The Taiyi Jinjing Shi Jing (Tang Dynasty, compiled by Wang Ximing)

太乙，天帝之神也。下司九宮，中建皇極。欽若則彝倫攸敘，怠棄三正，錯亂五常。黃帝以惠迪吉而為五帝之聖，大禹戒從逆凶而衍九疇之文。炎漢高祖受命，張良秘金刀之錄；吳主爭權，劉悵演炎旌之祥。神用於不言之載，容化於無為之間。閉戶而休咎自徵，拂鑑而毫髮皆極。非主精妙物、執契於混油之始者，又何足以知之？

The "Taiyi" is the name of a divine being of the heavenly emperor, who oversees the nine palace directions below and establishes the "Huangji" as the highest principle of governance in the center. When a ruler respects and follows the heavenly way, human relationships and moral order become clear and orderly; but once he becomes negligent or abandons the established systems of Xia, Shang, and Zhou dynasties, the five cardinal virtues will become disordered. The Yellow Emperor became a sage among the Five Emperors because he understood that following the way brings good fortune; Great Yu derived the text of the "Nine Categories" in the "Book of Documents" (Shangshu·Hongfan) because he warned against the dangers of going against the way. Han Gaozu received the mandate of heaven, and Zhang Liang kept the secret record of the red knife symbol; Sun and Wu's rulers contended for power, while Liu Chang interpreted the auspicious signs of the flourishing Han dynasty. The subtlety of this system of divination operates silently, encompassing change within non-action: good and bad fortune naturally manifest without leaving the door, and wiping the mirror surface reveals every minute detail. Unless one can control the subtlest things and hold the key at the very beginning of chaos, how could one truly understand it?

愛發上元，迄是帝載，幾千年而一聖，數百年而一賢。得隩隅有登龍之喜，窺閉鍵而若重關之隔。沿波獨往，泛滄海而不歸，討本窮源，恃孟門之嶄絕。至於計神審物，天日司奸，一三置將之數，四六對絕之氣，掩迫孤單，閉杜十精。喉交較以八節占水早，九州島言吉凶，五將定主客，亦猶兵戈勝負。

This discipline begins with the upper beginning and proceeds up to the dynasties of emperors, producing a saint once in thousands of years and a virtuous person once in hundreds. Those who偶然 glimpse the path are delighted as a carp leaps over the Dragon Gate; while those without the key trying to pry open a locked door are like trying to cross through countless barriers. Some follow the tributaries alone, drifting into the vast ocean and never looking back; others seek the source but are blocked by the perilous cliffs of Mengmen Mountain. As for using the "Ji Shen" to examine things, the "Tian Mu" to detect villains, and using numbers like one and three to arrange generals, using numbers like four and six to judge dangerous positions, and the various categories such as "Yan," "Po," "Gu," "Dan," and the ten "Jing" that block and close off, as well as comparing the eight seasonal energies to predict drought and flood, using the nine regions to determine fortune and misfortune, and using the five "Lai" to determine host and guest, all these are like battles with weapons, each having a definite rule.

丘明受經而作傳，見非公谷；子夏師聖而序詩，復殊毛魯。學而時習之，攻乎異端；籠他人之口，未忘已拙。以鼓測海，以管窺天；心見之外，愚衷謂盡。或指陳實錄，或涎錫嘉名。正二局，有陰陽之殊；糾六壬，附時計之謬。淮南分野，縱博我以多聞；黃道日躔，競有疑而則闕。源流則廣，枝葉扶疏。孤裘同士薦之風，玉石抵崑山之鵲。雖億則屢中，時自賢於仲尼，而謀之不藏，且推過於季氏。王大實遂偃弊風，國之事多惟慚德。

Left丘Ming personally received the principles of the Spring and Autumn Annals and wrote the Zuo Zhuan, yet he was criticized by the Gongyang Zhuan and Gu Liang Zhuan schools; Zi Xia studied under Confucius and composed the prefaces to the Shi Jing, but his transmission differed from the Mao Shi and Lu Shi schools: this shows that transmitting the classics has always been difficult to reach agreement. Later, those who studied Taiyi often learned to review the material at the right time, yet often wasted their efforts on heretical doctrines; they were only concerned with silencing others, forgetting that they themselves were clumsy. They used a drumstick to measure the depth of the sea, and a bamboo tube to observe the vastness of the sky. Whatever they could not think of themselves, they would declare that there was no other principle in the world. Some of these people at least spoke honestly, while others merely took beautiful names: they corrected the two sections of Yin Dun and Yang Dun, claiming there was a distinction of yin and yang within them; they connected the Six Rens and fabricated errors in time calculation; when discussing the nine regions of the Huainan region, they could overwhelm me with their extensive knowledge; when discussing the degrees of the Yellow Path, they would omit entire passages when faced with difficulties. This discipline originally had a broad source and flourishing branches, but now it is like a fox fur coat that only becomes valuable through the praise of many people, treating the stones from Kunshan as jade. They occasionally guessed correctly and took it as surpassing Confucius; once their plans failed, they would blame the Ji family and others. Wang Dashi intended to eliminate this decadent trend, but due to the complexity of state affairs, he left many regrets behind.

