Sixty-four Hexagram Circulation and Prediction Methods and Prediction of Misfortune

其下初合六十四卦流轉推之術：置天元甲寅巳來至受命，以三十二除之，餘不足除者，從乾坤始數，算外主卦，而取世陰陽斷之。世陽從陽，【陽爻三十六。】世陰從陰。【陰爻二十四。】陽從九除，陰從六除，啇得數，陽以三乘之，陰以二乘之，因而半之，即是忌耳。毎取卦月乘之。

The method for calculating the flow of the sixty-four hexagrams begins by listing the accumulated years from the beginning of the heavenly stem Jiayin to the year of the established mandate. Divide this by thirty-two, and take the remainder. Starting from the hexagrams Qian and Kun, count sequentially through them, and the hexagram that falls beyond the count is the main hexagram. Then determine whether the world line (Shi Yao) is yin or yang. If it is yang, use the yang number, as noted by Zheng Xuan, which is thirty-six. If it is yin, use the yin number, as noted by Zheng Xuan, which is twenty-four. For yang, divide by nine, and for yin, divide by six. After obtaining the quotient, multiply the yang quotient by three and the yin quotient by two, then take half of the result, which is the year to be avoided. Each time, multiply by the month governed by the hexagram.

假令賁卦世在初，十一月卦，世屬陽，陽爻三十六，以九除之，商得四，以三乘之得十二，因而半之，是忌耳。假令遁卦世在三，六月卦，世屬陰，陰之爻二十四，以六除之，商得四，以二乘之得六，因而半之，是忌耳。【按：以上二節闡明世卦推算之法，當是後人所附益，今退二字書之。】

For example, in the hexagram Bi, the world line is on the first line, which is the hexagram of the eleventh month. The world line is yang, so a yang line takes 36. Using the all nines to divide, we get 4, then multiply by three to get 12, and take half of that to get 6, which is the year to be avoided. Another example is the hexagram Dùn, where the world line is on the third line, which is the hexagram of the sixth month. The world line is yin, so a yin line takes 24. Using the all sixes to divide, we get 4, then multiply by two to get 8 (the original text says six), and take half of that, which is the year to be avoided. [Comment by the editors of the Siku Quanshu] The above two sections explain the method of calculating the world line, which should be additions by later scholars. Now written two lines lower.

推厄法：以入位年數除之軌合數，算盡厄也。甲乙飢，丙丁為旱，戊己為中興，庚辛為兵，壬癸為水。【按：此節別見後文，疑有重出。】

The method of calculating calamities: use the number of years since the beginning of the reign to divide the combined number of the orbit, and count until the end. The heavenly stem and earthly branch obtained at the end indicates the type of calamity. If it is Jia or Yi, it signifies famine. If it is Bing or Ding, it signifies drought. If it is Wu or Ji, it signifies a period of revival. If it is Geng or Xin, it signifies military disaster. If it is Ren or Gui, it signifies flood. [Comment by the editors of the Siku Quanshu] This section is also mentioned later in the text, and it is likely a repetition.

父相：甲寅景雲元年庚戍，積六萬四千三年算上，至開元九年辛酉，加上十一年算上，以三十二除之，不盡三，名入位年，合入需軌卦。陰爻二十四，以六除之，商得四，二乘之得八，因而半之四，是忌。需卦軌合數一千四百七十二，以入位年三，至甲寅加四算七，除需合數除二，從父相庚申命之，得辛，兵。推子厄用父軌，凡子受位但不得別立軌，乃可救災耳。

By using the father's destiny to calculate: from Jiayin to Gengxu of Jingyun year, there are 64,003 counts, then to Xinyou of Kaiyuan ninth year, adding another 11 counts, dividing by 32, the remainder is three, which is called the "year of entry." This should be placed in the pattern of the Xun hexagram. Xun is yin, taking 24 for the yin line, dividing by six, the quotient is four, then multiplying by two to get eight, then taking half to get four, which is what is to be avoided. The total number of the Xun hexagram is 1,472. Using the entry year three, adding four counts from Jiayin, totaling seven, dividing the total number of the Xun hexagram by seven, the quotient is two. Starting from the father's destiny Gengshen, counting the life span, we get "Xin," which indicates military calamity. To calculate the misfortune of the son, use the father's pattern. All sons who inherit the position must not establish a new pattern, in this way the calamity can be averted.

甲寅先天元年壬子，積六萬四千五年算上，至開元九年辛酉，加九算上，三十二除之，餘五十盡五，合入小畜軌卦。陽爻三十六，以九除之，啇得四，以三乘之十二，因而半之得六，忌十一月。【按：上推算至唐開元九年，亦唐時術士所加也。】

From Jiayin to the first year of the Xian Tian era, Renzi, the total is six thousand four hundred and five counts. From that to the ninth year of the Kaiyuan era, Xinyou, add nine counts. Divide by thirty-two, the remainder is five, which corresponds to the Xiao Xu hexagram. Xiao Xu is yang, so take thirty-six for the yang lines. Divide by yijing (yijing is the term for the number nine in this context), the quotient is four. Multiply by three to get twelve, then take half to get six. The forbidden time is in the eleventh month. [Comment by the editors of the Siku Quanshu] The calculation up to the ninth year of the Kaiyuan era is also an addition by Tang dynasty diviners.

