The Kaiyuan Treatise on Astrology (Tang Dynasty, compiled by Qutan Xida under imperial commission)

《繫辭》云：“易有太極，是生兩儀。’元氣已分，天地設位。清浮升乎上，沈濁居乎下。陰陽以之而變化，寒暑用此而相推。辨尊卑貴賤之道，正內外男女之位。在天成象，三辰顯曜；在地成形，五雲布澤。斯昏明於晝夜，榮落於春秋。大聖之所經綸，以合三才之道；

The Zhou Changes (I Ching) Great Treatise says: "The Book of Changes contains the Taiji, and the Taiji gives rise to the two principles." After the primordial qi was divided, heaven and earth each took their proper positions: the light and light-hearted rose upward, while the heavy and turbid sank downward. Thus yin and yang changed, cold and heat alternated; the principles of respect and humility, nobility and lowliness were established, and the positions of inside and outside, male and female were properly ordered. In the heavens, forms were condensed into images, and the sun, moon, and stars shone brightly. On the earth, forms were condensed into bodies, and the five-colored clouds spread their blessings. Thus day and night had light and darkness, and spring and autumn had prosperity and decay. All these were governed and arranged by the great sages, in accordance with the principles of heaven, earth, and humanity.

清浮之氣，升而為天，天以妙氣為妙氣之體，廣遠為量。彌覆無所不周，運行來住不息。一晝一夜，圓轉一周。張覆之廣，莫能際其邊際。運行之妙，無有見其始終。不可以度數而知，不可以形象而譬。此天之大體也。沈濁之氣，下凝為地。地以土水為質，廣厚為體，邊際遠近，亦不可知。質常安伏，寂然不動。山嶽水海，育載萬物，此地之大體也。

Clear and light qi rises to form heaven. Heaven takes refined and subtle qi as its body, and has vastness as its measure. It spreads widely and covers everything, never ceasing in its movement and circulation, completing a full cycle in one day and night. It spreads its vast coverage, and no one can measure its boundaries; its subtle movement is unseen from beginning to end. It cannot be measured by numbers or compared by form: this is the great nature of heaven. Turbid and heavy qi descends and condenses to form earth. Earth takes earth and water as its substance, and has thickness and breadth as its form. Its boundaries, whether far or near, are unknown; its substance is stable and constant, still and unmoving, nurturing and supporting all things through mountains, rivers, and seas: this is the great nature of earth.

天地之間，別有升降之氣，資始資生，以成萬物。《易》曰：‘大哉乾元，萬物資始；大載坤元，萬物資生。’資始之氣，能始萬物，一動一靜。或此乃天之別用，非即地之形體。資生之氣，能生萬物，一翕一闢，或此亦地之別用非即地之形體。

Between heaven and earth, there exists another kind of rising and falling energy. On one hand, it supports the beginning of all things, and on the other hand, it supports the growth of all things, thus achieving the completion of all things. The Zhou Changes say: "Great is the Qian Origin, by which all things begin; vast is the Kun Origin, by which all things grow." The energy that supports the beginning can initiate all things; with one movement and one stillness, perhaps this is another function of heaven, not the physical body of heaven itself. The energy that supports growth can foster all things; with one union and one separation, perhaps this is another function of earth, not the physical body of earth itself.

四大海之外，有金剛山，一名鐵圍山。金剛山北，又有黑山。日月循山而轉周廻四面，一晝一夜，圍繞環匝。於南則現，在北則隱，冬則陽降而下，夏則陽升而高。高則日長，下則日短。寒暑昏明，皆由此作。夏則陽升，故日高而出山之道遠。冬則陽降，故日下而出山之道促。出山遠則日長，出山促則日短。二分則合高下之中，故半隱半見，所以晝夜均等，無有所短。

Beyond the four great seas, there is a mountain called Jin Gang Shan, also known as Tie Wei Shan. To the north of Jin Gang Shan is another mountain called He Shan. The sun and moon revolve around the mountains, circling the four sides, completing one circuit in a day and night. When they reach the south, they appear; when they reach the north, they disappear. In winter, yang energy descends and its position is lower; in summer, yang energy ascends and its position is higher. When the position is higher, the day is longer; when the position is lower, the day is shorter. Cold and heat, darkness and brightness are all generated from this. In summer, yang energy ascends, so the sun is high and the path it travels around the mountain is long; in winter, yang energy descends, so the sun is low and the path it travels around the mountain is short. A long path around the mountain means a long day, and a short path means a short day. On the days of the two equinoxes, the sun is exactly in the middle of high and low positions, so the mountain is half visible and half hidden, resulting in equal day and night, with neither side being shorter.

日照於南，故南方之氣燠。日隱在北，故北方之氣寒。南方所以常溫者，冬月日近南而下，故雖冬而猶溫。夏則日近北而高，故雖夏猶不熱。北方所以以常寒者，日行繞黑山之南，日光常自不照，積陰所聚，熏氣遠及，無冬無夏，所以常寒。故北風則寒，南風則暖。一歲之中，則日夏升而冬降；一日一夜，則晝見而夜隱。

The Sun shines to the south, so the southern climate is warm; the Sun hides to the north, so the northern climate is cold. The southern region remains warm throughout the year because during winter the Sun is positioned to the south and lower, so even in winter it remains warm; in summer the Sun is positioned to the north and higher, so even in summer it is not excessively hot. The northern region remains cold throughout the year because the Sun circles south of the Black Mountain, and sunlight never reaches there. Accumulated Yin energy gathers, and cold air spreads far and wide, so whether in winter or summer, it remains cold. Therefore, when northern winds arise, it becomes cold, and when southern winds arise, it becomes warm. Throughout the year, the Sun rises higher in summer and lowers in winter; within a day and night, the Sun appears during the day and disappears at night.

黑山之峰正當北極之南，故夏日雖高，而不能不至寅而現，又至戌而隱。春秋分則居高下中，朝至金剛山之外，雖與山平，而去山猶遠，故為金剛所障，日未能出，須至卯然後乃現；西方亦復如是。冬則轉下。所隱亦多，朝至於辰則出金剛之上，夕至於申則入金剛之下，金剛四面略齊，黑山在北；當北彌峻，東西連峰，近前轉下，所以日在北而隱，在南而現。

The peak of Black Mountain is directly south of the North Pole, so although the summer sun is high, it still appears at the hour of Yin and disappears at the hour of Xu. At the vernal equinox and autumnal equinox, the sun is in the middle of its height, and in the morning it moves beyond the peak of the Jade Emperor Mountain. Although it has reached the same level as the mountain, it is still far away, so it is blocked by the Jade Emperor Mountain and cannot appear until the hour of Mao. The same situation occurs when the sun sets in the west. In winter, the sun is lower, and the part that is blocked is greater. In the morning, it rises above the Jade Emperor Mountain at the hour of Chen, and in the evening, it disappears below the Jade Emperor Mountain at the hour of Shen. The Jade Emperor Mountain is roughly level on all sides, with Black Mountain to the north, which becomes higher and more rugged as it goes north. The eastern and western sides have connected peaks, which gradually become lower as they approach the front. Therefore, when the sun moves north, it disappears, and when it moves south, it appears.