伏惟開元皇帝陛下明極稽疑，睿聖作範，察璇璣以齊七政，制禮樂以穆百揆，明太乙之威神，封泰山之能事，高視萬古名言。謂何神嘉承日月之照，荷覆躊之廣，參沼賜於金馬，觀秘籍於蘭臺。磋此《式經》，有乖微旨。乃上稽天象，中跡算術，下統人事，旁貫歲時，考帝先於神女之符，歷載紀於蒼頡之筆，甲乙之終數、宮元之往復、奇偶之二算、勝負之八門，與人惎法式之愆、陣圖水火之失、禮樂不興之論、周宇狂簡之文，或義通而即流，或理僻而便削，皆考經義，以一貫之。

I respectfully think: Your Majesty, the Emperor of Kaiyuan, is extremely discerning and capable of resolving doubts, establishing a model for the world with your wise and virtuous virtue. You examine the Xuanji Yuheng to correct the movement of the sun, moon, five planets, and the seven celestial bodies; you create rites and music to harmonize the officials. Your Majesty deeply understands the divine and mysterious power of "Taiyi", achieving the grand ceremony of the Fengshan on Mount Tai. Your vision is far-reaching, truly worthy of being called a saying of all time. How can I, with no virtue or ability, be honored with the grace of the sun and moon shining upon me, and receive the vast protection of heaven and earth? I have been allowed to participate in the rewards at the Jinma Gate and to consult the secret archives at the Lantai. I lament that the current "Shijing" is greatly deviating from the subtle essence of Taiyi. Therefore, I have examined the heavenly phenomena, relied on arithmetic, unified human affairs, and connected the seasons. I have verified the symbolic formulas passed down from the Yellow Emperor from the Nine Heavens, calculated the years since the time when Cangjie created characters, and examined the final numbers of the Jia and Yi day-counting system, the sequence of the Palace Yuan's cycle, the two methods of calculation based on odd and even numbers, the eight gates used to determine victory or defeat, and the mistakes in the use of formulas by people, the errors in the arrangement of battle formations that do not conform to the nature of water and fire, the discussions about the lack of rites and music, and the exaggerated and empty words in the world. All the meanings that can be understood are collected and passed on, while those that are obscure are directly deleted. Everything is decided by the meaning of the classics, and all these are unified under one consistent principle.

穆若蕙婉，聲如玉振。夫詩對惠連，輒得嘉句；筆因樂廣，便至能文。萬殊皆極而同歸，獨見忘言而既驗。校之以元紀，又精之以日時。代謀於述作之前，總括於天人之際。會披覽得意之妙，動契合如神之在，亦曠代之能事也。經凡十卷，名曰《太乙金境式經》。若筆削後於孔明用賢，則子房升堂，風后入室，宋琨樂產，李淳風屬，可座廊廡之下，如以爾言過矣。將侯來哲。

The entire work is as graceful as fragrant herbs, its rhythm as resonant as jade chimes. Xie Lingyun composed poetry and often achieved excellent lines when meeting his cousin Xie Huiian; Wei Jie's writing became fluent after being guided by Yue Guang. I also hope to meet such an understanding person. All different paths eventually converge, and unique insights need no further explanation—they naturally take effect. I first verified the text using the Upper Yuan calendar, then refined it further with daily and hourly calculations. Before putting pen to paper, I planned for future generations, summarizing at the intersection of heavenly principles and human affairs. Once readers open the book and understand its meaning, they will grasp its subtleties; once they begin calculations, it will fit perfectly as if a divine presence were guiding them—this is indeed a rare achievement. The entire text consists of ten volumes, titled "The Classic of the Great One's Golden Mirror." If my editing can be compared to Zhuge Kongming's use of virtuous talents, then Zhang Sifang is merely entering the hall, Feng Hou is entering the inner chamber, and figures like Song Kun, Yue Chan, and Li Chunfeng can sit in the hall. However, such a comparison may be excessive, so I leave the judgment to future discerning scholars.

其以歲、月、日、時為綱而以八將為緯，三基五福、十精之類為經亦猶夫歷也。其法以八將推其掩迫、囚擊、關格之類，占內外災福，又推四神所臨分野，占水旱、兵喪、饑饉、疾疫，又推三基、五福、大小游、二限易卦大運，占古今治亂。

This book takes four methods of calculation—by year, month, day, and hour—as its framework, with the Eight Generals as its threads, and treats categories such as "Three Foundations," "Five Blessings," and "Ten Spirits" as the main lines running through it, making the entire structure resemble the arrangement of a calendar. Its specific approach is as follows: first, using the Eight Generals to determine patterns such as "covering," "pressing," "capturing," "striking," "blocking," and "conflicting," and using these to predict calamities and blessings within the court and outside; then calculating the regions associated with the Four Spirits to determine droughts, floods, warfare, disasters, famine, and plague; further, calculating the "Three Foundations" (the foundation of the sovereign, the foundation of the minister, and the foundation of the people), the "Five Blessings," and the Great and Small Tours, combined with the two limits, the changing hexagrams, and the great years, to predict the rise and fall of dynasties throughout history.

