1
昔自在古，歷建正作於孟春。 於時冰泮發蟄，百草奮興，秭鳺先滜。 物乃歲具，生於東，次順四時，卒于冬分。 時雞三號，卒明。 撫十二［月］節，卒于丑。 日月成，故明也。 明者孟也，幽者幼也，幽明者雌雄也。 雌雄代興，而順至正之統也。 日歸于西，起明於東； 月歸於東，起明于西。 正不率天，又不由人，則凡事易壞而難成矣。
In ancient times, the calendar was established with the correct beginning in the first month of spring. At that time, the ice melts and awakens the hibernating creatures; the hundred grasses vigorously arise; the nesting duck is the first to swim. Things then complete the year, being born in the east, then following the four seasons in order, and ending at the winter division. When the rooster crows three times, it ends with brightness. It passes through the twelve monthly sections and ends at Chou. The sun and moon complete it; therefore it is bright. Bright means the first; dark means the young. Dark and bright mean female and male. Female and male alternately flourish, and this follows and arrives at the correct rule. The sun returns to the west and rises bright in the east. The moon returns to the east and rises bright in the west. If the correct beginning does not follow heaven, and moreover is not by human design, then all affairs are easily ruined and difficult to complete.
2
王者易姓受命，必慎始初，改正朔，易服色，推本天元，順承厥意。
When kings change their surname and receive the mandate, they must be careful with the beginning, correct the new moon, change the clothing colors, trace back to the root of the heavenly origin, and comply with and receive its intention.
3
太史公曰：神農以前尚矣。 蓋黃帝考定星歷，建立五行，起消息，正閏餘，於是有天地神祇物類之官，是謂五官。 各司其序，不相亂也。 民是以能有信，神是以能有明德。 民神異業，敬而不瀆，故神降之嘉生，民以物享，災禍不生，所求不匱。
The Grand Historian says: The time before Shennong is still remote. Indeed, the Yellow Emperor examined and fixed the star calendar, established the five phases, raised the wax and wane, and corrected the intercalary remainder. Thereupon there were officials for heaven, earth, spirits, deities, and things and categories. These are called the five officials. Each governs its own sequence and does not mutually interfere. The people were thus able to have trust; the spirits were thus able to have bright virtue. People and spirits had different occupations, were respectful and not profane. Therefore the spirits descended with auspicious births; the people enjoyed things; disasters and calamities did not arise; what was sought was not deficient.
4
少暤氏之衰也，九黎亂德，民神雜擾，不可放物，禍菑薦至，莫盡其氣。 顓頊受之，乃命南正重司天以屬神，命火正黎司地以屬民，使復舊常，無相侵瀆。
When the Shaohao clan declined, the Nine Li created chaotic virtue. People and spirits were mixed in disturbance; things could not be released. Calamities repeatedly arrived, and none could exhaust their qi. Zhuanxu received it and thereupon commanded the Southern Rectifier Chong to govern heaven and belong to the spirits, and commanded the Fire Rectifier Li to govern earth and belong to the people. He made them restore the old constant, with no mutual invasion or profanation.
5
其後三苗服九黎之德，故二官咸廢所職，而閏餘乖次，孟陬殄滅，攝提無紀，歷數失序。 堯復遂重黎之後，不忘舊者，使復典之，而立羲和之官。 明時正度，則陰陽調，風雨節，茂氣至，民無夭疫。 年耆禪舜，申戒文祖，云「天之歷數在爾躬」。 舜亦以命禹。 由是觀之，王者所重也。
Afterward, the Three Miao imitated the virtue of the Nine Li. Therefore the two officials all abandoned their duties, and the intercalary remainder was in the wrong sequence. The first month was extinguished; Sheti had no record; the calendar numbers lost their order. Yao again continued with the descendants of Chong and Li. Not forgetting the old ones, he made them again manage it and established the Xi He officials. When the bright time and correct measure were established, then yin and yang harmonized, wind and rain were moderate, luxuriant qi arrived, and the people had no premature epidemics. When he was old in years, he abdicated to Shun and repeatedly admonished the cultured ancestors, saying, 'The calendar numbers of heaven are in your person.' Shun also commanded Yu with the same words. From this we observe that this is what kings value.
6
夏正以正月，殷正以十二月，周正以十一月。 蓋三王之正若循環，窮則反本。 天下有道，則不失紀序； 無道，則正朔不行於諸侯。
The Xia calendar used the first month; the Yin calendar used the twelfth month; the Zhou calendar used the eleventh month. Indeed, the calendars of the three kings were like a cycle; when exhausted, they returned to the root. When the realm has the Way, then it does not lose the record and sequence. Without the Way, the correct calendar does not circulate among the feudal lords.
