Third Discussion: The Numbers of the Earthly Branches and Heavenly Stems

支干數者，凡有二種：一通數，二別數。今先辯通數，後論別數。通數者，十干、十二支也。干有十者，應天地之大數也。《易繫辭》言：天數五，地數五。天地之數，不過於十，故以干極於十。十主日，十日為一旬也。支十二者，《禮稽命徵》言：佈政十二，尊卑有序。《援神契》言：三三參行，四四相扶。天有四時之氣，以三月成一時，故言三三參行，四四相扶。天地人謂之三才，是為三者，物生之常數，因而各生三，本三而末九，所以十二。《元命苞》言：數成於三，故合於三。三月，陽極於九，故一時九十日也。支象於月，十二月為一歲也。此辨通數。

The numbers of the heavenly stems and earthly branches are divided into two categories: one is "general number" (total number), and the other is "distinct number" (individual numbers of each stem and branch). Now we first clarify the general number, and then discuss the distinct number. The general number refers to the total numbers of the ten heavenly stems and the twelve earthly branches. The heavenly stems are ten because they correspond to the great number of heaven and earth. The "Great Treatise" of the "Zhou Changes" says that the number of heaven is five and the number of earth is five, so the combined number of heaven and earth is only ten, hence the heavenly stems are limited to ten. The ten heavenly stems govern the "day," and ten days make a period. The earthly branches are twelve because the "Rites of the Mandate of Heaven" says that the implementation of government commands has twelve categories, with distinctions of rank and order. The "Xiao Jing Yuan Shen Qi" says: three threes interact, and four fours support each other. Heaven has the four seasons, and every three months form a season, so it is said "three threes interact." The four seasons support each other, so it is said "four fours support each other." Heaven, earth, and humanity are called the three elements, indicating that three is the constant number for the generation of all things. From this three, each produces another three, the original number is three and the derived number is nine, so three multiplied by four gives twelve. The "Chun Qiu Yuan Ming Bao" says: numbers are formed by three, so every three months form a season; the yang number reaches its peak at nine, so a season is ninety days. The earthly branches take their image from the moon, and twelve months make a year. This is how the general number is clarified.

別數者，支數則子數九，丑八，寅七，卯六，辰五，巳四，午九，未八，申七，酉六，戌五，亥四。《太玄經》云：子午九者，陽起於子，訖於午；陰起於午，訖於子。故子午對沖，而陰陽二氣之所起也。寅為陽始，申為陰始。從所起而左數，至所始而定數。故自子數至申，數九；自午數至寅，亦九。所以子午九也。

Now let us discuss the numbers of the Earthly Branches: Zi is nine, Chou is eight, Yin is seven, Mao is six, Chen is five, Si is four, Wu is nine, Wei is eight, Shen is seven, You is six, Xu is five, Hai is four. The Classic of Supreme Mystery explains that both Zi and Wu are assigned the number nine because the yang energy begins at Zi and ends at Wu, while the yin energy begins at Wu and ends at Zi. Therefore, Zi and Wu are directly opposite each other, representing the starting points of the two energies of yin and yang. Yin is the beginning of yang energy, and Shen is the beginning of yin energy. The method of calculation is: starting from the position where the branch 'begins,' count leftward in sequence until reaching the branch that marks the beginning of yin or yang. The number of positions counted is the number of that branch. Therefore, starting from Zi and counting to Shen (Zi, Chou, Yin, Mao, Chen, Si, Wu, Wei, Shen), there are nine positions; starting from Wu and counting to Yin (Wu, Wei, Shen, You, Xu, Hai, Zi, Chou, Yin), there are also nine positions. Hence, both Zi and Wu have the number nine.

丑未為對沖，自丑數至申，數八；自未數至寅，亦八，所以丑未八也。寅申為對沖，自寅數至申，數七；自申數至寅，亦七，所以寅申七也。卯酉為對沖，自卯數至申，數六；自酉數至寅，亦六，所以卯酉六也。辰戌為對沖，自辰數至申，數五；自戌數至寅，亦五，所以辰戌五也。巳亥為對沖，自巳數至申，數四；自亥數至寅，亦四，所以巳亥四也。又云：陽數極於九，子午為天地之經，故取陽之極數。自丑未巳下，各減一，從八至四，理自可知。

The Earthly Branches Chou and Wei are in opposition: counting from Chou to Shen involves eight steps, and counting from Wei to Yin also involves eight steps, so both Chou and Wei take the number eight. The Earthly Branches Yin and Shen are in opposition: counting from Yin to Shen involves seven steps, and counting from Shen to Yin also involves seven steps, so both Yin and Shen take the number seven. The Earthly Branches Mao and You are in opposition: counting from Mao to Shen involves six steps, and counting from You to Yin also involves six steps, so both Mao and You take the number six. The Earthly Branches Chen and Xu are in opposition: counting from Chen to Shen involves five steps, and counting from Xu to Yin also involves five steps, so both Chen and Xu take the number five. The Earthly Branches Si and Hai are in opposition: counting from Si to Shen involves four steps, and counting from Hai to Yin also involves four steps, so both Si and Hai take the number four. There is also a simpler way to understand this: the yang numbers reach their peak at nine, and Zi and Wu are the central positions of heaven and earth, so they take the number nine. Starting from the pair Chou and Wei, each subsequent pair decreases by one, from eight down to four, and the reasoning becomes clear.

干數者，甲九，乙八，丙七，丁六，戊五，己九，庚八，辛七，壬六，癸五。《太玄經》云：甲己九者，甲起甲子，從子故九；己為甲配，故與甲俱九。乙起乙丑，從丑故八；乙配於庚，與庚俱八。丙起丙寅，從寅故七；辛配於丙，與丙俱七。丁起丁卯，從卯故六；丁配於壬，與壬俱六。戊起戊辰，從辰故五；癸配於戊，與戊俱五。

The numbers of the Heavenly Stems are: Jia is nine, Yi is eight, Bing is seven, Ding is six, Wu is five, Ji is nine, Geng is eight, Xin is seven, Ren is six, and Gui is five. The Classic of Supreme Mystery explains that Jia and Ji both take nine because in the sixty Jiazi cycles, Jia first pairs with Zi to form Jiazi, so Jia takes nine following Zi; Ji combines with Jia (Jia and Ji combine), so Ji takes nine like Jia. Yi first pairs with Chou to form Yichou, so Yi takes eight following Chou; Yi combines with Geng, so Geng takes eight like Yi. Bing first pairs with Yin to form Bingyin, so Bing takes seven following Yin; Xin combines with Bing, so Xin takes seven like Bing. Ding first pairs with Mao to form Dingmao, so Ding takes six following Mao; Ding combines with Ren, so Ren takes six like Ding. Wu first pairs with Chen to form Wuchen, so Wu takes five following Chen; Gui combines with Wu, so Gui takes five like Wu.

支有十二，以對沖同數，故自九至四；干唯有十，以配合同數，故自九至五。又云：支從地，故數畢於陰，以四偶也；干從天，故數畢於陽，以五奇也。五則止於五氣，四則極於四時。上不過九者，陽之極數也。五行及支干之數，相則倍之，王則十而倍之，休則如本，因死半之。以此四而孳，數乃無極。此並從氣增減，氣盛則多，氣衰則少也。

The Earthly Branches consist of twelve, because the two branches that are opposite each other share the same number, and six pairs of branches use the numbers from nine to four; the Heavenly Stems have only ten, because the two stems that are paired together share the same number, and five pairs of stems use the numbers from nine to five. Another explanation is that the Earthly Branches belong to the Earth, so their numbers end with the yin number, with four as the final number; the Heavenly Stems belong to the Heaven, so their numbers end with the yang number, with five as the final number. Taking five signifies the end of the five elements' energies; taking four signifies the completion of the four seasons. The upper limit does not exceed nine, because nine is the extreme of the yang numbers. The numbers of the five elements and the Heavenly Stems and Earthly Branches also change according to the state of 'rest' and 'prosperity': if they are in the 'struggle' position, their original number is doubled; if they are in the 'prosperous' position, their number is multiplied by ten and then doubled again; if they are in the 'rest' position, their number remains the same; if they are in the 'death' position, their number is halved. According to these four conditions, the numbers continue to multiply endlessly. All these changes depend on the waxing and waning of the energies: when the energy is strong, the number is large; when the energy is weak, the number is small.

納音數者，謂人本命所屬之音也。音，卽宮商角徵羽也。納者，取此音以調姓所屬也。《樂緯》云：孔子曰，吹律定姓，一言得土曰宮，三言得火曰徵，五言得水曰羽，七言得金曰商，九言得木曰角。此並是陽數。

The concept of "Nayin" refers to the musical tone associated with a person's birth year's heavenly stem and earthly branch. Here, "sound" refers to the five tones: Gong, Shang, Jue, Zhi, and Yu. "Nayin" means taking this tone to determine the Five Phases (Wuxing) of the surname. The "Yue Wei" states that Confucius said, by blowing through the tuning pipes, one can determine the Five Phases of a surname. Calculating one step ("yiyan") corresponds to earth, with the tone Gong; three steps correspond to fire, with the tone Zhi; five steps correspond to water, with the tone Yu; seven steps correspond to metal, with the tone Shang; and nine steps correspond to wood, with the tone Jue. One, three, five, seven, and nine are all yang numbers (odd numbers), and only yang numbers are used in determining Nayin.

凡五行有生數、壯數、老數三種。木，生數三，壯數八，老數九。火，生數二，壯數七，老數三。土，生數五，壯數十，老數一。金，生數四，壯數九，老數七。水，生數一，壯數六，老數五。管輅云：土老數一者，土為萬物之主，一切歸之，所以一也。三才交而人理具，火之為德，取三才之義，故老數三。水，上應五星，下同五藏，故水老數五。金配七曜，故金老數七。木，在天為九星，在地為九州島，在人為九竅，故木老數九。先生數，次壯數，後老數。納音論其本命，故以終數言之。

The five phases have three kinds of numbers: the birth numbers, the vigorous numbers, and the old numbers. The birth number of wood is three, the vigorous number is eight, and the old number is nine; the birth number of fire is two, the vigorous number is seven, and the old number is three; the birth number of earth is five, the vigorous number is ten, and the old number is one; the birth number of metal is four, the vigorous number is nine, and the old number is seven; the birth number of water is one, the vigorous number is six, and the old number is five. Guan Lu explained the concept of the old numbers: the old number of earth is one because earth is the master of all things, and everything is summarized through it, so it takes one. Heaven, earth, and humanity meet together, and only then is the human way complete; fire's virtue corresponds to the meaning of the three principles, so its old number is three. Water corresponds to the five stars above and the five internal organs below the human body, so its old number is five. Metal corresponds to the seven luminaries, the sun, moon, and five stars, so its old number is seven. Wood corresponds to nine stars above, nine states below, and nine orifices on the human body, so its old number is nine. The order of these three numbers is: first the birth numbers, then the vigorous numbers, and finally the old numbers. The nayin sound element discusses a person's destiny, which is an ultimate conclusion, so it uses the old numbers to establish its theory.

