The second heavenly stem is Jia.

王藩者，廬江人也。吳時為中常侍，善術數。傳劉洪《乾象曆》，依乾象法而論渾天曰：前儒舊說，天地之體，狀如鳥卵。天包地外，猶殼之裹黃也。周旋無端，其形渾渾然，故曰：渾天也。

Wang Fan was from Lujiang, and during the Three Kingdoms period in the state of Wu, he held the position of Zhongchangshi. He was skilled in the study of divination and mathematics. He transmitted Liu Hong's "Ganxiang Li," and based on the Ganxiang calendar system, he discussed the concept of the "hun tian." He said that previous scholars believed the shape of heaven and earth was like that of a bird's egg. Heaven was enclosed outside the earth, similar to an eggshell surrounding the yolk. It rotated continuously without beginning or end, with a shape that was perfectly round, hence it was called "hun tian."

周天三百六十五度、五百八十二分度之百四十五半。半覆地上，半在地下。其二端謂之南極、北極。北極出地三十六度，南極入地亦三十六度，兩極相去一百八十二度半強。繞北極徑七十二度，常見不隱，謂之上規；繞南極七十二度，常隱不見，謂之下規；赤道橫絡，謂之中規。赤道帶天之紘，去兩極各九十一度少強。

The celestial sphere has a total of 365 degrees and 582 parts, with 145 and a half parts of the total. Half of it is above the ground, and half is below. The two ends of the celestial sphere are called the South Pole and the North Pole. The North Pole is 36 degrees above the horizon, and the South Pole is 36 degrees below the horizon, so the distance between the two poles is about 182 and a half degrees. Within a diameter of 72 degrees around the North Pole, the stars are always visible and never set, and this area is called the "upper circle." Within a diameter of 72 degrees around the South Pole, the stars are always hidden and never visible, and this area is called the "lower circle." The equator circles the middle of the celestial sphere, called the "middle circle." The equator is like a large belt around the middle of the sky, and it is about 91 degrees and a half away from both the North and South Poles.

黃道，日之所行也，半在赤道內，半在赤道外。與赤道東交於角五度稍弱，西交於奎十四度少強。其出赤道外，極遠者二十四度，斗二十一度是也；其入赤道內、極遠亦二十四度，井二十四度是也。

The Yellow Path is the path along which the Star of brightness and prestige moves. Half of it lies north of the equator, and half lies south of the equator. It intersects the equator eastward slightly before the fifth degree of the Horn mansion and westward a bit more than the fourteenth degree of the Legs mansion. The farthest point of the Yellow Path extending beyond the equator is twenty-four degrees, which corresponds to the twenty-first degree of the Well mansion. The farthest point of the Yellow Path extending within the equator is also twenty-four degrees, which corresponds to the twenty-fourth degree of the Well mansion.

日南至，在斗二十一度，去極一百一十五度少強。是日最南，去極最遠，故景最長。黃道斗二十一度，出辰入申，日晝行地上一百四十六度強，故晝短；夜行地下，二百一十九度稍弱，故夜長。自冬至之後，日漸去極近，故景稍短。日晝行地上漸多，故日稍長；夜行地下度漸少，故夜稍短。

The Sun moves southward until it reaches the solstice, which is the winter solstice. On this day, the Sun is located at 21 degrees of the Dipper mansion, and it is 115 degrees more than the North Pole. On this day, the Sun is furthest south and farthest from the North Pole, so the shadow is longest. At 21 degrees of the Dipper mansion on the Yellow Path, the Sun rises in the southeast from the Dragon position and sets in the southwest at the Monkey position. During the day, the Sun travels 146 degrees more than the ground, so the daylight is short. At night, the Sun travels 219 degrees slightly less beneath the ground, so the night is long. After the winter solstice, the Sun gradually approaches the North Pole, so the shadow becomes slightly shorter. The degrees the Sun travels above the ground gradually increase, so the daylight gradually becomes longer. The degrees the Sun travels beneath the ground gradually decrease, so the night gradually becomes shorter.

日所在度漸北，以至於夏至，日在井二十四度，去極六十七度少強，是日最近北極，故景最短。黃道井二十四度，出寅入戌，日晝行地上二百一十九度多弱，故日長；夜行地下百四十六度強，故夜短。自夏至之後，日漸去極遠，故景少長。日晝行地上度漸少，故日稍短；夜行地上度漸多，故夜稍長。日所在度漸南，故日出稍南，以至於冬至而復初焉。斗二十一度，井二十四度，南北相去四十八度。

The Sun's position gradually moves northward. By the summer solstice, the Sun is located at the 24th degree of the Well mansion, which is 67 degrees and a bit more from the North Pole. On this day, the Sun is closest to the North Pole, so the shadow is shortest. At the 24th degree of the Well mansion on the Yellow Path, the Sun rises in the northeast from the寅 position and sets in the northwest at the戌 position. During the day, the Sun travels approximately 219 degrees above the ground, so the daylight is long. At night, the Sun travels about 146 degrees more below the ground, so the night is short. After the summer solstice, the Sun gradually moves away from the North Pole, so the shadow becomes slightly longer. The degree the Sun travels above the ground during the day gradually decreases, so the daylight gradually shortens. The degree the Sun travels below the ground at night gradually increases, so the night gradually lengthens. As the Sun's position gradually moves southward, the place where the Sun rises also gradually shifts southward, until by the winter solstice it returns to its starting point. The 21st degree of the Dipper mansion and the 24th degree of the Well mansion are 48 degrees apart in the north-south direction.

