1
曆二○授時曆議下交食
Calendar 2 ○ Discussion on Eclipses under the Shoushi Calendar Treatise
2
曆法疏密，驗在交食，然推步之術難得其密，加時有早晚，食分有淺深，取其密合，不容偶然。 推演加時，必本於躔離朓朒； 考求食分，必本於距交遠近； 茍入氣盈縮、入轉遲疾未得其正，則合朔不失之先，必失之後。 合朔失之先後，則虧食時刻，其能密乎？ 日月俱東行，而日遲月疾，月追及日，是為一會。 交值之道，有陽曆陰曆； 交會之期，有中前中後； 加以地形南北東西之不同，人目高下邪直之各異，此食分多寡，理不得一者也。 今合朔既正，則加時無早晚之差； 氣刻適中，則食分無強弱之失； 推而上之，自《詩》、《書》、《春秋》及三國以來所載虧食，無不合焉者。 合於既往，則行之悠久，自可無弊矣。
The precision of a calendar is tested by eclipses, yet astronomical calculation is difficult to make exact: the predicted moment may come too early or too late, and the eclipse may be partial or total. A close match cannot be achieved by chance alone. Computing the moment of an eclipse must rest on the positions of the heavenly bodies and the phases of the moon; Determining the degree of eclipse must rest on how far the conjunction is from the lunar node; If the corrections for solar-term variation and the moon's anomalistic motion are not right, then when the new moon is not predicted too early, it will inevitably be predicted too late. If the new moon is off in timing, how can the eclipse moment be accurate? Sun and moon both travel eastward, but the sun moves slowly and the moon swiftly; when the moon overtakes the sun, that is one conjunction. The nodes have their yang and yin passages; Conjunctions at the nodes may occur before, at, or after the central crossing; When one further accounts for differences of latitude and longitude, and for whether an observer sees the event high or low, straight on or at an angle, the degree of eclipse cannot by nature be the same everywhere. With the new moon correctly determined, the predicted moment shows no early-or-late error; With the solar-term corrections properly applied, the degree of eclipse is no longer too large or too small; Working backward from the present, every eclipse recorded since the Classic of Poetry, the Documents, the Spring and Autumn Annals, and the Three Kingdoms period agrees with it. Agreement with past records assures that long use will be without defect.
3
《詩》、《書》所載日食二事
Two solar eclipses recorded in the Classic of Poetry and the Documents
4
《書·胤征》：「惟仲康肇位四海。 乃季秋月朔，辰弗集於房。」
From the Documents, "Punitive Expedition against Min": "When Zhong Kang first ascended and ruled the four quarters. On the new moon of the last month of autumn, the stars did not gather in the House constellation."
5
今按《大衍曆》作仲康即位之五年癸巳，距辛巳三千四百八年，九月庚戌朔，泛交二十六日五千四百二十一分入食限。
According to the Dayan Calendar, this was the fifth year of Zhong Kang's reign (guisi), 3,408 years after xinsi; on the gengxu new moon of the ninth month, the general nodal distance was 26 days and 5,421 parts within the eclipse limit.
6
《詩·小雅·十月之交》，大夫刺幽王也。 「十月之交，朔日辛卯，日有食之，亦孔之醜。」
From the Classic of Poetry, Minor Odes, "The Fullness of the Tenth Month": a minister's critique of King You of Zhou. "At the turning of the tenth month, on the xinmao new moon, the sun was eclipsed—a most terrible omen."
7
今按梁太史令虞絪云：十月辛卯朔，在幽王六年乙丑朔。 《大衍》亦以為然。 以《授時曆》推之，是歲十月辛卯朔，泛交十四日五千七百九分入食限。
According to Yu Yin, Grand Astrologer of Liang, the xinmao new moon of the tenth month occurred in the sixth year of King You (yichou). The Dayan Calendar agrees. By the Shoushi Calendar, the xinmao new moon of the tenth month of that year had a general nodal distance of 14 days and 5,709 parts within the eclipse limit.
8
《春秋》日食三十七事隱公三年辛酉歲，春王二月己巳，日有食之。
Thirty-seven solar eclipses in the Spring and Autumn Annals. In the third year of Duke Yin (xinyou), on jisi in the king's second month of spring, there was a solar eclipse.
9
杜預云：「不書朔，史官失之。」 《公羊》云：「日食或言朔或不言朔，或日或不日，或失之前或失之後，失之前者朔在前也，失之後者朔在後也。」 《穀梁》云：「言日不言朔，食晦日也。」 姜岌校《春秋》日食云：「是歲二月己亥朔，無己巳，似失一閏。
Du Yu said: "The new moon was not recorded; the historiographer had made an error." The Gongyang Commentary says: "For solar eclipses, the new moon may or may not be given, the day may or may not be given; the error may lie before or after the event—if before, the new moon was placed too early; if after, too late." The Guliang Commentary says: "Only the day is given, not the new moon—the eclipse fell on the last day of the month." Jiang Ji, reviewing Spring and Autumn eclipses, said: "That year the second month's new moon was jihai; there was no jisi day—it appears an intercalary month was omitted.
10
三月己巳朔，去交分入食限。」 《大衍》與姜岌合。 今《授時曆》推之，是歲三月己巳朔，加時在晝，去交分二十六日六千六百三十一入食限。 桓公三年壬申歲，七月壬辰朔，日有食之。
The jisi new moon of the third month fell within the eclipse limit by nodal distance." The Dayan Calendar agrees with Jiang Ji. By the Shoushi Calendar, the jisi new moon of the third month of that year occurred in daylight, with a nodal distance of 26 days and 6,631 parts within the eclipse limit. In the third year of Duke Huan (renshen), on the renchen new moon of the seventh month, there was a solar eclipse.
11
姜岌以為是歲七月癸亥朔，無壬辰，亦失閏。 其八月壬辰朔，去交分入食限。 《大衍》與姜岌合。 以今曆推之，是歲八月壬辰朔，加時在晝，食六分一十四秒。
Jiang Ji held that the seventh month's new moon that year was guihai; there was no renchen day—again an intercalary month had been omitted. The renchen new moon of the eighth month fell within the eclipse limit by nodal distance. The Dayan Calendar agrees with Jiang Ji. By the present calendar, the renchen new moon of the eighth month of that year occurred in daylight, with an eclipse of six parts and fourteen seconds.