夫人目所望，至遠則極，二山雖有高下，皆不能見。三辰之體，理繫陰陽，或升或降，隨時而動。至於天氣清妙，無所不周，雖自運動無間，日月星辰遲疾各異，晷度多少不繫乎天。金剛自近天之南，黑山則近天之北極，雖於金剛為偏，而南北為一。

What the human eye can see has a limit, and even the two mountains, though of different heights, are beyond sight. The forms of the sun, moon, and stars belong to the principles of yin and yang, rising and setting, moving with the time. As for the clear and subtle nature of the sky, it pervades everywhere. Although the body is constantly moving, the sun, moon, and stars each have their own varying speeds, and the length of shadows and degrees do not depend on the sky. The Diamond Mountain is originally near the southern side of the sky, while the Black Mountain is near the northern pole of the sky; although it is偏 on one side relative to the Diamond Mountain, in terms of the continuous line of north and south, they are on the same line.

制旨解釋云：‘金剛山自近天之南，黑山則近天之北極，準於金剛為偏，而於南北為一。令上林館學士虞劇穎，上林館倪徽仁、劉文道等，算其度數，開列於後。’臣履等謹奉依敕旨推按曆法表景知長短之差，日行南北之道；旁考經紀，近較目前，莫不事事符合，昭然可見。謹略條度數如左：

The explanation from "Zhi Zhi" says: The Diamond Mountain is originally close to the southern side of the sky, while the Black Mountain is near the northern pole of the sky; compared to the Diamond Mountain, it is considered biased, but in terms of the north-south direction, it is consistent. They ordered the scholars at the Shanglin Academy, Yu Juying, Ni Weiren, and Liu Wenda, to calculate its measurements and list them afterwards. The officials Yu Lü and others respectfully followed the imperial decree, examined the calendar, and used the gnomon's shadow to determine the variation in the length of the sun's shadow and the path of the sun's movement north and south; they also referred to classical texts and compared them with current observations, and everything matched perfectly, clearly evident. They carefully listed the measurements in a concise manner as follows:

日道圓周三百六十五度，分為十二辰，辰三十度半。春秋分出卯入酉，冬至則出辰入申，夏至則出寅入戌，春秋分出卯中左右十五度，冬至日出卯南，去卯中二十四度，則是侵辰九度。夏至日出卯北，去卯中亦二十四度，則是侵寅九度。春分日入酉，左右亦各十五度。冬至日入酉南，去酉中二十四度，是侵申九度。夏至日入酉北，去酉中亦二十四度，是侵戌九度。

The path of the Star of brightness and prestige covers a circle of 365 degrees, divided into twelve branches, each covering 30.5 degrees. At the vernal equinox and autumnal equinox, the Star of brightness and prestige rises at the Mao position and sets at the You position. At the winter solstice, it rises at the Chen position and sets at the Shen position. At the summer solstice, it rises at the Yin position and sets at the Xu position. At the vernal equinox and autumnal equinox, the Star of brightness and prestige rises exactly in the middle of the Mao position, within fifteen degrees to the left and right. At the winter solstice, the Star of brightness and prestige rises twenty-four degrees south of the Mao position, thus intruding nine degrees into the Chen position. At the summer solstice, the Star of brightness and prestige rises twenty-four degrees north of the Mao position, thus intruding nine degrees into the Yin position. At the vernal equinox and autumnal equinox, the Star of brightness and prestige sets exactly in the middle of the You position, within fifteen degrees to the left and right. At the winter solstice, the Star of brightness and prestige sets twenty-four degrees south of the You position, thus intruding nine degrees into the Shen position. At the summer solstice, the Star of brightness and prestige sets twenty-four degrees north of the You position, thus intruding nine degrees into the Xu position.

北極璇璣玉衡，上當天之北五十五度，北去黑山頂三十六度。夏至日在天南十二度。春秋分日在天南三十六度。冬至日中，日在天南五十度。冬至日中，日去金剛南三十度。梁武說云：‘四大海，外有金剛山，一名鐵圍山，山北又有黑山。虞履等又以璇璣玉衡在人之北五十五度，北去黑山三十六度。或曰：瞻星望月，蓋不及渾；度景量天，渾不及蓋。竊較醚之笠之，末盡天體之頤；而候之測之，才窮推出之妙。”

The North Celestial Pole, specifically the Xuan Ji Yu Heng, is positioned directly northward at an angle of fifty-five degrees from the heavens, and is thirty-six degrees north of the Black Mountain peak. On the summer solstice, the Sun is twelve degrees south of the heavens; on the vernal and autumnal equinoxes, it is thirty-six degrees south; and on the winter solstice, it is fifty degrees south. On the winter solstice at noon, the Sun is thirty degrees south of the southern side of the Jade Diamond Mountain. Liang Wu Di said: beyond the four great seas lies the Jade Diamond Mountain, also known as the Iron Encircling Mountain. To the north of this mountain is the Black Mountain. Yu Lu and others believed that the Xuan Ji Yu Heng is fifty-five degrees north of the human realm and thirty-six degrees north of the Black Mountain. Some people said: observing stars and the moon, the method of the Covering Heaven is inferior to the method of the Round Heaven; measuring shadows to determine the heavens, the method of the Round Heaven is inferior to the method of the Covering Heaven. (The original text of the last sentence has errors.) In essence, it means that using the hat-like shape of the Covering Heaven to measure the heavens can never fully comprehend the profound mysteries of the celestial bodies; while observation and calculation can only exhaust the skillful methods of prediction and calculation.

梁人朱史《定天論》：“日一千六百七十里，周天六十萬二百三十一里，徑率求之，得十九萬四千一百六十四里，即天東西南北相去之數也。求之得九萬七千八百里，即春、秋分日天去地之數也。夏至日天去地上八萬一千三百九十四里，冬至之日為天去地上十萬六千二十里也。”

Liang dynasty scholar Zhu Shi in his work "Ding Tian Lun" said: The diameter of the Sun is 1,670 li; the circumference of the sky is 600,231 li. Using the diameter ratio to calculate, it results in 194,164 li, which is the distance between the eastern and western ends of the sky. Further calculation gives 97,800 li, which is the distance between the sky and the earth at the time of the vernal and autumnal equinoxes. At the summer solstice, the distance between the sky and the earth is 81,394 li, and at the winter solstice, it is 106,020 li.

隋掖縣丞劉焯《渾天論》曰：“璇璣玉衡，正天之呂。帝王欽若，世傳其象。漢之孝武，詳考律曆，則落下閎，鮮于妄人共所營定。逮於張衡，又尋述作。亦體制不異閎等。雖閎制莫存，而衡造有器。至吳世陸績、王蕃，並更修鑄，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。

In the "Hol Tian Lun" (On the Sphere), Liu Zhuo, county magistrate of Ye County during the Sui Dynasty, said: The Xuan Ji Yu Heng is the standard for correcting celestial phenomena, and all successive emperors have respectfully followed it, with its form passed down through the generations. Emperor Wu of the Han Dynasty carefully examined the pitch-pipes and calendar systems, and had Luo Haoming and Xian Yu Wangren jointly construct and determine them; later, Zhang Heng further elaborated and wrote about them, and the system he established was not significantly different from that of Luo Haoming and others. Although the instruments made by Luo Haoming no longer exist, those made by Zhang Heng still remain as physical objects. During the Wu Kingdom period, Lu Ji and Wang Fen both re-constructed and cast new ones: Lu Ji's version had slight differences, while Wang Fen's was largely the same. During the Liu Song Dynasty, Qian Yuezi, and in the early Northern Wei Dynasty, Chao Chong and others, all used bronze and iron to cast them. Although their sizes varied, the circular framework and overall structure were essentially the same as those made by Wang Fen.