春分日在奎十四度少強，秋分日在角五度少弱，此黃、赤二道之交中也，去極俱九十一度少強。南北處交斗二十一度、井一十四度之中，故景居二至長短之中。奎十四度，角五度，故曰：在赤道。出卯入酉，日晝行地上，夜行地下，俱百八十二度半強。故曰：見之漏五十刻，不見之漏五十刻，謂之晝夜同。

At the time of the Spring Equinox, the Sun is located at the 14th degree of the Qiu mansion, and at the Autumn Equinox, it is at the 5th degree of the Jiao mansion. These two points are exactly the intersection points of the Yellow Path and the Celestial Equator, both being about 91 degrees away from the North Pole. Their positions in the north-south direction lie between the 21st degree of the Dou mansion and the 14th degree of the Jing mansion, so the length of the shadow is between the shortest and longest shadows of the solstices. The points at the 14th degree of Qiu and the 5th degree of Jiao are therefore on the Celestial Equator. The Sun rises in the east at the exact position of Mao and sets in the west at the exact position of You. During the day, it moves across the earth, and at night, it moves beneath the earth, covering about 182.5 degrees. Therefore, the visible hours of the water clock are fifty parts, and the invisible hours are also fifty parts, which is called equal day and night.

夫天之晝夜，以日出為分；人之晝夜，以昏明為限。日未出前二刻半為晚，日入後二刻半為昏。故損夜五刻以益晝，是以春秋二分之漏，晝五十五刻。

Calculating day and night from celestial phenomena uses sunrise and sunset as boundaries; calculating day and night from human activities uses the time when it becomes light and dark as the limits. Before the sun rises, two periods of time pass before the sky begins to brighten, and after the sun sets, two periods of time pass before the sky is completely dark. Therefore, five periods of time are subtracted from the night and added to the day. Thus, on the days of Spring Equinox and Autumn Equinox, the length of daylight is calculated as fifty-five periods of time.

王藩按：《周禮》曰：“夏至之景，尺有五寸，謂之地中。”鄭眾說云：“土圭之長，尺有五寸。以夏至之日，立八尺之表，其景與土圭等，謂之地中。今穎川陽城地也。”

Wang Fan remarked: The "Book of Rites · Department of the Grand Master of the People" says: "On the day of Summer Solstice, the shadow cast by the sun is one chi and five cun long; that place is called the center of the earth." Zheng Zhong explained: "The soil圭 is a jade measuring rod that is one chi and five cun long. On the day of Summer Solstice, if a pole eight chi high is erected, and its shadow is equal in length to the soil圭, then that place is the center of the earth, which is today's Yangcheng in the prefecture of Yingshui."

鄭玄云：“凡日景於地，千里而差一寸。景尺有五寸者，南戴日之下萬五千里也。以此推之，日當去其下地八萬里矣。日邪射陽城，為天徑之半也。天體圓如彈圓，故地處天之半，而陽城居其中，則日春秋冬夏、昏明晝夜，去陽城皆等。

Zheng Xuan said: "Whenever the sun's shadow is cast on the ground, the difference in shadow length over a distance of one thousand li is one inch. If the shadow is one chi and five cun long, it indicates that the location is one hundred and five thousand li north of the place where the sun shines directly overhead. Based on this calculation, the sun should be eight ten thousand li away from the ground directly beneath it. The distance from the sun to Yangcheng when it is inclined is exactly the radius of the celestial sphere. The celestial sphere is round like a ball, so the earth is exactly at the center of the celestial sphere, and Yangcheng is at the center of the earth. Therefore, the distance from the sun to Yangcheng remains the same throughout the seasons and day and night."

以勾股法言之：旁萬五千里，勾也；八萬里，股也；無盈縮矣。故知從日邪射陽城為天徑之半也。從日邪射陽城，弦也。以勾股求弦法，八之，得八萬一千三百九十四里三十步五尺三寸六分也。

Using the Pythagorean theorem: the horizontal distance of fifteen thousand li is the "gou," and the vertical distance of eight ten-thousand li is the "gu," with neither having any discrepancy. Therefore, the line from the Sun slanting to Yangcheng is the radius of the celestial sphere. The line from the Sun slanting to Yangcheng is the "xian." Calculating the xian using the Pythagorean theorem and taking the square root, the result is eighty-one thousand three hundred ninety-four li, thirty bu, five chi, three cun, six fen.