7
幽、厲之後，周室微，陪臣執政，史不記時，君不告朔，故疇人子弟分散，或在諸夏，或在夷狄，是以其禨祥廢而不統。 周襄王二十六年閏三月，而春秋非之。 先王之正時也，履端於始，舉正於中，歸邪於終。 履端於始，序則不愆； 舉正於中，民則不惑； 歸邪於終，事則不悖。
After You and Li, the Zhou house was weak. Attendant ministers seized the government; historians did not record the time; lords did not announce the new moon. Therefore the calendar officials' sons and disciples dispersed, some in the various Xia, some among the Yi and Di. Therefore their good omens were abandoned and not unified. In the twenty-sixth year of King Xiang of Zhou, there was an intercalary third month, and the Spring and Autumn Annals criticized it. The former kings' correction of time was to step the beginning at the start, raise the correct at the middle, and return the deviant at the end. When one steps the beginning at the start, the sequence does not err. When one raises the correct at the middle, the people are not confused. When one returns the deviant at the end, affairs are not contrary.
8
其後戰國并爭，在於彊國禽敵，救急解紛而已，豈遑念斯哉！ 是時獨有鄒衍，明於五德之傳，而散消息之分，以顯諸侯。 而亦因秦滅六國，兵戎極煩，又升至尊之日淺，未暇遑也。 而亦頗推五勝，而自以為獲水德之瑞，更名河曰「德水」，而正以十月，色上黑。 然歷度閏餘，未能睹其真也。
Afterward, the Warring States merged and contended. They existed in strong states capturing enemies, saving the urgent and resolving disputes only. How could they have leisure to think of this! At this time, only Zou Yan was clear about the transmission of the five virtues and scattered the divisions of wax and wane to display to the feudal lords. And also because Qin extinguished the six states, weapons were extremely troublesome. Moreover, the days since ascending to the supreme position were shallow, and there was no leisure time. And also somewhat extended the five victories, and considered himself to have obtained the auspiciousness of water virtue. He changed the name of the river to "Virtue Water" and set the calendar to begin with the tenth month, with black as the superior color. Yet in the calendar measure and intercalary remainder, he was not able to see their truth.
9
漢興，高祖曰「北畤待我而起」，亦自以為獲水德之瑞。 雖明習歷及張蒼等，咸以為然。 是時天下初定，方綱紀大基，高后女主，皆未遑，故襲秦正朔服色。
When Han rose, Gaozu said, 'The northern altar awaited me and arose.' He also considered himself to have obtained the auspiciousness of water virtue. Although those who were clear and practiced in the calendar, including Zhang Cang and others, all considered it to be so. At this time, the realm was newly settled and was just establishing the laws and great foundation. Empress Gao, the female ruler, had no leisure. Therefore they inherited the Qin calendar, new moon, and clothing colors.
10
至孝文時，魯人公孫臣以終始五德上書，言「漢得土德，宜更元，改正朔，易服色。 當有瑞，瑞黃龍見」。 事下丞相張蒼，張蒼亦學律歷，以為非是，罷之。 其後黃龍見成紀，張蒼自黜，所欲論著不成。 而新垣平以望氣見，頗言正歷服色事，貴幸，後作亂，故孝文帝廢不復問。
When it reached the time of Filial Wen, Gongsun Chen, a man from Lu, memorialized about the end and beginning of the five virtues, saying, 'Han has obtained earth virtue. It should change the era name, correct the new moon, and change the clothing colors. There should be an auspicious sign; the auspicious sign is that a yellow dragon will appear.' The matter was sent down to Chancellor Zhang Cang. Zhang Cang had also studied the pitchpipes and calendar and considered it not correct, so he dismissed it. Afterward, a yellow dragon appeared in Chengji. Zhang Cang demoted himself, and what he desired to discuss and write was not completed. And Xinyuan Ping was seen through observing qi and extensively spoke of correcting the calendar and clothing colors matters. He was noble and favored. Later he made rebellion; therefore Emperor Wen abandoned it and did not inquire again.
