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 set to begin in the first month of spring. At that time, the ice melts and the hibernating creatures stir; the hundred grasses flourish, and the cuckoo calls first. Things then complete the year, springing from the east, moving in order through the four seasons, and ending at the winter solstice. At the third crowing of the rooster, daylight finally arrives. It passes through the twelve monthly nodes and comes to completion at Chou. When the sun and moon are in order, brightness results. Bright means the elder; dark means the younger. Together, dark and bright mean female and male. Female and male rise in alternation, following the proper succession of the correct order. The sun returns to the west, then brings light forth in the east; the moon returns to the east, then brings light forth in the west. If the calendar neither follows Heaven nor rests on human ordering, then every undertaking becomes easy to ruin 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 rulers change their surname and receive the mandate, they must take care over the beginning, reform the calendar’s starting point, change the colors of dress, trace back to the heavenly origin, and follow its intent.
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 age before Shennong is remote antiquity indeed. The Yellow Emperor examined and fixed the stellar calendar, established the five phases, set the cycles of waxing and waning in motion, and corrected intercalary remainders. There were then officials for heaven, earth, spirits, and the categories of things; these were called the five officials. Each kept charge of its own sequence, and they did not throw one another into disorder. Because of this, the people could have trust, and the spirits could manifest bright virtue. People and spirits had separate duties. When the people were reverent and did not profane them, the spirits bestowed auspicious growth, the people enjoyed the things they offered, disasters did not arise, and what they sought was not lacking.
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 threw virtue into disorder. People and spirits were mixed together in confusion; things could not be properly regulated; disasters and calamities came repeatedly, and none could fully express their vital force. Zhuanxu inherited this situation and ordered Chong, the Southern Corrector, to govern heaven and attend to the spirits, and Li, the Fire Corrector, to govern earth and attend to the people. In this way he restored the old order, so that neither side invaded or profaned the other.
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 followed the disordered ways of the Nine Li, so the two officials both abandoned their duties. The intercalary remainder fell out of sequence, the first month was obliterated, Sheti went unrecorded, and the calendrical numbers lost their order. Yao in turn restored the descendants of Chong and Li, not forgetting the old order, and again made them administer it, establishing the offices of Xi and He. When the seasons are clearly measured and the standards are correct, yin and yang are harmonized, wind and rain come in season, flourishing qi arrives, and the people suffer no untimely epidemics. When he grew old, he yielded the throne to Shun and again earnestly instructed at the Wen ancestral shrine, saying, “The calendrical mandate of Heaven rests upon you.” Shun likewise passed this command to Yu. From this one can see how heavily kings valued the calendar.
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 began with the first month, the Yin calendar with the twelfth, and the Zhou calendar with the eleventh. Indeed, the calendars of the Three Kings moved in a cycle, returning to their root when the cycle was exhausted. When the realm possesses the Way, it does not lose its calendrical sequence and order; when it lacks the Way, the proper calendar and first day of the month do 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 the reigns of Kings You and Li, the Zhou house declined; subordinate ministers seized power; historians did not record the seasons; lords did not announce the new moon. Thus, the descendants of the calendar experts scattered, some among the various Xia states and some among the Yi and Di, so their omen observations fell into disuse and lost their system. In the twenty-sixth year of King Xiang of Zhou, there was an intercalary third month, which the Spring and Autumn Annals criticized. The former kings’ regulation of time set the beginning at the start, established the correct point in the middle, and brought what was askew back into order at the end. Set the starting point correctly at the beginning, and the sequence will not go astray; raise the correct standard at the center, and the people will not be confused; if what is askew is brought back into order at the end, affairs do not go awry.
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 contended with one another; they were occupied only with strong states subduing enemies and with emergency relief and untangling disputes. How could they have leisure for this? At that time, only Zou Yan clearly understood the transmission of the Five Virtues and explained the divisions of waxing and waning, presenting them to the feudal lords. Because Qin had destroyed the six states, military affairs were incessant, and only a short time had passed since its ruler rose to supreme power, he had no leisure for it. He also pressed the theory of the Five Conquests quite far, taking himself to have obtained the auspicious sign of water virtue. He renamed the Yellow River “Virtue Water,” adopted the tenth month as the calendar’s beginning, and made black the principal color. Yet in matters of calendrical measures and intercalary remainders, he did not grasp the 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 waited for me before it arose,” and he too took himself to have received the auspicious sign of water virtue. Even Zhang Cang and the others who understood the calendar clearly all took this to be correct. At that time the realm had only just been settled and the great foundation of order was being laid. Empress Gao, ruling as a woman, had no leisure for the matter, so the Qin calendar, monthly beginnings, and clothing colors were retained.
