（《素问·六节藏象论》）
黄帝问曰∶余闻天以六六之节，以成一岁，人以九九制会，计人亦有三百六十五节，以为天地久矣，不知其所谓也。
（天有上下四方，是为六合，地有正隅中外，是为九宫，此乾坤合一之大数也，凡寰中物理，莫不由之。故节以六六而
成岁，人因九九以制会。且人有三百六十五节，正以合天之度数，复有九岁以应地之九野，此其所以为天地人也。六六
九九，义如下文。）岐伯对曰∶昭乎哉问也！请遂言之。夫六六之节、九九制会者，所以正天之度、气之数也。（六六之
节，谓如天地合数则花甲生焉，花甲一周凡六十日，而所包天干各六，是一周之六六也。一岁之数三百六十日，而所包
甲子凡六周，三阴三阳凡六气，是一岁之六六也。九九制会者，天有四方，方各九十度有奇而制其会。岁有四季，季各
九十日有奇而制其会。以至地有九野，人有九藏，皆应此数。故黄钟之数生于九，而律度量衡准绳规矩之道，无不由之。
夫有气则有度，有度则有数，天度由此而正，气数由此而定，而裁制其会通之妙者则在乎人，其为功也亦大矣，故首节
曰人以九九制会也。又一九义详脉色类五。）天度者，所以制日月之行也。气数者，所以纪化生之用也。（制，节也，正
也。纪，记也。太虚廖廓，本不可测；所可测者，赖列宿周旋，附于天体，有宿度则天道昭然，而七政之迟疾有节，是
所以制日月之行也。气数无形，本不易察；所可察者，在阴阳往来，见于节序，有节序则时令相承，而万物之消长有期，
乃所以纪化生之用也。）天为阳，地为阴；日为阳，月为阴。（天包地外，地居天中，天动地静，干健坤顺，故天为阳，
地为阴。火之精为日，水之精为月，故日为阳，月为阴。）行有分纪，（凡天地日月之营运，各有所纪。天象正圆，周旋
不息。天体倚北，北高南下，南北二极居其两端，乃其枢轴不动之处也。天有黄赤二道。赤道者，当两极之中，横络天
腰，中半之界也。赤道之北为内郭，北极居之；赤道之南为外郭，南极居之。日月循天营运，各有其道，日行之道是为
黄道。黄道之行，春分后行赤道之北，秋分后行赤道之南。月行之道有九，与日不同。九道者，黑道二，出黄道北；赤
道二，出黄道南；白道二，出黄道西；青道二，出黄道东。故立春春分，月东从青道；立秋秋分，月西从白道；立冬冬
至，月北从黑道；立夏夏至，月南从赤道。此亦云赤道者，以五方五色言，又非天腹赤道之谓也。凡此青黑白赤道各二，
并黄道而为九。盖黄为土之正色，位居中央，亦曰中道。班固天文志曰∶日之所由，谓之黄道是也。凡节序之分，以日
为主，日则随天而行。邵子曰∶夏则日随斗而北，冬则日随斗而南。太玄曰∶一北而万物生，一南而万物死。刘昭曰∶
日行北陆谓冬，西陆谓春，南陆谓夏，东陆谓秋。夫以南北为夏冬者是也，以西陆为春、东陆为秋者何也？盖天地之道，
子午为经，卯酉为纬。一岁之气，始于冬至，一阳在子，为天日之会。由是斗建随天左旋以行于东方，日月挨宫右退以
会于西宿。故仲冬斗建在子，则日月会于星纪，斗宿丑宫也。季冬斗建在丑，则日月会于玄枵，女宿子宫也。此所以日
行北陆谓冬也。又由是则斗建自东北顺而南，日月自西北逆而南，故孟春斗建在寅，则日月会于 訾，室宿亥宫也。仲
春斗建在卯，则日月会于降娄，奎宿戌宫也。季春斗建在辰，则日月会于大梁，胃宿酉宫也。是皆以西纬东，此所以日
行西陆谓春也。又由是则斗建自东南顺而西，日月自西南逆而东，故孟夏斗建在巳，则日月会于实沉，毕宿申宫也。仲
夏斗建在午，则日月会于鹑首，井宿未宫也。季夏斗建在未，则日月会于鹑火，柳宿午宫也。此所以日行南陆谓夏也。
又由是则斗建自西南顺而北，日月自东南逆而北，故孟秋斗建在申，则日月会于鹑尾，翼宿巳宫也。仲秋斗建在酉，则
日月会于寿星，角宿辰宫也。季秋斗建在戌，则日月会于大火，房宿卯宫也。是皆以东纬西，此所以日行东陆谓秋也。
以至孟冬斗建在亥，则日月会于析木，尾宿寅宫，而复交乎冬至。故春不在东而在西，秋不在西而在东也。由此观之，
则天运本顺而左旋，日月似逆而右转，故星家以七政为右行。殊不知日月五星皆循天左行，其所以似右者，乃日不及天，
月不及日，并五星之退度耳。故天之与日，正会于子半之中，是为一岁之首，即冬至节也。自子半之后，则天渐余而东，
日渐缩而西，而时序节令从兹更改矣。五星之行，亦各有度。如木曰岁星，其行一年一宫，十二年一周天。火曰荧惑，
其行六十一日有零过一宫，七百四十日一周天。土曰镇星，其行二十八月过一宫，二十八年一周天。金曰太白，其行一
月一宫，一岁一周天。水曰辰星，常随太阳而行，然或前或后，不出三十度之外，亦一月一宫，一岁一周天。凡此五星，
皆所以佐日月而循序如纬者也。此行有分纪之谓。）周有道理。（按浑天说曰∶天地之体，状如鸟卵，天包地外，犹壳裹
黄，其形体混然，周旋无已，故曰混天。然则周天之度，何从考正？乃于日行之数，有以见之。日之行度，不及于天，
故以每日所短之数，纪为一度，凡行三百六十五日又四分日之一，竟天一周，复会于旧宿之处，故纪天为三百六十五度
又四分度之一，而周天二十八宿均此数焉。其行则自东而升，自西而降。安定胡氏曰∶人一呼一吸为一息，一息之间，
大约天行八十里。凡人昼夜呼吸，总计一万三千五百息，以八十里之数因之，共得一百八万里。考之洛书甄曜度及春秋
考异邮，皆云周天一百七万一千里，其大概亦不相远，此周天围圆之数也。以三百六十五度四分度之一分之，则每度得
二千九百三十二里，又千四百六十一分里之三百四十八。以围三径一言之，则周天上下四旁，直径三十五万七千里。地
面去天，又减此之半，而三光出入乎其中，此周有道理之谓。）日行一度，月行十三度而有奇焉，故大小月三百六十五日
而成岁，（日行一度、月行十三度者，言日月之退度也。日月循天营运，俱自东而西，天行速，日行迟，月行又迟。天体
至圆，绕地左旋，常一日一周而过日一度。日行迟，亦一日绕地一周，而比天少行一度。凡积三百六十五日又二十五刻，
仍至旧处而与天会，是为一岁，此日行之数也，故曰日行一度。月行又迟，亦一日绕地一周，而比天少十三度又十九分
度之七，积二十七日半有奇而与天会，是为一月，此月行之数也，故曰月行十三度而有奇焉。然于正度之外，阳气尚盈，
阴气常缩，是为盈缩，气有盈缩，故月有大小。盈者气盈，天之数也。缩者朔虚，日月之数也。凡月有三十日，岁有十
二月，是一岁之数，当以三百六十日为常。然天之气盈，每于过日一度之外，仍盈十三分七厘八丝三忽有奇，积三百六
十日，共得四千九百三十五分，以日法九百四十分为一日除之，合盈五日又二百三十五分，其合于刻数，则为二十五刻
零。此一岁三百六十日之外，天行过日之数也。月之朔虚，一日常不及日十二度十九分度之七，积二十九日又九百四十
分日之四百九十九，其合于刻数，则为五十三刻零，而与日会。是每月常虚四百四十一分，积十二个月，共得五千二百
九十二分，以日法九百四十分为一日除之，则每岁合虚五日又五百九十二分，其合于刻数，则为六十三刻零，故一岁日
数，止实得三百五十四日又三十七刻。以成数为言，则一岁约少六日，是当六大六小矣，此一岁月不及日之数也。故朱
子曰∶气言则三百六十五日，朔言则三百五十四日，举气盈朔虚之中数言，则三百六十日。尧典举成数言，故曰三百六
十六日也。此大小月三百六十五日而成岁之谓。）积气余而盈闰矣。（积气余者，岁气余分之积而成闰也。一岁之日，以
三百六十为常数，而月少于日，故每年止三百五十四日又三十七刻，而十二晦朔尽矣。是周岁月不及日者，凡五日又六
十三刻为朔虚。日又少于天，故周天之数，共三百六十五度四分度之一，是周岁天多于日者，凡五日又二十五刻为气盈。
合气盈朔虚，共得十日零八十八刻，此一岁气余之数而闰生焉。故以三岁而计，则得三十二日又六十四刻，是一闰而有
余。以五岁而计，则得五十四日又四十刻，是再闰而不足。故以十九年而计，则得二百六日又七十二刻，以月法二十九