11
至今上即位，招致方士唐都，分其天部； 而巴落下閎運算轉歷，然後日辰之度與夏正同。 乃改元，更官號，封泰山。 因詔御史曰：「乃者，有司言星度之未定也，廣延宣問，以理星度，未能詹也。 蓋聞昔者黃帝合而不死，名察度驗，定清濁，起五部，建氣物分數。 然蓋尚矣。 書缺樂弛，朕甚閔焉。 朕唯未能循明也，紬績日分，率應水德之勝。 今日順夏至，黃鐘為宮，林鐘為徵，太蔟為商，南呂為羽，姑洗為角。 自是以後，氣復正，羽聲復清，名復正變，以至子日當冬至，則陰陽離合之道行焉。 十一月甲子朔旦冬至已詹，其更以七年為太初元年。 年名『焉逢攝提格』，月名『畢聚』，日得甲子，夜半朔旦冬至。」
When the current emperor ascended the throne, he summoned the fangshi Tang Du and divided the heavenly divisions. And Luoxia Hong from Ba operated and calculated the rotating calendar. Then the degrees of the sun and days were the same as the Xia calendar. Thereupon he changed the era name, changed the official titles, and sealed Mount Tai. Therefore he commanded the Censor, saying: 'Formerly, the officials spoke of the star degrees not yet being settled. I broadly extended and announced questions to reason about the star degrees, but was not able to reach it. I have indeed heard that formerly the Yellow Emperor united and did not die. He named, examined, and verified the degrees; settled the clear and turbid; raised the five divisions; and established the divisions and numbers of qi and things. Yet this is indeed still remote. The documents are lacking and music is relaxed. I greatly pity this. I have only not been able to follow the bright way, continuing and refining the daily divisions, generally responding to water virtue's victory. Today, following the summer solstice, Huangzhong is gong, Linzhong is zhi, Tai Cu is shang, Nan Lü is yu, and Gu Xi is jiao. From this time onward, qi again became correct, the yu sound again became clear, and names again became correct and changed. When it reached the zi day at the winter solstice, then the way of yin and yang separating and combining proceeded there. The eleventh month, Jiazi, new moon dawn, and winter solstice had already been reached. They changed it so that the seventh year became the first year of Taichu. The year was named 'Yanfeng Shetige'; the month was named 'Biju'; the day obtained Jiazi; at midnight, the new moon dawn and winter solstice.'
12
歷術甲子篇太初元年，歲名「焉逢攝提格」，月名「畢聚」，日得甲子，夜半朔旦冬至。
The calendar method of the Jiazi chapter for the first year of Taichu: the year was named 'Yanfeng Shetige'; the month was named 'Biju'; the day obtained Jiazi; at midnight, the new moon dawn and winter solstice.
13
正北十二無大餘，無小餘； 無大餘，無小餘； 焉逢攝提格太初元年。
Due north, twelve months: no large remainder, no small remainder. No large remainder, no small remainder. Yanfeng Shetige, the first year of Taichu.
14
十二大餘五十四，小餘三百四十八； 大餘五，小餘八； 端蒙單閼二年。
Twelve months: the large remainder is fifty-four, and the small remainder is three hundred forty-eight. Large remainder five, small remainder eight. Duameng Dan E, the second year.
15
閏十三大餘四十八，小餘六百九十六； 大餘十，小餘十六； 游兆執徐三年。
Intercalary thirteen months: the large remainder is forty-eight, and the small remainder is six hundred ninety-six. Large remainder ten, small remainder sixteen. You Zhao Zhi Xu, the third year.
16
十二大餘十二，小餘六百三； 大餘十五，小餘二十四； 彊梧大荒落四年。
Twelve months: large remainder twelve, small remainder six hundred three. Large remainder fifteen, small remainder twenty-four. Qiang Wu Da Huang Luo, the fourth year.
17
十二大餘七，小餘十一； 大餘二十一，無小餘； 徒維敦牂天漢元年。
Twelve months: large remainder seven, small remainder eleven. Large remainder twenty-one, no small remainder. Tu Wei Dun Zang, the first year of Tianhan.
18
閏十三大餘一，小餘三百五十九； 大餘二十六，小餘八； 祝犁協洽二年。
Intercalary thirteen months: the large remainder is one, and the small remainder is three hundred fifty-nine. The large remainder is twenty-six, and the small remainder is eight. Zhu Li Xie Qiao, the second year.
19
十二大餘二十五，小餘二百六十六； 大餘三十一，小餘十六； 商橫涒灘三年。
Twelve months: the large remainder is twenty-five, and the small remainder is two hundred sixty-six. The large remainder is thirty-one, and the small remainder is sixteen. Shang Heng Dun Tan, the third year.