右六十四卦流轉註十二之辰。【按：此句為總題折軌三十六卦位之文，不應在此處，蓋後人以他文闌入，遂將原文移向後耳。】乾初子，坤初未。陽爻折數一爻三十六，計六千九百一十二；陽爻軌數一爻一百二十八，計二萬四千五百七十六；陰爻折數一爻二十之四，計四千六百八；陰爻軌數一爻一百一十二，計二萬一千五百四。陰爻又合折一萬一千五百二十，合二軌四萬一千八十。

The sixty-four hexagrams are arranged in a sequence and paired with the twelve earthly branches. [Comment by the editors of the Siku Quanshu] This sentence was originally meant to serve as the heading for the section titled "Folding Tracks of Thirty-six Hexagrams," and it should not be placed here. It is likely that later editors inserted other text, pushing the original text further down. The first line of the Qian hexagram corresponds to the Zi branch, and the first line of the Kun hexagram corresponds to the Wei branch. For yang lines, each line has a folding number of thirty-six, totaling six thousand nine hundred and twelve; each line has a track number of one hundred and twenty-eight, totaling twenty-four thousand five hundred and seventy-six. For yin lines, each line has a folding number of twenty-four, totaling four thousand six hundred and eight; each line has a track number of one hundred and twelve, totaling twenty-one thousand five hundred and four. The total folding numbers of yin lines amount to eleven thousand five hundred and twenty, and the combined track numbers amount to forty-one thousand and eighty.

於易即位年數術曰：已上各三十二乘之，即得其數，乘軌折之數。世屬陽卦者，以九除之，以三乘之，所得因而半之，則是即位期也；能過此者，三乘所半之數，即終矣。世屬陰卦者，以六除之，以二乘之，所得因而半之，則得即位期也；能過此者，加所得即中期也；復能過此者，以二乘所半之數，即終矣。

The method of using the Book of Changes to calculate the number of years on the throne is: take all the above numbers and multiply them by thirty-two, which gives the required number, that is, the number of tracks and the number of folds. For a hexagram with a Yang World Line, divide by nine, then multiply by three, take half of the result, which is the initial period of reign; if it exceeds this period, multiply the half by three, which is the final period. For a hexagram with a Yin World Line, divide by six, then multiply by two, take half of the result, which is the initial period of reign; if it exceeds this period, add the result to get the middle period; if it exceeds again, multiply the half by two, which is the final period.

以九除之皆盡無餘者，陽以三乘所，則其年當數也。以九、六除之有餘者，以所得乘之，陽得正位増九於所乘，陰得正位増六於所乘，則是位之數也。用陽日者屬陽卦，用陰日者屬陰卦。乾初以六乘者，謂姤也，陰失位在初；坤初以九乘者，謂復也，陽得正位在初。震、兊、離之象，陰所乘之數也；巽、艮之象，四所乘之數，是即位之時年數也。

When using the number nine to divide and the result is exact with no remainder, for yang lines, multiply by three, and the result is the number of years for that year. If there is a remainder when dividing by nine or six, multiply the obtained number by itself. For yang lines that are in the correct position, add nine to the multiplied number; for yin lines that are in the correct position, add six to the multiplied number. This gives the number of years in office. On a yang day, use a yang hexagram; on a yin day, use a yin hexagram. The first line of the Qian hexagram is multiplied by six because it transforms into the Guo hexagram, where a yin line is out of position and occupies the first position. The first line of the Kun hexagram is multiplied by nine because it transforms into the Fu hexagram, where a yang line is in the correct position and occupies the first position. The trigrams Zhen, Dui, and Li use the number obtained from multiplying by yin; the trigrams Xun and Gen use the number obtained from multiplying by four. These are the numbers of years at the time of taking office.

卦軌：軌陽爻六七，以四時乘之，各倍之，爻百二十八；陰爻八六，以四時乘之，各倍之，爻百十二。必用即位年，以即位時太歳呼之，盡算之上，則位之終歳也；算外是未入之年。孔子曰：終始之義在外內焉，進退在二年，觀其政以別知其泰延與否也。

The method of calculating the卦轨: For the yang lines, use six and seven, each multiplied by the numbers of the four seasons, then each doubled, resulting in 128 per line. For the yin lines, use eight and six, each multiplied by the numbers of the four seasons, then each doubled, resulting in 112 per line. It must be calculated using the year of the current reign, and the current heavenly stem is used to refer to it. When the numbers are exhausted, it indicates the last year of the reign; beyond the numbers, it refers to the years yet to come. Confucius said: The principle of beginning and end lies in the distinction between internal and external. Progress and retreat depend on these two years. By observing the affairs of the time, one can discern whether it is a period of stability and continuity or not.

推之術曰：置天元甲寅以來數至受命位之年數，以三十二數除之，不足除者，以乾坤始數算未，即得主歳之卦，知直事之爻在何辰。謂乾直事於十一月子，左行陽辰六；坤直事於六月未，右行陰辰六。陰陽交錯，行於十二辰，一歳十二月而周也。當以即主立時月為政，故曰知直事之爻在何辰也。所屬陰陽爻者也，陽爻三十六、陰爻二十四者，皆世所屬陰陽者也。

The method of calculation is: list the number of years from the beginning of the heavenly stem Jiayin to the year of ascending the throne, divide by thirty-two, and if there is a remainder, count from Qian and Kun in order until reaching the end, thus obtaining the main year's trigram. This indicates which line is in charge during that year. This means that when Qian trigram is in charge, it is in the position of the first month's Zi (rat) in the eleventh month, moving left through six yang chens; when Kun trigram is in charge, it is in the position of the sixth month's Wei (goat), moving right through six yin chens. Yin and yang alternate, covering all twelve chens, completing a cycle in twelve months. The policies should be determined according to the month when the ruler ascended the throne, hence the need to know which line is in charge. The referred yin and yang lines: for yang lines, take thirty-six; for yin lines, take twenty-four, all based on the yin and yang of the world line.

推之法：推世之所屬陰卦者，假令即位之年得遁卦，七月申也，遁六月二陰爻。陰爻二十四，以六除之得四，以二乘之得八，因而半之得四，則即位之期也；能過此者，所乘八歳之中期也；復能過此者，三乘所半十二歳終矣；陰得正位，増六於所乘，為三十六年終矣。

The method of calculation: first explain the method for a卦 with a yin line as the world line. For example, if the year of taking the throne corresponds to the Dùn hexagram, Dùn is paired with the seventh month and the position of Shen. Dùn has two yin lines in June. Take twenty-four for the yin line, divide it by six to get four, then multiply by two to get eight. Take half of that to get four, which represents the initial period. If it exceeds this period, it is eight years, the middle period. If it exceeds that, multiply half of the number by three to get twelve years, which is the final period. If the yin line is in its proper position, add six to the number obtained from the multiplication, making thirty-six years the final period.