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。
By the time of Emperor Xiaowen, Gongsun Chen of Lu memorialized on the succession of the Five Virtues, saying, “Han has obtained earth virtue. It should change the era, reform the calendar, and alter the clothing colors. There ought to be an auspicious sign, and that sign would be a yellow dragon appearing." The matter was referred to Chancellor Zhang Cang, who had also studied the pitch-pipes and calendar. He judged it incorrect, so it was dropped. Later, a yellow dragon appeared at Chengji. Zhang Cang resigned of his own accord, and what he had wished to compose and discuss never came to fruition. Xinyuan Ping, who became known through his observations of qi, spoke extensively on reforming the calendar and clothing colors, and he was favored and honored. Later he caused disorder, so Emperor Wen discarded the matter and did not pursue it 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 present emperor came to the throne, he summoned the fangshi Tang Du to divide the celestial sectors; then Luoxia Hong of Ba calculated the rotating calendar, and only afterward did the sun’s degrees and the days correspond with the Xia calendar. The emperor then changed the era name, revised the official titles, and performed the Feng sacrifice at Mount Tai. He therefore issued an edict to the imperial secretary, saying: “Recently the relevant officials reported that the stellar degrees had not yet been fixed. I have widely extended inquiry to rectify the stellar degrees, but have not yet gained full clarity. I have heard that in antiquity the Yellow Emperor joined with the Way and did not die; he named, examined, and verified the degrees, fixed the clear and the turbid, established the five divisions, and set up the numerical measures of qi and things. But this is still very remote indeed. The records are incomplete and music has slackened into decay; this deeply grieves me. I alone have not yet been able to follow and clarify the established calendar, but have only carried forward the daily divisions, broadly conforming to the ascendancy of water virtue. Now, in accord with the summer solstice, Huangzhong serves as gong, Linzhong as zhi, Taicu as shang, Nanlu as yu, and Guxi as jue. From this point on, the qi again became correct, the yu pitch again became clear, and the names again returned to their proper alternation. When the zi day coincides with the winter solstice, the way of yin and yang separating and joining is put into practice. When the eleventh month, the jiazi day, the new moon, dawn, and the winter solstice all coincided, they changed the calendar so that the seventh year became the first year of Taichu. The year was named “Yanfeng Shetige”; the month was named “Biju”; the day was Jiazi; and at midnight the new moon, dawn, and winter solstice coincided.”
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 was Jiazi; at midnight the new moon, dawn, and winter solstice coincided.
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。
Northern alignment, regular year of 12 months: the large remainder is 0, and the small remainder is 0. The large remainder is 0, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 54, and the small remainder is 348. The large remainder is 5, and the small remainder is 8. 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 year, 13 months: the large remainder is 48, and the small remainder is 696. The large remainder is 10, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 12, and the small remainder is 603. The large remainder is 15, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 7, and the small remainder is 11. The large remainder is 21, and the small remainder is 0. 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 year, 13 months: the large remainder is 1, and the small remainder is 359. The large remainder is 26, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 25, and the small remainder is 266. The large remainder is 31, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 19, and the small remainder is 614. The large remainder is 36, and the small remainder is 24. 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 year, 13 months: the large remainder is 14, and the small remainder is 22. The large remainder is 42, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 37, and the small remainder is 869. The large remainder is 47, and the small remainder is 8. 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 year, 13 months: the large remainder is 32, and the small remainder is 277. The large remainder is 52, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 56, and the small remainder is 184. The large remainder is 57, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 50, and the small remainder is 532. The large remainder is 3, and the small remainder is 0. 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 year, 13 months: the large remainder is 44, and the small remainder is 880. The large remainder is 8, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 8, and the small remainder is 787. The large remainder is 13, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 3, and the small remainder is 195. The large remainder is 18, and the small remainder is 24. 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 year, 13 months: the large remainder is 57, and the small remainder is 543. The large remainder is 24, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 21, and the small remainder is 450. The large remainder is 29, and the small remainder is 8. 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 year, 13 months: the large remainder is 15, and the small remainder is 798. The large remainder is 34, and the small remainder is 16. 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。
Western alignment, regular year of 12 months: the large remainder is 39, and the small remainder is 705. The large remainder is 39, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 34, and the small remainder is 113. The large remainder is 45, and the small remainder is 0. 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 year, 13 months: the large remainder is 28, and the small remainder is 461. The large remainder is 50, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 52, and the small remainder is 368. The large remainder is 55, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 46, and the small remainder is 716. There is large remainder is 0, and the small remainder is 24. 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 year, 13 months: the large remainder is 41, and the small remainder is 124. The large remainder is 6, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 5, and the small remainder is 31. The large remainder is 11, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 59, and the small remainder is 379. The large remainder is 16, and the small remainder is 16. 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 year, 13 months: the large remainder is 53, and the small remainder is 727. The large remainder is 21, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 17, and the small remainder is 634. The large remainder is 27, and the small remainder is 0. 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 year, 13 months: the large remainder is 12, and the small remainder is 42. The large remainder is 32, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 35, and the small remainder is 889. The large remainder is 37, and the small remainder is 16. Yanfeng Dun Tan, the first year of Yuanping: twelve months, the large remainder is 30, and the small remainder is 297. The large remainder is 42, and the small remainder is 24. 