以周率乘之，徑率約之，得五十一萬三千六百八十七里六十八步一尺八寸二分，周天之數也。一度凡一千四百六里二十四步六寸四分有奇。黃、赤二道相與交錯其間，相去二十四度，以兩儀準之。二道俱三百六十五度、五百八十二分度之一百四十五半，是以知天體圓如彈丸。”

Using the ratio of the circumference multiplied by it and then dividing by the diameter ratio, we get fifty-one thousand three hundred sixty-seven li, sixty-eight bu, one chi, eight cun, and two fen. This is the measure of the celestial circle. Each degree of the celestial circle corresponds to one thousand four hundred sixty li, twenty-four bu, six cun, and four fen, a little more. The Yellow Path and the Red Path intersect each other in between, with a distance of twenty-four degrees. Both paths are calibrated by the two principles of Heaven and Earth, each having three hundred sixty-five degrees and five hundred eighty-two parts of a degree, one hundred forty-five and a half. From this, we can know that the celestial sphere is a perfect sphere, like a ball.

淳風按：“王藩所論，冬夏二至，春秋二分，日度交黃道所在，並據劉洪乾象所說，今則並差矣。黃道與日相隨而交，據今正觀三年乙丑歲，則冬至日在斗十二度，夏至在井十五度，春分日在奎七度，秋分日在軫十五度，每六十年餘差一度矣。

Li Chunfeng remarked: Wang Fan's discussion on the degrees where the Sun intersects the Yellow Path at the solstices and equinoxes is based on Liu Hong's "Ganxiang Li." However, these measurements have all deviated from the current reality. The Yellow Path intersects with the Sun, and according to calculations for the third year of Zhenkuan, the Sun is at the twelfth degree of the Dipper mansion at winter solstice, at the fifteenth degree of the Well mansion at summer solstice, at the seventh degree of the Legs mansion at spring equinox, and at the fifteenth degree of the Chariot mansion at autumn equinox. Approximately every sixty years, these positions differ by more than one degree. (The original text "Zhengguan" refers to Zhenkuan, a term used by Tang dynasty scholars to avoid mentioning Emperor Taizong Li Shimin.)

淳風今略陳新法，以考天數及渾儀交道等法如左。周天三百六十五度，及分縱橫斜側皆定耳，更無盈縮。先以銅鐵為環卷六枚，兩兩合，周徑二小四大。大者適容其五枚，各均賦三百六十五度及分。其一大者，名為平準卷，唯雕刻六十四卦十二辰，先側立二大環卷，南北側之，以平準卷交合加之，令側者為南北，徑準為主。

I now briefly explain the new method, used to determine the degrees of the celestial circle and the methods for the ecliptic and equator on the armillary sphere. The celestial circle is 365 degrees and the remaining fractions, fixed regardless of direction, with no expansion or reduction. First, make six rings of copper or iron, pairing them two by two, dividing them into two small and four large. The large rings have a diameter just sufficient to hold the other rings, and each ring is evenly marked with 365 degrees and the remaining fractions. One of the large rings is called the "level ring," on which the sixty-four hexagrams and the twelve earthly branches are carved. First, set up the two large rings vertically, aligned north-south, then place the level ring across them, so that the vertical rings determine the north-south direction, with the level ring's diameter serving as the reference.

一曰遊環。遊環上安釭釧，遊環著雙軸，以內大環軸孔中，令得運轉。軸中一圓長筒管。其筒孔周徑，準儀大小而斟酌之。若長八尺，即須孔徑一寸，他皆準此。其側環安釭釧之處，在北者謂之北極，出平準北面上三十六度；在南者謂之南極，入平準南面下三十六度。從其南端北向斜上望之，即見北極星。

There is another ring called the "Yóu huán." The Yóu huán is fitted with a metal bushing and an axle ring, and has two axles connected to it. These axles are inserted into the holes of the main ring, allowing the Yóu huán to rotate. At the center of the axle is a long cylindrical tube. The diameter of the hole in the tube should be determined according to the size of the instrument: if the tube is eight feet long, the hole should be one inch in diameter, and so on. The places where the axle bushings are installed on the side ring are called "Běijí" (North Pole) on the northern side, which is thirty-six degrees above the level ring's northern side; and "Nánjí" (South Pole) on the southern side, which is thirty-six degrees below the level ring's southern side. Looking from the southern end of the tube toward the north at an upward angle, one can see the North Star.

又以一天環加於側環外，斜絡之，令東西合於卯酉平面之準，南北上下去二極，各九十一度強，以為赤道。然後轉其中游環，令得左右、東西、上下，以當所望處，轉軸中筒孔，使得南北以測去極遠近及赤道內外之度數，然則筒孔瞻察，無所不至矣。

Add another celestial ring outside the side ring, slanting it around so that its eastern and western ends align with the reference plane of the meridian, and set the distance from the north and south poles to be more than ninety-one degrees. Use this as the equator. Then rotate the central movable ring so that it can move left and right, east and west, and up and down, aligning it with the place to be observed. Then rotate the axial tube hole so that it can tilt north and south, used to measure the distance from the north pole and the degrees inside or outside the equator. In this way, by looking through the tube hole, there will be no place that cannot be observed.

