1
漢創渾天儀，謂即璣衡遺制，唐、宋皆仿為之。 至元始有簡儀、仰儀、闚幾、景符等器，視古加詳焉。 明于北京齊化門內倚城築觀象臺，仿元制作渾儀、簡儀、天體三儀，置於臺上。 台下有晷景堂、圭表、壺漏，清初因之。 康熙八年，聖祖用監臣南懷仁言，改造六儀，曰黃道經緯儀、赤道經緯儀、地平經儀、地平緯儀、紀限儀、天體儀。 五十二年，復將地平經、緯合為一儀。 乾隆九年，高宗御製璣衡撫辰儀，並安置臺上。 今考各形制用法，悉著於篇。
Under the Han the armillary sphere was built, held to be the heir of the ancient armillary chronograph; Tang and Song followed the same design. The Yuan added the simplified armillary, altitude instrument, sighting tablet, and shadow marker—finer in make than older models. In Ming Beijing, beside Qihua Gate, they raised the Observatory Terrace against the wall and placed Yuan-style armillary, simplified armillary, and celestial globe instruments upon it. Beneath the terrace stood the Gnomon Hall, a gnomon and table, and clepsydras, retained unchanged at the dynasty's founding. In Kangxi 8 the Kangxi emperor, on Verbiest's advice, commissioned six new instruments: ecliptic theodolite, equatorial theodolite, azimuth theodolite, altitude quadrant, astronomical quadrant, and celestial globe. In Kangxi 52 the azimuth and altitude instruments were merged into a single combined instrument. In Qianlong 9 the Qianlong emperor built the Armillary Sphere and Chronographic Instrument and set it on the Observatory Terrace. What follows records the design and operation of every instrument in full.
2
黃道經緯儀，儀之圈有四，各分四象限，限各九十度。 其外大圈恆定而不移者，名天元子午規，外徑六尺，規面厚一寸三分，側面寬二寸五分，規之下半夾入於雲座。 仰載之半圈，前後正直子午，上直天頂，中直地平。 從地平上下按京師南北兩極出入度分，定赤道兩極。 次內為過極至圈，圈周平分處，各以鋼樞貫於赤道二極。 又依黃赤大距度，於過極至圈上定黃道南北極。 距黃極九十度安黃道圈，與過極至圈十字相交，各陷其中以相入，令兩圈為一體，旋轉相從。 黃道圈之兩側面，一為十二宮，一為二十四節氣。 其兩交，一當冬至，一當夏至。 次內為黃道經圈，則以鋼樞貫于黃極焉。 圈之徑為圓軸，圍三寸。 軸之中心立圓柱為緯表，與經圈側面成直角，而黃道圈經圈上各設遊表，儀頂更設銅絲為垂線。 全儀以雙龍擎之，復為交梁以立龍足。 梁之四端，各承以獅，仍置螺柱以取平。 垂線有偏側，則轉螺柱，垂線正，則儀正矣。 用法，欲求某星黃道經緯度，須一人于黃道圈上查先所得某星之經緯度分，其上加遊表，而過南北軸中柱，表對星定儀； 又一人用游表於經圈上過柱，表對所測之星，遊移取置，則經圈上游表之指線定某星緯度。 又定儀查黃道圈兩表相距之度分，即某星之經度差。 或測日月，以距星為比，亦如之。
The ecliptic theodolite comprises four rings, each quartered into ninety-degree quadrants. Outermost is the fixed primary meridian ring, six chi across, one cun three fen thick on the face and two cun five fen on the edge; its lower half seats in the cloud pedestal. The upper semicircle aligns with the meridian, reaches the zenith, and meets the horizon at midpoint. From the horizon upward and downward, using Beijing's polar altitude and depression, the equatorial poles are set. Inside that lies the polar-transit circle, pierced at equal intervals by steel pivots through the equatorial poles. The ecliptic poles are then marked on that circle according to the obliquity of the ecliptic. The ecliptic ring, ninety degrees from the ecliptic pole, intersects the polar-transit circle at right angles in interlocking mortises so both rings move as one. One face of the ecliptic ring carries the twelve zodiac mansions; the other carries the twenty-four solar terms. The ring's two nodes mark winter solstice and summer solstice. Within sits the ecliptic meridian circle, pivoted on steel at the ecliptic pole. Its diameter is a cylindrical axle three cun around. A latitude pillar rises from the axle center perpendicular to the meridian ring; sliding sights mount on ecliptic and meridian rings, with a copper plumb line at the summit. Twin dragons support the whole; a cross-beam bears their feet. Lions support each end of the beam, with leveling screws beneath. Any tilt of the plumb line is corrected by the screws until the line hangs true and the instrument is aligned. To measure a star's ecliptic coordinates, one operator sets a sight on the ecliptic ring to the star's catalogued longitude and latitude, sights through the central pillar along the polar axis, and fixes the instrument on the star; a second slides a sight along the meridian ring over the pillar until it lines on the target; the meridian sight then reads the star's latitude. Once fixed, the arc between the two ecliptic sights gives the star's longitudinal separation. Sun and moon may be measured the same way against a reference star.