12
桓公十七年丙戌歲，冬十月朔，日有食之。
In the seventeenth year of Duke Huan (bingxu), on the new moon of the tenth month of winter, there was a solar eclipse.
13
《左氏》云：「不書日，史官失之。」 《大衍》推得在十一月交分入食限，失閏也。 以今曆推之，是歲十一月加時在晝，交分二十六日八千五百六十入食限。
The Zuo Commentary says: "The day was not recorded; the historiographer had made an error." The Dayan Calendar places it in the eleventh month within the eclipse limit by nodal distance—an intercalary month had been omitted. By the present calendar, the eleventh month of that year had a daylight eclipse, with a nodal distance of 26 days and 8,560 parts within the eclipse limit.
14
莊公十八年乙巳歲，春王三月，日有食之。
In the eighteenth year of Duke Zhuang (yisi), in the king's third month of spring, there was a solar eclipse.
15
《穀梁》云：「不言日，不言朔，夜食也。」 《大衍》推是歲五月朔，交分入食限，三月不應食。 以今曆推之，是歲三月朔，不入食限。 五月壬子朔，加時在晝，交分入食限，蓋誤五為三。
The Guliang Commentary says: "Neither the day nor the new moon is given—it was a nighttime eclipse." The Dayan Calendar places the eclipse at the fifth month's new moon of that year within the eclipse limit; the third month should not have had one. By the present calendar, the third month's new moon of that year does not fall within the eclipse limit. The renzi new moon of the fifth month occurred in daylight within the eclipse limit—likely "five" was written as "three."
16
莊公二十五年壬子歲，六月辛未朔，日有食之。
In the twenty-fifth year of Duke Zhuang (renzi), on the xinwei new moon of the sixth month, there was a solar eclipse.
17
《大衍》推之，七月辛未朔，交分入食限。 以今曆推之，是歲七月辛未朔，加時在晝，交分二十七日四百八十九入食限，失閏也。 莊公二十六年癸丑歲，冬十有二月癸亥朔，日有食之。
The Dayan Calendar places it at the xinwei new moon of the seventh month within the eclipse limit. By the present calendar, the xinwei new moon of the seventh month of that year occurred in daylight, with a nodal distance of 27 days and 489 parts within the eclipse limit—an intercalary month had been omitted. In the twenty-sixth year of Duke Zhuang (guichou), on the guihai new moon of the twelfth month of winter, there was a solar eclipse.
18
今曆推之，是歲十二月癸亥朔，加時在晝，交分十四日三千五百五十一入食限。 莊公三十年丁巳歲，九月庚午朔，日有食之。
By the present calendar, the guihai new moon of the twelfth month of that year occurred in daylight, with a nodal distance of 14 days and 3,551 parts within the eclipse limit. In the thirtieth year of Duke Zhuang (dingsi), on the gengwu new moon of the ninth month, there was a solar eclipse.
19
今曆推之，是歲十月庚午朔，加時在晝，去交分十四日四千六百九十六入食限，失閏也。 《大衍》同。 僖公十二年癸酉歲，春王三月庚午朔，日有食之。
By the present calendar, the gengwu new moon of the tenth month of that year occurred in daylight, with a nodal distance of 14 days and 4,696 parts within the eclipse limit—an intercalary month had been omitted. The Dayan Calendar agrees. In the twelfth year of Duke Xi (guiyou), on the gengwu new moon of the king's third month of spring, there was a solar eclipse.
20
姜氏云：「三月朔，交不應食，在誤條； 其五月庚午朔，去交分入食限。」 《大衍》同。 今曆推之，是歲五月庚午朔，加時在晝，去交分二十六日五千一百九十二入食限，蓋五誤為三。
Jiang Ji said: "The third month's new moon should not have had an eclipse by nodal distance; this belongs among erroneous entries; the gengwu new moon of the fifth month fell within the eclipse limit by nodal distance." The Dayan Calendar agrees. By the present calendar, the gengwu new moon of the fifth month of that year occurred in daylight, with a nodal distance of 26 days and 5,192 parts within the eclipse limit—likely "five" was written as "three."
21
僖公十五年丙子歲，夏五月，日有食之。
In the fifteenth year of Duke Xi (bingzi), in the fifth month of summer, there was a solar eclipse.
22
《左氏》云：「不書朔與日，史官失之也。」 《大衍》推四月癸丑朔，去交分入食限，差一閏。 今曆推之，是歲四月癸丑朔，去交分一日一千三百一十六入食限。
The Zuo Commentary says: "Neither the new moon nor the day was recorded; the historiographer had made an error." The Dayan Calendar places it at the guichou new moon of the fourth month within the eclipse limit—one intercalary month off. By the present calendar, the guichou new moon of the fourth month of that year had a nodal distance of 1 day and 1,316 parts within the eclipse limit.
23
文公元年乙未歲，二月癸亥朔，日有食之。
In the first year of Duke Wen (yiwei), on the guihai new moon of the second month, there was a solar eclipse.
24
姜氏云：「二月甲午朔，無癸亥。 三月癸亥朔，入食限。」 《大衍》亦以為然。 今曆推之，是歲三月癸亥朔，加時在晝，去交分二十六日五千九百十七分入食限，失閏也。
Jiang Ji said: "The second month's new moon was jiawu; there was no guihai day. The guihai new moon of the third month falls within the eclipse limit." The Dayan Calendar agrees. By the present calendar, the guihai new moon of the third month of that year occurred in daylight, with a nodal distance of 26 days and 5,917 parts within the eclipse limit—an intercalary month had been omitted.
25
文公十五年己酉歲，六月辛丑朔，日有食之。
In the fifteenth year of Duke Wen (jiyou), on the xinchou new moon of the sixth month, there was a solar eclipse.
26
今曆推之，是歲六月辛丑朔，加時在晝，交分二十六日四千四百七十三分入食限。 宣公八年庚申歲，秋七月甲子，日有食之。
By the present calendar, the xinchou new moon of the sixth month of that year occurred in daylight, with a nodal distance of 26 days and 4,473 parts within the eclipse limit. In the eighth year of Duke Xuan (gengshen), on jiazi in the seventh month of autumn, there was a solar eclipse.
