The two discuss the matters of life and death.

五行體別，生死之處不同，遍有十二月、十二辰而出沒。木，受氣於申，胎於酉，養於戌，生於亥，沐浴於子，冠帶於丑，臨官於寅，王於卯，衰於辰，病於巳，死於午，葬於未。火，受氣於亥，胎於子，養於丑，生於寅，沐浴於卯，冠帶於辰，臨官於巳，王於午，衰於未，病於申，死於酉，葬於戌。金，受氣於寅，胎於卯，養於辰，生於巳，沐浴於午，冠帶於未，臨官於申，王於酉，衰於戌，病於亥，死於子，葬於丑。

The forms of the Five Phases are different, so their places of birth and death vary. Each phase goes through the twelve months and twelve earthly branches in sequence, appearing and disappearing in order. This is what is later called the "Twelve Movements (the twelve houses of Longevity)." Wood: it receives qi in Shen, forms a fetus in You, is nourished in Xu, is born in Hai, is bathed in Zi, is crowned in Chou, is an official in Yin, reaches its peak in Mao, declines in Chen, is sick in Si, dies in Wu, and is buried in Wei. Fire: it receives qi in Hai, forms a fetus in Zi, is nourished in Chou, is born in Yin, is bathed in Mao, is crowned in Chen, is an official in Si, reaches its peak in Wu, declines in Wei, is sick in Shen, dies in You, and is buried in Xu. Metal: it receives qi in Yin, forms a fetus in Mao, is nourished in Chen, is born in Si, is bathed in Wu, is crowned in Wei, is an official in Shen, reaches its peak in You, declines in Xu, is sick in Hai, dies in Zi, and is buried in Chou. It can be seen that each phase begins with the branch of "Longevity" and proceeds through the twelve earthly branches in order, ending at the storage place.

水，受氣於巳，胎於午，養於未，生於申，沐浴於酉，冠帶於戌，臨官於亥，王於子，衰於丑，病於寅，死於卯，葬於辰。土，受氣於亥，胎於子，養於丑，寄行於寅，生於卯，沐浴於辰，冠帶於巳，臨官於午，王於未，衰病於申，死於酉，葬於戌。

Water: It begins to receive qi in Si, forms a fetus in Wu, gains nourishment in Wei, is born in Shen, is bathed in You, reaches the cap in Xu, is an official in Hai, reaches its peak in Zi, declines in Chou, becomes ill in Yin, dies in Mao, and enters the grave in Chen. Earth is slightly different: it begins to receive qi in Hai, forms a fetus in Zi, gains nourishment in Chou, and passes through a borrowed position in Yin, is born in Mao, is bathed in Chen, reaches the cap in Si, is an official in Wu, reaches its peak in Wei, declines and becomes ill in Shen, dies in You, and enters the grave in Xu. Earth requires to divide its peak into four seasons and rely on the fire position, so there is an additional term 'borrowed position' in the middle, and decline and illness are combined in one term.

戌是火墓，火是其母，母子不同葬；進行於丑，丑是金墓，金是其子，義又不合；欲還於未，未是木墓，木為土鬼，畏不敢入；進休就辰，辰是水墓，水為其妻，於義為合，遂葬於辰。昔舜葬蒼梧，二妃不從，故知合葬非古。然季武子云：自周公已來，未之有改。《詩》云：谷則異室，死則同穴。蓋以敦其義合，骨肉同歸。水土共墓，正取此也。

The previous text said that earth was buried in Xu, but Xu is actually the storage place for fire. Fire is the mother of earth, and mother and child should not be buried together. If moving forward to Chou, Chou is the storage place for metal. Metal is the son of earth, which is also inappropriate. If going back to Wei, Wei is the storage place for wood, and wood is the ghost that overcomes earth, so earth fears it and does not enter. Then moving forward to Chen, Chen is the storage place for water. Water is the wife of earth (since earth overcomes water, the one being overcome is considered the wife), which is appropriate, so earth finally is buried in Chen. In ancient times, Yu Shun was buried in Cangwu, and his two concubines did not join him in burial, showing that joint burial was not a practice in the ancient past. However, Ji Wu Zi said: since the Duke of Zhou, this custom has not changed. The Book of Poetry says: while living, they live separately, but after death, they should be buried together. This is probably to emphasize the virtue of husband and wife, and to have family members return to the same place. Water and earth share the same storage place, which is precisely the meaning behind this.

又以四季釋所理歸於斯。高堂隆以土生於未，盛於戌，壯於丑，終於辰，長為水土墓，故辰日不哭，以辰日重喪故也。袒踴之哀，豈待移日。高堂所說，蓋為浮淺。其生王意，又別是一家。《五行書》云：土雖有寄王於火鄉，生於巳，葬於辰，然土分王四季，各有生死之所。辰土，受氣於申酉，胎於戌，養於亥，生於子，沐浴於丑，冠帶於寅，臨官於卯，王於辰，衰病於巳，死於午，葬於未。未土，受氣於亥子，胎於丑，養於寅，生於卯，沐浴於辰，冠帶於巳，臨官於午，王於未，衰病於申，死於酉，葬於戌。

Using the principles of the last months of the four seasons, the conclusion also leads to this point. Gao Tanglong believed that earth is born in Wei, thrives in Xu, strengthens in Chou, and ends in Chen. Since Chen is a common tomb and repository for both water and earth, it is considered a day of great mourning, so one should not mourn on a Chen day. In reality, the heartfelt sorrow of tearing one's clothes and stamping one's feet comes from within; how could one wait until another day to weep? Gao Tanglong's view is superficial and shallow. As for his explanation of the order of earth's birth and prosperity, it is his own unique theory. The "Book of Five Phases" says: although earth is said to be "entrusted to the fire region, born in Si, and buried in Chen," in reality, earth's prosperity is distributed among the last months of the four seasons, and each of the four earth branches has its own place of birth and death. For Chen earth: it receives qi in Shen and You, forms a fetus in Xu, gains nourishment in Hai, attains birth in Zi, is bathed in Chou, crowned in Yin, becomes an official in Mao, reaches its peak in Chen, declines in Si, becomes ill in Wu, dies in Wei, and is buried in Xu. For Wei earth: it receives qi in Hai and Zi, forms a fetus in Chou, gains nourishment in Yin, attains birth in Mao, is bathed in Chen, crowned in Si, becomes an official in Wu, reaches its peak in Wei, declines in Shen, becomes ill in You, dies in Xu, and is buried in Hai. The pattern of this method is: take the branch where it is at its peak as the starting point, and count back four positions to find the place of birth, and count forward three positions to find the tomb.

戌土，受氣於寅卯，胎於辰，養於巳，生於午，沐浴於未，冠帶於申，臨官於酉，王於戌，衰病於亥，死於子，葬於丑。丑土，受氣於巳午，胎於未，養於申，生於酉，沐浴於戌，冠帶於亥，臨官於子，王於丑，衰病於寅，死於卯，葬於辰。

The Earthly Branch戌 (Xu) receives its qi in寅 (Yin) and卯 (Mao), forms its embryo in辰 (Chen), is nourished in巳 (Si), is born in午 (Wu), is bathed in未 (Wei), is crowned in申 (Shen), is in officialdom in酉 (You), reaches its prosperity in戌 (Xu), declines in亥 (Hai), dies in子 (Zi), and is buried in丑 (Chou). The Earthly Branch丑 (Chou) receives its qi in巳 (Si) and午 (Wu), forms its embryo in未 (Wei), is nourished in申 (Shen), is born in酉 (You), is bathed in戌 (Xu), is crowned in亥 (Hai), is in officialdom in子 (Zi), reaches its prosperity in丑 (Chou), declines in寅 (Yin), dies in卯 (Mao), and is buried in辰 (Chen). Each of the four Earthly Branches of earth is strong in its own position, buried in the next Earthly Branch, and cycles continuously.

《孝經援神契》云：五行，土出利以給天下。《龜經》云：土，木動為辰土，火動為未土，金動為戌土，水動為丑土。又云：甲乙寅卯為辰土，丙丁巳午為未土，庚辛申酉為戌土，壬癸亥子為丑土。凡五行之王，各七十二日，土居四季，季十八日，並七十二日，以明土有四方，生死不同。此蓋卜筮所用。

The "Xiao Jing Yuan Shen Qi" says: Among the Five Phases, earth produces benefits to provide for the world. The "Gui Jing" says: When discussing earth, if the yao of wood is active, take the earth of the辰 month; if the yao of fire is active, take the earth of the未 month; if the yao of metal is active, take the earth of the戌 month; if the yao of water is active, take the earth of the丑 month. It also says: The wood of Jia and Yi paired with寅 and卯 is matched with the earth of辰, the fire of Bing and Ding paired with巳 and午 is matched with the earth of未, the metal of Geng and Xin paired with申 and酉 is matched with the earth of戌, and the water of Ren and Gui paired with亥 and子 is matched with the earth of丑. All Five Phases have their peak periods lasting seventy-two days. Earth is distributed across the last months of the four seasons, each season contributing eighteen days, and four times eighteen days total seventy-two days. This shows that earth belongs to the four directions, and each has different places of birth and death. The above theory is mainly used in divination.