此釋猶為未盡。夫萬物皆稟五常之氣，化合而生。物生之後，必至成壯；成壯之後，必有衰老。故有三種義。為人之道，自壯及老，莫不本乎禮義而以立身。然存禮義者，靡不有初，鮮克有終。今既論納音人之所屬，非人莫能行其禮義，故以終老之數，禮義明之。

All things receive the vital energies of the Five Constants, undergo combination and generation, and thus come into being. After birth, they inevitably progress to maturity and strength, and after reaching maturity and strength, they must inevitably decline and decay. Therefore, there are three phases of numbers: birth, maturity, and old age. In human life, from youth to old age, one must rely on propriety and righteousness as the foundation for living and dealing with the world. However, those who can maintain propriety and righteousness often have a good beginning but rarely persist until the end. Now, since we are discussing the correspondence between the Nayin sound elements and human destiny, and only humans can practice propriety and righteousness, we use the phase of 'old age' in the numbers to illustrate this in conjunction with propriety and righteousness.

一言得土者，土以含弘德厚，位高為君。君為民主，主則無二，唱始之言，故數一也。三言得火者，火既主禮，孝敬為先，不敢棄所生之德，故其數三，從木數也。水居陰位，人臣之道，土能制水，如君制臣，縱之則行，壅之則止，水不自專，故從土數五也。金既主義，義是夫妻之道，妻無自專，有從夫之義，火為金夫，故用火數七也。木主仁孝，金能克木，宗廟之象。《式經》云：金為骸骨，木為棺槨。此明金木為鬼神之事，以敬事，故木從金數，故數九也。一示君德，二順父母，三表臣節，四敬從夫，五事鬼神，此則禮義備而人事畢矣，故納音數用之。

Counting one step gives earth: Earth contains and accommodates broadly, has deep virtue, holds the highest position and symbolizes the ruler; the ruler is the master of all people, and there can only be one master, not two, being the first and initiating sound, so the number one is chosen. Counting three steps gives fire: Fire governs 'rituals', which prioritize filial piety and respect, not daring to forsake the kindness of those who gave birth to it. Fire is born from wood, so the number three is taken—this three is the generating number of wood, and fire takes the number from the wood that generates it. Water resides in the yin position, representing the way of a minister; earth controls water, just as the ruler controls his ministers. If released, water flows; if blocked, it stops. Water cannot act on its own, so water takes the number five from the earth that controls it. Metal governs 'righteousness', which is embodied in the relationship between husband and wife; the wife cannot act on her own, there is the principle of obedience to the husband. Fire is the husband of metal (fire overcomes metal, the overcoming one is the husband), so metal uses the old number of fire, which is seven. Wood governs benevolence and filial piety; metal overcomes wood, which is the image of ancestral temple worship. The "Style Classic" says: Metal is the skeleton, Wood is the coffin. This indicates that metal and wood are related to matters of ghosts and spirits, and they should be treated with reverence and caution, so wood follows metal and takes its number, thus becoming nine. In summary: one shows the virtue of the ruler, two follows the parents, three shows the loyalty of the subject, four respects and obeys the husband, five serves the spirits—thus, rites and propriety are complete, and human affairs are fully covered, so the nayin numbers adopt this system.

納音者，子午屬庚，震卦所直日辰也；丑未屬辛，巽卦所直日辰也；寅申屬戊，坎卦所直日辰也；卯酉屬己，離卦所直日辰也；辰戌屬丙，艮卦所直日辰也；己亥屬丁，兌卦所直日辰也。一言得土者，本命庚子，子屬於庚，數之，一言便以得之是也。三言得火者，本命丙寅，寅屬於戊，從丙數至戊，凡三是也。五言得水者，本命壬戌，戌屬於丙，從壬數至丙，凡五是也。七言得金者，本命壬申，屬於戊，從壬數至戊，凡七是也。九言得木者，本命己巳，巳屬於丁，從己數至丁，凡九是也。六十甲子，例皆如是。支屬八卦為納音者，皆以次而取對沖，如子午屬庚，子午相對沖也，餘例悉然。

The basic assignment for determining the sound element (Nayin) is as follows: the branches Zi and Wu belong to the heavenly stem Geng, which corresponds to the trigram Zhen (Thunder); Chou and Wei belong to Xin, corresponding to Xun (Wind); Yin and Shen belong to Wu, corresponding to Kan (Water); Mao and You belong to Ji, corresponding to Li (Fire); Chen and Xu belong to Bing, corresponding to Gen (Mountain); and Si and Hai belong to Ding, corresponding to Dui (Lake). These six groupings come from the method of assigning heavenly stems to the eight trigrams (Najia), and they form the basis for calculating the sound element. The specific method is: starting from the heavenly stem of one's birth year, count through the ten heavenly stems in order until reaching the heavenly stem corresponding to the birth branch. The number of steps counted determines the number of 'yan' (sayings). One 'yan' corresponds to earth, such as if the birth year is Gengzi, since Zi belongs to Geng, you count one step from Geng to Geng, thus one 'yan', and the sound element is earth. Three 'yan' correspond to fire, such as if the birth year is Bingyin, since Yin belongs to Wu, you count from Bing to Wu (Bing, Ding, Wu), which is three steps, thus three 'yan', and the sound element is fire. Five 'yan' correspond to water, such as if the birth year is Jisi, since Xu belongs to Bing, you count from Ren to Bing (Ren, Gui, Jia, Yi, Bing), which is five steps, thus five 'yan', and the sound element is water. Seven 'yan' correspond to metal, such as if the birth year is Renshen, since Shen belongs to Wu, you count from Ren to Wu (Ren, Gui, Jia, Yi, Bing, Ding, Wu), which is seven steps, thus seven 'yan', and the sound element is metal. Nine 'yan' correspond to wood, such as if the birth year is Jisi, since Si belongs to Ding, you count from Ji to Ding (Ji, Geng, Xin, Ren, Gui, Jia, Yi, Bing, Ding), which is nine steps, thus nine 'yan', and the sound element is wood. All sixty Jiazi follow this method. The branches are assigned to the eight trigrams to determine the sound element, and each group is formed by taking the two branches that are opposite to each other, such as Zi and Wu both belong to Geng, because Zi and Wu are opposite; the other groups are also formed in this way.

夫陽施陰化，故受氣定形，皆資於陰陽，以養成之。是以人之所屬，皆以陽數言也。所以子午屬庚之例者，乾為父，坤為母，共有六子，故曰：干將三男震坎艮，坤將三女巽離兌。陰陽相生，故就干索女，就坤索男。所以干一索而得巽，曰長女；再索而得離，曰中女；三索而得兌，曰少女。坤一索而得離，曰長男；再索而得坎，曰中男；三索而得艮，曰少男。

Heavenly Yang is responsible for giving out, while Earthly Yin is responsible for nurturing and cultivating. Therefore, all things receive the vital energy and take form, and they all depend on both Yang and Yin for their growth and completion. Hence, the Nayin sound element of a person is always expressed using the Yang numbers (one, three, five, seven, nine). As for the origin of the system that assigns "Zi and Wu belong to Geng," it comes from the Eight Trigrams. Qian represents the father, and Kun represents the mother, and together they have six children. Therefore, Qian governs the three male Trigrams: Zhen, Kan, and Gen. Kun governs the three female Trigrams: Xun, Li, and Dui. Because Yang and Yin generate each other, one must seek female Trigrams from Qian and male Trigrams from Kun. Therefore, when Qian first seeks, it obtains Xun, which is called the Eldest Daughter. When it seeks again, it obtains Li, called the Middle Daughter. When it seeks a third time, it obtains Dui, called the Youngest Daughter. When Kun first seeks, it obtains Zhen, called the Eldest Son (the original text mistakenly writes "Li" instead of "Zhen"); when it seeks again, it obtains Kan, called the Middle Son; and when it seeks a third time, it obtains Gen, called the Youngest Son.

甲是陽干之始，乾下三爻取之；壬是陽干之末，乾上三爻取之；乙是陰干之始，坤下三爻取之；癸是陰干之末，坤上三爻取之。餘有六干，陽付其男，陰付其女。甲乙之後，次於丙丁，故以丙付少男艮，以丁付少女兌；丙丁之後，次於戊己，故以戊付中男坎，以己付中女離；戊己之後，次於庚辛，故以庚付長男震，以辛付長女巽。所以從少而付老，自小及大，從微至著故也。

Jia is the beginning of the yang stems and is assigned to the lower three lines of the Qian trigram; Ren is the end of the yang stems and is assigned to the upper three lines of the Qian trigram; Yi is the beginning of the yin stems and is assigned to the lower three lines of the Kun trigram; Gui is the end of the yin stems and is assigned to the upper three lines of the Kun trigram—this is called "Qian trigram takes Jia and Ren, Kun trigram takes Yi and Gui." The remaining six stems are assigned to the three yang trigrams and the three yin trigrams. After Jia and Yi come Bing and Ding, so Bing is assigned to the young male trigram Gen and Ding to the young female trigram Dui; after Bing and Ding come Wu and Ji, so Wu is assigned to the middle male trigram Kan and Ji to the middle female trigram Li; after Wu and Ji come Geng and Xin, so Geng is assigned to the elder male trigram Zhen and Xin to the elder female trigram Xun. The reason for starting with the smallest and then assigning to the older ones is based on the principle of beginning with small and moving to great, from subtle to manifest.

