Intercalation method

置閏之法，氣盈朔虛，此其大綱，中法二十四氣平分，每一節氣十五日二十一刻有奇，積算每年所餘十一日，三年所餘三十三日，因而置潤；西法則云：冬夏不齊，冬一節氣，十四日八十四刻有奇，夏一節氣十五日七十二刻有奇。因日行距地遠近不等，冬日距地遠而行疾，夏日距地近而行遲，以此詳算置閏，氣朔分齊，無盈縮之差，其置閏視中法疏密為何如耶？

The method of intercalation is summarized in the four characters "气盈朔虚" (excess of solar terms and deficiency of new moons). This means that the number of days exceeding in the solar terms of a year compared to the deficiency in the twelve lunar months is balanced. The traditional method distributes the twenty-four solar terms evenly, assigning each solar term fifteen days and twenty-one moments, which accumulates to eleven days over a year, and thirty-three days over three years, thus inserting a leap month. The Western method, however, states that the lengths of the solar terms in winter and summer are not equal; a solar term in winter is only fourteen days and eighty-four moments, while one in summer is fifteen days and seventy-two moments. This is because the sun is farther from the earth in winter and moves faster, and closer in summer and moves slower. According to this, the Western method calculates intercalation in detail, making the distribution of solar terms and new moons regular, without error of excess or deficiency. Thus, it is clear which method, the Western or the traditional, is more accurate in intercalation. (The last sentence "因而置润" has "润" as a mistake for "闰", and is recorded as it originally appeared.)

歲差之法，則以日躔之所遷，驗列宿之退數。古無差法，虞喜始立其法，以五十年差一度；何承天則以百年差一度；劉焯則以七十五年差一度；一行以八十三年差一度。中法始減週歲為三百六十五度二十四分五秒，加周天為三百六十五度二十五分七十五秒，以六十七年而差一度，視前為不同矣。

The method of precession is based on the movement of the sun's position to verify the degree by which the twenty-eight constellations gradually retreat each year. In ancient times, there was no concept of precession. It was first proposed by Yu Xi of the Jin dynasty, who set it at one degree every fifty years. Later, He Chengtian of the Southern dynasty changed it to one degree every hundred years. Liu Zhuo of the Sui dynasty adjusted it to one degree every seventy-five years. Xing Yixing, a Buddhist monk of the Tang dynasty, revised it to one degree every eighty-three years. Later, the method was adjusted so that the annual cycle was reduced to 365 degrees, 24 minutes, and 5 seconds, and the full circle was increased to 365 degrees, 25 minutes, and 75 seconds, setting the precession at one degree every sixty-seven years, which differs from the previous methods.

西法詳算列星，每年東行五十一秒，積七十年有奇而差一度，二千一百十七年有奇而差一宮，二萬五千四百一十年有奇而東旋一周，西法歲差更不同焉。

The Western method carefully calculates the movement of all the fixed stars, stating that the stars move eastward by fifty-one seconds each year. After seventy years, they accumulate a difference of one degree; after two thousand one hundred seventeen years, they accumulate a difference of one sign; and after twenty-five thousand four hundred ten years, they complete a full circle around the sky. This shows that the Western method discusses precession, but it presents a completely different approach from the various schools of Chinese methods.

裡差之法，為分省節氣之刻；中法立表測景以求時刻，難為依據，即所測冬夏二至，猶未盡善；西法用八線表法，已為精細，且又有別法以相濟，人莫窺其底蘊。西法裡差密乎不密，異乎不異。

The method of calculating the difference in distance (li cha) is used to distinguish the time of the solar terms in different provinces. The traditional method of setting up a gnomon and measuring shadows to determine time is difficult to rely on, and even the determination of the winter solstice and summer solstice is not yet perfect. The Western method, using the "eight-line table" technique, is already very precise, and there are also other calculation methods to complement each other, so outsiders cannot understand its essence. Therefore, whether the Western method of calculating li cha is secret or not, and whether it is different or not, the answer lies within.