若欲安星辰者，更著從脅上屈銅鐵，穿珠為星，以放上象，隨所在次第而安置之，轉令應天皆得，此渾天遊儀之法也。按渾儀，必先以水準地使平，夜占極，晝測日景，定其經緯，然後措之矣。餘近造乙巳元歷術，實為絕妙之極，日夜法度諸法，皆同一母，以通眾術。今列之以推天度，日月五星行度皆用焉。

If one wishes to place stars on the instrument, then one should bend copper or iron branches upward from the side of the ring, and string beads on them to represent stars, thus imitating the celestial configuration. The stars should be arranged in the order they appear in the sky, and when the instrument is rotated, it will correspond with the heavens. This is the method of the armillary sphere. In making the armillary sphere, one must first level the ground using the method of leveling, observe the North Star at night, and measure the shadow of the sun during the day to determine its meridian and latitude. Then the instrument can be properly set up. Recently, I have compiled the arithmetic of the "Yisi Calendar," which is truly exquisite: the methods for day, night, and degrees all originate from a single fundamental number, thus enabling various calculations. Now I present it below for calculating the degrees around the celestial sphere, and the movements of the sun, moon, and five planets will also require it.

日度法：一千三百四十，以此數為一度之長分數也。周天有三百六十五度、一千三百四十分度之三百四十一。南極去北極，巡規一百八十二度、一千三百四十分之八百四十半。赤道去二極，巡規各九十一度、一千三百四十分之四百二十分、小分四分之十，即春秋分之所在度，黃、赤二道交處，去北極之遠近也。

The measure of a degree is fixed at 1,340, using this number as the fraction contained within one degree. The entire celestial circle consists of 365 degrees and 341/1340 of a degree. Measured from the South Pole to the North Pole along the circle, it totals 182 degrees and 840/1340 of a degree and a half. The equator is at a distance of 91 degrees and 420/1340 of a degree from each of the North and South Poles, with an additional fraction of ten parts out of four. This is also the degree position of the Sun at the time of the spring and autumn equinoxes, that is, the distance from the North Pole to where the ecliptic intersects the equator.

黃道出入赤道二十四度，冬至日在赤道外二十四度，去極一百一十五度，一千三百四十分度之四百二十分、小分四分之一。夏至日在赤道內二十四度，去北極六十七度、一千三百四十分度之四百二十分、小分四分之一。此其常數也。

The Yellow Path enters and exits the equator by twenty-four degrees. On the day of the winter solstice, the Star of brightness and prestige is twenty-four degrees outside the equator, at a distance of one hundred fifteen degrees and four hundred twenty parts of one thousand three hundred forty parts from the North Pole, plus a quarter of a minute. On the day of the summer solstice, the Star of brightness and prestige is twenty-four degrees inside the equator, at a distance of sixty-seven degrees and four hundred twenty parts of one thousand three hundred forty parts from the North Pole, plus a quarter of a minute. These are all constant numbers.

淳風今又按張胄《玄象曆》及今傳《仁均歷》，春分、秋分，日皆在卯半以前，其沒亦在酉半以後，各四分刻之一。春、秋二分之日，晝漏五十刻半，夜漏四十九半，然則赤道、黃道交處，亦直在卯酉之北。又有北極去地三十六度，則天之正高在地中陽城之上。

Li Chunfeng now states that according to Zhang Zhouxuan's "Xuanxiang Li" and the currently used Fu Renjun calendar, on the days of spring equinox and autumn equinox, the sun rises before the hour of Mao and sets after the hour of You, each differing by a quarter of an hour. On the days of spring equinox and autumn equinox, the daylight lasts fifty and a half hours, and the night lasts forty-nine and a half hours. Thus, the intersection of the equator and the ecliptic is also located north of the Mao You line. Furthermore, since the north pole is thirty-six degrees above the horizon, the celestial zenith is directly above the central plain of the land.

以四維循規去地亦九十一度，一千三百四十分度之四百二十分、小分四分之一矣。以三十六度減之，餘五十五度，一千三百四十分度之四百二十分、小分四分之一。夏至日黃道在北極南六十七度、一千三百四十分度之四百二十、小分四分之一。

Measuring along the circle from the four cardinal directions and four intermediate directions to the horizon, it is ninety-one degrees and four hundred and twenty parts of one thousand three hundred and forty parts, plus a quarter of a minute. Subtracting the thirty-six degrees by which the North Pole is above the horizon from this, the remainder is fifty-five degrees and four hundred and twenty parts of one thousand three hundred and forty parts, plus a quarter of a minute. On the day of the Summer Solstice, the Ecliptic is sixty-seven degrees and four hundred and twenty parts of one thousand three hundred and forty parts, plus a quarter of a minute, south of the North Pole.