若論定位王相及生死之處，皆以季夏六月為土王之時。《禮記》云：中央土在季夏之後。此則歲之半，處四時之中央。天社、地神、人鬼，又並在未；坤亦在未卦，主於土，故云土德於未，終於丑。《易》曰：西南得朋，東北喪朋。此則明土王定在於未，墓定在辰也。

If discussing fixed directions of the ruler and the places of birth and death, then the season of Jixia sixth month is taken as the time when earth is at its peak. The "Book of Rites · Monthly Ordinances" places central earth after Jixia, which is the midpoint of the year, located at the center of the four seasons. The heavenly deity, earth deity, and human spirits are all associated with Wei; the Kun hexagram is also located in the direction of Wei, governing earth, so it is said that the virtue of earth is at Wei and ends at Chou. The "Zhou Yi · Kun Hexagram" says: going to the southwest brings friends, going to the northeast loses friends. This indicates that the prosperity of earth is fixed at Wei, and its storage is fixed at Chen.

五行皆以父母臨官中生者，取其盛壯能生養義。唯金在火中生者，巳中有方壯之土，能生金也。金非火不革其形，故金在火位中生。又云：金生鬼中者，金父土戊己，寄治丙丁，父不能獨養，要須母也。金在南方值己火，金得火方化，金化而水生。戊己土有化生之水，則金不畏火。己含水氣，則金之繼母也。五行皆以葬後之月而受氣者，以其死還復生，神氣不絕故也。

The Five Phases all achieve their "parents" in the position of Officialdom, which represents the period of vigorous growth, because it is based on the principle that parents must be strong and healthy in order to nurture offspring. However, metal is born in the position of Fire (Si), because the Si position contains the proper and vigorous Earth, which can generate metal. Moreover, metal cannot change its form without fire, so metal is born in the Fire position. Another explanation says that metal is born in the "ghost" position (which is the position that controls metal), because the father of metal is the Earth Phase of Wu and Ji, which are located in the position of Fire (Bing and Ding). The father cannot nurture alone, and must rely on the mother. When metal meets Ji and Fire in the South, it can be melted by fire, and once melted, water is produced. The Wu and Ji Earth contains generated water, so metal does not fear fire; Ji contains water vapor, which is equivalent to the mother of metal. As for the Five Phases all receiving their vital energy in the month following burial, it is because even after death, there is a possibility of revival, and the spirit does not cease.

休王之義，凡有三種：第一，辨五行體休王；第二，論支干休王；第三，論八卦休王。五行體休王者：春則木王，火相，水休，金囚，土死。夏則火王，土相，木休，水囚，金死。六月則土王，金相，火休，木囚，水死。秋則金王，水相，土休，火囚，木死。冬則水王，木相，金休，土囚，火死。

"The concept of 'Xiu Wang' (also written as 'Xiu Wang') refers to the five states of the Five Phases' energies as they wax and wane with the seasons. There are three approaches to discussing 'Xiu Wang': the first examines the inherent nature of the Five Phases, the second discusses 'Xiu Wang' in terms of Heavenly Stems and Earthly Branches, and the third relates to the Eight Trigrams. First, the 'Xiu Wang' of the Five Phases themselves: in spring, wood is in its prime (Wang), the fire that generates it is in the secondary prime (Xiang), the water that generates wood has declined (Xiu), the metal that controls wood is in captivity (Qiong), and the earth that is controlled by wood is in death (Si). In summer, fire is in its prime, earth is in the secondary prime, wood has declined, water is in captivity, and metal is in death. In the sixth month (late summer), earth is in its prime, metal is in the secondary prime, fire has declined, wood is in captivity, and water is in death. In autumn, metal is in its prime, water is in the secondary prime, earth has declined, fire is in captivity, and wood is in death. In winter, water is in its prime, wood is in the secondary prime, metal has declined, earth is in captivity, and fire is in death."

支干休王者：春則甲乙寅卯王，丙丁巳午相，壬癸亥子休，庚辛申酉囚，戊己辰戌丑未死。夏則丙丁巳午王，戊己辰戌丑未相，甲乙寅卯休，壬癸亥子囚，庚辛申酉死。六月則戊己辰戌丑未王，庚辛申酉相，丙丁巳午休，甲乙寅卯囚，壬癸亥子死。秋則庚辛申酉王，壬癸亥子相，戊己辰戌丑未休，丙丁巳午囚，甲乙寅卯死。冬則壬癸亥子王，甲乙寅卯相，庚辛申酉休，戊己辰戌丑未囚，丙丁巳午死。

The concept of the rest and kingship of heavenly stems and earthly branches is essentially replacing the rest and kingship of the Five Phases with the corresponding heavenly stems and earthly branches. In spring: Jia and Yi (wood) are in their prime, Bing and Ding (fire) are in their auxiliary phase, Gui and Hai (water) are in rest, Geng and Xin (metal) are in captivity, and Wu and Ji (earth) are in death. In summer: Bing and Ding (fire) are in their prime, Wu and Ji (earth) are in their auxiliary phase, Jia and Yi (wood) are in rest, Gui and Hai (water) are in captivity, and Geng and Xin (metal) are in death. In June: Wu and Ji (earth) are in their prime, Geng and Xin (metal) are in their auxiliary phase, Bing and Ding (fire) are in rest, Jia and Yi (wood) are in captivity, and Gui and Hai (water) are in death. In autumn: Geng and Xin (metal) are in their prime, Gui and Hai (water) are in their auxiliary phase, Wu and Ji (earth) are in rest, Bing and Ding (fire) are in captivity, and Jia and Yi (wood) are in death. In winter: Gui and Hai (water) are in their prime, Jia and Yi (wood) are in their auxiliary phase, Geng and Xin (metal) are in rest, Wu and Ji (earth) are in captivity, and Bing and Ding (fire) are in death.

八卦休王者：立春艮王，震相，巽胎，離沒，坤死，兌囚，干廢，坎休。春分震王，巽相，離胎，坤沒，兌死，干囚，坎廢，艮休。立夏巽王，離相，坤胎，兌沒，乾死，坎囚，艮廢，震休。夏至離王，坤相，兌胎，乾沒，坎死，艮囚，震廢，巽休。

The eight states of the trigrams are called Wuxiang, Xiang, Tai, Mei, Si, Qiu, Fei, and Xiu. These states follow the eight solar terms. At the beginning of spring, the Qian trigram is in its prime, Zhen is in its ministerial state, Xun is in its fetal state, Li is in its decline, Kun is in its death, Dui is in its imprisonment, Gen is in its decay, and Kan is in its rest. At the vernal equinox, the Zhen trigram is in its prime, Xun is in its ministerial state, Li is in its fetal state, Kun is in its decline, Dui is in its death, Qian is in its imprisonment, Kan is in its decay, and Gen is in its rest. At the beginning of summer, the Xun trigram is in its prime, Li is in its ministerial state, Kun is in its fetal state, Dui is in its decline, Qian is in its death, Kan is in its imprisonment, Gen is in its decay, and Zhen is in its rest. At the summer solstice, the Li trigram is in its prime, Kun is in its ministerial state, Dui is in its fetal state, Qian is in its decline, Kan is in its death, Gen is in its imprisonment, Zhen is in its decay, and Xun is in its rest. It can be seen that the eight states rotate in the order of the Later Heaven Trigrams.

立秋坤王，兌相，干胎，坎沒，艮死，震囚，巽廢，離休。秋分兌王，干相，坎胎，艮沒，震死，巽囚，離廢，坤休。立冬干王，坎相，艮胎，震沒，巽死，離囚，坤廢，兌休。冬至坎王，艮相，震胎，巽沒，離死，坤囚，兌廢，干休。其卦從八節之氣，各四十五日。

When the autumn begins, the Kun trigram is in its prime, Dui is in its auxiliary phase, Qian is in the fetal phase, Kan is in the hidden phase, Gen is in the dead phase, Zhen is in the captive phase, Xun is in the wasted phase, and Li is in the resting phase. When the autumn equinox comes, the Dui trigram is in its prime, Qian is in its auxiliary phase, Kan is in the fetal phase, Gen is in the hidden phase, Zhen is in the dead phase, Xun is in the captive phase, Li is in the wasted phase, and Kun is in the resting phase. When the winter begins, the Qian trigram is in its prime, Kan is in its auxiliary phase, Gen is in the fetal phase, Zhen is in the hidden phase, Xun is in the dead phase, Li is in the captive phase, Kun is in the wasted phase, and Dui is in the resting phase. When the winter solstice comes, the Kan trigram is in its prime, Gen is in its auxiliary phase, Zhen is in the fetal phase, Xun is in the hidden phase, Li is in the dead phase, Kun is in the captive phase, Dui is in the wasted phase, and Qian is in the resting phase. Each of the eight trigrams is dominant during one of the eight solar terms: the beginning of spring, the spring equinox, the beginning of summer, the summer solstice, the beginning of autumn, the autumn equinox, the beginning of winter, and the winter solstice. Each trigram rules for forty-five days, and altogether the eight trigrams account for exactly three hundred and sixty days.

凡當王之時，皆以子為相者，以其子方壯，能助治事也。父母為休者，以其子當王，氣正盛，父母衰老，不能治事，如堯老，委舜以國政也。所畏為死者，以其身王，能制殺之。所克者為囚者，以其子為相，能囚讎敵也。

When a particular element is in its prime, it uses the element it generates, known as its 'son,' as its phase, because the son is in the prime of life and can assist in affairs. It uses the element that generates it, known as its 'parents,' as its decline, because when the son is strong and vigorous, the parents are old and unable to manage affairs, just like when the Emperor Yao grew old, he entrusted the state affairs to Yu the Great. It uses the element that fears it, the one that overcomes it, as its death, because when it is strong, it can overcome and eliminate that element. It uses the element it overcomes as its imprisonment, because its son is in the phase position and can imprison the enemy. This is the origin of the five states of generation and overcoming: prosperity, decline, death, imprisonment, and rest.