俞正夑《癸巳類纂》十史記用蓋天論云：「渾天所有箕義雲；萬物之根棋，徐廣本作橫，則橫非基無疑，大一十神之君棋、臣棋、民棋，沈括《蘿溪筆談》謂是基字，因唐諱改棋，熙寧中，領太史欲正之而未能也。《雲麗漫抄》亦言十神君基、民基。唐明皇諱為碁，至今不改，今所見邱溶太乙淘金歌，已改從基，其亦未之思矣。」

In the "Kui Si Leigao" by Yu Zhengxie of the Qing dynasty, the article "Ten Histories Record the Use of the Gaitian Theory" says: The "root of all things" mentioned by the Ji Zi in the writings of the Huntu school was written as "heng" in Xu Guang's version, showing that the original text should not have been "ji". This point is without doubt. Among the Ten Spirits of Taiyi, the terms "jun qi", "chén qi", and "min qi" were originally all "ji" according to Shen Ku's "Mengxi Bitan", as they were changed to "qi" to avoid the taboo of the Tang dynasty emperor. Those in charge of the Taishi Bureau during the Xining period wanted to restore the original form, but ultimately failed to do so. The "Yunlu Manchao" also refers to the Ten Spirits as "jun ji" and "min ji". The Tang emperor Minghuang changed them to "qi" to avoid the taboo, and this change has not been reversed to this day. The "Taiyi Taojin Ge" by Qiu Rong, which is currently available, has already changed back to "ji", showing that previous scholars did not think about this carefully.

又《九宮紀年論》云：「太乙金鏡式經云：太一十神、五福、君棋，大游、小游、天一、地一、四神，臣棋、民棋、直符，皆天之尊神，行五宮五移而周，」《蘿溪筆談》小遊作太一，四神作十神，直符作九氣，三年一移」，又云：「棋應作基，案其式君棋、臣棋、民棋行十二次天，一行十二宮，或行八卦或行十六神，不得總云行五宮五移而周也。」其下詳論諸法，有一月—移，一年—移，三年一移，四十五年一移，不錄。

Yu's "Discourse on the Nine Palaces and the Calendar" also says: The Ten Spirits of Taiyi mentioned in "The Taiyi Mirror Classic" are the Five Blessings, the King's Base, the Great Movement, the Small Movement, Tianyi, Diyi, the Four Spirits, the Minister's Base, the People's Base, and the Straight Symbol, all of which are exalted deities from Heaven, each "moving through the five palaces and five shifts to complete a cycle." However, the "Dream Pool Essays" records a different account: it writes "Small Movement" as "Taiyi," "Four Spirits" as "Ten Spirits," and "Straight Symbol" as "Nine Qi," and states that the movement occurs once every three years. Yu also says: the character "qi" should be read as "ji"; examining this pattern board, the King's Base, Minister's Base, and People's Base move through the twelve times, Tianyi moves through the twelve palaces, and the other deities move through the Eight Trigrams or the Sixteen Spirits, and cannot be generally described as "moving through the five palaces and five shifts to complete a cycle." This discussion further elaborates on various methods of movement, including one shift per month, one per year, one every three years, and one every forty-five years; here, they are not repeated.

元朝曉山老人輯《太乙統宗寶鑑》序文中曰：「太乙理蘊於數之中，數顯於理之外，主管三元，分佈四方。」

In the Yuan dynasty, the old man Xiaoshan compiled the "Ta Yi Tongzong Baojian." In his preface, he said: The principles of Ta Yi are contained within the calculation of numbers, and numbers reveal these principles beyond form and appearance. Ta Yi oversees the three great eras: Shangyuan, Zhongyuan, and Xiayuan. The deities and ominous influences under its jurisdiction are distributed across the four directions and their respective regions.

何謂十六神，以天有十二次配地十二辰，以天有四時配地有四維，通之十六也。

The so-called "Sixteen Spirits" are formed by pairing the twelve celestial stems with the twelve earthly branches, and then pairing the four seasons of heaven with the four cardinal directions (the four corner positions of乾, 艮, 巽, and 坤). These twelve plus four make sixteen positions, and the names of the spirits listed on the outer layer of the Taiyi chart are arranged according to this system.

自上元以來，歲代綿遠，紀法差殊。雖設繁詞，備而靡用。今從上元甲子到唐開元十二年甲子歲，通前計四萬八百一算。臣按宋琨置元，似童兒戲。推求人紀之年，下求不得日辰，上求不得冬至。自三百餘年，學者何多，逮於淳風，但效尤而已。

From the beginning of the Upper Yuan to today, the period is very long, and different schools have used different systems of reckoning, which differ from each other. Although predecessors have elaborated many complicated methods, which seem complete, in reality they are of no use. Now, starting from the Upper Yuan Jiazi, up to the twelfth year of the reign of Emperor Xuanzong of the Tang dynasty, which is also a Jiazi year, there are a total of forty thousand and eighty-one calculations. The minister examined the system of the beginning of the calendar established by Song Kun, which is almost childish: according to his method, calculating the years of human history, one cannot proceed to calculate the day branches, and one cannot go back to calculate the winter solstice. For more than three hundred years, those who have studied this subject have not been few, but even up to Li Chunfeng, they have only followed his mistakes.