是正北子地一百三度，一千三百四十分度之四百二十分有奇矣。以天頂去四維各九十一度，一千三百四十分度之四百二十分、小分四分之一減之，餘一十二度矣。是夏至日在天頂南一十二度，他悉仿此求之，皆可知也。

Thus, it is one hundred and three degrees and four hundred and twenty parts of a thousand three hundred and forty parts, plus a little more, from the level of the north point Zi. Then subtract from this the ninety-one degrees and four hundred and twenty parts of a thousand three hundred and forty parts, plus a quarter of a minute, from the zenith to each of the four directions. The remainder is twelve degrees. This means that on the summer solstice, the sun is twelve degrees south of the zenith. The other solar terms can be calculated in the same way, and thus everything can be known.

是知繞北極循規徑七十二度，常見不隱；繞南極循規徑七十二度，常隱不見。去極三十六度外，一百一十度內，四時辰昏，有時而隱，有時而見，為日在其中故也。繞北極常見者，謂之上規；南極常隱者，謂之下規；赤道橫絡謂之中規焉。

From this we can understand that within a circle around the North Pole spanning seventy-two degrees in diameter, the stars are visible all year round without setting; within a circle around the South Pole spanning seventy-two degrees in diameter, the stars are always hidden and never visible. In the region outside thirty-six degrees from the North Pole but within one hundred and ten degrees, during the times of dawn and dusk in each season, some stars appear and some disappear, because the Sun is moving through this area. The circle around the North Pole that is always visible is called the "upper circle," the circle around the South Pole that is always hidden is called the "lower circle," and the circle around the equator passing through the middle is called the "central circle."

然圖體以平物為之易辨，若作渾儀，始識於事稍難。今世供傳星圖者，蓋皆天圖，其四畔外，即是南極下規矣。分佈二十八宿距度、與黃、赤二道、上規並具焉。

However, drawing celestial bodies as flat figures is easier to recognize, but if one wants to make a horary instrument, it is somewhat more difficult for beginners. The star charts that are currently passed down mostly belong to what is called the "celestial map." The area outside the map's borders corresponds to the region under the South Pole. The chart includes the distances of the Twenty-Eight Mansions, the Yellow Path, the Equator, and the upper circle, all marked out together.

天之運也，一晝一夜，而運過周天所過之度，則一日所行之數，在天謂之一度，在歷謂之一日一夜。度之天數無常準，各隨一家之法令，一千三百四十是也。日行三百六十五日而周天，故天一周有三百六十五日有奇矣。天運渾渾然不思，東出西沒，周而復始，永無窮焉。

The movement of Heaven turns through the entire circle of the sky in one day and one night, but it goes a little further. This extra portion corresponds to the distance the Star of brightness and prestige travels in one day. In the sky, this is called one degree, and in the calendar, it is called one day and one night. The number of fractions contained within one degree has no fixed standard; different calendar systems set their own rules. This calendar takes 1,340 as the measure. The Star of brightness and prestige completes a full circle around the sky in 365 days, so the rotation of Heaven corresponds to 365 days and a little more. The movement of Heaven is natural and effortless, rising from the east and setting in the west, continuing in a cycle without end.

淳風按：自黃帝占已後，向數十家，其間或真或偽，不可悉從。今略取其理當者，刪而次比，以著於篇。其間亦有出自經傳子史，但有關涉，理可存者，並不棄之，今錄古占書目於此，以表其人。自入占已後，並不復具記名氏，非敢隱之，併為是幼小所習誦，前後錯亂，恐失本真故耳。

Li Chunfeng remarked: Since the time when works of divination attributed to the Yellow Emperor appeared, there have been nearly dozens of schools of divination, among which some are genuine and some are fake, so they cannot all be followed without discrimination. Now I have briefly selected those with reasonable principles, and after cutting out the redundant parts and arranging them in order, I have written this essay. Among them, some are derived from classic texts and writings of the philosophers and historians, and as long as they are related to divination and their reasoning is acceptable, none of them will be discarded. Here I first list the catalog of ancient divination books below, to indicate the affiliations of each school. From the moment I enter the main body of the divination verses, I will no longer mention the names one by one - it is not that I dare to conceal them, but actually because these are all works I recited when I was young, and their order has already become mixed, and I fear that annotating them incorrectly might lead to losing their original meaning.

《黃帝》、《巫咸》、《石氏》、《甘氏》、劉向《洪範》、《五行大傳》、《五經緯圖》、《天鏡占》、《白虎通占》、《海中占》、京房《易祅占》、《易傳對異占》

The ancient divination texts relied upon are as follows: the divination book attributed to the Yellow Emperor, the divination book of Wu Xian, the "Shi Shi Star Classic" by Shi Shen, the "Gan Shi Star Classic" by Gan De, the "Hong Fan Wu Xing Zhuan" by Liu Xiang, as well as the "Wu Xing Da Zhuan," "Wu Jing Wei Tu," "Tian Jing Zhan," "Bai Hu Tong Zhan," "Hai Zhong Zhan," the "Yi Yao Zhan" by Jing Fang, and the "Yi Zhuan Dui Yi Zhan."