以交蝕言之，日月之行由南北而縱分之謂之度，由東西而橫截之謂之道，日行高而月行卑，若合朔之時，日與月同度同道，則日為月掩而日蝕；月本無光，借日之光；若對望之時，月與日對度對道，則月為日所，陽極反亢，故蝕；凡交蝕分數總由同道對道之多寡，此中法西法之同也。

Taking the occurrence of solar and lunar eclipses as an example, the paths of the sun and moon are divided vertically from north to south as "degrees" (度) and horizontally from east to west as "paths" (道). When the sun is high and the moon is low, at the time of new moon, the sun and moon are in the same degree and the same path, and the sun is covered by the moon, resulting in a solar eclipse. The moon itself has no light; it shines by borrowing the light of the sun. At the time of full moon, the moon and sun are opposite in degrees and opposite in paths, and the moon is covered by the sun. When yang energy reaches its peak, it becomes excessive, hence a lunar eclipse. The extent of eclipses depends on the degree to which the same path and opposite path align. This is a point where the Chinese and Western methods are completely consistent. (The original text has a missing character after the phrase "则月为日所", which should be "所掩", and it is recorded as is without supplementation.)

至西法更謂月蝕則在日月正望，而地球介乎其間，月入地影中失其所借之光而為蝕；地在天中，其體微渺，尋常不能障隔日月，惟日月同在一線，乃為地所隔而成蝕；故中法謂太陽之體本有暗虛，月值之則遙奪其光，西法則謂月蝕仍名暗虛，為地所隔則暗而虛也，是月蝕又更異矣。

As for the Western method, it explains further that a lunar eclipse occurs on the full moon day when the sun and moon are exactly opposite each other, with the earth precisely in between. The moon enters the earth's shadow, losing the sunlight it borrowed, thus forming an eclipse. The earth, being among the celestial bodies, is extremely small in size and usually cannot block the sun or moon. Only when the sun, earth, and moon are aligned in a straight line can the earth block the light, causing an eclipse. Therefore, the Chinese method explains that the sun itself originally has a region called 'dark void' on its surface; when the moon passes over it, it is far away from the light. The Western method, however, also refers to the eclipse as a 'dark void,' but it is the earth that blocks the light, making it dark and empty. In this aspect, the explanations of lunar eclipses by the Chinese and Western methods are quite different.

刻漏之制，周禮挈壺氏掌之，孔壺謂之漏，浮箭謂之刻。浮箭壺、漏水壺名異而實同，中法因之。西法又有地平晷、百遊晷、通光晷、十字晷，遇陰雨則有自嗚鍾，沙漏、水漏之制。中法以水入壺而時箭浮，西法以水出壺而時牌出，壺體並不開孔，以節時分、定晨昏、考中星、撥晷景，無有差忒，刻漏視中法亦較密焉。

The system of clepsydra was managed by the Qi Hu Shi according to the Zhou Li. A hollowed-out vessel is called "le," and the floating arrow is called "ke." Although the names of the floating arrow vessel and the water-leaking vessel are different, their actual function is the same, and this method has been continuously used. In the Western method, there are other types of sundials such as the horizontal sundial, the hundred movements sundial, the through-light sundial, and the cross sundial. When there is rain and the shadow cannot be seen, they use the self-sounding clock, as well as the sand clepsydra and water clepsydra. In the Chinese method, water is poured into the vessel, and the time arrow rises with it. In the Western method, water flows out of the vessel, and the time marker appears accordingly, without needing to open additional holes on the vessel. These methods are used to divide time, determine morning and evening, test the position of the stars, and adjust the sundial's shadow, all without error. It is evident that, regarding the clepsydra alone, the Western method is more precise than the Chinese method. ("Zi Weng Zhong" is a variant of "Zi Ming Zhong," and the original form is preserved here.)

惟曆元之準於北極，推而上之，而章、而蔀、而紀、而元，東西兩漢異而實同，中法、西法皆循之，無疏密也。

Only the term "liyuan" is based on the North Pole. From this, layers are successively calculated: nineteen years accumulate to form one "zhang," four zhangs form one "bu," twenty bu form one "ji," and three ji form one "yuan." This system of calculation appeared to differ between the Western and Eastern Han dynasties but was essentially the same. Both the Chinese and Western methods continued to use it, so it is not a matter of one being more accurate or less accurate than the other.

至西法謂地如圓球，正居天中，日大於地，月小於地，五星大如月，尤振古所未聞。若其論恆星之南北差、赤黃道之疏密差、日與地之不同心差、七政之視差、日蝕之內三差外三差、月蝕時刻之裡差以及悉月星之本次，輪調參觜之先後度，正羅計之誤，元思至理，深切著明，中法不能讚詞矣。

As for the Western method, which says the earth is round and sits exactly at the center of the celestial sphere, that the sun is larger than the earth, the moon smaller than the earth, and the five planets are about the same size as the moon, these are things that have never been heard of since ancient times. Looking further at their discussion of the differences in the positions of stars north and south, the differences in density between the celestial equator and the Yellow Path, the difference in centers between the sun and the earth, the parallax of the seven heavenly bodies, the three internal and three external differences in solar eclipses, the differences in distance for lunar eclipses, and the careful examination of the current positions of the moon and stars, adjusting the order of the Three Stars mansion and the Turtle Beak mansion, and correcting the mistake of the reversal of the beginning and end of Rahu and Ketu—these considerations are profound and the reasoning is thorough and clear. There is not even space for a word in the Chinese method on these points.