27
杜預以七月甲子晦食。 姜氏云：「十月甲子朔，食。」 《大衍》同。 今曆推之，是歲十月甲子朔，加時在晝，食九分八十一秒，蓋十誤為七。 宣公十年壬戌歲，夏四月丙辰，日有食之。
Du Yu held that the eclipse fell on the last day of the seventh month, jiazi. Jiang Ji said: "The jiazi new moon of the tenth month had the eclipse." The Dayan Calendar agrees. By the present calendar, the jiazi new moon of the tenth month of that year occurred in daylight, with an eclipse of nine parts and eighty-one seconds—likely "ten" was written as "seven." In the tenth year of Duke Xuan (renxu), on bingchen in the fourth month of summer, there was a solar eclipse.
28
今曆推之，是月丙辰朔，加時在晝，交分十四日九百六十八分入食限。 宣公十七年己巳歲，六月癸卯，日有食之。
By the present calendar, the bingchen new moon of that month occurred in daylight, with a nodal distance of 14 days and 968 parts within the eclipse limit. In the seventeenth year of Duke Xuan (jisi), on guimao in the sixth month, there was a solar eclipse.
29
姜氏云：「六月甲辰朔，不應食。」 《大衍》云：「是年五月在交限，六月甲辰朔，交分已過食限，蓋誤。」 今曆推之，是歲五月乙亥朔，入食限。 六月甲辰朔，泛交二日已過食限，《大衍》為是。
Jiang Ji said: "The jiachen new moon of the sixth month should not have had an eclipse." The Dayan Calendar says: "That year the fifth month was within the nodal limit; the jiachen new moon of the sixth month had already passed the eclipse limit by nodal distance—likely an error." By the present calendar, the yihai new moon of the fifth month of that year falls within the eclipse limit. The jiachen new moon of the sixth month had a general nodal distance two days past the eclipse limit—the Dayan Calendar is right.
30
成公十六年丙戌歲，六月丙寅朔，日有食之。
In the sixteenth year of Duke Cheng (bingxu), on the bingyin new moon of the sixth month, there was a solar eclipse.
31
今曆推之，是歲六月丙寅朔，加時在晝，去交分二十六日九千八百三十五分入食限。 成公十七年丁亥歲，十有二月丁巳朔，日有食之。
By the present calendar, the bingyin new moon of the sixth month of that year occurred in daylight, with a nodal distance of 26 days and 9,835 parts within the eclipse limit. In the seventeenth year of Duke Cheng (dinghai), on the dingsi new moon of the twelfth month, there was a solar eclipse.
32
姜氏云：「十二月戊子朔，無丁巳，似失閏。」 《大衍》推十一月丁巳朔，交分入食限。 今曆推之，是歲十一月丁巳朔，加時在晝，交分十四日二千八百九十七分入食限，與《大衍》同。
Jiang Ji said: "The twelfth month's new moon was wuzi; there was no dingsi day—it appears an intercalary month was omitted." The Dayan Calendar places it at the dingsi new moon of the eleventh month within the eclipse limit. By the present calendar, the dingsi new moon of the eleventh month of that year occurred in daylight, with a nodal distance of 14 days and 2,897 parts within the eclipse limit—the same as the Dayan Calendar.
33
襄公十四年壬寅歲，二月乙未朔，日有食之。
In the fourteenth year of Duke Xiang (renyin), on the yiwei new moon of the second month, there was a solar eclipse.
34
今曆推之，是歲二月乙未朔，加時在晝，交分十四日一千三百九十三分入食限也。 襄公十五年癸卯歲，秋八月丁巳朔，日有食之。
By the present calendar, the yiwei new moon of the second month of that year occurred in daylight, with a nodal distance of 14 days and 1,393 parts within the eclipse limit. In the fifteenth year of Duke Xiang (guimao), on the dingsi new moon of the eighth month of autumn, there was a solar eclipse.
35
姜氏云：「七月丁巳朔，食，失閏也。」 《大衍》同。 今曆推之，是歲七月丁巳朔，加時在晝，去交分二十六日三千三百九十四分入食限。 襄公二十年戊申歲，冬十月丙辰朔，日有食之。
Jiang Ji said: "The dingsi new moon of the seventh month had the eclipse—an intercalary month had been omitted." The Dayan Calendar agrees. By the present calendar, the dingsi new moon of the seventh month of that year occurred in daylight, with a nodal distance of 26 days and 3,394 parts within the eclipse limit. In the twentieth year of Duke Xiang (wushen), on the bingchen new moon of the tenth month of winter, there was a solar eclipse.
36
今曆推之，是歲十月丙辰朔，加時在晝，交分十三日七千六百分入食限。 襄公二十一年己酉歲，秋七月庚戌朔，日有食之。
By the present calendar, the bingchen new moon of the tenth month of that year occurred in daylight, with a nodal distance of 13 days and 7,600 parts within the eclipse limit. In the twenty-first year of Duke Xiang (jiyou), on the gengxu new moon of the seventh month of autumn, there was a solar eclipse.
37
今曆推之，是月庚戌朔，加時在晝，交分十四日三千六百八十二分入食限。 冬十月庚辰朔，日有食之。
By the present calendar, the gengxu new moon of that month occurred in daylight, with a nodal distance of 14 days and 3,682 parts within the eclipse limit. In the tenth month of winter, on the gengchen new moon, there was a solar eclipse.
38
姜氏云：「比月而食，宜在誤條。」 《大衍》亦以為然。 今曆推之，十月已過交限，不應頻食，姜說為是。 襄公二十三年辛亥歲，春王二月癸酉朔，日有食之。
Jiang Ji said: "Two eclipses in the same month—this should be listed among erroneous entries." The Dayan Calendar agrees. By the present calendar, the tenth month had already passed the nodal limit, so a second eclipse so soon was impossible—Jiang Ji was right. In the twenty-third year of Duke Xiang (xinhai), on the guiyou new moon of the king's second month of spring, there was a solar eclipse.