柳世隆云：木，王時為林園竹樹，相時為葦荻草萊，休時為椽柱船車，囚時為薪樵榛梗，死時為棺槨朽株。火，王時為陶冶炎光，相時為燈燭，休時為煙氣，囚時為炭燼，死時為灰。土，王時為國邑山嶽，相時為城社丘陵，休時為田宅，囚時為牆垣，死時為糞壤。金，王時為金玉寶器，相時為銀銅利刃，休時為鉛錫犂鋤，囚時為焦器釜鑊，死時為沙礫碎鐵。水，王時為海瀆，相時為湖澤陂泉，休時為溝渠，囚時為酒漿，死時為枯池涸井。此並王時氣盛，故為洪大之物；相時氣劣，其比漸小；休時氣衰，故復轉微之；囚時於惡，所以最下；死時棄不用，故是枯朽之類也。

Liu Shilong assigned specific objects to the Five Phases according to the state of the Resting King: Wood, when in its prime, corresponds to forests and bamboo trees; in the phase of decline, it corresponds to beams, rafters, ships, and carts; in the state of rest, it corresponds to roof timbers and vehicles; in the state of imprisonment, it corresponds to firewood and tangled branches; and in the state of death, it corresponds to coffins and rotten stumps. Fire, when in its prime, corresponds to the fierce flames of kilns and forges; in the phase of decline, it corresponds to lamps and candles; in the state of rest, it corresponds to smoke; in the state of imprisonment, it corresponds to smoldering embers; and in the state of death, it corresponds to ash. Earth, when in its prime, corresponds to the capital city and high mountains; in the phase of decline, it corresponds to city walls, altars, and hills; in the state of rest, it corresponds to fields and dwellings; in the state of imprisonment, it corresponds to walls; and in the state of death, it corresponds to dung. Metal, when in its prime, corresponds to gold and jade treasures; in the phase of decline, it corresponds to silver and copper and sharp weapons; in the state of rest, it corresponds to lead and tin and plows; in the state of imprisonment, it corresponds to charred vessels and cauldrons; and in the state of death, it corresponds to sand and broken iron. Water, when in its prime, corresponds to the sea and great rivers; in the phase of decline, it corresponds to lakes, swamps, and ponds; in the state of rest, it corresponds to ditches; in the state of imprisonment, it corresponds to wine and liquor; and in the state of death, it corresponds to dry ponds and shallow wells. The reasoning behind these associations is that when something is in its prime, its energy is strong, so it corresponds to large objects; in the phase of decline, its energy is slightly weaker, so the corresponding objects are gradually smaller; in the state of rest, its energy has already weakened, so it corresponds to subtle objects; in the state of imprisonment, the situation is poor, so it corresponds to the lowest objects; and in the state of death, it is discarded and unused, so it corresponds to decayed and withered things.

趙怡云：五行之位，得其方為盛，得其所畏為終。故木畏金，甲以女弟乙妻庚，庚得木氣，故木胎於金卿，而生於水中，盛於其方，衰於火卿。火中有生金，故終於未，至西方而木終，以金王也。丙以女弟丁妻壬，壬得火氣，故火胎於水卿，生於木中，盛於其方，衰於金位，至北方而終，以水王也。

Zhao Yi said: Each of the Five Phases thrives when it is in its own native direction, but declines when it reaches the direction it fears. Therefore, wood fears metal: Jia marries his younger sister Yi to Geng (Yi and Geng are compatible), and Geng thus receives the energy of wood. Therefore, wood forms a fetus in the metal plate, is born in water, thrives in its native direction (east), and declines in the fire plate. Fire contains metal that can generate it, so wood ends in Wei; when it reaches the west, wood completely declines, because metal is strong there. Bing marries his younger sister Ding to Ren (Ding and Ren are compatible), and Ren thus receives the energy of fire. Therefore, fire forms a fetus in the water plate, is born in wood, thrives in its native direction (south), declines in the metal plate, and ends in the north, because water is strong there.

戊以女弟己妻甲，甲得土氣，故土胎於木卿，而生於火中，盛於其位，衰於水卿，至東方而終，以木王也。庚以女弟辛妻丙，丙得金氣，故金胎火卿，生火位，盛於其方，衰於水卿，至東方而終，有生火也。壬以女弟癸妻戊，戊得水氣，故水胎於土卿，生於金中，盛於其方，衰於木卿，至南方而終，有強土也。更互相生相畏，終始不絕之義也。

Wu married his sister Ji to Jia (Jia and Ji are compatible), and Jia thus received the energy of earth. Therefore, earth is in the earth plate of wood and is in the fetal stage, is born in fire, thrives in its own position (east), declines in the water plate, and ends when it reaches the east, because that is where wood is strong. Geng married his sister Xin to Bing (Bing and Xin are compatible), and Bing thus received the energy of metal. Therefore, metal is in the fire plate and is in the fetal stage, is born in the fire position, thrives in its own position (west), declines in the water plate, and ends when it reaches the east, because that is where fire is able to generate it. Ren married his sister Gui to Wu (Wu and Gui are compatible), and Wu thus received the energy of water. Therefore, water is in the earth plate and is in the fetal stage, is born in metal, thrives in its own position (north), declines in the wood plate, and ends when it reaches the south, because that is where strong earth is. This is the principle of the Five Phases alternatingly generating and alternatingly fearing each other, continuing endlessly in a cycle.

支干之義，多所配合，今略論方位及配所。干不獨立，支不虛設，要須配合，以定歲月日時而用。如君臣夫婦，必配合以相成。總而言之，從甲至癸為陽、為干、為日；從寅至丑為陰、為支、為辰。別而言之，干則甲丙戊庚壬為陽，乙丁己辛癸為陰；支則寅辰午申戌子為陽，卯巳未酉亥丑為陰。

The significance of the Heavenly Stems and Earthly Branches lies in their various combinations. Here we briefly discuss their directions and the things they are paired with. The Heavenly Stems cannot exist in isolation, nor can the Earthly Branches be empty; they must be combined with each other to determine years, months, days, and hours for practical use. Just as a ruler and minister, or a husband and wife, must be paired to achieve mutual success. In general, from Jia to Gui, this sequence belongs to the Yang, called "Stems," which govern days; from Yin to Chou, this sequence belongs to the Yin, called "Branches," which govern the hours. Individually, among the Heavenly Stems, Jia, Bing, Wu, Geng, and Ren are Yang, while Yi, Ding, Ji, Xin, and Gui are Yin. Among the Earthly Branches, Yin, Chen, Wu, Shen, Xu, and Zi are Yang, while Mao, Si, Wei, You, Hai, and Chou are Yin.

陽則為剛，為君，為夫，為上，為外，為表，為動，為進，為起，為仰，為前，為左，為德，為施，為開。陰則為柔，為臣，為妻，為妾，為財，為下，為內，為裡，為止，為退，為伏，為俯，為後，為右，為刑，為藏，為閉。陰陽所擬，例多且略，大綱如此。

The yang aspect represents strength, rulers, husbands, upper positions, externality, surface, motion, advancement, standing up, looking up, front, left side, virtue, giving, and opening. The yin aspect represents flexibility, subordinates, wives, concubines, property, lower positions, interior, stillness, retreat, concealment, bowing, back, right side, punishment, storage, and closure. There are many more things that yin and yang can represent, but these are just examples to give a general idea. When making a divination, if encountering a yang heavenly stem or earthly branch, one should take images related to strength, motion, externality, and advancement; if encountering a yin heavenly stem or earthly branch, one should take images related to flexibility, stillness, interiority, and retreat.

甲乙寅卯，木也，位在東方。丙丁巳午，火也，位在南方。戊己辰戌丑未，土也，位在中央，分王四季，寄治丙丁。庚辛申酉，金也，位在西方。壬癸亥子，水也，位在北方。甲為干首，子為支初，相配者，太陽之氣，動於黃泉之下，在建子之月，黃鐘之律，為氣之源，在子，故以子為先。萬物湊出於建寅之月，皆以見形，甲屬此月，故以甲為先，而配子。見者為陽，故從干；未見者為陰，故從支。所以用甲子相配，為六旬之始。

The Heavenly Stems Jia and Yi belong to wood and are located in the east; the Heavenly Stems Bing and Ding belong to fire and are located in the south; the Earthly Branches Chen, Xu, Chou, and Wei belong to earth and are located in the center, flourishing in the last months of the four seasons, and also associated with the fire position of Bing and Ding. The Heavenly Stems Geng and Xin belong to metal and are located in the west; the Heavenly Stems Ren and Gui belong to water and are located in the north. Jia is the first of the Heavenly Stems, and Zi is the first of the Earthly Branches. The reason they are paired is because the energy of the Star of brightness and prestige begins to stir beneath the earth in the month of Ji Zi (November), which is the beginning of the year according to the Huangzhong pitch pipe, which is located at the Zi position. Therefore, Zi is taken first. When all things gather and emerge, showing their forms, it is in the month of Ji Yin (January), and Jia is assigned to this month, so Jia is taken first to pair with Zi. What has already emerged belongs to yang and is assigned to the Heavenly Stems; what has not yet emerged belongs to yin and is assigned to the Earthly Branches. Therefore, Jia and Zi are paired to mark the beginning of the sixty Jiazi cycles.