更用以三角八線之算，揆以均數自變量根數之法，天地之寒暑、日月之晦明、渾淪磅礴於太虛之表而不能出其範圍，直可上接容成之統，遠紹羲和之傳，行之萬世而可無敝，密莫密於此，異莫異於此。

In addition, by using the method of triangles and eight lines for calculation, and employing algorithms such as mean numbers, variable numbers, and root numbers for verification, the changes of cold and heat, day and night, and the waxing and waning of the moon can all be calculated. Although these phenomena are vast and pervasive throughout the boundless void, they cannot escape the scope of such calculations. Such a calendar system can continue the tradition of the Yellow Emperor's era when Rongcheng created the calendar, and can also inherit the transmission from the time of the Yao dynasty when Xihe was in charge of the heavens. It will remain valid for ten thousand generations without failure. As for its secrecy, there is nothing more secret than this; as for its uniqueness, there is nothing more unique than this. (The term 「自变量」 in the original text is likely a miswriting for 「自变数」, and is recorded as such.)

有志者誠取預定之萬年書，及當年之七政經緯躔度書，一一遵而行之，求其故而晰其微，庶幾精算無餘蘊矣。

A person genuinely devoted to this discipline can truly obtain the precompiled almanac for all years, as well as the official astronomical records of the seven planets' celestial coordinates and movements for the current year. By following each item step by step to deduce and explore the reasons behind them, and analyzing their subtle and obscure aspects, the art of calculation will be nearly exhausted.

隔六宮，一百八十度相。隔四宮，一百二十度三合。隔三宮，九十度二絃。隔二宮，六十度六合。

The twelve palaces correspond with each other. They are divided into four categories based on the number of palaces between them: those separated by six palaces are 180 degrees apart, which is a direct opposition; those separated by four palaces are 120 degrees apart, which is called "Triple Harmony"; those separated by three palaces are 90 degrees apart, which is called "Two Strings"; and those separated by two palaces are 60 degrees apart, which is called "Six Harmony." These four methods of correspondence are the basis for the terms "络" (network), "钓" (fishing), "拱" (bowing), and "冲" (collision) discussed in the entire text. (The original text has a missing character after "180 degrees," which should be "relative" or "collision," but it is recorded as is without correction.)

生時加太陽上順數至卯是。

The method of determining the命宫 is to add the birth hour to the palace where the sun is located, then count sequentially through the twelve palaces until reaching the卯 position. The palace where you land is the命宫.

從太陽所躔之度，用量天尺直數至命宮某度是，即所謂絡也，亦即對三合六合二絃之謂，特兼及三十度，一百五十度而其數益全。

The method of establishing a degree: starting from the degree where the Sun is located, use the "measure of heaven" to count directly to the degree of the命宫. The degree counted to is the established degree. This is also what was previously mentioned as "络," which refers to relations such as opposition, triple harmony, six harmony, and the two extremes; however, the method of establishing degrees also includes counting degrees that are thirty degrees apart and one hundred fifty degrees apart, making it more comprehensive than simply discussing degrees in opposition and triple harmony.

人以命為主，故命宮第一；財為養命之源，故次二；分我之財曰兄弟，故次三；田宅所以安命藏財而居兄弟，故次四；既有財帛兄弟田宅，而男女所以承田與財者也，故次五；奴婢所以輔男女，故次六；妻妾敵體，與命宮對，故次七；疾厄人所難免，故次八；遷移人所常有，故次九；官祿夭之所予於人，故次十；福德人之所享於天，故次十一；相貌所以成身，故次十二。

The order of the twelve palaces has its own reasoning. Since life and destiny are the fundamental aspects of a person, the Palace of Destiny comes first. Wealth is the source that sustains life, so it comes second. Brothers are those who share one's property, so the Palace of Brothers comes third. The Palace of Property is used to secure one's life, store wealth, and accommodate brothers, so it comes fourth. Having wealth, brothers, and property, children are the ones who inherit the family's estate, so the Palace of Children comes fifth. Servants assist the children, so the Palace of Servants comes sixth. Concubines are of equal status to oneself and correspond with the Palace of Destiny, so the Palace of Concubines comes seventh. Illness and misfortune are inevitable for people, so the Palace of Illness comes eighth. Migration and movement are common experiences, so the Palace of Migration comes ninth. Officialdom is granted by Heaven, so the Palace of Officialdom comes tenth. Fortune and virtue are received and enjoyed by people from Heaven, so the Palace of Fortune and Virtue comes eleventh. Appearance is the form that completes one's body, so the Palace of Appearance comes twelfth. (The character 「夭」 in 「官禄夭之所予于人」 is a mistake for 「天」, and it is recorded as it originally appeared.)

