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天文一
Treatise on Astronomy, Part One.
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自司馬遷述《天官》，而歷代作史者皆志天文。 惟《遼史》獨否，謂天象昭垂，千古如一，日食、天變既著本紀，則天文志近於衍。 其說頗當。 夫《周髀》、《宣夜》之書，安天、窮天、昕天之論，以及星官占驗之說，晉史已詳，又見《隋志》，謂非衍可乎。 論者謂天文志首推晉、隋，尚有此病，其他可知矣。 然因此遂廢天文不志，亦非也。 天象雖無古今之異，而談天之家，測天之器，往往後勝於前。 無以志之，使一代製作之義泯焉無傳，是亦史法之缺漏也。 至於彗孛飛流，暈適背抱，天之所以示儆戒者，本紀中不可盡載，安得不別志之。 明神宗時，西洋人利瑪竇等入中國，精於天文、歷算之學，發微闡奧，運算制器，前此未嘗有也。 茲掇其要，論著於篇。 而《實錄》所載天象星變殆不勝書，擇其尤異者存之。 日食備載本紀，故不復書。
Ever since Sima Qian set forth the 'Heavenly Offices' in the Records, successive dynastic histories have included a treatise on astronomy. The History of Liao alone demurred, arguing that the heavens display the same omens age after age and that, since solar eclipses and celestial anomalies already appear in the annals, a separate astronomy treatise verged on redundancy. That objection has considerable force. Yet the Zhou Bi and Xuan Ye texts, debates over whether heaven is at rest or exhaustible, methods of inspecting the sky, and the whole literature of star-offices and omen verification were already treated at length in the Jin History and repeated in the Sui bibliographic monographs—are those to be dismissed as mere padding? Critics observe that even the astronomy treatises of the Jin and Sui histories—often held up as the best—suffer this flaw; lesser compilations need hardly be mentioned. Still, to abandon the astronomy treatise altogether on that account would itself be mistaken. The visible heavens may not change from age to age, but theories of the cosmos and the instruments used to measure it frequently improve with time. If nothing is recorded, an entire generation's observational and computational achievements may vanish without trace—a real breach of historiographic duty. Comets, meteors, halos, occultations, and mutual embraces—the heavens' warnings—cannot all be crowded into the annals; they must have a separate treatise. Under the Wanli emperor, Western scholars such as Matteo Ricci arrived in China versed in astronomy and calendrics, opening subtle doctrines, explaining recondite principles, and devising computational methods and instruments unlike anything known before. What follows selects their chief points and sets them out in this chapter. The Veritable Records alone contain more celestial and stellar anomalies than could be listed; only the most remarkable are retained here. Solar eclipses already appear in full in the annals and are not repeated here.
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▲兩儀《楚詞》言「圜則九重，孰營度之」，渾天家言「天包地如卵裡黃」，則天有九重，地為渾圓，古人已言之矣。 西洋之說，既不背於古，而有驗於天，故表出之。
▲ Heaven and Earth The Songs of Chu ask, 'Round and ninefold—who measured it?' Armillary cosmologists said, 'Heaven enfolds the earth as the yolk lies in an egg'—nine celestial tiers and a spherical earth were already ancient ideas. The Western account neither contradicts the ancients nor fails when tested against the sky; it is therefore set forth here.
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其言九重天也，曰最上為宗動天，無星辰，每日帶各重天，自東而西左旋一周，次曰列宿天，次曰填星天，次曰歲星天，次曰熒惑天，次曰太陽天，次曰金星天，次曰水星天，最下曰太陰天。 自恆星天以下八重天，皆隨宗動天左旋。 然各天皆有右旋之度，自西而東，與蟻行磨上之喻相符。 其右旋之度，雖與古有增減，然無大異。 惟恆星之行，即古歲差之度。 古謂恆星千古不移，而黃道之節氣每歲西退。 彼則謂黃道終古不動，而恆星每歲東行。 由今考之，恆星實有動移，其說不謬。 至於分周天為三百六十度，命日為九十六刻，使每時得八刻無奇零，以之布算制器，甚便也。
On the nine celestial spheres: the highest is the primum mobile, bearing no stars; each day it drags every lower sphere in one westward (apparent) rotation; below it lie, in order, the sphere of fixed stars (xiu), Saturn, Jupiter, Mars, the Sun, Venus, Mercury, and at the bottom the Moon. All eight spheres below the primum mobile—including the sphere of fixed stars—share its daily westward motion. Each sphere also has its own eastward (prograde) motion, west to east—the familiar image of an ant crawling on a turning millstone. Those prograde rates differ slightly from ancient figures but not materially. The apparent drift of the fixed stars is precisely what the ancients called precession. Older Chinese astronomy held the fixed stars eternally unmoved while the solar terms along the ecliptic slipped westward year by year. The Western school holds the ecliptic fixed and the fixed stars advancing eastward annually. Modern observation confirms that the fixed stars do shift; the Western account is sound. They also divide the celestial circle into 360 degrees and the day into 96 ke (quarter-hours), so each of the twelve double-hours contains exactly eight ke without fractional scraps—a great convenience for calculation and instrument design.
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其言地圓也，曰地居天中，其體渾圓，與天度相應。 中國當赤道之北，故北極常現，南極常隱。 南行二百五十里則北極低一度，北行二百五十里則北極高一度。 東西亦然。 亦二百五十里差一度也。 以周天度計之，知地之全周為九萬里也。 以周徑密率求之，得地之全徑為二萬八千六百四十七里又九分裡之八也。 又以南北緯度定天下之縱。 凡北極出地之度同，則四時寒暑靡不同。 若南極出地之度與北極出地之度同，則其晝夜永短靡不同。 惟時令相反，此之春，彼為秋，此之夏，彼為冬耳。 以東西經度定天下之衡，兩地經度相去三十度，則時刻差一辰。 若相距一百八十度，則晝夜相反焉。 其說與《元史》札馬魯丁地圓之旨略同。
On the earth's form: it rests at the center of the heavens, a sphere whose dimensions match celestial degrees. China stands north of the equator, so the north celestial pole is always above the horizon and the south pole always below. Travel two hundred fifty li south and the north pole sinks one degree; travel two hundred fifty li north and it rises one degree. The same principle governs east–west motion. Again, one degree corresponds to two hundred fifty li on the ground. From the 360 degrees of the celestial circle one derives the earth's full circumference: ninety thousand li. Applying the precise ratio of circumference to diameter yields a terrestrial diameter of 28,647 li and eight-ninths of a li. North–south latitude fixes the north–south span of the world. Places sharing the same polar altitude experience the same seasons and climate. Where the south pole rises as far above the horizon as the north pole does in the northern hemisphere, day and night lengths match those latitudes in the north. Only the seasons are reversed—spring here is autumn there, summer here winter there. East–west longitude fixes the world's lateral extent: a difference of thirty degrees in longitude equals one double-hour (chen) in local time. At one hundred eighty degrees apart, day and night are reversed. This doctrine broadly agrees with Jamal al-Din's spherical-earth theory recorded in the History of Yuan.
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▲七政日月五星各有一重天，其天皆不與地同心，故其距地有高卑之不同。 其最高最卑之數，皆以地半徑准之。 太陽最高距地為地半徑者一千一百八十二，最卑一千一百零二。 太陰最高五十八，最卑五十二。 填星最高一萬二千九百三十二，最卑九千一百七十五。 歲星最高六千一百九十，最卑五千九百一十九。 熒惑最高二千九百九十八，最卑二百二十二。 太白最高一千九百八十五，最卑三百。 辰星最高一千六百五十九，最卑六百二十五。 若欲得七政去地之裡數，則以地半徑一萬二千三百二十四里通之。
▲ The Seven Luminaries The sun, moon, and five planets each occupy its own sphere; none is centered on the earth, so their distances vary. Maximum and minimum distances are all expressed in units of the earth's radius. The sun's greatest distance is 1,182 earth radii, its least 1,102. The moon's greatest distance is 58 earth radii, its least 52. Saturn's greatest distance is 12,932 earth radii, its least 9,175. Jupiter's greatest distance is 6,190 earth radii, its least 5,919. Mars's greatest distance is 2,998 earth radii, its least 222. Venus's greatest distance is 1,985 earth radii, its least 300. Mercury's greatest distance is 1,659 earth radii, its least 625. To convert these figures into li from the earth's surface, multiply by the terrestrial radius of 12,324 li.
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又謂填星形如瓜，兩側有兩小星如耳。 歲星四周有四小星，繞行甚疾。 太白光有盈缺，如月之弦望。 用窺遠鏡視之，皆可悉睹也。 余詳《歷志》。
They also report Saturn shaped like a gourd, flanked by two small stars like ears. Four small stars circle Jupiter rapidly on all sides. Venus shows phases like the moon—from thin crescent to full disk. Viewed through the telescope, all these features can be seen clearly. Further particulars appear in the Treatise on the Calendar.
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▲恆星崇禎初，禮部尚書徐光啟督修曆法，上《見界總星圖》。 以為回回《立成》所載，有黃道經緯度者止二百七十八星，其繪圖者止十七座九十四星，並無赤道經緯。 今皆崇禎元年所測，黃赤二道經緯度畢具。 後又上《赤道兩總星圖》。 其說謂常現常隱之界，隨北極高下而殊，圖不能限。 且天度近極則漸狹，而《見界圖》從赤道以南，其度反寬，所繪星座不合仰觀。 因從赤道中剖渾天為二，一以北極為心，一以南極為心。 從心至周，皆九十度，合之得一百八十度者，赤道緯度也。 周分三百六十度者，赤道經度也。 乃依各星之經緯點之，遠近位置形勢皆合天象。
▲ Fixed Stars Early in the Chongzhen reign, Xu Guangqi, minister of rites, oversaw calendar reform and presented the General Star Map of the Visible Horizon. He noted that the Islamic Licheng tables listed ecliptic coordinates for only 278 stars and illustrated only 17 asterisms (94 stars), with no equatorial coordinates whatsoever. The present survey, completed in Chongzhen 1, supplies both ecliptic and equatorial coordinates throughout. He later submitted the Two General Star Maps of the Equator. He argued that the always-visible and always-hidden zones shift with the observer's latitude and cannot be fixed on a single chart. Moreover, degrees crowd narrower near the poles, yet south of the equator the Visible-Horizon Map spreads them wider—so its constellations do not match what one sees overhead. He therefore split the celestial globe at the equator into two charts, one centered on the north pole and one on the south. From each pole to the circumference is ninety degrees; the two hemispheres together make 180 degrees of equatorial latitude. The full 360 degrees around the circumference is equatorial longitude. Stars were plotted at their coordinate points so that distance, placement, and configuration all matched the sky.