干既有十，支有十二，輪轉相配，終於癸亥，故有六十日。十日一旬，故有六旬。一旬盡一甲癸，便以甲配子盡干，至癸酉便盡干，餘支有戌亥；又起甲配戌，盡干，至癸未，餘支有申酉；又起甲配申，盡干，至癸巳，餘支有午未；又起甲配午，盡干，至癸卯，餘支有辰巳；又起甲配辰，盡干，至癸丑，餘支有寅卯；又起甲配寅，盡干，至癸亥。十干有十二支相配，周畢，還從甲子起，故六甲輪轉，止六十日。

There are ten heavenly stems and twelve earthly branches. They are paired in sequence until Guihai, resulting in a total of sixty days. Ten days make a shen, so there are six shens. Each shen starts with Jia and ends with Gui. First, Jia is paired with Zi, using up all ten heavenly stems, and the shen ends at Guiyou, leaving Xu and Hai unpaired. Then Jia is paired with Xu, using up all ten heavenly stems to reach Guiwei, leaving Shen and You unpaired. Next, Jia is paired with Shen, using up all ten heavenly stems to reach Guisi, leaving Chen and Si unpaired. Then Jia is paired with Chen, using up all ten heavenly stems to reach Guimao, leaving Yin and Mao unpaired. Next, Jia is paired with Yin, using up all ten heavenly stems to reach Guichou, leaving Zi and Chou unpaired. Finally, Jia is paired with Zi, using up all ten heavenly stems to reach Guihai. After the heavenly stems and earthly branches are paired in this way for a full cycle, the sequence starts again from Jiazi. Thus, six Jia shens cycle through, completing exactly sixty days.

十日一旬，一旬之內，二支無配偶者，為之孤；所對沖者，為之虛。卜筮所云空亡，以支孤無干，故名為空亡。亡者，無也，無干故亡；所對者全虛，故云空也。算法：橫下十二支，位於四方；縱下八干，位於四方；下戊己，位於中央。若甲子旬，取甲干以配子支，如此次第相配，至戊辰，位在中央，土為四行主，不可移，故取辰支、巳支入中央，配戊己，餘悉以干就支。至戌亥，無干配之，單故為孤；辰巳之位，支干並無，故名為虛。

Ten days make a unit called a "shen." Within each shen, there are two earthly branches that cannot be paired with heavenly stems, and these two branches are called "gu." The two branches that are opposite to these two are called "xu." In divination, the term "kongwang" refers to these two branches that are left alone without a heavenly stem to pair with. "Wang" means absence, so they are called "kongwang" because there is no heavenly stem to pair with them. Their opposite positions are completely empty, hence "kong." The method of arranging counting rods is: place the twelve earthly branches horizontally and divide them into four sections; place the eight heavenly stems vertically (excluding wu and ji), also dividing them into four sections; then place the stems wu and ji in the center. Taking the jiazi shen as an example, start by pairing the jia stem with the zi branch, proceeding in order. When reaching wuchen, the wu and ji stems are in the center, and earth is the master of the four elements, so they cannot move. Therefore, the branches chen and si are placed in the center to pair with wu and ji. The rest continue pairing stems with branches. When reaching xu and hai, there are no more heavenly stems to pair, so they are left alone, hence called "gu." The original positions of chen and si have both branches and stems moved away, so they are called "xu."

其空亡之辰，從五行言之。如甲子旬，無戌亥，水土半空亡，以戌是土，亥是水也，不全無亥子，故云半也。甲戌旬，無申酉，為金全空亡，以金二支並無也。甲申旬，無午未，為火土半空亡，以巳午不全無也。甲午旬，無辰巳，亦然。甲辰旬，無寅卯，亦云木全空亡。甲寅旬，無子丑，亦水土半空亡。並以二支不俱無也。

The concept of Kongwang (空亡) can be further divided into full Kongwang and half Kongwang when considered in terms of the Five Phases. For example, in the Jiazi (甲子) sheng (旬), the branches Shen and You are missing. Shen belongs to metal and You also belongs to metal. Since both branches of metal are missing, this is called "metal full Kongwang." In the Jiaxu (甲戌) sheng, the branches Shen and You are missing. Shen and You both belong to metal, so this is called "metal full Kongwang." In the Jiashen (甲申) sheng, the branches Wu and Wei are missing. Wu belongs to fire and Wei belongs to earth. Since the two branches of fire (Si and Wu) are not both missing, fire and earth each have half Kongwang. The same situation occurs in the Jiawu (甲午) sheng. In the Jiachen (甲辰) sheng, the branches Yin and Mao are missing. Yin and Mao both belong to wood, so this is called "wood full Kongwang." In the Jiayin (甲寅) sheng, the branches Zi and Chou are missing. Zi belongs to water and Chou belongs to earth, so this is called "water and earth half Kongwang." The key to distinguishing between full and half Kongwang lies in whether the two branches of the same phase are both missing.

《兵書》云：陽生甲子，不足戌亥，仍為天門；陰生甲午，不足辰巳，仍為地戶；陽界甲寅，不足子丑，仍為鬼門；陰界甲申，不足午未，仍為人門；陽盛甲辰，卯為之隔；陰興甲戌，酉為之隔。此並是六甲之空支也。《春秋元命苞》云：地不足東南，右動終而入虛門。此明甲子孤在戌亥，虛在辰巳也。

The Book of Military Strategy says: Yang energy originates in the Jiazi decade, which lacks Xu and Hai, so Xu and Hai are called "Heaven's Gate"; Yin energy originates in the Jiawu decade, which lacks Chen and Si, so Chen and Si are called "Earth's Gate"; Yang energy divides in the Jiayin decade, which lacks Zi and Chou, so Zi and Chou are called "Ghost's Gate"; Yin energy divides in the Jiashen decade, which lacks Wu and Wei, so Wu and Wei are called "Human's Gate"; Yang energy is strong in the Jiachen decade, with Mao as the dividing point; Yin energy rises in the Jiaxu decade, with You as the dividing point. All of these refer to the six Jia decades' respective Kongwang branches. The Spring and Autumn Original Mandate says: The earth is lacking in the southeast direction, and when moving right to the end, it enters the empty gate. This clearly indicates that in the Jiazi decade, the isolated branches are Xu and Hai, and the empty branches are Chen and Si.

一干一支為一日者，以周天三百六十五度四分度之一日，日行一度，故正用一干一支，以主一日也。三旬為一月者，月日行十三度四分度之一，三旬而周天也。十二月為一歲者，四時時有三月，生殺之功，備遍十二支也。一歲合三百六十日者，六六三十六，六甲之數也。六甲閒兩月之日者，以陰陽奇偶備也。陽者為奇，陰者為偶。萬物庶類，吉凶之理，以此彰矣。

A heavenly stem combines with an earthly branch to form a day, because the celestial sphere consists of 365 and 1/4 degrees, and the sun moves one degree each day, so one heavenly stem and one earthly branch are exactly sufficient to govern a day. Three ten-day periods make a month, because the moon moves 13 and 1/4 degrees each day, and three ten-day periods (30 days) exactly complete a full circle around the celestial sphere. Twelve months make a year, because each season has three months, and the functions of growth and decline must cover all twelve earthly branches to be complete. A year consists of 360 days, because six multiplied by six equals thirty-six, which is the number of the Six Jia (sixty multiplied by six equals three hundred and sixty). The difference of about two months beyond the Six Jia accounts for the completeness of both yin and yang, odd and even numbers. The principles of good and bad fortune for all things are thus revealed.

其支干相配，歲月日時並然。立歲之元，起於上元甲子；立月之元，起甲巳之歲，十一月甲子；立日之元，六旬起自甲子；立時之元，冬夏二至後，得甲巳之日，夜半起甲子。四事皆以甲子為首也。

The rules for pairing heavenly stems and earthly branches are the same for years, months, days, and hours. To determine the beginning of a year, it starts from the Jiazi year of the first heavenly stem. To determine the beginning of a month, it starts from the Jia or Ji year's eleventh month, beginning on the Jiazi day. To determine the beginning of a day, it starts from the Jiazi day in the sixty-day cycle. To determine the beginning of an hour, it starts from the middle of the night at the beginning of the Zi hour on the Jia or Ji day, after the winter solstice or summer solstice. The four aspects of year, month, day, and hour all begin with Jiazi.

其上配九星、下配九州島者，《黃帝兵決》云：甲子從北斗魁第一星起，順數至庚午，在第七剛星，至辛未，還從第六星，逆數至丙子，又從第一星，順數盡六甲。其下配九州島者，史書云：甲齊，乙東夷，丙楚，丁南夷，戊魏，己韓，庚秦，辛西夷，壬燕，癸北夷。《漢書·五行志》云：甲乙，海外，日月不治；丙丁，江淮海岱；戊己，中州河濟；庚辛，華山以西；壬癸，常山以北。子，周；丑，翟；寅，楚；卯，鄭；辰，邯鄲；巳，衛；午，秦；未，中山、宋；申，齊；酉，魯；戌，越；亥，燕。

As for the method of matching the Heavenly Stems and Earthly Branches with the Nine Stars and the Nine States, the "Yellow Emperor's Military Decisions" states: starting from Jiazi, count sequentially from the first star of the Big Dipper's handle until reaching Gengwu, which falls exactly on the seventh star (Yao Guang). When reaching Xinwei, return to the sixth star and count backwards until reaching Bingzi. Then start again from the first star, counting forward through all sixty Jiazi. Regarding the matching of the Earthly Branches with the Nine States, historical texts say: Jia matches Qi land, Yi matches the Eastern夷, Bing matches Chu land, Ding matches the Southern夷, Wu matches Wei land, Ji matches Han land, Geng matches Qin land, Xin matches the Western夷, Ren matches Yan land, and Gui matches the Northern夷. The "Book of Han: Five Phases Chapter" says: Jia and Yi are assigned to the overseas regions, which are places where sunlight and moonlight do not reach; Bing and Ding are assigned to the areas around the Yangtze and Huai rivers and the Hai and Dai regions; Wu and Ji are assigned to the central plains and the regions around the Yellow River and the Ji River; Geng and Xin are assigned to the area west of the Hua Mountains; Ren and Gui are assigned to the area north of Changshan. The distribution of the Earthly Branches is as follows: Zi matches Zhou, Chou matches Zhai, Yin matches Chu, Mao matches Zheng, Chen matches Handan, Si matches Wei, Wu matches Qin, Wei matches Zhongshan and Song, Shen matches Qi, You matches Lu, Xu matches Yue, and Hai matches Yan.

