi; multiply, add, extract root for divisor. Heaven height × gnomon height ÷ divisor = forty-two thousand six hundred fifty-eight li odd—winter solstice sun height. Heaven height × winter solstice shadow ÷ divisor = sixty-nine thousand three hundred twenty li odd—winter solstice southern nadir. Equinox method: gnomon height and shadow five chi three cun nine fen; same procedure. Winter solstice sun height dividend ÷ method = sixty-seven thousand five hundred two li odd—equinox sun height. Heaven height × equinox shadow ÷ method = forty-five thousand four hundred seventy-nine li odd—equinox southern nadir. Beneath the southern cap lies the Cinnabar Cave. North Pole method: at night south of the central gnomon, sight the Pivot star's end aligned with the gnomon top. Eye-to-gnomon distance and gnomon height: multiply, add, root for divisor. Heaven height × gnomon height ÷ method = Pivot star height at North Pole. Heaven height × eye distance ÷ method = distance below northern cap. The northern cap at the Dipper pole is Kongtong.

日去赤道表裡二十四度，遠寒近暑而中和。二分之日，去天頂三十六度。日去地中，四時同度，而有寒暑者，地氣上騰，天氣下降，故遠日下而寒，近日下而暑，非有遠近也。猶火居上，雖遠而炎，在傍，雖近而微。視日在傍而大，居上而小者，仰矚為難，平觀為易也。由視有夷險，非遠近之效也。今懸珠於百仞之上，或置之於百仞之前，從而觀之，則大小殊矣。先儒弗斯取驗，虛繁翰墨，夷途頓轡，雄辭析辯，不亦迂哉！今大寒在冬至後二氣者，寒積而未消也。大暑在夏至後二氣者，暑積而未歇也。寒暑均和，乃在春秋分後二氣者，寒暑積而未平也。譬之火始入室，而未甚溫，弗事加薪，久而逾熾。既已遷之，猶有餘熱也。

The sun stands twenty-four degrees inside or outside the equator—far means cold, near means heat, between is temperate. At equinox the sun stands thirty-six degrees from Heaven's zenith. The sun's distance from Earth's center is constant through seasons; cold and heat come from earthly qi rising and heavenly qi descending—not from varying distance. Fire overhead burns hot though far; at the side it fades though near. The sun looks larger at the side and smaller overhead because upward sight is difficult, level sight easy. Viewing angle, not distance, causes the apparent size difference. Suspend a pearl a hundred ren overhead or a hundred ren ahead—viewed from either spot, its size looks very different. Earlier scholars never tested this, wasting pages in debate—is that not pointless? Great cold comes two qi after winter solstice because cold accumulates before it fades. Great heat comes two qi after summer solstice because heat accumulates before it breaks. Even temperance falls two qi after the equinoxes, when accumulated cold and heat have not yet balanced. Like fire entering a room: not warm at first, yet without new fuel it grows fiercer with time. Even after the fire moves on, heat lingers.

○渾天儀

The Armillary Sphere

案《虞書》：「舜在〔璣玉衡，以齊七政，」則《考靈曜》所謂觀玉儀之遊，昏明主時，乃命中星者也。〔璣中而星未中為急，急則日過其度，月不及其宿。〔璣未中而星中為舒，舒則日不及其度，月過其宿。〔璣中而星中為調，調則風雨時，庶草蕃蕪，而五穀登，萬事康也。所言〔璣者，謂渾天儀也。故《春秋文耀鉤》云：「唐堯即位，羲、和立渾儀。」而先儒或因星官書，北斗第二星名旋，第三星名璣，第五星名玉衡，仍七政之言，即以為北斗七星。載筆之官，莫之或辨。史遷、班固，猶且致疑。馬季長創謂璣衡為渾天儀。鄭玄亦云；「其轉運者為璣，其持正者為衡，皆以玉為之。七政者，日月五星也。以璣衡視其行度，以觀天意也。」故王蕃云：「渾天儀者，羲、和之舊器，積代相傳，謂之璣衡。其為用也，以察三光，以分宿度者也。又有渾天象者，以著天體，以布星辰。而渾象之法，地當在天中，其勢不便，故反觀其形，地為外匡，于已解者，無異在內。詭狀殊體，而合於理，可謂奇巧。然斯二者，以考于天，蓋密矣。」又云：「古舊渾象，以二分為一度，周七尺三寸半分。而莫知何代所造。」今案虞喜云：「落下閎為漢孝武帝於地中轉渾天，定時節，作《泰初曆》。」或其所制也。

The Yu Documents say Shun used the ji-yu heng to align the seven regulators—what Kao Ling Yao calls observing the jade instrument's motion to govern dusk and dawn means ordering the central stars. When the ji is centered but stars are not, this is urgent: the sun overshoots its degree and the moon misses its lodge. When the ji is off but stars are centered, this is relaxed: the sun falls short and the moon overshoots its lodge. When both ji and stars are centered, all is balanced: seasons hold, crops flourish, and affairs prosper. The ji mentioned here is the armillary sphere. Chunqiu Wen Yao Gou says: "When Yao took the throne, Xi and He set up the armillary instrument. Some scholars, noting the Dipper's second star Xuan, third Ji, and fifth Yu Heng in star catalogues, mistook them for the seven regulators. Historiographers failed to distinguish this. Even Sima Qian and Ban Gu doubted it. Ma Rong first identified ji-heng as the armillary sphere. Zheng Xuan likewise wrote: "The rotating part is the ji, the fixed part the heng—both of jade. The seven regulators are sun, moon, and five planets. Ji-heng measures their degrees to read Heaven's intent. Wang Fan said: "The armillary sphere is Xi and He's ancient instrument, transmitted as ji-heng. It inspects the three luminaries and divides lodge degrees. The spherical model displays Heaven's body and arrays stars. The spherical model ideally places Earth at center; impractically one reverses the view with Earth as outer frame—equivalent for those who grasp it. Odd in form yet sound in principle—ingeniously clever. Both, tested against Heaven, prove precise." The old spherical model used two fen per degree, circumference seven chi three cun and a half. Its age is unknown. Yu Xi records Luo Xiahong turning spherical Heaven at Earth's center for Emperor Wu, fixing seasons and composing the Taichu Calendar. Perhaps he made this instrument.

漢孝和帝時，太史揆候，皆以赤道儀，與天度頗有進退。以問典星待詔姚崇等，皆曰《星圖》有規法，日月實從黃道。官無其器。至永元十五年，詔左中郎將賈逵乃始造太史黃道銅儀。至桓帝延熹七年，太史令張衡更以銅制，以四分為一度，周天一丈四尺六寸一分。亦於密室中以漏水轉之，令司之者，閉戶而唱之，以告靈臺之觀天者。〔璣所加，某星始見，某星已中，某星今沒，皆如合符。蕃以古制局小，以布星辰，相去稠概，不得了察。張衡所作，又複傷大，難可轉移。蕃今所作，以三分為一度，週一丈九寸五分、四分分之三。長古法三尺六寸五分、四分分之一，減衡法亦三尺六寸五分、四分分之一。渾天儀法，黃赤道各廣一度有半。故今所作渾象，黃赤道各廣四分半，相去七寸二分。又云「黃赤二道，相共交錯，其間相去二十四度。以兩儀準之，二道俱三百六十五度有奇。又赤道見者，常一百八十二度半強。又南北考之，天見者亦一百八十二度半強。是以知天之體圓如彈丸，南北極相去一百八十二度半強也。而陸績所作渾象，形如鳥卵，以施二道，不得如法。若使二道同規，則其間相去不得滿二十四度。若令相去二十四度，則黃道當長於赤道。又兩極相去，不翅八十二度半強。案績說云：'天東西徑三十五萬七千里，直徑亦然。 '則績意亦以天為正圓也。器與言謬，頗為乖僻。」然則渾天儀者，其制有機有衡。既動靜兼狀，以效二儀之情，又周旋衡管，用考三光之分。所以揆正宿度，准步盈虛，求古之遺法也。則先儒所言圓規徑八尺，漢候臺銅儀，蔡邕所欲寢伏其下者是也。

Under Han Emperor He, observers used equatorial instruments that diverged slightly from true degrees. Asked, Yao Chong and others replied the Star Chart prescribed methods and sun and moon truly follow the Yellow Path. The bureau lacked such an instrument. In Yongyuan 15, Emperor He ordered Jia Kui to cast the Grand Astrologer's Yellow Path bronze instrument. In Yanxi 7, Zhang Heng recast it in bronze at four fen per degree, circumference one zhang four chi six cun one fen. In a sealed chamber, water-driven, an attendant closed the door and announced to Spirit Platform observers. Where the ji pointed—star rising, culminating, setting—all matched tallies. Wang Fan found the ancient form too cramped to array stars clearly. Zhang Heng's version was too large to move easily. Fan's version used three fen per degree, circumference one zhang nine cun five fen and three quarter-fifths. Three chi six cun five fen and a quarter longer than the ancient form; the same amount shorter than Heng's. By armillary method, Yellow and red paths each span one and a half degrees. Fan's spherical model made each path four and a half fen wide, seven cun two fen apart. "Yellow and red paths cross, twenty-four degrees apart. By both principles each path totals three hundred sixty-five degrees odd. The visible equator spans one hundred eighty-two and a half strong degrees. Measured north and south, visible Heaven also spans one hundred eighty-two and a half strong degrees. Hence Heaven is round as a pellet; the poles stand one hundred eighty-two and a half strong degrees apart. Lu Ji's egg-shaped model with two paths cannot follow proper method. If both paths shared one circle, their separation could not reach twenty-four degrees. Set twenty-four degrees apart, the Yellow Path would exceed the equator. Also pole separation falls short of eighty-two and a half strong degrees. Ji wrote: "Heaven's east-west diameter is three hundred fifty-seven thousand li; north-south likewise." Ji too held Heaven perfectly round. Instrument and doctrine contradict—quite mistaken. The armillary sphere combines mechanism and crossbars. It images both principles in motion and rest and uses revolving tubes to measure the three luminaries. Thus it rectifies lodge degrees and tracks surplus and deficit—the ancient transmitted method. The eight-chi round compass and Han observatory bronze instrument are what Cai Yong wished to study beneath.

梁華林重雲殿前所置銅儀，其制則有雙環規相並，間相去三寸許，正豎當子午。其子午之間，應南北極之衡，各合而為孔，以象南北樞。植楗於前後以屬焉。又有單橫規，高下正當渾之半。皆周市分為度數；署以維辰之位，以象地。又有單規，斜帶南北之中，與春秋二分之日道相應。亦周匝分為度數，而署以維辰，並相連者。屬楗植而不動。其裡又有雙規相並，如外雙規。內徑八尺，週二丈四尺，而屬雙軸。軸兩頭出規外各二寸許，合兩為一。內有孔，圓徑二寸許，南頭入地下，注於外雙規南樞孔中，以象南極。北頭出地上，入於外雙規北樞孔中，以象北極。其運動得東西轉，以象天行。其雙軸之間，則置衡，長八尺，通中有孔，圓徑一寸。當衡之半，兩邊有關，各注著雙軸。衡即隨天象東西轉運，又自於雙軸間得南北低仰。所以准驗辰曆，分考次度，其於揆測，唯所欲為之者也。檢其鐫題，是偽劉曜光初六年，史官丞南陽孔挺所造，則古之渾儀之法者也。而宋御史中丞何承天及太中大夫徐爰，各著《宋史》，咸以為即張衡所造。其儀略舉天狀，而不綴經星七曜。魏、晉喪亂，沉沒西戎。義熙十四年，宋高祖定咸陽得之。梁尚書沈約著《宋史》，亦云然，皆失之遠矣。

Liang's Chongyun Hall bronze instrument had paired rings three cun apart, upright on the meridian. Meridian holes imaged the north-south pivots. Tenons front and rear attached to them. A single transverse ring sat at the sphere's midpoint. All were circled and marked in degrees; marked with lodge positions to image Earth. A slanting ring through north-south center matched the equinox sun path. Also circled, divided, and marked with lodges, all linked. Fixed to immobile tenons. Inside, paired rings like the outer pair. Inner diameter eight chi, circumference two zhang four chi, on paired axles. Axle ends projected two cun and joined as one. A two-cun hole: south end entered Earth at the outer south pivot, imaging the South Pole. North end rose into the outer north pivot, imaging the North Pole. It turned east-west to image Heaven's motion. Between axles an eight-chi crossbar with a one-cun hole was set. Mid-crossbar hinges attached to both axles. The crossbar turned with the sky and tilted north-south between axles. Thus it verified the calendar and measured degrees as desired. Its inscription falsely dated it Liu Yao Guangchu 6 by Astrological Assistant Kong Ting of Nanyang—the ancient armillary method. He Chengtian and Xu Ai both wrote it was Zhang Heng's work. It showed Heaven's form but omitted fixed stars and seven luminaries. Wei-Jin chaos sank it in the Western Rong. In Yixi 14, Song Gaozu recovered it at Xianyang. Shen Yue's Song History agrees—all mistaken.