付干既訖，次付其支。震為長子，故其卦，初九得干之子，九四得干之午，震干庚，故子午屬庚。巽為長女，子後次丑，故其卦，初六得坤之丑，午後次未，六四得坤之未，巽干辛，故丑未屬辛。坎為中男，丑後次寅，其卦，初六得干之寅，未後次申，六四得干之申，坎干戊，故寅申屬戊。

The heavenly stems have been assigned, and now the earthly branches are distributed. Zhen is the eldest son, so the first line of the Zhen hexagram receives the Zi branch from Qian, and the fourth line receives the Wu branch from Qian; the earthly branches Zi and Wu belong to Geng, which is the heavenly stem incorporated by Zhen. Xun is the eldest daughter, following Zi comes Chou, so the first line of the Xun hexagram receives the Chou branch from Kun; following Wu comes Wei, so the fourth line receives the Wei branch from Kun; the earthly branches Chou and Wei belong to Xin, which is the heavenly stem incorporated by Xun. Kan is the middle son, following Chou comes Yin, so the first line of the Kan hexagram receives the Yin branch from Qian; following Wei comes Shen, so the fourth line receives the Shen branch from Qian; the earthly branches Yin and Shen belong to Wu, which is the heavenly stem incorporated by Kan. It is evident that the distribution of the earthly branches follows the order of the twelve earthly branches, sequentially assigned to the first and fourth lines of the six sons' hexagrams.

離為中女，寅後次卯，故其卦，初九得坤之卯，申後次酉，九四得坤之酉，離干己，故卯酉屬己。艮為少男，卯後次辰，故其卦，初六得干之辰，酉後次戌，六四得干之戌，艮干丙，故辰戌屬丙。兌為少女，辰後次己，故其卦，初九得坤之己，戌後次亥，九四得坤之亥，兌干丁，故己亥屬丁。

The trigram Li represents the middle daughter. After Yin comes Mao, so the first line of the Li trigram, initial nine, receives the Mao (which belongs to the Earth trigram Kun). After Shen comes You, so the fourth line of the Li trigram, nine in the fourth, receives the You (which belongs to the Earth trigram Kun). The trigram Li incorporates the heavenly stem Ji, so Mao and You are assigned to Ji. The trigram Gen represents the young son. After Mao comes Chen, so the first line of the Gen trigram, initial six, receives the Chen (which belongs to the Heaven trigram Qian). After You comes Xu, so the fourth line of the Gen trigram, six in the fourth, receives the Xu (which belongs to the Heaven trigram Qian). The trigram Gen incorporates the heavenly stem Bing, so Chen and Xu are assigned to Bing. The trigram Dui represents the young daughter. After Chen comes Si, so the first line of the Dui trigram, initial nine, receives the Si (which belongs to the Earth trigram Kun). After Xu comes Hai, so the fourth line of the Dui trigram, nine in the fourth, receives the Hai (which belongs to the Earth trigram Kun). The trigram Dui incorporates the heavenly stem Ding, so Si and Hai are assigned to Ding.

六子取干，則乾坤之餘；取支，並從乾坤而得。陽取於干，陰取於坤，皆受於父母。故六子並主十二辰，人之納音，皆所繼焉。甲乙壬癸不為納音者，以屬乾坤故也。或問曰：六子用干，則取父母之不用者；用支，則並同於父母者，何？答曰：干，是陽也，陽體奇，故正得一往分用；支，是陰也，陰體偶，故以再往用之。又復龜則用日，是以正求於干，故發兆分為十分；筮則用辰，正求於支，是以飛伏六爻，並論十二支。雖復體不兼要，須相配以明義。干為尊，故不得不先設，而後求支。筮雖不正用干，亦須干助，以顯其趣；猶如龜判十二支，兆體雖無支象，必約而論之。筮雖闕三甲、三壬、三乙、三癸，亦約虛以求實。

The heavenly stems used in the six subordinate trigrams are those remaining from the trigrams Qian and Kun. The earthly branches used in the six subordinate trigrams are all taken from the trigrams Qian and Kun. A yang trigram takes the earthly branches from the trigram Qian, while a yin trigram takes the earthly branches from the trigram Kun. These are all inherited from the parent trigrams. Therefore, the six subordinate trigrams each govern one of the twelve earthly branches, and the nayin sound elements of people are also derived from this. The heavenly stems Jia, Yi, Ren, and Gui are not involved in nayin calculations because they belong to the parent trigrams Qian and Kun, which are esteemed and not included in the distribution of the six subordinate trigrams. Someone asks: the heavenly stems used in the six subordinate trigrams are those not used in the parent trigrams, but the earthly branches used are exactly the same as those of the parent trigrams. Why is this? The answer is: heavenly stems belong to yang, and yang is based on odd numbers, so they are only used once and are fully distributed. Earthly branches belong to yin, and yin is based on even numbers, so they are used twice to be fully exhausted (the twelve earthly branches are divided among the six trigrams, each trigram receiving two branches). Furthermore, divination by龟卜 (divination with turtle shells) mainly seeks from heavenly stems, so the turtle omens are divided into ten parts. Divination by蓍筮 (divination with yarrow stalks) mainly seeks from earthly branches, so the concepts of flying god and hidden god, as well as the six lines and the nayin branches, are all discussed in relation to the twelve earthly branches. Although the two methods have different focuses and cannot be combined, they still need to complement each other to explain the meaning. Heavenly stems are esteemed, so they must be arranged first, and then the earthly branches can be sought. Although divination by yarrow stalks does not directly use heavenly stems, it still relies on them to reveal the meaning. It is like divination by turtle shells, which needs to judge the twelve earthly branches, but the turtle omens themselves do not have the image of earthly branches, so they must roughly infer them. Divination by yarrow stalks, although lacking three Jia, three Ren, three Yi, and three Gui (the heavenly stems of the trigrams Qian and Kun, each occupying three lines), still relies on empty positions to obtain practical results.

且設干往，先從父母而為始，後及六子。以甲付干，以乙付坤，以丙付艮，以丁付兌，以戊付坎，以己付離，以庚付震，以辛付巽，歷八卦訖，壬還到干，次癸還到坤。十干所在六爻，乾坤位尊，取其始末理，然體各得二。干支既當爻正用，故卦別皆備。陽卦取其陽支，陰卦取其陰支，四卦同陽，四卦同陰，非正同於父母。當伏羲畫八卦，為三爻，備天地人，所以分乾卦，別取三。乾坤居始，故取甲乙。後神農重之以為八，純子有重來之理，所以卦六干並同。父母無二之義，故後卦取乎壬癸。其甲乙壬癸各少三者，皆排在虛用之中，不全無者，陰有從陽之義。

Suppose the ten heavenly stems are assigned in sequence: starting from the parent hexagrams, then proceeding to the six child hexagrams. Jia is assigned to Qian, Yi to Kun, Bing to Gen, Ding to Dui, Wu to Kan, Ji to Li, Geng to Zhen, Xin to Xun; after the eight trigrams have been assigned once, Ren returns to Qian, and Gui returns to Kun. The ten heavenly stems are distributed over the six lines of each hexagram. Qian and Kun hold a high status, and they are given two heavenly stems each, following the principle of beginning and end. Since both heavenly stems and earthly branches must be applied to the lines of a hexagram, each hexagram is fully equipped. Yang hexagrams take yang branches, and yin hexagrams take yin branches. The four yang hexagrams share the same yang branches, and the four yin hexagrams share the same yin branches, which is not exactly the same as the parent hexagrams. When Fuxi originally drew the eight trigrams, each trigram had three lines, used to represent the three elements of heaven, earth, and humanity. Therefore, when assigning heavenly stems, each trigram was given an additional three lines. Qian and Kun were at the beginning, so Jia and Yi were assigned first. Later, Shen Nong overlapped the three lines of each trigram to form a hexagram with six lines, which follows the principle of repeating the cycle. Therefore, the heavenly stems on the six lines are the same at the beginning and end. Also, since the parent hexagrams cannot have a second assignment, when the cycle returns to Qian and Kun, Ren and Gui are used instead. As for Jia, Yi, Ren, and Gui, each is missing three lines, and they are placed in a position that is reserved but not entirely discarded. This reflects the principle that yin follows yang.

九宮者，上分於天，下別於地，各以九位。天則二十八宿、北斗九星，地則四方四維及中央，分配九有。謂之宮者，皆神所遊處，故以名宮也。鄭司農云：太一行八卦之宮，每四乃入中央。中央雲者，地神之所居，故謂之九宮。

The so-called "Nine Palaces" correspond to the heavens above and distinguish the earth below. Both heaven and earth are divided into nine positions. In the heavens there are the Twenty-Eight Mansions and the Nine Stars of the Big Dipper, while on the earth there are the four cardinal directions—east, south, west, and north—the four intermediate directions—southeast, southwest, northeast, and northwest—and the central position. By distributing these nine directions, the Nine Regions (Nine States) are formed. The term "palace" is used because these positions are places where deities move and rest, hence the name "Nine Palaces." Zheng Sizhong said: The deity Taiyi travels through the palaces of the Eight Trigrams, returning to the central palace after passing through four palaces. The central palace is where the earth deity resides, thus it is called the "Nine Palaces."

《易緯乾鑿度》云：易一陰一陽之謂道也，故太一取其數以行九宮。《易》曰：天一，地二，天三，地四，天五，地六，天七，地八，天九，地十。天地之數，合五十有五。九宮用者，天除一，地除二，人除三，餘四十九，以當蓍策之數。又四時除四，餘四十五。五者，五行；四十者，五行之成數。合之，則一節之數。分置五方，方各九者，一時九十日之數，四方成四時也。三宮相對，止十五者，為一氣之數，成二十四氣也。

The "Yi Wei · Qian Zao Du" says: The "Zhou Yi" states that "a combination of yin and yang is called the Dao," so the Taiyi takes this number to move through the nine palaces. The "Zhou Yi · Xi Ci" says: Heaven one, Earth two, Heaven three, Earth four, Heaven five, Earth six, Heaven seven, Earth eight, Heaven nine, Earth ten. The total number of Heaven and Earth is fifty-five. When using the nine palaces, subtract one from Heaven, two from Earth, and three from Man, leaving forty-nine, which corresponds exactly to the number of yarrow stalks used in divination. Then subtract four for the four seasons, leaving forty-five. Among these forty-five, five represents the Five Phases, and forty is the sum of the five generated numbers (six, seven, eight, nine, ten). Together, they correspond to the number of days in a solar term. Divide forty-five into the five directions, each direction gets nine, and when multiplied by ten days in a sheng (decade), it equals ninety days, forming a season. The four directions constitute the four seasons. In the nine palace diagram, three opposite palaces add up to fifteen, which is the number of days in a solar term. Accumulated, they form the twenty-four solar terms.