20
十二大餘十九，小餘六百一十四； 大餘三十六，小餘二十四； 昭陽作鄂四年。
Twelve months: the large remainder is nineteen, and the small remainder is six hundred fourteen. The large remainder is thirty-six, and the small remainder is twenty-four. Zhao Yang Zuo E, the fourth year.
21
閏十三大餘十四，小餘二十二； 大餘四十二，無小餘； 橫艾淹茂太始元年。
Intercalary thirteen months: the large remainder is fourteen, and the small remainder is twenty-two. The large remainder is forty-two, and there is no small remainder. Heng Ai Yan Mao, the first year of Taishi.
22
十二大餘三十七，小餘八百六十九； 大餘四十七，小餘八； 尚章大淵獻二年。
Twelve months: the large remainder is thirty-seven, and the small remainder is eight hundred sixty-nine. The large remainder is forty-seven, and the small remainder is eight. Shang Zhang Da Yuan Xian, the second year.
23
閏十三大餘三十二，小餘二百七十七； 大餘五十二，小餘一十六； 焉逢困敦三年。
Intercalary thirteen months: the large remainder is thirty-two, and the small remainder is two hundred seventy-seven. The large remainder is fifty-two, and the small remainder is sixteen. Yanfeng Kun Dun, the third year.
24
十二大餘五十六，小餘一百八十四； 大餘五十七，小餘二十四； 端蒙赤奮若四年。
Twelve months: the large remainder is fifty-six, and the small remainder is one hundred eighty-four. The large remainder is fifty-seven, and the small remainder is twenty-four. Duameng Chi Fen Ruo, the fourth year.
25
十二大餘五十，小餘五百三十二； 大餘三，無小餘； 游兆攝提格征和元年。
Twelve months: the large remainder is fifty, and the small remainder is five hundred thirty-two. The large remainder is three, and there is no small remainder. You Zhao Shetige, the first year of Zhenghe.
26
閏十三大餘四十四，小餘八百八十； 大餘八，小餘八； 彊梧單閼二年。
Intercalary thirteen months: the large remainder is forty-four, and the small remainder is eight hundred eighty. The large remainder is eight, and the small remainder is eight. Qiang Wu Shan E, the second year.
27
十二大餘八，小餘七百八十七； 大餘十三，小餘十六； 徒維執徐三年。
Twelve months: the large remainder is eight, and the small remainder is seven hundred eighty-seven. The large remainder is thirteen, and the small remainder is sixteen. Tu Wei Zhi Xu, the third year.
28
十二大餘三，小餘一百九十五； 大餘十八，小餘二十四； 祝犁大芒落四年。
Twelve months: the large remainder is three, and the small remainder is one hundred ninety-five. The large remainder is eighteen, and the small remainder is twenty-four. Zhu Li Da Mang Luo, the fourth year.
29
閏十三大餘五十七，小餘五百四十三； 大餘二十四，無小餘； 商橫敦牂後元元年。
Intercalary thirteen months: the large remainder is fifty-seven, and the small remainder is five hundred forty-three. The large remainder is twenty-four, and there is no small remainder. Shang Heng Dun Zang, the first year of Houyuan.
30
十二大餘二十一，小餘四百五十； 大餘二十九，小餘八； 昭陽汁洽二年。
Twelve months: the large remainder is twenty-one, and the small remainder is four hundred fifty. The large remainder is twenty-nine, and the small remainder is eight. Zhao Yang Zhi Qiao, the second year.
31
閏十三大餘十五，小餘七百九十八； 大餘三十四，小餘十六； 橫艾涒灘始元元年。
Intercalary thirteen months: the large remainder is fifteen, and the small remainder is seven hundred ninety-eight. The large remainder is thirty-four, and the small remainder is sixteen. Heng Ai Dun Tan, the first year of Shiyuan.
32
正西十二大餘三十九，小餘七百五； 大餘三十九，小餘二十四； 尚章作噩二年。
Due west, twelve months: the large remainder is thirty-nine, and the small remainder is seven hundred five. The large remainder is thirty-nine, and the small remainder is twenty-four. Shang Zhang Zuo E, the second year.
33
十二大餘三十四，小餘一百一十三； 大餘四十五，無小餘； 焉逢淹茂三年。
Twelve months: the large remainder is thirty-four, and the small remainder is one hundred thirteen. The large remainder is forty-five, and there is no small remainder. Yanfeng Yan Mao, the third year.