後魏道武天興初，命太史令晁崇修渾儀，以觀星象。十有餘載，至明元永興四年壬子，詔造太史候部鐵儀，以為渾天法，考〔璣之正。其銘曰；「於皇大代，配天比祚。赫赫明明，聲烈遐布。爰造茲器，考正宿度。貽法後葉，永垂典故。」其制並以銅鐵，唯志星度以銀錯之。南北柱曲抱雙規，東西柱直立，下有十字水準，以植四柱。十字之上，以龜負雙規。其餘皆與劉曜儀大同。即今太史候臺所用也。

Northern Wei Daowu in Tianxingthe cited text ordered Chao Chong to repair the armillary sphere. Ten years later, Yongxing 4 renchen, an edict cast the iron Astrological Bureau instrument as spherical Heaven method. Its inscription reads: "In the august Great Dynasty, matching Heaven and fortune. Brilliant and bright, fame spreading afar. Thus making this instrument to verify lodge degrees. Leaving method for posterity, eternally transmitting the canonical example. Copper and iron throughout; star degrees inlaid in silver. Curved north-south pillars embraced paired rings; east-west pillars stood upright on a cross water level. A tortoise on the cross bore the paired rings. The rest largely matches Liu Yao's instrument. This is what the observatory platform uses today.

○渾天象

The Spherical Model

渾天象者，其制有機而無衡，梁末秘府有，以木為之。其圓如丸，其大數圍。南北兩頭有軸。遍體布二十八宿、三家星、黃赤二道及天漢等。別為橫規環，以匡其外。高下管之，以象地。南軸頭入地，注于南植，以象南極。北軸頭出於地上，注於北植，以象北極。正東西運轉。昏明中星，既其應度，分至氣節，亦驗，在不差而已。不如渾儀，別有衡管，測揆日月，分步星度者也。吳太史令陳卓云：「先賢制木為儀，名曰渾天。」即此之謂耶？由斯而言，儀象二器，遠不相涉。則張衡所造，蓋亦止在渾象七曜，而何承天莫辨儀象之異，亦為乖失。

The spherical model has mechanism but no crossbars; Liang's secret repository held a wooden one. Round as a pellet, several arm-spans around. Axles project from north and south ends. Its surface bears the twenty-eight lodges, three schools' stars, both paths, and the Milky Way. A transverse ring girds the exterior. Tubes above and below control it to image Earth. The south axle enters Earth at the south pillar, imaging the South Pole. The north axle rises at the north pillar, imaging the North Pole. It rotates east-west. Dusk and dawn centered stars match their degrees; solstices, equinoxes, and seasonal nodes verify without error. Unlike the armillary sphere, it lacks cross-tubes for measuring sun, moon, and star degrees. Chen Zhuo of Wu said: "Ancient sages made a wooden instrument called Spherical Heaven. Is this what he meant? Thus the armillary sphere and spherical model are distinct instruments. Zhang Heng likely made only the spherical model's seven luminaries—He Chengtian's failure to distinguish the instruments was also an error.

宋文帝以元嘉十三年詔太史更造渾儀。太史令錢樂之依案舊說，采效儀象，鑄銅為之。五分為一度，徑六尺八分少，週一丈八尺二寸六分少。地在天內，不動。立黃赤二道之規，南北二極之規，布列二十八宿、北斗極星。置日月五星于黃道上。為之杠軸，以象天運。昏明中星，與天相符。梁末，置於文德殿前。至如斯制，以為渾儀，儀則內闕衡管。以為渾象，而地不在外。是參兩法，別為一體。就器用而求，猶渾象之流，外內天地之狀，不失其位也。吳時又有葛衡，明達天官，能為機巧。改作渾天，使地居於天中。以機動之，天動而地止，以上應晷度，則樂之之所放述也。到元嘉十七年，又作小渾天，二分為一度，徑二尺二寸，週六尺六寸。安二十八宿中外官星備足。以白青黃等三色珠為三家星。其日月五星，悉居黃道。亦象天運，而地在其中。宋元嘉所造儀象器，開皇九年平陳後，併入長安。大業初，移於東都觀象殿。

Song Emperor Wen in Yuanjia 13 ordered a new armillary sphere. Grand Astrologer Qian Lezhi cast bronze following old sphere and model methods. Five fen per degree; diameter six chi eight fen odd, circumference one zhang eight chi two cun six fen odd. Earth rests inside Heaven, unmoving. Compasses for both paths and both poles; twenty-eight lodges and pole stars arrayed. Sun, moon, and five planets set on the Yellow Path. Axles image Heaven's motion. Dusk and dawn stars match Heaven. At Liang's end it stood before Wende Hall. As an armillary sphere it lacked inner cross-tubes. As a spherical model, Earth was not placed outside. It combined two methods into one hybrid instrument. In use it remained a spherical model—Heaven and Earth's inner-outer relation preserved. Wu also had Ge Heng, expert in astronomy and ingenious in mechanism. He remade Spherical Heaven with Earth at center. Mechanism turned Heaven while Earth stayed still, matching gnomon degrees—what Lezhi described. By Yuanjia 17 he made a small sphere at two fen per degree, diameter two chi two cun. All twenty-eight lodges and inner and outer official stars were installed. White, green, and yellow beads distinguished the three schools. Sun, moon, and five planets all rode the Yellow Path. Heaven's motion was imaged with Earth inside. Liu Song's Yuanjia instrument entered Chang'an after Chen was pacified in Kaihuang 9. At Daye's start it moved to the Eastern Capital's Observational Hall.

○蓋圖

The Canopy Chart

晉侍中劉智云：「顓頊造渾儀，黃帝為蓋天。」然此二器，皆古之所制，但傳說義者，失其用耳。昔者聖王正曆明時，作圓蓋以圓列宿。極在其中，回之以觀天象。分三百六十五度、四分度之一，以定日數。日行于星紀，轉回右行，故圓規之，以為日行道。欲明其四時所在，故於春也，則以青為道；于夏也，則以赤為道；于秋也，則以白為道；于冬也，則以黑為道。四季之末，各十八日，則以黃為道。蓋圖已定，仰觀雖明，而未可正昏明，分晝夜，故作渾儀，以象天體。今案自開皇已後，天下一統，靈臺以後魏鐵渾天儀，測七曜盈縮，以蓋圖列星坐，分黃赤二道距二十八宿分度，而莫有更為渾象者矣。

Liu Zhi of Jin said: "Zhuanxu made the armillary sphere; the Yellow Emperor made Canopy Heaven. Both are ancient instruments—later transmitters lost their proper use. Ancient sage kings rectified the calendar and made a round canopy chart to array the lodges. The pole stood within; turning the chart observed the sky. Three hundred sixty-five and a quarter degrees fixed the day count. The sun travels the Star Record path—circled with a compass as its road. Seasonal paths were color-coded: green for spring; red for summer; white for autumn; black for winter. The last eighteen days of each season were marked yellow. The canopy chart clarified the sky but could not fix dusk, dawn, or day-night division—hence the armillary sphere. From Kaihuang onward the realm was unified: the Spirit Platform used Northern Wei's iron armillary sphere for the seven luminaries and the canopy chart for star positions—no new spherical model was made.

仁壽四年，河間劉焯造《皇極曆》，上啓於東宮。論渾天云：

In Renshou 4, Liu Zhuo of Hejian presented the Huangji Calendar to the crown prince. On Spherical Heaven:

璿璣玉衡，正天之器，帝王欽若，世傳其象。漢之孝武，詳考律曆，糾落下閎、鮮于妄人等，共所營定。逮于張衡，又尋述作，亦其體制，不異閎等。雖閎制莫存，而衡造有器。至吳時，陸績、王蕃，並要修鑄。績小有異，蕃乃事同。宋有錢樂之，魏初晁崇等，總用銅鐵，小大有殊，規域經模，不異蕃造。觀蔡邕《月令章句》，鄭玄注《考靈曜》，勢同衡法，迄今不改。焯以愚管，留情推測，見其數制，莫不違爽。失之千里，差若毫釐，大象一乖，余何可驗。況赤黃均度，月無出入，至所恆定，氣不別衡。分刻本差，輪回守故。其為疏謬，不可複言。亦既由理不明，致使異家間出。蓋及宣夜，三說並驅，平、昕、安、穹，四天騰沸。至當不二，理唯一揆，豈容天體，七種殊說？又影漏去極，就渾可推，百骸共體，本非異物。此真已驗，彼偽自彰，豈朗日未暉，爝火不息，理有而闕，詎不可悲者也？昔蔡邕自朔方上書曰：「以八尺之儀，度知天地之象，古有其器，而無其書。常欲寢伏儀下，案度成數，而為立說。」邕以負罪朔裔，書奏不許。邕若蒙許，亦必不能。邕才不逾張衡，衡本豈有遺思也？則有器無書，觀不能悟。焯今立術，改正舊渾。又以二至之影，定去極晷漏，並天地高遠，星辰運周，所宗有本，皆有其率。祛今賢之巨惑，稽往哲之群疑，豁若雲披，朗如霧散。為之錯綜，數卷已成，待得影差，謹更起送。

Xuanji-yuheng rectifies Heaven; emperors reverently conform; generations transmit its form. Emperor Wu corrected Luo Xiahong, Xianyu Wangren, and others who jointly established the system. Zhang Heng continued the tradition in the same system. Hong's form is lost, but Heng's instrument survives. In Wu, Lu Ji and Wang Fan both recast instruments. Ji differed slightly; Fan matched the standard. Song's Qian Lezhi and early Wei's Chao Chong used copper and iron in varied sizes but followed Fan's pattern. Cai Yong and Zheng Xuan follow Heng's method—unchanged to this day. Zhuo examined the system and found every measure in error. Miss by a thousand li over hairsbreadth—once the great image fails, nothing verifies. Red and yellow paths equal in degrees; the moon never enters or exits; solstice points fixed; crossbars fail to distinguish qi. Clepsydra marks were wrong; wheels merely preserved the old errors. The errors are beyond recounting. Unclear principle spawned rival schools. Canopy, Overnight, and Spherical Heaven competed; Ping, Xin, An, and Qiong theories proliferated. Heaven should have one standard—how can seven theories coexist? Shadow, clepsydra, and polar distance derive from one sphere—one body, not separate things. Truth verified, falsehood exposed—must bright sun wait for torches? To have principle yet lack it is lamentable. Cai Yong from Shuofang wrote: "An eight-chi instrument can measure Heaven and Earth's image—the instrument existed but no book. He wished to lie beneath it, derive the numbers, and write doctrine. Yong's memorial was denied because he was exiled to the frontier. Even if permitted, he could not have succeeded. Yong's talent did not exceed Zhang Heng—did Heng leave the problem unfinished? Instrument without book—observation cannot enlighten. Zhuo now establishes method to correct the old sphere. Using solstice shadows he fixes polar distance, gnomon clepsydra, Heaven-Earth height, and stellar circuit—all with proper rates. He clears today's confusion and past sages' doubts—as clouds part and mist clears. Several scrolls are complete; he awaits shadow measurements to send them.