日零五十三刻除之，正得七个月不差时刻。此所以十九年而七闰，则气朔分齐，是谓一章。大约三十二个月有奇置一闰，
虽不尽同，亦不相远。故三年不置闰，则春之一月入于夏，子之一月入于丑。积之之久，至于三失闰则春季皆为夏，十
二失闰则子年皆为丑，寒暑反易，岁时变乱，农桑庶务，全失其时矣。故以余日置闰于其间，然后岁气不差，四时得成，
而众功皆立也。）立端于始，（端，首也。始，初也。天地有气运，气运有元首，元首立而始终正矣。天有其端，北极是
也。气有其端，子半是也。节有其端，冬至是也。故立天之端而宿度见，立气之端而辰次见，立节之端而时候见。如周
正建子为天统，商正建丑为地统，夏正建寅为人统，皆所以立岁首而授民以时也，即立端于始之义。）表正于中，（表，
识记也。正者，正其子午。中者，中其四方。盖天道玄远，窥测不易，虽立端以察其始，尚不足以探其微，故又立表以
正其中也。如周公营洛置五表，颖川阳城居中表，其度景处，古迹犹存。中表南千里置一表，北千里置一表，东西亦然，
此正日景以求地中也。考之周礼曰∶大司空之职，立土圭之法，测土深，正日景，以求地中。日南则景短多暑，日北则
景长多寒，日东则景夕多风，日西则景朝多阴。此在郑康成固有注疏，但亦未甚明悉。朱子曰∶今人都不识土圭，康成
亦误。圭尺是量表景底尺，长一尺五寸，以玉为之是也。按古制土圭之长，尺有五寸，而测景之表，其长八尺。立表以
测景，用圭以量景，而天地之中，气候之序，于斯乎正矣。详求其法，盖以天体混圆，半复地上，半在地下。其上下二
端，谓之二极，北极出地三十六度，南极入地三十六度，两极相去一百八十二度半有奇。两极之中，横络天腰者，是为
赤道，其去两极，各九十一度有奇。日行之道，是为黄道，由赤道内外周行各半。其入于赤道之内，最近者，日行于参
九度之间，在赤道之北二十四度，其去北极六十七度少强，是为夏至日行之道，去极最近，其景最短，故立八尺之表，
而景唯一尺五寸，此以地在日中之南，时当阳极，故曰日南则景短多暑也。斯时也，黄道在参宿度中，出寅末，入戌初。
凡昼行地上者二百一十九度强，故昼长；夜行地下一百四十六度强，故夜短也。其出于赤道之外，最远者，日行于箕四
度之间，在赤道之南二十四度，其去北极一百一十五度有奇，是为冬至日行之道，去极最远，其景最长，故以八尺之表，
而景长一丈三尺，此以地在日中之北，时当阴极，故曰日北则景长多寒也。斯时也，黄道在箕宿度中，出辰初，入申末。
凡昼行地上者一百四十六度强，故昼短；夜行地下二百一十九度强，故夜长也。其黄道交行于赤道之间者，是为日行之
中道。春分日黄赤二道交于西北壁三度，秋分日交于东南翼十七度，各去极九十一度有奇，此度在南北远近之中，故景
居二至长短之半而寒热匀也。斯时也，黄道出卯中，入酉中，日行地上地下各一百八十二度有奇而昼夜平也。所谓日东
则景夕多风者，言地在日中之东，则日甫中而景已如夕，是地偏于左而东方木气多风也。所谓日西则景朝多阴者，言地
在日中之西，则日已中而景犹如朝，是地偏于右而西方金气多阴也。所谓日至之景、尺有五寸、谓之地中者，言夏至为
一岁之中，日在中天，其景最短，故景唯一尺五寸与土圭之长正相合处，此便是地之中，亦所以见岁之中也。故嵩高正
当天之中。极南五十五度，当嵩高之上。又其南十二度，为夏至之日道。又其南二十四度，为春秋分之日道，即赤道也。
又其南二十四度，为冬至之日道，南下去地，三十一度而已。是夏至日去北极六十七度，春秋分日去北极九十一度，冬
至日去北极一百一十五度，乃其大数。此天地之所合也，四时之所交也，风雨之所会也，阴阳之所和也。故邵子曰∶天
地之本，其起于中乎。天之中何在？曰∶在辰极。地之中何在？曰∶在嵩山。惟天以辰极为中，故可以起历数而推节候；
惟地以嵩山为中，故可以定方隅而均道里。子午其天地之中乎。冬至阳生子，夜半时加子，所以干始于坎而终于离，此
南北二极独为天枢而不动也。夏至阴生午，天中日在午，所以坤始于离而终于坎，此冬夏二至，一在南，一在北，而不
(Suwen · Liu Jie Zang Xiang Lun)
The Yellow Emperor asked: I have heard that Heaven uses six cycles of six days (i.e., 360 days) as a solar term unit to constitute a year; Man uses nine cycles of nine numbers (i.e., 81) to formulate corresponding laws, calculating that the human body also has 365 joints, thereby aligning with Heaven and Earth. This concept has existed for a long time, but I do not know its specific meaning.
(Heaven has up, down, front, back, left, and right, called the Six Harmonies (Liu He); Earth has central, corner, middle, and outer positions, called the Nine Palaces (Jiu Gong). This is the great number of the unity of Qian and Kun. All principles in the world follow this rule. Thus, solar terms are formed by the number of six-six, and humans formulate convergence methods based on the number of nine-nine. Moreover, humans have 365 joints, which exactly correspond to the degrees of Heaven, and there is a nine-year period to correspond to the Nine Fields (Jiu Ye) of Earth. This is why humans are considered part of Heaven and Earth. The meanings of six-six and nine-nine are explained below.) Qi Bo replied: Your question is indeed profound! Please allow me to elaborate. The so-called "six-six" solar terms and "nine-nine" convergence methods are used to rectify the degrees of Heaven and determine the quantity of Qi (Vital Energy). (The "six-six" solar terms refer to the generation of the Sexagenary Cycle (Hua Jia) through the combination of Heaven and Earth stems and branches. One cycle of Hua Jia