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至於恆星循黃道右旋，惟黃道緯度無古今之異，而赤道經緯則歲歲不同。 然亦有黃赤俱差，甚至前後易次者。 如觜宿距星，唐測在參前三度，元測在參前五分，今測已侵入參宿。 故舊法先觜後參，今不得不先參後觜，不可強也。
Fixed stars drift eastward along the ecliptic; ecliptic latitude is unchanged from antiquity, but equatorial coordinates shift annually. Sometimes both ecliptic and equatorial coordinates shift enough to reverse the order of neighboring asterisms. The determining star of Zi xiu (Turtle Beak): Tang observers placed it 3° ahead of Shen (Three Stars); Yuan observers 5 fen ahead; the present survey finds it inside Shen. Older tables listed Zi before Shen; today Shen must precede Zi—no convention can override observation.
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又有古多今少，古有今無者。 如紫微垣中六甲六星今止有一，華蓋十六星今止有四，傳捨九星今五，天廚六星今五，天牢六星今二。 又如天理、四勢、五帝內座、天柱、天床、大贊府、大理、女御、內廚，皆全無也。 天市垣之市樓六星今二。 太微垣之常陳七星今三，郎位十五星今十。 長垣四星今二。 五諸侯五星全無也。 角宿中之庫樓十星今八。 亢宿中之折威七星今無。 氐宿中之亢池六星今四，帝席三星今無。 尾宿中天龜五星今四。 斗宿中之鱉十四星今十三，天籥、農丈人俱無。 牛宿中之羅堰三星今二，天田九星俱無。 女宿中之趙、周、秦、代各二星今各一，扶匡七星今四，離珠五星今無。 虛宿中之司危、司祿各二星今各一，敗臼四星今二，離瑜三星今二，天壘城十三星今五。 危宿中之人五星今三，杵三星今一，臼四星今三，車府七星今五，天鉤九星今六，天鈔十星今四，蓋屋二星今一。 室宿中之羽林軍四十五星今二十六，螣蛇二十二星今十五，八魁九星今無。 壁宿中之天廄十星今三。 奎宿中之天溷七星今四。 畢宿中之天節八星今七，鹹池三星今無。 觜宿中之座旗九星今五。 井宿中之軍井十三星今五。 鬼宿中之外廚六星今五。 張宿中之天廟十四星今無。 翼宿中之東甌五星今無。 軫宿中之青丘七星今三，其軍門、土司空、器府俱無也。
Some asterisms counted more stars in antiquity than now; others recorded then have vanished. In the Purple Forbidden Enclosure, for instance: the six Jia stars are now one; Canopy (Huagai), 16 stars now 4; Relay Lodges (Chuanshe), 9 now 5; Celestial Kitchen (Tianchu), 6 now 5; Celestial Prison (Tianlao), 6 now 2. Heavenly Principle, Four Supports, Five Emperors Inner Seat, Celestial Pillar, Celestial Bed, Great Praise Office, Great Adjudication, Female Attendants, and Inner Kitchen—entirely gone. In the Heavenly Market Enclosure, Market Tower: 6 stars anciently, 2 today. In the Supreme Palace Enclosure, Regular Array: 7 stars now 3; Court Gentlemen (Langwei): 15 now 10. Long Wall: 4 stars anciently, 2 today. Five Feudal Lords: all 5 stars absent. In Jiao xiu (Horn), Treasury Tower: 10 stars anciently, 8 today. In Kang xiu (Gullet), Broken Halberd (Zhewei): 7 stars anciently, none today. In Di xiu (Root), Gullet Pool (Kangchi): 6 now 4; Emperor's Banquet (Dixi): 3 stars gone. In Wei xiu (Tail), Heavenly Tortoise: 5 stars anciently, 4 today. In Dou xiu (Dipper), Turtle (Bie): 14 stars now 13; Celestial Key (Tianyue) and Agricultural Overseer (Nongzhangren) absent. In Niu xiu (Ox), Net Weir (Luoyan): 3 stars now 2; Celestial Field (Tiantian): all 9 gone. In Nü xiu (Girl), Zhao, Zhou, Qin, and Dai: 2 stars each anciently, 1 each now; Supporting Frame (Fukuang): 7 now 4; Detached Pearls (Lizhu): 5 stars gone. In Xu xiu (Emptiness), Director of Peril (Siwei) and Director of Salary (Silu): 2 each now 1; Broken Mortar (Baijiu): 4 now 2; Separated Luster (Liyu): 3 now 2; Heavenly Rampart (Tianleicheng): 13 now 5. In Wei xiu (Rooftop), Man: 5 stars now 3; Pestle (Chu): 3 now 1; Mortar (Jiu): 4 now 3; Chariot Office (Chef): 7 now 5; Heavenly Hook (Tiangou): 9 now 6; Heavenly Ladle (Tianchao): 10 now 4; Canopy House (Gaiwu): 2 now 1. In Shi xiu (Encampment), Feathered Forest Army (Yulinjun): 45 stars now 26; Flying Serpent (Tengshe): 22 now 15; Eight Chiefs (Bakui): 9 stars gone. In Bi xiu (Wall), Celestial Stables (Tianma): 10 stars anciently, 3 today. In Kui xiu (Strider), Heavenly Mire (Tianhun): 7 stars now 4. In Bi xiu (Net), Heavenly Knot (Tianjie): 8 now 7; Salt Pool (Xianchi): 3 stars gone. In Zi xiu (Turtle Beak), Seat Banner (Zuozi): 9 stars now 5. In Jing xiu (Well), Army Well (Junjing): 13 stars now 5. In Gui xiu (Ghost), Outer Kitchen (Waiyu): 6 stars now 5. In Zhang xiu (Extended Net), Heavenly Temple (Tianmiao): 14 stars gone. In Yi xiu (Wings), Eastern Ou (Dong'ou): 5 stars gone. In Zhen xiu (Chariot), Green Mound (Qingqiu): 7 stars now 3; Army Gate, Earth Director, and Arsenal Office—all absent.
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又有古無今有者。 策星旁有客星，萬歷元年新出，先大今小。 南極諸星，古所未有，近年浮海之人至赤道以南，往往見之，因測其經緯度。 其余增入之星甚多，並詳《恆星表》。
Conversely, some stars appear now that antiquity did not record. Beside the Whip (Ce) star a guest star appeared in Wanli 1—bright at first, now faint. Stars around the south celestial pole were unknown to the ancients; mariners crossing the equator in recent years have sighted them, and their coordinates have been measured. Many further stars have been added; see the Fixed-Star Tables for particulars.
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其論雲漢，起尾宿，分兩派。 一經天江、南海、市樓，過宗人、宗星，涉天津至螣蛇。 一由箕、斗、天弁、河鼓、左右旗，涉天津至車府而會於螣蛇，過造父，直趨附路、閣道、大陵、天船，漸下而南行，歷五車、天關、司怪、水府，傍東井，入四瀆，過闕丘、弧矢、天狗之墟，抵天社、海石之南，逾南船，帶海山，置十字架、蜜蜂，傍馬腹，經南門，絡三角、龜、杵，而屬於尾宿，是為帶天一周。 以理推之，隱界自應有雲漢，其所見當不誣。 又謂雲漢為無數小星，大陵鬼宿中積屍亦然。 考《天官書》言星漢皆金之散氣，則星漢本同類，得此可以相證。 又言昴宿有三十六星，皆得之於窺遠鏡者。
On the Milky Way: it rises at Wei xiu (Tail) and splits into two branches. One branch runs through Tianjiang (Heavenly River), Nanhai (South Sea), and Shilou (Market Tower), past Zongren (Clan Person) and Zongxing (Clan Star), crosses Tianjin, and reaches Tengshe (Flying Serpent). The second branch runs from Winnowing Basket and the Dipper through Celestial Flank, River Drum, and the Left and Right Banners, crosses Celestial Ford to Chariot Office and converges at Flying Serpent; it passes Zaofu and drives straight toward Attached Road, Cloud Path, Great Mound, and Celestial Boat, then slopes south by degrees through Five Chariots, Celestial Pass, Director of Oddities, and Water Office, skirts Eastern Well, enters the Four Streams, crosses the grounds of Que Hill, Bow and Arrow, and Celestial Dog, reaches the south of Celestial Altar and Sea Rock, crosses Southern Boat and spans Sea Mountain, sets Crux and the Beehive beside Horse's Belly, passes Southern Gate, links Triangle, Tortoise, and Pestle, and rejoins Tail lodge—completing one circuit about the sky. By reason alone, the hidden hemisphere ought to carry a Milky Way as well; what observers see should not be deceiving. They also hold that the Milky Way is made of innumerable small stars, and that the Accumulated Corpses in Ghost lodge within Great Mound are likewise so. The Treatise on the Heavenly Offices says the starry stream is scattered essence of metal; the star stream and the Milky Way belong to the same class, and the present findings confirm it. They further report thirty-six stars in Hairy Head lodge, every one revealed through the telescope.
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凡測而入表之星共一千三百四十七，微細無名者不與。 其大小分為六等：內一等十六星，二等六十七星，三等二百零七星，四等五百零三星，五等三百三十八星，六等二百一十六星。 悉具黃赤二道經緯度。 列表二卷，入光啟所修《崇禎歷書》中。
Stars measured and entered in the tables total one thousand three hundred forty-seven; faint stars without established names are omitted. By apparent size they fall into six grades: first magnitude, sixteen stars; second, sixty-seven; third, two hundred seven; fourth, five hundred three; fifth, three hundred thirty-eight; sixth, two hundred sixteen. Each is given ecliptic and equatorial longitude and latitude. The work fills two scrolls of tables, incorporated into the Chongzhen Reign Treatise on the Calendar that Xu Guangqi helped compile.
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茲取二十八宿距星及一二等大星存之，其小而有名者，間取一二，備列左方。
What follows retains the twenty-eight lodges' determinant stars and all stars of the first and second magnitude; among smaller stars that still bear names, only a sample of one or two is listed at left for reference.
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表格略
The tables are abbreviated here.