《尚書洪範》云：初一曰五行，位在北方，陽氣之始，萬物將萌。次二曰敬用五事，位在西南方，謙虛就德，朝謁嘉慶。次三曰農用八政，位在東方，耕種百穀，麻枲蠶桑。次四曰協用五紀，位在東南方，日月星辰，雲雨並興。次五曰建用皇極，位在中宮，百官立表，政化公卿。次六曰乂用三德，位在西北，抑伏強暴，斷制獄訟。次七曰明用稽疑，位在西方，決定吉凶，分別所疑。次八曰念用庶徵，位在東北，肅敬德方，狂僭亂行。次九曰向用五福、威用六極，位在南方，萬物盈實，陰氣宣佈，時成歲德，陰陽和調，五行不忒。

The nine categories listed in the "Book of Documents · Hongfan" correspond exactly with the nine palaces. The first is "Five Phases," located in the north, where yang energy begins and all things are about to sprout. The second is "Respecting and Using the Five Affairs," located in the southwest, emphasizing humility to cultivate virtue, paying homage to the Son of Heaven, and performing auspicious ceremonies. The third is "Agricultural Use of the Eight Affairs," located in the east, governing the planting of various grains and the cultivation of flax and silkworms. The fourth is "Coordinating the Five Records," located in the southeast, where the sun, moon, and stars move in order, and clouds and rain arise together. The fifth is "Establishing the Son of Heaven's Great Principle," located in the central palace, where officials set examples and ministers carry out governance and education. The sixth is "Maintaining Order with the Three Virtues," located in the northwest, suppressing violence and adjudicating lawsuits. The seventh is "Clarifying Doubts through Inquiry," located in the west, deciding fortune and misfortune and distinguishing doubts. The eighth is "Considering the Various Signs," located in the northeast, requiring reverence and cultivation of virtue, and avoiding reckless and overstepping misconduct. The ninth is "Facing the Five Blessings and Using the Six Evils," located in the south, where all things are full and abundant, and yin energy begins to manifest, the seasons complete the virtue of a year, yin and yang are in harmony, and the five phases do not go awry.

故《黃帝九宮經》云：戴九，履一，左三，右七，二四為肩，六八為足，五居中宮，總御得失。其數則坎一、坤二、震三、巽四、中宮五、干六、兌七、艮八、離九。太一行九宮，從一始，以少之多，順其數也。配算曰：中央及四仲，各分九算。命雲木落歸本，分六至亥，故取震六算，以置於干；水流向末，分八至丑，故取坎八算，以置於艮；金義而堅，分二還未，故取兌二算，以置於坤；火本炎盛，自處其鄉，故離算不動；土王四季，本生於巳，故分中宮四算，以置於巽。故成戴九履一之位也。

Therefore, the Yellow Emperor's Nine Palaces Classic says: "On the head is nine, on the feet is one, on the left is three, on the right is seven, two and four are the shoulders, six and eight are the feet, and five is in the Central Palace, overseeing the gains and losses of the whole situation." In terms of trigrams, this corresponds to Kan one, Kun two, Zhen three, Xun four, Central Palace five, Qian six, Dui seven, Gen eight, and Li nine. The Supreme One moves through the nine palaces, starting from one, proceeding from few to many, moving in order. The method of arranging the counting rods in the nine palaces is: the Central Palace and the four cardinal directions, Zi, Wu, Mao, and You, each initially receive nine counting rods. The mnemonic says "wood falls back to its root"—leaves fall back to their origin, so six counting rods are taken from the Zhen Palace and moved to the Hai direction, thus placing the six counting rods of Zhen into the Qian Palace. The mnemonic says "water flows to its end"—water flows to the end, so eight counting rods are taken from the Kan Palace and moved to the Chou direction, thus placing the eight counting rods of Kan into the Gen Palace. The mnemonic says "metal is righteous and firm"—metal is righteous and has a firm nature, so two counting rods are taken from the Dui Palace and moved to the Wei direction, thus placing the two counting rods of Dui into the Kun Palace. Fire is hot and vigorous by nature, staying in its own place, so the counting rods in the Li Palace remain untouched. Earth is strong in the last months of the four seasons and originates in Si, so four counting rods are taken from the Central Palace and moved to the Xun Palace. In this way, the "nine palaces with nine on top and one below" layout is formed.

又，初成八卦之法，命方之算。先取北方九算，命曰水生木，縱一算置寅上，一算置卯上，一算置辰上；又橫一算置甲上，一算置乙上。次取東方九算，命曰木生火，於南方布五位。又取南方之算，命曰火生土，於中央一算，於西北為戊，一算於西南為巳。又取中央之算，命曰土生金，於西方布五位。又取西方之算，命曰金生水，於北方布五位。五方布十干十二支位訖，然後加陰干各一，命曰陰數偶也；次加陽支各一，命曰支體本。加其始餘算，十二月之數也。一算置西北，命曰干之始也；二算置西南，命曰坤之始也。又餘算九，置於中央，為易象也。

In addition, the original method of arranging counting rods to form the Eight Trigrams was as follows: first, assign counting rods to each direction. Begin with the northern direction, using nine counting rods, with the mnemonic "water generates wood": place one rod vertically at the寅 position, one at the卯 position, and one at the辰 position; then place one rod horizontally at the甲 position and one at the乙 position. Next, take nine counting rods for the eastern direction, with the mnemonic "wood generates fire," and arrange them in five positions in the southern direction. Then take the counting rods for the southern direction, with the mnemonic "fire generates earth," placing one rod in the center, one rod in the northwest as戊, and one rod in the southwest as己. Next, take the counting rods for the center, with the mnemonic "earth generates metal," and arrange them in five positions in the western direction. Then take the counting rods for the western direction, with the mnemonic "metal generates water," and arrange them in five positions in the northern direction. After completing the ten heavenly stems and twelve earthly branches in the five directions, add one rod to each yin stem, with the mnemonic stating this is "yin numbers are even"; and add one rod to each yang branch, with the mnemonic stating this is "the essence of the earthly branches." Combine the remaining counting rods from the beginning, which exactly matches the number of twelve months. Then place one rod in the northwest, stating this is the beginning of the Qian Trigram; place two rods in the southwest, stating this is the beginning of the Kun Trigram. The remaining nine counting rods are placed in the center, representing the image of the Book of Changes.

命曰干主甲壬，卽取甲壬上算，以成乾卦。又命曰坤主乙癸，次取乙癸上算，以成坤卦。父母之卦，爻象既定，次及六子。先起長男，命曰震主庚子午，卽取庚及子午上算，以成震卦。又次長女，命曰巽主辛丑未，次取辛及丑未上算，以成巽卦。又次中男，命曰坎主戊寅申，次取戊及寅申上算，以成坎卦。又次中女，命曰離主己卯酉，次取己及卯酉上算，以成離卦。又次少男，命曰艮主丙辰戌，次取丙及辰戌上算，以成艮卦。又次少女，命曰兌主丁巳亥，次取丁及巳亥上算，以成兌卦。

The mnemonic says "Qian governs Jia and Ren," so take the counting sticks from the Jia and Ren positions to form the Qian trigram. It also says "Kun governs Yi and Gui," so take the counting sticks from the Yi and Gui positions to form the Kun trigram. Having determined the yao images of the parents trigrams, the next step is to form the six child trigrams. First comes the Elder Son, and the mnemonic says "Zhen governs Geng and Zi, Wu," so take the counting sticks from the Geng position and the Zi and Wu positions to form the Zhen trigram. Next comes the Elder Daughter, and the mnemonic says "Xun governs Xin and Chou, Wei," so take the counting sticks from the Xin position and the Chou and Wei positions to form the Xun trigram. Then comes the Middle Son, and the mnemonic says "Kan governs Wu and Yin, Shen," so take the counting sticks from the Wu position and the Yin and Shen positions to form the Kan trigram. Next comes the Middle Daughter, and the mnemonic says "Li governs Ji and Mao, You," so take the counting sticks from the Ji position and the Mao and You positions to form the Li trigram. Then comes the Younger Son, and the mnemonic says "Gen governs Bing and Chen, Xu," so take the counting sticks from the Bing position and the Chen and Xu positions to form the Gen trigram. Lastly comes the Younger Daughter, and the mnemonic says "Dui governs Ding and Si, Hai," so take the counting sticks from the Ding position and the Si and Hai positions to form the Dui trigram. This method of pairing corresponds exactly with the earlier method of assigning trigrams to the heavenly stems and earthly branches used in the Nayin sound element system.

八卦既成，問曰：八卦從何而始？曰：因五行生。又問：五行因何生？曰：因天地生。天地因何生？曰：因太一生。太一因何生？曰：因易生。故云：易有太極，是生兩儀。故變易字為太一，變太一字為天，天一生，地二生也；變天字為水，天生水也；變水字為木，水生木也；變木字成火，木生火也；變火字成土，火生土也；變土字成金，土生金也；變金字成八卦字，八卦因五行生也；變八卦字為十二月字，八卦所主，月也；變十二月字，成地出萬物，以終歸乎地也。此九宮八卦創制之法備矣。

After the eight trigrams have been formed, someone asked: From where do the trigrams begin? The answer was: From the Five Phases. Another question: From what do the Five Phases arise? The answer was: From heaven and earth. Another question: From what do heaven and earth arise? The answer was: From the Taiyi. Another question: From what does the Taiyi arise? The answer was: From the Book of Changes. Therefore it is said: The Book of Changes contains the Taiyi, and the Taiyi gives rise to the two principles. Thus, in the process of arranging the counting rods, the character "Yi" is transformed into "Taiyi," and "Taiyi" into "Heaven"—Heaven produces one, Earth produces two; "Heaven" is transformed into "Water," because Heaven produces Water; "Water" is transformed into "Wood," because Water produces Wood; "Wood" becomes "Fire," because Wood produces Fire; "Fire" becomes "Earth," because Fire produces Earth; "Earth" becomes "Metal," because Earth produces Metal; "Metal" becomes the eight trigrams, because the trigrams arise from the Five Phases; "Eight Trigrams" becomes the twelve months, because the trigrams govern the months; finally, the twelve months become "the earth produces all things," indicating that all things ultimately return to the earth. The method of creating the nine palaces and eight trigrams is thus complete. This continuous process of changing characters is not a mere word game, but a mnemonic used by diviners to sequentially change the labels on the counting rods: each time a new name is introduced, the generative relationship from the previous level is implemented on the counting rod positions, proceeding from "Yi" all the way to "the earth produces all things," corresponding in order to the opening statement "The Book of Changes contains the Taiyi, which gives rise to the two principles."