3
赤道經緯儀，儀有三圈，外大圈者，天元子午規也。 以一龍南向而負之。 規之分度定極，皆與黃道儀同。 去極九十度安赤道圈，與子午規十字相交，恆定不動。 圈內規面及上側面皆鋟二十四時，時各四刻。 外規面分三百六十度，內安赤道經圈。 以南北極為樞，而可東西遊轉，與赤道圈內規面相切。 經圈徑為圓軸，軸中心立圓柱，以及遊表、垂線、交梁、螺柱等法，皆同黃道儀。 用法，若測日時刻，則赤道圈上用時刻遊表，即通光耳，對於南北軸表，視赤道圈內遊表所指，即時刻分秒。 若諸曜經度，用兩通光耳，即兩徑表，在赤道圈上一定一遊。 一人從定耳窺南北軸表，與先得星相參測之； 一人以遊耳轉移遷就，而窺本軸表與所測參相直，視兩耳間應赤道圈上之度分，即兩經度之差也。 緯度亦以通光耳於經圈上轉移而遷就焉。 務欲令目與表與所測相參直，視本耳下經圈在赤道或南或北之度分，即所測距赤道南北之度分也。
The equatorial theodolite has three rings; the outermost is again the primary meridian ring. One dragon, facing south, supports it. Its graduations and polar settings match the ecliptic theodolite. The equatorial ring, ninety degrees from the pole, crosses the meridian ring at right angles and does not move. The inner face and upper edge bear twenty-four hours, each divided into four quarters. The outer face carries three hundred sixty degrees; inside sits the equatorial meridian circle. Pivoted at the poles, it swings east and west against the equatorial ring's inner surface. Its meridian ring forms a cylindrical axle with a central pillar; sliding sights, plumb line, cross-beam, and leveling screws follow the ecliptic instrument. To tell time by the sun, align the hour sight—a light aperture—on the equatorial ring with the polar sight; the inner sight's reading gives hour, minute, and second. For planetary or stellar longitude, two light apertures (diameter sights) are used on the equatorial ring, one fixed and one sliding. One observer sights through the fixed aperture along the polar axis against a reference star; the other shifts the sliding aperture until polar sight and target align; the equatorial arc between the two apertures is the longitudinal difference. Latitude is read by sliding the light aperture along the meridian ring into alignment. Eye, sight, and body observed must share one line; the meridian reading below the aperture, north or south of the equator, gives the object's declination.
4
地平經儀，儀只一地平圈，全徑六尺，其平面寬二寸五分，厚一寸二分。 分四象限，各九十度。 以四龍立于交梁以承之。 梁之四端，各施取平之螺柱。 梁之交處安立柱，高與地平圈等，適當地平圈之中心。 又于地平圈上東西各立一軸，約高四尺，柱各一龍，盤旋而上，從柱端各伸一爪，互捧圓珠。 下有立軸，其形扁方，空其中如窗櫺，以安直線。 軸之上端入於珠，下端入立柱中心，令可旋轉。 而軸中之線，恆為天頂之垂線焉。 又為長方橫表，長如地平圈，全徑厚一寸，寬一寸五分，中心開方孔管於立軸下端，使隨立軸旋轉。 復剡其兩端令銳，以指地平圈之度分。 又自兩端各出一線，而上會於立軸中直線之頂，成兩三角形。 凡有所測，則旋轉遊表，使三線與所測參相直，乃視表端所指，即所測之地平經度也。
The azimuth theodolite consists of a single horizon ring six chi in diameter, two cun five fen wide and one cun two fen thick. The ring is quartered, ninety degrees per quadrant. Four dragons on a cross-beam support it. Leveling screws sit at each end of the beam. Where the beams cross, a pillar rises to the ring's height at its center. East and west on the ring stand pillars about four chi tall, each with a coiling dragon whose claws meet to clasp a pearl. A vertical axle, square and hollow like a window frame, holds the sighting wire. Its top fits the pearl, its foot the pillar center, allowing rotation. The wire within remains the zenith plumb line. A rectangular cross-arm as long as the ring's diameter, one cun thick and one cun five fen wide, sleeves the pillar axle at center and turns with it. Both ends are tapered to indicate degrees on the horizon ring. Lines from each end meet the summit of the central wire, forming two triangles. For any observation the sliding sight is turned until three lines align on the target; the cross-arm's reading is the azimuth.