又云：「《周官》夏至日影，尺有五寸。張衡、鄭玄、王番、陸績先儒等，皆以為影千里差一寸。言南戴日下萬五千里，表影正同，天高乃異。考之演算法，必為不可。寸差千里，亦無典說，明為意斷，事不可依。今交、愛之州，表北無影，計無萬里，南過戴日。是千里一寸，非其實差。焯今說渾，以道為率，道裡不定，得差乃審。既大聖之年，升平之日，厘改群謬，斯正其時。請一水工並解算術士，取河南、北平地之所，可量數百里，南北使正。審時以漏，平地以繩，隨氣至分，同日度影。得其差率，裡即可知。則天地無所匿其形，辰象無所逃其數，超前顯聖，效象除疑。請勿以人廢言。」不用。至大業三年，敕諸郡測影，而焯尋卒，事遂寢廢。

He also noted: "Zhou Offices give summer solstice shadow as one chi five cun. Zhang Heng, Zheng Xuan, Wang Fan, and Lu Ji held shadow differs one cun per thousand li. They said ten thousand five thousand li south of the cap shadows match yet Heaven's height differs. Calculation proves this impossible. One cun per thousand li lacks canonical support—it is arbitrary. Jiao and Ai provinces show no shadow north of the gnomon—not ten thousand li yet south of the cap. One cun per thousand li is not the true rate. Zhuo uses the path as rate—fixed li unknown until difference is measured. In an age of sage rule and ascending peace, correcting errors is timely. He requested a surveyor and mathematician on level ground north and south of the Yellow River for hundreds of li. Fix time by clepsydra, level by cord, measure shadows on the same day. From the difference rate, li can be known. Then Heaven and Earth cannot hide their form and stars cannot escape their numbers. Do not reject the proposal because of the proposer. It was not adopted. In Daye 3 an edict ordered shadow measurement—but Zhuo died and the project was abandoned.

○地中

Earth's Center

《周禮·大司徒職》：「以土圭之法，測土深，正日景，以求地中。」此則渾天之正說，立儀象之大本。故云：「日南則景短多暑，日北則景長多寒，日東則景夕多風，日西則景朝多陰。日至之景，尺有五寸，謂之地中。天地之所合也。四時之所交也，風雨之所會也，陰陽之所和也。然則百物阜安，乃建王國焉。」又《考工記·匠人》：「建國，水地以縣。置Ｓ以縣，眡以景。為規，識日出之景與日入之景。晝參諸日中之景，夜考之極星，以正朝夕。」案土圭正影，經文闕略，先儒解說，又非明審。祖暅錯綜經注，以推地中。其法曰：「先驗昏旦，定刻漏，分辰次。乃立儀錶于准平之地，名曰南表。漏刻上水，居日之中，更立一表于南表影末，名曰中表。夜依中表，以望北極樞，而立北表，令參相直。三表皆以懸准定，乃觀。三表直者，其立表之地，即當子午之正。三表曲者，地偏僻。每觀中表，以知所偏。中表在西，則立表處在地中之西，當更向東求地中。若中表在東，則立表處在地中之東也，當更向西求地中。取三表直者，為地中之正。又以春秋二分之日，旦始出東方半體，乃立表於中表之東，名曰東表。令東表與日及中表參相直。視日之夕，日入西方半體，又立表於中表之西，名曰西表。亦從中表西望西表及日，參相直。乃觀三表直者，即地南北之中也。若中表差近南，則所測之地在卯酉之南。中表差在北，則所測之地在卯酉之北。進退南北，求三表直正東西者，則其地處中，居卯酉之正也。」

Rites of Zhou, Grand Steward: "By the earth-tablet method, measure depth and rectify the sun's shadow to find Earth's center. This is Spherical Heaven's correct doctrine—the foundation of instruments and models. It says: "Sun south—short shadow, much heat; north—long shadow, much cold; east—evening shadow, much wind; west—morning shadow, much yin. Solstice shadow one chi five cun marks Earth's center. Where Heaven and Earth converge. Where seasons cross, wind and rain gather, and yin and yang harmonize. Then all things flourish and the royal state is founded. Records of the Craftsman: "Establishing the state, level ground with a plumb line. Set the gnomon plumb and read its shadow. With a compass mark sunrise and sunset shadows. By day use midday shadow; by night the pole star—to fix morning and evening. Classic texts on the earth-tablet method are incomplete; earlier explanations are unclear. Zu Geng synthesized classics and commentaries to find Earth's center. His method: "First fix dusk and dawn and clepsydra marks, dividing chronogram positions. Erect an instrument on level ground—the south gnomon. At solar noon erect a center gnomon at the south gnomon's shadow tip. At night sight the North Pole Pivot from the center gnomon and erect the north gnomon aligned. All three fixed plumb—then observe. Straight alignment marks true meridian. Bent alignment means off-center ground. Observe the center gnomon to detect deviation. Center gnomon west—site is west of center; move east. Center gnomon east—site is east of center; move west. True center is where all three align straight. At equinox, when half the sun shows in the east, erect an east gnomon east of center. Align east gnomon, sun, and center gnomon. At evening half-sunset, erect a west gnomon west of center. From center, align west gnomon and setting sun. Straight three gnomons mark true north-south center. Center gnomon south of line—site is south of mao-you. Center gnomon north—site is north of mao-you. Adjust north-south until east-west gnomons align—the site sits on true mao-you."

○晷影

Gnomon Shadows

昔者周公測晷影于陽城，以參考曆紀。其于《周禮》，在《大司徒之職》：「以土圭之法，測土深，正日景，以求地中。日至之景，尺有五寸，則天地之所合，四時之所交。百物阜安，乃建王國。」然則日為陽精，玄象之著然者也。生靈因之動息，寒暑由其遞代。觀陰陽之升降，揆天地之高遠，正位辨方，定時考閏，莫近於茲也。古法簡略，旨趣難究，術家考測，互有異同。先儒皆云：「夏至立八尺表于陽城，其影與土圭等。」案《尚書考靈曜》稱：「日永，景尺五寸；日短，景尺三寸。」《易通卦驗》曰：「冬至之日，樹八尺之表，日中視其晷景長短，以占和否。夏至景一尺四寸八分，冬至一丈三尺。」《周髀》云：「成周土中，夏至景一尺六寸，冬至景一丈三尺五寸。」劉向《鴻範傳》曰：「夏至景長一尺五寸八分，冬至一丈三尺一寸四分，春秋二分，景七尺三寸六分。」後漢《四分曆》、魏《景初曆》、宋《元嘉曆》、《大明》祖沖之曆，皆與《考靈曜》同。漢、魏及宋，所都皆別，四家曆法，候影則齊。且緯候所陳，恐難依據。劉向二分之影，直以率推，非因表候定其長短。然尋晷影尺丈，雖有大較，或地域不改，而分寸參差，或南北殊方，而長短維一。蓋術士未能精驗，馮占所以致乖。今刪其繁雜，附於此云。

The Duke of Zhou measured gnomon shadows at Yangcheng to verify the calendar. Rites of Zhou, Grand Steward: "By the earth-tablet method rectify the sun's shadow to find Earth's center. Solstice shadow one chi five cun—Heaven and Earth meet and seasons cross. All things flourish and the royal state is founded. The sun is yang essence—the manifest brightness of the dark image. Living creatures move and rest by it; cold and heat alternate. Observing yin-yang motion, measuring Heaven-Earth distance, fixing position and time—nothing serves better. Ancient methods are brief and obscure; technicians disagree. Earlier scholars say: "At summer solstice an eight-chi gnomon at Yangcheng matches the earth tablet. Documents Kao Ling Yao: "Long day—shadow one chi five cun; short day—shadow one chi three cun. Changes Tong Gua Yan: "On winter solstice plant an eight-chi gnomon; at midday read shadow length for harmony or disorder. Summer solstice shadow one chi four cun eight fen; winter solstice one zhang three chi." Zhou Bi: "At Chengzhou center, summer solstice one chi six cun, winter solstice one zhang three chi five cun." Liu Xiang: "Summer solstice one chi five cun eight fen, winter solstice one zhang three chi one cun four fen, equinox seven chi three cun six fen." Later Han Four Parts, Wei Jingchu, Song Yuanjia, and Zu Chongzhi's Daming calendars all match Kao Ling Yao. Han, Wei, and Song had different capitals yet shadow measures aligned. Apocryphal observations are hard to rely on. Liu Xiang's equinox shadows were calculated, not measured. Shadow measures vary by region even when texts give single values. Technicians failed to verify precisely; divination led to error. Redundant material is deleted here.

梁天監中，祖暅造八尺銅表，其下與圭相連。圭上為溝，置水，以取平正。揆測日晷，求其盈縮。至大同十年，太史令虞廣刂又用九尺表格江左之影。夏至一尺三寸二分，冬至一丈三尺七分，立夏、立秋二尺四寸五分，春分、秋分五尺三寸九分。陳氏一代，唯用梁法。齊神武以洛陽舊器並徙鄴中，以暨文宣受終，竟未考驗。至武平七年，訖幹景禮始薦劉孝孫、張孟賓等於後主。劉、張建表測影，以考分至之氣。草創未就，仍遇朝亡。周自天和以來，言曆者紛紛複出。亦驗二至之影，以考曆之精粗。及高祖踐極之後，大議造曆。張胄玄兼明揆測，言日長之瑞。有詔司存，而莫能考決。至開皇十九年，袁充為太史令，欲成胄玄舊事，複表曰：「隋興已後，日景漸長。開皇元年冬至之影，長一丈二尺七寸二分，自爾漸短。至十七年冬至影，一丈二尺六寸三分。四年冬至，在洛陽測影，長一丈二尺八寸八分。二年夏至影，一尺四寸八分，自爾漸短。至十六年夏至影，一尺四寸五分。其十八年冬至，陰雲不測。元年、十七年、十八年夏至，亦陰雲不測。《周官》以土圭之法正日影，日至之影，尺有五寸。鄭玄云：'冬至之景，一丈三尺。 '今十六年夏至之影，短於舊五分，十七年冬至之影，短於舊三寸七分。日去極近，則影短而日長；去極遠，則影長而日短。行內道則去極近，行外道則去極遠。《堯典》云：'日短星昴，以正仲冬。 '據昴星昏中，則知堯時仲冬，日在須女十度。以歷數推之，開皇以來冬至，日在斗十一度，與唐堯之代，去極俱近。謹案《元命包》云：'日月出內道，〔璣得其常，天帝崇靈，聖王初功。 '京房《別對》曰：'太平日行上道，升平日行次道，霸代日行下道。 '伏惟大隋啓運，上感乾元，影短日長，振古稀有。」是時廢庶人勇，晉王廣初為太子，充奏此事，深合時宜。上臨朝謂百官曰：「景長之慶，天之祐也。今太子新立，當須改元，宜取日長之意，以為年號。」由是改開皇二十一年為仁壽元年。此後百工作役，並加程課，以日長故也。皇太子率百官詣闕陳賀。案日徐疾盈縮無常，充等以為祥瑞，大為議者所貶。