九宮數一起，自北方始者，坎一正北，應天之始，始無二，故一。北方五行之始，所以五行在北方，故云陽氣之始，萬物將萌。五事數二在西南者，五事，貌言視聽思也，別在後篇解。因五行而有五事次之，故二。又云：坤二在西南，應地之數。西南，林鐘之管，氣之次，二也。五事，人事之先也，故曰謙虛就德、朝謁嘉慶，並五事所主也。

The numbers of the Nine Palaces start from one and begin in the north because the trigram Kan (Water) is located in the north, corresponding to the beginning of heaven. The beginning can only be one, not two, so they take one. The north is also the starting point of the Five Phases, so the Classic of Documents places the category of the Five Phases in the north, saying it is the beginning of yang energy and the time when all things begin to sprout. The number of the Five Elements (Wu Shi) is two and its position is in the southwest. The Five Elements refer to appearance, speech, sight, hearing, and thought (details will be explained in later chapters). Since there are first the Five Phases, the Five Elements follow after, so it is two. Another explanation is that the trigram Kun (Earth) is located in the southwest, corresponding to the number of the earth; the southwest is where the Lingzhong pitch pipe is located, which is the second in the sequence of musical tones, so it is two. The Five Elements are the most important among human affairs, so it says 'humility and virtue bring auspiciousness and joy in court,' which refers to the content governed by the Five Elements.

八政之數三在東方者，八政，食、貨、祀、司空、司徒、司寇、賓、師也。既有五事，次修八政，故三。又云：震三正東，應人之數，三才義畢。東方春，農之始也。食者，耕種炊烹也；貨者，畜積儲博，錢布金兵也；祀者，祭祀供神也；司空者，土地畝也；司徒者，民戶口大小數也；司寇者，禁備盜賊，糾察非常也；賓者，注籍往來，受容嘉慶也；師者，教訓農夫，耒耜設法也。故云耕種百穀，麻枲蠶桑也。

The number of the Eight Administrations is three, and their position is in the East. The Eight Administrations refer to food, goods, worship, the Minister of Works, the Minister of People, the Minister of Justice, guests, and military affairs. Since there are already the Five Matters, the next step is to govern the Eight Administrations, hence the number three. Another interpretation says that the trigram Zhen (Thunder) is in the third position and is located in the East, corresponding to human numbers. The meaning of Heaven, Earth, and Humanity, the three elements, is thus complete. The East belongs to spring, which is the beginning of agricultural activities. "Food" refers to farming and cooking; "goods" refers to storing, money, silk, and weapons; "worship" refers to worshipping and offering to deities; the Minister of Works manages land and fields; the Minister of People manages the population; the Minister of Justice is responsible for preventing theft and investigating anomalies; "guests" refers to recording and receiving guests and handling festive ceremonies; "military" refers to teaching farmers and establishing the methods for making farming tools. Therefore, this palace governs "planting all grains, hemp, flax, silk, and sericulture."

五紀數四在東南者，五紀，歲、日月、奉化、日辰、曆數也。八政既修，非歲時日月，無以敷播植，次之故四。又云：巽四，東南，風行四時，以應四時之數。東南巳，純干用事，干主天，巽主號令，故居東南。歲者，以四時有序，盛衰始終也；日月者，照明萬物，氣候遠近也；奉化者，卽仰王化，須建功貢寶也；日辰者，次序陰陽，斷制產物也；曆數者，記綴度數，農夫候望，賦斂隨時也。故曰：王者惟歲，稅數握成，以化下也；卿士惟月，奉化行道，立寶；師允惟日，陳列眾職，制作於萬品。歲月日時，無易修務，敬時以順紀也。故云日月星辰，雲雨並興也。

The number of the Five Constants is four, and their position is in the southeast. The Five Constants refer to years, days and months, the implementation of virtue, the day branch, and the calendar system. After the eight administrative affairs have been properly managed, without the standard of years, days, and months, there would be no way to arrange sowing and farming, so they come after the eight administrative affairs and are the fourth. Another explanation says that the trigram Xun (Wind) is located in the southeast, as wind moves through the four seasons, corresponding to the number of the four seasons. The southeast is the position of Si (Snake), where the pure energy of Qian (Heaven) prevails. Qian represents Heaven, and Xun represents the issuance of commands, so it is located in the southeast. "Years" refers to the orderly succession of the four seasons, with their prosperity and decline, and their beginning and end. "Days and months" refer to the illumination of all things and the variation in climatic distance. "Implementation of virtue" refers to the reverence for the king's teachings, requiring the establishment of achievements and the offering of precious treasures. "Day branch" refers to the arrangement of the order of yin and yang and the determination of the suitability of resources. "Calendar system" refers to the recording of the measurements of celestial bodies, allowing farmers to observe the heavenly signs and collect taxes in accordance with the seasons. Therefore, the ruler governs the affairs of a year, determines the tax data, and uses this to educate the people. The officials govern the affairs of a month, implementing the teachings, promoting righteousness, and setting examples. The ministers govern the affairs of a day, arranging various duties and making various tools. Years, months, days, and hours must not be altered; each should carry out their respective duties, respecting the seasons to follow the principles. Therefore, this section is associated with "the sun, moon, stars, clouds, and rain all arise together."

皇極數五在中央者，皇王建萬國，處中，分別四方，百官以治，萬事畢理，歲時成就，職貢均等，租稅五穀，以供王事，故在其中央。中央之數本五也。又云：土居中央，應五行之數。若王者動不得中，則不能建萬事，故曰皇之不極，是謂不建也。故曰百官立表，政化公卿也。

The number of "Huangji" is five and its position is in the center: the sovereign establishes myriad states, resides in the center, and governs the four directions, with officials each performing their duties, all affairs properly managed, harvests successful each year, and contributions from all regions balanced, taxes and grain used to supply the royal household. Therefore, it is placed in the center. The number of the center is originally five. Another explanation is that earth is located in the center, corresponding to the five, the generating number of the Five Phases. If the sovereign's actions do not maintain the center, he cannot establish all things. Therefore, the "Hongfan" says: if the sovereign fails to attain "Huangji," this is called "Bu Jian." Thus, this palace governs "the establishment of officials' standards and the public education of ministers."

三德數六在西北者，三德，正直、剛克、柔克。乾為天位，人君之象，過五故數六。又云：干在西北，陰陽氣分於西北，故應六律之數也。西北，干之所處，故人君居之。正直者，人德也，君子方正以義，無所曲私，故云平康正直，不疑其德。剛克者，天德也，法度不失，輕重罪服，故曰沈潛剛克。柔克者，地德也，有德秩祿，安定眾職，賞賜萬國，故曰高明柔克。故云抑服強暴，斷制獄訟也。

The number of the Three Virtues is six, and their position is in the Northwest. The Three Virtues refer to uprightness, strong overcoming, and gentle overcoming. Qian is the position of Heaven, symbolizing the sovereign; it surpasses the five of the center, hence its number is six. Another explanation says that Qian is located in the Northwest, where the yin and yang energies divide, hence corresponding to the number of the six laws. The Northwest is the place where Qian resides, thus the sovereign resides there. "Uprightness" is the virtue of humans: the gentleman is upright and conforms to righteousness, without partiality or favoritism, so the "Hóng Fàn" says, "When the world is peaceful, the path of uprightness is used,"—there is no need to doubt this virtue. "Strong overcoming" is the virtue of Heaven: the law is not violated, and punishment is appropriate, so it is said, "Submerging and overcoming with strength"—using strength to correct those who are immersed in weakness. "Gentle overcoming" is the virtue of Earth: giving officials rank and salary, stabilizing various duties, and bestowing rewards upon all states, so it is said, "High and bright, overcoming with gentleness"—using gentleness to regulate those who are lofty and discerning. Therefore, this palace governs "restraining violence and resolving disputes."

稽疑數七在西方者，稽疑者，建立卜筮，問疑擇善，占天地之象，以定吉凶。蓍圓卦方，龜筮共知可否。三人占，從二人之言。昔者聖人慎謀重始，動事作業，樹本開基，決嫌定疑，必謀以賢知，諮以耆艾，參以蓍龜，故舉無過事，慮無失計。蠻夷雖無君臣之序，亦有決疑之卜，或以金石，或以木草。故知稽疑之事，聖人所尚。以其次干之後，故數七也。又云：兌正西，卯酉為天地之門，卯主始，酉主終，故斗指卯則萬物皆出，指酉則萬物皆入。兌應七星之數，兌為金，主悅言，故在西方。故云決定吉凶，分別所疑也。

The number of "Kji Yi" is seven and its position is in the west: "Kji Yi" refers to establishing the method of divination, asking questions when encountering doubts, choosing the better course, and determining fortune and misfortune by observing the signs of heaven and earth. The yarrow stalks are taken in a circular form to symbolize heaven, and the hexagram structure is taken in a square form to symbolize earth. Divination by tortoise shells and yarrow stalks together determine whether something is feasible. When three people perform divination, they follow the opinion of the two who agree. In ancient times, sages were cautious in their planning and valued the beginning. Whenever there was an action, the founding of a cause, the establishment of a foundation, or the initiation of an enterprise, and when deciding on doubtful matters, they first consulted wise and knowledgeable people, then sought the advice of elders, and finally verified with yarrow stalks and tortoise shells. Therefore, their actions had no mistakes, and their plans had no miscalculations. Although the four barbarian tribes may not have the rituals of lord and subject, they also have divination to resolve doubts, some using metal and stone, others using plants and trees. This shows that the practice of "Kji Yi" is highly valued by sages. It is placed after Qian (the trigram of Heaven), so its number is seven. Another explanation: Dui is located in the west. The moment of卯 (Mao) and酉 (You) are the gates of heaven and earth. Mao signifies the beginning, while You signifies the end. When the handle of the Big Dipper points to Mao, all things are born; when it points to You, all things are stored away. Dui corresponds to the number of the seven stars of the Big Dipper. Dui belongs to metal, which governs joy and speech, so it is assigned to the west. Therefore, this trigram is responsible for "deciding fortune and misfortune, distinguishing doubts."