5
地平緯儀，即象限儀，蓋取全圓四分之一以測高度者也。 其弧九十度，其兩邊皆圓半徑，長六尺。 兩半徑交處為儀心。 儀架東西立柱，各以二龍拱之。 上架橫樑，又立中柱上管於橫樑，令可轉動儀心，上指儀之兩邊，一與中柱平行，一與橫樑平行。 又於儀心立短圓柱以為表，又加窺衡，長與半徑等，上端安於儀心，剡其下端，以指弧面度分，更安表耳。 有所測，乃以窺衡上下遊移，從表耳縫中窺圓柱，令與所測相參直。 其衡端所指度分，即所測之地平緯度也。
The altitude quadrant is literally a quarter-circle used to measure elevation. The arc spans ninety degrees; each radial side is six chi, half the full radius. Their intersection is the instrument center. East and west pillars frame it, each pair of dragons forming an arch. A crossbeam above carries a central pillar socketed so the center pivots, one radius parallel to the pillar, one to the beam. At the center a short pillar forms the index; a sighting arm equal to the radius pivots there, its tip reading the arc, with a sighting slit. To observe, the arm is slid until the slit sights the pillar in line with the object. The arc at the arm's tip gives the altitude.
6
紀限儀，弧面為全圓六分之一，分六十度。 一弧一幹，幹長六尺，即全圓之半徑。 弧之寬二寸五分，幹之左右，細雲糾縵纏連，所以固之。 幹之上端有小衡，與幹成十字。 儀心與衡兩端皆立圓柱為表，弧面設遊表。 承儀之台，約高四尺，中植立柱，以系儀之重心，則左右旋轉，高低斜側，無所不可，故又名百遊儀焉。 用法，測兩曜，不論黃赤經緯，而求大圈相距之度，一人從衡端耳表窺中心柱表，對定此曜； 又一人從游耳表向中心柱表窺彼曜相參直，視衡端至遊耳表下度分，即兩曜相距度分也。
The astronomical quadrant's arc is one sixth of a circle, graduated to sixty degrees. One arc and one radius—the radius six chi, the full circle's radius. The arc is two cun five fen wide; cloud-scroll filigree flanks the radius to stiffen the frame. A short transom crosses the radius at its head. Round index pillars stand at center and transom ends; a sliding sight rides the arc. A stand about four chi tall centers a pillar at the instrument's balance point so it may swing in every attitude—hence its alias, the Hundred-Motion Instrument. To measure angular distance between two bodies regardless of coordinate system, one sights from the transom slit through the center index onto the first body; the second sights from the sliding slit through the center index onto the second; the arc from transom to sliding sight is their separation.
7
天體儀，儀為圓球，徑六尺，宛然穹象，故以天體名之。 中貫鋼軸，露其兩端，以屬於子午規之南北極，令可轉運。 座高四尺七寸。 座上為地平圈，寬八寸。 當子午處各為闕，以入子午規。 闕之度與子午規之寬厚等，則兩圈十字相交，內規面恰平，而左右上下環抱乎儀。 周圍皆空五分，以便高弧遊表進退。 又安時盤於子午規外，徑二尺，分二十四時。 以北極為心，其指時刻之表，亦定於北極，令能隨天體轉移，又能自轉焉。 座下復設機輪，運轉子午規，使北極隨各方出地升降，各方天象隱見之限，皆可究觀矣。
The celestial globe is a sphere six chi across, shaped like the dome of heaven. A steel polar axis pierces it and joins the meridian ring's poles so the sphere may revolve. The stand rises four chi seven cun. On the stand sits a horizon ring eight cun wide. Notches at north and south admit the meridian ring. The notches match the meridian ring's section so the rings cross squarely, the inner face flush, cradling the globe on all sides. A five-fen gap all around lets the altitude sight travel freely. Outside the meridian ring a two-chi hour dial shows twenty-four hours. An hour pointer pivoted at the north pole moves with the globe and may also spin independently. Gears beneath drive the meridian ring so the pole lifts and sinks for any latitude, revealing what stars each region may see.