觀蔡氏《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，差在毫釐，大象一乖，餘何可驗。況赤黃均度，月無出入，分至所恆，定氣不別。衡分刻本差，輪!守故，其為疏謬，不可復言。

Now looking at Cai Yong's "Monthly Orders and Comments" and Zheng Xuan's annotations on "The Book of Documents: Examination of the Celestial Phenomena," their approaches are the same as Zhang Heng's methods, and have not changed until today. I, Liu Zhuo, with my limited perspective, have carefully considered and discovered that the data and systems of these instruments are all incorrect and unrealistic. A small error in measurement leads to a great deviation; once the overall pattern of celestial phenomena is wrong, what else can be verified? Moreover, both the equator and the Yellow Path are divided into degrees, and the moon is said to have no movement in and out, while the two solstices and two equinoxes are fixed and unchanging, without distinguishing the fixed points of the seasons. The divisions of the Zuben (the pointer of the armillary sphere) originally had errors, and the rings still follow the old pattern (the original text here contains an error), its omissions and mistakes are really beyond description.

亦既由理不明，致使眾家問出，蓋及宣夜，三說並驅，平昕安穹，四天騰沸。至當不二，理惟一揆，豈容天體七種殊說，又漏景去極，就渾可推，百骸共體，本非異物。此真已驗，彼偽自彰。豈朗日未輝而爝火不息；理有而闕，詎不可悲者也。

Precisely because the principles of celestial phenomena are difficult to explain clearly, various schools have emerged to offer their own theories: the Covering Heaven, the Expanse Heaven, and the Interwoven Heaven schools have all competed with each other, and there are also four other schools, the Level Heaven, the Dawn Heaven, the Secure Heaven, and the Dome Heaven, all clamoring together. There is only one proper principle in the universe, and there should be only one standard for measurement. How can there be seven conflicting theories about celestial phenomena? Moreover, methods such as using water clocks to measure time and using shadows to determine the altitude of the North Pole can all be calculated according to the model of the Interwoven Heaven theory. Just as a person's limbs all belong to the same body, celestial phenomena and calculations are inherently not two separate things. Since the Interwoven Heaven theory has already been verified as true by actual observations, the false claims of the other schools naturally become evident. How could there be a case where the bright sun has already risen, yet a small oil lamp still refuses to be extinguished? The correct principle is clearly there yet is ignored, is that not a cause for sorrow?

昔蔡伯喈自朔方上書曰：以八尺之儀，度知天地之象。古有器而無其書，常欲寢伏儀下，案度在數，而為立說。伯喈以負罪朔方，書奏不許。伯喈若蒙許，亦必不能。伯喈才不逾張衡，衡本豈有遺思也。則有器無書，觀不能悟。焯今立術，改正舊渾，又以二至之景，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。待得景左，謹更啟送。

At that time, Cai Yong, who was given the courtesy name Boyue, submitted a memorial to the court from his place of exile in Shuofang, saying: With a single armillary sphere of eight chi in height, one can determine the shape of heaven and earth; since ancient times, there have only been instruments but no explanatory writings about them. He wished to stay day and night beneath the armillary sphere, following the markings and based on actual measurements, to compose a system of theory for it. However, Cai Yong was then in exile for a crime, and his memorial was not approved by the court. In fact, even if it had been approved, he might not have been able to complete it — Cai Yong's abilities did not surpass Zhang Heng's. Could Zhang Heng have left all the thoughts unconsidered? This shows that having only instruments without explanatory writings, one cannot by mere observation grasp the principles. Now I, Liu Zhuo, have established a new system of calculation, correcting the old methods of the armillary sphere. I have also measured the degree of the North Pole above the horizon, the length of day and night, and the distances and heights between heaven and earth, based on the shadows at the winter solstice and summer solstice. The regular patterns of the movement of the stars can all be traced back to their origins and provide corresponding constants of motion, sufficient to resolve the great doubts of contemporary scholars and settle the various conjectures left by ancient sages. It is like dispelling clouds to see the sun or clearing mist to reveal the sky, making things suddenly clear. I have already compiled and organized these contents into several volumes; once the actual measurements of the shadows are obtained, I will respectfully present them.

又云：周官夏至日景，尺有五寸。張衡、鄭玄、王蕃、陸績先儒等，皆以為景千里差一寸，言南戴日下，萬五千里。表景正同，天高乃異。考之算法，必為不可。寸差千里，亦無典據。明為意斷，事不可依。今交愛之州，表北無景，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。道里既定，得差乃審。既大聖之年，昇平之日，釐改群謬，斯正其時。請一水工，並解算術士，取河南北平地之所，可時數百里。南北使正，審時以漏，平地以繩。隨氣至分，同日度景。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。”

Liu Zhuo also said: The "Rites of Zhou" records that on the day of Summer Solstice, the shadow of a gnomon is one foot five inches long. Zhang Heng, Zheng Xuan, Wang Fan, and Lu Ji, these previous scholars, all believed that for every thousand li of distance north and south, the shadow differs by one inch. Based on this, they concluded that the place directly facing the Sun is fifteen thousand li to the south. However, if the shadows at different places are exactly the same, then the calculated height of the heavens would vary accordingly. When checked with calculations, this claim is definitely untenable. The idea of "a difference of one inch for every thousand li" has no basis in the classics, and clearly comes from subjective assumptions, and cannot be used as a standard. Now in the areas of Jiaozhou and Aizhou, the north side of an eight-foot gnomon shows no shadow at all. Calculating the distance from the Central Plains, it is not even ten thousand li, yet its position has already passed the place directly facing the Sun. This shows that "a difference of one inch for every thousand li" is not an accurate measure. I, Liu Zhuo, explain the theory of the浑天 (spherical heavens), using actual measured distances as the standard: once the distance is measured, the difference in shadows can be accurately determined. Now, during the time of a sage ruler and a peaceful world, it is the best time to correct these long-standing errors. Please send a skilled craftsman who is expert in level measurement, and a person who understands arithmetic, to select a flat area along the Yellow River, measure a section of several hundred li in length, correct the north-south direction to be perfectly straight, use water clocks to accurately determine the time, use a measuring rope to level the ground, and on the day of the solstices or the equinoxes, measure the shadows at the same time at both the northern and southern locations. By determining the rate of difference, we can calculate how much one li corresponds to in shadow length. In this way, the shape of heaven and earth will no longer be hidden, and the stars will no longer be able to escape the calculations. This is a method surpassing previous ones, clarifying the virtue of the sage, and eliminating doubts through actual observation of the heavens. Please do not discard this statement just because of my personal opinion.