推之法【陽卦】：推世之所屬陽卦陰卦者，假令即位之年得賁卦，十月亥也，賁初陽爻三十六，以九除之得四，以三乘之得十二，因而半之則得六，則是即位之期也；能過此者，如所乘得一十，則中期也；復能過此者，三乘所半六得十八年終矣；陽得正位，増九以所乘為五十四；巽、艮之家四所乘得三十六，遠期算。

The method of calculation (for a yang hexagram): Now let us discuss the method of calculation for the world line belonging to a yang hexagram and one belonging to a yin hexagram. For example, if the year of taking the throne corresponds to the hexagram Bi, which is paired with the tenth month, the position of the亥 (Hai) stem, and the first line of Bi is a yang line, take thirty-six, divide it by the number of all nines (yongjiu) to get four, then multiply by three to get twelve, and take half of that to get six, which represents the initial period of rule. If this number is exceeded, such as multiplying to get ten, that represents the middle period. If it is exceeded again, multiply the half of six by three to get eighteen years, which represents the final period. For a yang line that is in its proper position, add nine to the multiplied number to get fifty-four. For the hexagrams Xun and Gen, multiply by four to get thirty-six, which is the furthest period.

天元甲寅歳以來，至宋髙祖劉裕禪晉，歳在庚辰，號為永初元年，凡得積年二百七十六萬八百四十七年算上，以三十二【半六十四卦得三十二，以為法。】除之，不盡十五，入坎離軌。以宋辛酉至周宣帝宣政元年戊戌歳，有一百五十八年。元嘉元年即當魏氏世祖太武皇帝始光元年，以三十二除之，不盡七，命之入大有軌；一本雲不盡十三，為入無妄、大畜軌。

Since the year Jiayin of the Heavenly Stems, up to the time when Liu Yu, the High Ancestor of the Liu Song dynasty, received the mandate from the Jin dynasty, the year was Gengchen, and the era name was changed to Yongchu Year One. In total, 2,760,847 years were counted. Using thirty-two, as noted by Zheng Xuan, out of sixty-four trigrams, half is thirty-two, which is used as the divisor. Dividing, the remainder is fifteen, which is assigned to the trigrams Kan and Li. From the year Xinyou of the Liu Song dynasty to the year Wuxu of the Northern Zhou dynasty's Xuanzhi era, there were 158 years. The first year of Yuanjia coincided with the first year of Shiguang of the Northern Wei dynasty's Taowu Emperor. Using thirty-two as the divisor, the remainder is seven, which is assigned to the trigram Dàyǒu. Another version says the remainder is thirteen, which is assigned to the trigrams Wúwàng and Dàxù.

六月未也，六月位陰爻八，以四乘之八得三十二，以六除之得五餘不盡二，以二乘之得十，因而半之得五初忌；能過此者，如所乘得十；復能過此者，三乘所半五得十五終矣。不忌失位，陰増八，終二十三除之得四十七丙午歳，天下憂重侵逼也，有餘福也。

June belongs to the position of Wei. The position of June corresponds to the eighth yao of yin. Using four to multiply by eight gives thirty-two. Using six to divide thirty-two gives five with a remainder of two. Then using two to multiply gives ten. Taking half of this gives five, which is the initial prohibition. If one can surpass this period, it is like the number obtained by multiplying, which is ten. If one can surpass that, multiply the half taken, five, by three to get fifteen years, which is the final limit. If there is no prohibition due to losing position, add eight to the yin number, making the final limit twenty-three. Dividing this gives forty-seven years, which corresponds to the year Bingwu, a time of great worries and troubles for the world. If there is still a remainder, it turns into good fortune.

假令失位陽者，四七二十八，以九除之得三餘不盡一，以三乘所得九，因而半之得四有餘，則是即位初期；能過此者得九，中期也；増復能過此者，得十三年終矣；下期失位陽七於所乘得四十二，厄所遭；有餘算福之也。

For example, if a yang element is out of its proper position, multiplying four by seven gives twenty-eight. Dividing this by nine gives three with a remainder of one. Multiplying the quotient three by nine gives twenty-seven, then taking half of this gives fourteen with a remainder. This represents the initial period. If it exceeds this period by nine years, it is the middle period. Adding further and exceeding again to reach thirteen years, this is the final limit. For the next level, a yang element that is out of position, when seven is added to the multiplier, gives forty-two, which signifies a year of calamity. If there is a remainder, it is converted into a measure of fortune.

假令得位陰在六，四六二十四，以六除之得四無餘，以二乘之得八，因而半之得四初忌；能過此者得八，中忌；復能過此者得十二終矣；下忌得位陰増六於乘得三十六，厄所遭也。

For example, if something is of the yin nature and has the number six, multiplying four by six gives twenty-four. Dividing twenty-four by six results in four with no remainder. Then multiplying by two gives eight, and taking half of that gives four, which is the initial taboo period. If one exceeds this period by eight years, it is the middle taboo period. If one further exceeds by twelve years, that is the final limit. For the next level of taboo, if the yin number is added to the multiplied number to reach thirty-six, that year is considered a year of calamity.