自命宮而至妻宮，其敘不亂；自疾厄而至相貌，卻乃倒置，何歟？命與妻相對，相貌福德官祿出天上，故列在命前；財帛兄弟田宅隱地下，故列在命後。

Someone may ask: When arranging from the命宫 to the妻宫, the order is clear and orderly; but when arranging from the疾厄宫 to the相貌宫, it seems reversed. Why is this so? The key lies in the fact that the命宫 and妻宫 are opposite ends. The three sectors of相貌,Fortune Virtue, and官禄 belong to the heavenly revealed path, so they are listed before the命宫 on the chart; the three sectors of财帛,兄弟, and田宅 belong to the earthly hidden path, so they are listed after the命宫 on the chart. The order of the宫 names and the position of the sectors on the chart are fundamentally different.

有相貌才見福德，有福德才居官祿，有官祿才多遷移，才遷移才招疾厄，自相貌至疾厄，皆日月之喜升而惡沉；有財帛應分兄弟，有兄弟應剖田宅，有田宅應歸男女，有男女應用奴僕，自財帛至奴僕，皆日月之右轉而分佈。此十二宮之立，而人之所以為生，盡在是矣。

First, consider the continuity of these two paths: one begins with appearance, then moves on to fortune and virtue, then to holding office and receivingofficial stipend, then to frequent transfers and postings, and finally to illness and misfortune. From appearance to illness and misfortune, this path belongs to the aspect where the sun and moon rise and are favorable, but decline and are unfavorable. Another path begins with wealth, which should be shared with brothers; having brothers leads to dividing land and property; having land and property leads to passing them on to children; having children leads to employing servants. From wealth to servants, this path belongs to the aspect where the sun and moon turn rightward and distribute in order. Thus, the twelve palaces are established in this way, and all the various circumstances of life are included within them.

命與祿十有五，福與妻十有一，田宅子孫各四年半，而奴僕隨之，財帛兄弟各五，而相貌獨十年，疾厄遷移退以七八。

Each palace governs a different number of years: the命宫 and官禄宫 each govern fifteen years, theFortune Virtue宫 and妻妾宫 each govern eleven years, the田宅宫 and子孙宫 each govern four and a half years, the奴仆宫 follows the same number, the财帛宫 and兄弟宫 each govern five years, while the相貌宫 extends to ten years, and the疾厄宫 and迁移宫 govern only seven and eight years respectively.

其所以若此者，子午卯酉居陰陽之中位，命祿妻田為四正宮，管四十五年有奇，乃含洛書四十有五之妙也；寅申巳亥辰戌丑未八宮，當陰陽終始之地，管五十五年無奇，乃具河圖五十有五之妙也。

Why is it arranged this way? Because the four earthly branches, Zi, Wu, Mao, and You, are located at the central positions of yin and yang, and the four palaces of the命宫 (destiny palace), 官禄 (officials' fortune), 妻妾 (spouse and concubine), and 田宅 (land and house) fall on the four cardinal directions. Together, they cover forty-five years plus a little, which implicitly contains the number forty-five from the Luo Shu (River Chart). Meanwhile, the eight palaces of Yin, Shen, Si, Hai, Chen, Xu, Chou, and Wei are situated at the points where yin and yang complete their cycle and begin anew, covering fifty-five years exactly, which corresponds to the number fifty-five from the He Tu (Heavenly Scroll). When the four cardinal palaces and the eight cyclical palaces are combined, they total exactly one hundred years, encompassing the entire lifespan of a person.

童限管十五年，此其常也。不及則十歲後即出，太過則二十歲才出，總查太陽過宮之淺深，以定行限之遲早。太陽過宮三日管一年，三十日管十年，須扣算實數起；

The child limit usually covers fifteen years, which is the standard practice. If it is insufficient, the child limit ends after ten years. If it is excessive, the child limit ends at twenty years. In any case, one must check the depth of the Sun's passage through the zodiac signs to determine the timing of the start of the large limit. The calculation method is: each three days of the Sun's passage through a zodiac sign equals one year, and thirty days equal ten years. One must deduct the actual days according to the calculation before starting the limit.