8
地平經緯合儀，經儀中心立柱安緯儀。 用法，旋轉緯儀，對定所測游表，於緯儀上得緯度； 視緯儀邊切經儀之處，即得經度：一測而兩得焉。
The combined instrument mounts the altitude quadrant on the azimuth instrument's central pillar. In use one swings the altitude quadrant, sights the target, and reads latitude from it; where its edge meets the azimuth ring gives longitude—both coordinates in one observation.
9
璣衡撫辰儀，儀制三重，其在外者，即古六合儀，而不用地平圈，其正立雙環為子午圈。 兩面皆刻周天三百六十度，自南北極起，初度至中要九十度，是為天經。 斜倚單環為天常赤道圈，兩面皆刻周日十二時，以子正午正當子午雙環中空之半，而結於其中要，是為天緯。 其南北二極皆設圓軸，軸本實於子午雙環中空之間，而軸內向，以貫內二重之環。 其下承以雲座，仰面正中開雙槽以受雙環，東面正中開雲窩以受垂線。 下面置十字架，施螺旋以取平。 架之東西兩端各植龍柱，龍口銜珠，開孔以承天常赤道卯酉之兩軸，依觀象臺測定南北正線，將座架安定，則平面之四方正。 又依京師北極出地度分，上數至成一象限，即天頂。 依南極入地度分，下數成一象限，即地心。 于天頂施小釘懸垂線，而垂適當地心，又適切於雙環之面。 線末垂球，又適當云窩，不即不離，則上下正立面之四方亦正，而地平已在其中。
The Armillary Sphere and Chronographic Instrument has three nested frames; the outer recreates the ancient six-ring armillary without a horizon ring, its upright double ring serving as meridian. Both faces bear three hundred sixty degrees of celestial longitude, ninety degrees from each pole to the equator crossing. An oblique single ring is the fixed equator, engraved with twelve double-hours; noon and midnight sit in the meridian gap at its center—that is celestial latitude. Polar axles seat in the meridian ring and turn inward to carry the inner rings. A cloud pedestal supports it with twin slots for the meridian ring and an eastern cloud niche for the plumb line. A four-footed cross below carries leveling screws. Dragon pillars east and west grip pearls pierced to hold the equator's east-west axis; aligned to the terrace's meridian, the base squares to the four directions. Counting up from Beijing's polar altitude through one quadrant marks the zenith. Counting down from the south polar depression through one quadrant marks the nadir. A nail at the zenith suspends the plumb line to the nadir, grazing the meridian ring's plane. A sphere at the line's foot nests in the cloud niche without binding; then vertical, horizontal, and horizon are all true.
10
次其內即古三辰儀，而不用黃道圈。 其貫於二極之雙環，為赤極經圈。 兩極各設軸孔，以受天經之軸，兩面皆刻周天三百六十度。 結於赤極圈之中要，與天常赤道平運者，為遊旋赤道圈，兩面皆刻周天三百六十度，與宗動天赤道旋轉相應。 自經圈之南極，作兩象限弧以承之，使不傾墊。
Inside that lies the ancient three-luminaries armillary, omitting the ecliptic ring. The polar double ring is the equatorial meridian circle. Polar sockets take the longitude axle; both faces repeat the three hundred sixty-degree circuit. At its center a revolving equator, parallel to the fixed ring and engraved with three hundred sixty degrees, tracks the primum mobile's equator. Quadrant arcs from the southern meridian support it against tilt.
11
次最內即古四遊儀，貫於二極之雙環，為四遊圈，兩面皆刻三百六十度。 定于遊圈之兩極者為直距，綰於直距之中心者為窺衡。 遊圈中要設直表，以指經度及時，窺衡右旁設直表，以指緯度。 別設借弧指時度表、立表、平行立表、平行借弧表，以濟所測之窮。 又設綰經度表、綰時度表、平行線測經度表，以期兩測之合。
Innermost is the four-motion armillary: a polar double ring, the four-motion circle, engraved with three hundred sixty degrees on both faces. The straight pivot is fixed at both poles of the motion ring; the sight-tube is lashed to its center. A straight sight inside the ring marks right ascension and time; another beside the sight-tube marks latitude. Auxiliary borrowed-arc, upright, parallel upright, and parallel borrowed-arc sights cover cases the main setup cannot reach. Pin gauges for right ascension and time plus a parallel-line right-ascension gauge align paired readings.