臣今別修甲子元四分曆法，與太乙同元。舉而備用，得上元甲子冬至；引而下之，齊距歲計大乙行官。進不違於四分，退不失於元紀。自上元混沌甲子之歲，至今大唐開元十二年甲子歲，積得一百九十三萬七千二百八十一算。上考注古，每年減一算；下撿將來，每年加一算。

I now intend to revise a new calendar system based on the Jiazi cycle, making it consistent with the starting point of the Taiyi system. Here is the complete set of calculations for reference: by going back, we can determine the winter solstice of the upper beginning Jiazi year; by moving forward, it can align with the degrees of the Taiyi palace in the annual calculation. Moving backward does not contradict the constant numbers of the four-part calendar, and moving forward does not deviate from the order of the original era. From the chaotic Jiazi year of the upper beginning to the current year of Jiazi in the twelfth year of the Taizong era, a total of one million nine hundred thirty-seven thousand two hundred eighty-one calculations have been accumulated. Using this, we can examine ancient times by subtracting one calculation for each preceding year, and check future times by adding one calculation for each subsequent year.

置上元甲子積年，以三百六十去之；不盡，以六十去之；又不盡，命甲子算外，即太歲所在辰也。

The method of determining the position of the Supreme Year: first list the accumulated years since the beginning of the upper period Jiazi, divide by 360 to find the full cycles, then take the remainder and divide by 60 to find the full decades. If there is still a remainder, start counting from Jiazi in the order of the heavenly stems and earthly branches, count the number of the remainder, and then take the next one, which is called 'calculated beyond' by the diviners. The resulting earthly branch is the position of the Supreme Year for the desired year.

置上元以來距所求積年，以周紀法三百六十去之；不盡，紀法六十去之，所得為紀數；不盡，為入紀年數也。

To determine which of the six jis a given year falls into, first list the accumulated years from the beginning of the upper period up to the desired year. Divide this total by the "zhou ji fa" of 360 to find the full cycles; the remainder is then divided by the "ji fa" of 60. The quotient obtained is the number of completed jis. Sixty years make one ji, and six jis together make 360 years, which is one zhou. The remaining remainder indicates the number of years since the beginning of the current ji.

推上元積年，以周紀法三百六十去之；不盡，以元法七十二去之；又不盡，以太乙小周法二十四除之，又不盡，以三約之，為宮數，不滿，為入宮以來年數。其宮數易其命起一宮，順行八宮，不遊中五，算外，即得太乙所在及入官以來年數也。

To determine the position of Taiyi (the Supreme Pole) in the current year, first calculate the accumulated years since the beginning of the upper yuan. Divide this by the "Zhou Ji Fa" (Cycle Method) of 360 to find the full cycles; the remainder is then divided by the "Yuan Fa" (Yuan Method) of 72. If there is still a remainder, divide it by the "Taiyi Xiao Zhou Fa" (Taiyi Small Cycle Method) of 24. If there is still a remainder, divide it by 3, since Taiyi moves to a new palace every three years. The resulting whole number is the palace number, and any remainder less than three indicates the number of years since Taiyi entered that palace. After determining the palace number, start counting from the first palace and proceed through the eight palaces in order, skipping the central fifth palace. Count until reaching the palace number, then move one more palace to determine the current position of Taiyi and the number of years it has been in that palace.

置上元積年，以周紀法去之；不盡，以元法七十二去之；不盡，以天目周法十八去之，不滿者，命起武德，順行十六神，遇武德、大武，重留一算外，即天目所在。

To determine the position of the "Heavenly Eye": first list the accumulated years since the beginning of the upper period, then divide by the Zhou cycle of 360 to remove full cycles; the remainder is then divided by the original method of 72; if there is still a remainder, divide it by the "Heavenly Eye cycle method" of 18; if the remainder is less than 18, start from "Wu De" and count sequentially through the sixteen spirits in order. When encountering "Wu De" and "Da Wu", pause for an extra count. After completing the count, move to the next position, and the resulting spirit position is where the Heavenly Eye is located. The Heavenly Eye serves as the basis for placing Wen Chang and other generals in the Taiyi system, so it must be determined first.

置積年，以紀法六十去之；不盡，命起寅宮，逆行十二辰，算外，即計神所在也。

To determine the position of the "Ji Shen" (Counter God): list the accumulated years since the beginning of the upper period, divide by the sixty-year cycle, and take the remainder. Starting from the寅 (Yin) palace, count backwards through the twelve earthly branches according to their order. After counting the number of the remainder, move one step forward to determine the position of the Ji Shen. The Ji Shen is a key position in the annual calculation, paired with Taiyi (the Supreme Ultimate), and is essential for calculating the numbers of the master and guest forces. Therefore, it must be determined first.

假令太歲在子，合神在丑，逆行十二辰，十二年一周天矣。

"The 'Heavenly God' is based on the concept of the Earthly Branches being in harmony. It pairs with the Master of the Year in a forward and backward manner. For example, if the Master of the Year is in Zi, then the Heavenly God is in Chou. The Heavenly God moves backward through the twelve earthly branches, and over twelve years it completes a full cycle around the Heaven Plate. Zi and Chou are harmonious, Yin and Hai are harmonious, and the rest follow the same pattern. The Master of the Year advances one position forward, while the Heavenly God retreats one position backward, and the two always correspond at the beginning and end."