按劉焯《皇極曆》云：“凡日食，由月行黃道，體所映蔽大，較正交正如累璧，漸減則有差，在內食分多，在外無損，雖外全而月下，內損而更高。交淺則間遙，交渾則相博。或由近而不掩，因遙而蔽多，所觀之地又偏，所食之時又別。月居外道，此不見虧，月外之人，反以為食。交分正等，因在南方，冬損則多，夏虧乃少。假均冬夏，早晚又殊。處南北體則高，居東西傍而下。視有邪正，理不可一。且古史所說，本有紛互，今故推其梗概，求者知其指歸。

The editor's note cites Liu Zhuo's "Huangji Li" saying: "Whenever there is an eclipse of the sun, it is because the moon travels along the Yellow Path, and the amount of the moon covering the sun's surface varies. When the moon is exactly at the intersection point, it is like two jade disks stacked together. As the intersection point gradually moves away, the coverage differs: if the moon is inside the Yellow Path, the eclipse is more pronounced; if it is outside, the sun's surface is not affected. Although when the moon is outside, the sun's surface remains intact, the moon's position is lower; when it is inside, the sun's surface is obscured, but the moon's position is higher. If the intersection points are shallow, the sun and moon appear distant; if they are close, they seem near and in conflict. Sometimes because they are close, the moon cannot fully cover the sun; sometimes because they are far apart, the moon can cover more. Moreover, the location of observation differs east or west, so the time of the eclipse varies. When the moon is on the outer side of the Yellow Path, people here cannot see the eclipse, but people elsewhere can. Even if the eclipse proportions are the same, when the sun is in the southern sky, the eclipse is more severe in winter and less in summer. Assuming the conditions of winter and summer are the same, the eclipse observed in the morning or evening is different: when the sun is in the south or north, its position is higher; when it is in the east or west, it is near the horizon and lower. Vision is either slanting or straight, so the principle cannot be generalized. Moreover, ancient records are inconsistent, so now we merely provide a general idea, allowing those who study it to understand the general trend."

苟地非於陽城，皆隨所而漸異。然月食以月行虛道，暗氣所沖，日有暗氣，天有虛道，正黃道常與日對，如鏡居日下，魄曜見陰，名曰暗虛，月則食。故張衡稱：當月月食，當星星亡。雖夜半之辰，子午相對，正隔於地，值虛即虧。既月兆日光，當午更曜，時亦隔地，無廢稟明。諒以天光神秘，應感玄通。比陸績於愚凡，意天彰於靈曜。正當夜半，何害虧稟。月由虛道，表裡俱食。日之與月，體同勢等。較其食分，月盡為多。容或形差，微增虧數。疏而不漏，納要克舉。

As long as the observation location is not at Yangcheng, the phenomena seen from different places will gradually differ according to location. Regarding lunar eclipses, they occur when the moon travels along the "Xu Dao" and is attacked by dark energy: the sun has dark energy, and there is a Xu Dao in the sky, which is directly opposite the Yellow Path. It is like a mirror placed under the sun, and the moon's brightness becomes shadowed here, which is called "dark Xu." When the moon enters this area, a lunar eclipse occurs. Therefore, Zhang Heng said: if the opposite is the moon, the moon will be eclipsed; if the opposite is a star, the star will disappear. Even at midnight, when the Zi position and the Wu position are directly opposite, with the earth clearly in between, the moon will still be eclipsed if it encounters the dark Xu. Since the moon shines by receiving sunlight, it should be brighter at the Wu position, yet it is not hindered from receiving light even though the earth is in between. It seems that the heavenly light is mysterious and profound, with subtle correspondences that connect deeply. Liu Chuo compared Lu Ji to an ignorant and mediocre person, meaning that the will of heaven is clearly manifested above the sun, moon, and stars. At midnight, how could it affect the moon's eclipse or its reception of light? When the moon passes through the Xu Dao, both the sun and moon will be eclipsed. The sun and moon have similar forms and equal conditions, so comparing the extent of their eclipses, the moon is more often completely eclipsed. Perhaps this is because their shapes are slightly different, which slightly increases the amount of eclipse. This theory is rough but not entirely lacking, and if one grasps the main point, it can be applied.

議曰：月隔奩匣，鏡不生菱，地隔高天，月寧含景。竊稽諸典，比陸績於愚凡，意天彰於錄曜者，殆以虛而喻實，亦理所絕，無必求知也。凡事可依，必須取論無滯。或以當夜半，何害虧稟。日輪所照，日光所臨，何關大地。近驗應符，乃華言之飾辨，非忘私之至公。弱於德，強於辨，為後人通弊，信乎其然矣。”

Commentators say: A mirror placed behind a makeup box cannot reflect the image of a rhombus flower; likewise, the earth lying between the sky and the moon, how can the moon possibly bear the light of the sun? Upon private examination of various classical texts, Liu Zhao compared Lu Ji to a foolish and mediocre person, saying that heavenly will is clearly manifested in the sun, moon, and stars. This is probably using abstract comparisons to explain concrete truths, which already fails to make sense, and there is no need to insist on understanding it. Any principle that can be used as a basis for argument must be clear and unimpeded. He also said that during the middle of the night, there is no harm in being in a state of deficiency and receiving light. But how can the range of the sun's illumination and the areas it reaches have any relation to the earth that lies between the sky and the moon? As for the claim that recent verification matches perfectly, this is merely superficial rhetoric, not an impartial and unbiased argument. Weakness in virtue yet striving for eloquence in debate is a common flaw among later scholars, and this seems indeed to be the case.

夫言天體者，蓋非一家也。世之所覆傳有渾天，有蓋天。說渾天者，言渾然而圓，地在其中；蓋天者，言天形如車蓋，地形如覆槃。皆中高外下，二曜推移，五星迭觀，見伏昏明，皆由遠近運移，麗天不入於地。日之將沒，去人彌遠，明衰光滅，故暗其明。及其將出，去人彌近，光明炎熾，故顯其照。揚雄以為渾天得之，難蓋天曰：“於高山之上，設水平以望日，則日出水平下，若天體常高，地體常卑，日無出下之理。”於是蓋天無以對也。

Discussions about the structure of celestial bodies are not confined to a single school of thought. The main theories passed down through history are the Heavenly Sphere Theory and the Covering Heaven Theory. Advocates of the Heavenly Sphere Theory argue that the heavens form a single, spherical body, with the earth suspended at its center. Proponents of the Covering Heaven Theory claim that the heavens resemble the canopy of a carriage, while the earth is like an inverted wooden plate. Both schools agree that the center of heaven and earth is high and the surroundings are low, with the sun and moon, the two great luminous bodies, moving across the sky, and the five wandering stars—Jupiter, Mars, Mercury, Venus, and Saturn—appearing in succession. Their appearances and disappearances, brightness and darkness, are caused by their varying distances and movements. The sun, moon, and stars are attached to the heavens and move along with them, not actually sinking into the earth. When the sun is about to set, it moves farther away from the observer, its light weakens and eventually fades, appearing dim. When it is about to rise, it comes closer, its light becomes intense, and thus shines clearly. Yang Xiong believed the Heavenly Sphere Theory was correct and criticized the Covering Heaven Theory, saying, "If you set up a level on the top of a mountain to observe the sun, you will see it rise below the level's surface. If the heavens are always above and the earth always below, then the sun would not rise from below." The proponents of the Covering Heaven Theory had no response to this argument.