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▲黃赤宿度崇禎元年所測二十八宿黃赤度分，皆不合於古。 夫星既依黃道行，而赤道與黃道斜交，其度不能無增減者，勢也。 而黃道度亦有增減者，或推測有得失，抑恆星之行亦或各有遲速歟。 謹列其數，以備參考。
▲ Yellow and red lodge degrees: the ecliptic and equatorial degree-minutes of the twenty-eight lodges measured in the first year of the Chongzhen reign all diverge from ancient values. Since stars move along the ecliptic while the equator cuts it obliquely, their measured degrees must shift—a matter of geometry, not error alone. Ecliptic degrees likewise show increase and decrease: this may reflect mistakes in computation, or it may mean that fixed stars themselves advance at unequal rates. The figures are set out below for consultation.
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赤道宿度周天三百六十度，每度六十分。 黃道同黃道宿度角，一十一度四十四分。 一十度三十五分。 亢，九度一十九分。 一十度四十分。 氐，一十六度四十一分。 一十七度五十四分。 房，五度二十八分。 四度四十六分。 心，六度零九分。 七度三十三分。 尾，二十一度零六分。 一十五度三十六分。 箕，八度四十六分。 九度二十分。 鬥，二十四度二十四分。 二十三度五十一分。 牛，六度五十分。 七度四十一分。 女，一十一度零七分。 一十一度三十九分。 虛，八度四十一分。 九度五十九分。 危，一十四度五十三分。 二十度零七分。 室，一十七度。 一十五度四十一分。 壁，一十度二十八分。 一十三度一十六分。 奎，一十四度三十分。 一十一度二十九分。 婁，一十二度零四分。 一十三度。 胃，一十五度四十五分。 一十三度零一分。 昴，一十度二十四分。 八度二十九分。 畢，一十六度三十四分。 一十三度五十八分。 參，二十四分。 一度二十一分。 觜，一十一度二十四分。 一十一度三十三分。 井，三十二度四十九分。 三十度二十五分。 鬼，二度二十一分。 五度三十分。 柳，一十二度零四分。 一十六度零六分。 星，五度四十八分。 八度二十三分。 張，一十七度一十九分。 一十八度零四分。 翼，二十度二十八分。 一十七度。 軫，一十五度三十分。 一十三度零三分。
Equatorial lodge degrees: the full circuit of heaven is three hundred sixty degrees, each degree divided into sixty minutes. The ecliptic uses the same reckoning. Horn on the equator: eleven degrees forty-four minutes. Horn on the ecliptic: ten degrees thirty-five minutes. Neck on the equator: nine degrees nineteen minutes. Neck on the ecliptic: ten degrees forty minutes. Root on the equator: sixteen degrees forty-one minutes. Root on the ecliptic: seventeen degrees fifty-four minutes. Room on the equator: five degrees twenty-eight minutes. Room on the ecliptic: four degrees forty-six minutes. Heart on the equator: six degrees nine minutes. Heart on the ecliptic: seven degrees thirty-three minutes. Tail on the equator: twenty-one degrees six minutes. Tail on the ecliptic: fifteen degrees thirty-six minutes. Winnowing Basket on the equator: eight degrees forty-six minutes. Winnowing Basket on the ecliptic: nine degrees twenty minutes. Dipper on the equator: twenty-four degrees twenty-four minutes. Dipper on the ecliptic: twenty-three degrees fifty-one minutes. Ox on the equator: six degrees fifty minutes. Ox on the ecliptic: seven degrees forty-one minutes. Girl on the equator: eleven degrees seven minutes. Girl on the ecliptic: eleven degrees thirty-nine minutes. Void on the equator: eight degrees forty-one minutes. Void on the ecliptic: nine degrees fifty-nine minutes. Rooftop on the equator: fourteen degrees fifty-three minutes. Rooftop on the ecliptic: twenty degrees seven minutes. Encampment on the equator: seventeen degrees. Encampment on the ecliptic: fifteen degrees forty-one minutes. Wall on the equator: ten degrees twenty-eight minutes. Wall on the ecliptic: thirteen degrees sixteen minutes. Striding Legs on the equator: fourteen degrees thirty minutes. Striding Legs on the ecliptic: eleven degrees twenty-nine minutes. Bond on the equator: twelve degrees four minutes. Bond on the ecliptic: thirteen degrees. Stomach on the equator: fifteen degrees forty-five minutes. Stomach on the ecliptic: thirteen degrees one minute. Hairy Head on the equator: ten degrees twenty-four minutes. Hairy Head on the ecliptic: eight degrees twenty-nine minutes. Net on the equator: sixteen degrees thirty-four minutes. Net on the ecliptic: thirteen degrees fifty-eight minutes. Three Stars on the equator: twenty-four minutes. Three Stars on the ecliptic: one degree twenty-one minutes. Turtle Beak on the equator: eleven degrees twenty-four minutes. Turtle Beak on the ecliptic: eleven degrees thirty-three minutes. Well on the equator: thirty-two degrees forty-nine minutes. Well on the ecliptic: thirty degrees twenty-five minutes. Ghost on the equator: two degrees twenty-one minutes. Ghost on the ecliptic: five degrees thirty minutes. Willow on the equator: twelve degrees four minutes. Willow on the ecliptic: sixteen degrees six minutes. Star on the equator: five degrees forty-eight minutes. Star on the ecliptic: eight degrees twenty-three minutes. Extended Net on the equator: seventeen degrees nineteen minutes. Extended Net on the ecliptic: eighteen degrees four minutes. Wings on the equator: twenty degrees twenty-eight minutes. Wings on the ecliptic: seventeen degrees. Chariot Axle on the equator: fifteen degrees thirty minutes. Chariot Axle on the ecliptic: thirteen degrees three minutes.
18
▲黃赤宮界十二宮之名見於《爾雅》，大抵皆依星宿而定。 如婁、奎為降婁，心為大火，硃鳥七宿為鶉首、鶉尾之類。 故宮有一定之宿，宿有常居之宮，由來尚矣。 唐以後始用歲差，然亦天自為天，歲自為歲，宮與星仍舊不易。 西洋之法，以中氣過宮，如日躔冬至，即為星紀宮之類。 而恆星既有歲進之差，於是宮無定宿，而宿可以遞居各宮，此變古法之大端也。 茲以崇禎元年各宿交宮之黃赤度，分列於左方，以志權輿雲。
▲ Yellow and red palace boundaries: the twelve celestial palaces are named in the Erya, and for the most part each name is anchored to particular lodges. Bond and Striding Legs mark Lower Harvester; Heart marks Great Fire; the Vermilion Bird's seven lodges yield Quail Head, Quail Tail, and their sister palaces. Each palace therefore owned fixed lodges, and each lodge had its habitual palace—a correspondence honored since antiquity. After the Tang, astronomers acknowledged precession, yet heaven was still heaven and the year still the year; palace names and star positions were left unchanged in practice. Western method ties each palace to the middle qi that crosses it: when the sun stands at winter solstice, for example, the palace is Xingji. Because fixed stars drift year by year, palaces no longer keep permanent lodges, and lodges may migrate from palace to palace—this is the decisive departure from ancient practice. Below are listed, for the first year of the Chongzhen reign, the ecliptic and equatorial degrees at which each lodge entered its palace—marking the new starting point.
19
赤道交宮宿度黃道交宮宿度箕，三度零七分，入星紀。 箕，四度一十七分，入星紀。 鬥，二十四度二十一分，入玄枵。 牛，一度零六分，入玄枵危，三度一十九分，入娵訾。 危，一度四十七分，入娵訾。 壁，一度二十六分，入降婁。 室，一十一度四十分，入降婁。 婁，六度二十八分，入大梁。 婁，一度一十四分，入大梁。 昴，八度三十九分，入實沈。 昴，五度一十三分，入實沈。 觜，一十一度一十七分，入鶉首。 觜，一十一度二十五分，入鶉首。 井，二十九度五十三分，入鶉火。 井，二十九度五十二分，入鶉火。 張，六度五十一分，入鶉尾。 星，七度五十一分，入鶉尾。 翼，一十九度三十二分，入壽星。 翼，一十一度二十四分，入壽星。 亢，一度五十分，入大火。 亢，初度四十六分，入大火。 心，初度二十二分，入析木。 房，二度一十二分，入析木。
Equatorial degrees where lodges cross palaces; ecliptic degrees where lodges cross palaces—Winnowing Basket at three degrees seven minutes, entering Xingji (equator). Winnowing Basket at four degrees seventeen minutes, entering Xingji (ecliptic). Dipper at twenty-four degrees twenty-one minutes, entering Xuanyuan (equator). Ox at one degree six minutes, entering Xuanyuan (ecliptic); Rooftop at three degrees nineteen minutes, entering Ziwei (equator). Rooftop at one degree forty-seven minutes, entering Ziwei (ecliptic). Wall at one degree twenty-six minutes, entering Lower Harvester (equator). Encampment at eleven degrees forty minutes, entering Lower Harvester (ecliptic). Bond at six degrees twenty-eight minutes, entering Daliang (equator). Bond at one degree fourteen minutes, entering Daliang (ecliptic). Hairy Head at eight degrees thirty-nine minutes, entering Real Shen (equator). Hairy Head at five degrees thirteen minutes, entering Real Shen (ecliptic). Turtle Beak at eleven degrees seventeen minutes, entering Quail Head (equator). Turtle Beak at eleven degrees twenty-five minutes, entering Quail Head (ecliptic). Well at twenty-nine degrees fifty-three minutes, entering Quail Fire (equator). Well at twenty-nine degrees fifty-two minutes, entering Quail Fire (ecliptic). Extended Net at six degrees fifty-one minutes, entering Quail Tail (equator). Star at seven degrees fifty-one minutes, entering Quail Tail (ecliptic). Wings at nineteen degrees thirty-two minutes, entering Longevity Star (equator). Wings at eleven degrees twenty-four minutes, entering Longevity Star (ecliptic). Neck at one degree fifty minutes, entering Great Fire (equator). Neck at the lodge's first degree forty-six minutes, entering Great Fire (ecliptic). The Heart lodge, at its initial degree of twenty-two parts, enters Split Wood. The Room lodge, at two degrees and twelve parts, enters Split Wood.