34
閏十三大餘二十八，小餘四百六十一； 大餘五十，小餘八； 端蒙大淵獻四年。
Intercalary thirteen months: the large remainder is twenty-eight, and the small remainder is four hundred sixty-one. The large remainder is fifty, and the small remainder is eight. Duameng Da Yuan Xian, the fourth year.
35
十二大餘五十二，小餘三百六十八； 大餘五十五，小餘十六； 游兆困敦五年。
Twelve months: the large remainder is fifty-two, and the small remainder is three hundred sixty-eight. The large remainder is fifty-five, and the small remainder is sixteen. You Zhao Kun Dun, the fifth year.
36
十二大餘四十六，小餘七百一十六； 無大餘，小餘二十四； 彊梧赤奮若六年。
Twelve months: the large remainder is forty-six, and the small remainder is seven hundred sixteen. There is no large remainder, and the small remainder is twenty-four. Qiang Wu Chi Fen Ruo, the sixth year.
37
閏十三大餘四十一，小餘一百二十四； 大餘六，無小餘； 徒維攝提格元鳳元年。
Intercalary thirteen months: the large remainder is forty-one, and the small remainder is one hundred twenty-four. The large remainder is six, and there is no small remainder. Tu Wei Shetige, the first year of Yuanfeng.
38
十二大餘五，小餘三十一； 大餘十一，小餘八； 祝犁單閼二年。
Twelve months: the large remainder is five, and the small remainder is thirty-one. The large remainder is eleven, and the small remainder is eight. Zhu Li Shan E, the second year.
39
十二大餘五十九，小餘三百七十九； 大餘十六，小餘十六； 商橫執徐三年。
Twelve months: the large remainder is fifty-nine, and the small remainder is three hundred seventy-nine. The large remainder is sixteen, and the small remainder is sixteen. Shang Heng Zhi Xu, the third year.
40
閏十三大餘五十三，小餘七百二十七； 大餘二十一，小餘二十四； 昭陽大荒落四年。
Intercalary thirteen months: the large remainder is fifty-three, and the small remainder is seven hundred twenty-seven. The large remainder is twenty-one, and the small remainder is twenty-four. Zhao Yang Da Huang Luo, the fourth year.
41
十二大餘十七，小餘六百三十四； 大餘二十七，無小餘； 橫艾敦牂五年。
Twelve months: the large remainder is seventeen, and the small remainder is six hundred thirty-four. The large remainder is twenty-seven, and there is no small remainder. Heng Ai Dun Zang, the fifth year.
42
閏十三大餘十二，小餘四十二； 大餘三十二，小餘八； 尚章汁洽六年。
Intercalary thirteen months: the large remainder is twelve, and the small remainder is forty-two. The large remainder is thirty-two, and the small remainder is eight. Shang Zhang Zhi Qiao, the sixth year.
43
十二大餘三十五，小餘八百八十九； 大餘三十七，小餘十六； 焉逢涒灘元平元年十二大餘三十，小餘二百九十七； 大餘四十二，小餘二十四； 端蒙作噩本始元年。
Twelve months: the large remainder is thirty-five, and the small remainder is eight hundred eighty-nine. The large remainder is thirty-seven, and the small remainder is sixteen. Yanfeng Dun Tan, the first year of Yuanping: twelve months, the large remainder is thirty, and the small remainder is two hundred ninety-seven. The large remainder is forty-two, and the small remainder is twenty-four. Duameng Zuo E, the first year of Benshi.
44
閏十三大餘二十四，小餘六百四十五； 大餘四十八，無小餘； 游兆閹茂二年。
Intercalary thirteen months: the large remainder is twenty-four, and the small remainder is six hundred forty-five. The large remainder is forty-eight, and there is no small remainder. You Zhao Yan Mao, the second year.
45
十二大餘四十八，小餘五百五十二； 大餘五十三，小餘八； 彊梧大淵獻三年。
Twelve months: the large remainder is forty-eight, and the small remainder is five hundred fifty-two. The large remainder is fifty-three, and the small remainder is eight. Qiang Wu Da Yuan Xian, the third year.
46
十二大餘四十二，小餘九百； 大餘五十八，小餘十六； 徒維困敦四年。
Twelve months: the large remainder is forty-two, and the small remainder is nine hundred. The large remainder is fifty-eight, and the small remainder is sixteen. Tu Wei Kun Dun, the fourth year.