39
今曆推之，是月癸酉朔，加時在晝，交分二十六日五千七百三分入食限。 襄公二十四年壬子歲，秋七月甲子朔，日有食之，既。 今曆推之，是月甲子朔，加時在晝，日食九分六秒。
By the present calendar, the guiyou new moon of that month occurred in daylight, with a nodal distance of 26 days and 5,703 parts within the eclipse limit. In the twenty-fourth year of Duke Xiang (renzi), on the jiazi new moon of the seventh month of autumn, there was a total solar eclipse. By the present calendar, the jiazi new moon of that month occurred in daylight, with a solar eclipse of nine parts and six seconds.
40
八月癸巳朔，日有食之。
In the eighth month, on the guisi new moon, there was a solar eclipse.
41
《漢志》：「董仲舒以為比食又既。」 《大衍》云：「不應頻食，在誤條。」 今曆推之，立分不葉，不應食，《大衍》說是。 襄公二十七年乙卯歲，冬十有二月乙亥朔，日有食之。
The Han Treatise on Astronomy says: "Dong Zhongshu held that these were two eclipses in the same month, both total." The Dayan Calendar says: "A second eclipse so soon was impossible—it belongs among erroneous entries." By the present calendar, the nodal distance does not accord, so no eclipse should have occurred—the Dayan Calendar is right. In the twenty-seventh year of Duke Xiang (yimao), on the yihai new moon of the twelfth month of winter, there was a solar eclipse.
42
姜氏云：「十一月乙亥朔，交分入限，應食。」 《大衍》同。 今曆推之，是歲十一月乙亥朔，加時在晝，交分初日八百二十五分入食限。 昭公七年丙寅歲，夏四月甲辰朔，日有食之。
Jiang Ji said: "The yihai new moon of the eleventh month fell within the nodal limit—an eclipse was due." The Dayan Calendar agrees. By the present calendar, the yihai new moon of the eleventh month of that year occurred in daylight, with a nodal distance of 825 parts on the first day within the eclipse limit. In the seventh year of Duke Zhao (bingyin), on the jiachen new moon of the fourth month of summer, there was a solar eclipse.
43
今曆推之，是月甲辰朔，加時在晝，交分二十七日二百九十八分入食限。 昭公十五年甲戌歲，六月丁巳朔，日有食之。
By the present calendar, the jiachen new moon of that month occurred in daylight, with a nodal distance of 27 days and 298 parts within the eclipse limit. In the fifteenth year of Duke Zhao (jiaxu), on the dingsi new moon of the sixth month, there was a solar eclipse.
44
《大衍》推五月丁巳朔，食，失一閏。 今曆推之，是歲五月丁巳朔，加時在晝，交分十三日九千五百六十七分入食限。 昭公十七年丙子歲，夏六月甲戌朔，日有食之。
The Dayan Calendar places the eclipse at the dingsi new moon of the fifth month—one intercalary month had been omitted. By the present calendar, the dingsi new moon of the fifth month of that year occurred in daylight, with a nodal distance of 13 days and 9,567 parts within the eclipse limit. In the seventeenth year of Duke Zhao (bingzi), on the jiaxu new moon of the sixth month of summer, there was a solar eclipse.
45
姜氏云：「六月乙巳朔，交分不葉，不應食，當誤。」 《大衍》云：「當在九月朔，六月不應食，姜氏是也。」 今曆推之，是歲九月甲戌朔，加時在晝，交分二十六日七千六百五十分入食限。
Jiang Ji said: "The yisi new moon of the sixth month did not accord by nodal distance; no eclipse should have occurred—the entry must be wrong." The Dayan Calendar says: "It should have been the ninth month's new moon; the sixth month should not have had an eclipse—Jiang Ji is right." By the present calendar, the jiaxu new moon of the ninth month of that year occurred in daylight, with a nodal distance of 26 days and 7,650 parts within the eclipse limit.
46
昭公二十一年庚辰歲，七月壬午朔，日有食之。
In the twenty-first year of Duke Zhao (gengchen), on the renwu new moon of the seventh month, there was a solar eclipse.
47
今曆推之，是月壬午朔，加時在晝，交分二十六日八千七百九十四分入食限。 昭公二十二年辛巳歲，冬十有二月癸酉朔，日有食之。
By the present calendar, the renwu new moon of that month occurred in daylight, with a nodal distance of 26 days and 8,794 parts within the eclipse limit. In the twenty-second year of Duke Zhao (xinsi), on the guiyou new moon of the twelfth month of winter, there was a solar eclipse.
48
今曆推之，是月癸酉朔，交分十四日一千八百入食限。 杜預以長曆推之，當為癸卯，非是。 昭公二十四年癸未歲，夏五月乙未朔，日有食之。
By the present calendar, the guiyou new moon of that month had a nodal distance of 14 days and 1,800 parts within the eclipse limit. Du Yu, using the long calendar, held it should have been guimao—this is incorrect. In the twenty-fourth year of Duke Zhao (guiwei), on the yiwei new moon of the fifth month of summer, there was a solar eclipse.
49
今曆推之，是月乙未朔，加時在晝，交分二十六日三千八百三十九分入食限。 昭公三十一年庚寅歲，十有二月辛亥朔，日有食之。
By the present calendar, the yiwei new moon of that month occurred in daylight, with a nodal distance of 26 days and 3,839 parts within the eclipse limit. In the thirty-first year of Duke Zhao (gengyin), on the xinhai new moon of the twelfth month, there was a solar eclipse.
50
今曆推之，是月辛亥朔，加時在晝，交分二十六日六千一百二十八分入食限。 定公五年丙申歲，春三月辛亥朔，日有食之。
By the present calendar, the xinhai new moon of that month occurred in daylight, with a nodal distance of 26 days and 6,128 parts within the eclipse limit. In the fifth year of Duke Ding (bingshen), on the xinhai new moon of the third month of spring, there was a solar eclipse.
51
今曆推之，三月辛卯朔，加時在晝，交分十四日三百三十四分入食限。 定公十二年癸卯歲，十一月丙寅朔，日有食之。
By the present calendar, the xinmao new moon of the third month occurred in daylight, with a nodal distance of 14 days and 334 parts within the eclipse limit. In the twelfth year of Duke Ding (guimao), on the bingyin new moon of the eleventh month, there was a solar eclipse.