假令得位陽在九，四九三十六，九除之得四無餘，以三乘之得十二，因而半之得六，六初忌；能過此者，中忌也；復能過此者得十八，忌終也；得位陽増九於所乘得九五十四，忌所遭也。【按：以上自「推之術」以下，皆後人因卦軌之義而闡衍其法，故推至南北朝年數，非《易緯》本文也。】

For example, if something belongs to the yang and occupies a position, and its number is nine, multiplying four by nine gives thirty-six. Dividing thirty-six by nine results in four with no remainder. Then multiply three by four to get twelve, and take half of that to get six, which is the initial taboo period. If one can surpass this period, it is the middle taboo period. If one can further surpass to reach eighteen, that is the final taboo period. The yang that occupies a position, when added to the number being multiplied by nine, results in fifty-four, which indicates the year of encountering a taboo. [Comment by the editors of the Siku Quanshu] The above content from "Pushing the Method" onwards is all calculations derived by later scholars based on the principles of the hexagrams' tracks. Therefore, these calculations have been extended up to the years of the Southern and Northern Dynasties, and they are not the original text of the Yi Zhuan.

推厄所遭法：以入位年數餘軌數，算盡厄所遭。甲乙為飢，丙丁為旱，戊己為中興，庚辛為兵，壬癸為水，元算為月。【按：此文已見前，此處疑復見，或亦後人所引耳。

The method of calculating the calamities encountered: use the number of years since ascending the throne to divide the track number, observe the remainder, and the place where the count ends is where the calamity occurs. If the result is Jia or Yi, it indicates famine; if Bing or Ding, it indicates drought; if Wu or Ji, it indicates revival; if Geng or Xin, it indicates warfare; if Ren or Gui, it indicates flooding. The original calculation is converted into months. [Comment by the editors of the Siku Quanshu] This passage has already appeared earlier, and here it is likely a repetition, possibly added by a later compiler.

宋軌七百三十六，庚申歳至今甲子歳，宋元嘉元年甲子，宋髙祖第二息文帝義隆年號，為入位五年，以五除軌數上所得積周一百四十七，餘所一，厄所遭也。丙寅歳入位七年，以七除軌數上得積周一百五，軌命得庚寅主兵，其年起兵荊州謝晦也。

The track number of the Liu Song dynasty is seven hundred and thirty-six, from the year of Geng Shen to the current year of Jia Zi. In the first year of Yuanjia, the first year of the reign of Emperor Wen of Song, Liu Yilong, which is the fifth year of his reign, the track number is divided by five, resulting in a total of one hundred and forty-seven with a remainder of one, indicating the calamity encountered. In the year of Bing Yin, which is the seventh year of his reign, the track number is divided by seven, resulting in a total of one hundred and five. According to the track mandate, it corresponds to Geng Yin, which signifies military disaster. Indeed, in that year, Xie Hui of Jingzhou rebelled.

癸未歳入位二十四年，以除軌數上得積周三十，餘十六不盡，以庚申命之得乙亥，乙主飢，其年河南大飢，豫州人相食。甲申歳入位二十五年，除軌數上積得二十九，餘不盡十一，以庚申命之得庚午，庚主兵馬，其年九州發兵征蠻。

The year Guiwei is the twenty-fourth year of ascending the throne. Using it to divide the track number, the accumulated weeks total thirty with a remainder of sixteen. Starting from Gengshen and counting the remainder, it arrives at Yihai. Yi signifies famine, and that year there was a great famine in Henan, with people eating each other in Yuzhou. The year Jiashen is the twenty-fifth year of ascending the throne. Dividing the track number gives a total of twenty-nine with a remainder of eleven. Starting from Gengshen and counting the remainder, it arrives at Gengwu. Geng signifies military forces, and that year the nine provinces sent armies to suppress the barbarians.

乙酉歳入位二十六年，除軌數上得積周二十八，不盡八，以庚申命之得丁卯，丁主旱，其年大旱不收豆麥，豫州禾粟皆旱死。丙戌歳入位二十七年，除軌數上得積周二十七，餘不盡七，以庚申命之得丙，丙主旱，其年淮北二州春旱不能種稻。

In the year Yiyou, which was the twenty-sixth year of the reign, after subtracting the track number, the accumulated number of weeks was twenty-eight, with a remainder of eight. Starting from Gengshen, counting the remainder led to Dingmao. Ding indicates a drought, and that year there was a severe drought, with beans and millet failing to be harvested, and the millet and grain in Yu State all dying from drought. In the year Bingxu, which was the twenty-seventh year of the reign, after subtracting the track number, the accumulated number of weeks was twenty-seven, with a remainder of seven. Starting from Gengshen, counting the remainder led to Bing. Bing also indicates a drought, and that year in the two states north of the Huai River, there was a severe drought in spring, preventing the planting of rice.

丁亥歳入位二十八年，除軌數上積周三十六，餘不盡八，以庚申命之得丁卯，丁主旱，其年大旱。戊子歳入位二十九年，除軌數上得積周二十五，不盡十一，以庚申命之得庚午，庚主兵，其年大兵。己丑歳入位三十年，除軌數上得積周二十四，餘不盡十六，以庚申命之得乙亥，乙主飢，其年荒，糴貴。

In the year of Dinghai, which was the twenty-eighth year of the reign, after subtracting the track number, the accumulated weeks were thirty-six, with a remainder of eight. Starting from Gengshen, counting the cycles led to Dingmao. Ding indicates drought, and that year experienced a severe drought. In the year of Wuzi, which was the twenty-ninth year of the reign, after subtracting the track number, the accumulated weeks were twenty-five, with a remainder of eleven. Starting from Gengshen, counting the cycles led to Gengwu. Geng indicates military disaster, and that year had major military conflicts. In the year of Jichou, which was the thirtieth year of the reign, after subtracting the track number, the accumulated weeks were twenty-four, with a remainder of sixteen. Starting from Gengshen, counting the cycles led to Yihai. Yi indicates famine, and that year had a poor harvest, with expensive grain prices.