20
▲儀象
▲ Armillary Sphere and Celestial Globe
21
璇璣玉衡為儀象之權輿，然不見用於三代。 《周禮》有圭表、壺漏，而無璣衡，其制遂不可考。 漢人創造渾天儀，謂即璣衡遺制，其或然歟。 厥後代有制作。 大抵以六合、三辰、四游、重環湊合者，謂之渾天儀； 以實體圓球，繪黃赤經緯度，或綴以星宿者，謂之渾天象。 其制雖有詳略，要亦青藍之別也。 外此則圭表、壺漏而已。 迨元作簡儀、仰儀、窺幾、景符之屬，制器始精詳矣。
The armillary of jade transparencies was the wellspring of armillary spheres and celestial globes, yet the Three Dynasties never put it to use. The Rites of Zhou records the gnomon table and clepsydra but not the armillary, and its form can no longer be recovered. Han craftsmen devised the armillary heaven instrument, claiming it as the armillary’s surviving design—and they may have been right. Thereafter every age produced instruments of its own. In general, instruments built up from the Six Harmonies, Three Luminaries, Four Excursions, and nested rings were called armillary heaven instruments; those fashioned as solid spheres painted with ecliptic and equatorial coordinates, sometimes studded with lodges, were called armillary heaven images. Though their designs differed in fineness and scope, in essence they were only shades of the same indigo. Beyond these there remained only the gnomon table and clepsydra. Under the Yuan, with the simplified instrument, azimuth instrument, sighting gauge, shadow tablet, and their kind, the craft of instruments first grew truly precise.
22
明太祖平元，司天監進水晶刻漏，中設二木偶人，能按時自擊鉦鼓。 太祖以其無益而碎之。 洪武十七年，造觀星盤。 十八年，設觀象台於雞鳴山。 二十四年，鑄渾天儀。 正統二年，行在欽天監正皇甫仲和奏言：「南京觀象台設渾天儀、簡儀、圭表以窺測七政行度，而北京乃止於齊化門城上觀測，未有儀象。 乞令本監官往南京，用木做造，挈赴北京，以較驗北極出地高下，然後用銅別鑄，庶幾占測有憑。」 從之。 明年冬，乃鑄銅渾天儀、簡儀於北京。 御制《觀天器銘》。 其詞曰：「粵古大聖，體天施治，敬天以心，觀天以器。 厥器伊何？ 璇璣玉衡。 璣象天體，衡審天行。 歷世代更，垂四千祀，沿制有作，其制寢備。 即器而觀，六合外儀，陽經陰緯，方位可稽。 中儀三辰，黃赤二道，日月暨星，運行可考。 內儀四游，橫簫中貫，南北東西，低昂旋轉。 簡儀之作，爰代璣衡，制約用密，疏朗而精。 外有渾象，反而觀諸，上規下矩，度數方隅。 別有直表，其崇八尺，分至氣序，考景鹹得。 縣象在天，制器在人，測驗推步，靡忒毫分。 昔作今述，為制彌工，既明且悉，用將無窮。 惟天勤民，事天首務，民不失寧，天其予顧。 政純於仁，天道以正，勒銘斯器，以勵予敬。」 十一年，監臣言：「簡儀未刻度數，且地基卑下，窺測日星，為四面台宇所蔽。 圭表置露台，光皆四散，影無定則。 壺漏屋低，夜天池促，難以注水調品時刻。 請更如法修造。」 報可。 明年冬，監正彭德清又言：「北京北極出地度、太陽出入時刻與南京不同，冬夏晝長夜短亦異。 今宮禁及官府漏箭皆南京舊式，不可用。」 有旨，令內官監改造。 景泰六年又造內觀象台簡儀及銅壺。 成化中，尚書周洪謨復請造璇璣玉衡，憲宗令自制以進。 十四年，監臣請修晷影堂，從之。
When the Ming Founder pacified the Yuan, the Directorate of Astronomy presented a crystal clepsydra fitted with two puppet figures that could strike bells and drums by themselves at the proper hours. The Founder judged it worthless and had it smashed. In Hongwu year seventeen an observational star disk was made. In year eighteen an observatory was established on Cockcrow Mountain. In year twenty-four an armillary sphere was cast. In Zhengtong year two, Huangfu Zhonghe, acting director of the Directorate at the capital, memorialized: "At the Nanjing Observatory an armillary sphere, simplified instrument, and gnomon table are installed to measure the courses of the seven luminaries, yet at Beijing we observe only from atop the Qi Gate wall, with no armillary instruments at all. I beg that officials of this directorate go to Nanjing, reproduce them in wood, and carry them to Beijing to compare how high the north pole stands above the horizon here; only then should separate bronze castings be made, so that observation and divination may rest on firm ground. The court assented. The following winter bronze armillary sphere and simplified instrument were cast at Beijing. The emperor composed the "Inscription on the Heaven-Observing Apparatus." Its words run: "In antiquity the great sages embodied Heaven in their rule, revered Heaven in the heart, and read Heaven through instruments. What instrument was it? The armillary of jade transparencies. The armillary mirrors the body of Heaven; the balance weighs the motion of Heaven. Dynasty after dynasty renewed it across four thousand years; along the inherited design work was added until the design stood complete. Through the instrument one views the outer frame of the Six Harmonies—yang tracks and yin tracks—so that positions may be reckoned. The inner frame of the Three Luminaries, the two tracks of yellow and red: sun, moon, and stars—their courses may be examined. The innermost frame of the Four Excursions: a transverse tube pierced through the center—north, south, east, and west, sinking and rising in turn. When the simplified instrument was fashioned it took the armillary’s place—tighter in design, yet spare and exact. Outside stands the armillary image, viewed in reverse; compass above and square below, degrees and cardinal directions. Apart from these is the vertical table, eight feet tall; solstices and seasonal qi—all shadows may be taken from it. The image hangs in Heaven; the instrument is wrought by man; measurement and stepwise reckoning miss not a hair’s breadth. What the ancients made and what we now set down—the craft grows finer, lucid and complete, fit for endless use. Heaven labors for the people; to serve Heaven is the first duty; if the people are not disturbed, Heaven will look upon us. When rule is pure in benevolence, Heaven’s Way is set right; we inscribe this instrument to quicken our reverence. In year eleven directorate officials said: "The simplified instrument has not been graduated, and its platform sits too low; when we observe sun and stars, terrace buildings block us on every side. The gnomon table stands on a terrace; light scatters on all sides and the shadow has no fixed rule. The clepsydra house is low and the night-celestial pool cramped, so it is hard to pour water and tune the hour-gradations. We ask that these be rebuilt according to regulation. The request was granted. The next winter Director Peng Deqing again said: "Beijing’s north-pole altitude and the times of the sun’s rising and setting differ from Nanjing’s; winter days and summer nights are likewise not the same length. The clepsydra arrows now used in the palace precinct and government offices are all in the old Nanjing pattern and will not serve. An edict ordered the Directorate of Palace Manufactories to remake them. In Jingtai year six a simplified instrument and bronze clepsydra were again made for the inner observatory. During the Chenghua reign Minister Zhou Hongmo again petitioned to make an armillary of jade transparencies; Emperor Xianzong ordered him to craft it himself and present it. In year fourteen directorate officials asked to repair the gnomon-shadow hall; the court assented.
23
弘治二年，監正吳昊言：「考驗四正日度，黃赤二道應交於壁軫。 觀象台舊制渾儀，黃赤二道交於奎軫，不合天象，其南北兩軸不合兩極出入之度，窺管又不與太陽出沒相當，故雖設而不用。 所用簡儀則郭守敬遺制，而北極雲柱差短，以測經星去極，亦不能無爽。 請修改或別造，以成一代之制。」 事下禮部，覆議令監副張紳造木樣，以待試驗，黃道度許修改焉。 正德十六年，漏刻博士硃裕復言：「晷表尺寸不一，難以准測，而推算歷數用南京日出分秒，似相矛盾。 請敕大臣一員總理其事，鑄立銅表，考四時日中之影。 仍於河南陽城察舊立土圭，以合今日之晷，及分立圭表於山東、湖廣、陝西、大名等處，以測四方之影。 然後將內外晷影新舊歷書錯綜參驗，撰成定法，庶幾天行合而交食不謬。」 疏入不報。 嘉靖二年修相風桿及簡、渾二儀。 七年始立四丈木表以測晷影，定氣朔。 由是欽天監之立運儀、正方案、懸晷、偏晷、盤晷諸式具備於觀象台，一以元法為斷。
In Hongzhi year two Director Wu Hao said: "When we verify the sun’s positions at the four cardinal points, the yellow and red tracks should intersect at Wall and Axletree. The old armillary on the observatory has them intersecting at Stride and Axletree, which does not match the sky; its north and south axes do not match the poles’ rising and setting, and the sighting tube does not line up with the sun’s emergence and disappearance—so though it stands there, we do not use it. The simplified instrument we use is Guo Shoujing’s surviving design, but the cloud pillar at the north pole is a little short; when we measure how far lodges stand from the pole, error still creeps in. We ask that it be altered or newly cast, to complete this dynasty’s instruments. The matter went to the Ministry of Rites, which replied that Vice-Director Zhang Shen should make a wooden model for testing, and that the ecliptic degrees might be adjusted. In Zhengde year sixteen Clepsydra Doctor Zhu Yu again said: "Gnomon tables differ in size and cannot serve as a single standard, yet calendar reckoning uses Nanjing sunrise minutes and seconds—as if the two methods contradicted each other. I beg that one senior minister be charged to oversee the work: cast and erect a bronze table and measure the noon shadow through the four seasons. Also examine the old earthen gnomon at Yangcheng in Henan and bring it into accord with today’s gnomon; and set up separate gnomon tables in Shandong, Huguang, Shaanxi, Daming, and other places to measure shadows in the four quarters. Then cross-check the old and new calendar records of gnomon shadows inside and out, compose a fixed method, and so bring celestial motion into accord and keep eclipse conjunctions from going astray. The memorial was filed; no answer came. In Jiajing year two the wind-indicating pole and the simplified and armillary instruments were repaired. In year seven a forty-chi wooden table was first erected to measure gnomon shadow and fix qi and new moon. From then on the Directorate’s revolving instrument, azimuth plate, suspended gnomon, oblique gnomon, dial gnomon, and other forms were all in place on the observatory, with Yuan methods taken as the sole standard.