渾天之說，天體包裹，地在其中，七曜躔離，道有常率，天體旁倚，故日道南高而北下，運轉之樞，南下而北高。二樞為轂，日道為輪，周廻運移，終則復始。北樞謂之北極，北極出地上三十六度，故天南際七十二度，常見而不伏。南樞謂之南極，南極入地下亦三十六度，故天北際七十二度，常伏而不見。

The theory of the浑天家 says that celestial bodies are like a shell surrounding the outside, with the earth at its center. The sun, moon, and five wandering stars, totaling seven luminaries, each move along their respective orbits, coming together and separating, all following fixed paths. Since the celestial sphere is inclined, the sun's path is higher in the south and lower in the north, while the axis of the celestial rotation is lower in the south and higher in the north. The two ends of the axis are like the hub of a wheel, and the sun's path is like the rim of a wheel, rotating continuously and repeating its cycle. The northern end of the axis is called the North Pole, which is thirty-six degrees above the horizon, so the region of the sky centered on it with a span of seventy-two degrees is always visible and never sinks below the ground. The southern end of the axis is called the South Pole, which is thirty-six degrees below the horizon, so the region of the sky centered on it with a span of seventy-two degrees is always hidden and never visible.

《周髀》云：日一度二千九百三十二里有奇，夏至景一尺四寸，冬至一丈三尺五寸，周天百七萬一千里，徑三千五萬七千里，四表內萬五千里，其外亦萬五千里。故天日四遊於三萬里之中，冬南、夏北、秋東，皆薄四表而止，地亦升降於天之中，旁遊之數，與天遊同。日道星宿之外，亦萬五千里，圓周之徑，正與四表等。

The Zhou Bi Suan Jing says: The Sun travels one degree every day, covering a distance of more than 29,320 li; on the summer solstice, the shadow of a gnomon is one foot four inches long, while on the winter solstice, it is thirteen feet five inches long; the circumference of the sky is one million and seventy thousand li, and its diameter is three million and fifty-seven thousand li; within the four cardinal boundaries, the distance is fifteen thousand li, and outside the boundaries it is also fifteen thousand li. Therefore, the sky moves within a range of thirty thousand li, traveling south in winter, north in summer, and east in autumn, reaching the four cardinal boundaries each time; the earth also rises and falls in the center of the sky, moving laterally by the same amount as the sky's movement. The Sun's orbit is also fifteen thousand li outside the twenty-eight constellations, and the radius of this circular path is equal to the distance to the four cardinal boundaries.

冬至之日，出辰入申；夏至之日，出寅入戌；進退於六十度之中焉，非專四遊之差，亦有地之升降。冬至之後，日轉北移，非專日之也，亦由天地遊而南，故物在生而不死。夏至之後，日轉南移，非專日之移，亦由天地遊而南，故物在生而不死。夏至之後，日轉南移，非專日之移也。亦由天地遊而北，故物有伏而不生。

On the day of Winter Solstice, the Sun rises at the Chen position and sets at the Shen position; on the day of Summer Solstice, it rises at the Yin position and sets at the Xu position. Throughout the year, the Sun moves within a range of sixty degrees. This is not only due to the difference caused by the Sun's "four wanderings," but also involves the movement of the Earth's rising and falling. After Winter Solstice, the Sun turns northward. This is not solely the movement of the Sun itself, but also because the heavens and earth move southward, thus allowing all things to sprout without dying. After Summer Solstice, the Sun turns southward. This is not solely the movement of the Sun itself, but also because the heavens and earth move northward, thus causing all things to become dormant without growing. The original text repeats the section about "after Summer Solstice" twice. The first version states "the heavens and earth move southward... things sprout without dying," while the second version says "the heavens and earth move northward... things become dormant without growing." These two versions contradict each other, clearly due to a copying error. The latter sentence should be considered correct, and I still follow the original text as it is.

二分之日，出卯入酉；正與地上平，故半表之徑，得天地相去十九萬里，然則地處天半而下也，故曰出地上百八十二度八分度之五，謂之晝；入地下百八十二度八分度之五，謂之夜。晝則出地上而西，夜則入地下而東，周匝百刻，昏明五十刻分之，日刻數既均，天度又等，與極應規，謂之中繩；居寒暑景之和，處遲疾之中。

On the days of Spring Equinox and Autumn Equinox, the Sun rises at the Mao position and sets at the You position, exactly matching the horizon. Therefore, by taking half the distance of the boundary, it is calculated that the distance between heaven and earth is nineteen ten-thousand li. This shows that the earth is at half the height of the celestial sphere, slightly lower. Therefore, the Sun travels 182 degrees and five degrees of eight parts above the horizon during the day, and this period is called "day"; it also travels 182 degrees and five degrees of eight parts below the horizon during the night, and this period is called "night." During the day, the Sun rises above the horizon and moves westward; during the night, it sinks below the horizon and moves eastward. In one day and night, there are a total of one hundred parts, each divided into fifty parts by dusk and dawn. Since the number of parts the Sun travels during the day and night are equal, the degrees it passes through are also the same, corresponding exactly to the positions of the north and south poles. This path is called "the central line." It is located at the midpoint between cold and heat and the length of shadows, as well as at the midpoint of the Sun's apparent motion, being slow or fast.

春分之後，日行中繩之北，故晝長而夜短，伏少而見多，景短而溫氣甚。秋分之後，日行中繩之南，故晝短而夜長，伏多而見少，景長而寒氣多。《易》說冬至之景，一丈三尺。夏至之景，一尺四寸八分。並二至之景，得一丈四尺四寸八分。春分之景七尺二寸四分，秋分之景與春分等。並二分之景，亦得一丈四尺四寸分八分，然東西南北，經緯均也。太平時和，七曜順軌，伏遊兩儀之中，不內不外。

After the spring equinox, the sun moves north of the "central line," so the day is longer and the night shorter, the hidden celestial regions are fewer and the visible ones more, the shadow is short and the heat is intense. After the autumn equinox, the sun moves south of the "central line," so the day is shorter and the night longer, the hidden celestial regions are more and the visible ones fewer, the shadow is longer and the cold is stronger. The "Yi Wei" states that on the winter solstice, the shadow is one zhang three chi long, and on the summer solstice, it is one chi four cun and eight fen long. Adding the lengths of the shadows on these two solstices gives a total of one zhang four chi four cun and eight fen. On the spring and autumn equinoxes, the shadow is seven chi two cun and four fen long, and since the shadows on these two equinoxes are equal, their total is also one zhang four chi four cun and eight fen. This shows that the numerical values in the east-west and north-south directions are balanced and equivalent. When the world is peaceful and the cold and heat are in harmony, the seven luminaries follow their regular paths, moving up and down between the two cosmic principles, neither exceeding the track inside nor outside it.