47
閏十三大餘三十七，小餘三百八； 大餘三，小餘二十四； 祝犁赤奮若地節元年。
Intercalary thirteen months: the large remainder is thirty-seven, and the small remainder is three hundred eight. The large remainder is three, and the small remainder is twenty-four. Zhu Li Chi Fen Ruo, the first year of Dijie.
48
十二大餘一，小餘二百一十五； 大餘九，無小餘； 商橫攝提格二年。
Twelve months: the large remainder is one, and the small remainder is two hundred fifteen. The large remainder is nine, and there is no small remainder. Shang Heng Shetige, the second year.
49
閏十三大餘五十五，小餘五百六十三； 大餘十四，小餘八； 昭陽單閼三年。
Intercalary thirteen months: the large remainder is fifty-five, and the small remainder is five hundred sixty-three. The large remainder is fourteen, and the small remainder is eight. Zhao Yang Shan E, the third year.
50
正南十二大餘十九，小餘四百七十； 大餘十九，小餘十六； 橫艾執徐四年。
Due south, twelve months: the large remainder is nineteen, and the small remainder is four hundred seventy. The large remainder is nineteen, and the small remainder is sixteen. Heng Ai Zhi Xu, the fourth year.
51
十二大餘十三，小餘八百一十八； 大餘二十四，小餘二十四； 尚章大荒落元康元年。
Twelve months: the large remainder is thirteen, and the small remainder is eight hundred eighteen. The large remainder is twenty-four, and the small remainder is twenty-four. Shang Zhang Da Huang Luo, the first year of Yuankang.
52
閏十三大餘八，小餘二百二十六； 大餘三十，無小餘； 焉逢敦牂二年。
Intercalary thirteen months: the large remainder is eight, and the small remainder is two hundred twenty-six. The large remainder is thirty, and there is no small remainder. Yanfeng Dun Zang, the second year.
53
十二大餘三十二，小餘一百三十三； 大餘三十五，小餘八； 端蒙協洽三年。
Twelve months: the large remainder is thirty-two, and the small remainder is one hundred thirty-three. The large remainder is thirty-five, and the small remainder is eight. Duameng Xie Qiao, the third year.
54
十二大餘二十六，小餘四百八十一； 大餘四十，小餘十六； 游兆涒灘四年。
Twelve months: the large remainder is twenty-six, and the small remainder is four hundred eighty-one. The large remainder is forty, and the small remainder is sixteen. You Zhao Dun Tan, the fourth year.
55
閏十三大餘二十，小餘八百二十九； 大餘四十五，小餘二十四； 彊梧作噩神雀元年。
Intercalary thirteen months: the large remainder is twenty, and the small remainder is eight hundred twenty-nine. The large remainder is forty-five, and the small remainder is twenty-four. Qiang Wu Zuo E, the first year of Shenque.
56
十二大餘四十四，小餘七百三十六； 大餘五十一，無小餘； 徒維淹茂二年。
Twelve months: the large remainder is forty-four, and the small remainder is seven hundred thirty-six. The large remainder is fifty-one, and there is no small remainder. Tu Wei Yan Mao, the second year.
57
十二大餘三十九，小餘一百四十四； 大餘五十六，小餘八； 祝犁大淵獻三年。
Twelve months: the large remainder is thirty-nine, and the small remainder is one hundred forty-four. The large remainder is fifty-six, and the small remainder is eight. Zhu Li Da Yuan Xian, the third year.
58
閏十三大餘三十三，小餘四百九十二； 大餘一，小餘十六； 商橫困敦四年。
Intercalary thirteen months: the large remainder is thirty-three, and the small remainder is four hundred ninety-two. The large remainder is one, and the small remainder is sixteen. Shang Heng Kun Dun, the fourth year.
59
十二大餘五十七，小餘三百九十九； 大餘六，小餘二十四； 昭陽赤奮若五鳳元年。
Twelve months: the large remainder is fifty-seven, and the small remainder is three hundred ninety-nine. The large remainder is six, and the small remainder is twenty-four. Zhao Yang Chi Fen Ruo, the first year of Wufeng.
60
閏十三大餘五十一，小餘七百四十七； 大餘十二，無小餘； 橫艾攝提格二年。
Intercalary thirteen months: the large remainder is fifty-one, and the small remainder is seven hundred forty-seven. The large remainder is twelve, and there is no small remainder. Heng Ai Shetige, the second year.