一紀：二甲仲辰。甲子、甲午，二甲仲辰。十一月建甲子，太乙在一宮，武德為天目，計神寅，合神丑；二紀：二己孟辰。己巳、己亥，二已孟辰。十一月建甲子，太乙在六宮，地主為天目，計神、合神如上同；三紀：二甲季辰。甲辰、甲戍，二甲季辰。十一月建甲子，太乙在一宮，大靈為天目，計神、合神如上同；

A cycle of sixty years is called a jì, and six jìs make a week of three hundred and sixty years. The starting years of each jì differ in terms of the positions of Taiyi and Tianmu. The first jì begins with the two Jia years, the middle chén years, namely Jiazi and Jiawu. Zi and Wu are both middle chén positions. In the eleventh month of this jì, the month builder is Jiazi, Taiyi is in the first palace, and Tianmu is "Wude". The counting god is in寅, and the harmonizing god is in丑. The second jì begins with the two Ji years, the beginning chén years, namely Jisi and Jihai. Si and Hai are both beginning chén positions. The eleventh month also has the month builder as Jiazi, Taiyi is in the sixth palace, and Tianmu is "Dizhu". The counting god and harmonizing god are the same as in the previous jì. The third jì begins with the two Jia years, the end chén years, namely Jiachen and Jiaxu. Chen and Xu are both end chén positions. In the eleventh month, the month builder is again Jiazi, Taiyi is in the first palace, and Tianmu is "Daling". The counting god and harmonizing god remain the same as before.

四紀：二己仲辰。已卯、己酉，二已仲辰。十一月建甲子，太乙在六官，武德為天目，計神、合神如上同；五紀：二甲孟辰。甲申、甲寅，二甲孟辰。十一月建甲子，太乙在一官，地主為天目，計神、合神如上同；六紀：二已季辰。己丑、已未，二已季辰。十一月建甲子，太乙在六宮，大靈為天目，計神、合神如上同。

The fourth era began in the middle of the years Ji Mao and Ji You; in November, the month builder was Jia Zi, and Taiyi was in the sixth palace, with "Wu De" as the heavenly eye, and the counting god and the accompanying god were the same as in the previous eras. The fifth era began in the beginning of the years Jia Shen and Jia Yin; in November, the month builder was Jia Zi, and Taiyi was in the first palace, with "Di Zhu" as the heavenly eye, and the counting god and the accompanying god were the same as before. The sixth era began in the end of the years Ji Chou and Ji Wei; in November, the month builder was Jia Zi, and Taiyi was in the sixth palace, with "Da Ling" as the heavenly eye, and the counting god and the accompanying god were also the same as in the previous eras. Thus we can see: among the six eras, Taiyi alternates only between the first and sixth palaces, while the heavenly eye rotates among the three deities Wu De, Di Zhu, and Da Ling, and the counting god and the accompanying god remain unchanged across all six eras.

凡三十有六紀。三十年有三百六十個月，是以甲子、甲午同建，太乙、天目、計神、合神用式之法一同歲計之法，占驗逆顧，其義亦等。臣今為李淳風定時，計五日六十時。法以為月，計五年六十個月，三十年有三百六十個月。若有閏月，只以逐月節氣時刻為正也。

The six at the top are repeated in cycles, totaling thirty-six cycles. Thirty years correspond to three hundred and sixty months, so the month builder in the Jiazi year is the same as in the Jiawu year. The methods for using the heavenly stems and earthly branches in monthly calculations are exactly the same as those for annual calculations. When making predictions, one can proceed in the order of time or reverse the order for verification, and the meanings derived are equivalent. Now, I wish to correct and supplement Li Chunfeng's method for determining the time of day: five days consist of sixty hours. Applying this proportion to the months, five months make sixty months, and thirty years make three hundred and sixty months. If there is a leap month in between, the month builder should be determined solely by the time of the solar term transition for each month, without needing a separate calculation.

章歲六百五十七。章月八千七百二十六。閏差二十秒二十七。周紀法三百六十。秒法二百。

The various constants used in calculating the months are as follows: the chapter age is 657 years, the chapter month is 8,726 months, the intercalation difference is 20 and 27 seconds, the weekly cycle method is 360, and the second method is 200. "Chapter age" refers to the number of years within a chapter, and "chapter month" refers to the number of months within the same chapter. Multiplying these two and dividing gives the monthly count and the intercalary remainder for each year. The "intercalation difference" and "second method" are used to accumulate the accumulated seconds and minutes each month, to determine which month should have an intercalary month. The weekly cycle method of 360 is a constant for a six-year cycle, and it is used to eliminate whole cycles in annual and monthly calculations.

置積年，所求年以章月乘之。章歲而一，為積月；不盡，為閏餘。若有餘月，隨數加之。

To calculate the accumulated months: first list the accumulated years since the beginning of the era for the desired year, multiply by 8726 chapter months; then divide the resulting number by 657 chapter years. The quotient is the accumulated months since the beginning of the era, and the remainder is called "leap remainder." If there are additional months, add them directly to the accumulated months.