52
今曆推之，是歲十月丙寅朔，加時在晝，交分十四日二千六百二十二分入食限，蓋失一閏。 定公十五年丙午歲，八月庚辰朔，日有食之。
By the present calendar, the bingyin new moon of the tenth month of that year occurred in daylight, with a nodal distance of 14 days and 2,622 parts within the eclipse limit—an intercalary month had likely been omitted. In the fifteenth year of Duke Ding (bingwu), on the gengchen new moon of the eighth month, there was a solar eclipse.
53
今曆推之，是月庚辰朔，加時在晝，交分十三日七千六百八十五分入食限。 哀公十四年庚申歲，夏五月庚申朔，日有食之。
By the present calendar, the gengchen new moon of that month occurred in daylight, with a nodal distance of 13 days and 7,685 parts within the eclipse limit. In the fourteenth year of Duke Ai (gengshen), on the gengshen new moon of the fifth month of summer, there was a solar eclipse.
54
今曆推之，是月庚申朔，加時在晝，交分二十六日九千二百一分入食限。
By the present calendar, the gengshen new moon of that month occurred in daylight, with a nodal distance of 26 days and 9,201 parts within the eclipse limit.
55
右《詩》、《書》所載日食二事，《春秋》二百四十二年間，凡三十有七事，以《授時曆》推之，惟襄公二十一年十月庚辰朔及二十四年八月癸巳朔不入食限，蓋自有曆以來，無比月而食之理。 其三十五食，食皆在朔，《經》或不書日，不書朔，《公羊》、《穀梁》以為食晦，二者非； 《左氏》以為史官失之者，得之。 其間或差一日二日者，蓋由古曆疏闊，置閏失當之弊，姜岌、一行已有定說。 孔子作書，但因時曆以書，非大義所關，故不必致詳也。
Above are the two solar eclipses recorded in the Classic of Poetry and the Documents. Over the Spring and Autumn Annals' 242 years, there are thirty-seven cases in all. By the Shoushi Calendar, only the gengchen new moon of the tenth month in Duke Xiang's twenty-first year and the guisi new moon of the eighth month in his twenty-fourth year fall outside the eclipse limit—for as long as calendars have existed, two eclipses in the same month is impossible. Of the thirty-five eclipses, all fell on new moons; the Classic sometimes omits the day or the new moon, and the Gongyang and Guliang commentaries hold they were last-day eclipses—both views are wrong; The Zuo Commentary's view that the historiographers had made errors is correct. Cases off by a day or two stem from the imprecision of ancient calendars and faulty intercalation—Jiang Ji and Yi Xing had already settled this question. Confucius wrote according to the calendar of his day; this was not a matter of fundamental principle, so he did not need to be exhaustive.
56
三國以來日食蜀章武元年辛丑，六月戊辰晦，時加未。 《授時曆》，食甚未五刻。 《大明曆》，食甚未五刻。
Solar eclipses since the Three Kingdoms. Shu, first year of Zhangwu (xinchou): on the last day wuchen of the sixth month, at the wei double-hour. Shoushi Calendar: greatest eclipse at five ke before the wei hour. Daming Calendar: greatest eclipse at five ke before the wei hour.
57
右皆親。 二曆推戊辰皆七月朔。 魏黃初三年壬寅，十一月庚申晦食，時加西南維。 《授時曆》，食甚申二刻。 《大明曆》，食甚申三刻。
Both are close matches. Both calendars place wuchen on the seventh month's new moon. Wei, third year of Huangchu (renyin): eclipse on the last day gengshen of the eleventh month, at the southwest corner of the sky. Shoushi Calendar: greatest eclipse at the second ke of the shen hour. Daming Calendar: greatest eclipse at the third ke of the shen hour.
58
右《授時》親，《大明》次親。 二曆推庚申皆十二月朔。 梁中大通五年癸丑，四月己未朔食，在丙。 《授時曆》，虧初午四刻。 《大明曆》，虧初午四刻。
The Shoushi Calendar is a close match; the Daming Calendar is a second-close match. Both calendars place gengshen on the twelfth month's new moon. Liang, fifth year of Zhongdatong (guichou): eclipse on the jiwei new moon of the fourth month, at the bing double-hour. Shoushi Calendar: beginning of eclipse at the fourth ke of the wu hour. Daming Calendar: beginning of eclipse at the fourth ke of the wu hour.
59
右皆親。 太清元年丁卯，正月己亥朔食，時加申。 《授時曆》，食甚申一刻。 《大明曆》，食甚申三刻。
Both are close matches. First year of Taiqing (dingmao): eclipse on the jihai new moon of the first month, at the shen double-hour. Shoushi Calendar: greatest eclipse at the first ke of the shen hour. Daming Calendar: greatest eclipse at the third ke of the shen hour.
60
右《授時》次親，《大明》親。 陳太建八年丙申，六月戊申朔食，於卯甲間。 《授時曆》，食甚卯二刻。 《大明曆》，食甚卯四刻。
The Shoushi Calendar is a second-close match; the Daming Calendar is a close match. Chen, eighth year of Taijian (bingshen): eclipse on the wushen new moon of the sixth month, between the mao and jia double-hours. Shoushi Calendar: greatest eclipse at the second ke of the mao hour. Daming Calendar: greatest eclipse at the fourth ke of the mao hour.
61
右《授時》次親，《大明》疏遠。 唐永隆元年庚辰，十一月壬申朔食，巳四刻甚。 《授時曆》，食甚巳七刻。 《大明曆》，食甚巳五刻。
The Shoushi Calendar is a second-close match; the Daming Calendar is far off. Tang, first year of Yonglong (gengchen): eclipse on the renshen new moon of the eleventh month, with greatest eclipse at the fourth ke of the si hour. Shoushi Calendar: greatest eclipse at the seventh ke of the si hour. Daming Calendar: greatest eclipse at the fifth ke of the si hour.