61
十二大餘十五，小餘六百五十四； 大餘十七，小餘八； 尚章單閼三年。
Twelve months: the large remainder is fifteen, and the small remainder is six hundred fifty-four. The large remainder is seventeen, and the small remainder is eight. Shang Zhang Shan E, the third year.
62
十二大餘十，小餘六十二； 大餘二十二，小餘十六； 焉逢執徐四年。
Twelve months: the large remainder is ten, and the small remainder is sixty-two. The large remainder is twenty-two, and the small remainder is sixteen. Yanfeng Zhi Xu, the fourth year.
63
閏十三大餘四，小餘四百一十； 大餘二十七，小餘二十四； 端蒙大荒落甘露元年。
Intercalary thirteen months: the large remainder is four, and the small remainder is four hundred ten. The large remainder is twenty-seven, and the small remainder is twenty-four. Duameng Da Huang Luo, the first year of Ganlu.
64
十二大餘二十八，小餘三百一十七； 大餘三十三，無小餘； 游兆敦執二年。
Twelve months: the large remainder is twenty-eight, and the small remainder is three hundred seventeen. The large remainder is thirty-three, and there is no small remainder. You Zhao Dun Zhi, the second year.
65
十二大餘二十二，小餘六百六十五； 大餘三十八，小餘八； 彊梧協洽三年。
Twelve months: the large remainder is twenty-two, and the small remainder is six hundred sixty-five. The large remainder is thirty-eight, and the small remainder is eight. Qiang Wu Xie Qiao, the third year.
66
閏十三大餘十七，小餘七十三； 大餘四十三，小餘十六； 徒維涒灘四年。
Intercalary thirteen months: the large remainder is seventeen, and the small remainder is seventy-three. The large remainder is forty-three, and the small remainder is sixteen. Tu Wei Dun Tan, the fourth year.
67
十二大餘四十，小餘九百二十； 大餘四十八，小餘二十四； 祝犁作噩黃龍元年。
Twelve months: the large remainder is forty, and the small remainder is nine hundred twenty. The large remainder is forty-eight, and the small remainder is twenty-four. Zhu Li Zuo E, the first year of Huanglong.
68
閏十三大餘三十五，小餘三百二十八； 大餘五十四，無小餘； 商橫淹茂初元元年。 正東十二大餘五十九，小餘二百三十五； 大餘五十九，小餘八； 昭陽大淵獻二年。
Intercalary thirteen months: the large remainder is thirty-five, and the small remainder is three hundred twenty-eight. The large remainder is fifty-four, and there is no small remainder. Shang Heng Yan Mao, the first year of Chu Yuan. Due east, twelve months: the large remainder is fifty-nine, and the small remainder is two hundred thirty-five. The large remainder is fifty-nine, and the small remainder is eight. Zhao Yang Da Yuan Xian, the second year.
69
十二大餘五十三，小餘五百八十三； 大餘四，小餘十六； 橫艾困敦三年。
Twelve months: the large remainder is fifty-three, and the small remainder is five hundred eighty-three. The large remainder is four, and the small remainder is sixteen. Heng Ai Kun Dun, the third year.
70
閏十三大餘四十七，小餘九百三十一； 大餘九，小餘二十四； 尚章赤奮若四年。
Intercalary thirteen months: the large remainder is forty-seven, and the small remainder is nine hundred thirty-one. The large remainder is nine, and the small remainder is twenty-four. Shang Zhang Chi Fen Ruo, the fourth year.
71
十二大餘十一，小餘八百三十八； 大餘十五，無小餘； 焉逢攝提格五年。
Twelve months: the large remainder is eleven, and the small remainder is eight hundred thirty-eight. The large remainder is fifteen, and there is no small remainder. Yanfeng Shetige, the fifth year.
72
十二大餘六，小餘二百四十六； 大餘二十，小餘八； 端蒙單閼永光元年。
Twelve months: the large remainder is six, and the small remainder is two hundred forty-six. The large remainder is twenty, and the small remainder is eight. Duameng Shan E, the first year of Yongguang.
73
閏十三無大餘，小餘五百九十四； 大餘二十五，小餘十六； 游兆執徐二年。
Intercalary thirteen months: there is no large remainder, and the small remainder is five hundred ninety-four. The large remainder is twenty-five, and the small remainder is sixteen. You Zhao Zhi Xu, the second year.
74
十二大餘二十四，小餘五百一； 大餘三十，小餘二十四； 彊梧大荒落三年。
Twelve months: the large remainder is twenty-four, and the small remainder is five hundred one. The large remainder is thirty, and the small remainder is twenty-four. Qiang Wu Da Huang Luo, the third year.