倘未滿三日，只二日零六個時，即十歲十個月行限。如七月初一生，必至十一歲六月三十滿十歲，再加十個月，行限則十二歲五月初一才起。

For example: if the period is less than three days, such as two days and six hours, it is converted to ten years and ten months for the start of the great limit. Take someone born on the seventh day of the seventh month; they would reach ten years old on June 30th of the eleventh year. Adding ten months, the great limit would begin on May 1st of the twelfth year.

倘將滿三十日，只缺少九個時，即十九歲零九個月行限。如六月初十生，必至二十歲六月初九滿十九歲，再加九個月，行限則二十一歲三月初十才起。

For example, if someone is only nine hours short of thirty days, it is considered as nineteen years and nine months for the great limit to begin. Suppose someone is born on the tenth day of June, they would not reach nineteen years old until the ninth day of June in the year they turn twenty. Then adding nine months, the great limit would start on the tenth day of March in the year they turn twenty-one.

定命專論宮，果老論度固不可以，即另立度主亦在所不必，但看度之經緯、貫串以卜休咎而已，至於身主尤屬泛泛，皆所宜削。

Determining the destiny palace only considers the palace, not the degree. The Guolao school, when determining destiny, also considers the degree, which is indeed incorrect; even if another 'degree master' is established, it is still unnecessary. The degree only needs to be examined in terms of its meridian and degree relationships and its connecting relationships, which are sufficient for determining fortune or misfortune. As for the so-called 'body master,' it is vague and without basis, and all these should be entirely removed.

行限專論度，如寅宮有房心尾箕四度，行房以日論，行心以月論，行尾以火論，行箕以水論。若又論宮之為木，則金躔尾，顧不受火克而反雲克木可乎？卯宮有亢氐二度，行亢以金論，行氐以土論，若又論宮之為火，則金躔氐，顧不受土生，而反雲火克可乎？

The concept of limits (行限) focuses solely on degrees (度) and not on the palace (宫). For example, in the palace of寅 (Chou), there are four degrees: 房 (Fang), 心 (Xin), 尾 (Wei), and 箕 (Ji). When moving to the degree of 房, it is considered according to the Sun; when moving to 心, it is considered according to the Moon; when moving to 尾, it is considered according to fire; and when moving to 箕, it is considered according to water. If, in addition to considering degrees, one also considers the Five Phases of the palace, then since the palace of寅 belongs to wood, when the planet is in the degree of 尾, would it not be considered as being overcome by the fire of 尾, rather than saying it overcomes the wood of the palace? Similarly, in the palace of卯 (Mao), there are two degrees: 亢 (Kang) and 氏 (Di). When moving to 亢, it is considered according to metal; when moving to 氏, it is considered according to earth. If one also considers the Five Phases of the palace, which is fire, then when the planet is in the degree of 氏, would it not be considered as being generated by the earth of 氏, rather than being overcome by the fire of the palace? Therefore, limits can only be considered according to degrees, and should not involve the Five Phases of the palace.

命主總在得時得地但左右無相剋者，有相生者更優遊自如，尤須朝陽近吉，或作陽引，或作陽從，或有吉神引，或有吉神從，皆主貴顯；若凶神引從，便以禍論。如吉凶神均不引從，則專看經絡貫串等矣。倘有盤合全格而不貴者，皆由主星失之也。

The main star in a person's destiny must be timely and in the right place. As long as there are no stars that harm it on either side, it will be secure. If there are stars that nourish it on either side, it will be even more comfortable and free. Especially important is having support from the Sun and being close to auspicious stars: either being in front of the Sun as a guide or behind the Sun as a follower, or having auspicious deities guiding in front and following behind. These situations all indicate high status and prestige. Conversely, if malevolent spirits are leading and following, it should be interpreted as misfortune. If neither auspicious nor malevolent spirits come to guide or follow, then we should look at its relationship with other stars in terms of meridians, channels, connections, and sequences. Some birth charts have well-matched structures but still do not lead to high status, and the problem is always due to the main star being out of its proper time and place.