12
其數，子午圈外徑六尺三寸，內徑五尺六寸六分，環面闊三寸二分，厚九分，中空一寸。 天常赤道外徑六尺一寸二分，內徑五尺六寸四分，環面闊二寸四分，厚一寸四分。 赤極經圈外徑五尺五寸六分，內徑五尺一寸二分，環面闊二寸八分，厚八分，中空一寸二分。 遊旋赤道外徑五尺五寸六分，內徑五尺一寸二分，環面闊二寸二分，厚一寸二分。 四遊圈外徑五尺，內徑四尺六寸八分，環面闊一寸六分，厚七分，中空一寸四分。 直距長如圓之通徑，闊一寸六分，厚七分，中空一寸四分。 窺衡長四尺七寸二分，方一寸二分，中空一寸。 上下兩端施方銅蓋，厚五分，內三分，方一寸，入于管中，外二分，方一寸二分，齊于管面，中心開圓孔。
The meridian circle measures 6 ft 3 in outer, 5 ft 6.6 in inner, 3.2 in face width, 0.9 in thick, with a 1 in hollow center. The constant celestial equator ring is 6 ft 1.2 in outer, 5 ft 6.4 in inner, 2.4 in face width, and 1.4 in thick. The celestial-pole meridian circle is 5 ft 5.6 in outer, 5 ft 1.2 in inner, 2.8 in face width, 0.8 in thick, with a 1.2 in hollow center. The revolving equator ring is 5 ft 5.6 in outer, 5 ft 1.2 in inner, 2.2 in face width, and 1.2 in thick. The four-motion ring is 5 ft outer, 4 ft 6.8 in inner, 1.6 in face width, 0.7 in thick, with a 1.4 in hollow center. The straight pivot spans the ring's full diameter, 1.6 in wide, 0.7 in thick, with a 1.4 in hollow center. The sight-tube is 4 ft 7.2 in long, 1.2 in square, with a 1 in hollow bore. Square copper caps cap both ends: 0.5 in thick, 1 in square inside the tube, 1.2 in square flush outside, with a central round hole.
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指時度表，通長七寸三分，本長一寸六分，形如方筒，入于四遊雙環中空之間，闊一寸四分，橫帶長三寸二分，闊五分，兩端各鉤回二分，扣於環面之外。 表長五寸二分，闊一寸。 其指時度之邊線，對方筒之正中，下端二寸四分，厚三分，切于遊旋赤道之面，以指度分。 上端二寸八分，厚二分，切于天常赤道之面，以指時刻。
The time-degree indicator is 7.3 in overall, 1.6 in body, a square tube in the four-motion ring hollow, 1.4 in wide, with a 3.2 by 0.5 in cross-strap hooked 0.2 in at each end over the ring face. The indicator plate is 5.2 in long and 1 in wide. The time-degree edge aligns with the tube center; the lower 2.4 in, 0.3 in thick, lies tangent to the revolving equator to mark degrees. The upper 2.8 in, 0.2 in thick, lies tangent to the constant celestial equator to mark the hour.
14
指緯度表，其形兩曲，安於窺衡之右面。 底長三寸，闊九分，曲橫七分，與四遊環之厚等。 又曲長一寸七分，切于四遊環之外面，從中線減闊之半，所以指緯度也。
The latitude indicator is doubly curved and mounted on the sight-tube's right face. Its base is 3 in long, 0.9 in wide; the curve spans 0.7 in, matching the four-motion ring's thickness. A further 1.7 in curve lies tangent to the ring's outer face; half the width is trimmed from the center line to mark latitude.
15
借弧指時度表，其本方筒及橫帶長闊並與前指時度表同。 橫帶之下，自左向右，立安弧背一道，長九寸三分，闊一寸二分，厚一分六釐。 弧背之末，平安指時度表，除弧背之厚，長五寸二分，闊一寸。 計自表本方筒之中線至指時度表之內邊，長六寸七分，當遊旋赤道之十五度，當天常赤道之一小時。
The borrowed-arc time-degree indicator matches the main indicator's square tube and cross-strap dimensions. Below the cross-strap a curved back is set left to right: 9.3 in long, 1.2 in wide, 0.16 in thick. At the arc's end sits a level time-degree indicator, 5.2 by 1 in apart from the arc's thickness. From the square-tube center to the indicator's inner edge is 6.7 in — fifteen degrees on the revolving equator, one hour on the constant celestial equator.