In Liang Tianjian, Zu Geng made an eight-chi bronze gnomon joined to its tablet. A water channel on the tablet ensured level. He measured solar gnomon shadows for surplus and deficit. By Datong 10, Grand Astrologer Yu Guangce used a nine-chi gnomon for Jiangzuo shadows. Summer solstice one chi three cun two fen, winter solstice one zhang three chi seven fen, Lixia and Liqiu two chi four cun five fen, equinox five chi three cun nine fen. Chen used only Liang methods. Northern Qi Shenwu moved Luoyang instruments to Ye but never verified them under Wenxuan. By Wuping 7, Gan Jingli recommended Liu Xiaosun and Zhang Mengbin. Liu and Zhang erected gnomons to test solstice qi. The project was unfinished when the dynasty fell. From Zhou Tianhe onward calendar debates proliferated. Solstice shadows tested calendar precision. After Gaozu's accession, debate on calendar reform ensued. Zhang Zhouxuan cited lengthening days as an auspicious omen. Offices were ordered to decide—none could. In Kaihuang 19, Yuan Chong memorialized: "Since Sui's rise, sun shadows gradually lengthened. Kaihuang 1 winter solstice shadow one zhang two chi seven cun two fen—then gradually shorter. Year 17 winter solstice one zhang two chi six cun three fen. Year 4 winter solstice at Luoyang: one zhang two chi eight cun eight fen. Year 2 summer solstice one chi four cun eight fen—then shorter. Year 16 summer solstice one chi four cun five fen. Year 18 winter solstice—clouds blocked measurement. Years 1, 17, and 18 summer solstice—also unmeasured due to clouds. Zhou Offices rectify sun shadow; solstice shadow one chi five cun. Zheng Xuan: "Winter solstice shadow one zhang three chi." Year 16 summer solstice five fen shorter; year 17 winter solstice three cun seven fen shorter. Far from pole—short shadow, long day; near pole—long shadow, short day. Inner path—near pole; outer path—far from pole. Documents of Yao: "Short day, Pleiades centered—mid-winter." Pleiades at dusk implies Yao's mid-winter sun at Maiden 10°. Since Kaihuang winter solstice sun at Dipper 11°—like Yao's era, both near the pole. Yuan Ming Bao: "Sun and moon on inner path, ji holds norm, Heaven exalts the sage's first achievement." Jing Fang: "Great peace—upper path; ascending peace—middle; hegemonic age—lower." Great Sui opened fortune under Qian yuan—short shadow, long day, rare since antiquity. Deposed Yong, new crown prince Guang—Chong's memorial suited the moment. The emperor told officials: "Lengthening shadows are Heaven's blessing. The crown prince is new—we should take long days as the era name. Kaihuang 21 became Renshou 1. Public works intensified—because days were supposedly longer. The crown prince led officials in congratulation. Sun motion is irregular—critics condemned Chong's omen reading.

又《考靈曜》、《周髀》張衡《靈憲》及鄭玄注《周官》，並云：「日影於地，千里而差一寸。」案宋元嘉十九年壬午，使使往交州測影。夏至之日，影出表南三寸二分。何承天遙取陽城，云夏至一尺五寸。計陽城去交州，路當萬里，而影實差一尺八寸二分。是六百里而差一寸也。又當梁大同中，二至所測，以八尺表率取之，夏至當一尺一寸七分強。後魏信都芳注《周髀四術》，稱永平元年戊子，當梁天監之七年，見洛陽測影，又見公孫崇集諸朝士，共觀秘書影。同是夏至日，其中影皆長一尺五寸八分。以此推之，金陵去洛，南北略當千里，而影差四寸。則二百五十裡而影差一寸也。況人路迂回，山川登降，方於鳥道，所校彌多，則千里之言，未足依也。其揆測參差如此，故備論之。

Kao Ling Yao, Zhou Bi, Ling Xian, and Zheng Xuan all say shadow differs one cun per thousand li. Yuanjia 19 renwu envoys measured shadows at Jiao Province. Summer solstice shadow extended three cun two fen south of the gnomon. He Chengtian used Yangcheng's summer solstice one chi five cun remotely. Yangcheng to Jiao Province should be ten thousand li by road, yet shadows differed by one chi eight cun two fen. That is one cun difference per six hundred li. Liang Datong solstice measures with an eight-chi gnomon gave summer solstice about one chi one cun seven fen strong. Xin Du Fang noted that in Yongping 1 (Liang Tianjian 7) Luoyang shadows were measured and Gongsun Chong gathered officials to view Secretariat shadows. On the same summer solstice all midday shadows measured one chi five cun eight fen. Jinling to Luoyang is roughly one thousand li north-south, yet shadows differed four cun. That yields one cun per two hundred fifty li. Human roads wind and terrain varies—unlike bird flight—so the thousand-li rule cannot be relied on. Measurements diverge thus—hence this full discussion.

○漏刻

Clepsydra Marks

昔黃帝創觀漏水，制器取則，以分晝夜。其後因以命官，《周禮》挈壺氏則其職也。其法，總以百刻，分於晝夜。冬至晝漏四十刻，夜漏六十刻。夏至晝漏六十刻，夜漏四十刻。春秋二分，晝夜各五十刻。日未出前二刻半而明，既沒後二刻半乃昏。減夜五刻，以益晝漏，謂之昏旦。漏刻皆隨氣增損。冬夏二至之間，晝夜長短，凡差二十刻。每差一刻為一箭。冬至互起其首，凡有四十一箭。晝有朝，有禺，有中，有晡，有夕。夜有甲、乙、丙、丁、戊。昏旦有星中。每箭各有其數，皆所以分時代守，更其作役。

The Yellow Emperor first observed dripping water and made instruments to divide day and night. Offices were named accordingly—the Rites of Zhou Pitcher Bearer held this duty. The method totals one hundred marks between day and night. Winter solstice: forty day marks, sixty night marks. Summer solstice: sixty day marks, forty night marks. Equinoxes: fifty marks each for day and night. Light begins two and a half marks before sunrise; dusk two and a half marks after sunset. Five night marks transfer to day clepsydra—dusk and dawn allowance. Clepsydra marks adjust with seasonal qi. Between solstices day and night length differs twenty marks. Each one-mark change equals one arrow. From winter solstice forty-one arrows alternate. Day periods: court, yu, center, bu, evening. Night watches: jia, yi, bing, ding, wu. Dusk and dawn have centered stars. Each arrow has its count to divide eras, guard time, and schedule labor.

漢興，張蒼因循古制，猶多疏闊。及孝武考定星曆，下漏以追天度，亦未能盡其理。劉向《鴻範傳》記武帝時所用法云：「冬夏二至之間，一百八十餘日，晝夜差二十刻。」大率二至之後，九日而增損一刻焉。至哀帝時，又改用晝夜一百二十刻，尋亦寢廢。至王莽竊位，又遵行之。光武之初，亦以百刻九日加減法，編於《甲令》，為《常符漏品》。至和帝永元十四年，霍融上言：「官曆率九日增減一刻，不與天相應。或時差至二刻半，不如夏曆漏刻，隨日南北為長短。」乃詔用夏曆漏刻。依日行黃道去極，每差二度四分，為增減一刻。凡用四十八箭，終於魏、晉，相傳不改。

Han's Zhang Cang followed ancient practice but left much loose. Emperor Wu lowered clepsydra to match heavenly degrees—yet principle was not fully grasped. Liu Xiang records Wu's method: between solstices one hundred eighty-odd days differ twenty marks in day-night length. Generally one mark changes every nine days after a solstice. Emperor Ai tried one hundred twenty marks—soon abandoned. Wang Mang followed it again. Early Guangwu used hundred marks with nine-day adjustment in Edict A. Huo Rong in Yongyuan 14: official calendar's nine-day mark change does not match Heaven. Error reached two and a half marks—inferior to Xia calendar clepsydra following solar latitude. An edict adopted Xia calendar clepsydra. Each two degrees four fen of solar polar distance changes clepsydra one mark. Forty-eight arrows were used through Wei and Jin unchanged.

宋何承天以月蝕所在，當日之衡，考驗日宿，知移舊六度。冬至之日，其影極長，測量晷度，知冬至移舊四日。前代諸漏，春分晝長，秋分晝短，差過半刻。皆由氣日不正，所以而然。遂議造漏法。春秋二分，昏旦晝夜漏各五十五刻。齊及梁初，因循不改。至天監六年，武帝以晝夜百刻，分配十二辰，辰得八刻，仍有餘分。乃以晝夜為九十六刻，一辰有全刻八焉。至大同十年，又改用一百八刻。依《尚書考靈曜》晝夜三十六頃之數，因而三之。冬至晝漏四十八刻，夜漏六十刻。夏至晝漏七十刻，夜漏三十八刻。春秋二分，晝漏六十刻，夜漏四十八刻。昏旦之數各三刻。先令祖暅為《漏經》，皆依渾天黃道日行去極遠近，為用箭日率。陳文帝天嘉中，亦命舍人硃史造漏，依古百刻為法。周、齊因循魏漏。晉、宋、梁大同，並以百刻分於晝夜。

He Chengtian found the sun's lodge shifted six degrees from eclipse data. Winter solstice shadow measurement showed a four-day shift. Older clepsydra made spring days too long and autumn days too short by over half a mark. All because seasonal days were incorrect. He then proposed a new clepsydra method. Equinox dusk-dawn clepsydra: fifty-five marks each for day and night. Qi and early Liang followed unchanged. Tianjian 6: hundred marks divided among twelve chronograms left remainders. Day-night became ninety-six marks—eight full marks per chronogram. Datong 10 changed to one hundred eight marks. Following Kao Ling Yao's thirty-six qing count, trebled. Winter solstice: forty-eight day, sixty night marks. Summer solstice: seventy day, thirty-eight night marks. Equinox: sixty day, forty-eight night marks. Dusk and dawn: three marks each. Zu Geng's Clepsydra Classic used solar polar distance for arrow rates. Chen Wendi ordered Zhu Shi to make clepsydra by the ancient hundred-mark method. Zhou and Qi followed Wei clepsydra. Jin, Song, and Liang Datong used hundred marks between day and night.

隋初，用周朝尹公正、馬顯所造《漏經》。至開皇十四年，鄜州司馬袁充上晷影漏刻。充以短影平儀，均布十二辰，立表，隨日影所指辰刻，以驗漏水之節。十二辰刻，互有多少，時正前後，刻亦不同。其二至二分用箭辰刻之法，今列之云。

Early Sui used Yin Gongzheng and Ma Xian's Clepsydra Classic. Kaihuang 14: Yuan Chong submitted gnomon and clepsydra reforms. Chong used a level instrument and gnomon shadows to verify clepsydra nodes by chronogram. Twelve chronogram marks varied; marks differed before and after true center. Solstice and equinox arrow-chronogram methods are listed below:

冬至：日出辰正，入申正，晝四十刻，夜六十刻。

Winter solstice: sunrise at chen center, sunset at shen center; forty day, sixty night marks.

子、醜、亥各二刻，寅、戌各六刻，卯、酉各十三刻，辰、申各十四刻，巳、未各十刻，午八刻。

Zi, chou, hai two marks each; yin, xu six; mao, you thirteen; chen, shen fourteen; si, wei ten; wu eight.

右十四日改箭。

Arrow changes every fourteen days.

春秋二分：日出卯正，入酉正，晝五十刻，夜五十刻。

Equinox: sunrise mao center, sunset you center; fifty day, fifty night marks.

子四刻，醜、亥七刻，寅、戌九刻，卯、酉十四刻，辰、申九刻，巳、未七刻，午四刻。

Zi four; chou, hai seven; yin, xu nine; mao, you fourteen; chen, shen nine; si, wei seven; wu four.

右五日改箭。

Arrow changes every five days.

夏至：日出寅正，入戌正，晝六十刻，夜四十刻。

Summer solstice: sunrise yin center, sunset xu center; sixty day, forty night marks.

子八刻，醜、亥十刻，寅、戌十四刻，卯、酉十三刻，辰、申六刻，巳、未二刻，午二刻。

Zi eight; chou, hai ten; yin, xu fourteen; mao, you thirteen; chen, shen six; si, wei two; wu two.

右一十九日，加減一刻，改箭。

Every nineteen days adjust one mark and change arrow.

袁充素不曉渾天黃道去極之數，苟役私智，變改舊章，其於施用，未為精密。

Yuan Chong did not understand polar distance; his private alterations were imprecise.