置閏餘，每月加閏差及秒，滿法從閏餘，或六百三十秒者，以上無中氣者，詳之。

To determine the leap month: list the leap remainder obtained earlier. Then, every month thereafter, add the leap difference of twenty and twenty-seven seconds. When the seconds accumulate to two hundred, carry over the excess to the leap remainder. The month in which the accumulated seconds exceed six hundred thirty is the month without a solar term, and should be designated as the leap month. However, it is also necessary to verify the actual situation of the solar terms for that month, and only after careful examination can the leap month be confirmed.

置積月，以周紀法三百六十去之；不盡，以元法七十二去之，又不盡，以太乙小周法二十四去之；不盡，以三約之，為宮數；不滿，為入宮月數。命起一宮，順行八宮，不遊中五，算外，即月計大乙所在也。

To determine the palace where Taiyi (the Supreme Martial God) resides in the lunar month count: list the accumulated months, divide by 360 using the Zhou Ji method to get a full cycle; take the remainder and divide it by 72 using the Yuan method; if there is still a remainder, divide it by 24 using the Taiyi small cycle method; if there is still a remainder, divide it by 3; the resulting whole number is the palace number, and any remainder less than 3 is the number of months since Taiyi entered that palace. After determining the palace number, start counting from the first palace and proceed through eight palaces in order, skipping the central fifth palace. When the count reaches the palace number, move one more palace to determine where Taiyi resides in the lunar month count. The method for calculating the monthly count is the same as the annual count, except that "year" is replaced with "month," so Taiyi moves to a new palace every three months in the monthly count.

置入月紀，以天目周法十八去之；不盡，命起武德，順行十六神，遇陰德大武，重留一算外，即天目所在也。

To calculate the monthly heavenly eye (天目): list the number of months since the beginning of the current era, divide by the heavenly eye cycle of eighteen; if there is a remainder, start counting from "Wude" (武德) and proceed in the order of the sixteen spirits. When encountering "Yinde" (阴德) and "Dawu" (大武), which are positioned in the four cardinal directions, pause for an extra count. After completing the count, move to the next position and use that spirit as the monthly heavenly eye. Each of the four cardinal direction spirits occupies two counts, which is why the number of sixteen spirits does not match the eighteen cycle.

置積月，以紀法去之；不滿者，以周法十二去之；不盡，命起寅，逆行十二辰，算外，即計神所在也。

To determine the counting god (计神) for the month, list the accumulated months, divide by the sixty-jing cycle to get the full cycle; the remainder is then divided by the twelve-week cycle. If there is a remainder, starting from the寅 position, count backwards through the twelve earthly branches for the number of the remainder, and take the next position as the counting god. The counting god moves one earthly branch each month, completing a full cycle in twelve months.

日法四十九。 月法二千四百四十七。 朔策二十九。 小餘二十六。紀法六十。

The constants used in calculating the days are as follows: the daily method is 49, the monthly method is 2447, the lunar cycle is 29, the small remainder is 26, and the cycle method is 60. The daily method is the denominator used to divide a day into 49 parts. The monthly method is the total number of these parts equivalent to a synodic month. The lunar cycle of 29 days plus a small remainder of 26 parts equals the actual length of a synodic month. The cycle method of 60 is the number of days in a complete cycle of the heavenly stems and earthly branches.

置積月，以月法乘之，日法而一，為積日；不盡，為小餘。以紀法除積日，不滿，為月餘。命甲子算外，即所求年天正十一月經朔日辰及小餘也。若更有餘日，隨數加之，求次月，每月加二十九，小餘三十六，各加法求之。弦望，算如大曆，非此所須也。

To determine the day branch of the new moon for each month: list the accumulated months, multiply by the monthly method of 2447, then divide by the day method of 49. The resulting whole number is the accumulated days, and the remainder is the small remainder. Divide the accumulated days by the cycle method of 60. The part that does not reach 60 is the remainder for the month. Starting from Jiazi, count the number of the remainder and take the next one as the heavenly stem and earthly branch, which gives the day branch of the new moon of the tenth month of the year. Record this along with the small remainder. If there are additional days from the remainder, add them as they are. To calculate the new moon of the next month, add 29 days and 36 parts to the current month. Continue this method for each subsequent month. As for the calculation of the upper conjunction, lower conjunction, and full moon, they follow the same method as the common great calendar, which is not required for this text and will not be explained further.

臣按：梁武帝天監三年甲申，帝召太史虞履、樂茂言之：今日太乙在八宮，和德為天目，文昌將外宮，迫災輕，無所畏也。退謂人曰：外宮迫，為外人之迫也。四十年後辰巳之年，同於桓公大亨之歲。臣以日計太乙求之，積至梁天監三年甲申歲六月八日，凡得七億七百五十萬一千六十一日。以周紀法除之，得一百九十六萬五千二百八十；不盡二百六十一，以小紀法除之，得四；不盡二十一，為入第五紀也。