24
萬歷中，西洋人利瑪竇制渾儀、天球、地球等器。 仁和李之藻撰《渾天儀說》，發明制造施用之法，文多不載。 其制不外於六合、三辰、四游之法。 但古法北極出地，鑄為定度，此則子午提規，可以隨地度高下，於用為便耳。
In the Wanli reign the Westerner Matteo Ricci made armillary spheres, celestial globes, terrestrial globes, and other instruments. Li Zhizao of Renhe wrote the Explanation of the Armillary Sphere, setting forth how to make and use them; most of that text is not recorded here. The design did not go beyond the methods of Six Harmonies, Three Luminaries, and Four Excursions. In the old method the north-pole altitude was cast as a fixed degree; here the meridian is set by an adjustable rule that can follow the horizon’s height wherever one stands—far more convenient in practice.
25
崇禎二年，禮部侍郎徐光啟兼理曆法，請造像限大儀六，紀限大儀三，平懸渾儀三，交食儀一，列宿經緯天球一，萬國經緯地球一，平面日晷三，轉盤星晷三，候時鐘三，望遠鏡三。 報允。 已，又言：
In Chongzhen year two Vice Minister of Rites Xu Guangqi, who also oversaw the calendar, requested six large limit-measuring instruments, three epoch-limit large instruments, three level-suspended armillary instruments, one eclipse instrument, one lodge longitude-latitude celestial globe, one myriad-countries longitude-latitude terrestrial globe, three plane solar gnomons, three revolving star gnomons, three timekeeping clocks, and three telescopes. The request was granted. Soon after, he spoke again:
26
定時之法，當議者五事：一曰壺漏，二曰指南針，三曰表臬，四曰儀，五曰晷。
On fixing time, five matters must be weighed: first the clepsydra; second the compass needle; third the gnomon table; fourth the instrument; fifth the gnomon dial.
27
漏壺，水有新舊滑濇則遲疾異，漏管有時塞時磷則緩急異。 正漏之初，必於正午初刻。 此刻一誤，靡所不誤。 故壺漏特以濟晨昏陰晦儀晷表臬所不及，而非定時之本。
In a clepsydra, fresh or stale, slick or gritty water runs fast or slow; when the outlet is blocked or fouled by turns, the drip slackens or hurries. When one first sets a clepsydra right, one must begin at the first quarter of noon. Err at that moment, and nothing afterward can be true. So the clepsydra only fills the gaps left by instruments, gnomon dials, and tables at dawn, dusk, cloud, and gloom—it is not the foundation of fixing time.
28
指南針，術人用以定南北，辨方正位鹹取則焉。 然針非指正子午，曩雲多偏丙午之間。 以法考之，各地不同。 在京師則偏東五度四十分。 若憑以造晷，冬至午正先天一刻四十四分有奇，夏至午正先天五十一分有奇。
The compass needle: technicians use it to fix north and south, and for bearings and cardinal alignment it is treated as law. Yet the needle does not aim at true south and north; formerly it was said to lean mostly toward the direction between wu and zi. Measured by method, it differs from place to place. At the capital it leans five degrees forty minutes east. If one built a gnomon dial by it alone, at winter-solstice noon it would run ahead of heaven by one quarter and forty-four-odd minutes; at summer-solstice noon, ahead by fifty-one-odd minutes.
29
若表臬者，即《考工》匠人置{埶木}之法，識日出入之影，參諸日中之影，以正方位。 今法置小表於地平，午正前後累測日影，以求相等之兩長影為東西，因得中間最短之影為正子午，其術簡甚。
The gnomon table is the Craftsman’s Canon method of setting the yi-post: one reads the shadows at sunrise and sunset, compares them with the noon shadow, and so rectifies the cardinal directions. Today we set a small table on level ground, measure the sun’s shadow repeatedly before and after noon, take two equal long shadows as east and west, and from the shortest shadow between derive true south-north—a method altogether simple.
30
儀者，本台故有立運儀，測驗七政高度。 臣用以較定子午，於午前屢測太陽高度，因最高之度，即得最短之影，是為南北正線。
As for instruments, this directorate already possesses the revolving instrument, used to measure the altitudes of the seven luminaries. I used it to fix south-north: before noon I measured the sun’s altitude again and again; from the highest degree I obtained the shortest shadow—that is the true north-south line.
31
既定子午卯酉之正線，因以法分佈時刻，加入節氣諸線，即成平面日晷。 又今所用員石欹晷是為赤道晷，亦用所得正子午線較定。 此二晷皆可得天之正時刻，所為晝測日也。 若測星之晷，實《周禮》夜考極星之法。 然古時北極星正當不動之處，今時久漸移，已去不動處三度有奇，舊法不可復用。 故用重盤星晷，上書時刻，下書節氣，仰測近極二星即得時刻，所謂夜測星也。
Once the true lines of south-north and east-west were fixed, I laid out the hours by rule, added the lines of seasonal qi, and so made a plane solar gnomon. The slanted stone dial we now use is the equatorial dial; it too was verified against the true south-north line we obtained. Both dials can yield heaven’s true hours—this is what is meant by measuring the sun by day. The star-measuring dial is in fact the Rites of Zhou method of examining the pole star by night. In antiquity the north pole star stood exactly at the unmoving point; over long ages it has drifted and now lies more than three degrees away—the old method can no longer serve. So we use the double-disk star gnomon: hours on the upper disk, seasonal qi on the lower; gazing up at the two stars near the pole through it we read the hour—this is what is called measuring stars by night.
32
七年，督修曆法右參政李天經言：
In year seven Li Tianjing, right vice commissioner supervising calendar reform, said:
33
輔臣光啟言定時之法，古有壺漏，近有輪鐘，二者皆由人力遷就，不如求端於日星，以天合天，乃為本法，特請制日晷、星晷、望遠鏡三器。 臣奉命接管，敢先言其略。
Assistant Minister Xu Guangqi said that in fixing time antiquity had clepsydras and recent times wheel-clocks—both are human makeshifts. Better to seek the origin in sun and stars: heaven matched to heaven is the true method. He therefore asked especially for three instruments—the solar gnomon, star gnomon, and telescope. Your servant received the charge and ventures first to set out the outline.
34
日晷者，礱石為平面，界節氣十三線，內冬夏二至各一線，其余日行相等之節氣，皆兩節氣同一線也。 平面之周列時刻線，以各節氣太陽出入為限。 又依京師北極出地度，范為三角銅表置其中。 表體之全影指時刻，表中之銳影指節氣。 此日晷之大略也。
As for the solar gnomon: a stone is polished flat and marked with thirteen lines of seasonal qi; within, winter and summer solstice each have a line, while the other equal-moving qi share one line between every two seasons. Around the plane’s rim hour-lines are drawn, bounded by the sun’s rising and setting at each seasonal qi. According to the capital’s north-pole altitude, a triangular bronze table is cast and set at the center. The table’s full shadow points to the hour; the sharp inner shadow points to the seasonal qi. Such is the outline of the solar gnomon.
35
星晷者，治銅為柱，上安重盤。 內盤鐫周天度數，列十二宮以分節氣，外盤鐫列時刻，中橫刻一縫，用以窺星。 法將外盤子正初刻移對內盤節氣，乃轉移銅盤北望帝星與句陳大星，使兩星同見縫中，即視盤面銳表所指，為正時刻。 此星晷之大略也。
As for the star gnomon: bronze is cast into a pillar with a double disk above. The inner disk is engraved with degrees of the whole heaven and the twelve palaces to divide seasonal qi; the outer disk with hours; a horizontal slit is cut through the center for sighting stars. The method: set the outer disk’s zi initial quarter against the inner disk’s seasonal qi, then turn the bronze disk and look north at the Imperial Star and the great Gouchen star until both appear together in the slit; wherever the sharp pointer on the disk face points is the true hour. Such is the outline of the star gnomon.
36
若夫望遠鏡，亦名窺筒，其制虛管層疊相套，使可伸縮，兩端俱用玻璃，隨所視物之遠近以為長短。 不但可以窺天象，且能攝數裡外物如在目前，可以望敵施砲，有大用焉。
The far-sight tube—also called the peeping tube—consists of hollow tubes nested one inside another so they can slide in and out. Glass caps both ends, and you adjust the length to match the distance of whatever you wish to see. It serves not only to watch the heavens but to pull objects miles away up before your eyes—as if they stood at arm's length—so you can spy on the foe and lay cannon. Its uses are considerable.
37
至於日晷、星晷皆用措置得宜，必須築台，以便安放。
Sundials and star-dials alike must be set up with care, and a terrace must be built to receive them.
38
帝命太監盧維寧、魏國徵至局驗試用法。
The emperor sent the eunuchs Lu Weining and Wei Guozheng to the bureau to test how the instruments were to be used.
39
明年，天經又請造沙漏。 明初，詹希元以水漏至嚴寒水凍輒不能行，故以沙代水。 然沙行太疾，未協天運，乃以斗輪之外復加四輪，輪皆三十六齒。 厥後周述學病其竅太小，而沙易堙，乃更制為六輪，其五輪悉三十齒，而微裕其竅，運行始與晷協。 天經所請，殆其遺意歟。
The following year Li Tianjing again petitioned for a sand clepsydra to be built. Early in the dynasty Zhan Xiyuan found that in bitter cold the water clepsydra froze and would not run, so he substituted sand for water. But sand flows too fast to keep pace with the sky. He therefore added four wheels beyond the dipper-wheel, each cut with thirty-six teeth. Later Zhou Shuxue judged the holes too fine and the sand too prone to clogging. He rebuilt the device with six wheels—the five outer wheels each bore thirty teeth—and widened the holes slightly. Only then did its pace match the gnomon. Tianjing's request was very likely meant to follow this earlier design.
40
夫制器尚象，乃天文家之首務。 然精其術者可以因心而作。 故西洋人測天之器，其名未易悉數，內渾蓋、簡平二儀其最精者也。 其說具見全書，茲不載。
Fashioning instruments that embody the heavens is the first duty of anyone who studies the sky. Yet those who truly master the art can invent according to the mind's own design. The Westerners' celestial instruments are too many to list in full; among them the armillary sphere and the simplified plane instrument are the finest. Their theory is given at length in the full treatise and is not repeated here.