開皇十七年，張胄玄用後魏渾天鐵儀，測知春秋二分，日出卯酉之北，不正當中。與何承天所測頗同，皆日出卯三刻五十五分，入酉四刻二十五分。晝漏五十刻十一分，夜漏四十九刻四十分，晝夜差六十分刻之四十。仁壽四年，劉焯上《皇極曆》，有日行遲疾，推二十四氣，皆有盈縮定日。春秋分定日，去冬至各八十八日有奇，去夏至各九十三日有奇。二分定日，晝夜各五十刻。又依渾天黃道，驗知冬至夜漏五十九刻、一百分刻之八十六，晝漏四十刻一十四分，夏至晝漏五十九刻八十六分，夜漏四十刻一十四分。冬夏二至之間，晝夜差一十九刻、一百分刻之七十二。胄玄及焯漏刻，並不施用。然其法制，皆著在曆術，推驗加時，最為詳審。

Kaihuang 17: Zhang Zhouxuan found equinox sunrise north of mao-you, not centered. Matching He Chengtian: sunrise mao 3 marks 55 fen, sunset you 4 marks 25 fen. Day fifty marks eleven fen, night forty-nine forty—difference sixty forty-hundredths marks. Renshou 4: Liu Zhuo's Huangji Calendar derived twenty-four qi with surplus and deficit days. Equinox fixed days: eighty-eight odd from winter solstice, ninety-three odd from summer solstice. Equinox fixed days: fifty marks day and night. By Yellow Path: winter solstice night fifty-nine marks 86 hundredths, day forty fourteen; summer reversed. Between solstices day-night differs nineteen marks seventy-two hundredths. Neither Zhouxuan nor Zhuo's clepsydra was adopted. Their methods remain in calendar texts—the most detailed for time verification.

大業初，耿詢作古欹器，以漏水注之，獻於煬帝。帝善之，因令與宇文愷依後魏道士李蘭所修道家上法稱漏制，造稱水漏器，以充行從。又作候影分箭上水方器，置於東都乾陽殿前鼓下司辰。又作馬上漏刻，以從行辨時刻。揆日晷，下漏刻，此二者，測天地正儀象之本也。晷漏沿革，今古大殊，故列其差，以補前闕。

At Daye's start Geng Xun made an ancient tilt vessel for Emperor Yang. Emperor Yang ordered Yuwen Kai to make traveling scale clepsydra after Li Lan's method. Also a shadow-dividing water vessel at Qianyang Hall for timekeeping. Also a horse-mounted clepsydra for travel. Gnomon and clepsydra are the roots of correct celestial measurement. Gnomon and clepsydra evolved greatly—differences are listed to fill prior gaps.

○經星中宮

Fixed Stars: Inner Palace

北極五星，鉤陳六星，皆在紫宮中。北極，辰也。其紐星，天之樞也。天運無窮，三光迭耀，而極星不移。故曰：「居其所而眾星共之。」賈逵、張衡、蔡邕、王蕃、陸績，皆以北極紐星為樞，是不動處也。祖暅以儀准候不動處，在紐星之末，猶一度有餘。北極大星，太一之座也。第一星主月，太子也。第二星主日，帝王也。第三星主五星，庶子也。所謂第二星者，最赤明者也。北極五星，最為尊也。中星不明，主不用事。右星不明，太子憂。鉤陳，後宮也，太帝之正妃也，太帝之坐也。北四星曰女御宮，八十一御妻之象也。鉤陳口中一星，曰天皇太帝。其神曰耀魄寶，主御群靈，秉萬神圖。抱極樞四星曰四輔，所以輔佐北極，而出度授政也。太帝上九星曰華蓋，蓋所以覆蔽太帝之坐也。又九星直曰杠。蓋下五星曰五帝內坐，設敘順，帝所居也。客犯紫宮中坐，大臣犯主。華蓋杠旁六星曰六甲，可以分陰陽而紀節候，故在帝旁，所以布政教而授人時也。極東一星曰柱下史，主記過。古者有左右史，此之象也。柱史北一星曰女史，婦人之微者，主傳漏。故漢有侍史。傳舍九星在華蓋上，近河，賓客之館，主胡人入中國。客星守之，備奸使，亦曰胡兵起。傳舍南河中五星曰造父，御官也，一曰司馬，或曰伯樂。星亡，馬大貴。西河中九星如鉤狀，曰鉤星，伸則地動。天一一星，在紫宮門右星南，天帝之神也，主戰鬭，知人吉凶者也。太一一星，在天一南，相近，亦天帝神也，主使十六神，知風雨水旱，兵革饑饉，疾疫災害所生之國也。

The five North Pole stars and six Goutchen stars all lie within the Purple Palace. The North Pole is the celestial pivot. Its pivot star is Heaven's pivot. Heaven turns without end as the three luminaries pass in turn, yet the pole star holds its place. Hence the saying: "It dwells in its place while all stars attend it. Jia Kui, Zhang Heng, Cai Yong, Wang Fan, and Lu Ji all held the North Pole pivot star to be the fixed pivot. Zu Geng measured the unmoving point with instruments and placed it beyond the pivot star by more than one degree. The North Pole's great star is the throne of the Supreme One. The first star governs the moon; it is the Heir Apparent. The second star governs the sun; it is the emperor. The third star governs the five planets; it is the secondary son. The so-called second star is the brightest red star. The five North Pole stars are the most exalted. When the central star is unclear, the sovereign neglects governance. When the right star fades, the Heir Apparent faces worry. Goutchen represents the inner palace—the Great Emperor's chief consort and throne. The four northern stars form the Palace of Female Attendants, symbolizing eighty-one consorts. A star in Goutchen's mouth is the Celestial August Emperor. Its god Yaopobao governs the host of spirits and bears the map of ten thousand gods. Four stars encircling the pole pivot are the Four Assistants, helping the North Pole measure degrees and grant rule. Nine stars above the Great Emperor form the Canopy, shielding his throne. Nine stars in a line are the Pole—the canopy's handle. Five stars under the Canopy are the Inner Seats of the Five Emperors, marking the imperial residence in proper order. A guest star striking the Purple Palace's central seat means ministers rebel against the sovereign. Six stars by the Canopy Pole are the Six Jia, marking yin-yang and seasonal nodes to teach governance and set the calendar. East of the pole is the Historian beneath the Column, recording transgressions. Ancient courts had left and right historians; these stars mirror them. North of the Column Historian is the Female Historian, a minor female officer in charge of timekeeping. Therefore the Han dynasty maintained attendant historians. Nine Transfer Lodging stars above the Canopy by the river mark the guest lodge for tribes entering China. When a guest star lingers there, prepare for spies—and northern armies may rise. Five stars south in the river are Zaofu, overseers of the imperial stud—also Sima or Bo Le. When the star vanishes, horses fetch high prices. Nine hook-shaped stars in the western river are Hook Star; if they straighten, the earth trembles. Heaven One lies south of the Purple Palace gate; the Celestial Emperor's god presides over war and reads human fates. Supreme One, close south of Heaven One, commands sixteen spirits and reveals which countries face storms, drought, war, famine, and plague.

紫宮垣十五星，其西蕃七，東蕃八，在北斗北。一曰紫微，太帝之坐也，天子之常居也，主命，主度也。一曰長垣，一曰天營，一曰旗星，為蕃衛，備蕃臣也。宮闕兵起，旗星直，天子出，自將宮中兵。東垣下五星曰天柱，建政教，懸圖法之所也。常以朔望日懸禁令於天柱，以示百司。《周禮》以正歲之月，懸法象魏，此之類也。門內東南維五星曰尚書，主納言，夙夜諮謀，龍作納言，此之象也。尚書西二星曰陰德、陽德，主周急振無。宮門左星內二星曰大理，主平刑斷獄也。門外六星曰天床，主寢舍，解息燕休。西南角外二星曰內廚，主六宮之飲食，主後夫人與太子宴飲。東北維外六星曰天廚，主盛饌。

Fifteen rampart stars of the Purple Palace, seven west and eight east, lie north of the Northern Dipper. Also Purple Subtlety: the Great Emperor's throne and the Son of Heaven's dwelling, governing mandate and celestial degrees. Also Long Rampart, Celestial Camp, and Banner Stars—bastion guards for frontier officials. When palace armies mobilize and Banner Stars align straight, the Son of Heaven leads the palace troops himself. Five stars under the eastern wall are the Heavenly Pillar, displaying governance and legal charts. At new and full moons edicts are posted on the Heavenly Pillar for all departments. The Rites of Zhou hangs laws at the symbolic tower in the first month—this follows that practice. Five stars at the inner southeast are the Imperial Secretariat, receiving memorials and advising day and night. West of the Secretariat are Yin Virtue and Yang Virtue, overseeing emergency relief. Inside the left gate are the Grand Judge stars, adjudicating punishment and lawsuits. Six stars outside the gate are the Celestial Bed, governing rest and repose. Outside the southwest corner, the Inner Kitchen oversees palace food and royal feasts. Six stars beyond the northeast corner are the Celestial Kitchen, holding banquet fare.

北斗七星，輔一星在太微北，七政之樞機，陰陽之元本也，故運乎天中，而臨制四方，以建四時而均五行也。魁四星為〔璣，杓三星為玉衡。又象號令之主，又為帝車，取乎運動之義也。又魁第一星曰天樞，二曰璇，三曰璣，四曰權，五曰玉衡，六曰開陽，七曰搖光。一至四為魁，五至七為杓。樞為天，璇為地，璣為人，權為時，玉衡為音，開陽為律，搖光為星。石氏云：「第一曰正星，主陽德，天子之象也。二曰法星，主陰刑，女主之位也。三曰令星，主禍害也。四曰伐星，主天理，伐無道。五曰殺星，主中央，助四旁，殺有罪。六曰危星，主天倉五穀。七曰部星，亦曰應星，主兵。」又云：「一主天，二主地，三主火，四主水，五主土，六主木，七主金。」又曰：「一主秦，二主楚，三主樑，四主吳，五主趙，六主燕，七主齊。」

Seven stars of the Northern Dipper, with an Assistant north of the Supreme Palace, pivot the seven regulators and yin-yang, turning at Heaven's center to rule the four quarters and seasons. The bowl's four stars are Ji; the handle's three are Jade Balance. It also represents the commander of edicts and the imperial chariot—in motion. The bowl stars are Celestial Pivot, Xuan, Ji, Quan; the handle stars Jade Balance, Kaiyang, Yaoguang. Stars one to four are the bowl; five to seven the handle. Pivot stands for Heaven, Xuan for Earth, Ji for humanity, Quan for season, Jade Balance for pitch, Kaiyang for measure, Yaoguang for stars. Master Shi says: "The first is the Correct Star, governing yang virtue—the Son of Heaven's image. The second is the Law Star, governing yin punishment—the empress's seat. The third is the Command Star, governing disaster. The fourth is the Punitive Star, upholding Heaven's justice against the lawless. The fifth is the Killing Star, at the center aiding the four quarters to execute the guilty. The sixth is the Danger Star, governing Heaven's storehouse of grain. The seventh is the Department or Responding Star, governing warfare. It also states: "The first governs Heaven, the second Earth, the third Fire, the fourth Water, the fifth Earth, the sixth Wood, the seventh Metal." It also states: "The first governs Qin, the second Chu, the third Liang, the fourth Wu, the fifth Zhao, the sixth Yan, the seventh Qi."

魁中四星，為貴人之牢，曰天理也。輔星傅乎開陽，所以佐斗成功也。又曰：「主危正，矯不平。」又曰：「丞相之象也。」七政星明，其國昌。不明，國殃。斗旁欲多星則安，斗中少星則人恐上，天下多訟法者。無星二十日。有輔星明而斗不明，臣強主弱。半明輔不明，主強臣弱也。杓南三星及魁第一星，皆曰三公，宣德化，調七政，和陰陽之官也。

Four stars in the bowl form the nobles' prison—the Heavenly Principle. The Assistant Star lies by Kaiyang, aiding the Dipper's success. It also says: "It governs danger and correction, straightening what is crooked. It also says: "It images the Chancellor." Bright seven regulator stars mean a flourishing realm. When they fade, the state faces calamity. Many companion stars bring peace; few within the Dipper mean popular fear and many lawsuits. Twenty days with no stars visible. A bright Assistant with a dim Dipper means strong ministers and a weak ruler. Half brightness with a dim Assistant means a strong ruler and weak ministers. The handle's southern three stars and the bowl's first star are the Three Dukes, spreading virtue and harmonizing yin-yang.