《陳卓占》、《郄萌占》、《韓楊占》、祖暅《天文錄占》、孫僧化《大象集占》、劉表《荊州占》、《列宿占》、《五官占》、《易緯》、《春秋佐助期占》、《尚書緯》、《詩緯》、《禮緯》、張衡《靈憲》

There are also the "Chen Zhuo's Divination," "Xie Meng's Divination," "Han Yang's Divination," Zu Gengzhi's "Astronomical Records and Divination," Sun Senghua's "Collection of Great Images and Divination," Liu Biao's "Jingzhou Divination," as well as "Divination of Celestial Objects," "Divination of the Five Officials," "Yi Jing Wei," "Chunqiu Zuo Zhu Qi Divination," "Shangshu Wei," "Shi Wei," "Li Wei," and Zhang Heng's "Lingxian." All of these are the sources from which the present book has drawn its divinatory statements.

夫天地者，萬物之父母也。覆載育養，左右無方。況人稟最靈之性，君為率上天之宗，天見人君得失之跡也，必極吉凶，故隨其所在，以見變異。

Heaven and Earth are the parents of all things. They cover above and carry below, nurturing all creatures and providing care without fixed direction. Moreover, humans possess the most refined nature, and the sovereign is the chief representative of Heaven. Heaven observes the success or failure of the sovereign's actions and certainly reveals extreme fortune or misfortune. Therefore, it manifests various changes according to the sovereign's domain.

天有災變者，所以譴告人君覺悟之，令其悔過，慎思慮也。行有玷缺，氣逆於天，精氣感出，變見以誡之。若天忽變色，是謂易常，四夷來侵，不出八年，有兵戰。若陽不足，臣盛將害君上，則天裂。

Heaven sends calamities to admonish and warn the sovereign, prompting him to awaken and repent for his mistakes, and to think carefully. When the sovereign's actions have flaws, his vital energy rises against Heaven, and the vital energies interact and emerge, causing Heaven to display anomalies to warn him. If the sky suddenly changes color, this is called "changing the constant," indicating that foreign tribes will invade. Within no more than eight years, there will be warfare. If the yang energy is insufficient, the ministers will become powerful and threaten the sovereign, and Heaven will split open.

按：馬續《天文志》云：“孝惠二年，天開東北，廣十丈，長二十餘丈，天裂，陽不足；地震，陰有餘：皆下盛將害上之變。”當時呂氏臨朝干位，卒有兵亂，此其驗也。

According to Ma Xu's continuation of the "Astronomical Records" in the "Book of Han," it is said: "In the second year of Emperor Hui of Han, the sky split open in the northeast direction, with a width of ten zhang and a length of more than twenty zhang. The splitting of the sky indicates an insufficiency of yang energy, while the movement of the earth indicates an excess of yin energy. These are all signs of the lower position becoming strong, which will eventually threaten the upper position." At that time, Lady Lu was ruling the court and violating the imperial position, and later chaos broke out, which was the fulfillment of this omen.

若天分裂，作君之亂，無道之臣欲裂國，其下之主當之。若天開見光，流血滂滂；天裂見人，兵起國亡；天鳴有聲，至尊憂而且驚。

If the sky splits apart, it signifies a disturbance among the rulers, with wicked ministers plotting to divide the territory, and this should be observed in the ruler corresponding to the area where the sky splits. If the sky cracks and light shines through, there will be a continuous flow of blood; if the sky splits and reveals a human form, it indicates the outbreak of warfare and the fall of the state; if the sky produces a loud sound, it signifies that the supreme ruler will be both anxious and frightened.

劉向曰：春秋之前，天鳴地坼，災異並臻，其主不知驚懼修德，上帝降災，禍變必極，皆亂國之所生也。

Liu Xiang said: Before the Spring and Autumn period, heaven would emit sounds, the earth would crack open, and various calamities and strange phenomena would appear together. However, the rulers of that time did not understand the warning and cultivate virtue, so the heavenly sovereign would send down calamities. These calamities would inevitably reach their extreme. These phenomena are all signs that arise from chaotic states.

凡國亂，五星化下為之祅，而降之自天。是故歲星降為貴臣，熒惑降為童兒嬉戲歌謠，填星降為老人婦女，太白降為壯夫處於林麓，辰星降為婦女，或變化無所不為，以見異而告之也。

Whenever a country is about to become chaotic, the five planets transform into strange beings and descend to the human world. These strange beings come from the heavens. Therefore, the planet Jupiter (the Year Star) descends and becomes a prominent official, the planet Mars (the Malefic of Violence) descends and becomes children's songs and games, the planet Saturn (the Filling Star) descends and becomes old people and women, the planet Venus (the Supreme White) descends and becomes strong men appearing in mountains and forests, and the planet Mercury (the Morning Star) descends and becomes women. Sometimes they change in unpredictable ways, doing anything, appearing as strange phenomena to warn people.