41
▲極度晷影宣城梅文鼎曰：
▲ Pole altitude and gnomon shadow. Mei Wending of Xuancheng writes:
42
極度晷影常相因。 知北極出地之高，即可知各節氣午正之影。 測得各節氣午正之影，亦可知北極之高。 然其術非易易也。 圭表之法，表短則分秒難明，表長則影虛而淡。 郭守敬所以立四丈之表，用影符以取之也。 日體甚大，豎表所測者日體上邊之影，橫表所測者日體下邊之影，皆非中心之數，郭守敬所以於表端架橫梁以測之也，其術可謂善矣。 但其影符之制，用銅片鑽針芥之孔，雖前低後仰以向太陽，但太陽之高低每日不同，銅片之欹側安能俱合。 不合則光不透，臨時遷就，而日已西移矣。 須易銅片以圓木，左右用兩板架之，如車軸然，則轉動甚易。 更易圓孔以直縫，而用始便也。 然影符止可去虛淡之弊，而非其本。 必須正其表焉，平其圭焉，均其度焉，三者缺一，不可以得影。 三者得矣，而人心有粗細，目力有利鈍，任事有誠偽，不可不擇也。 知乎此，庶幾晷影可得矣。
Pole altitude and gnomon shadow always depend on one another. Know how high the north pole stands above the horizon, and you can derive the noon shadow for every solar term. Measure those noon shadows, and you can work back to the pole's height. The method itself, however, is far from easy. With the gnomon table, a short post makes minutes and seconds hard to read; a tall post yields a shadow so faint and diffuse that precision fails. That is why Guo Shoujing raised a gnomon forty chi tall and took his readings with a shadow marker. The sun is a vast disk. A vertical gnomon catches the shadow of its upper rim; a horizontal one catches the lower rim—neither gives the sun's center. Guo Shoujing therefore bridged the top of the gnomon with a crossbeam for the measurement. The method is as clever as it is sound. His shadow marker, however, was a copper plate pierced with a hole no larger than a mustard seed. Though the plate was pitched to face the sun, the sun's height changes daily; the plate's angle cannot follow every shift. When the angle is wrong, no light passes through; you adjust by hand—and the sun has already slipped westward. Replace the copper with a round wooden cylinder, braced on either side by boards like an axle, and it turns with ease. Trade the round aperture for a straight slit, and the device is far easier to use. Even so, the shadow marker only remedies faint, diffuse shadows—it does not touch the root of the problem. The gnomon must stand true, the table must lie level, and the graduations must be even. Fail in any one of these three, and no trustworthy shadow can be had. Even when all three are right, minds differ in fineness, eyes in keenness, and workers in honesty. The observer must be chosen with care. Only with this understood may one hope to read the gnomon shadow aright.
43
西洋之法又有進焉。 謂地半徑居日天半徑千餘分之一，則地面所測太陽之高，必少於地心之實高，於是有地半徑差之加。 近地有清蒙氣，能升卑為高，則晷影所推太陽之高，或多於天上之實高，於是又有清蒙差之減。 是二差者，皆近地多而漸高漸減，以至於無，地半徑差至天頂而無，清蒙差至四十五度而無也。
Western methods go further still. They hold that because the earth's radius is scarcely more than one part in a thousand of the sun's celestial radius, the sun's altitude measured from the ground is always lower than the true altitude from the earth's center. A correction for the earth's radius must therefore be added. Near the surface, clear haze lifts low things so they appear higher. The sun's altitude inferred from the gnomon shadow may therefore exceed its true height in the sky. A correction for this clear haze must be subtracted. Both corrections are largest near the ground and taper away with altitude until they disappear entirely—the earth-radius correction at the zenith, the haze correction at forty-five degrees.
44
崇禎初，西洋人測得京省北極出地度分：北京四十度，周天三百六十度，度六十分立算，下同。 南京三十二度半，山東三十七度，山西三十八度，陝西三十六度，河南三十五度，浙江三十度，江西二十九度，湖廣三十一度，四川二十九度，廣東二十三度，福建二十六度，廣西二十五度，雲南二十二度，貴州二十四度。 以上極度，惟兩京、江西、廣東四處皆系實測，其余則據地圖約計之。 又以十二度度六十分之表測京師各節氣午正日影：夏至三度三十三分，芒種、小暑三度四十二分，小滿、大暑四度十五分，立夏、立秋五度六分，谷雨、處暑六度二十三分，清明、白露八度六分，春、秋分十度四分，驚蟄、寒露十二度二十六分，雨水、霜降十五度五分，立春、立冬十七度四十七分，大寒、小雪二十度四十七分，小寒、大雪二十三度三十分，冬至二十四度四分。
Early in the Chongzhen reign Western astronomers measured how far the north pole stood above the horizon for the capital and provinces: Beijing, forty degrees. The full circle is three hundred sixty degrees, each degree divided into sixty minutes in calculation—the same rule holds throughout what follows. Nanjing, thirty-two and a half degrees; Shandong, thirty-seven; Shanxi, thirty-eight; Shaanxi, thirty-six; Henan, thirty-five; Zhejiang, thirty; Jiangxi, twenty-nine; Huguang, thirty-one; Sichuan, twenty-nine; Guangdong, twenty-three; Fujian, twenty-six; Guangxi, twenty-five; Yunnan, twenty-two; Guizhou, twenty-four. Of these pole altitudes, only the two capitals, Jiangxi, and Guangdong were measured on site; the remainder were approximated from maps. With a gnomon scaled at twelve degrees and sixty minutes they measured Beijing's noon shadows through the year: at the summer solstice, three degrees thirty-three minutes; at Grain in Beard and Lesser Heat, three degrees forty-two; at Lesser Fullness and Greater Heat, four degrees fifteen; at Beginning of Summer and Beginning of Autumn, five degrees six; at Grain Rain and End of Heat, six degrees twenty-three; at Clear Bright and White Dew, eight degrees six; at the equinoxes, ten degrees four; at Waking of Insects and Cold Dew, twelve degrees twenty-six; at Rain Water and Frost's Descent, fifteen degrees five; at Beginning of Spring and Beginning of Winter, seventeen degrees forty-seven; at Greater Cold and Lesser Snow, twenty degrees forty-seven; at Lesser Cold and Greater Snow, twenty-three degrees thirty; at the winter solstice, twenty-four degrees four.
45
▲東西偏度以京師子午線為中，而較各地所偏之度。 凡節氣之早晚，月食之先後，胥視此。 蓋人各以見日出入為東西為卯酉，以日中為南為午。 而東方見日早，西方見日遲。 東西相距三十度則差一時。 東方之午乃西方之巳，西方之午乃東方之未也。 相距九十度則差三時。 東方之午乃西方之卯，西方之午乃東方之酉也。 相距一百八十度則晝夜時刻俱反對矣。 東方之午乃西方之子。 西洋人湯若望曰「天啟三年九月十五夜，戌初初刻望，月食，京師初虧在酉初一刻十二分，而西洋意大裡雅諸國望在晝，不見。 推其初虧在巳正三刻四分，相差三時二刻八分，以裡差計之，殆距京師之西九十九度半也。 故欲定東西偏度，必須兩地同測一月食，較其時刻。 若早六十分時之二則為偏西一度，遲六十分時之二則為偏東一度。 節氣之遲早亦同。 今各省差數未得測驗，據廣輿圖計裡之方約略條列，或不致甚舛也。 南京應天府、福建福州府並偏東一度，山東濟南府偏東一度十五分，山西太原府偏西六度，湖廣武昌府、河南開封府偏西三度四十五分，陝西西安府、廣西桂林府偏西八度半，浙江杭州府偏東三度，江西南昌府偏西二度半，廣東廣州府偏西五度，四川成都府偏四十三度，貴州貴陽府偏西九度半，雲南雲南府偏西十七度。」
▲ East-west offset in degrees. With Beijing's meridian as the standard, one compares how far each region lies to east or west. Whether the solar terms arrive early or late, or an eclipse is seen sooner or later, all hinge on this. Every observer takes sunrise and sunset for east and west—the mao and you hours—and midday for south and the wu hour. Yet the east sees the sun before the west does. Where east and west are separated by thirty degrees, local time differs by one double-hour. When it is noon in the east, it is already si in the west; when it is noon in the west, it is still wei in the east. At ninety degrees' separation the difference is three double-hours. Noon in the east corresponds to mao in the west; noon in the west to you in the east. At one hundred eighty degrees, day and night—and every hour—stand directly opposed. Noon in the east is midnight—zi—in the west. The Westerner Adam Schall wrote: "On the night of the fifteenth of the ninth month in the third year of Tianqi, at the opening of the xu watch, the moon was full and suffered eclipse. At the capital first contact came at the start of you, one ke and twelve fen; in Italy and the other Western realms the moon was full by day and the eclipse went unseen. Working backward, their first contact would have been at exact si, three ke and four fen—three double-hours, two ke, and eight fen earlier than Beijing. By the longitudinal correction, that country lies about ninety-nine and a half degrees west of the capital. To fix the east-west offset, two places must observe the same lunar eclipse and compare their times. If one site is early by two sixtieths of a double-hour, it lies one degree to the west; if late by two sixtieths, one degree to the east. The earliness or lateness of the solar terms follows the same rule. The offsets for the provinces have not yet been measured on the ground. The figures below are roughly estimated from the broad map by squaring distances in li, and are given so that gross error may be avoided. Nanjing in Yingtian and Fuzhou in Fujian each lie one degree east; Jinan in Shandong, one degree fifteen fen east; Taiyuan in Shanxi, six degrees west; Wuchang in Huguang and Kaifeng in Henan, three degrees forty-five fen west; Xi'an in Shaanxi and Guilin in Guangxi, eight and a half degrees west; Hangzhou in Zhejiang, three degrees east; Nanchang in Jiangxi, two and a half degrees west; Guangzhou in Guangdong, five degrees west; Chengdu in Sichuan, forty-three degrees west; Guiyang in Guizhou, nine and a half degrees west; Yunnan in Yunnan, seventeen degrees west."
46
右偏度，載《崇禎歷書》交食歷指。 其時開局修歷，未暇分測，度數實多未確，存之以備考訂雲。
These offsets are recorded in the Eclipse Treatise of the Chongzhen Calendar. When the calendar office was first opened to revise the almanac, there was no time to survey each region separately; many of the figures were still uncertain. They are preserved here for later revision.
47
▲中星古今中星不同，由於歲差。 而歲差之說，中西復異。 中法謂節氣差而西，西法謂恆星差而東，然其歸一也。 今將李天經、湯若望等所推崇禎元年京師昏旦時刻中星列於後。
▲ Culminating stars at dusk and dawn. The stars culminating at dusk and dawn differ between antiquity and today because of precession. Chinese and Western accounts of precession, however, do not agree. Chinese theory says the solar terms slip westward; Western theory says the fixed stars slip eastward—yet both describe the same motion. Below are the dusk and dawn times and culminating stars for Beijing in the first Chongzhen year, as calculated by Li Tianjing, Adam Schall, and their colleagues.