文昌六星，在北斗魁前，天之六府也，主集計天道。一曰上將，大將建威武。二曰次將，尚書正左右。三曰貴相，太常理文緒。四曰司祿、司中，司隸賞功進。五曰司命、司怪，太史主滅咎。六曰司寇，大理佐理寶。所謂一者，起北斗魁前，近內階者也。明潤，大小齊，天瑞臻。

Six Literary Glory stars before the Dipper bowl are Heaven's six treasuries, accounting Heaven's order. First: the supreme general, the great commander establishing martial majesty. Second: the deputy general, the Secretariat correcting left and right. Third: the honored minister, the Grand Steward overseeing documents. Fourth: Directors of Emolument and the Center; the Inspector rewards achievement. Fifth: Directors of Fate and Omens; the Grand Historian removes fault. Sixth: Director of Punishment; the Grand Judge aids in managing treasures. The first begins before the Dipper bowl, near the Inner Steps. When bright, moist, and evenly sized, Heaven sends auspicious signs.

文昌北六星曰內階，天皇之陛也。相一星在北斗南。相者總領百司而掌邦教，以佐帝王，安邦國，集眾事也。其明吉。太陽守一星，在相西，大將大臣之象也，主戒不虞，設武備也。非其常，兵起。西北四星曰勢。勢，腐刑人也。天牢六星在北斗魁下，貴人之牢也，主愆過，禁暴淫。

Six stars north of Literary Glory are the Inner Steps, the Celestial Sovereign's stair. The Chancellor Star lies south of the Northern Dipper. The Chancellor Star represents one who leads all offices, teaches the state, aids the emperor, and gathers affairs. Brightness brings good fortune. Taiyang Shou west of the Chancellor images great commanders, guarding against surprise and keeping arms ready. When abnormal, armies mobilize. Four northwestern stars are Power. Power represents corrupt executioners. Six Celestial Prison stars under the Dipper bowl imprison nobles, governing faults and restraining violence.

太微，天子庭也，五帝之坐也，亦十二諸侯府也。其外蕃，九卿也。一曰太微為衡。衡，主平也。又為天庭，理法平辭，監升授德，列宿受符，諸神考節，舒情稽疑也。南蕃中二星間曰端門。東曰左執法，廷尉之象也。西曰右執法，御史大夫之象也。執法，所以舉刺凶奸者也。左執法之東，左掖門也。右執法之西，右掖門也。東蕃四星，南第一曰上相，其北東太陽門也。第二星曰次相，其北中華東門也。第三星曰次將，其北東太陰門也。第四星曰上將。所謂四輔也。西蕃四星：南第一星曰上將，其北西太陽門也。第二星曰次將，其北中華西門也。第三曰次相，其北西太陰門也。第四星曰上相。亦四輔也。東西蕃有芒及搖動者，諸侯謀天子也。執法移則刑罰尤急。月、五星所犯中坐，成刑。月、五星入太微軌道，吉。

The Supreme Palace is the imperial court, seat of the Five Emperors and twelve feudal lords. Its outer bastion represents the Nine Ministers. It is also said the Supreme Palace is the balance. The balance oversees equity. It is Heaven's court: fair law, promotion of virtue, tokens to stars, gods reviewing seasons, probing doubts. The southern bastion's two central stars form the Central Gate. To the east is the Left Enforcer, imaging the Minister of Justice. To the west is the Right Enforcer, imaging the Grand Censor. Enforcers impeach the wicked. East of the Left Enforcer lies the Left Side Gate. West of the Right Enforcer lies the Right Side Gate. Eastern bastion: southern first is chief minister; its north is the Eastern Sun Gate. Second is deputy minister; north is the Central East Gate. Third is deputy general; north is the Eastern Moon Gate. Fourth is the supreme general. These are the Four Assistants. Western bastion: southern first is supreme general; north is the Western Sun Gate. Second is deputy general; north is the Central West Gate. Third is deputy minister; north is the Western Moon Gate. Fourth is the chief minister. These too are the Four Assistants. Rays or motion in east and west bastions mean lords plot against the throne. Shifting enforcers bring especially harsh punishments. Moon or five planets hitting the central seat bring execution. Moon or five planets entering the Supreme Palace orbit are auspicious.

西南角外三星曰明堂，天子布政之宮也。明堂西三星曰靈臺，觀臺也。主觀雲物，察符瑞，候災變也。左執法東北一星曰謁者，主贊賓客也。謁者東北三星曰三公內坐，朝會之所居也。三公北三星曰九卿內坐，主治萬事。九卿西五星曰內五諸侯，內侍天子，不之國者也。辟雍之禮得，則太微諸侯明。

Three stars beyond the southwest corner are the Bright Hall, where the Son of Heaven promulgates policy. West of the Bright Hall are three Spirit Terrace stars, the observation tower. It oversees cloud signs, auspicious portents, and calamities. Northeast of the Left Enforcer is the Usher, receiving guests. Three stars northeast of the Usher are the Inner Three Dukes' seats for court assembly. North of the Three Dukes are the Inner Nine Ministers, managing all business. Five stars west of the Nine Ministers are Inner Feudal Lords who attend court and do not rule abroad. When Piyong rites are correct, the Supreme Palace lords' stars are bright.

黃帝坐一星，在太微中，含樞紐之神也。天子動得天度，止得地意，從容中道，則太微五帝坐明，坐以光。黃帝坐不明，人主求賢士以輔法，不然則奪勢。又曰太微五坐小弱青黑，天子國亡。四帝坐四星，四星夾黃帝坐。東方星，蒼帝靈威仰之神也。南方星，赤帝熛怒之神也。西方星，白帝招距之神也。北方星，黑帝葉光紀之神也。

Within the Supreme Palace is the Yellow Emperor's Seat, spirit of pivot and hub. When the ruler attains Heaven's measure and Earth's intent along the middle Way, the Five Emperors' seats blaze bright. A dim Yellow Emperor's Seat makes the ruler seek worthy aides—or lose power. If the five Supreme Palace seats are small, weak, and dark, the dynasty falls. Four Emperors' Seat stars flank the Yellow Emperor. The eastern star is Green Emperor Lingweiyang. The southern star is Red Emperor Biaonu. The western star is White Emperor Zhaoju. The northern star is Black Emperor Yeguangji.

五帝坐北一星曰太子，帝儲也。太子北一星曰從官，侍臣也。帝坐東北一星曰幸臣。屏四星在端門之內，近右執法。屏，所以壅蔽帝庭也。執法主刺舉，臣尊敬君上，則星光明潤澤。郎位十五星，在帝坐東北，一曰依烏，郎位也。周官之元士，漢官之光祿、中散、諫議、議郎、三署郎中，是其職也。或曰今之尚書也。郎位主衛守也。其星明，大臣有劫主。又曰客犯上。其星不具，後死，幸臣誅。客星入之，大臣為亂。郎將一星在郎位北，主閱具，所以為武備也。武賁一星，在太微西蕃北，下臺南，靜室旄頭之騎官也。常陳七星，如畢狀，在帝坐北，天子宿衛武賁之土，以設強毅也。星搖動，天子自出，明則武兵用，微則武兵弱。

North of the Five Emperors' Seats is the Heir Apparent star. North of the Heir Apparent is the Attendant Official. Northeast of the throne is the Favored Minister star. Four Screen stars inside the Central Gate screen the court near the Right Enforcer. The Screen shields the imperial court. Enforcers impeach; when ministers revere the ruler, their stars shine moist and bright. Fifteen Officer Position stars northeast of the throne are the attendant corps. They image Zhou chief clerks and Han attendants, counselors, and bureau gentlemen. Some say they represent today's Imperial Secretariat. Officer Positions oversee guard duty. Bright Officer Position stars mean ministers seize the sovereign. A guest star striking them also menaces the ruler. Incomplete stars mean the empress dies and favorites are executed. A guest star entering brings ministerial rebellion. North of Officer Positions is the Commandant of Attendants, reviewing arms and equipment. An Elite Guard star north of the western bastion, south of the Lower Terrace, images Maotou cavalry. Seven Net-shaped Constant Array stars north of the throne are the emperor's elite night guard. Wavering stars mean the emperor leads in person; brightness brings war; faintness weakens arms.

三台六星，兩兩而居，起文昌，列招搖、太微。一曰天柱，三公之位也。在天曰三台，主開德宣符也。西近文昌二星曰上臺，為司命，主壽。次二星曰中台，為司中，主宗。東二星曰下臺，為司祿，主兵，所以昭德塞違也。又曰三台為天階，太一躡以上下。一曰泰階，上星為天子，下星為女主；中階，上星為諸侯三公，下星為卿大夫；下階，上星為士，下星為庶人。所以和陰陽而理萬物也。其星有變，各以所主占人。君臣和集，如其常度。

Six Three Terrace stars in pairs rise from Literary Glory toward Swaying Spear and the Supreme Palace. Also the Heavenly Pillar—the Three Dukes' place. In Heaven they are the Three Terraces, opening virtue and proclaiming mandates. Two stars west near Literary Glory are the Upper Terrace, Director of Fate for longevity. Next two are the Middle Terrace, Director of the Center for the imperial clan. Two eastern stars are the Lower Terrace, Director of Emolument for war—displaying virtue, blocking wrong. The Three Terraces are also Heaven's stairway where the Supreme One treads. The Grand Stairway's upper star is the Son of Heaven, lower the empress; middle stair: upper feudal lords and Three Dukes, lower ministers and grand masters; lower stair: upper gentlemen, lower commoners. They harmonize yin-yang and govern the myriad things. Star changes are read by what each governs among people. When ruler and ministers accord with their proper stations.

南四星曰內平，近職執法平罪之官也。中台之北一星曰大尊，貴戚也。下臺南一星曰武賁，衛官也。

Four southern stars are Inner Peace, nearby judges of crime. North of the Middle Terrace is Great Honored, imaging noble kin. South of the Lower Terrace is Elite Guard, guard officers.

攝提六星，直斗杓之南，主建時節，伺禨祥。攝提為楯，以夾擁帝席也，主九卿。明大，三公恣，客星入之，聖人受制。西三星曰周鼎，主流亡。大角一星，在攝提間。大角者，天王座也。又為天棟，正經紀。北三星曰帝席，主宴獻酬酢。梗河三星，在大角北。梗河者，天矛也。一曰天鋒，主胡兵。又為喪，故其變動應以兵喪也。星亡，其國有兵謀。招搖一星在其北，一曰矛楯，主胡兵。占與梗河略相類也。招搖與北斗杓間曰天庫。星去其所，則有庫開之祥也。招搖欲與棟星、梗河、北斗相應，則胡常來受命於中國。招搖明而不正，胡不受命。玄戈二星，在招搖北。玄戈所主，與招搖同。或云主北夷。客星守之，胡大敗。天槍三星，在北斗杓東。一曰天鉞，天之武備也。故在紫宮之左，所以禦難也。女床三星，在其北，後宮御也，主女事。天棓五星，在女床北，天子先驅也，主忿爭與刑罰，藏兵，亦所以禦難也。槍棓皆以備非常也。一星不具，國兵起。

Six Sheti stars south of the handle establish seasons and watch omens. Sheti shields the Imperial Mat and governs the Nine Ministers. Great brightness lets the Three Dukes run wild; a guest star entering constrains the sage. Three western stars are Zhou Cauldrons, governing dynastic collapse. Great Horn is one star amid Sheti. Great Horn is the throne of the Heavenly King. It is also Heaven's ridgepole, setting governance straight. Three northern stars are the Imperial Mat for feasts and toasts. Three Geng River stars lie north of Great Horn. Geng River is the Celestial Spear. Also the Celestial Point, governing northern armies. It also governs funerals; its changes bring war and mourning. A vanished star means military plotting in that state. Swaying Spear north of it is spear-and-shield, governing northern armies. Its omens resemble Geng River's. Between Swaying Spear and the handle is the Celestial Storehouse. Stars leaving their places mean the storehouse opens—auspicious. When Swaying Spear aligns with Ridgepole, Geng River, and the Dipper, northern tribes accept China's mandate. Bright but crooked Swaying Spear means the Hu reject mandate. Two Dark Halberd stars lie north of Swaying Spear. Dark Halberd's governance matches Swaying Spear. Some say it governs northern barbarians. A guest star lodging there brings great defeat to the Hu. Three Heavenly Spear stars lie east of the handle. Also the Celestial Battle-axe—Heaven's martial readiness. It stands left of the Purple Palace to repel peril. Three Female Couch stars north govern the inner palace and women's affairs. Five Heavenly Club stars north of Female Couch are the imperial vanguard, governing strife, punishment, and stored arms. Spear and club both meet emergencies. One missing star raises national armies.