The minister examined historical events: In the third year of Liang Wudi's Tianjian reign, which was the Jiashen year, Emperor Wudi summoned the historian Yu Lu and the musician Luo Mao to inquire about the state of affairs. They replied that on that day, Taiyi was in the eighth palace, with "Harmony and Virtue" as the heavenly eye, and the Wen Chang star would fall into the outer palace, creating an "external pressure" in the outer palace, resulting in minor disasters, which were not to be feared. After court, they privately told others that the pressure in the outer palace referred to the pressure from outsiders; forty years later, in the years of Chen and Si, the situation would be similar to the year when Duke Huan of Lu had a grand feast. The minister verified this using the daily Taiyi method: Accumulating up to the sixth day of the sixth month in the Jiashen year of the third year of Tianjian, he obtained a total of seven hundred million and seven hundred fifty thousand one hundred and six days. Dividing this by the Zhou Ji method of three hundred and sixty, he obtained one hundred ninety-six thousand five hundred and twenty, with a remainder of two hundred and sixty-one. Then dividing by the small Ji method of sixty, he obtained four, with a remainder of twenty-one, indicating that this day fell within the fifth Ji. The calculation matches what the two men said, proving that the daily method is indeed reliable.

置積日，以周紀法三百六十去之；不盡者，以元法七十二去之；不盡，以大乙小周法二十四去之；又不盡，以三約之，不滿，為入宮以來日數。其宮數命起一宮，不遊中五，算外，即太乙所在也。

To determine the position of Taiyi (the Supreme Pole) in the daily count: list the accumulated days from the beginning of the upper period up to the desired day, divide the total by 360 using the Zhou Ji method to find the full cycle; take the remainder and divide it by 72 using the original method; if there is still a remainder, divide it by 24 using the Taiyi small cycle method; if there is still a remainder, divide it by 3; the quotient is the palace number, and the remainder is the number of days since entering the palace. After determining the palace number, start counting from the first palace and proceed in order, skipping the fifth palace in the center. Count until reaching the palace number, then move one more palace to determine the position of Taiyi on that day. The method for daily, annual, and monthly counts is the same, except that Taiyi moves to the next palace every three days in the daily count.

置積月，以元法七十二去之；不盡，以天目周法十八去之；又不盡，命起武德，順行十六神，遇陰德大武，重留一算外，即天目所在也。

To determine the position of the Heavenly Eye in the monthly calculation: list the accumulated months, divide by the cycle of seventy-two to get the full cycles; take the remainder and divide it by the Heavenly Eye cycle of eighteen; if there is still a remainder, start from 'Wu De' and count sequentially through the sixteen spirits. When encountering 'Yin De' and 'Da Wu', these two spirits are counted twice. After completing the count, move one step forward to determine the position of the Heavenly Eye. The Heavenly Eye corresponds with Taiyi in sequence, and it is the fundamental position for placing the Wen Chang and Shi Ji generals. Therefore, the calculations for years, months, and days all need to be determined first.

置積日，以紀法六十去之；不盡者，又以計神十二除之。命起寅，逆行二十辰，算外，即計神所在也。

To determine the position of the Ji Shen (accounting god) for a given day: list the accumulated days, divide by 60 using the Jifa (cycle method) to get a full cycle; if there is a remainder, divide this remainder by 12, which is the number of days for one cycle of the Ji Shen. Starting from the position of Yin, count backwards through the Sheng (earthly branches) according to the remainder, and when the count is complete, move to the next position. The resulting Sheng position is where the Ji Shen is located for that day. The Ji Shen moves through one Sheng position each day, completing a full cycle in twelve days.

全數二十六萬口千八百四十三。氣法三萬三千一百九十三。辰法三千六百八十二。 小分十二分之也。 半辰法一千三百四十一。 小分十二分之四半。

The constants used in time calculation are as follows: the total number is twenty-six thousand □ hundred and eighty-three (the original text has a missing character marked as 'mouth', so it is not conjectured), the qi method is thirty-three thousand one hundred and ninety-three, the shen method is three thousand six hundred and eighty-two, the small fraction is twelve parts, the half shen method is one thousand three hundred and forty-one, and the small fraction is four and a half parts. The 'total number' represents the total fraction of one year, the 'qi method' is the fraction each of the twenty-four solar terms occupies, the 'shen method' is the fraction corresponding to one hour, and the 'half shen method' is half of the shen method, used for rounding up or down in time addition calculations.

置積年減一，以餘數乘之，為氣法，而一，得積日；不盡，為小餘。以紀法去積日，不盡，為大餘。命大餘起甲子，算外，天正冬至日辰也。

To find the day branch of the winter solstice: first subtract one year from the accumulated years, then multiply the remainder. Divide this product by 33,193 according to the solar term method, the quotient is the accumulated days, and the remainder is the small remainder. Divide the accumulated days by 60 according to the cycle method, the remainder is the large remainder. Starting from Jiazi, count forward through the heavenly stems and earthly branches according to the large remainder, advancing one position each time until the corresponding stem and branch is reached. This stem and branch is the day branch of the winter solstice of that year.