庚寅歳入位三十一年，除軌數上得積周二十三，不盡二十三，以庚申命之得壬，壬主水，其年徐、兗州大水，官軍因勢汎舟至滑臺，虜走，後果失利也。辛卯歳入位三十二年，除軌即算死所遭也，以不盡法二十三於上方除餘三十二，以庚申命之得辛卯，辛主兵，其年魏兵至江淮。

The year of Gengyin was the thirty-first year of the reign, when after subtracting the tracks, the accumulated number of two weeks was twenty-three, and the remaining number was twenty-three, which was not fully accounted for. Starting from Gengshen, counting the number of years led to Xin. Xin represents military calamity. That year, there was a great flood in Xuzhou and Yanzhou. The imperial army took advantage of the water to row boats all the way to Huatai, and the enemy retreated. Later, they indeed suffered a defeat. The year of Xinmao was the thirty-second year of the reign. After subtracting the tracks, it was considered the year of encountering a death omen. Using the method of the remaining number twenty-three, dividing it by the superior position, the remainder was thirty-two. Starting from Gengshen, counting the number of years led to Xinmao. Xin represents military calamity. That year, the Northern Wei army reached the Yangtze and Huai River regions.

壬辰歳入位三十三年，除軌數上得積周二十，餘不盡，以庚申命之得己巳，己主中興。癸巳歳入位三十四年，除軌數上得積周二十一，餘不盡二十二，以庚申命之得辛巳，辛主兵，其年二月二十日甲子東宮大逆。○按：以上宋軌取宋文帝在位年數依法推算，穿鑿無謂，文義亦不倫，蓋為後人淺陋者所加，今改用細字附註。】

In the year of Renchen, which is the thirty-third year of the reign, after subtracting the track number, the accumulated weeks total twenty, and there is still a remainder. Starting from Gengshen, counting the remainder leads to Jisi, and Ji signifies a revival. In the year of Guisi, which is the thirty-fourth year of the reign, after subtracting the track number, the accumulated weeks total twenty-one, and the remainder is twenty-two. Starting from Gengshen, counting the remainder leads to Xinsi, and Xin signifies military calamity. On the twenty-second day of the second month, the day Jiazi, the Eastern Palace experienced a great rebellion. [Comment by the editors of the Siku Quanshu] The above passage from "Song Gu" is an attempt to calculate the years of Emperor Wen of Song's reign according to certain rules, but it is forced and meaningless, with incoherent wording and reasoning. It is likely added by later superficial scholars. Now it is rephrased in small font as a footnote.

推軌之術：以天元甲寅已來至今受命位之年，以三十二除之，餘不盡從乾坤始數算，則得主歳之卦，知直事之辰在何辰。以甲寅年至大唐先天元年壬子，積二百七十六萬一千一百三十九，以三十六【或云以十二。】除之，積八萬六千二百八十五周，不盡十九，入家人、睽軌。

The method of calculating the track number: use the accumulated years from the beginning of the heavenly stem Jiayin to the current year when the ruler ascended the throne, divide by thirty-two, and count the remainder sequentially from Qian and Kun in order to determine the hexagram of the current year, thereby knowing the current hour of the day. Using the year Jiayin to calculate to the year Renzi of the Taichang era, the accumulated years are two million seven hundred and sixty-one thousand one hundred and thirty-nine. Dividing by thirty-six [another account says twelve], gives eighty-six thousand two hundred and eighty-five full cycles, with a remainder of nineteen, which falls into the track of the hexagram Jiaoren and Weizhi.

至元和十四年，合二百七十六萬一千二百三十六；元和十五年庚午，或云庚子，積二百七十六萬一千二百四十七。法：陽爻以老陽數乘之，陰爻以老陰數乘之，隨六爻陰陽多少乘訖，並之為分，各數倍分，各為折合數也。【按：上「推軌之術」與前文略同，而重複錯見者，蓋前為南北朝術士所發明，而此推至元和十五年，則又唐人所附益也。】

Calculating for the year Yuanhe 14, the total is two million seven hundred and sixty-one thousand two hundred and thirty-six; for Yuanhe 15, Gengwu, one account says Gengzi, the total is two million seven hundred and sixty-one thousand two hundred and forty-seven. The method is: use the number of old yang for yang lines and the number of old yin for yin lines, multiply according to the number of yin and yang lines in the six lines, then add them together as 'fen'. Doubling each of these numbers gives the 'zhe' and 'he' numbers. [Comment by the editors of the Siku Quanshu] The above 'pushing the track method' is roughly the same as the previous passage, and the repetition is likely due to the fact that the former was invented by a scholar of the Northern and Southern Dynasties, while this passage, which calculates up to the year Yuanhe 15, was added by a Tang dynasty person.

中孚（純坎）公丨，初六冬至，十一月中，廣漠風。解（純震出），初九春分，二月中，明庶風。咸（純離），初九夏至，五月中，凱風。【按：《乾元序制記》作「景風」。】賁（純兊），初九秋分，八月中，閶闔風。

The hexagram Zhong Fu corresponds to pure Kan, with the rank of 'Gong', and the initial line of Kan governs the winter solstice, which is the middle solar term of the eleventh month, matching the vast northern wind. The hexagram Jie corresponds to pure Zhen, with Zhen's initial line governing the spring equinox, which is the middle solar term of the second month, matching the bright eastern wind. The hexagram Xian corresponds to pure Li, with Li's initial line governing the summer solstice, which is the middle solar term of the fifth month, matching the southern warm wind. [Comment by the editors of the Siku Quanshu] The "Dian Feng" in the "Qian Yuan Xu Zhi Ji" is written as "Jing Feng". The hexagram Ben corresponds to pure Dui, with Dui's initial line governing the autumn equinox, which is the middle solar term of the eighth month, matching the western Chang He wind.