東七星曰扶筐，盛桑之器，主勸蠶也。七公七星，在招搖東，天之相也，三公之象，主七政。貫索九星在其前，賤人之牢也。一曰連索，一曰運營，一曰天牢，主法律，禁暴強也。牢口一星為門，欲其開也。九星皆明，天下獄煩。七星見，小赦；五星，大赦。動則斧钅質用，中空則更元。《漢志》云十五星。天紀九星，在貫索東，九卿也。九河主萬事之紀，理怨訟也。明則天下多辭訟，亡則政理壞，國紀亂，散絕則地震山崩。織女三星，在天紀東端，天女也，主果瓜絲帛珍寶也。王者至孝，神祇咸喜，則織女星俱明，天下和平。大星怒角，布帛貴。東足四星曰漸臺，臨水之臺也。主晷漏律呂之事。西之五星曰輦道，王者嬉遊之道也，漢輦道通南、北宮象也。

Seven eastern Mulberry Basket stars encourage sericulture. Seven Lords east of Swaying Spear image the Three Dukes and govern the seven regulators. Nine Girdle Rope stars before them imprison base people. Also Linked Rope, Moving Camp, Celestial Prison—law restraining violence. The prison-mouth star is the gate—they wish it open. All nine bright means prisons everywhere are overburdened. Seven visible brings minor amnesty; five visible brings major amnesty. Motion brings executions; hollowness within changes the reign era. The Han Treatise records fifteen stars. Nine Celestial Record stars east of Girdle Rope are the Nine Ministers. Nine Rivers records all affairs and settles lawsuits. Brightness brings lawsuits; vanishing ruins order; scattering brings quakes. Three Weaving Maid stars at Celestial Record's east govern produce, silk, and treasures. Ultimate filial piety makes Weaving Maid bright and the realm peaceful. An angry-horned great star makes cloth and silk costly. Four eastern-foot stars are Gradual Terrace by the water. It governs gnomon, clepsydra, and pitch pipes. Five western Carriage Way stars are the emperor's pleasure route, imaging Han's north-south palace road.

左右角間二星曰平道之官。平道西一星曰進賢，主卿相舉逸才。角北二星曰天田。亢北六星曰亢池。亢，舟航也；池，水也。主送往迎來。氐北一星曰天乳，主甘露。房中道一星曰歲，守之，陰陽平。房西二星南北列，曰天福，主乘輿之官，若《禮》巾車、公車之政。主祠事。東咸、西咸各四星，在房、心北，日月五星之道也。房之戶，所以防淫佚也。星明則吉，暗則凶。月、五星犯守之，有陰謀。東咸西三星，南北列，曰罰星，主受金贖。鍵閉一星，在房東北，近鉤鈐，主關鑰。

Two stars between the Horns are Level Way officials. West of Level Way is Advance the Worthy, recommending talent. Two stars north of the Horn are Celestial Field. Six Kang Pool stars lie north of Kang. Kang means boats; Pool means water. It governs departures and welcomes. North of Di is Celestial Milk, governing sweet dew. A Heart corridor star is Jupiter; lodging there balances yin and yang. Two stars west of Heart are Celestial Blessing, chariot offices of the Rites. It governs sacrifices. Four Eastern and four Western Salt stars north of Heart and Fang mark the luminaries' path. Fang's door guards against licentiousness. Bright stars are lucky; dim stars unlucky. Moon or five planets striking there bring secret plots. Three Penalty stars west of Eastern Salt govern gold ransom. Key and Lock northeast of Fang near Gouqian guards locks.

天市垣二十二星，在房心東北，主權衡，主聚眾。一曰天旗庭，主斬戮之事也。市中星眾潤澤則歲實，星稀則歲虛。熒惑守之，戮不忠之臣。又曰，若怒角守之，戮者臣殺主。慧星除之，為徙市易都。客星入之，兵大起，出之有貴喪。市中六星臨箕，曰市樓市府也，主市價律度。其陽為金錢，其陰為珠玉。變見，各以所主占之。北四星曰天斛，主量者也。斛西北二星曰列肆，主寶玉之貨。市門左星內二星曰車肆，主眾賈之區。

Twenty-two Celestial Market stars northeast of Heart and Fang govern scales and crowds. Also the Banner Court governing executions. Many moist market stars mean rich harvests; sparse stars mean poor ones. Mars lodging there executes disloyal ministers. Also: angry horned Mars there means ministers kill the sovereign. A comet clearing it moves the market and changes the capital. Guest star entry brings war; exit brings noble death. Six Market Tower stars by Ji govern prices and market law. Yang side is coin; yin side gems. Changes are read by each star's domain. Four northern Celestial Dipper stars govern measuring. Two Ranked Shop stars northwest govern jade goods. Inside the left gate are Chariot Market stars for many traders.

帝坐一星，在天市中，候星西，天庭也。光而潤則天子吉，威令行。微小凶，大人當之。侯一星，在帝坐東北，主伺陰陽也。明大輔臣強，四夷開。候細微則國安，亡則主失位，移則主不安。宦者四星，在帝坐西南，侍主刑餘之人也。星微則吉，明則凶，非其常，宦者有憂。斗五星，在宦者南，主平量。仰則天下斗斛不平，覆則歲穰。宗正二星，在帝坐東南，宗大夫也。慧星守之，若失色，宗正有事。客星守動，則天子親屬有變。客星守之，貴人死。宗星二，在候星東，宗室之象，帝輔血脈之臣也。客星守之，宗人不和。東北二星曰帛度，東北二星曰屠肆，各主其事。

Imperial Seat in the market west of Observer Star is the celestial court. Bright and moist means the emperor thrives and orders run. Slight fading is ill-omen for great men. Observer Star northeast watches yin and yang. Brightness and size mean strong aides and open frontiers. Faint observer means peace; vanished means lost throne; shifted means unrest. Four Eunuch stars southwest attend the mutilated. Faint eunuch stars are good; bright or abnormal ones trouble eunuchs. Five Dipper stars south of Eunuchs level measure. Upturned means uneven measures; overturned means abundance. Two Clan Director stars southeast image clan grand masters. Comet lodging or fading color troubles the clan director. Guest star motion changes imperial kin. Guest star lodging kills nobles. Two Clan Stars east of Observer image imperial blood kin. Guest star lodging brings clan discord. Silk Measure and Butcher Market stars northeast each govern their trades.

天江四星在尾北，主太陰。江星不具，天下津河關道不通。明若動搖，大水出，大兵起。參差則馬貴。熒惑守之，有立王。客星入之。河津絕。

Four Celestial River stars north of Tail govern the Great Yin. Incomplete river stars block rivers and passes. Bright motion brings floods and war. Uneven stars make horses costly. Mars lodging installs a king. If a guest star enters, river crossings are severed.

天籥八星，在南斗杓西，主關閉。建星六星，在南斗北，亦曰天旗，天之都關也。為謀事，為天鼓，為天馬。南二星，天庫也。中央二星，市也，鈇钅質也。上二星，旗跗也。斗建之間，三光道也。星動則人勞。月暈之，蛟龍見，牛馬疫。月、五星犯之，大臣相譖，臣謀主；亦為關梁不通，有大水。東南四星曰狗國，主鮮卑、烏丸、沃且。熒惑守之，外夷為變。太白逆守之，其國亂。客星犯守之，有大盜，其王且來。狗國北二星曰天雞，主候時。天弁九星在建星北，市官之長也。主列肆圜闠，若市籍之事，以知市珍也。星欲明，吉。慧星犯守之，糴貴，囚徒起兵。

Eight Celestial Key stars west of the Dipper handle govern closing. Six Establishment stars north of the Dipper are Heaven's capital pass. They govern planning, the Celestial Drum, and Celestial Horse. Southern pair is Celestial Storehouse. Central pair is market and axe-mace. Upper pair is banner base. Between Dipper markers lies the luminaries' path. Star motion means popular toil. Lunar halos bring dragons and livestock plague. Moon or five planets striking bring slander and regicide plots; also blocked passes and great floods. Four Dog Country stars govern Xianbei, Wuhuan, and Woju. Mars lodging changes outer tribes. Retrograde Venus lodging brings that state's chaos. Guest star strike brings bandits and the king's arrival. Two Celestial Cock stars north observe time. Nine Celestial Cap stars north head market officers. It governs shops, market lanes, registers, and market goods. Stars should shine bright for luck. Comet strike makes grain costly and convicts rebel.

河鼓三星，旗九星，在牽牛北，天鼓也，主軍鼓，主鈇钅質。一曰三武，主天子三將軍。中央大星為大將軍，左星為左將軍，右星為右將軍。左星，南星也，所以備關梁而距難也，設守阻險，知謀徵也。旗即天鼓之旗，所以為旌表也。左旗九星，在鼓左旁。鼓欲正直而明，色黃光澤，將吉；不正，為兵憂也。星怒馬貴，動則兵起，曲則將失計奪勢。旗星戾，亂相陵。旗端四星南北列，曰天桴。桴，鼓桴也。星不明，漏刻失時。前近河鼓，若桴鼓相直，皆為桴鼓用。

Three River Drum and nine Banner stars north of Ox govern war drums and arms. Also Three Warriors for the emperor's three generals. Center is Grand General; left Left General; right Right General. The southern left star guards passes, holds defiles, and reads omens. The banner is River Drum's standard. Nine Left Banner stars sit left of the drum. Straight bright yellow drums mean lucky generals; crooked drums mean military trouble. Angry stars raise horse prices; motion brings war; bending loses the general's plan. Skewed banners bring chaos and oppression. Four tip stars north-south are Celestial Drumstick. Fu is the drumstick. Dim stars mean clepsydra error. Aligned drumstick and drum near River Drum mean they are deployed.

離珠五星，在須女北，須女之藏府也，女子之星也。星非故，後宮亂。客星犯之，後宮凶。虛北二星曰司命，北二星曰司祿，又北二星曰司危，又北二星曰司非。司命主舉過行罰，滅不祥。司祿增年延德，故在六宗北。犯司危，主驕佚亡下。司非以法多就私。瓠瓜五星，在離珠北，主陰謀，主後宮，主果食。明則歲熟，微則歲惡，后失勢。非其故，則山搖，谷多水。旁五星曰敗瓜，主種。天津九星，梁，所以度神通四方也。一星不備，津關道不通。星明動則兵起如流沙，死人亂麻。微而參差，則馬貴若死。星亡，若從河水為害，或曰水賊稱王也。東近河邊七星曰車府，主車之官也。車府東南五星曰人星，主靜眾庶，柔遠能邇。一曰臥星，主防淫。其南三星內析，東南四星曰杵臼，主給軍糧。客星入之，兵起，天下聚米。天津北四星如衡狀，曰奚仲，古車正也。

Five Separated Pearls north of Xunu are women's stars in Xunu's storehouse. Abnormal stars disorder the inner palace. Guest star strike harms the inner palace. North of Void: Director of Fate, Emolument, Peril, and Wrong pairs. Director of Fate reports faults, punishes, and removes bad omens. Director of Emolument extends years and virtue, north of the Six Ancestors. Hitting Director of Peril brings arrogant rulers and ruined subjects. Director of Wrong bends law to private ends. Five Gourd stars north govern plots, the inner palace, and fruit. Bright Gourd means good harvest; faint means bad harvest and empress wanes. Abnormal Gourd shakes mountains and floods valleys. Five Failed Gourd stars govern planting. Nine Celestial Ford stars are a beam spanning the four quarters. One missing star blocks ferry passes. Bright motion brings war like sand and corpses like hemp. Faint uneven stars mean costly or dying horses. Vanished stars bring river disaster or river kings. Seven Chariot Office stars by the river govern chariots. Five Human stars southeast calm people and cherish near and far. Also Reclining Star guarding against lust. Split southern three and southeast four Mortar-Pestle stars supply army grain. Guest star entry brings war and grain hoarding. Four balance-shaped stars north are Xi Zhong, ancient chariot master.