consists of 60 days, during which each of the Ten Heavenly Stems appears six times, constituting the "six-six" of one cycle. A year has 360 days, encompassing six cycles of Jia Zi (Sexagenary pairs), and there are Six Qi (Liu Qi) corresponding to Three Yin and Three Yang, representing the "six-six" of a year. The "nine-nine" convergence refers to Heaven having four directions, each covering slightly more than 90 degrees to form its convergence. A year has four seasons, each lasting slightly more than 90 days to form its convergence. Similarly, Earth has Nine Fields, and the human body has Nine Zang Organs (Jiu Zang), all corresponding to these numbers. Thus, the number of Huangzhong (the first pitch pipe) originates from nine, and all laws regarding music, measurement, and standards derive from it. Where there is Qi, there are degrees; where there are degrees, there are quantities. The degrees of Heaven are rectified thereby, and the quantity of Qi is determined thereby. The one who controls the subtlety of their convergence is Man, whose merit is great. Hence, the first section states, "Man uses nine-nine to formulate convergence." For further details on "one-nine," see Section Five of Pulse and Color.) The degrees of Heaven are used to regulate the movement of the Sun and Moon. The quantity of Qi is used to record the function of transformation and generation. ("Zhi" means restraint and rectification. "Ji" means recording. The Great Void is vast and originally immeasurable; what can be measured relies on the rotation of constellates attached to the celestial sphere. With fixed stellar degrees, the Way of Heaven becomes clear, and the speed of the Seven Governors (Qi Zheng - Sun, Moon, and five planets) has rhythm. This is how the movement of the Sun and Moon is regulated. The quantity of Qi is formless and hard to observe; what can be observed is the interplay of Yin and Yang manifesting in seasonal order. With seasonal order, solar terms succeed one another, and the waxing and waning of all things have their timing. This is how the function of transformation and generation is recorded.) Heaven is Yang, Earth is Yin; the Sun is Yang, the Moon is Yin. (Heaven envelops Earth from outside, and Earth resides within Heaven. Heaven moves, Earth is still; Qian is vigorous, Kun is compliant. Therefore, Heaven is Yang, and Earth is Yin. The essence of Fire becomes the Sun, and the essence of Water becomes the Moon. Therefore, the Sun is Yang, and the Moon is Yin.) Their movements have divisions and records. (All operations of Heaven, Earth, Sun, and Moon have their respective records. The celestial image is perfectly round, rotating endlessly. The celestial sphere leans towards the North, higher in the North and lower in the South. The North and South Poles are at the two ends, serving as the stationary axis. There are two paths in Heaven: the Ecliptic and the Celestial Equator. The Celestial Equator is located between the two poles, crossing the waist of Heaven, marking the midpoint. North of the Celestial Equator is the Inner Circle, where the North Pole resides; South of the Celestial Equator is the Outer Circle, where the South Pole resides. The Sun