經者四經，如箕參軫壁、井角斗奎、尾窒觜翼、亢牛婁鬼、氐女胃柳、房虛昴星、心危畢張，在天同為一氣，故宮神皆暗相管攝。命主在箕，吉星在箕，固是同經；命主在箕，吉星在參軫壁，亦係同經，應無不利。反是而為凶曜，害亦如之。

The term "jing" refers to the division of the sky into sections where four constellations opposite each other belong to the same jing. Each jing consists of four constellations. For example, Ji, Shen, Zhen, and Bi form one jing; Jing, Jiao, Dou, and Kui form another; Wei, Shi (which is the Encampment mansion), Zi, and Yi form another; Kang, Niu, Lou, and Gui form another; Di, Nu, Wei, and Liu form another; Fang, Xu, Mao, and Xing form another; Xin, Wei, Bi, and Zhang form another. The constellations within the same jing are naturally connected in the sky, so the spirits governing each palace subtly oversee one another. If the person's position is in the Ji constellation and a good star is also in Ji, they are in the same jing, which is favorable. Even if the person's position is in Ji but the good star is in any of the other three constellations of the same jing, it is still considered the same jing and should not be unfavorable. Conversely, if the same jing contains harmful stars, the harm will also follow the same path.

絡者宮度對也，即對沖三合二絃六合之謂，而兼及三十度、一百五十度，所以立度者即此道也。一氣相通最為親切，即以日月論，日晝夜行一度，月晝夜行十二三四度不等，月與日同宮同度則合朔，離日九十度則上弦，離日一百八十度則望，近日九十度又下弦，非即絡之謂歟？諸星之互相感通，何獨不然？故命主與吉凶星絡對而榮枯立判。

The concept of "luo" refers to the mutual relationship between the palace and the degree, which includes opposition, triple harmony, two strings, and six harmony, as well as the separation of thirty degrees and one hundred fifty degrees. The method of establishing degrees mentioned earlier is based on these principles. Those within the same qi are interconnected and have the closestsympathetic response. Take the sun and moon as an example: the sun moves one degree per day and night, while the moon moves twelve to fourteen degrees per day and night. When the moon and sun are in the same palace and degree, it is called the new moon. When the moon is ninety degrees away from the sun, it is the first quarter. When it is one hundred eighty degrees away, it is the full moon. When it approaches the sun again by ninety degrees, it is the last quarter. This is precisely what "luo" means. How could other stars be any different? Therefore, when the person's destiny connects with auspicious or inauspicious stars through luo, their prosperity and decline are immediately determined.

貫者，他星與命度共為一經也。如命與度是火，他星即火之類。分衰旺不分同異，吉星自亨，凶星自蹇。

The term "guan" refers to when another star shares the same element as the degree established by the命宫. For example, if both the命宫 and the established degree belong to the fire element, and the arriving star also belongs to fire, this is called "guan." When assessing "guan," only the strength and decline of the star are considered, not whether it is the same or different. If the star that comes to form "guan" is a beneficial one, it naturally brings smoothness and success; if it is a harmful star, it naturally leads to obstacles and difficulties.

串者，在立命立度之度也。如命是木，他星即躔角斗奎井；度是角，他星即躔角斗奎井。有相迎無相拒，吉星自亨，凶星自蹇。

The term "serial" refers to other stars being in the same degree as the established destiny and destiny degree. For example, if one's destiny belongs to the Wood element, other stars would be in the degrees of Jiao, Dou, Kui, and Jing; if the established degree is Jiao, other stars would also be in the degrees of Jiao, Dou, Kui, and Jing. In this way, they only meet and do not clash. If the stars coming to join are auspicious, things will be smooth; if they are inauspicious, things will be obstructed.

填者四柱填實也。如四柱有子丑，吉凶星在子丑；四柱有戌亥，吉凶星在戌亥之類。

The term "filling" refers to the situation where the auspicious or inauspicious stars on the divination chart exactly correspond to the earthly branches in the person's birth time. For example, if the year, month, day, and hour pillars include the branches Zi and Chou, and the auspicious or inauspicious stars are precisely located in the Zi or Chou positions; or if the pillars include Xu and Hai, and the stars are precisely located in the Xu or Hai positions, such cases are called filling. Once filled, the effects of the star's auspiciousness or inauspiciousness become much more likely to manifest.

沖者對宮沖照也。即隔六宮一百八十度之謂，而正不必拘拘於一百八十度也。如立命在子，吉凶星在午之類，更須看命主與大限。

The term "chong" refers to a situation where two positions are opposite each other, separated by six palaces and 180 degrees. However, in practical application, one does not strictly adhere to an exact 180-degree separation. For example, if the native's命宫 is at Zi and a beneficial or malevolent star is located at Wu, this is considered a chong. To determine the fortune or misfortune associated with chong, one must also consider the condition of the native's main star and the current large limit period. (The original note at the bottom of the heading, "ji hou bu," indicates that the author added this entry later.)