凡天雨雜物，其類甚多。若雨禽獸，是謂不祥，不出三年，其下兵興。天雨蟲，人君不親骨肉而親他人，與裸蟲同類，故蟲從天墜地，骨肉去也。不救，兵大起。其起也，立王公，率同姓諸侯，無偏黨側，災消。

Whenever various kinds of objects fall from the sky, there are many different types. If birds or beasts fall from the sky, this is considered an omen of ill fortune, and within three years, warfare will arise in that region. If insects fall from the sky, it indicates that the ruler does not show affection to his close relatives but instead favors outsiders. Humans and hairless creatures, known as 'luo chong', are of the same category, so when insects fall from the sky to the earth, it symbolizes the dispersion of close family members. If no measures are taken to address this, great warfare will ensue. The method to remedy this is: to enfeoff princes and have them lead fellow-surname feudal lords, without partiality or factionalism, and the ominous signs will be dispelled.

劉向云：春秋時蟲者，蟲之災也。以刑罰暴虐而取於天下，貪叨無厭以興師動眾，聚邑治城而失眾心，蟲為害矣。故宋文公三年秋，雨蟲於宋。是時宋公暴虐重刑，賦斂無已，故應是雨蟲。

Liu Xiang said: The "chong" recorded in "Chun Qiu" refers to pestilence. Using cruel punishments to search throughout the land, being insatiable in military campaigns, gathering the people's strength to build cities and losing the people's hearts, pests will cause disaster. Therefore, in the third year of Duke Wen of Song, there was a rain of insects in the autumn of Song. At that time, Duke Wen of Song was cruel and imposed severe punishments, with endless taxation and levies, so it was verified by this rain of insects.

天雨魚鱉，國有兵喪。天雨骨，是謂陽消。王者德衰，令不行，佞不用，不出三年，內有爭。天雨筋，國大飢。天雨膏如蟲，輔臣多貪，賢智隱之應也，君臣無道暴虐。天雨肉，天不享其德，將易其君。

Heavenly fish and turtles descending indicate military strife and deaths within the country. Heavenly bones descending signify "Yang declining": the king's virtue is deteriorating, his orders are not being carried out, even佞men refuse to serve him, and within three years there will be internal conflicts. Heavenly sinews descending indicate a great famine in the country. Heavenly oil-like creatures descending indicate that the ministers assisting the ruler are greedy, virtuous men have withdrawn, and it shows that the ruler and ministers are both corrupt and tyrannical. Heavenly flesh descending indicates that heaven no longer enjoys his virtue and is about to replace this ruler.

天雨爵錫，如甘露著樹，不出三年，改易王。白者為甘露，黃者為爵錫。天雨如水銀，是謂刑祖。不出三年，兵喪並起，亡國失土。天雨血，是謂天見其祅。不肖者不得久處其位，不出一年兵起。

Heavenly decree descends as "Jue Xi," appearing on trees like sweet dew, and within three years, a change of ruler will occur; among them, the white one is sweet dew, and the yellow one is Jue Xi. If something like quicksilver falls from heaven, it is called "Xing Zu," and within three years, warfare and mourning will arise together, leading to the fall of the state and loss of territory. If blood falls from heaven, this is called the heavens displaying their strange phenomena: the unvirtuous cannot remain in power for long, and within a year, warfare will break out.

京房曰：“臨獄不解，茲謂進非，厥咎天罰。故天雨血者，茲謂不親，民有怨恐，不出三年，亡其宗人。”又曰：“佞人用，功臣棄戮，故天雨血。”

Jing Fang said: "If cases are delayed and not decided, this is called employing the wrong people, and its punishment is the heavens' retribution. Therefore, the heavens send blood rain, which is called the heavens and the people not being in harmony. The people hold resentment and fear, and within three years, he will lose his clan." He also said: "When wicked ministers are appointed and meritorious officials are discarded and executed, therefore the heavens send blood rain."

天雨毛，邪人進，賢人逃，貴人出走。天雨羽，君德不通，逆施天下。天雨金、銀、鐵、錢、花，兵將興，失道之君當之。

Heavenly downpour of feathers signifies the promotion of wicked ministers and the retreat of virtuous men, with the nobleman fleeing. Heavenly downpour of down signifies the ruler's virtue not reaching the people, and his policies being misapplied in reverse. Heavenly downpour of gold, silver, iron, money, or flowers signifies the outbreak of military conflict, which will occur upon an unjust ruler.

淳風按：“隋仁壽四年甲子諸州造舍利塔時，陝州天雨金銀花，時人以作像，象祥瑞，以奏於高祖，高祖知其非吉。其後有楊諒之亂、二世失道，斯其驗也。”

Li Chunfeng remarked: In the fourth year of Renshou of Emperor Wen of Sui, during the construction of stupas in various states, golden and silver flowers fell from the sky in Shaan Prefecture. The people at that time cast them into Buddhist images, considering them a sign of auspiciousness, and reported this to Emperor Gaozu Wen of Tang. However, Emperor Wen knew this was not a good omen. Later, there was the rebellion of Prince Han Yang Liang, and the second emperor Yang of Sui lost the way and lost the country, which was the fulfillment of this omen.