and Moon move along their respective paths. The path of the Sun is called the Ecliptic (Huang Dao). The Ecliptic runs north of the Celestial Equator after the Spring Equinox and south of it after the Autumn Equinox. The Moon has nine paths, different from the Sun's. These nine paths include: two Black Paths (Hei Dao) emerging north of the Ecliptic; two Red Paths (Chi Dao) emerging south of the Ecliptic; two White Paths (Bai Dao) emerging west of the Ecliptic; and two Green Paths (Qing Dao) emerging east of the Ecliptic. Thus, during Lichun and Chunfen, the Moon travels on the Green Path in the East; during Liqiu and Qiufen, on the White Path in the West; during Lidong and Dongzhi, on the Black Path in the North; and during Lixia and Xiazhi, on the Red Path in the South. Here, "Red Path" refers to the five directions and colors, not the Celestial Equator mentioned earlier. These two each of Green, White, Black, and Red Paths, plus the Ecliptic, make nine. Since Yellow is the true color of Earth and occupies the center, it is also called the Central Path. Ban Gu in *Tianwen Zhi* said: "Where the Sun passes is called the Ecliptic." Seasonal divisions are primarily based on the Sun, which follows the Heaven. Shao Yong said: "In summer, the Sun follows the Dipper northward; in winter, it follows southward." *Tai Xuan Jing* says: "One northward brings life to all things; one southward brings death." Liu Zhao said: "Sun moving in the Northern Land is Winter; Western Land is Spring; Southern Land is Summer; Eastern Land is Autumn." It is correct to consider North/South as Summer/Winter, but why is West Spring and East Autumn? Because the Way of Heaven and Earth uses Zi-Wu as longitude and Mao-You as latitude. The Qi of the year begins at the Winter Solstice, when one Yang arises at Zi, marking the convergence of Heaven and Sun. From then on, the Dipper rotates counter-clockwise (left) in the East, while the Sun and Moon move clockwise (right) to converge at western stars. In mid-winter, when the Dipper points to Zi, the Sun and Moon converge at Xingji (Dou constellation, Chou palace). In late winter, pointing to Chou, they converge at Xuanxiao (Nü constellation, Zi palace). This is why the Sun moving in the Northern Land is called Winter. Then, the Dipper moves clockwise from Northeast to South, while the Sun and Moon move counter-clockwise from Northwest to South. In early spring, pointing to Yin, they converge at Zi (Shi constellation, Hai palace). In mid-spring, pointing to Mao, they converge at Jianglou (Kui constellation, Xu palace). In late spring, pointing to Chen, they converge at Daliang (Wei constellation, You palace). These are all West-latitude East-longitude, hence the Sun moving in the Western Land is called Spring. Then, the Dipper moves clockwise from Southeast to West, while the Sun and Moon move counter-clockwise from Southwest to East. In early summer, pointing to Si, they converge at Shichen (Bi constellation, Shen palace). In mid-summer, pointing to Wu, they converge at Chunshou (Jing constellation, Wei palace). In late summer, pointing to Wei, they converge at Chunhuo (Liu constellation, Wu palace). This is why the Sun moving in