庶徵數八在東北者，庶徵者，眾征也。王者以及眾庶，莫不內省咎過，外察徵祥，順征知機，則無禍患。不審其過，不念庶徵，則禍至不悟，敗亡無日矣。有機徵見者，必恭事上帝，用不為過，則降以福應。《詩》云：昭事上帝，聿懷多福。如不共御善，不畏上帝，群神乃怒，必有譴罰。數八者，次七後也。又云：艮八在東北，艮是止義，艮為徑路。萬物大出於震，小出於艮。震為眾男之長，艮為眾男之少，故應八卦之數。艮既為止，令止惡就善也，故在東北。故云肅敬德方，狂僭亂行。

The number of "Shu Zheng" is eight and its position is in the Northeast:the so-called "Shu Zheng" refers to various omens. From the sovereign down to the common people, everyone should examine their own faults internally and observe signs and portents externally. By following the signs and understanding the omens in advance, calamities can be avoided. If one does not examine their faults or pay attention to the signs, when calamity comes, they will not realize it, and ruin will come swiftly. Once an omen appears, one must respectfully serve the Supreme Deity and act without error, and the Deity will bestow blessings. The "Book of Poetry" says: "Clearly serving the Supreme Deity brings many blessings." If people do not jointly practice goodness and do not revere the Deity, the gods will be angry and surely bring punishment. The number is eight because it comes after seven. Another explanation says: "Gen" (the eighth trigram) is located in the Northeast, and "Gen" means "to stop." "Gen" also symbolizes a narrow path. All things are born in great numbers through "Zhen" (Thunder) and in small numbers through "Gen" (Mountain). "Zhen" is the eldest son among the sons, while "Gen" is the youngest son, so it corresponds to the number of the Eight Trigrams. Since "Gen" represents stillness, it means to stop evil deeds and return to goodness, hence it is placed in the Northeast. Therefore, this trigram governs "reverence for virtue, disorder and lawlessness."

五福六極，數九在南方。五福，壽、富、康寧、攸好德、考終命。壽者，孝悌道德備，然後修神丹，延壽命；富者，德化所及，豐穰無闕；康寜者，國化安寜，長樂無事；攸好德者，論理比類，進善抑惡；考終命者，順時成務，可以壽命，統著善德。六極者，凶短折、疾、憂、惡、貧、弱。凶短折者，斬梟誅裂，大罪也；疾者，榜笞毆擊，疾臥養視也；憂，論作望，兢朝日也；惡，髡赭剝，戮辱錮棄也；貧，償贓賦，沒財產也；弱，離邑里，徙邊地，以戒後也。此罪罰之理居後，故數九。又云：離既在午，以為子沖，極則還反，故離最其末，以為九宮之數。離為明，人君南面以聽政，象離之明，刑罰須明，故在南方。故云萬物率盈實也。

The numbers of "Five Blessings" and "Six Curses" total nine and are positioned in the south. The Five Blessings are longevity, wealth, health and peace, preference for virtue, and a peaceful death. "Longevity" refers to after practicing filial piety and moral virtue, further cultivating elixirs to prolong life; "wealth" refers to where virtue spreads, the harvest is abundant without deficiency; "health and peace" refers to the state's education and governance being tranquil, enjoying long-lasting happiness without troubles; "preference for virtue" refers to discussing principles and understanding by analogy, employing virtuous people and restraining evil deeds; "a peaceful death" refers to following the seasons to achieve success, thus enjoying a full life span, summarizing to demonstrate goodness. The Six Curses are sudden death, illness, worry, evil, poverty, and weakness. "Sudden death" refers to beheading and public display, execution and division, which are major crimes; "illness" refers to being whipped and beaten, lying ill needing care; "worry" refers to being charged with a crime and awaiting judgment, living in constant fear; "evil" refers to shaving the head and painting the face with red clay, losing one's status, suffering disgrace and being exiled; "poverty" refers to paying off stolen goods and taxes, having property confiscated; "weakness" refers to leaving one's hometown and migrating to remote areas, used to warn future generations. These are the principles of punishment and crime, positioned at the end, hence the number nine. Another explanation: since the trigram Li is located at the position of Wu and opposes Zi, when things reach their extreme, they return, so Li is placed at the end, as the final point of the nine palaces. Li represents brightness, the ruler faces south to govern, symbolizing the clarity of Li; punishment must also be clear, hence it is paired with the south. Therefore, this palace governs "all things are full and real."

宮唯有九，不十者，八方與中央，數終於九。上配九天、九星、二十八宿，下配五嶽、四瀆、九州島也。九宮經言：一主恆山，二主三江，三主太山，四主淮，五主嵩高，六主河，七主華山，八主濟，九主霍山。又，一為冀州，二為荊州，三為青州，四為徐州，五為豫州，六為雍州，七為梁州，八為兗州，九為揚州。九州島之名，互有改變。禹貢九州島，卽此配唐時名同者，以堯命禹治洪水，分九州島，因而不易。故周虞有十二州，加幽並營。舜以青州越海，分齊為營州；冀州南北太遠，分衛為幷州；燕以北分置幽州。殷時九州島，有幽營，無青梁；周官九州島，有幽並，無徐梁；漢立十二州，增交益焉。

The nine palaces are only nine rather than ten, because eight directions plus the center total nine and then stop. Upward, they correspond to the nine heavens, nine stars, and the twenty-eight constellations. Downward, they correspond to the five mountains, four rivers, and the nine states. The "Classic of the Nine Palaces" says: one corresponds to Mount Heng, two to the three rivers, three to Mount Tai, four to the Huai River, five to Mount Song, six to the Yellow River, seven to Mount Hua, eight to the Ji River, and nine to Mount Huo. It also says: one is Jiuzhou, two is Jingzhou, three is Qingzhou, four is Xuzhou, five is Yuzhou, six is Yongzhou, seven is Liangzhou, eight is Yanzhou, and nine is Yangzhou. The names of the nine states have changed through different dynasties. The nine states in the "Book of Yu's Tribute" are arranged in this way, and their names are the same as those in the time of Emperor Yao, because Yao ordered Yu to control the floods and divide the nine states. After that, the system remained unchanged. During the time of the Shang Dynasty, the nine states included Youzhou and Yingzhou but not Qingzhou or Liangzhou. The nine states in the "Rites of Zhou: The Regional Offices" included Youzhou and Bingzhou but not Xuzhou or Liangzhou. The Han Dynasty established twelve states, adding Jiaozhou and Yizhou. The reason for associating the palace numbers with famous mountains, great rivers, and the nine states is to enable diviners, upon seeing a palace number, to know which celestial region it corresponds to in the sky and which land area it corresponds to on earth. However, the names of the states have changed over time, so when using them, one must first determine which dynasty's system is being referred to.

冀州者，《釋名》云：冀州取地為名，有險易，帝王所都。《太康地記》曰：冀，近，其氣相近也。其地自太行東至碣石、王屋、底柱。《禹貢》云：冀州既載。《呂氏春秋》云：兩河之間為冀州，正北方。荊州者，《釋名》云：荊，警也，南蠻數為寇逆，州道先強，當警備之也。其地北據荊山，南及衡山之陽。《禹貢》云：荊及衡陽惟荊州。《爾雅》云：漢南曰荊州。《呂氏》曰：荊，楚也。青州者，《釋名》云：青，在東生也。《太康地記》曰：少陽色青，歲始事首，卽以為名。其地東北據海，西距岱。《禹貢》云：海岱惟青州。《呂氏》云：東方海隅青州，齊也。

First, we discuss Ji Zhou. The "Shi Ming" says: Ji Zhou is named according to its land. It has both dangerous and level areas, and it is the place where emperors established their capitals. The "Tai Kang Di Ji" says: Ji means "near," indicating that the energies of the four directions are close to each other here. Its territory extends from the Taihang Mountains to the east, until Jieshi Mountain, Wangwu Mountain, and Dizhu Mountain. The "Yu Gong" says: "Ji Zhou has already been managed," meaning that Ji Zhou's water control achievements were first recorded. The "Lüshi Chunqiu" says: Between two rivers is Ji Zhou, located in the north. Now, let's talk about Jingzhou. The "Shi Ming" says: Jing means "alert," as the southern barbarians often invaded and caused disturbances, and this state is in a strategic position with strong terrain, so it should be on alert. Its territory is to the north of Jing Mountain and reaches to the south of Heng Mountain. The "Yu Gong" says: "Jing and the southern part of Heng Mountain is Jingzhou." The "Eya" says: The area south of the Han River is called Jingzhou. The "Lüshi Chunqiu" says: Jing is the land of Chu. Now, let's talk about Qingzhou. The "Shi Ming" says: Qing refers to the meaning of growth in the east. The "Tai Kang Di Ji" says: The color of the young yang is green, and the year begins here, with all things starting from here, so it is named Qing. Its territory is to the northeast by the sea and to the west by Dai Mountain (Taishan). The "Yu Gong" says: "The sea and Dai Mountain is Qingzhou." The "Lüshi Chunqiu" says: Qingzhou, the eastern coastal area, is the land of Qi.