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 year, 13 months: the large remainder is 24, and the small remainder is 645. The large remainder is 48, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 48, and the small remainder is 552. The large remainder is 53, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 42, and the small remainder is 900. The large remainder is 58, and the small remainder is 16. 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 year, 13 months: the large remainder is 37, and the small remainder is 308. The large remainder is 3, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 1, and the small remainder is 215. The large remainder is 9, and the small remainder is 0. 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 year, 13 months: the large remainder is 55, and the small remainder is 563. The large remainder is 14, and the small remainder is 8. 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。
Southern alignment, regular year of 12 months: the large remainder is 19, and the small remainder is 470. The large remainder is 19, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 13, and the small remainder is 818. The large remainder is 24, and the small remainder is 24. 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 year, 13 months: the large remainder is 8, and the small remainder is 226. The large remainder is 30, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 32, and the small remainder is 133. The large remainder is 35, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 26, and the small remainder is 481. The large remainder is 40, and the small remainder is 16. 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 year, 13 months: the large remainder is 20, and the small remainder is 829. The large remainder is 45, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 44, and the small remainder is 736. The large remainder is 51, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 39, and the small remainder is 144. The large remainder is 56, and the small remainder is 8. 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 year, 13 months: the large remainder is 33, and the small remainder is 492. The large remainder is 1, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 57, and the small remainder is 399. The large remainder is 6, and the small remainder is 24. 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 year, 13 months: the large remainder is 51, and the small remainder is 747. The large remainder is 12, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 15, and the small remainder is 654. The large remainder is 17, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 10, and the small remainder is 62. The large remainder is 22, and the small remainder is 16. 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 year, 13 months: the large remainder is 4, and the small remainder is 410. The large remainder is 27, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 28, and the small remainder is 317. The large remainder is 33, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 22, and the small remainder is 665. The large remainder is 38, and the small remainder is 8. 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 year, 13 months: the large remainder is 17, and the small remainder is 73. The large remainder is 43, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 40, and the small remainder is 920. The large remainder is 48, and the small remainder is 24. 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 year, 13 months: the large remainder is 35, and the small remainder is 328. The large remainder is 54, and the small remainder is 0. Shang Heng Yan Mao, the first year of Chu Yuan. Eastern alignment, regular year of 12 months: the large remainder is 59, and the small remainder is 235. The large remainder is 59, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 53, and the small remainder is 583. The large remainder is 4, and the small remainder is 16. 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 year, 13 months: the large remainder is 47, and the small remainder is 931. The large remainder is 9, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 11, and the small remainder is 838. The large remainder is 15, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 6, and the small remainder is 246. The large remainder is 20, and the small remainder is 8. 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 year, 13 months: the large remainder is 0, and the small remainder is 594. The large remainder is 25, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 24, and the small remainder is 501. The large remainder is 30, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 18, and the small remainder is 849. The large remainder is 36, and the small remainder is 0. 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 year, 13 months: the large remainder is 13, and the small remainder is 257. The large remainder is 41, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 37, and the small remainder is 164. The large remainder is 46, and the small remainder is 16. 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 year, 13 months: the large remainder is 31, and the small remainder is 512. The large remainder is 51, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 55, and the small remainder is 419. The large remainder is 57, and the small remainder is 0. 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。
Regular year, 12 months: the large remainder is 49, and the small remainder is 767. The large remainder is 2, and the small remainder is 8. 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 year, 13 months: the large remainder is 44, and the small remainder is 175. The large remainder is 7, and the small remainder is 16. 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。
Regular year, 12 months: the large remainder is 8, and the small remainder is 82. The large remainder is 12, and the small remainder is 24. 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。
Regular year, 12 months: the large remainder is 2, and the small remainder is 430. The large remainder is 18, and the small remainder is 0. 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 year, 13 months: the large remainder is 56, and the small remainder is 778. The large remainder is 23, and the small remainder is 8. 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。
Regular year, 12 months: the large remainder is 20, and the small remainder is 685. The large remainder is 28, and the small remainder is 16. 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 year, 13 months: the large remainder is 15, and the small remainder is 93. The large remainder is 33, and the small remainder is 24. 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。
As for the calendar text above: the large remainder refers to days. The small remainder refers to months. Duan (Zhan) Meng are year names. For the earthly branches, Chou is named Chi Fen Ruo, and Yin is named Shetige. For the heavenly stems, Bing is named You Zhao. Northern alignment: at the winter solstice the zi hour is added; Western alignment: the you hour is added; Southern alignment: the wu hour is added; Eastern alignment: the mao hour is added.