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立表二座，形直底平，表高底長各三寸二分，闊九分，厚一分。 一表向上開長方孔，長一寸，中留直線，又上五分開圓孔，徑四分，中留十字線，安於窺衡之上端。 一表依前度下開直縫，上開小圓孔，安於窺衡下端，各對衡面中線，以螺旋結之。
Two upright sights, straight with flat bases, each 3.2 in high and long, 0.9 in wide, 0.1 in thick. One sight has a 1 in rectangular slot with a center line, then a 0.4 in round hole 0.5 in above with crosshairs, on the sight-tube's upper end. The other has a lower slit and upper pinhole on the lower end, each aligned to the tube center line and screwed fast.
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平行立表二座，形曲底平，底盤長四寸，闊一寸二分，厚一分，中空三寸二分，闊九分。 表曲如勾股。 股直如立表，高三寸二分，闊九分。 勾橫連於股末，長五寸，闊九分，橫植於底盤之末。 底盤中空，冒於立表底盤之外，以掐表固之。
Two parallel upright sights curve from flat bases: base plate 4 by 1.2 in, 0.1 in thick, with a 3.2 by 0.9 in hollow center. Each sight forms a right triangle. The vertical leg stands like an upright sight, 3.2 in high and 0.9 in wide. The horizontal leg joins the foot, 5 by 0.9 in, cross-mounted at the base plate's end. The hollow base plate sleeves over the upright sight's base and clamps it fast.
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平行借弧表，制如平行立表，而倒正異。 一表上植於衡面，高四寸一分零八毫，一表自衡面下垂，長六寸二分零八毫。 距表端下六分開圓孔，又下五分開長方孔，皆與立表制同。
The parallel borrowed-arc sight matches the parallel upright sight but reversed in orientation. One sight rises 4.108 in from the tube face; the other hangs 6.208 in below it. Each has a round hole 0.6 in from the end and a rectangular slot 0.5 in lower, as on the upright sights.
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綰經度表，通長四寸，闊一寸四分。 其本方筒長一寸六分，高一寸八分，入于四遊雙環之間，以左右螺旋固之。 其末上下二面，以夾遊旋赤道，上面闊七分，減本之半，與窺衡中線相直，下面以螺旋固之。
The pin right-ascension gauge is 4 in long and 1.4 in wide overall. Its 1.6 by 1.8 in square tube sits between the four-motion double rings and is screwed fast on both sides. The end's upper and lower jaws clamp the revolving equator; the upper jaw, 0.7 in wide and half the body trimmed, aligns with the sight-tube center line; the lower is screwed fast.
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綰時度表，內外二截，內截上下內三面，綰于遊旋赤道之內規。 上面之末，承於外截之下，開二方孔，以受外截之方足，下面以螺旋固之。 外截上下外三面，綰于天常赤道之外規。 上面之末，覆於內截之上，下面以螺旋固之。
The pin time gauge has inner and outer sections; the inner section's three inner faces lash to the revolving equator's inner rim. The inner upper end supports the outer section below, with square holes for the outer feet; the lower face is screwed fast. The outer section's three outer faces lash to the constant celestial equator's outer rim. The outer upper end caps the inner section; the lower face is screwed fast.