48
春分，戌初二刻五分昏，北河三中； 寅正一刻一十分旦，尾中。 清明，戌初三刻十三分昏，七星偏東四度； 昏旦時或無正中之星，則取中前、中後之大星用之。 距中三度以內者，為時不及一刻，可勿論。 四度以上，去中稍遠，故紀其偏度焉。 寅正初刻二分旦，帝座中。 谷雨，戌正一刻七分昏，翼偏東七度； 寅初二刻八分旦，箕偏東四度。 立夏，戌正三刻二分昏，軫偏東五度； 寅初初刻十三分旦，箕偏西四度。 小滿，亥初初刻十二分昏，角中； 醜正三刻三分旦，箕中。 芒種，亥初一刻十二分昏，大角偏西六度； 醜正二刻三分旦，河鼓二中。
Spring equinox—dusk at five fen past the second ke of early xu, with the third star of Beihe on the meridian; dawn at ten fen past the first ke of exact yin, with Wei on the meridian. Clear Bright—dusk at thirteen fen past the third ke of xu, the Seven Stars four degrees east of the meridian; when no star stands exactly on the meridian at dusk or dawn, use a bright star slightly before or after culmination. Within three degrees of the meridian the time error is less than one ke and may be ignored. Beyond four degrees, farther from the meridian, the offset is recorded in degrees. dawn at two fen past the first ke of exact yin, Emperor's Seat on the meridian. Grain Rain—dusk at seven fen past the first ke of exact xu, Wings seven degrees east of the meridian; dawn at eight fen past the second ke of early yin, Winnowing Basket four degrees east of the meridian. Beginning of Summer—dusk at two fen past the third ke of exact xu, Chariot Shaft five degrees east of the meridian; dawn at thirteen fen past the first ke of early yin, Winnowing Basket four degrees west of the meridian. Lesser Fullness—dusk at twelve fen past the first ke of early hai, Horn on the meridian; dawn at three fen past the third ke of exact chou, Winnowing Basket on the meridian. Grain in Beard—dusk at twelve fen past the first ke of hai, Great Horn six degrees west of the meridian; dawn at three fen past the second ke of exact chou, the second star of River Drum on the meridian.
49
夏至，亥初二刻五分昏，房中； 醜正一刻一十分旦，須女中。 小暑，亥初一刻十二分昏，尾中； 醜正二刻三分旦，危中。 大暑，亥初初刻十二分昏，箕偏東七度； 醜正三刻三分旦，營室中。 立秋，戌正三刻二分昏，箕中； 寅初三刻十三分旦，婁偏東六度。 處暑，戌正一刻七分昏，織女一中； 寅初二刻八分旦，婁中。 白露，戌初三刻十三分昏，河鼓二偏東四度； 寅正初刻二分旦，昴偏東四度。
Summer solstice—dusk at five fen past the second ke of early hai, Room on the meridian; dawn at ten fen past the first ke of exact chou, Maid on the meridian. Lesser Heat—dusk at twelve fen past the first ke of hai, Tail on the meridian; dawn at three fen past the second ke of exact chou, Rooftop on the meridian. Greater Heat—dusk at twelve fen past the first ke of early hai, Winnowing Basket seven degrees east of the meridian; dawn at three fen past the third ke of exact chou, Encampment on the meridian. Beginning of Autumn—dusk at two fen past the third ke of exact xu, Winnowing Basket on the meridian; dawn at thirteen fen past the third ke of early yin, Bond six degrees east of the meridian. End of Heat—dusk at seven fen past the first ke of exact xu, the first star of Weaver Girl on the meridian; dawn at eight fen past the second ke of early yin, Bond on the meridian. White Dew—dusk at thirteen fen past the third ke of xu, the second star of River Drum four degrees east of the meridian; dawn at two fen past the first ke of exact yin, Hairy Head four degrees east of the meridian.
50
秋分，戌初二刻五分昏，河鼓二中； 寅正一刻十一分旦，畢偏西五度。 寒露，戌初初刻十四分昏，牽牛中； 寅正三刻一分旦，參四中。 霜降，酉正三刻十一分昏，須女偏西五度； 卯初初刻四分旦，南河三偏東六度。 立冬，酉正二刻一十分昏，危偏東四度； 卯初一刻五分旦，輿鬼中。 小雪，酉正一刻十二分昏，營室偏東七度； 卯初二刻二分旦，張中。 大雪，酉正一刻五分昏，營室偏西八度； 卯初二刻一十分旦，翼中。
Autumn equinox—dusk at five fen past the second ke of early xu, the second star of River Drum on the meridian; dawn at eleven fen past the first ke of exact yin, Net five degrees west of the meridian. Cold Dew—dusk at fourteen fen past the first ke of early xu, Ox Leader on the meridian; dawn at one fen past the third ke of exact yin, the fourth star of Shen on the meridian. Frost's Descent—dusk at eleven fen past the third ke of exact you, Maid five degrees west of the meridian; dawn at four fen past the first ke of early mao, the third star of the southern River six degrees east of the meridian. Beginning of Winter—dusk at ten fen past the second ke of exact you, Rooftop four degrees east of the meridian; dawn at five fen past the first ke of early mao, Chariot Ghost on the meridian. Lesser Snow—dusk at twelve fen past the first ke of exact you, Encampment seven degrees east of the meridian; dawn at two fen past the second ke of early mao, Extended Net on the meridian. Greater Snow—dusk at five fen past the first ke of exact you, Encampment eight degrees west of the meridian; dawn at ten fen past the second ke of early mao, Wings on the meridian.
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冬至，酉正一刻二分昏，土司空中； 卯初二刻十三分旦，五帝座中。 小寒，酉正一刻五分昏，婁中； 卯初二刻一十分旦，角偏東五度。 大寒，酉正一刻十三分昏，天囷一中； 卯初二刻二分旦，亢中。 立春，酉正二刻一十分昏，昴偏西六度； 卯初一刻五分旦，氐中。 雨水，酉正三刻十一分昏，參七中； 卯初初刻四分旦，貫索一中。 驚蟄，戌初初刻十四分昏，天狼中； 寅正三刻一分旦，心中。
Winter solstice—dusk at two fen past the first ke of exact you, Sikong on the meridian. dawn at thirteen fen past the second ke of early mao, Five Emperors Seat on the meridian. Lesser Cold—dusk at five fen past the first ke of exact you, Bond on the meridian; dawn at ten fen past the second ke of early mao, Horn five degrees east of the meridian. Greater Cold—dusk at thirteen fen past the first ke of exact you, the first star of Celestial Granary on the meridian; dawn at two fen past the second ke of early mao, Neck on the meridian. Beginning of Spring—dusk at ten fen past the second ke of exact you, Hairy Head six degrees west of the meridian; dawn at five fen past the first ke of early mao, Root on the meridian. Rain Water—dusk at eleven fen past the third ke of exact you, the seventh star of Shen on the meridian; dawn at four fen past the first ke of early mao, the first star of Coiled Thong on the meridian. Waking of Insects—dusk at fourteen fen past the first ke of early xu, Celestial Wolf on the meridian; dawn at one fen past the third ke of exact yin, Heart on the meridian.
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▲分野《周禮﹒保章氏》以星土辨九州之地，所封之域皆有分星，以觀妖祥。 唐貞觀中，李淳風撰《法象志》，因《漢書》十二次度數以唐州縣配，而一行則以為天下山河之象，存乎南北兩界，其說詳矣。 洪武十七年，《大明清類天文分野書》成，頒賜秦、晉二王。 其書大略謂「《晉天文志》分野始角、亢者，以東方蒼龍為首也。 唐始女、虛、危者，以十二支子為首也。 今始斗、牛者，以星紀為首也。 古言天者皆由斗、牛以紀星，故曰星紀，是之取耳。」 茲取其所配直隸十三布政司府州縣衛及遼東都司分星錄之。
▲ Field allocation. The Rites of Zhou’s Master of Territories matches stars to soils to map the Nine Provinces; every enfeoffed territory has its allotment star, by which to read omens of fortune and disaster. During Tang Zhenguan, Li Chunfeng wrote the Treatise on Astro-omen Patterns, applying the Book of Han’s twelve celestial-degree stations to Tang prefectures and counties. Yi Xing argued that the pattern of the realm’s mountains and rivers is held between a northern and a southern limit—his account is far more detailed. In Hongwu year seventeen the Comprehensive Treatise on Astronomy and Field Allocation for the Great Ming was finished and issued to the princes of Qin and Jin. The treatise holds, in brief: ‘The Jin History of Astronomy starts allotment at Horn and Neck because the Azure Dragon of the east leads the sky. Tang begins at Maid, Void, and Rooftop because the twelve earthly branches start at zi. Our dynasty begins at Dipper and Ox because Xingji is taken as first. Ancient discourse on Heaven always reckoned the stars from Dipper and Ox—hence the name Xingji, Star Era—and that is the ground of our choice.’ Below are recorded its allotment stars for the thirteen Zhili provincial commissions’ prefectures, departments, counties, and guards, and for the Liaodong regional command.
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斗三度至女一度，星紀之次也。 直隸所屬之應天、太平、寧國、鎮江、池州、徽州、常州、蘇州、松江九府暨廣德州，屬斗分。 鳳陽府壽、滁、六安三州，泗州之盱眙、天長二縣，揚州府高郵、通、泰三州，廬州府無為州，安慶府和州，皆斗分。 淮安府，斗、牛分。 浙江布政司所屬之杭州、湖州、嘉興、嚴州、紹興、金華、衢州、處州、寧波九府皆牛、女分。 台州、溫州二府，斗、牛、須、女分。 江西布政司所屬皆斗分。 福建布政司所屬皆牛、女分。 廣東布政司所屬之廣州府亦牛、女分。 惠州，女分。 肇慶、南雄二府，德慶州，皆牛、女分。 潮州府，牛分。 雷州、瓊州二府，崖、儋、萬三州，高州府化州，廣西布政司所屬梧州府之蒼梧、籐、岑溪、容四縣，皆牛、女分。
From three degrees Dipper to one degree Maid—the Xingji station. In Zhili: Yingtian, Taiping, Ningguo, Zhenjiang, Chizhou, Huizhou, Changzhou, Suzhou, and Songjiang prefectures, with Guangde department—all Dipper allotment. Fengyang’s Shou, Chu, and Lu’an departments; Huai’an’s Xuyi and Tianchang counties; Yangzhou’s Gaoyou, Tong, and Tai departments; Luzhou’s Wuwei department; Anqing’s He department—all Dipper. Huai’an prefecture—Dipper and Ox. Zhejiang’s Hangzhou, Huzhou, Jiaxing, Yanzhou, Shaoxing, Jinhua, Quzhou, Chuzhou, and Ningbo prefectures—all Ox and Maid. Taizhou and Wenzhou—Dipper, Ox, Beard, and Maid. All of Jiangxi—Dipper. All of Fujian—Ox and Maid. Guangdong’s Guangzhou prefecture—also Ox and Maid. Huizhou—Maid. Zhaoqing and Nanxiong prefectures and Deqing department—all Ox and Maid. Chaozhou—Ox. Leizhou and Qiongzhou; Ya, Dan, and Wan departments; Gaozhou’s Huazhou; and Wuzhou’s Cangwu, Teng, Cenxi, and Rong counties in Guangxi—all Ox and Maid.