《龍首經》曰：子，齊，青州；丑，吳、越，揚州；寅，燕，幽州；卯，宋，豫州；辰，晉，兗州；巳，楚，荊州；午，周，三河；未，秦，雍州；申，蜀，益州；酉，梁州；戌，徐州；亥，衛，幷州。若地辰之位，史漢近之；星次而論，龍首為當。其配人身，甲乙為頭，丙丁為胸脅，戊己為心腹，庚辛為股，壬癸為手足。則子為頭，丑亥為胸臂，寅戌為手，卯酉為腰脅，辰申為尻肱，巳未為脛，午為足。此皆初為首，末為足，配五藏也。干以甲乙為肝，丙丁為心，戊己為脾，庚辛為肺，壬癸為腎也；支以寅卯為肝，巳午為心，辰戌丑未為脾，申酉為肺，亥子為腎。此皆從五行配之。

The Long Head Classic presents a different system of matching: Zi corresponds to Qi Di and Qingzhou; Chou corresponds to Wu Yue and Yangzhou; Yin corresponds to Yan Di and Youzhou; Mao corresponds to Song Di and Yuzhou; Chen corresponds to Jin Di and Yanzhou; Si corresponds to Chu Di and Jingzhou; Wu corresponds to the Zhou royal house and San He; Wei corresponds to Qin Di and Yongzhou; Shen corresponds to Shu Di and Yizhou; You corresponds to Liangzhou; Xu corresponds to Xuzhou; Hai corresponds to Wei Di and Bingzhou. If considering the actual positions of the twelve earthly branches on the ground, the system in historical texts and the Han Shu is closer to reality. If discussing the division of star positions in the sky, the system in the Long Head Classic is more appropriate. The heavenly stems correspond to the human body: Jia and Yi correspond to the head, Bing and Ding to the chest and ribs, Wu and Ji to the heart and abdomen, Geng and Xin to the thighs, Ren and Gui to the hands and feet. The earthly branches correspond to: Zi to the head, Chou and Hai to the chest and arms, Yin and Xu to the hands, Mao and You to the waist and ribs, Chen and Shen to the buttocks and upper arms, Si and Wei to the lower legs, Wu to the feet. This system treats the first as the head and the last as the feet, arranging them from top to bottom. For the five internal organs: the heavenly stems correspond to Jia and Yi as the liver, Bing and Ding as the heart, Wu and Ji as the spleen, Geng and Xin as the lungs, Ren and Gui as the kidneys; the earthly branches correspond to Yin and Mao as the liver, Si and Wu as the heart, Chen, Xu, Chou, and Wei as the spleen, Shen and You as the lungs, Hai and Zi as the kidneys. All these match according to the Five Phases.

又干以甲乙為皮毛，丙丁為爪筋，戊己為肉，庚辛為骨，壬癸為血脈也；支以寅卯為皮毛，巳午為爪筋，辰戊丑未為肉，申酉為骨，亥子為血脈也。木生在地上，故為皮毛；火有猛毅，故為爪筋；土有持載，故以為肉；金性堅剛，故為骨；水本流潤，故是血脈。並支干所配，故以備釋。

In addition, the Heavenly Stems are also associated with parts of the human body: Jia and Yi correspond to the skin and hair, Bing and Ding to nails and tendons, Wu and Ji to muscles, Geng and Xin to bones, and Ren and Gui to blood vessels. The Earthly Branches are similarly associated: Yin and Mao correspond to the skin and hair, Si and Wu to nails and tendons, Chen, Xu, Chou, and Wei to muscles, Shen and You to bones, and Hai and Zi to blood vessels. The reasoning behind these associations is as follows: Wood grows above the ground, so it corresponds to the skin and hair; Fire is fierce and resolute, so it corresponds to nails and tendons; Earth supports all things, so it corresponds to muscles; Metal is hard and strong, so it corresponds to bones; Water flows and moistens naturally, so it corresponds to blood vessels. All of these are the things associated with the Heavenly Stems and Earthly Branches, so they are explained in detail here.

凡五行均布，徧在萬有，不可定守一途。今先論五行體雜。但其氣周流，隨事而用。若言不雜，水只應一，何故謂五而為六？火、金、木、土並爾。當知生數為本，成數為雜。既有雜，故一行當體，卽有五義。如木有曲直，此是木也；木中有火，則是火也；木堪為兵仗，有擊觸之能，卽是金也；木中有潤，卽是水也；木吐華葉子實，卽是土也。

The Five Phases are evenly distributed and present in all things, and one should not rigidly adhere to a fixed interpretation. Here we first discuss the mixture inherent in the Five Phases. The energies of the Five Phases flow continuously and function according to different circumstances. If they were not mixed, water would simply be the number 'one'. But when discussing the Five Phases, water becomes 'six' (the sum of the generating number 'one' and the number 'five' representing earth). The same applies to fire, metal, wood, and earth. One should understand that the generating numbers represent the essence of each phase, while the completed numbers already include the mixture. Since there is mixture, each phase inherently contains all five elements. For example, wood can be bent or straight, which is the nature of wood itself; wood contains fire, which is fire; wood can be made into weapons with the ability to strike and pierce, which is metal; wood contains moisture, which is water; and wood can produce flowers, leaves, and fruits, which is earth.

火，外陽卽是火也，內陰卽是水也，能殺卽是金也，能熟卽是木也，能生卽是土也。土，能生卽是土也，能容卽是水也，能成卽是木也，能防卽是金也，含陽卽是火也。金，能斷卽是金也，從革卽是木也，含火卽是火也，有汗卽是水也，能生卽是土也。水，外陰卽是水也，內陽卽是火也，含養卽是木也，潤生卽是土也，能殺卽是金也。此皆以義釋一行通有五氣。

Fire is also like this: its outer form is yang, which is fire itself; its inner nature is yin, which is water; it can burn and destroy all things, which is metal; it can ripen food, which is wood (wood governs growth and ripening); it can produce ash and soil, which is earth. Earth: it can nurture all things, which is earth itself; it can contain and hold, which is water; it can form and complete all things, which is wood; it can build barriers and block, which is metal; it can contain yang energy, which is fire. Metal: it can cut and sever, which is metal itself; it can follow the mold and change, which is wood; it contains the nature of fire, which is fire; it can exude water-like sweat on its surface, which is water; it can generate water and nurture things, which is earth. Water: its outer form is yin, which is water itself; its inner nature contains yang, which is fire; it can contain and nurture, which is wood; it can moisten and nourish living beings, which is earth; it can flood and destroy all things, which is metal. All of these explanations are based on meaning: any one of the five elements contains the energies of the five phases.

就事而論，義則不爾，或有或無。質弱者，則體相容；質堅者，則體不相容。金中無木，木中無金，金木以正相害故；水中無火，火中無水，兩法正相害故，亦無金。金中有水，木中亦有水，木中亦有火，石中亦有火。而水能生木，則木中有水；水生於金，金中有水；火生於木，木中有火；水復從金生，金中有水；水能生木，木中有火。火克於金，那得石復有火？此是火性弱，故能入堅；而水中無金，是堅不能入弱。

But if we examine specific things, the situation is not entirely the same. Some contain elements of other categories, while others do not. Soft substances can contain each other, while hard substances cannot. Gold does not contain wood, and wood does not contain gold, because gold and wood are in a direct relationship of mutual control and harm. Water does not contain fire, and fire does not contain water, for the same reason. Fire also does not contain gold. However, water is contained in gold, and water is also contained in wood. Wood also contains fire, and fire is contained in stone. This is because water generates wood, so wood contains water; water is generated by gold, so gold contains water; fire is generated by wood, so wood contains fire; water is generated by gold, so gold contains water; water generates wood, and wood contains fire. Someone might ask: fire naturally controls gold, so how can fire be present in stone (which belongs to gold)? This is because fire is soft and can penetrate hard substances, while gold does not contain water, showing that hard substances cannot enter soft ones.

木生於水，木中含水；金能生水，金中含水。所以水中無金木者，金木在水中，不得言水體有金木；溼潤在木石中，木石便得有水義。此亦是弱能入堅，堅不能入弱。炎州有樹，生於火中，此非火能生樹，是火不能燒樹；亦非火在樹中，乃是樹在火中，而體不相雜，無異金在水中而不能雜水體。亦如海中陰火潛燃，此水中有火，但非水體雜火。此稍涉靈奇，亦非五行常準。

Wood is born from water, so wood contains water; metal produces water, so metal contains water. The reason we say water does not contain metal or wood is because metal and wood are merely floating in water, not because water's essence contains them. Moisture seeps into wood and stone, so wood and stone can be said to contain the meaning of water. This is similar to how the weak can enter the strong, but the strong cannot enter the weak. In the southern region of the fiery land, there is a tree that grows in fire, which does not mean fire produces trees, but rather that fire cannot burn this tree; it is not that fire is inside the tree, but that the tree is in fire. The essences of the two are not mixed, just as a block of metal in water does not mix with the water. Similarly, there is hidden fire beneath the sea that burns in darkness, which seems as if fire is in water, but in reality, the essence of water does not mix with fire. Such phenomena are somewhat strange and supernatural, and should not be considered as part of the regular principles of the Five Phases.