屯丨，九二小寒，十二月節。豫，六二清明，三月節。鼎，二小暑，六月節。歸妹，九二寒露，九月節。升（公），六三大寒，十二月中，日在坎。革，六三穀雨，三月中，日在震。履，九三大暑，六月中，日在離。困，六三霜降，九月中，日在兊。

The Second Line of the Zun hexagram governs Xiaohan, which is the solar term of December. The Second Line of the Yu hexagram governs Qingming, which is the solar term of March. The Second Line of the Ding hexagram governs Xiaoshu, which is the solar term of June. The Second Line of the Gui Mei hexagram governs Hanshu, which is the solar term of September. The Third Line of the Sheng hexagram corresponds to the rank of 'gong', and the Third Line of the Kun hexagram governs Dahan, which is the solar term of December. At that time, the sun is in the position of Kan. The Third Line of the Ge hexagram governs Guyu, which is the solar term of March. At that time, the sun is in the position of Zhen. The Third Line of the Li hexagram governs Dashu, which is the solar term of June. At that time, the sun is in the position of Li. The Third Line of the Kun hexagram governs Shuangjiang, which is the solar term of September. At that time, the sun is in the position of Dui.

小過（侯），六四立春，正月節，條風。旅，九四立夏，四月節。【按：此下當脫「溫風」二字。】恆，九四立秋，七月節，涼風。艮，九四立冬，十月節。【按：此下當脫「不周風」三字。】漸（公），九五雨水，正月節。小畜，六五小滿，四月中。損，六五處暑，七月中。大過，九五小雪，十月中。

The卦 of Xiao Guo (Small Overcoming) belongs to the rank of Hou (Marquis), with the line six in the fourth governing the beginning of spring, which is the solar term of the first month, paired with the wind of the Northeast, called Tiaofeng (Opening Wind). The卦 of Lu (Travel) has the line nine in the fourth governing the beginning of summer, which is the solar term of the fourth month. [Comment by the editors of the Siku Quanshu] The text below should have the words "Wenfeng" (Warm Wind) omitted. The卦 of Heng (Permanence) has the line nine in the fourth governing the beginning of autumn, which is the solar term of the seventh month, paired with the wind of the Southwest, called Liangfeng (Cool Wind). The卦 of Gen (Stillness) has the line nine in the fourth governing the beginning of winter, which is the solar term of the tenth month. [Comment by the editors of the Siku Quanshu] The text below should have the words "Bu Zhoufeng" (Wind from the Non-Direction) omitted. The卦 of Zhen (Gradual Progress) belongs to the rank of Gong (Duke), with the line nine in the fifth governing the rain water, which is the solar term of the first month. The卦 of Xiao Xu (Small Accumulation) has the line six in the fifth governing Xiaoman (Minor Fullness), which is the solar term of the fourth month. The卦 of Shen (Loss) has the line six in the fifth governing Chushu (Heat Abatement), which is the solar term of the seventh month. The卦 of Da Guo (Great Overcoming) has the line nine in the fifth governing Xiaoxue (Minor Snow), which is the solar term of the tenth month.

需（侯），上六驚蟄，三月節。大有，上六芒種，五月節。巽，上九白露，八月節。未濟，上六大雪，十月節。【按：以上以四正卦爻配二十四氣，其說亦見於《乾元序制記》，當是《易緯》本文。】冬至日在坎，春分日在震，夏至日在離，秋分日在兊。

The Need卦 (Xu) corresponds to the rank of Hou, and its upper sixth line (Shang Liu) corresponds to the solar term Jingzhe, which is in the third lunar month. The Da You卦 (Da You) upper sixth line (Shang Liu) corresponds to Mangzhong, the solar term in the fifth lunar month. The Xun卦 (Xun) upper ninth line (Shang Jiū) corresponds to Baolu, the solar term in the eighth lunar month. The Wei Ji卦 (Wei Ji) upper sixth line (Shang Liu) corresponds to Daxue, the solar term in the tenth lunar month. [Comment by the editors of the Siku Quanshu] This method of matching the yao positions of the four cardinal trigrams with the twenty-four solar terms is also found in the Qianyuan Xuzhi Ji, and it should be the original text of the Yi Wei. On the day of Winter Solstice, the sun is at the Kan position; on the day of Spring Equinox, it is at the Zhen position; on the day of Summer Solstice, it is at the Li position; and on the day of Autumn Equinox, it is at the Dui position.

《易緯·是類謀》以此四正之卦，卦有六爻，爻主一氣；餘六十卦，卦主六日七分——八十分日之七。正歳三歳六十五日四分日之一，六十而一周。《乾象》以中孚當十一月，六十中氣後十五日，準兩卦強，可得十二月，餘少三日，當取十二月卦日也。

The "Yi Wei · Shi Leiu" discusses these four main hexagrams: each hexagram has six lines, with each line corresponding to one solar term, totaling twenty-four solar terms; the remaining sixty hexagrams each correspond to six days and seven parts, which is seven eightieths of a day. The regular year spans three years, with each year being three hundred sixty-five and one fourth days, and the sixty hexagrams complete a cycle. The "Gan Xiang Li" uses the Zhongfu hexagram to correspond to the eleventh month, and after the sixty middle terms, fifteen days are added, which is equivalent to more than two hexagrams, allowing the formation of twelve months, differing by three days. Therefore, the number of days in the twelve monthly hexagrams should be used to make up for the difference.

右各以六日於決次，乃不可簡取其孤，如此非是驗也。以《易緯》推之，無勞更算二十四氣，以成五日七分，正五日準四分之一未消息即為善矣。【按：以上亦當為後人所加。】

The hexagrams listed on the right are connected in sequence over six days and should not be taken individually at random, as doing so would make the calculations ineffective. According to the Yi Wei, there is no need to calculate the twenty-four solar terms separately. Instead, one should form a period of five days and seven parts. The five days are considered equivalent to one day and a quarter, excluding the message hexagram, and this is considered sufficient. [Comment by the editors of the Siku Quanshu] This passage should also have been added by later commentators.