62
右《授時》疏，《大明》親。 開耀元年辛巳，十月丙寅朔食，巳初甚。 《授時曆》，食甚辰正三刻。 《大明曆》，食甚辰正一刻。
The Shoushi Calendar is loose; the Daming Calendar is a close match. First year of Kaiyao (xinsi): eclipse on the bingyin new moon of the tenth month, with greatest eclipse at the start of the si hour. Shoushi Calendar: greatest eclipse at the third ke of the exact chen hour. Daming Calendar: greatest eclipse at the first ke of the exact chen hour.
63
右《授時》親，《大明》疏。 嗣聖八年辛卯，四月壬寅朔食，卯二刻甚。 《授時曆》，食甚寅八刻。 《大明曆》，食甚卯初刻。
The Shoushi Calendar is a close match; the Daming Calendar is loose. Eighth year of Sisheng (xinmao): eclipse on the renyin new moon of the fourth month, with greatest eclipse at the second ke of the mao hour. Shoushi Calendar: greatest eclipse at the eighth ke of the yin hour. Daming Calendar: greatest eclipse at the first ke of the mao hour.
64
右皆次親。 十七年庚子，五月己酉朔食，申初甚。 《授時曆》，食甚申初二刻。 《大明曆》，食甚申正初刻。
Both are second-close matches. Seventeenth year (gengzi): eclipse on the jiyou new moon of the fifth month, with greatest eclipse at the start of the shen hour. Shoushi Calendar: greatest eclipse at the second ke from the start of the shen hour. Daming Calendar: greatest eclipse at the first ke of the exact shen hour.
65
右《授時》次親，《大明》疏遠。 十九年壬寅，九月乙丑朔食，申三刻甚。 《授時曆》，食甚申一刻。 《大明曆》，食甚申四刻。
The Shoushi Calendar is a second-close match; the Daming Calendar is far off. Nineteenth year (renyin): eclipse on the yichou new moon of the ninth month, with greatest eclipse at the third ke of the shen hour. Shoushi Calendar: greatest eclipse at the first ke of the shen hour. Daming Calendar: greatest eclipse at the fourth ke of the shen hour.
66
右《授時》次親，《大明》親。 景龍元年丁未，六月丁卯朔食，午正甚。 《授時曆》，食甚午正二刻。 《大明曆》，食甚未初初刻。
The Shoushi Calendar is a second-close match; the Daming Calendar is a close match. First year of Jinglong (dingwei): eclipse on the dingmao new moon of the sixth month, with greatest eclipse at the exact wu hour. Shoushi Calendar: greatest eclipse at the second ke of the exact wu hour. Daming Calendar: greatest eclipse at the very first ke of the wei hour.
67
右《授時》次親，《大明》疏遠。 開元九年辛酉，九月乙巳朔食，午正後三刻甚。 《授時曆》，食甚午正一刻。 《大明曆》，食甚午正二刻。
The Shoushi Calendar is a second-close match; the Daming Calendar is far off. Ninth year of Kaiyuan (xinyou): eclipse on the yisi new moon of the ninth month, with greatest eclipse three ke after the exact wu hour. Shoushi Calendar: greatest eclipse at the first ke of the exact wu hour. Daming Calendar: greatest eclipse at the second ke of the exact wu hour.
68
右《授時》次親，《大明》親。 宋慶曆六年丙戌，三月辛巳朔食，申正三刻復滿。 《授時曆》，復滿申正三刻。 《大明曆》，復滿申正一刻。
The Shoushi Calendar is a second-close match; the Daming Calendar is a close match. Song, sixth year of Qingli (bingxu): eclipse on the xinsi new moon of the third month, with repletion at the third ke of the exact shen hour. Shoushi Calendar: repletion at the third ke of the exact shen hour. Daming Calendar: repletion at the first ke of the exact shen hour.
69
右《授時》密合，《大明》次親。 皇祐元年己丑，正月甲午朔食，午正甚。 《授時曆》，食甚午初三刻。 《大明曆》，食甚午正初刻。
The Shoushi Calendar is an exact match; the Daming Calendar is a second-close match. First year of Huangyou (jichou): eclipse on the jiawu new moon of the first month, with greatest eclipse at the exact wu hour. Shoushi Calendar: greatest eclipse at the third ke from the start of the wu hour. Daming Calendar: greatest eclipse at the first ke of the exact wu hour.
70
右《授時》親，《大明》密合。 五年癸巳歲，十月丙申朔食，未一刻甚。 《授時曆》，食甚未三刻。 《大明曆》，食甚未初刻。
The Shoushi Calendar is a close match; the Daming Calendar is an exact match. Fifth year of Huangyou (guisi): eclipse on the bingchen new moon of the tenth month, with greatest eclipse at the first ke of the wei hour. Shoushi Calendar: greatest eclipse at the third ke of the wei hour. Daming Calendar: greatest eclipse at the first ke from the start of the wei hour.
71
右《授時》次親，《大明》親。 至和元年甲午，四月甲午朔食，申正一刻甚。 《授時曆》，食甚申正一刻。 《大明曆》，食甚申正二刻。
The Shoushi Calendar is a second-close match; the Daming Calendar is a close match. First year of Zhihe (jiawu): eclipse on the jiawu new moon of the fourth month, with greatest eclipse at the first ke of the exact shen hour. Shoushi Calendar: greatest eclipse at the first ke of the exact shen hour. Daming Calendar: greatest eclipse at the second ke of the exact shen hour.
72
右《授時》密合，《大明》親。 嘉祐四年己亥，正月丙申朔食，未三刻復滿。 《授時曆》，復滿未初二刻。 《大明曆》，復滿未初二刻。
The Shoushi Calendar is an exact match; the Daming Calendar is a close match. Fourth year of Jiayou (jihai): eclipse on the bingchen new moon of the first month, with repletion at the third ke of the wei hour. Shoushi Calendar: repletion at the second ke from the start of the wei hour. Daming Calendar: repletion at the second ke from the start of the wei hour.
73
右皆親。 六年辛丑，六月壬子朔食，未初虧初。 《授時曆》，虧初未初刻。 《大明曆》，虧初未一刻。
Both are close matches. Sixth year of Jiayou (xinchou): eclipse on the renzi new moon of the sixth month, with the beginning of eclipse at the start of the wei hour. Shoushi Calendar: beginning of eclipse at the first ke from the start of the wei hour. Daming Calendar: beginning of eclipse at the first ke of the wei hour.