騰虵二十二星，在營室北，天蛇星主水蟲。星明則不安，客星守之，水雨為災，水物不收。王良五星，在奎北，居河中，天子奉車御官也。其四星曰天駟，旁一星曰王良，亦曰天馬。其星動，為策馬，車騎滿野。亦曰王良梁，為天橋，主御風雨水道，故或占津梁。其星移，有兵，亦曰馬病。客星守之，橋不通。前一星曰策，王良之御策也，主天子僕，在王良旁。若移在馬後，是謂策馬，則車騎滿野。閣道六星，在王良前，飛道也。從紫宮至河，神所乘也。一曰閣道，主道裡，天子游別宮之道也。亦曰閣道，所以捍難滅咎也。一曰王良旗，一曰紫宮旗，亦所以為旌表，而不欲其動搖。旗星者，兵所用也。傅路一星，在閣道南，旁別道也。備閣道之敗，複而乘之也。一曰太僕，主御風雨，亦遊從之義也。東壁北十星曰天廄，主馬之官，若今驛亭也，主傳令置驛，逐漏馳騖，謂其行急疾，與晷漏競馳。

Twenty-two Soaring Serpent stars north govern water creatures. Brightness brings unrest; guest star lodging brings flood disaster and lost aquatic harvest. Five Wang Liang stars in the river north of Kui are the imperial chariot master. Four are Celestial Team; beside one is Wang Liang or Celestial Horse. Motion whips horses and fills fields with riders. Also Wang Liang Bridge governing wind, rain, and crossings. Shifting stars bring war or horse plague. Guest star lodging blocks the bridge. Ahead is Whip, Wang Liang's riding crop for the emperor's servant. Shifted behind the horse it whips horses and fills the plain with riders. Six Gallery Road stars before Wang Liang are the flying path. From Purple Palace to river where gods travel. Also governs roads and pleasure routes to detached palaces. Also wards danger and removes fault. Also Wang Liang or Purple Palace Banner standards that should not waver. Banner stars serve armies. Auxiliary Road south is a side path. Guards Gallery Road failure to return and ride again. Also Grand Coachman governing wind, rain, and travel escort. Ten Celestial Stable stars north of Eastern Wall govern post horses racing time.

天將軍十二星，在婁北，主武兵。中央大星，天之大將也。外小星，吏士也。大將星搖，兵起，大將出。小星不具，兵發。南一星曰軍南門，主誰何出入。太陵八星，在胃北。陵者，墓也。太陵捲舌之口曰積京，主大喪也。積京中星絕，則諸侯有喪，民多疾，兵起，粟聚。少則粟散。星守之，有土功。太陵中一星曰積屍，明則死人如山。天船九星，在太陵北，居河中。一曰舟星，主度，所以濟不通也，亦主水旱。不在漢中，津河不通。中四星欲其均明，即天下大安。不則兵若喪。客彗星出入之，為大水，有兵。中一星曰積水，候水災。昴西二星曰天街，三光之道，主伺候關梁中外之境。天街西一星曰月。捲舌六星在北，主口語，以知佞讒也。曲者吉，直而動，天下有口舌之害。中一星曰天讒，主巫醫。

Twelve Heavenly General stars north of Lou govern war. The central great star is Heaven's commander. Outer small stars are officers and troops. Wavering great general star brings war and the general's emergence. Incomplete small stars mobilize armies. Southern Army South Gate star challenges traffic. Eight Great Mound stars north of Stomach. Ling means tomb. Curled Tongue mouth of Great Mound is Accumulated Capital, governing great mourning. Cut Accumulated Capital stars bring lordly mourning, sickness, war, and grain hoarding. Few stars scatter grain. Lodging stars bring earthworks. Accumulated Corpses within Great Mound bright means dead like mountains. Nine Celestial Boat stars in the river north of Great Mound. Also Boat Star for crossing blocked waters and flood-drought. Outside Han River region, rivers block. Four even bright central stars mean realm at peace. Otherwise war or mourning. Guest comets bring flood and war. Central Accumulated Water watches floods. Two Celestial Street stars west of Mao watch borders and the luminaries' path. West of Celestial Street is Moon star. Six Curled Tongue stars north govern speech and detect slander. Curved is lucky; straight moving brings scandal. Central Celestial Slander governs shamans and doctors.

五車五星，三柱九星，在畢北。五車者，五帝車舍也，五帝坐也，主天子五兵，一曰主五穀豐耗。西北大星曰天庫，主太白，主秦。次東北星曰獄，主辰星，主燕、趙。次東星曰天倉，主歲星，主魯、衛。次東南星曰司空，主填星，主楚。次西南星曰卿星，主熒惑，主魏。五星有變，皆以其所主而占之。三柱，一曰三泉，一曰休，一曰旗。五車星欲均明，闊狹有常也。天子得靈臺之禮，則五車、三柱均明。中有五星曰天潢。天潢南三星曰咸池，魚囿也。月、五星入天潢，兵起，道不通，天下亂，易政。咸池明，有龍墮死，猛獸及狼害人，若兵起。

Five Chariots and nine Three Pillars north of Net. Five Chariots are Five Emperors' lodges governing the emperor's five arms and grain harvests. Northwest great star Celestial Storehouse governs Venus and Qin. Next northeast Prison governs Mercury, Yan, and Zhao. Next east Celestial Granary governs Jupiter, Lu, and Wei. Next southeast Minister of Works governs Saturn and Chu. Next southwest Minister Star governs Mars and Wei. Five planet changes are read by their domains. Three Pillars also Three Springs, Rest, and Banner. Five Chariots should shine evenly with constant spacing. Spirit Terrace rites make Five Chariots and Three Pillars evenly bright. Within are five Celestial Ford stars. Three Salty Pool stars south are the fish preserve. Moon or planets entering Celestial Ford bring war, blocked roads, chaos, and regime change. Bright Salty Pool kills dragons, beasts harm people, like war.

五車南六星曰諸王，察諸侯存亡。西五星曰厲石，金若客星守之，兵動。北八星曰八穀，主候歲。八穀一星亡，一穀不登。天關一星，在五車南，亦曰天門，日月所行也，主邊事，主開閉。芒角，有兵。五星守之，貴人多死。

Six Various Princes stars south watch lords' fate. Five Sharp Stone stars west—metal or guest star brings armies. Eight Grains stars north watch the harvest. One vanished grain star fails one crop. Celestial Pass south governs frontiers, sun-moon path, and gates. Rays and horns mean war. Five planets lodging kill many nobles.

東井鉞前四星曰司怪，主候天地日月星辰變異，及鳥獸草木之妖，明主聞災，修德保福也。司怪西北九星曰坐旗，君臣設位之表也。坐旗西四星曰天高，臺榭之高，主遠望氣象。天高西一星曰天河，主察山林妖變。南河、北河各三星，夾東井。一曰天高天之闕門，主關梁。南河曰南戍，一曰南宮，一曰陽門，一曰越門，一曰權星，主火。北河一曰北戍，一曰北宮，一曰陰門，一曰胡門，一曰衡星，主水。兩河戍間，日月五星之常道也。河戍動搖，中國兵起。南河三星曰闕丘，主宮門外象魏也。五諸侯五星，在東井北，主刺舉，戒不虞。又曰理陰陽，察得失。亦曰主帝心。一曰帝師，二曰帝友，三曰三公，四曰博士，五曰太史。此五者常為帝定疑議。星明大潤澤，則天下大治，角則禍在中。五諸侯南三星曰天樽，主盛饘粥，以給酒食之正也。積薪一星，在積水東，供給庖廚之正也。水位四星，在東井東，主水衡。客星若水火守犯之，百川流溢。

Director of Omens before Well's axe watches cosmic and natural omens for virtuous rulers. Nine Seated Banner stars northwest model court ranks. Four Heavenly Height stars west oversee distant weather signs. Celestial River west watches mountain-forest omens. Three Southern and three Northern River stars flank Eastern Well. Also Heaven's gate tower governing passes. Southern River is Southern Garrison, Yang Gate, Power Star—fire. Northern River is Northern Garrison, Yin Gate, Balance Star—water. Between the rivers is the luminaries' regular path. Wavering river garrisons raise war in China. Three Gate Mound stars are the palace gate watchtower. Five Feudal Lords north of Well impeach and guard surprises. Also regulates yin-yang and weighs right and wrong. Also governs the emperor's mind. First Imperial Teacher, second Friend, third Three Dukes, fourth Erudite, fifth Historian. These five settle the emperor's doubts. Bright large stars mean great order; horns mean inner calamity. Three Celestial Goblet stars south supply proper food and drink. Accumulated Firewood east of Accumulated Water feeds the kitchen. Four Water Level stars east of Well govern water balance. Guest star or water-fire strike makes streams overflow.

軒轅十七星，在七星北。軒轅，黃帝之神，黃龍之體也。後妃之主，士職也。一曰東陵，一曰權星，主雷雨之神。南大星，女主也。次北一星，妃也。次，將軍也。其次諸星，皆次妃之屬也。女主南小星，女御也。左一星少民，少後宗也。右一星大民，太后宗也。欲其色黃小而明也。軒轅右角南三星曰酒旗，酒官之旗也，主饗宴飲食。五星守酒旗，天下大酺，有酒肉財物，賜若爵宗室。酒旗南二星曰天相，丞相之象也。軒轅西四星曰爟，爟者烽火之爟也，邊亭之警候。

Seventeen Xuanyuan stars north of Seven Stars. Xuanyuan is Yellow Emperor's god, the yellow dragon's body. Mistress of empresses; scholars' office. Also Eastern Mound and Power Star, thunder-rain god. The great southern star is empress. Next north is consort. Next is general. Lower stars are subordinate consorts. Empress's southern small star is Female Attendant. Left Lesser People star is lesser empress clan. Right Greater People star is dowager clan. They should appear yellow, small, and bright. Three Wine Banner stars south govern feasts. Five planets at Wine Banner bring realm-wide feasts and imperial gifts. Two Celestial Minister stars south image the Chancellor. Four Signal Fire stars west are frontier beacon warnings.

爟北四星曰內平。少微四星，在太微西，士大夫之位也。一名處士，亦天子副主，或曰博士官。一曰主衛掖門。南第一星處士，第二星議士，第三星博士，第四星大夫。明大而黃，則賢士舉也。月、五星犯守之，處士、女主憂，宰相易。南四星曰長垣，主界域及胡夷。熒惑入之，胡入中國。太白入之，九卿謀。

Four Inner Peace stars north judge crimes. Four Lesser Supreme stars west are scholar-officials' seats. Also Recluse Scholar, deputy ruler, or erudites. Also guards side gates. South: Recluse, Counselor, Erudite, Grand Master. Bright yellow stars raise worthy men. Moon or five planets there trouble recluses and empress and change the Chancellor. Four Long Wall stars south govern borders and barbarians. Mars entering brings Hu into China. Venus entering makes Nine Ministers plot.

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