漢之《乾象》魏之《景初》，皆以二分之時，行渾儀之內；故南北闊而東西狹，冬至去極百一十五度，景長一丈三尺。夏去極六十七有奇，景長一尺五寸，並度得百八十二度八分度之五，並景得一丈四尺五寸。春分去極八十九，度景長五尺二寸五分。秋分去極九十度，景長五尺五寸。並度得百七十九度，並景得一丈七寸五分，東西少於南北三度焉。東西九千度弱，東西之景短於南北之景三尺七寸五分，為裡三萬七千五百。東西之徑定也，而度與景裡則有殊。然則一度之裡，一寸之差，及四遊之說，殆難明矣。

The Han dynasty's "Qianxiang Calendar" and the Wei dynasty's "Jingchu Calendar" both believed that during the vernal and autumnal equinoxes, the seven luminaries were within the orbit indicated by the armillary sphere, resulting in a wide north-south span and a narrow east-west span. According to their data: on the winter solstice, the sun was 115 degrees from the north pole, with a shadow length of thirteen feet; on the summer solstice, it was more than 67 degrees from the north pole, with a shadow length of one foot five inches. The total degrees from the north pole on the two solstices added up to 182 and five-eighths degrees, and the total shadow lengths added up to thirteen feet five inches. On the vernal equinox, the sun was 89 degrees from the north pole, with a shadow length of five feet two and a half inches; on the autumnal equinox, it was 90 degrees from the north pole, with a shadow length of five feet five inches. The total degrees from the north pole on the two equinoxes added up to 179 degrees, and the total shadow lengths added up to ten feet seven and a half inches. Thus, the east-west span was three degrees less than the north-south span, approximately nine thousand li less. The shadow length in the east-west direction was three feet seven and a half inches shorter than in the north-south direction. If converted using the standard of one li per inch, this would equate to thirty-seven thousand five hundred li. However, the east-west diameter is a fixed value, and calculations based on degrees do not match those based on shadow lengths. Therefore, the question of how many li one degree corresponds to, how many li one inch of shadow difference corresponds to, and the so-called "four wanderings" theory, may all be difficult to clarify.

鄭玄以二至之景，一寸俱差千里。夏至之日，八尺之表景，得一尺五寸。日下之地，南於嵩高一萬五千里。冬至之日，八尺之表景，得一丈三尺。日下之地，南於嵩高十三萬里。夫日高則景小，卑則景差多。日無上下之說，而天地有升降，安得千里同差一寸也。故東西之徑小於南北之徑，以度言之，則九千里；以景言之，則三萬七千五百里。二分之日，南北千里蓋當景差四寸矣。鄭氏之言，豈合理哉。

Zheng Xuan believed that the difference in the length of shadows cast by the sun on the two solstices, each inch difference, corresponded to a distance of one thousand li between north and south. On the summer solstice, a gnomon eight chi high cast a shadow of one chi and five cun, meaning the location directly under the sun was fifteen thousand li south of Songshan; on the winter solstice, the shadow cast by the same gnomon was thirteen chi long, meaning the location directly under the sun was thirteen ten thousand li south of Songshan. In reality, when the sun is higher, the shadow is shorter, and when the sun is lower, the shadow is longer. The sun does not rise or fall, but the heavens and the earth do rise and fall. How can we uniformly calculate a difference of one li for every inch difference in shadow? According to the previous calculation, the diameter in the east-west direction is smaller than that in the north-south direction: according to the degree measurement, it is nine thousand li less, but according to the shadow length calculation, it is thirty-seven thousand five hundred li less. On the vernal equinox and autumnal equinox, a distance of one thousand li north-south should correspond to a shadow difference of about four cun. Does Zheng Xuan's view make sense?

天遊薄四面而止，日道與四表等，不升不降，常與四表交錯。二分之日道，與二極應規，而天地居四遊之中。春分之後，天地降而下游西南，至於夏至，天遊至南表而止，故視日北而高。景差少高之故自此以後，而北至秋分，還與日道應規。故分之後，天地升而上游，而北至於冬至，則天遊至北表而止，故視日插而南。景差多卑之故計其進退，南北不繫於三萬里之內。春分之後，至夏之差度二十四，除其鉤弦之數，乃常南遊六萬餘里，此蓋升降之度，裡則少矣。

Heaven moves to the four cardinal directions and stops at the borders, while the path of the sun is equidistant from the four cardinal boundaries, neither rising nor falling, but always intersecting with them. On the days of the vernal and autumnal equinoxes, the sun's path aligns with the positions of the north and south poles, and heaven and earth are at the center of the four directional range. After the vernal equinox, heaven and earth descend and move southwest, reaching the southern boundary at the summer solstice, so the sun appears to be northward and high in the sky—this is due to the small shadow difference and the high position of the sun. From then on, it moves northward again, and at the autumnal equinox, it aligns once more with the sun's path. After the autumnal equinox, heaven and earth ascend and move northward, continuing until the winter solstice, when heaven and earth reach the northern boundary and stop, so the sun appears low and southward—this is due to the large shadow difference and the low position of the sun. Calculating the extent of its movement, the north-south distance does not remain within three ten-thousand li. From the vernal equinox to the summer solstice, the difference from the extreme is twenty-four degrees. After subtracting the conversion numbers of the Pythagorean theorem, it usually moves southward by over sixty ten-thousand li. This is merely the degree of ascent and descent, but when converted into actual distance, it is not very great.

今置渾天於地，以衡望日，地升渾上則日去極遠，地降下渾下則日去極近；遠近之驗，不必在於南北，亦由升降可知矣。然則旁遊與外降各十二度，與天在遊三萬里相近矣。日月麗天，有虧有盈，有交有會，日行日出，經半周天焉；即月道交錯，半入日道之內，半出日道之外；在外謂之行陽，在內謂之行陰，當交則會，會則有食。

Now the armillary sphere is placed on the ground, and the Zuben sighting tube is directed toward the sun for observation: when the ground rises above the armillary sphere, the sun appears farther from the North Pole; when the ground sinks below the armillary sphere, the sun appears closer to the North Pole. The verification of distance does not necessarily have to be observed from the north-south direction; it can also be known from the rising and setting. Thus, the lateral movement and the outward descent each amount to twelve degrees, which is close to the statement that "the heavens move within thirty thousand li." The sun and moon are attached to the sky, waxing and waning, meeting and separating. The sun rises and sets each day, completing half a celestial circle in a day and night. The moon's orbit crosses the sun's orbit, with half of it inside the sun's path and half outside: the part outside is called "moving in the yang," and the part inside is called "moving in the yin." When it reaches the node, they meet, and when they meet, solar and lunar eclipses occur.

蔡氏《月令章句》曰：“天者，純陽精剛，轉運無窮，其體渾而包地。地上者一百八十二度八分之五，地下亦如之。其上中北偏，出地三十六度，謂之北極，極星是也。史官以玉衡長八寸，孔徑一寸，從下端望之，此星常見孔端，無有移動，是以知其為天中也。其下中南偏，入地亦三十六度，謂之南極。從上端望之，當孔下端是也。此兩中者，天之輻軸所在，轉運之所由也。

In the Eastern Han dynasty, Cai Yong of the "Yue Ling Zhang Ju" wrote: "Heaven is the pure essence of yang and the strong and vigorous energy, rotating and moving without cease, its form is round and encompasses the earth. The part of heaven above the horizon is one hundred eighty-two degrees and five degrees of eight parts, and the part below the horizon is the same. The center of the celestial sphere, which is slightly northward, is thirty-six degrees above the horizon, called the 'North Pole,' where the North Star is located. The officials used a jade measuring tube eight inches long and one inch in diameter, looking upward from the bottom end, and this star was always seen at the top of the tube's hole, never moving, thus determining it as the center of heaven. The center of the celestial sphere, which is slightly southward, is thirty-six degrees below the horizon, called the 'South Pole'; looking upward from the top end of the jade tube, it is directly opposite the bottom of the tube's hole. These two centers, north and south, are the location of the celestial axis, upon which the celestial sphere rotates."