天雨石，為政者質信不施，為詐妄行，國君死亡。甘氏曰：“無雲而雷，隕石墜地，大可一丈，圓形如雞子，兩頭銳，名曰天鼓。所下之邦，必有大戰，伏尸數萬，不可救。”春秋魯僖公十六年，隕石於宋五，此時宋襄公之應也。望之是星，至地為石。失其所，無光榮之象也。

Heavenly stones fall from above, indicating that those in power do not act with sincerity and righteousness, but instead engage in deceit and wrongdoing, and the ruler will die. Gan De said, "Without clouds, thunder occurs, and falling stones strike the ground. The large ones can be up to a zhang in size, round like eggs, with pointed ends, called 'Heavenly Drum.' The country where these stones fall will surely experience a great battle, with tens of thousands of dead, which cannot be prevented." The Spring and Autumn Annals record that in the sixteenth year of Duke Xi of Lu, five stones fell upon the State of Song, which precisely corresponds to the fate of Duke Xiang of Song. This phenomenon appears as a star in the sky but becomes a stone upon falling to the ground; its departure from its proper place signifies a loss of honor.

皇甫士安曰：“殷紂暴虐，天雨灰。”天雨灰，邑君有來歸邑者。墨子曰：“商紂不德，十日雨土於毫。”天雨土，君失封。

Huang Fu Mi said: "Yin Zhou was cruel and tyrannical, and ash fell from heaven." When ash falls from heaven, it indicates that a ruler of a foreign state will come to submit. The "Mozi" says: "Shang Zhou lacked virtue, and for ten days a rain of earth fell over Bo Du." When earth falls from heaven, it indicates that the ruler will lose his territory.

天雨五穀，是謂禾不熟。人君賦斂重數，故示戒。不出五年，國乏軍糧。天雨粟，不肖者食祿，三公易位。天雨黍豆麥粟稻，是謂惡祥。不出一年，人民父子流亡，莫知所向。

Heaven sends down grain, which is called "the crops are not ripe": when the ruler imposes excessive and oppressive taxes, thus the heavens show a warning, within no more than five years, the country will lack military provisions. When heaven sends down millet, it indicates that an unworthy person enjoysofficial stipend without merit, and the three ministers will be replaced. When heaven sends down millet, beans, wheat, millet, and rice, this is called an ominous sign, within no more than one year, the common people will have fathers and sons fleeing, not knowing where to go.

若國君失信，專祿去賢，則天雨草。君信讒，臣不和，天雨草木，其歲人多兵死。天雨釜甑，歲大豐穰。此釜甑適如小錢許大，從地中生出，餘親見之。其中有如小麻黍粟大，世人謂之蒸餅，豐穰之驗也。

If the sovereign loses his integrity and appropriates the official positions while expelling the virtuous, then grass will fall from the sky. If the sovereign listens to slander and the ministers are in discord, then grass and trees will fall from the sky, and in that year many people will die from military calamities. If the sky sends down "fu zeng" (a cooking vessel), it indicates a great harvest. This kind of "fu zeng" object is as small as a coin and grows out of the ground; I have seen it with my own eyes. Inside it are grains the size of millet, foxtail millet, and sorghum, and people call it "zheng bing" (steamed bread), which is a sign of a bountiful harvest.

天雨絮，其國將喪，無後有兵。天雨櫱，君有咎。天雨墨，臣多陰謀。天火燒國郭門，其地有謀人慾發。天光蟠邑城門，其國圍。天火焚宗廟社稷，大殃，國將亡主。

Heavenly Fire descending brings calamity to the country, leading to the loss of the ruler's descendants and military disaster. If curved yeast falls from the sky, it indicates the ruler will face misfortune. If black ink falls from the sky, it signifies many conspiracies among the ministers. If Heavenly Fire burns the outer gate of the capital city, it indicates that there will be a plot against the place. If a luminous disk circles around the city gate, it signifies that the country will be besieged. If Heavenly Fire burns the ancestral temple and state altars, it is a great calamity, indicating the country will lose its ruler.

淳風按：“漢魏時，造作宮室過度，而頻有天災，其後尋有兵亂。隋末大業十二年，東京災宮，西京災顯揚門。至十三年，二邑並被圍沒，即絕其宗廟社稷，亦天告之驗。”

Li Chunfeng remarked: During the Han and Wei dynasties, excessive construction of palaces and buildings led to frequent calamities of heavenly fire, and shortly after, there were military uprisings. In the twelfth year of the Great Peace era of the Sui dynasty, a fire broke out in the palace of the eastern capital, Luoyang, and another fire occurred at the Xianyang Gate in the western capital, Chang'an. In the thirteenth year, both capitals were besieged and captured, leading to the destruction of ancestral temples and state altars. This was also a fulfillment of the heavenly warning.

天雨下物，非人所聞見者，皆大兵也。其災見所主國分，應發遠近。皆在略例篇中。

Phenomena that descend from heaven, if they are things that people have never heard of or seen before, indicate great military affairs. Such omens of calamity should manifest in the territory corresponding to the country's heavenly division. The distance and speed of their occurrence are recorded in the chapter "Examples of Divination." The term "national division" refers to the territory assigned to a particular state under the heavenly regions, which is also called "division."