八百諸侯：正月侯、三月侯、五月侯、七月侯、九月侯、十一月。小過立春，豫清明，大有芒種，恆立秋，歸妹寒露，未濟大雪。初六一日，六二六日，九三十一日，九四十六日，六五二十一日，上六二十六日。

Eight hundred feudal lords are divided into six groups, each corresponding to the侯 (feudal lord) of the first, third, fifth, seventh, ninth, and eleventh months. The卦 (hexagram) Xiao Guo corresponds to the beginning of spring, Yu corresponds to Qingming, Da You corresponds to Mangzhong, Heng corresponds to the beginning of autumn, Gui Mei corresponds to Hanlu, and Wei Ji corresponds to Daxue. Each line of the hexagram governs a specific day: Six at the Beginning governs the first day, Six in the Second governs the sixth day, Nine in the Third governs the eleventh day, Nine in the Fourth governs the sixteenth day, Six in the Fifth governs the twenty-first day, and Six at the Top governs the twenty-sixth day.

二十七大夫：蒙正月大夫，訟三月大夫，家人五月大夫，節七月大夫，無妄九月大夫，蹇十一月。初六二日，九二七日，六三十二日，六四十七日，六五二十二日，上九二十七日。

The twenty-seventh class of officials corresponds to the hexagrams. The hexagram Meng is the hexagram of officials in the first month, Song in the third month, Jia Shen in the fifth month, Jie in the seventh month, Wu Wang in the ninth month, and Jian in the eleventh month. Each line corresponds to a specific day: Six at the Beginning corresponds to the second day, Nine in the Second corresponds to the seventh day, Six in the Third corresponds to the twelfth day, Six in the Fourth corresponds to the seventeenth day, Six in the Fifth corresponds to the twenty-second day, and Nine at the Top corresponds to the twenty-seventh day.

九卿：益正月九卿，蠱三月九卿，井五月九卿，同人七月九卿，明夷九月九卿，頥十一月。初九三日，六二八日，六三十三日，六四十八日，九五二十三日，上九二十八日。

The Nine Ministers correspond to specific hexagrams for each month: the Hexagram of Benefit is for the first month, the Hexagram of蛊 is for the third month, the Hexagram of Well is for the fifth month, the Hexagram of Fellowship is for the seventh month, the Hexagram of Brightness in Darkness is for the ninth month, and the Hexagram of Nourishment is for the eleventh month. Each line of the hexagram corresponds to a specific day: Nine at the Beginning governs the third day, Six in the Second governs the eighth day, Six in the Third governs the thirteenth day, Six in the Fourth governs the eighteenth day, Nine in the Fifth governs the twenty-third day, and Nine at the Top governs the twenty-eighth day.

三公：漸正月三公，革三月三公，咸五月三公，損七月三公，困九月三公，中孚十一月。初六四日，六二九日，九三十四日，六四十九日，九五二十四日，上九二十九日。

The three high officials correspond to these hexagrams: the hexagram Zhan (Gradual Progress) is the hexagram of the three high officials for the first month, the hexagram Ge (Revolution) for the third month, the hexagram Xian (Mutual Attraction) for the fifth month, the hexagram Shen (Loss) for the seventh month, the hexagram Kun (Impediment) for the ninth month, and the hexagram Zhongfu (Sincerity in the Center) for the eleventh month. Each line governs a specific day: Six at the Beginning governs the fourth day, Six in the Second governs the ninth day, Nine in the Third governs the fourteenth day, Six in the Fourth governs the nineteenth day, Nine in the Fifth governs the twenty-fourth day, and Nine at the Top governs the twenty-ninth day.

天子：泰正月天子，夬三月天子，姤五月天子，否七月天子，剝九月天子，復十一月。初九五日，九二十日，九三十五日，六四二十日，六五二十五日，上六三十日。右是六陽月三十卦直事日，依氣定日主一爻。

The heavenly ruler corresponds to the following hexagrams for each month: The hexagram Tai is the ruler for the first month, Guai for the third month, Gou for the fifth month, Po for the seventh month, Bo for the ninth month, and Fu for the eleventh month. Each line of the hexagram governs a specific day: Nine at the Beginning governs the fifth day, Nine in the Second governs the tenth day, Nine in the Third governs the fifteenth day, Six in the Fourth governs the twentieth day, Six in the Fifth governs the twenty-fifth day, and Six at the Top governs the thirtieth day. These are the six yang months, each with thirty hexagrams governing the days according to the solar terms, with each line governing one day.

八百諸侯：二月侯、四月侯、六月侯、八月侯、十月侯、十二月。需驚蟄，旅立夏，鼎小暑，巽白露，艮立冬，屯小寒。初九一日，九二六日，九三十一日，六四十六日，九五二十一日，上六二十六日。

Eight hundred feudal lords are divided into those corresponding to the second, fourth, sixth, eighth, tenth, and twelfth months. The hexagram Qian should be used at the time of Jingzhe, the hexagram Lu at the time of Lixia, the hexagram Ding at the time of Xiaoshu, the hexagram Xun at the time of BaiLu, the hexagram Gen at the time of Lidong, and the hexagram Tun at the time of Xiaohan. Each line of the hexagram governs a specific day: Nine at the Beginning governs the first day, Nine in the Second governs the sixth day, Nine in the Third governs the eleventh day, Six in the Fourth governs the sixteenth day, Nine in the Fifth governs the twenty-first day, and Six at the Top governs the twenty-sixth day.

二十七大夫：隨二月大夫，師四月大夫，豐六月大夫，萃八月大夫，既濟十月大夫，謙十二月。初九二日，九二七日，九三十二日，六四十七日，九五二十二日，上六二十七日。

The second class of officials, the twenty-seventh rank, corresponds to the hexagrams of the months: the hexagram of Following corresponds to the second month, the hexagram of the Army corresponds to the fourth month, the hexagram of Abundance corresponds to the sixth month, the hexagram of Convergence corresponds to the eighth month, the hexagram of Completion corresponds to the tenth month, and the hexagram of Humility corresponds to the twelfth month. Each line governs a specific day: Nine at the Beginning governs the second day, Nine in the Second governs the seventh day, Nine in the Third governs the twelfth day, Six in the Fourth governs the seventeenth day, Nine in the Fifth governs the twenty-second day, and Six at the Top governs the twenty-seventh day.