徐州者，《釋名》曰：徐，舒也，土氣舒緩也。其地東至海，北至岱，南及淮。《禹貢》云：海岱及淮惟徐州。《呂氏》云：泗上為徐州，魯也。《爾雅》云：濟東曰徐州。豫州者，《釋名》曰：豫，在九州島之中安豫也。《太康地記》云：稟中和之氣，性理安舒。其地南據荊，北距河。《禹貢》云：荊河惟豫州。《呂氏》云：河漢之間為豫州。《爾雅》云：河南曰豫州。雍州者，《太康地記》云：雍居西北之位，陽所不至，陰氣壅閼，取以為名。其地西據黑水，東距西河。《禹貢》云：黑水西河惟雍州。《呂氏》云：雍州，秦也。《爾雅》云：河西曰雍州。

Now let us talk about Xu Prefecture. The book Shiming says that Xu means "shu," meaning that the soil there is gentle and easygoing. Its territory extends east to the sea, north to Da Mountain, and south to the Huai River. The Yuguang says, "The sea, Da Mountain, and Huai River are the territory of Xu Prefecture." The Lüshi Chunqiu says that the area along the Si River is Xu Prefecture, which is the land of Lu. The Erya says that the area east of the Ji River is called Xu Prefecture. Now let us talk about Yu Prefecture. The Shiming says that Yu is because it is in the central position of the nine provinces and is peaceful and pleasant. The Taikang Diji says that Yu Prefecture receives the harmonious qi of the center, and its nature and affairs are calm and gentle. Its territory is to the south of Jing Mountain and to the north of the Yellow River. The Yuguang says, "Jing Mountain and the Yellow River are the territory of Yu Prefecture." The Lüshi Chunqiu says that the area between the Yellow River and the Han River is Yu Prefecture. The Erya says that the area south of the Yellow River is called Yu Prefecture. Now let us talk about Yong Prefecture. The Taikang Diji says that Yong is located in the northwest position, where yang qi does not reach, and yin qi is blocked and accumulated, so it is named after "yong." Its territory is to the west of Hei Water and to the east of Xi He. The Yuguang says, "Hei Water and Xi He are the territory of Yong Prefecture." The Lüshi Chunqiu says that Yong Prefecture is the land of Qin. The Erya says that the area west of the Yellow River is called Yong Prefecture.

梁州者，《太康地記》云：梁者，剛也，取西方金剛之氣，剛強以為名也。其地東據華山，西距黑水。《禹貢》曰：華陽黑水惟梁州。兗州者，《釋名》云：取兗水為名。《太康地記》曰：辨其履信稟貞正之意也。其地東南據濟，西北距河。《禹貢》曰：濟河惟兗州。揚州者，《釋名》云：揚州多水，水波揚也。其地北據淮，東距海。《禹貢》云：淮海惟揚州。《呂氏》曰：揚州，越也。《爾雅》曰：江南曰揚州。

Now let us speak of Liangzhou. The "Tai Kang Di Ji" says: Liang is "Gang," taking the meaning of the western metal element's firmness and hardness, and naming it with the idea of strength. Its territory extends east to Huashan Mountain and west to Hei Water. The "Yu Gong" says: "Huayang Hei Water is Liangzhou." Now let us speak of Yanzhou. The "Shi Ming" says: Yanzhou is named after Yanshui (a tributary of Jishui). The "Tai Kang Di Ji" says: the name contains the meaning of distinguishing sincerity and receiving uprightness. Its territory extends southeast to Jishui and northwest to the Yellow River. The "Yu Gong" says: "Jishui He is Yanzhou." Now let us speak of Yangzhou. The "Shi Ming" says: Yangzhou is named because there is much water, and the waves rise and spread, hence called Yang. Its territory extends north to Huai Water and east to the sea. The "Yu Gong" says: "Huaihai is Yangzhou." The "Lüshi Chunqiu" says: Yangzhou is the land of Yue. The "Eya" says: the area south of the Yangtze River is called Yangzhou.

今依九宮之位，冀州正北，在坎宮；荊州西南，在坤宮；青州正東，在震宮；徐州東南，在巽宮；豫州中央，在中宮；雍州西北，在干宮；梁州正西，在兌宮；兗州東北，在艮宮；揚州正南，在離宮。其位與此解相似。太一以兗州在正北坎位，青州在東北艮位，徐州在正東震位，揚州在東南巽位，荊州在正南離位，梁州在西南坤位，雍州在正西兌位，冀州在西北干位。此並從五行本始之氣，西北亥地，故坎水居之；東北寅地，故震木居之；西南巳地，故離火居之；西南申地，故兌金居之；乾為金，故從本金位；巽為木，故從本木位；坤艮俱土，故取地之經，居正南正北。此並依《周禮·職方》之始位，雖宮位微移，五行氣一。

Now, according to the nine palace directions, the regions are assigned as follows: Jiuzhou is in the due north, belonging to the Kan palace; Jingzhou is in the southwest, belonging to the Kun palace; Qingzhou is in the due east, belonging to the Zhen palace; Xuzhou is in the southeast, belonging to the Xun palace; Yuzhou is in the center, belonging to the Central Palace; Yongzhou is in the northwest, belonging to the Qian palace; Liangzhou is in the due west, belonging to the Dui palace; Yanzhou is in the northeast, belonging to the Gen palace; Yangzhou is in the due south, belonging to the Li palace. This arrangement is largely consistent with the previous order. There is another arrangement according to the Taiyi school: Yanzhou is in the due north Kan position, Qingzhou is in the northeast Gen position, Xuzhou is in the due east Zhen position, Yangzhou is in the southeast Xun position, Jingzhou is in the due south Li position, Liangzhou is in the southwest Kun position, Yongzhou is in the due west Dui position, Jiuzhou is in the northwest Qian position. This system is arranged according to the original energies of the Five Phases: the northwest is the亥 position (the birthplace of water), so the water phase Kan resides there; the northeast is the寅 position (the birthplace of wood), so the wood phase Zhen resides there; the southwest is the巳 position (the birthplace of fire), so the fire phase Li resides there; the southwest is also the申 position (the birthplace of metal), so the metal phase Dui resides there; Qian belongs to metal, so it returns to the metal position; Xun belongs to wood, so it returns to the wood position; Kun and Gen both belong to earth, so the earth's meridian line is taken, placing them in the due south and due north. All of this is based on the original directions recorded in the "Zhou Li · Zifang," although the palace positions have slightly shifted, the Five Phase energies remain the same.

此九州島上對九天分，二十八宿屬焉。《淮南子》云：中央鈞天，數五，其星角亢氐，韓鄭分。鈞，極也，布極四方，亦曰極天，為四行主，對中宮豫州。東方蒼天，數三，其星房心尾，房心，宋分；尾，燕分。東方色青也，對震宮青州。東北變天，數八，其星箕斗牛，箕，燕分；斗，吳分；牛，岱分。水之季，陰氣盡，陽始作，萬物將變，對艮宮兗州。北方玄天，數一，其星女虛危室，女，越分；虛危，齊分；室，衛分。水色黑，故云玄天，對坎宮冀州。

The nine provinces correspond upward to the nine heavens, and the twenty-eight star mansions are also assigned to them. The "Astronomical Treatise" in the "Huainanzi" says: The central region is called "Juntian" (Heavenly Center), with the number five, and the star mansions associated with it are Jiao, Kang, and Di, which are the territories of the states of Han and Zheng. "Jun" means extreme, so "Juntian" refers to spreading the extreme point to all directions, also called "Jitian" (Heavenly Pole), which is the master of the other four elements, corresponding to the Central Palace and the state of Yu. The eastern region is called "Cangtian" (Blue Heaven), with the number three, and the star mansions associated with it are Fang, Xin, and Wei; Fang and Xin are the territories of the state of Song, and Wei is the territory of the state of Yan. The color of the east is blue, corresponding to the Zhen Palace and the state of Qing. The northeast region is called "Biattian" (Changing Heaven), with the number eight, and the star mansions associated with it are Ji, Dou, and Niu; Ji is the territory of the state of Yan, Dou is the territory of the state of Wu, and Niu is the territory of the Tai region. This is the end of the water season, when yin energy is about to end and yang energy begins to arise, and all things are about to change, corresponding to the Gen Palace and the state of Yuan. The northern region is called "Xuantian" (Black Heaven), with the number one, and the star mansions associated with it are Nu, Xu, Wei, and Shi; Nu is the territory of the state of Yue, Xu and Wei are the territories of the state of Qi, and Shi is the territory of the state of Wei. Water is black in color, so it is called Xuantian, corresponding to the Kan Palace and the state of Ji.

西北幽天，數六，其星壁奎婁，壁，衛分；奎婁，魯分。金之季，卽太陰幽闇也，對干宮雍州。西方昊天，數七，其星胃昴畢，胃，魯分；畢昴，趙分。金色白，故曰昊天，對兌宮梁州。西南朱天，數二，其星觜參井，觜參，晉分；井，秦分。居火之季，陽色朱也，對坤宮荊州。南方炎天，數九，其星鬼柳星，鬼，秦分也；柳星，周分也。火性炎上，故曰炎天也，對離宮揚州。東南陽天，數四，其星張翼軫，張，周分；翼軫，楚分。木之季，將卽太陽，故曰陽天也，對巽宮徐州。

The Northwest is called 「幽天」, with a number of six, and belongs to the star mansions of Wall, Wei, and Lou; Wall is the territory of the State of Wei, while Wei and Lou are the territories of the State of Lu. This is at the end of the metal season, which corresponds to the dark area of the Too Yin, and matches the Qian trigram and the Yongzhou region. The West is called 「昊天」, with a number of seven, and belongs to the star mansions of Wei, Mao, and Bi; Wei is the territory of the State of Lu, while Mao and Bi are the territories of the State of Zhao. Metal is white in color, so it is called 「昊天」, and corresponds to the Dui trigram and the Liangzhou region. The Southwest is called 「朱天」, with a number of two, and belongs to the star mansions of Zi, Shen, and Jing; Zi and Shen are the territories of the State of Jin, while Jing is the territory of the State of Qin. This is at the end of the fire season, and the color of yang energy is vermilion red, so it corresponds to the Kun trigram and the Jingzhou region. The South is called 「炎天」, with a number of nine, and belongs to the star mansions of Gui, Liu, and Xing; Gui is the territory of the State of Qin, while Liu and Xing are the territories of the Zhou dynasty. Fire is hot and rises, so it is called 「炎天」, and corresponds to the Li trigram and the Yangzhou region. The Southeast is called 「阳天」, with a number of four, and belongs to the star mansions of Zhang, Yi, and Zhen; Zhang is the territory of the Zhou dynasty, while Yi and Zhen are the territories of the State of Chu. This is at the end of the wood season, and it is about to enter the area of the Star of Brightness and Prestige, so it is called 「阳天」, and corresponds to the Xun trigram and the Xuzhou region.