74
右《授時》親，《大明》次親。 治平三年丙午，九月壬子朔食，未二刻甚。 《授時曆》，食甚未三刻。 《大明曆》，食甚未四刻。
The Shoushi Calendar is a close match; the Daming Calendar is a second-close match. Third year of Zhiping (bingwu): eclipse on the renzi new moon of the ninth month, with greatest eclipse at the second ke of the wei hour. Shoushi Calendar: greatest eclipse at the third ke of the wei hour. Daming Calendar: greatest eclipse at the fourth ke of the wei hour.
75
右《授時》親，《大明》次親。 熙寧二年己酉，七月乙丑朔食，辰三刻甚。 《授時曆》，食甚辰五刻。 《大明曆》，食甚辰四刻。
The Shoushi Calendar is a close match; the Daming Calendar is a second-close match. Second year of Xining (jiyou): eclipse on the yichou new moon of the seventh month, with greatest eclipse at the third ke of the chen hour. Shoushi Calendar: greatest eclipse at the fifth ke of the chen hour. Daming Calendar: greatest eclipse at the fourth ke of the chen hour.
76
右《授時》次親，《大明》親。 元豐三年庚申，十一月己丑朔食，巳六刻甚。 《授時曆》，食甚巳五刻。 《大明曆》，食甚巳二刻。
The Shoushi Calendar is a second-close match; the Daming Calendar is a close match. Third year of Yuanfeng (gengshen): eclipse on the jichou new moon of the eleventh month, with greatest eclipse at the sixth ke of the si hour. Shoushi Calendar: greatest eclipse at the fifth ke of the si hour. Daming Calendar: greatest eclipse at the second ke of the si hour.
77
右《授時》親，《大明》疏遠。 紹聖元年甲戌，三月壬申朔食，未六刻甚。 《授時曆》，食甚未五刻。 《大明曆》，食甚未五刻。
The Shoushi Calendar is a close match; the Daming Calendar is far off. First year of Shaosheng (jiaxu): eclipse on the renshen new moon of the third month, with greatest eclipse at the sixth ke of the wei hour. Shoushi Calendar: greatest eclipse at the fifth ke of the wei hour. Daming Calendar: greatest eclipse at the fifth ke of the wei hour.
78
右皆親。
Both are close matches.
79
大觀元年丁亥，十一月壬子朔食，未二刻虧初，未八刻甚，申六刻復滿。 《授時曆》，虧初未三刻，食甚申初刻，復滿申六刻。 《大明曆》，虧初未初刻，食甚未七刻，復滿申五刻。
First year of Daguan (dinghai): eclipse on the renzi new moon of the eleventh month, with the beginning of eclipse at the second ke of the wei hour, greatest eclipse at the eighth ke of the wei hour, and repletion at the sixth ke of the shen hour. Shoushi Calendar: beginning of eclipse at the third ke of the wei hour, greatest eclipse at the first ke from the start of the shen hour, and repletion at the sixth ke of the shen hour. Daming Calendar: beginning of eclipse at the first ke from the start of the wei hour, greatest eclipse at the seventh ke of the wei hour, and repletion at the fifth ke of the shen hour.
80
右《授時曆》虧初、食甚皆親，復滿密合； 《大明》虧初次親，食甚、復滿皆親。 紹興三十二年壬午，正月戊辰朔食，申初虧初。 《授時曆》，虧初申一刻。
The Shoushi Calendar is a close match for the beginning of eclipse and greatest eclipse, and an exact match for repletion; the Daming Calendar is a second-close match for the beginning of eclipse, and a close match for greatest eclipse and repletion. Thirty-second year of Shaoxing (renwu): eclipse on the wuchen new moon of the first month, with the beginning of eclipse at the start of the shen hour. Shoushi Calendar: beginning of eclipse at the first ke of the shen hour.
81
《大明曆》，虧初未七刻。 右皆親。 淳熙十年癸卯，十一月壬戌朔食，巳正二刻甚。 《授時曆》，食甚巳正二刻。
Daming Calendar: beginning of eclipse at the seventh ke of the wei hour. Both are close matches. Tenth year of Chunxi (guimao): eclipse on the renxu new moon of the eleventh month, with greatest eclipse at the second ke of the exact si hour. Shoushi Calendar: greatest eclipse at the second ke of the exact si hour.
82
《大明曆》，食甚巳正一刻。 右《授時》密合，《大明》親。 慶元元年乙卯，三月丙戌朔食，午初二刻虧初。 《授時曆》，虧初午初一刻。
Daming Calendar: greatest eclipse at the first ke of the exact si hour. The Shoushi Calendar is an exact match; the Daming Calendar is a close match. First year of Qingyuan (yimao): eclipse on the bingxu new moon of the third month, with the beginning of eclipse at the second ke from the start of the wu hour. Shoushi Calendar: beginning of eclipse at the first ke from the start of the wu hour.
83
《大明曆》，虧初午初二刻。 右《授時》虧初親，《大明》虧初密合。 嘉泰二年壬戌，五月甲辰朔食，午初一刻虧初。 《授時曆》，虧初巳正三刻。
Daming Calendar: beginning of eclipse at the second ke from the start of the wu hour. The Shoushi Calendar is a close match for the beginning of eclipse; the Daming Calendar is an exact match for the beginning of eclipse. Second year of Jiatai (renxu): eclipse on the jiachen new moon of the fifth month, with the beginning of eclipse at the first ke from the start of the wu hour. Shoushi Calendar: beginning of eclipse at the third ke of the exact si hour.
84
《大明曆》，虧初午初三刻。 右皆親。 嘉定九年丙子，二月甲申朔食，申正四刻甚。 《授時曆》，食甚申正三刻。
Daming Calendar: beginning of eclipse at the third ke from the start of the wu hour. Both are close matches. Ninth year of Jiading (bingzi): eclipse on the jiashen new moon of the second month, with greatest eclipse at the fourth ke of the exact shen hour. Shoushi Calendar: greatest eclipse at the third ke of the exact shen hour.