置天正冬至大小餘，每氣加一十五日，餘七十三千五秒，滿二十四，從小餘一；滿氣法，從大餘；滿紀法去之，即次氣大、餘也。

To determine the next solar term, start with the excess days (大余) and excess minutes (小余) of the day of the winter solstice (天正冬至). Add fifteen days for each solar term, along with an additional seventy-three minutes and fifteen seconds. When the seconds accumulate to twenty-four, they convert to one minute of the excess minutes (小余). When the excess minutes accumulate to the term's cycle (气法), they convert to one day of the excess days (大余). When the excess days accumulate to sixty (纪法), subtract one full cycle. Continue this process, and the resulting excess days and excess minutes will indicate the day and remaining minutes of the next solar term's transition. By sequentially adding fifteen days for each of the twenty-four solar terms, all solar terms of the year can be determined.

先置半辰法之數一千三百四十一、以十二小分之四半，以夏至小餘加之，滿法而一，所得為辰數。命甲子算外，則氣應加時也。不盡，以三乘之，辰法而一，得致命為一辰中孟、仲季數也。

To determine the exact time of the solar term transition: first take the half-chi method of 1341, add to it four and a half parts of the twelve, and then add this total to the small remainder of the summer solstice. When the resulting number reaches the chi method, increment by one, and the quotient is the chi number. Using this chi number, count from Jiazi, and when the count is complete, move to the next one; this is the time when the solar term should transition. If there is a remainder that does not divide evenly, multiply it by three, then divide by the chi method. The resulting number determines which of the three parts—beginning, middle, or end—of the hour it falls into. The ancient method divided each hour into three parts: beginning, middle, and end, so multiplying by three is necessary.

陽遁太乙冬至起乾，陰遁太乙夏至起巽，凡一百八十二日三萬二千二百九十三分日之二萬三十五，為太乙變行。

The Taiyi moves in the time count divided into Yang Dun and Yin Dun. Yang Dun begins from the winter solstice, with Taiyi starting from the Qian position (the first palace). Yin Dun begins from the summer solstice, with Taiyi starting from the Xun position (the ninth palace). From the winter solstice to the summer solstice, and from the summer solstice to the winter solstice, each period lasts 182 days and 32,293 parts of a day, two ten thousand and thirty-five parts. At this time, Taiyi changes from moving forward to moving backward, or from moving backward to moving forward. This change is called "Taiyi transformation."

臣希明按，張良云：太神變順氣為餘。今置上元所求年天正積日及小餘，先加半辰法，以辰法除之，得為加時辰數。及置積日減一，以十二乘之，並加時辰數，為天正時實。以周紀法去之；不盡，為入紀實。置入紀實，以太乙周法去之，餘者，以三約之，為宮數；不盡，為入宮時數。命起第一宮，順行入宮，不遊中五，算外，即天正加時太乙所在宮也。

Minister Wang Ximing examined: Zhang Liang once said that the deity Taiyi changes its direction according to the solar terms, and the remaining fractions are generated from this change. Now, to calculate the position of Taiyi at the time of the winter solstice: first list the accumulated days and the remainder from the beginning of the upper period to the desired year's Tianzheng, add the remainder to half the hour method of 1341, then divide by the hour method of 3682, and the result is the hour number at the time of the winter solstice. Then take the accumulated days and subtract one day, multiply by twelve (since one day has twelve hours), and combine this with the previously calculated hour number to form the "Tianzheng hour actual." Divide the "Tianzheng hour actual" by the Zhouji method of 360, and the remainder is called "entry into the Zhouji actual." Then take the "entry into the Zhouji actual," divide it by the Taiyi Zhou method of 24, and the remainder is divided by three; the quotient is the palace number, and the remainder is the number of hours since entering the palace. Starting from the first palace, proceed in order through eight palaces, skipping the central fifth palace, and when the count is full, proceed to the next palace. The resulting palace is where Taiyi is located at the time of the winter solstice.

置天正積日及小餘秒，加陽遁一百八十二日三萬二千二百九十三分日之二萬三十五為小餘秒。滿秒法，從小餘一；不盡，為秒。其小餘先加半辰法，以辰法除之，為加時辰數。乃置積日減一，以十二乘之，併入加時辰數，為夏至加時實，亦以周紀除之；不盡，為入紀實。

To calculate the Taiyi at the time of the summer solstice: first list the accumulated days and the small remainder and seconds of Tianzheng. Add to this 182 days and 20,350 parts of a day from the Yang Dun period. Combine this into the small remainder and seconds. When the seconds accumulate to the full seconds method, they are converted into one part of the small remainder, and any remaining seconds are kept as seconds. The resulting small remainder is first added to half the hour method, which is 1,341. Then divide by the hour method to get the number of hours for the added time. Then take the accumulated days and subtract one day, multiply by twelve, and combine with the added hour number to form the "Summer Solstice Added Time". Similarly, divide by the Zhou Ji method of 360 to get the remainder, which is the "Entry into the Ji".

置入紀實，以太乙周法二十四去之；不盡，以三約之數；不滿，為入宮時數。命起一宮，順行八官，不遊中五，則為陰遁大乙變行也。

Take the actual number obtained above and divide it by the twenty-four of the Taiyi cycle; if there is a remainder, use three to approximate it, and the result is the palace number. The leftover fraction less than three represents the time since entering this palace. Still start from the first palace and proceed in order through the eight palaces, skipping the central fifth palace. After the summer solstice, when yang reaches its peak and yin begins to arise, Taiyi changes to move according to the Yin Dun method, which is called 'Yin Dun Taiyi changing movement'.