the Southern Land is called Summer. Then, the Dipper moves clockwise from Southwest to North, while the Sun and Moon move counter-clockwise from Southeast to North. In early autumn, pointing to Shen, they converge at Chunwei (Yi constellation, Si palace). In mid-autumn, pointing to You, they converge at Shouxing (Jue constellation, Chen palace). In late autumn, pointing to Xu, they converge at Dahuo (Fang constellation, Mao palace). These are all East-latitude West-longitude, hence the Sun moving in the Eastern Land is called Autumn. Finally, in early winter, pointing to Hai, they converge at Ximu (Wei constellation, Yin palace), returning to the Winter Solstice. Thus, Spring is not in the East but in the West, and Autumn is not in the West but in the East. From this, we see that Heaven's motion is naturally counter-clockwise (left), while the Sun and Moon appear to move clockwise (right). Astrologers consider the Seven Governors to move right. However, the Sun, Moon, and five planets all move left with Heaven. Their apparent rightward motion is because the Sun is slower than Heaven, the Moon slower than the Sun, and due to the retrograde motion of the five planets. Thus, Heaven and the Sun meet exactly at midnight (Zi half), marking the beginning of the year, i.e., the Winter Solstice. After midnight, Heaven gradually drifts East, and the Sun shrinks West, changing the seasons. The five planets also have their own degrees. Jupiter (Sui Xing) moves one palace per year, completing the sky in 12 years. Mars (Ying Huo) moves one palace every ~61 days, completing the sky in 740 days. Saturn (Zhen Xing) moves one palace every 28 months, completing the sky in 28 years. Venus (Tai Bai) moves one palace per month, completing the sky in one year. Mercury (Chen Xing) follows the Sun, never exceeding 30 degrees, moving one palace per month, completing the sky in one year. These five planets assist the Sun and Moon in orderly progression like warp and weft. This is what is meant by "movements have divisions and records.") The circumference of Heaven has principles. (According to the Hun Tian theory: The shape of Heaven and Earth is like a bird's egg, with Heaven enveloping Earth like a shell enclosing yolk. Its form is integrated, rotating endlessly, hence called Hun Tian. So, how is the degree of the celestial sphere verified? It is seen from the Sun's motion. The Sun's motion is slower than Heaven, so the daily deficit is recorded as one degree. It travels 365 and 1/4 days to complete one revolution around Heaven, meeting the original star position again. Thus, Heaven is recorded as 365 and 1/4 degrees, equally distributed among the 28 Mansions. Its motion rises in the East and sets in the West. Hu Shi of Anding said: One breath is one Xi. In one Xi, Heaven moves about 80 li. Humans breathe 13,500 times day and night. Multiplying by 80 li gives 1,080,000 li. *Luoshu Zhenyao Du* and *Chunqiu Kaoyiyou* state the celestial circumference is 1,071,000 li, which is close. This is the circumference of Heaven. Dividing 365.25 degrees by this, each degree is approx. 