天左旋出地上而西，入地下而東。其繞北極，徑七十二度，常見不伏，圖內赤小規是也。繞南極，徑七十二度，常見不伏，圖內赤小規是也。繞南極，徑七十二度，常見不伏，圖外赤大規是也。據天地之中，而察東西，則天半見半不見，圖中赤規截婁角者是也。”

The sky rotates to the left; when it rises above the horizon, it moves westward, and when it descends below the horizon, it moves eastward. The circle around the North Pole with a diameter of seventy-two degrees, which is always visible and never disappears, is the small red circle within the star chart. The circle around the South Pole with a diameter of seventy-two degrees, which is always visible and never disappears, is the large red circle outside the star chart. Standing at the center of heaven and earth to observe the east-west direction, half of the sky is visible and half is not, which corresponds to the red circular line on the star chart that crosses the mansion of Niu and the mansion of Jiao. According to the original text, the sentence about "circling the South Pole" is repeated twice, and the phrase "commonly visible and not hidden, the small red circle within the chart" in the first instance should be "always hidden and not visible, the large red circle outside the chart," which is an error caused by repeated copying. The current version follows the original text without alteration.

岌按：此與張衡所說不殊，則雲玉衡長八寸，則似是古儀矣。又云據天地之中所云規數，據蓋圖綴星是也。後漢末，吳人陸績，字公紀，於孫權時，又作《渾天儀說》。績造渾天圖，漸於土室居，令不覺晝夜。已在內推步度數，擊鼓節與外相應，而不失毫釐。

The editor's note says: This passage is essentially the same as what Zhang Heng discussed; as for the statement that the Yu Heng is eight inches long, that seems to be an ancient instrument. It also mentions that standing at the center of heaven and earth to observe, the measurements and degrees mentioned are based on the star positions depicted in the Gaitian diagram. In the late Eastern Han dynasty, Lu Ji, a man from Wu region, whose name was Gongji, wrote the "Hun Tian Yi Shuo" during the time of Sun Quan. Lu Ji created the Hun Tian diagram and gradually moved into a sealed earth chamber to live, so that he would not be aware of the actual day and night outside. Inside the chamber, he calculated the movements of celestial bodies and struck the drum according to the calculated time to indicate the seasons, and it matched perfectly with the actual time outside without any discrepancy.

陸公紀《渾天說》云：先王之道，存乎治曆明時，本之驗著，在於天儀。夫法象莫如渾天，渾天之設外矣。昔在顓頊，使南正重司天，而帝嚳變序三辰。堯命羲和，欽若昊天，曆象日月星辰。舜之受禪，在璇璣玉衡，以齊七政。以是數者言之，曩時已立渾天之象明矣。

Lü Ji's "Holistic Heaven Theory" states: The way of the former kings in governing the country was implemented through the study and regulation of calendars and the clarification of seasonal changes. The most fundamental evidence for this lies in the instruments used to observe the heavens. To follow the heavenly phenomena, nothing is more suitable than the holistic heaven instrument. The establishment of the holistic heaven instrument has a long history. In ancient times, during the reign of Zhuan Xu, he entrusted Nan Zheng Chong with the affairs of the heavens; during the reign of Di Ku, he further regulated the order of the three celestial bodies, the sun, moon, and stars. Yao appointed Xi Shi and He Shi to respectfully follow the heavens, observing and calculating the movements of the sun, moon, and stars. After Shun accepted the mandate of heaven, he first examined the Xuan Ji Yu Heng, using it to correct the seven celestial bodies. From these events, it is clear that the holistic heaven instrument was already established at that time.

周公序次六十四卦，兩兩相承，反覆成象，以法天行，周而復始，晝夜之義。故《晉卦彖》曰：“晝日三接。”《明夷象》曰：“初登于天，照四國也；後入于地。”仲尼說之曰：“明出地上，晉進而麗乎大明，是以晝日三接。”明入地中明夷，明夷夜也，先晝後夜，先晉後明夷，故曰先登於天，照四國也；後入于地，失則也。日月麗乎天，隨天轉運，出入乎地，以成晝夜也。渾天之義，蓋與此同。

The Duke of Zhou arranged the sixty-four hexagrams in pairs, each following the other, with their forms reversed to form the images of the hexagrams, thus imitating the operation of Heaven, which is cyclical and ever-repeating. This contains the meaning of the alternation of day and night. Therefore, the Commentary on the Judgment of the Hexagram of Progress says, "Being received three times within a single day." The Image Commentary of the Hexagram of Diminishing Light says, "At first rising to the heavens, it shines over all the four directions; later it sinks into the earth." Confucius explained, "When light rises above the earth, it is the Hexagram of Progress; advancing and attaching itself to the great illumination, thus being received three times within a single day." When light enters the earth, it is the Hexagram of Diminishing Light; the Hexagram of Diminishing Light refers to night. Since day comes before night, the Hexagram of Progress comes before the Hexagram of Diminishing Light. Therefore, it says first rising to the heavens, shining over all the four directions, and later sinking into the earth, thus losing its regular course. The sun and moon attach themselves to the heavens, rotating with the sky, appearing and disappearing on the earth, thus forming day and night. The principle of the spherical heavens is probably similar to this.

雲雲餘已見前篇，至與蔡氏張衡同，故略雲。故曰：言天體非一家也。吳時，廬江王蕃，字興元，為中常侍，善數術，嘗造渾儀及《渾天象說》云：“幽平之後，周室遂卑。”雲雲，至日光不得曜星也，與前說並同。

The following passage has already been recorded before, and its content is the same as what Cai Yong and Zhang Heng discussed, so it is omitted here. Therefore, it is said that talking about celestial phenomena is not the work of a single school. During the Three Kingdoms period in Wu, Wang Fen, a man from Lujiang, whose name was Xingyuan, held the office of Zhongchangshi, was skilled in numerology, and once made a浑仪 and wrote a text called《浑天象说》. He said: "After King You of Zhou and King Ping of Zhou, the royal house of Zhou declined," and so on, up to the sentence "the sunlight cannot illuminate the stars," which is the same as the previous quotation.

《易》曰：“天地貞觀，日月貞明。”《洪範傳》曰：“清明者，天之體也。”《易》曰：“天行健，君子以自強不息。”《易說卦》曰：“乾為天，乾健也。”《河圖葉光紀》曰：“元氣闓陽為天。”《易乾鑿度》曰：“清輕者上為天，重濁者下為地。”《禮統》曰：“天、地，元氣之所生，萬物之祖也。天之為言顛也，神水珍也。”

The Zhou Yi: Xi Ci Xia says: "Heaven and earth reveal the correct path to mankind, and the sun and moon illuminate all things through the correct path." The Hong Fan Zhuan says: "Clear and bright, this is the nature of heaven." The Zhou Yi: Qian Gua: Xiang Zhuan says: "The way of heaven is strong and vigorous without ceasing, and the gentleman thus ceaselessly strives for self-improvement." The Zhou Yi: Shuo Gua Zhuan says: "The Qian Gua symbolizes heaven, and the nature of Qian is strength and vigor." The esoteric text He Tu Ye Guang Ji says: "The primordial qi initiates the yang qi, thus becoming heaven." The esoteric text Yi Qian Zao Du says: "The light and subtle part rises to become heaven, while the heavy and turbid part sinks to become earth." The Li Tong says: "Heaven and earth are both born from primordial qi, and are the ancestors of all things. The character 'heaven' derives its meaning from 'dian,' meaning the highest point." (The last four characters 'shen shui zhen ye' in the original text are corrupted and the meaning is unclear.)