75
十二大餘十八，小餘八百四十九； 大餘三十六，無小餘； 徒維敦牂四年。
Twelve months: the large remainder is eighteen, and the small remainder is eight hundred forty-nine. The large remainder is thirty-six, and there is no small remainder. Tu Wei Dun Zang, the fourth year.
76
閏十三大餘十三，小餘二百五十七； 大餘四十一，小餘八； 祝犁協洽五年。
Intercalary thirteen months: the large remainder is thirteen, and the small remainder is two hundred fifty-seven. The large remainder is forty-one, and the small remainder is eight. Zhu Li Xie Qiao, the fifth year.
77
十二大餘三十七，小餘一百六十四； 大餘四十六，小餘十六； 商橫涒灘建昭元年。
Twelve months: the large remainder is thirty-seven, and the small remainder is one hundred sixty-four. The large remainder is forty-six, and the small remainder is sixteen. Shang Heng Dun Tan, the first year of Jianzhao.
78
閏十三大餘三十一，小餘五百一十二； 大餘五十一，小餘二十四； 昭陽作噩二年。
Intercalary thirteen months: the large remainder is thirty-one, and the small remainder is five hundred twelve. The large remainder is fifty-one, and the small remainder is twenty-four. Zhao Yang Zuo E, the second year.
79
十二大餘五十五，小餘四百一十九； 大餘五十七，無小餘； 橫艾閹茂三年。
Twelve months: the large remainder is fifty-five, and the small remainder is four hundred nineteen. The large remainder is fifty-seven, and there is no small remainder. Heng Ai Yan Mao, the third year.
80
十二大餘四十九，小餘七百六十七； 大餘二，小餘八； 尚章大淵獻四年。
Twelve months: the large remainder is forty-nine, and the small remainder is seven hundred sixty-seven. The large remainder is two, and the small remainder is eight. Shang Zhang Da Yuan Xian, the fourth year.
81
閏十三大餘四十四，小餘一百七十五； 大餘七，小餘十六； 焉逢困敦五年。
Intercalary thirteen months: the large remainder is forty-four, and the small remainder is one hundred seventy-five. The large remainder is seven, and the small remainder is sixteen. Yanfeng Kun Dun, the fifth year.
82
十二大餘八，小餘八十二； 大餘十二，小餘二十四； 端蒙赤奮若竟寧元年。
Twelve months: the large remainder is eight, and the small remainder is eighty-two. The large remainder is twelve, and the small remainder is twenty-four. Duameng Chi Fen Ruo, the first year of Jingning.
83
十二大餘二，小餘四百三十； 大餘十八，無小餘； 游兆攝提格建始元年。
Twelve months: the large remainder is two, and the small remainder is four hundred thirty. The large remainder is eighteen, and there is no small remainder. You Zhao Shetige, the first year of Jianshi.
84
閏十三大餘五十六，小餘七百七十八； 大餘二十三，小餘八； 彊梧單閼二年。
Intercalary thirteen months: the large remainder is fifty-six, and the small remainder is seven hundred seventy-eight. The large remainder is twenty-three, and the small remainder is eight. Qiang Wu Shan E, the second year.
85
十二大餘二十，小餘六百八十五； 大餘二十八，小餘十六； 徒維執徐三年。
Twelve months: the large remainder is twenty, and the small remainder is six hundred eighty-five. The large remainder is twenty-eight, and the small remainder is sixteen. Tu Wei Zhi Xu, the third year.
86
閏十三大餘十五，小餘九十三； 大餘三十三，小餘二十四； 祝犁大荒落四年。
Intercalary thirteen months: the large remainder is fifteen, and the small remainder is ninety-three. The large remainder is thirty-three, and the small remainder is twenty-four. Zhu Li Da Huang Luo, the fourth year.
87
右歷書：大餘者，日也。 小餘者，月也。 端（旃）蒙者，年名也。 支：丑名赤奮若，寅名攝提格。 干：丙名游兆。 正北，冬至加子時； 正西，加酉時； 正南，加午時； 正東，加卯時。
The calendar book above: the large remainder refers to days. The small remainder refers to months. Duanzhan Meng are year names. Earthly branches: Chou is named Chi Fen Ruo, and Yin is named Shetige. Heavenly stems: Bing is named You Zhao. Due north: the winter solstice is added to the zi hour; Due west: the you hour is added; Due south: the wu hour is added; Due east: the mao hour is added.