2,932 li and 348/1461 parts of a li. Using the ratio of circumference to diameter as 3:1, the diameter of Heaven is 357,000 li. The distance from Earth surface to Heaven is half this, with the three lights (Sun, Moon, stars) moving within. This is the principle of "circumference of Heaven".) The Sun moves one degree per day, and the Moon moves thirteen degrees and a fraction, thus forming a year of 365 days with large and small months. (Moving one degree per day for the Sun and thirteen degrees for the Moon refers to their retrograde motion relative to Heaven. Both move East to West. Heaven moves fast, Sun slow, Moon slower. Heaven rotates around Earth counter-clockwise, completing one circle in a day and passing the Sun by one degree. The Sun, moving slowly, also completes one circle around Earth in a day but lags behind Heaven by one degree. Accumulating 365 days and 25 ke (quarters of an hour), it returns to the original position and meets Heaven, forming one year. This is the Sun's motion, hence "Sun moves one degree per day." The Moon moves even slower, lagging behind Heaven by 13 and 7/19 degrees per day. Accumulating 27.5 days, it meets Heaven, forming one lunar month. This is the Moon's motion, hence "Moon moves thirteen degrees and a fraction." However, besides the standard degree, Yang Qi is surplus, and Yin Qi is contracted, creating surplus and deficit (Ying Suo). Due to this, lunar months vary in length. "Surplus" refers to Qi Surplus (Tian's count). "Deficit" refers to New Moon Void (Sun/Moon count). A month has 30 days, a year 12 months, totaling 360 days as the constant. But Heaven's Qi surplus exceeds the daily one-degree mark by 13.783... fen. Accumulated over 360 days, this totals 4,935 fen. Divided by the daily method of 940 fen, it equals 5 days and 235 fen, or 25 ke. This is the excess of Heaven's motion over the Sun beyond 360 days. The Moon's new moon void is 12 and 7/19 degrees less than the Sun daily. Accumulated over 29 days and 499/940 days, it equals 53 ke to meet the Sun. Each month is short by 441 fen. Over 12 months, this totals 5,292 fen. Divided by 940, it equals 5 days and 592 fen, or 63 ke. Thus, the actual solar days in a year are 354 days and 37 ke. By rounded numbers, a year is short by about 6 days, requiring six large and six small months. This is the Moon's deficit compared to the Sun. Zhu Xi said: By Qi, it is 365 days; by New Moon, 354 days; taking the mean of Qi Surplus and New Moon Void, it is 360 days. *Book of Documents* uses rounded numbers, stating 366 days. This explains the 365-day year with large and small months.) Accumulating the surplus of Qi generates leap months. (Accumulating Qi surplus means the fractional remainder of the annual Qi forms leap months. A year's days are constant at 360, but the Moon is shorter than the Sun, resulting in only 354 days and 37 ke for twelve lunations. The annual deficit of Moon vs. Sun is 5 days and 63 ke (New Moon Void). The Sun is shorter than Heaven, so the celestial degree is 365 and 1/4. The annual surplus of Heaven vs. Sun is 5 days and 25 ke (Qi Surplus). Combining Qi Surplus and New Moon Void yields 10 days and 88 ke, the annual Qi surplus, generating leap months. Calculating over three years yields 32 days and 64 ke, slightly more than one leap