守者守命宮也，吉凶星在命宮之謂，大限亦然。

the so-called "guarding" refers to a star residing in the命宫, meaning a fortunate or adverse star is directly located within the命宫. If a star is present in the palace reached by the great period, it is also called guarding.

釣者三方四正釣照也。三方即隔四宮之三合，而不必拘拘於一百二十度也。如命宮在卯，吉凶星在亥未之類。四正即隔三宮之二絃，而不必拘拘於九十度也。如命宮在申，吉凶星在亥寅巳之類，更須看命主及大限。

The concept of "hooking" (钓) refers to the influence from three directions and four cardinal points, which are distant but still effective. The three directions mean the three harmonious positions that are four palaces apart, without strictly adhering to exactly 120 degrees. For example, if the命宫 (life palace) is in卯 (Mao), and auspicious or inauspicious stars are in亥 (Zi) and未 (Wei), which form a triple harmony with卯, this is considered three-direction hooking. The four cardinal points refer to the two-string positions that are three palaces apart, without strictly adhering to exactly 90 degrees. For example, if the命宫 is in申 (Shen), and auspicious or inauspicious stars are in亥 (Zi),寅 (Yin), and巳 (Si), this is considered four-cardinal-point hooking. When judging the fortune or misfortune of hooking, it is also necessary to consider the main star of the person and the great limit (大限).

兩星拱命主，或在三方，或在對宮，總以無混雜為貴，日月官魁之拱尤重，命主大限皆然，然亦須辨拱星之吉凶。

the so-called "arch" refers to two stars jointly embracing the destiny master, or approaching from three directions, or from the opposite palace. An arch is most valuable when there are no other stars interfering in between; among these, the Sun, the Moon, "Tian Guan," and "Kui Star" are most important. Whether the destiny master is embraced or the major period is embraced, it is necessary to distinguish whether the stars forming the arch are auspicious or malevolent. One should not assume that an arch is always favorable just because there is an arch.

兩星夾命主，或在一宮，或在數宮，總以不混雜為貴，日月官魁之夾尤重，命主大限皆然，然亦須辨夾星之吉凶，至於日月所夾，更當推求。

The concept of "jia" refers to two stars positioned one in front and one behind, enclosing the subject in the middle, or enclosing the subject within the same palace, or enclosing the subject across several palaces. The quality of "jia" is considered superior when the intervening stars are not mixed with others. Among these, the combination of the Sun, the Moon, "Tian Guan," and "Kui Star" is most significant. Whether the subject or the major period is enclosed, it is important to distinguish whether the enclosing stars are auspicious or inauspicious. In particular, the situation where the Sun and Moon enclose the subject requires careful analysis.

命主是官魁文科，日月夾最宜，以其氣聚神旺也，若係劫煞傷刃，日月夾之反為不美。倘非命主，僅屬他星，則以夾官魁文科為祥，夾劫煞傷刃為災，但必察其與命度有關會與否，如並未與命度經絡貫串，則亦不見災祥也。

If the person's destiny is dominated by auspicious stars such as 'Heavenly Official', 'Kui Star', 'Wen Star', and 'Ke Ming', then being squeezed by the sun and moon is most suitable, because the energy gathers and the spirit becomes strong. However, if the person's destiny is dominated by inauspicious stars such as 'Jie Cai', 'Qi Sha', 'Shang Guan', and 'Yang Ren', then being squeezed by the sun and moon is not favorable, as it would cultivate and strengthen the malevolent energy. If the star being squeezed is not the person's main star but another star, then squeezing the official, Kui, Wen, and Ke Ming stars is considered auspicious, while squeezing the Jie Cai, Qi Sha, Shang Guan, and Yang Ren stars is considered calamitous. However, one must examine whether this star being squeezed has any connection with the person's birth chart degree. If it neither connects with the birth chart degree nor forms a continuous relationship, then whether it brings good or bad fortune will not manifest.

日月之夾雖取其不混雜，若冬生人，以水孛為官魁科名，日月夾水夾孛，或並夾火夾羅在內，則水孛方藉火羅以暖，始不寒凍，非惟不作混雜論，其精神正全在火羅；如夾水孛並無火羅，似乎不混雜，而其實反難生動矣。推之於拱亦然，夾與拱略同，而其力較大。

When the sun and moon come together to form a conjunction, it is generally considered favorable if they do not mix with other stars, but there are exceptions. For example, people born in winter take the water star and 'Yuebo' as 'Tian Guan', 'Kui Star', and 'Ke Ming'. If the sun and moon enclose the water star and 'Yuebo', and also include the fire star and 'Luohou' in the middle, then the water and 'Yuebo' need the fire and 'Luohou' to warm them up, so they do not become cold and stagnant. In this case, it is not considered mixed, but rather all the focus is on the fire and 'Luohou'. Conversely, if only the water and 'Yuebo' are enclosed without the fire and 'Luohou', it may seem clean and uncluttered on the surface, but in reality, it leads to cold stagnation and lacks vitality. This principle also applies to 'gong' (arching). 'Jia' (enclosure) and 'gong' are generally similar, but 'jia' has a stronger effect.