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平行線測經度表，于直距南北極之兩端，各安銅版，如工字形，正方二寸八分，與直距二面之分等。 兩要各缺一長方，長一寸六分，闊七分，扣於直距中空之間。 中心開圓孔，貫於天經之軸。 四隅距中心一寸九分，各安立柱，圓頂開孔，以穿直線，與直距中徑平行。 下安小環，以為結赤經平行線之用。 又按距星宮度，于游旋赤道安赤經平行線表，其制上畫半圓，內容半方，自對角斜線起，初度至橫徑為四十五度，其中直徑與指度表之邊線相參直。 半圓中心安二遊表，各長二寸，距中心一寸九分。 邊留小臍，中開小圓孔，以線穿之。 上端系於北極銅版對角之兩環，下端貫於南極銅版對角之兩環，各以垂球墜之。
On the straight pivot's north and south ends sit gong-shaped copper plates, 2.8 in square, matching the pivot's face divisions. Each arm has a 1.6 by 0.7 in rectangular notch clasping the pivot's hollow center. A central round hole receives the celestial-axis shaft. At each corner 1.9 in from center stands a post with a holed round cap for a line parallel to the pivot's bore axis. A small ring below serves to tie the right-ascension parallel line. By the reference star's mansion and degree a right-ascension parallel-line gauge on the revolving equator bears a semicircle over a half square; from the diagonal, initial degree to cross diameter is forty-five degrees, its vertical diameter aligned with the degree indicator's edge. Two traveling indicators, each 2 in long, sit 1.9 in from the semicircle's center. Each edge has a small navel with a central hole for a line. The upper end ties to the north plate's diagonal rings; the lower passes the south plate's diagonal rings, each weighted with a plummet.
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用法，測日時刻，以四遊圈東西推轉，窺衡南北低昂，令日光透孔圓正，視四遊圈下指時度表臨天常赤道某時刻，即得。 若日景為赤道所礙，則用窺衡上立表測之，令表兩孔正透，仍于指時度表視時刻。 或為龍柱所礙，則用平行立表測之，亦于指時度視時刻。 若指時度表為子午圈所礙，則易用借弧指時度表，次用平行立表。 測定日景，視借弧指時度表所指時刻，加一小時，即得。 測經度，取所知正午前後一恆星，以其赤道經度之對沖，用綰經度表于遊旋赤道綰定四遊圈。 又任設一時，用綰時度表，于其時之對沖，綰天常赤道。 乃將四遊圈帶定遊旋赤道，用窺衡測准距星，隨之左旋。 候至所設時刻，視綰時度表對遊旋赤道某宮度分，即日赤道經度。 或以本時太陽赤道經度，用綰時度表于遊旋赤道綰定，又以所設時刻之對沖，于天常赤道綰定。 候至所設時刻，用四遊窺測月星，乃視指時度表所指游旋赤道宮度，加半周，即得所測月星赤道經度。 測兩曜相距經度，用平行線測經度表于游旋赤道初宮初度安定，令一人用此平行線表、左兩線、右兩線，並窺定距西之曜，隨之左旋； 一人用四遊窺衡測距東之曜，視指時度表所指遊旋赤道之度分，即所測兩曜相距赤道經度也。 測緯度，凡得經度時，隨察指緯度表所指四遊圈之度分，即得所測赤道緯度。 其有所礙，皆如測時刻法易之。 其近北極之星，則以平行借弧表測之。
To read solar time, turn the four-motion ring east-west and tilt the sight-tube north-south until sunlight through the aperture is round and true; the time-degree indicator under the ring against the constant celestial equator gives the hour. If the equator blocks the sun's ray, use the sight-tube's upper upright sight with both holes aligned and still read the time-degree indicator. If dragon pillars block the view, use the parallel upright sight and read the time-degree indicator. If the meridian circle blocks the time-degree indicator, switch to the borrowed-arc indicator, then the parallel upright sight. For a shadow reading, take the borrowed-arc indicator's hour and add one hour. To measure right ascension, take a known star near noon, set the pin right-ascension gauge at the opposition of its equatorial right ascension, and lash the four-motion ring to the revolving equator. Choose an hour and lash the constant celestial equator with the pin time gauge at its opposition. Lock the four-motion ring to the revolving equator, sight the reference star through the sight-tube, and rotate west with it. At the set hour read the pin time gauge against the revolving equator's mansion and degree for the sun's equatorial right ascension. Alternatively lash the revolving equator with the sun's current equatorial right ascension and the constant celestial equator at the set hour's opposition. At the set hour sight moon or star through the four-motion tube; the time-degree indicator's mansion on the revolving equator plus half a circuit gives its equatorial right ascension. To measure separation between two bodies, fix the parallel-line right-ascension gauge at the revolving equator's first mansion, first degree; one observer sights the western body with left and right line pairs and rotates west with it; another sights the eastern body through the four-motion sight-tube; the time-degree indicator's degrees on the revolving equator give their equatorial longitudinal separation. For latitude, whenever right ascension is found, read the latitude indicator's degrees on the four-motion ring for equatorial latitude. Any obstruction is handled by the same substitutions used for hour measurement. Stars near the north pole are measured with the parallel borrowed-arc sight.