month. Over five years, 54 days and 40 ke, slightly less than two leap months. Over nineteen years, 206 days and 72 ke. Dividing by the lunar month method (29 days 53 ke) yields exactly seven months without error. This is why nineteen years have seven leaps, balancing Qi and New Moons, called a "Chapter" (Zhang). Approximately one leap is added every 32+ months. Without leap months for three years, the first month of Spring would shift to Summer, and Zi month to Chou. Long-term accumulation leads to three missed leaps turning Spring into Summer, and twelve missed leaps turning Zi years into Chou years, reversing cold and heat, confusing seasons, and disrupting agriculture. Thus, placing surplus days as leap months ensures accurate yearly Qi, proper seasons, and successful undertakings.) Establish the beginning at the start. (Duan means head/beginning. Shi means initial. Heaven and Earth have Qi operations, which have a head. Once the head is established, beginning and end are rectified. Heaven has its Duan, which is the North Pole. Qi has its Duan, which is midnight (Zi half). Solar terms have their Duan, which is the Winter Solstice. Thus, establishing Heaven's Duan reveals stellar degrees; establishing Qi's Duan reveals time zones; establishing Term's Duan reveals seasons. For example, Zhou calendar establishes Zi as Heaven's統 (System), Shang establishes Chou as Earth's System, Xia establishes Yin as Human System. All establish the year's start to teach people the time, embodying "establishing the beginning at the start.") Set the marker in the center to rectify. (Biao means marker/record. Zheng means rectifying Zi-Wu line. Zhong means centering the four directions. Since Heaven's Way is profound and hard to measure, establishing the Duan to observe the start is insufficient to probe the subtle. Thus, a Biao is set to rectify the center. For instance, Duke of Zhou set five markers in Luoyang. Yangcheng in Yingchuan was the central marker. Its shadow location remains as historical site. One marker was set 1,000 li South, 1,000 li North, East, and West of the central marker. This rectifies the Earth's center by correcting the sun's shadow. *Rites of Zhou* states: The Grand Minister of Works establishes the Tu Gui (Earth Square) method to measure earth depth and rectify shadows to find the Earth's center. South of the sun, shadows are short and hot; North, long and cold; East, evening shadows and windy; West, morning shadows and cloudy. Zheng Kangcheng had annotations, but they were unclear. Zhu Xi said: People today don't know Tu Gui; even Kangcheng was mistaken. The Gui ruler is for measuring shadow length, 1 chi 5 cun, made of jade. Anciently, Tu Gui was 1 chi 5 cun, and the Biao (pole) for measuring shadow was 8 chi tall. Setting the Biao to measure shadow and using Gui to quantify shadow rectifies the center of Heaven and Earth and the order of climate. Detailed calculation: Heaven is spherical, half above ground, half below. The two ends are the Poles. North Pole is 36 degrees above ground; South Pole 36 degrees below. Distance between poles is 182.5 degrees. Midway between poles is the Celestial Equator, 91+ degrees from each pole. The