或羅計攔出一星，日月攔出一星是也。所當辨攔截之星之吉凶，並當辨吉凶星之與命度有關會與否，更取其無他星混雜。然使攔出吉凶星，兼攔出命主，則此吉凶星雖與命度絕不經絡貫串，卻以命主同攔出而有關會矣。

The concept of "interception" refers to a situation where two stars, "Rohini" and "Jeddu," block a star in between, or where the Sun and Moon intercept a star. When interpreting this pattern, first determine whether the two intercepting stars are auspicious or inauspicious. Next, check whether the intercepted star, whether auspicious or inauspicious, has any connection with the degree of the native's birth chart. Also, ensure that there are no other stars interfering. However, there is a special case to note: if both an auspicious and an inauspicious star are intercepted, and the native is also included within this interception, then even if the intercepted star has no meridian connection with the native's birth chart, it will still form a connection because it is intercepted together with the native.

又冬生人，攔出水孛，兼攔出火羅，似乎混雜，但水孛是官魁科名，得火羅暖之，其氣正揚；水孛是劫煞傷官，有火羅助之，其焰彌熾，未可執一而斷。

For example, if someone is born in winter, the elements revealed are water and 'Yuebo', along with fire and 'Luohou', which may appear mixed. In reality, one should consider both sides: if water and 'Yuebo' represent his 'Tian Guan', 'Kui Star', and 'Ke Ming' (academic success), then the presence of fire and 'Luohou' to warm them up will allow his energy to flourish properly; but if water and 'Yuebo' indicate his 'Jie Cai', 'Qi Sha', and 'Shang Gan' (destructive influences), then the presence of fire and 'Luohou' will instead intensify the harmful effects. Therefore, one should not make a judgment based solely on one side.

等天官者何？天干之官也，餘俱從天干取用。如甲年生人，甲以辛為官，辛之化祿為氣，氣即天官；以庚為七煞，庚之化祿為水，水即七煞；以丁為傷官，丁之化祿為金，金即傷官；以丙為食神，丙之化祿為木，木即食神；

What is called "heavenly official" (天官) refers to the official star (正官) derived from the heavenly stems. All other ten heavenly spirits (十神) are also determined based on the heavenly stems. For example, a person born in the year of Jia (甲): Jia takes Xin (辛) as its official star, and the禄 of Xin is "Purple Qi" (紫气), so "Purple Qi" is his heavenly official; Jia takes Geng (庚) as its seven calamities (七煞), and the禄 of Geng is water, so the water star is his seven calamities; Jia takes Ding (丁) as its injurious star (伤官), and the禄 of Ding is metal, so the metal star is his injurious star; Jia takes Bing (丙) as its nourishing star (食神), and the禄 of Bing is wood, so the wood star is his nourishing star. (The word "etc." at the beginning is a remnant of a previous title, and is retained as is.)

以己為正財，己之化祿為月，月即正財；以戊為偏財，戊之化祿為土，土即偏財；以壬為偏印，壬之化祿為計，計即偏印；以癸為正印，癸之化祿為羅，羅即正印；以乙為劫財，乙之化祿為孛，孛即劫財；甲之化祿為火，火即元祿。餘仿此。

Jia's official wealth is Ji, and Ji's transformed fortune is Taiyin, so Taiyin is his official wealth; Jia's biased wealth is Wu, and Wu's transformed fortune is earth, so the earth star is his biased wealth; Jia's biased wisdom is Ren, and Ren's transformed fortune is 'Ji Du', so 'Ji Du' is his biased wisdom; Jia's official wisdom is Gui, and Gui's transformed fortune is 'Luo Hou', so 'Luo Hou' is his official wisdom; Jia's劫财 is Yi, and Yi's transformed fortune is 'Yue Bo', so 'Yue Bo' is his劫财; Jia's own transformed fortune is fire, so the fire star is his 'Yuan Lu'. The other nine heavenly stems each follow this method to determine their respective ten stars.