此九天亦屬北斗九星之數，故下對九州島。炎天數九，屬斗第一樞星，應離宮，對揚州。變天數八，屬斗第二璇星，應艮宮，對兗州。昊天數七，屬斗第三璣星，應兌宮，對梁州。幽天數六，屬斗第四權星，應干宮，對雍州。鈞天數五，屬斗第五衡星，應中宮，對豫州。陽天數四，屬斗第六開陽星，應巽宮，對徐州。蒼天數三，屬斗第七瑤光星，應震宮，對青州。朱天數二，屬斗第八星，應坤宮，對荊州。玄天數一，屬斗第九星，應坎宮，對冀州。屬斗第八第九二星，陰而不見，以其對陰宮也。又郭璞《易占》云：干一，坤二，震三，巽四，坎五，離六，艮七，兌八。占人及物數皆準此，蓋以父母男女為次也。此九宮八卦之數，故以備釋。

The nine heavens also correspond to the number of the nine stars of the Big Dipper, so they can be matched downward with the nine states. The number nine of the fiery heaven corresponds to the first star of the Big Dipper, Tian Su, and is associated with the Li palace, corresponding to Yangzhou. The number eight of the changing heaven corresponds to the second star of the Big Dipper, Tian Xuan, and is associated with the Gen palace, corresponding to Yanzhou. The number seven of the bright heaven corresponds to the third star of the Big Dipper, Tian Ji, and is associated with the Dui palace, corresponding to Liangzhou. The number six of the dark heaven corresponds to the fourth star of the Big Dipper, Tian Quan, and is associated with the Qian palace, corresponding to Yongzhou. The number five of the balanced heaven corresponds to the fifth star of the Big Dipper, Yu Heng, and is associated with the Central Palace, corresponding to Yuzhou. The number four of the yang heaven corresponds to the sixth star of the Big Dipper, Kai Yang, and is associated with the Xun palace, corresponding to Xuzhou. The number three of the苍 heaven corresponds to the seventh star of the Big Dipper, Yao Guang, and is associated with the Zhen palace, corresponding to Qingzhou. The number two of the red heaven corresponds to the eighth star of the Big Dipper, associated with the Kun palace, corresponding to Jingzhou. The number one of the dark heaven corresponds to the ninth star of the Big Dipper, associated with the Kan palace, corresponding to Jizhou. The eighth and ninth stars of the Big Dipper belong to the yin and are invisible to the naked eye, precisely because they correspond to the yin palaces. Additionally, Guo Pu's "Yi Zhan" states: Qian one, Kun two, Zhen three, Xun four, Kan five, Li six, Gen seven, Dui eight. The numbers used for divination about people and things are based on this sequence, which is arranged according to the order of father, mother, son, and daughter. The eighth and ninth stars of the Big Dipper are the two hidden stars, Fu and Bi, mentioned in later times, which are invisible to the naked eye, so they are appropriately assigned to the yin palaces of Kun and Kan. Guo Pu's system of trigram numbers differs from the system used in the nine palaces, which uses Kan one and Kun two. This is a separate system, and when making divinations, one must first clarify which system is being used. This is the system of numbers for the nine palaces and the eight trigrams, so it is explained in detail here.

經云：天生一，始於北方水；地生二，始於南方火；人生三，始於東方木；時生四，始於西方金；五行生五，始於中央土。又曰：天始生一者，因一而生天，非天生一也。故云：一生二，二生三，三生萬物。地生二者，亦因二而生地；因三生人，因四生時。五行皆由一而生，數至於五，土最在後，得五而生五行也。

The classic texts say: Heaven begins with the number one, starting from the water of the north; Earth begins with the number two, starting from the fire of the south; Humanity begins with the number three, starting from the wood of the east; Time begins with the number four, starting from the metal of the west; the Five Phases begin with the number five, starting from the soil of the center. It is further explained that the phrase "Heaven begins with one" actually means that Heaven came into being after the number one was formed, not that Heaven produced the number one. Therefore, the Tao Te Ching says: One gives rise to two, two gives rise to three, and three gives rise to all things. The phrase "Earth begins with two" means that Earth came into being after the number two was formed; Humanity came into being after the number three was formed; the four seasons came into being after the number four was formed. All five phases originate from "one," and the numbers progress to five. The element of soil is last and receives the number five, thus completing the entire system of the Five Phases.

五行同出而異時者，出離其親，有所配偶。譬如人生，亦同元氣而生，各出一家，配為夫妻，化生子息。故五行皆相須而成也。五行同胎而異居，有先後耳。夫五行皆資陰陽氣而生，故云：濡氣生水，溫氣生火，強氣生木，剛氣生金，和氣生土。故知五行同時而起，托義相生。傳曰：五行並起，各以名別。然五行既以名別，而更互用事，輪轉休王，故相生也。

The Five Phases all originate from the same source but appear at different times, much like children leaving their parents to have their own spouses. For example, when a person is born, they also receive the original qi, and after growing up, they leave their family to form a marriage and then have their own children. Therefore, the Five Phases must rely on each other to achieve their forms. The Five Phases are born from the same womb but live apart in different places, differing only in the order of their emergence. The Five Phases are generated by the qi of yin and yang, so it is said: moist qi produces water, warm and hot qi produces fire, strong and resilient qi produces wood, hard and rigid qi produces metal, and harmonious qi produces earth. From this we can understand that the Five Phases originally arise simultaneously, but the order is arranged through the principle of mutual generation. The transmitted text says: the Five Phases arise together, differing only by their names. Since the Five Phases are distinguished by their names and take turns to be dominant, experiencing periods of decline and prosperity in succession, there arises the relationship of mutual generation.

穎容云：凡五行相生，謂異類相化，如男女異姓，能至繁殖；若以水濟水，不生嘉味。河閒獻王問溫城董君曰：孝者，天之經，地之義也，何謂也？對曰：天有五行，木火土金水是也。木生火，火生土，土生金，金生水，水生木。木為春，春主生，夏主長養，秋主收，冬主藏，藏者，冬之所成也。是故父之所生，其子長之；父之所長，其子養之；父之所養，其子成之。不敢不致如父之意，盡為人之道也。故五行者，五常也。

Ying Rong said: Whenever the Five Phases mutually generate, it refers to different things nurturing each other, just like how men and women of different surnames can produce offspring; if water is added to water, it cannot produce a good taste. He Ji Xian Wang Liu De asked Wen Cheng person Dong Zhongshu: The "Xiao Jing" says that filial piety is the constant way of heaven and the great principle of earth, what does this mean? Dong Zhongshu answered: Heaven has the Five Phases, which are wood, fire, earth, metal, and water. Wood generates fire, fire generates earth, earth generates metal, metal generates water, and water generates wood. Wood corresponds to spring, which governs growth, summer governs flourishing, autumn governs gathering, and winter governs storage, which is exactly what winter accomplishes. Therefore, what the father produces, the son continues to develop; what the father develops, the son continues to nurture; what the father nurtures, the son continues to complete. The son dares not fail to fully express the father's intention, thus fulfilling the way of being a person. Therefore, the Five Phases are also the way of the Five Constants.

《白虎通》云：木生火者，木性溫暖，火伏其中，鑽灼而出，故木生火。火生土者，火熱，故能焚木，木焚而成灰，灰卽土也，故火生土。土生金者，金居石，依山津潤而生，聚土成山，山必生石，故土生金。金生水者，少陰之氣潤澤，流津銷金亦為水，所以山雲而從潤，故金生水。水生木者，因水潤而能生，故水生木也。《元命苞》云：陽吐陰化，故水生木也。

The White Tiger Classic says: Wood produces fire because wood is warm in nature, and fire is hidden within the wood. When you rub wood and create heat, fire emerges, so wood generates fire. Fire produces earth because fire has heat, which can burn wood. When wood is burned, it turns into ash, and ash is earth, so fire generates earth. Earth produces metal because metal is hidden in stone, and it is formed by the moist vapor in mountains. Accumulated earth forms mountains, and mountains necessarily contain stone, so earth generates metal. Metal produces water because the slight yin energy brings moisture, and the liquid from this moisture can melt metal into water. Therefore, clouds rise in mountains along with the moist vapor, so metal generates water. Water produces wood because grass and trees grow only when they receive the nourishment of water, so water generates wood. The Spring and Autumn Original Mandate says: Yang energy gives birth, and yin energy nurtures, so water can generate wood.

《春秋繁露》云：東方木，木，農之本，司農尚仁，五穀畜積，司馬食之，故木生火。火，本朝司馬，尚知，天時形兆未萌，昭然獨見，天下既寧，以安君臣，故火生土也。土，君，尚信，因時之威武強御，以成大理司徒，故土生金。金，大理司徒，尚義，邊境安寧，寇賊不發，邑無獄訟，則安執法司寇，故金生水。水，執法司寇，尚禮，君臣有位，長幼有序，百工維時，以成歲用，器械既成，以給司農田官，故水生木。兩說事義雖別，而相生是同。五行各定形，唯火鑽灼方出者，火是大陽之氣，溫故乃生。鑽木出者，還寄託萬物耳，如聖人無名，能理萬物，還以萬物為名。陽氣至神，故有隱顯。

The "Chunqiu Fanlu" explains mutual generation through official positions: the East belongs to wood, which is the foundation of agriculture. Officials in charge of farming value "benevolence." Stored grain is provided for the military commander, so wood generates fire. Fire corresponds to the military commander, who values "wisdom." Before signs of the heavens are evident, he can perceive them alone, and after the world is at peace, he uses fire to establish order between the ruler and ministers, so fire generates earth. Earth corresponds to the ruler, who values "trustworthiness." By relying on his strength, he achieves the roles of the Grand Judge and the Minister of Works, so earth generates metal. Metal corresponds to the Grand Judge and the Minister of Works, who value "righteousness." With the borders at peace and no bandits, there are no lawsuits in the cities, allowing the judicial officials to be secure, so metal generates water. Water corresponds to the judicial officials, who value "ritual." The ruler and ministers have their proper positions, the young and old their proper order, and all craftsmen work on time, completing the year's provisions. After tools are made, they are handed over to the agricultural officials, so water generates wood. Both the "Baihu Tong" and the "Chunqiu Fanlu" explain mutual generation based on different phenomena, but they agree on the principle of mutual generation. The Five Phases each have a fixed form, but fire appears only when wood is struck and burned, because fire is the essence of the Sun's energy, which emerges with warmth. Striking wood to produce fire is merely a temporary manifestation on the surface of all things. This is similar to the sage, who has no name, but is called by the names of all things because he governs them. Yang energy is extremely subtle, so it appears and disappears intermittently.