又木中有火，火還燒木，此是生火方盛，故能燒木。石中有火，火不燒石，是火至金鄉，氣巳衰，故不能燒石。其以火消金者，亦取其盛，故能爍金，是不取衰火。猶如金能克木，鉛錫不能斷，此是不堅之金也。土性包含，無所不受，故土中皆備有水金木火。火非直陽氣，猶如范陽地燃，是陰也。土火不相害，雖不恆爾，不得言無。等是四行，何故獨爾？土既居地，地卽是陰，火卽是太陽之氣，故不得恆有也。

Furthermore, wood contains fire, but fire can burn wood because the fire generated from wood is at its peak, so it can burn the wood. Stone also contains fire, but fire cannot burn stone because when fire reaches the area of metal (the western direction), its energy has already weakened, so it cannot burn the stone. As for using fire to melt metal, it is also necessary to take fire at its peak to melt metal; weak fire is unable to do so. This is similar to how metal can naturally overcome wood, but lead and tin, which are not hard metals, cannot cut through wood. Earth has the ability to contain and accept all things, so water, metal, wood, and fire are all present within it. The fire here does not refer solely to yang energy; for example, the naturally burning fire found underground in Fanyang is considered yin fire. Earth and fire do not mutually control each other, although fire is contained within earth and is not the norm, it cannot be said that there is absolutely none. Someone may ask: since all four elements are the same, why is fire within earth treated separately? The answer is: since earth is located on the ground, which is itself yin, and fire is the energy of the sun, it cannot remain for long within earth.

支干雜者，《五行書》云：甲以女弟乙嫁庚為妻，故乙中有雜金。立春木王，甲召乙還，乙懷金氣來，故仲春殺榆莢白也。丙以女弟丁嫁壬為妻，丁中有雜水。立夏火王，丙召丁還，丁懷水氣來，故仲夏桑椹熟黑也。戊以女弟己嫁甲為妻，己中有雜木。季夏土王，戊召己還，己懷木氣來，故季夏有果實青也。庚以女弟辛嫁丙為妻，辛中有雜火。立秋金王，庚召辛還，辛懷火氣來，故仲秋棗熟朱也。壬以女弟癸嫁戊為妻，癸中有雜土。立冬水王，壬召癸還，癸懷土氣來，故仲冬草木皆黃也。

The Heavenly Stems and Earthly Branches are intermingled in a certain way. The "Book of Five Phases" uses the analogy of marriage to explain this. Jia marries his younger sister Yi to Geng, making Yi contain the quality of metal. When the beginning of spring arrives and wood is in its prime, Jia recalls Yi back to his family, and Yi returns with the quality of metal, so in the second month of spring, the elm fruits appear white, showing the quality of metal. Bing marries his younger sister Ding to Ren, making Ding contain the quality of water. When the beginning of summer arrives and fire is in its prime, Bing recalls Ding back to his family, and Ding returns with the quality of water, so in the fifth month of summer, the mulberry fruits ripen and appear black, showing the quality of water. Wu marries his younger sister Ji to Jia, making Ji contain the quality of wood. When the beginning of late summer arrives and earth is in its prime, Wu recalls Ji back to his family, and Ji returns with the quality of wood, so in the sixth month of late summer, the fruits appear green, showing the quality of wood. Geng marries his younger sister Xin to Bing, making Xin contain the quality of fire. When the beginning of autumn arrives and metal is in its prime, Geng recalls Xin back to his family, and Xin returns with the quality of fire, so in the eighth month of autumn, the jujubes ripen and appear red, showing the quality of fire. Ren marries his younger sister Gui to Wu, making Gui contain the quality of earth. When the beginning of winter arrives and water is in its prime, Ren recalls Gui back to his family, and Gui returns with the quality of earth, so in the eleventh month of winter, grass and trees appear yellow, showing the quality of earth.

甲丙戊庚壬為男剛強，故自有德不雜；乙丁己辛癸為女柔弱，不自專，從夫，故有雜。猶出嫁之女，卽稱夫氏，歸寧之日，攜子而來，氏族便雜。《五行十雜》云：甲為木，乙為材，丙為火，丁為灰，戊為土，己為泥，庚為金，辛為爐銻，壬為水，癸為濁汙。此皆雜義也。

The heavenly stems Jia, Bing, Wu, Geng, and Ren are yang stems, characterized by strong nature, so they each maintain the pure essence of their own element without mixture. The heavenly stems Yi, Ding, Ji, Xin, and Gui are yin stems, characterized by gentle nature, unable to act independently, and thus must follow their husbands, hence they carry mixed qualities. This is like a woman who takes her husband's surname after marriage and brings her children back to her parents' home for visits, thus mixing the family lineage. The "Ten Mixtures of the Five Phases" states: Jia is wood, Yi is timber; Bing is fire, Ding is ash; Wu is earth, Ji is mud; Geng is metal, Xin is dross from a furnace; Ren is water, Gui is dirty water. Yang stems take the pure form of their own element, while yin stems take the impure form resulting from processing and decay, all referring to the concept of mixture.

寅卯為木，春懷火，故卯為純木，寅為雜木。巳午為火，夏懷土，故午為純火，巳為雜火。申酉為金，秋懷水，故酉為純金，申為雜金。亥子為水，冬懷木，故子為純水，亥為雜水。土居中央，分主四氣，故辰中有餘木，未中有餘火，戌中有餘金，丑中有餘水，各十二日。故四孟為懷任，生氣之所由；四仲，盛壯之所立；四季，葬送之所在。懷任及葬，皆有雜義。

The Earthly Branches are also like this. Yin and Mao belong to Wood, and since spring carries the Qi of the fire that is about to be born, Mao is pure Wood, while Yin is mixed Wood (Yin contains the birth of fire). Si and Wu belong to Fire, and since summer carries the Qi of the earth that is about to be born, Wu is pure Fire, while Si is mixed Fire. Shen and You belong to Metal, and since autumn carries the Qi of the water that is about to be born, You is pure Metal, while Shen is mixed Metal. Zi and Hai belong to Water, and since winter carries the Qi of the wood that is about to be born, Zi is pure Water, while Hai is mixed Water. Earth is in the center and governs the Qi of the four seasons, so Chen retains the remaining Qi of Wood, Wei retains the remaining Qi of Fire, Xu retains the remaining Qi of Metal, and Chou retains the remaining Qi of Water, each for twelve days. Therefore, the four "Clan" Branches, Yin, Shen, Si, and Hai, are places of conception and birth, the source of life Qi; the four "Middle" Branches, Zi, Wu, Mao, and You, are places of strength and establishment; and the four "Season" Branches, Chen, Wei, Xu, and Chou, are places for burial and final rest. All places of conception and burial contain the meaning of mixture.

五行非直性相雜，當方亦有雜義。東方甲乙寅卯辰：甲，木也；乙中有雜金；寅中有生火；辰，土也；卯中有死水。南方丙丁巳午未：丙，火也；丁中有雜水；巳中有生金；未，土也；午中有死木。西方庚辛申酉戌：庚，金也；辛中有雜火；申中有生水；戌，土也；又，酉中有胎木。北方壬癸亥子丑：壬，水也；癸中有雜土；亥中有生木；子中有胎火；丑中有死金。此並方別有五行也。

The Five Phases are not only mixed in their inherent natures, but also in each direction, there is a sense of mixture. The East includes Jia, Yi, Yin, Mao, and Chen: Jia is Wood; Yi contains the Qi of Metal; Yin contains the birth of Fire; Chen is Earth; and Mao contains the death place of Water. The South includes Bing, Ding, Si, Wu, and Wei: Bing is Fire; Ding contains the Qi of Water; Si contains the birth of Metal; Wei is Earth; and Wu contains the death place of Wood. The West includes Geng, Xin, Shen, You, and Xu: Geng is Metal; Xin contains the Qi of Fire; Shen contains the birth of Water; Xu is Earth; and You contains the fetal position of Wood. The North includes Ren, Gui, Hai, Zi, and Chou: Ren is Water; Gui contains the Qi of Earth; Hai contains the birth of Wood; Zi contains the fetal position of Fire; and Chou contains the death place of Metal. It is evident that within each direction, all Five Phases are present.