Sun's path is the Ecliptic, circling inside and outside the Equator. Inside the Equator, closest point: Sun moves between Canis Minor 9 degrees, 24 degrees North of Equator, 67+ degrees from North Pole. This is the Summer Solstice path, closest to pole, shortest shadow. An 8-chi Biao casts a 1-chi 5-cun shadow. This is because Earth is South of the Sun, Yang is extreme, hence "South of Sun, short shadow, hot." At this time, Ecliptic is in Canis Minor, rising Yin-end, setting Xu-start. Daytime above ground: 219+ degrees (long day); nighttime below: 146+ degrees (short night). Outside Equator, farthest point: Sun moves between Sagittarius 4 degrees, 24 degrees South of Equator, 115+ degrees from North Pole. This is Winter Solstice path, farthest from pole, longest shadow. An 8-chi Biao casts a 1-zhang 3-chi shadow. Earth is North of Sun, Yin is extreme, hence "North of Sun, long shadow, cold." Ecliptic in Sagittarius, rising Chen-start, setting Shen-end. Daytime above: 146+ degrees (short day); nighttime below: 219+ degrees (long night). When Ecliptic intersects Equator, it is the Middle Path of Sun. Spring Equinox: Ecliptic and Equator intersect at Northwest wall 3 degrees. Autumn Equinox: Intersect at Southeast Wing 17 degrees. Both are 91+ degrees from poles, midway in distance, so shadow is midway between solstices, balanced heat/cold. Ecliptic rises Mao-center, sets You-center. Sun travels 182+ degrees above and below ground, equal day/night. "East of Sun, evening shadow, windy": Earth is East of Sun, so when Sun is mid-heaven, shadow looks like evening. Earth is偏 Left, East Wood Qi is windy. "West of Sun, morning shadow, cloudy": Earth is West of Sun, so when Sun is mid-heaven, shadow looks like morning. Earth is偏 Right, West Metal Qi is cloudy. "Shadow of Solstice, 1 chi 5 cun, called Earth Center": Summer Solstice is mid-year, Sun in mid-heaven, shadow shortest. Shadow 1 chi 5 cun matches Tu Gui length. This is Earth Center, also Year Center. Songshan Mountain is directly under Heaven's center. 55 degrees South is above Songshan. 12 degrees further South is Summer Solstice path. 24 degrees further South is Spring/Autumn Equinox path (Equator). 24 degrees further South is Winter Solstice path, 31 degrees above ground. Summer Solstice Sun is 67 degrees from North Pole; Equinoxes 91 degrees; Winter Solstice 115 degrees. These are general numbers. This is where Heaven and Earth combine, Four Seasons intersect, Wind and Rain meet, Yin and Yang harmonize. Shao Yong said: Does the root of Heaven and Earth begin in the Center? Where is Heaven's Center? In Chen Ji (Polar Star). Where is Earth's Center? In Songshan. Only with Chen Ji as Center can calendars be started and seasons deduced; only with Songshan as Center can directions be fixed and distances equalized. Are Zi-Wu the centers of Heaven and Earth? Winter Solstice Yang arises at Zi, midnight adds to Zi. Thus, Heavenly Stems begin at Kan and end at Li. These North and South Poles are unique Heavenly Pivot, unmoving. Summer Solstice Yin arises at Wu, Sun in mid-heaven is at Wu. Thus, Earthly Branches begin at Li and end at Kan. These Winter and Summer Solstices, one South, one North, do not...