《爾雅》曰：“穹蒼，蒼天也。春為蒼天，夏為昊天，秋為旻天，冬為上天。”《太玄經》曰：“九天：一為中天，二為羨天，三為順天，四為更天，五為$天，六為廓天，七為咸天，八為沈天，九為成天。”

The Er Ya · Shi Tian says: "Qiong cang is the same as cang tian. The sky in spring is called cang tian, in summer hao tian, in autumn min tian, and in winter shang tian." Yang Xiong's The Classic of Supreme Mystery says: "Heaven is divided into nine layers: the first is zhong tian, the second xian tian, the third shun tian, the fourth geng tian, the fifth is unknown, marked with a symbol $, the current version of The Classic of Supreme Mystery reads 'cui tian.' The sixth is kuo tian, the seventh xian tian, the eighth shen tian, and the ninth cheng tian."

《考靈曜》曰：“觀玉儀之遊，昏明主時，乃命中星。中央鈞天，其星角、亢、氐。東方蒼天，其星房、心、尾。東北變天，其星箕、斗、牽牛。北方玄天，其星須女、虛、危、營室。西北幽天，其星東壁、奎、婁。西方昊天，其星胃、昴、畢。西南方朱天，其星觜、參、東井。南方炎天，其星輿鬼、柳、七星。東南方陽天，其星張、翼、軫。”《淮南子》曰：“道始於虛廓，虛廓生宇宙，宇宙生氣，清陽者薄靡而為天。”

The Wei text "Shangshu Kaolingyao" says: "Observe the movement indicated by the Yu Heng instrument, determine the seasons according to the star formations at dusk and at dawn, and thus establish the star mansions at the southern mid-heaven. The central region is called Jun Tian, with the star mansions of Jiao, Kang, and Di; the eastern region is called Cang Tian, with the star mansions of Fang, Xin, and Wei; the northeast region is called Bian Tian, with the star mansions of Ji, Dou, and Qian Niu; the northern region is called Xuan Tian, with the star mansions of Xu Nu, Xu, Wei, and Ying Shi; the northwest region is called You Tian, with the star mansions of Dong Bei, Kui, and Lou; the western region is called Hao Tian, with the star mansions of Wei, Mao, and Bi; the southwest region is called Zhu Tian, with the star mansions of Zi, Shen, and Dong Jing; the southern region is called Yan Tian, with the star mansions of Yu Gui, Liu, and Qi Bing; the southeast region is called Yang Tian, with the star mansions of Zhang, Yi, and Zhen." The "Huainanzi · Tianwen Xun" says: "The Dao originates from the void, the void gives rise to the universe, and the universe gives rise to the original qi. The clear and light part of the original qi rises and becomes the sky."

《洛書甄曜度》曰：“周天三百六十五度四分度之一，一度為二千九百三十二里，則天地相去十七萬八千五百里。”《廣雅》曰：“天圍廣，南北二億三萬三千五百里七十五步，東西短減四步，周六億十萬七百里二十五步。”從地至天，一億一萬六千七百八十七里。下度地之厚，與天高等。”《靈憲》曰：“天有九位，自地至天，一億一萬六千二百五十里。懸天之景，薄地之儀，皆移千里而差一寸。”

The Luo Writing, as explained in the book of Weishi "Luo Shu Zhen Yao Du", says: "The entire celestial circle measures 365 and 1/4 degrees. Each degree corresponds to 2,932 li. Therefore, the distance between heaven and earth is 178,500 li." Zhang Yi's "Guangya" states: "The sky is vast, extending north-south for 233,350 li and 75 bu, while its east-west span is 4 bu shorter. The total circumference is 610,070,000 li and 25 bu. The distance from the earth's surface to the sky is 116,787 li. The thickness of the earth, measured downward, is equal to the height of the sky." Zhang Heng's "Ling Xian" explains: "The sky has nine layers. The distance from the earth to the sky is 116,250 li. The shadow cast by the sun at a high altitude and the shadow measured by a gnomon on the ground differ by one inch for every thousand li of distance between them."

關令《內傳》曰：“南午北子，相去九千一萬里。東卯西酉，亦九千一萬里。四隅空無，相去亦爾。天去地四十萬九千里。”徐整《三五曆紀》曰：“天地渾沌如雞子，盤古生其中，一萬八千歲天地開闢，清陽為天，濁陰為地，盤古在其中一日九變，神於天，聖於地。天日高一丈，地日厚一丈，盤古日長一丈。如此一萬八千數，天數極高，地數極深，盤古極長。後乃有三皇。數起於一，立於三，成於五，盛於七，處於九；故天去地九萬里。”

Guan Ling Yin Xi's Inner Transmission says: "The southern Wu position to the northern Zi position, spans nine million and one ten-thousand li; the eastern Mao position to the western You position, also spans nine million and one ten-thousand li; the four corners, though empty and void, are also separated by the same distance. The distance between heaven and earth is forty million and nine thousand li." Xu Zheng of the Three Kingdoms period's San Wu Li Ji says: "When heaven and earth were not yet divided, the chaos was like an egg, and Pangu was born within it. After eighteen thousand years, heaven and earth were created: the clear part became heaven, the heavy part became earth. Pangu was in the center of heaven and earth, changing nine times a day, more miraculous than heaven and more wise than earth. Heaven rose one zhang per day, earth thickened one zhang per day, and Pangu also grew one zhang per day. After eighteen thousand days, heaven reached its highest point, earth reached its deepest point, and Pangu's body also reached its full height. Then came the Three Emperors. Numbers begin with one, stand on three, are formed by five, flourish by seven, and end with nine, so the distance between heaven and earth is nine ten-thousand li."

《淮南子》曰：“九野，九千九百九十里，去地一億一萬里。”《春秋內事》曰：“天下十二分次，日月之所躔也。”《孝經援神契》曰：“周天七衡、六間者，相去萬九千八百三十三里三分裡之一，合十一萬九千里。從內衡以至中衡，從中衡以至外衡。各五萬九千五百里。”

The Huainanzi says: "The area of the nine wilds is nine thousand nine hundred and ninety li, and it is one hundred and one ten thousand li above the earth." The Spring and Autumn Inner Affairs says: "The world is divided into twelve sections, which are the positions passed through by the sun and moon." The esoteric text Xiaojing Yu Shenqi says: "The entire sky is divided into seven horizontal paths and six intervals. The distance between each adjacent horizontal path is nineteen thousand eight hundred and thirty-three li and one third of a li, totaling eleven thousand nine hundred li. From the innermost horizontal path to the middle horizontal path, and from the middle horizontal path to the outermost horizontal path, each is five thousand nine hundred and fifty li."