寅午戌，火之位也：寅中有生火，在東方；午中有王火，在南方；戌中有死火，在西方。亥卯未，木之位也：亥中有生木，在北方；卯中有王木，在東方；未中有死木，在南方。申子辰，水之位也：申中有生水，在西方；子中有王水，在北方；辰中有死水，在東方。巳酉丑，金之位也：巳中有生金，在南方；酉中有王金，在西方；丑中有死金，在北方。此一行之體，雜在三方也。未辰丑戌，土之位也：未中有王土，辰中有死土，丑中有衰土，戌中有壯土。此土體雜在四方也。趙怡言：五行相雜，如錦綺焉。斯言當矣。

Now looking at the Triple Harmony Formation. The positions of the Triple Harmony for fire are寅, 午, and 戌: 寅 contains the growth of fire, belonging to the East; 午 contains the prosperity of fire, belonging to the South; 戌 contains the burial of fire, belonging to the West. The positions of the Triple Harmony for wood are 亥, 卯, and 未: 亥 contains the growth of wood, belonging to the North; 卯 contains the prosperity of wood, belonging to the East; 未 contains the burial of wood, belonging to the South. The positions of the Triple Harmony for water are 申, 子, and 辰: 申 contains the growth of water, belonging to the West; 子 contains the prosperity of water, belonging to the North; 辰 contains the burial of water, belonging to the East. The positions of the Triple Harmony for metal are 巳, 酉, and 丑: 巳 contains the growth of metal, belonging to the South; 酉 contains the prosperity of metal, belonging to the West; 丑 contains the burial of metal, belonging to the North. This means that the essence of the same element is dispersed and mixed among three different directions — this is the reason for the concept of "Triple Harmony" taking the three branches of birth, prosperity, and burial. 未, 辰, 丑, and 戌 are the directions of earth: 未 contains the prosperity of earth, 辰 contains the burial of earth, 丑 contains the decline of earth, and 戌 contains the strength of earth. This means that the essence of earth is mixed among four directions. Zhao Yi said: The five elements are interwoven with each other, like a finely woven silk and brocade, with threads crossing and colors blending. This statement is very appropriate.

德者，得也，有益於物，各隨所欲，無悔恡，故謂之為德也。《五行書》云：若有一德，能禳百災。凡陰陽用事，遇德為善，謂之福德，為有救助，萬事皆吉，災害消亡。德有四德，三者從支干論之，一者從月氣論之。支干三種者：一曰干德，二曰支德，三曰支干合德。

"De" means "De," which refers to the ability to benefit things and allow all parties to achieve their wishes without leaving regret or sorrow, hence it is called De. The "Book of Five Phases" says: as long as one obtains a De, it can eliminate hundreds of calamities. Whenever yin and yang are in charge, encountering De brings good fortune, known as "Fortune Virtue," because it brings aid and makes all things auspicious, with disasters vanishing. De has four types: three of them are based on the Heavenly Stems and Earthly Branches, and one is based on the monthly trigrams. The three based on the Heavenly Stems and Earthly Branches are: one is called "Stem De," two is called "Branch De," and three is called "Combined Stem and Branch De."

干德者：甲德自在，乙德在庚，丙德自在，丁德在壬，戊德自在，己德在甲，庚德自在，辛德在丙，壬德自在，癸德在戊。此十干者，甲丙戊庚壬為陽尊，故德自處；乙丁己辛癸為陰卑，故配德於陽，有從夫之義，所以不自為德。

First, the "dryness of virtue" (干德): Jia's virtue is in itself, Yi's virtue is in Geng, Bing's virtue is in itself, Ding's virtue is in Ren, Wu's virtue is in itself, Ji's virtue is in Jia, Geng's virtue is in itself, Xin's virtue is in Bing, Ren's virtue is in itself, and Gui's virtue is in Wu. Among these ten heavenly stems, Jia, Bing, Wu, Geng, and Ren are yang and noble, so their virtue resides in their own position. Yi, Ding, Ji, Xin, and Gui are yin and humble, so their virtue must be paired with the yang stems that are compatible with them, following the principle that the wife follows the husband. Therefore, they cannot possess virtue on their own.

揚子雲：配日之道，正有五日：甲己為木，丙辛為火，戊癸為土，乙庚為金，丁壬為水。陰陽之理，必相配偶，以則君臣夫婦之義。甲為君、為夫，己為臣、為妻，君位自在，臣位由君，故己德在甲，乙德在庚也，餘四皆然，陰從陽之道。

Yang Xiong said: The principle of the heavenly stems being paired is exactly five pairs: Jia pairs with Ji to generate wood, Bing pairs with Xin to generate fire, Wu pairs with Gui to generate earth, Yi pairs with Geng to generate metal, and Ding pairs with Ren to generate water. The principle of yin and yang must necessarily be paired in pairs, to exemplify the meaning of sovereign and subject, husband and wife. Jia is the sovereign and the husband, Ji is the subject and the wife; the position of the sovereign is inherent, and the position of the subject is determined by the sovereign, so the virtue of Ji resides upon Jia, and the virtue of Yi resides upon Geng; the other four pairs are also like this, all demonstrating the principle that yin follows yang.

支德者：子德在巳，丑德在午，寅德在未，卯德在申，辰德在酉，巳德在戌，午德在亥，未德在子，申德在丑，酉德在寅，戌德在卯，亥德在辰。此皆以其夫生助之所也。子以巳為德者，子，水也，以土為夫，巳中有生土。丑以午為德者，丑，土也，以木為夫，午中有死木。寅以未為德者，寅，木也，以金為夫，未中有冠帶金。卯以申為德者，卯，木也，以金為夫，申中有相金。辰以酉為德者，辰，土也，以木為夫，酉中有胎木。巳以戌為德者，巳，火也，以水為夫，戌中有冠帶水。

Now discussing "branch virtue": The virtue of the branch Zi is in Si, Chou in Wu, Yin in Wei, Mao in Shen, Chen in You, Si in Xu, Wu in Hai, Wei in Zi, Shen in Chou, You in Yin, Xu in Mao, Hai in Chen. The pattern is that each branch's virtue is five positions ahead. These are all places where the "husband" (the element that overcomes it) receives support. The virtue of Zi is in Si because Zi belongs to water, and the earth, which overcomes water, is its husband, and Si contains the birth of earth. The virtue of Chou is in Wu because Chou belongs to earth, and the wood, which overcomes earth, is its husband, and Wu contains the death position of wood. The virtue of Yin is in Wei because Yin belongs to wood, and the metal, which overcomes wood, is its husband, and Wei contains the capping position of metal. The virtue of Mao is in Shen because Mao belongs to wood, and metal is its husband, and Shen contains the position of metal in its phase. The virtue of Chen is in You because Chen belongs to earth, and wood is its husband, and You contains the fetal position of wood. The virtue of Si is in Xu because Si belongs to fire, and water, which overcomes fire, is its husband, and Xu contains the capping position of water.

午以亥為德者，午，火也，以水為夫，亥中有相水。未以子為德者，未，土也，以木為夫，子中有沐浴木。申以丑為德者，申，金也，以火為夫，丑中有養火。酉以寅為德者，酉，金也，以火為夫，寅中有生火。戌以卯為德者，戌，土也，以木為夫，卯中有王木。亥以辰為德者，亥，水也，以土為夫，辰中有死土。

The branch 午 (Wu) takes 亥 (Hai) as its virtue because 午 belongs to fire, and water is its husband, while 亥 contains water in the phase position. The branch 未 (Wei) takes 子 (Zi) as its virtue because 未 belongs to earth, and wood is its husband, while 子 contains wood in the bathing position. The branch 申 (Shen) takes 丑 (Chou) as its virtue because 申 belongs to metal, and fire, which overcomes metal, is its husband, while 丑 contains fire in the nourishing position. The branch 酉 (You) takes 寅 (Yin) as its virtue because 酉 belongs to metal, and fire is its husband, while 寅 contains fire in the growth position. The branch 戌 (Xu) takes 卯 (Mao) as its virtue because 戌 belongs to earth, and wood is its husband, while 卯 contains wood in the prosperity position. The branch 亥 (Hai) takes 辰 (Chen) as its virtue because 亥 belongs to water, and earth is its husband, while 辰 contains earth in the death position. Thus, the virtues of the twelve branches all fall upon the particular position of the husband star's movement.

或問云：從夫之義，生者有德，能相和養，故從；死者離背，不能和從，何以死猶為德？答曰：婦無再醮，一降適人，便稱夫氏，雖死猶從其族，豈得生而稱之，死便舍棄？故陰之從陽，生死常存。

Someone asked: Since it speaks of the principle of following the husband, then the husband's star should be in a prosperous and vital position to be considered virtuous, because it can harmonize and support the wife, so the wife can follow him. But if the husband's star is in a dead position, it has already turned away and cannot harmonize or follow, so why is the dead position still considered virtuous? The answer is: Women do not have the custom of remarrying, once they are married they take their husband's surname, and even if the husband dies, they remain part of his family clan. How could they follow him when he is alive and abandon him when he is dead? Therefore, the yin follows the yang, remaining constant whether the husband is alive or dead.

支干合德者：子德在甲，丑德在辛，寅德在丙，卯德在丁，辰德在庚，巳徳在己，午德在戊，未德在辛，申德在壬，酉德在癸，戌德在庚，亥德在乙。此皆從子為德也，謂子能扶助其母，有孝養之性，以為德也。

The concept of "branch and stem harmony in virtue" involves matching the virtue of the earthly branches with the heavenly stems: the virtue of Zi is associated with Jia, Chou with Xin, Yin with Bing, Mao with Ding, Chen with Geng, Si with Ji, Wu with Wu, Wei with Xin, Shen with Ren, You with Gui, Xu with Geng, and Hai with Yi. This system takes "Zi" (the thing I give birth to) as the standard of virtue, meaning that the son can support the mother, reflecting a filial and nurturing nature, hence regarded as virtue.