九卿：晉二月九卿，比四月九卿，渙六月九卿，大畜八月九卿，噬嗑十月九卿，暌十二月。初六三日，六二八日，六三十三日，九四十八日，六五二十三日，上九二十八日。

The Nine Ministers correspond to specific hexagrams for each month: the hexagram Jin (晋) corresponds to the second month, the hexagram Bi (比) to the fourth month, the hexagram Huan (涣) to the sixth month, the hexagram Da Xu (大畜) to the eighth month, the hexagram Shi He (噬嗑) to the tenth month, and the hexagram Kui (睽) to the twelfth month. Each line of the hexagram corresponds to a specific day: Six at the Beginning governs the third day, Six in the Second governs the eighth day, Six in the Third governs the thirteenth day, Nine in the Fourth governs the eighteenth day, Six in the Fifth governs the twenty-third day, and Nine at the Top governs the twenty-eighth day.

三公：解二月三公，小畜四月三公，履六月三公，賁八月三公，大過十月三公，升十二月。初六四日，九二九日，六三十四日，九四十九日，六五二十四日，上九二十九日。

The three high officials correspond to the hexagrams associated with the second month, fourth month, sixth month, eighth month, tenth month, and twelfth month respectively: the hexagram of Jie is for the second month, the hexagram of Xiaoxu is for the fourth month, the hexagram of Lu is for the sixth month, the hexagram of Ben is for the eighth month, the hexagram of Daguogua is for the tenth month, and the hexagram of Sheng is for the twelfth month. Each line corresponds to a specific day: Six at the Beginning corresponds to the fourth day, Nine in the Second corresponds to the ninth day, Six in the Third corresponds to the fourteenth day, Nine in the Fourth corresponds to the nineteenth day, Six in the Fifth corresponds to the twenty-fourth day, and Nine at the Top corresponds to the twenty-ninth day.

天子：大壯二月天子，乾四月天子，遁六月天子，觀八月天子，坤十月天子，臨十二月。初九五日，九二十日，九三十五日，九四二十日，六五二十五日，上六三十日。【按：上文各卦圖俱取五徳首一卦六爻依日配之，以例其餘，原本多有脫落錯誤，今各依本卦補入；至策數亦有脫者，未敢妄補，姑仍其舊。】

The heavenly sovereign's corresponding hexagrams are as follows: The Great Strength hexagram corresponds to the second month, the Heaven hexagram to the fourth month, the Retreat hexagram to the sixth month, the Contemplation hexagram to the eighth month, the Earth hexagram to the tenth month, and the Approach hexagram to the twelfth month. Each line corresponds to a specific day: the first line corresponds to the fifth day, the second line to the tenth day, the third line to the fifteenth day, the fourth line to the twentieth day, the fifth line to the twenty-fifth day, and the top line to the thirtieth day. [Comment by the editors of the Siku Quanshu] The hexagrams mentioned above are derived by taking the first line of each of the five ranks of the hexagrams and matching them with the days, to infer the rest. However, the original texts have many missing or incorrect parts. Now, each hexagram has been supplemented according to its own structure. As for the numbers used in divination, some are also missing, and we dare not arbitrarily add them, so we have preserved them as they were.

應已上盡卦爻日，並上一同。右是六陰月三十卦直事日，依氣定日主一爻。候六甲子日中寒暑風雨，記其日，占發時方來，萬不失一：幽、冀起坎初六候之，兗、鄭坎六四候之，青、齊震初九候之，徐、魯震九四候之，揚、呉、越離初九候之，涼、益、衛兊初九候之，並、雍、秦兊九四候之。

The remaining trigrams' corresponding lines are determined in the same way as above. This is how the thirty trigrams correspond to the days for actions in the six yin months, determined by the solar terms, with each line corresponding to one day. To predict the cold, heat, wind, and rain within the six Jiazi days, record these conditions on the respective days and use them to determine the time and direction of the occurrence, with certainty. In Youshou and Jizhou, the initial line of the Kan trigram is used. In Yanyou and Zhengdi, the fourth line of the Kan trigram is used. In Qingzhou and Qidi, the initial line of the Zhen trigram is used. In Xuzhou and Ludi, the fourth line of the Zhen trigram is used. In Yangzhou and Wu, Yue, the initial line of the Li trigram is used. In Liangzhou, Yizhou, and Weidi, the initial line of the Dui trigram is used. In Baozhou, Yongzhou, and Qindi, the fourth line of the Dui trigram is used.

推四正：寒不侵公者夷兵，若和氣者解；入方伯，寒氣凶、和吉；風盛雨者坐刑殺；霧將死；若有和氣王相三十日，當沴妖氣為賊盜。右是六陰卦月三十卦直事日，依氣定日主一爻。【按：此句已見前，此處重出。】

Calculating the four cardinal trigrams: if the cold qi does not invade the position of 'public', it indicates that the four barbarian states will engage in warfare; if there is harmonious qi, it can be removed. If the cold qi invades the position of 'feudal lord', it is ominous; if there is harmonious qi, it is auspicious. If there is strong wind and heavy rain, it indicates being punished by legal punishment. If there is fog, it indicates there will be death and mourning. If harmonious qi is in the position of the sovereign and minister for thirty days, there will be abnormal and malevolent qi transforming into bandits. These are the six trigrams of the Yin months, each corresponding to thirty days, determined by the solar terms, with each line of the trigram governing one day. [Comment by the editors of the Siku Quanshu] This sentence has already appeared earlier, and this is a repetition.