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女二度至危十二度，玄枵之次也。 山東布政司所屬之濟南府樂安、德、濱三州，皆危分。 泰安州、青州府，皆虛、危分。 萊州府膠州、登州府寧海州、東昌府高塘州，皆危分。 東平州之陽谷、東阿、平陰三縣，北平布政司所屬之滄州，皆須、女、虛、危分。
From two degrees Maid to twelve degrees Rooftop—the Xuanxiao station. Shandong: Jinan’s Le’an, De, and Bin departments—all Rooftop. Tai’an department and Qingzhou prefecture—all Void and Rooftop. Laizhou’s Jiaozhou, Dengzhou’s Ninghai department, Dongchang’s Gaotang department—all Rooftop. Dongping’s Yanggu, Dong’e, and Pingyin counties; Beiping’s Cangzhou—all Beard, Maid, Void, and Rooftop.
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危十三度至奎一度，娵訾之次也。 河南布政司所屬之衛輝、彰德、懷慶三府，北平之大名府開州，山東東昌之濮州，館陶、冠、臨清三縣，東平州之汶上、壽張二縣，皆室、壁分。
From thirteen degrees Rooftop to one degree Straddler—the Juzi station. Henan’s Weihui, Zhangde, and Huaqing prefectures; Beiping Daming’s Kaizhou; Shandong Dongchang’s Puzhou and Guantao, Guan, and Linqing counties; Dongping’s Wenshang and Shouzhang—all Encampment and Wall.
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奎二度至胃三度，降婁之次也。 山東濟寧府之兗州滕、嶧二縣，青州府之莒州、安丘、諸城、蒙陰三縣，濟南府之沂州，直隸鳳陽府之泗、邳二州，五河、虹、懷遠三縣，淮安府之海州，桃源、清河、沭陽三縣，皆奎、婁分。
From two degrees Straddler to three degrees Stomach—the Jianglou station. Shandong Jining’s Yanzhou with Teng and Yi counties; Qingzhou’s Juzhou with Anqiu, Zhucheng, and Mengyin; Jinan’s Yizhou; Zhili Fengyang’s Si and Pi departments with Wuhe, Hong, and Huaiyuan counties; Huai’an’s Haizhou; Taoyuan, Qinghe, and Shuyang—all Straddler and Bond.
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胃四度至畢六度，大梁之次也。 北平之真定府，昴、畢分。 定、冀二州，皆昴分。 晉、深、趙三州，皆畢分。 廣平、順德二府，皆昴分。 祁州，昴、畢分。 河南彰德府之磁州，山東高唐州之恩縣，山西布政司所屬之大同府應、朔、渾源、蔚四州，皆昴、畢分。
From four degrees Stomach to six degrees Net—the Daliang station. Beiping’s Zhending prefecture—Hairy Head and Net. Ding and Ji departments—all Hairy Head. Jin, Shen, and Zhao departments—all Net. Guangping and Shunde prefectures—all Hairy Head. Qizhou—Hairy Head and Net. Henan Zhangde’s Cizhou; Shandong Gaotang’s En county; Shanxi Datong’s Ying, Shuo, Hunyuan, and Yu departments—all Hairy Head and Net.
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畢七度至井八度，實沈之次也。 山西之太原府石、忻、代、平定、保德、岢嵐六州，平陽府，皆參分。 絳、蒲、吉、隰、解、霍六州皆觜、參分。 澤、汾二州，皆參分。 潞、沁、遼三州，皆參、井分。
From seven degrees Net to eight degrees Well—the Shishen station. Shanxi Taiyuan’s Shi, Xin, Dai, Pingding, Baode, and Kelan departments and Pingyang prefecture—all Triaster. Jiang, Pu, Ji, Xi, Jie, and Huo departments—all Turtle Beak and Triaster. Ze and Fen departments—all Triaster. Lu, Qin, and Liao departments—all Triaster and Well.
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井九度至柳三度，鶉首之次也。 陝西布政司所屬之西安府同、華、乾、耀、邠五州，鳳翔府隴州，延安府鄜、綏德、葭三州，漢中府金州，臨洮、平涼二府，靜寧州，皆井、鬼分。 涇州，鬼分。 慶陽府寧州，鞏昌府階、徽、秦三州，皆井、鬼分。 四川布政司所屬惟綿州觜分，合州參、井分，余皆井、鬼分。 雲南布政司所屬皆井、鬼分。
From nine degrees Well to three degrees Willow—the Chunshou station. Shaanxi Xi’an’s Tong, Hua, Qian, Yao, and Bin departments; Fengxiang’s Longzhou; Yan’an’s Fu, Suide, and Jia; Hanzhong’s Jin department; Lintao and Pingliang prefectures; Jingning department—all Well and Ghost. Jing department—Ghost. Qingyang’s Ning department; Gongchang’s Jie, Hui, and Qin departments—all Well and Ghost. Sichuan: only Mian is Turtle Beak; He is Triaster and Well; all else is Well and Ghost. All of Yunnan—Well and Ghost.
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柳四度至張十五度，鶉火之次也。 河南之河南府陝州，皆柳分。 南陽府鄧、汝、裕三州，汝寧府之信陽、羅山二縣，開封府之均、許二州，陝西西安府之商縣，華州之洛南縣，湖廣佈政司所屬德安府之隨州，襄陽府之均州、光化縣，皆張分。
From four degrees Willow to fifteen degrees Extended Net—the Chunhuo station. Henan prefecture’s Shan department—all Willow. Nanyang’s Deng, Ru, and Yu departments; Runing’s Xinyang and Luoshan counties; Kaifeng’s Jun and Xu departments; Shaanxi Xi’an’s Shang county and Hua’s Luonan; Huguang De’an’s Suizhou; Xiangyang’s Jun department and Guanghua county—all Extended Net.
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張十六度至軫九度，鶉尾之次也。 湖廣之武昌府興國州，荊州府歸、夷陵、荊門三州，黃州府蘄州，襄陽、德安二府，安陸、沔陽二州，皆翼、軫分。 長沙府軫旁小星曰長沙，應其地。 衡州府桂陽州，永州府全、道二州，岳州、常德二府，澧州，辰州府沅州，漢陽府靖、郴二州，寶慶府武岡、鎮遠二州，皆翼、軫分。 廣西所屬除梧州府之蒼梧、籐、容、岑溪四縣屬牛、女分，余皆翼、軫分。 廣東之連州、廉州府欽州、韶州府，皆翼、軫分。
From sixteen degrees Extended Net to nine degrees Chariot—the Chunwei station. Huguang Wuchang’s Xingguo department; Jingzhou’s Gui, Yiling, and Jingmen; Huangzhou’s Qizhou; Xiangyang and De’an prefectures; Anlu and Mianyang departments—all Wings and Chariot. A small star beside Chariot in Changsha prefecture is named Changsha and answers to that territory. Hengzhou’s Guiyang department; Yongzhou’s Quan and Dao; Yuezhou and Changde; Li department; Chenzhou’s Yuan; Hanyang’s Jing and Chen; Baoqing’s Wugang and Zhenyuan—all Wings and Chariot. Guangxi: except Wuzhou’s Cangwu, Teng, Rong, and Cenxi counties under Ox and Maid, all else is Wings and Chariot. Guangdong’s Lian department; Lianzhou’s Qin department; and Shaozhou—all Wings and Chariot.
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軫十度至氐一度，壽星之次也。 河南之開封府，角、亢分。 鄭州，氐分。 陳州，亢分。 汝寧府光州，懷慶府之孟、濟源、溫三縣，直隸壽州之霍丘縣，皆角、亢、氐分。
From ten degrees Chariot to one degree Root—the Shouxing station. Henan’s Kaifeng prefecture—Horn and Neck. Zheng department—Root. Chen prefecture—Neck. Runing’s Guang department; Huaqing’s Meng, Jiyuan, and Wen counties; Zhili Shou department’s Huoqiu—all Horn, Neck, and Root.
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氐二度至尾二度，大火之次也。 河南開封府之杞、太康、儀封、蘭陽四縣，歸德、睢二州，山東之濟寧府，皆房、心分。 直隸鳳陽府之穎州，房分。 徐、宿二州，壽州之蒙城縣，穎州之亳縣，皆房、心分。
From two degrees Root to two degrees Tail—the Dahu station. Henan Kaifeng’s Qi, Taikang, Yifeng, and Lanyang counties; Guide and Sui departments; Shandong’s Jining prefecture—all Room and Heart. Zhili Fengyang’s Ying department—Room. Xu and Su departments; Shou’s Mengcheng; Ying’s Bo county—all Room and Heart.
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尾三度至斗二度，析木之次也。 北平之北平府，尾、箕分。 涿、通、薊三州，皆尾分。 霸州、保定府，皆尾、箕分。 易、安二州，皆尾分。 河間府、景州，皆尾、箕分。 永平府，尾分。 灤州，尾、箕分。 遼東都指揮司，尾、箕分。 朝鮮，箕分。
From three degrees Tail to two degrees Dipper—the Ximu station. Beiping’s Beiping prefecture—Tail and Winnowing Basket. Zhuo, Tong, and Ji departments—all Tail. Bazhou and Baoding prefecture—all Tail and Winnowing Basket. Yi and An departments—all Tail. Hejian prefecture and Jing department—all Tail and Winnowing Basket. Yongping prefecture—Tail. Luan department—Tail and Winnowing Basket. Liaodong regional command—Tail and Winnowing Basket. Korea—Winnowing Basket.