凡干為陽，支為陰，陽體剛強自在，陰體柔順從陽。婦人有三從之禮，每無自專之義，夫死從子，故以子為德。若有支干，各自為德，皆從其夫；既今支干共為德，故離其夫位，故便從子也。子德在甲者，水為木母故也，例皆如之。

In general, the Heavenly Stems are yang and the Earthly Branches are yin. Yang is strong and self-restraining, able to hold its position. Yin is gentle and compliant, needing to follow yang. A woman has the "three obediences," following without making her own decisions, and after her husband's death, she follows her son. Therefore, the character "zi" is used to determine virtue. If the Heavenly Stem and Earthly Branch are considered separately for virtue, they would both follow their respective husbands. But when considered together, they leave the husband's position and follow the son instead. Thus, the virtue of "zi" is associated with Jia, because "zi" belongs to water and water is the mother of wood (water nourishes wood, and wood is the son of water). The other branches follow this pattern as well.

一從月氣為德者，德不孤立，對之以刑。德為陽以從干，刑為陰以從坤。亦如人之治政，刑德兩施：德有慶賜爵賞，所以配陽；刑有殺罰削奪，所以配陰。故王者日蝕則修德，月蝕則修刑。

The fourth method determines virtue based on the hexagram energy of each month. Virtue cannot exist in isolation; it must have "punishment" as its counterpart. Virtue belongs to yang, so it follows the hexagram Qian (Heaven); punishment belongs to yin, so it follows the hexagram Kun (Earth). This is similar to governance in human society, where both punishment and virtue are used together. Virtue includes rewards, celebrations, and granting titles, which are yang; punishment includes executions, punishments, and revoking titles, which are yin. Therefore, when a king encounters a solar eclipse, he should improve his virtuous governance, and when he encounters a lunar eclipse, he should regulate his punishments.

董仲舒《春秋繁露》云：天道之常，一陽一陰。陽者天之德，陰者天之刑。陰陽以終歲之行，以觀天之所親任，可以見德刑之用矣。然天之任陽不任陰，好德不好刑，故陽出而積於夏，任德以歲事；陰出而積於冬，錯刑以空處也。太公云：人主舉事善，則天應之以德；惡，則天應之以刑。此並陰陽相對，德不獨治，須偶之以刑也。

Dong Zhongshu in "Chunqiu Fanlu" says: The regular pattern of the heavenly way is one yin and one yang. Yang is the virtue of heaven, and yin is the punishment of heaven. Observing the course of yin and yang through the whole year, and seeing which side heaven is close to and entrusts with tasks, one can understand the function of virtue and punishment. Heaven uses yang but not yin, and prefers virtue over punishment: thus yang energy arises and accumulates in summer, entrusting the agricultural affairs of the year to virtue; yin energy arises and accumulates in winter, leaving punishment in a state of idleness. Jiang Taigong said: When a ruler acts properly, heaven responds with virtue; when he acts improperly, heaven responds with punishment. All this shows that yin and yang are opposite to each other, and virtue cannot govern alone; it must be combined with punishment.

從干巛二卦之氣者，十詤韋卦用事，自十一月而陽氣動，陰爻變；四月乾卦用事，自五月而陰氣動，陽爻變。故黃鐘蕤賓，陰陽之氣始也，德刑在焉。建子之月，坤初六爻變為陽，復卦用事，陽氣動於黃泉之下，陰氣布在蒼天之上，為德在室，而刑在野。建丑之月，坤六二爻變為陽，臨卦用事，陽氣稍出，萬物萌芽，陰氣將降，威怒已衰，為德在堂，而刑在街。

Now, considering the influence of the Qian and Kun hexagrams to determine the principles of punishment and virtue. In the tenth month, the Kun hexagram is in charge, but the original text says '十詤韦卦用事' which has errors and omissions. From the eleventh month, yang energy begins to emerge, and the yin lines of the Kun hexagram change one by one from the bottom up to yang lines. In the fourth month, the Qian hexagram is in charge, and from the fifth month, yang energy begins to decline, and the yang lines of the Qian hexagram change one by one from the bottom up to yin lines. Therefore, the two tones Huangzhong (eleventh month) and Rui Bin (fifth month) are the starting points of yin and yang energies, and punishment and virtue are connected to these points. In the month of Jianzi (eleventh month), the first line of the Kun hexagram changes to yang, forming the hexagram Fu, which is in charge. Yang energy begins to emerge from beneath the earth, while yin energy spreads across the heavens. At this time, virtue is within the inner chamber, and punishment is in the outskirts. In the month of Jianchou (twelfth month), the second line of the Kun hexagram changes to yang, forming the hexagram Lin, which is in charge. Yang energy begins to show slightly, and all things start to sprout. Yin energy is about to descend, and the severe punishment of the cold season has already weakened. At this time, virtue is on the hall, and punishment is in the marketplaces.

建寅之月，坤六三爻變為陽，泰卦用事，陽氣已達，陰氣降入，陰陽交泰，萬物抽其牙葉，為德在庭，而刑在巷。建卯之月，坤六四爻變為陽，大壯卦用事，陽氣上騰乎天，陰氣下入乎地，陰陽氣交，萬物成出，德刑俱會於門。建辰之月，坤六五爻變為陽，夬卦用事，陽氣上達，陰氣衰微，為德在巷，而刑在庭。建巳之月，坤上六爻變為陽，純陽用事，陽氣大盛，陰氣消除，萬物悅壯，無復刑殺，為德在街，而刑在堂。

In the month of Jiapan (the first lunar month), the sixth line of the Kūn hexagram becomes yang, transforming into the Tai hexagram, which governs the season. Yang energy has already become通畅, and yin energy descends underground. Yin and yang are in harmonious union, and all things sprout buds and leaves. At this time, virtue is in the courtyard, and punishment is in the alleyways. In the month of Jiemao (the second lunar month), the sixth line of the Kūn hexagram becomes yang, transforming into the Dazhuang hexagram, which governs the season. Yang energy rises to the heavens, and yin energy sinks into the earth. The two energies intersect, and all things take form and emerge. At this time, punishment and virtue meet at the gate. In the month of Jichen (the third lunar month), the fifth line of the Kūn hexagram becomes yang, transforming into the Guai hexagram, which governs the season. Yang energy ascends, and yin energy wanes. At this time, virtue is in the alleyways, and punishment retreats to the courtyard. In the month of Jisi (the fourth lunar month), the top line of the Kūn hexagram becomes yang, transforming into the Qian hexagram, which is entirely yang and governs the season. Yang energy is at its peak, and yin energy is completely eliminated. All things rejoice and grow strong, with no punishment. At this time, virtue is in the marketplace, and punishment retreats to the hall. It is evident that virtue moves from within outward, while punishment moves from outside inward, advancing and retreating in exactly opposite directions.

建午之月，乾初九爻變為陰，遘卦用事，陰氣動於黃泉之下，陽氣佈於蒼天之上，為德在野，而刑在室。建未之月，乾九二爻變為陰，遁卦用事，陰氣稍升，陽氣將損，萬物壯極，皆以衰老，為德在街，而刑在堂。建申之月，乾九三爻變為陰，否卦用事，陽氣沈退，陰氣進升，陰陽否隔，殺威方盛，為德在巷，而刑在庭。

In the month of Wu (May), the first line of the Qian hexagram becomes yin, transforming into the Gou hexagram, which governs the period. Yin energy begins to stir beneath the yellow springs, while yang energy spreads across the heavens. At this time, virtue retreats to the outskirts, and punishment enters the inner chambers. In the month of Wei (June), the second line of the Qian hexagram becomes yin, transforming into the Dun hexagram, which governs the period. Yin energy gradually ascends, and yang energy is about to diminish. All things reach their peak of prosperity and then begin to wither. At this time, virtue is present in the marketplaces, and punishment is in the hall. In the month of Shen (July), the third line of the Qian hexagram becomes yin, transforming into the Po hexagram, which governs the period. Yang energy descends and retreats, while yin energy ascends and rises. Yin and yang are separated and uncommunicative. The severe and sharp forces are at their height. At this time, virtue is in the alleys, and punishment is in the courtyard.

建酉之月，乾九四爻變為陰，觀卦用事，陽氣內入，陰氣外施，陰陽合爭，萬物變衰，為德在門，刑復會於門。建戌之月，乾九五爻變為陰，剝卦用事，陽氣將盡，陰氣上達，萬物枯悴，殺害盛行，為德在庭，而刑在巷。建亥之月，乾上九爻變為陰，純坤復位，陽氣消除，陰氣大盛，萬物收藏，未見刑犯，為德在堂，而刑在街。此刑德二事，出入向趣，皆以用之，彌忘拙鑿。遇德則吉，逢刑則凶，故於此釋。

In the month of You (August), the fourth line of the Qian hexagram changes to yin, forming the Guan hexagram, which becomes dominant. Yang energy turns inward, while yin energy spreads outward. Yin and yang contend, and all things transition from prosperity to decline. At this time, the Hour Virtue is at the door, and punishment again converges at the door. In the month of Xu (September), the fifth line of the Qian hexagram changes to yin, forming the Bo hexagram, which becomes dominant. Yang energy is about to be exhausted, while yin energy ascends. All things wither and appear weary, and the energies of killing and injury prevail. At this time, the Hour Virtue is in the courtyard, and punishment is in the alleyways. In the month of Hai (October), the top line of the Qian hexagram changes to yin, reverting to the pure yin Kun hexagram. Yang energy is completely exhausted, while yin energy is greatly dominant. All things are stored away, and there is no further punishment. At this time, the Hour Virtue is on the hall, and punishment is in the marketplace. These two matters, one going out and one coming in, each with their own direction, are used by diviners. The more they use them, the more they find them not to be forced or fabricated. When encountering the Hour Virtue, good fortune arises; when encountering punishment, misfortune occurs. Therefore, here we explain them.