85
《大明曆》，食甚申正二刻。 右《授時》親，《大明》次親。 淳祐三年癸卯，三月丁丑朔食，巳初二刻甚。 《授時曆》，食甚巳初一刻。
Daming Calendar: greatest eclipse at the second ke of the exact shen hour. The Shoushi Calendar is a close match; the Daming Calendar is a second-close match. Third year of Chunyou (guimao): eclipse on the dingchou new moon of the third month, with greatest eclipse at the second ke from the start of the si hour. Shoushi Calendar: greatest eclipse at the first ke from the start of the si hour.
86
《大明曆》，食甚巳初初刻。 右《授時》親，《大明》次親。 本朝中統元年庚申，三月戊辰朔食，申正二刻甚。 《授時曆》，食甚申正一刻。
Daming Calendar: greatest eclipse at the very first ke from the start of the si hour. The Shoushi Calendar is a close match; the Daming Calendar is a second-close match. Our dynasty, first year of Zhongtong (gengshen): eclipse on the wuchen new moon of the third month, with greatest eclipse at the second ke of the exact shen hour. Shoushi Calendar: greatest eclipse at the first ke of the exact shen hour.
87
《大明曆》，食甚申初三刻。 右《授時》親，《大明》疏。
Daming Calendar: greatest eclipse at the third ke from the start of the shen hour. The Shoushi Calendar is a close match; the Daming Calendar is loose.
88
至元十四年丁丑，十月丙辰朔食，午正初刻虧初，未初一刻食甚，未正二刻復滿。 《授時曆》，虧初午正初刻，食甚未初一刻，復滿未正一刻。 《大明曆》，虧初午正三刻，食甚未正一刻，復滿申初二刻。
Fourteenth year of Zhiyuan (dingchou): eclipse on the bingchen new moon of the tenth month, with the beginning of eclipse at the first ke of the exact wu hour, greatest eclipse at the first ke from the start of the wei hour, and repletion at the second ke of the exact wei hour. Shoushi Calendar: beginning of eclipse at the first ke of the exact wu hour, greatest eclipse at the first ke from the start of the wei hour, and repletion at the first ke of the exact wei hour. Daming Calendar: beginning of eclipse at the third ke of the exact wu hour, greatest eclipse at the first ke of the exact wei hour, and repletion at the second ke from the start of the shen hour.
89
右《授時》虧初、食甚皆密合，復滿親； 《大明》虧初疏，食甚、復滿皆疏遠。
The Shoushi Calendar is an exact match for the beginning of eclipse and greatest eclipse, and a close match for repletion; the Daming Calendar is loose for the beginning of eclipse, and far off for greatest eclipse and repletion.
90
前代考古交食，同刻者為密合，相較一刻為親，二刻為次親，三刻為疏，四刻為疏遠。 今《授時》、《大明》校古日食，上自後漢章武元年，下訖本朝，計三十五事。 密合者，《授時》七，《大明》二。 親者，《授時》十有七，《大明》十有六。 次親者，《授時》十，《大明》八。 疏者，《授時》一，《大明》三。 疏遠者，《授時》無，《大明》六。
When comparing against ancient eclipse records, an identical ke is an exact match; a difference of one ke is a close match, two ke a second-close match, three ke loose, and four ke distant. Comparing the Shoushi and Daming Calendars against ancient solar eclipses—from the first year of Zhangwu in the Later Han down to our dynasty—there are thirty-five cases in all. Of exact matches, the Shoushi Calendar has seven and the Daming Calendar two. Of close matches, the Shoushi Calendar has seventeen and the Daming Calendar sixteen. Of second-close matches, the Shoushi Calendar has ten and the Daming Calendar eight. Of loose matches, the Shoushi Calendar has one and the Daming Calendar three. Of distant matches, the Shoushi Calendar has none and the Daming Calendar six.
91
前代月食
Lunar Eclipses of Prior Ages
92
宋元嘉十一年甲戌，七月丙子望食，四更二唱虧初，四更四唱食既。 《授時曆》，虧初四更三點，食既在四更四點。 《大明曆》，虧初在四更二點，食既在四更五點。
Song, eleventh year of Yuanjia (jiaxu): lunar eclipse on the bingzi full moon of the seventh month, with the beginning of eclipse at the second chime of the fourth watch and total lunar eclipse at the fourth chime of the fourth watch. Shoushi Calendar: beginning of eclipse at the third point of the fourth watch, total lunar eclipse at the fourth point of the fourth watch. Daming Calendar: beginning of eclipse at the second point of the fourth watch, total lunar eclipse at the fifth point of the fourth watch.
93
右《授時》虧初親，食既密合； 《大明》虧初密合，食既親。 十三年丙子，十二月癸巳望食，一更三唱食既。 《授時曆》，食既在一更三點。 《大明曆》，食既在一更四點。
The Shoushi Calendar is a close match for the beginning of eclipse and an exact match for total lunar eclipse; the Daming Calendar is an exact match for the beginning of eclipse and a close match for total lunar eclipse. Thirteenth year of Yuanjia (bingzi): lunar eclipse on the guisi full moon of the twelfth month, with total lunar eclipse at the third chime of the first watch. Shoushi Calendar: total lunar eclipse at the third point of the first watch. Daming Calendar: total lunar eclipse at the fourth point of the first watch.
94
右《授時》密合，《大明》親。 十四年丁丑，十一月丁亥望食，二更四唱虧初，三更一唱食既。 《授時曆》，虧初在二更五點，食既在三更二點。 《大明曆》，虧初在二更四點，食既在三更二點。
The Shoushi Calendar is an exact match; the Daming Calendar is a close match. Fourteenth year of Yuanjia (dingchou): lunar eclipse on the dinghai full moon of the eleventh month, with the beginning of eclipse at the fourth chime of the second watch and total lunar eclipse at the first chime of the third watch. Shoushi Calendar: beginning of eclipse at the fifth point of the second watch, total lunar eclipse at the second point of the third watch. Daming Calendar: beginning of eclipse at the fourth point of the second watch, total lunar eclipse at the second point of the third watch.
95
右《授時》虧初、食既皆親； 《大明》虧初密合，食既親。 梁中大通二年庚戌，五月庚寅望月食，在子。 《授時曆》，食甚在子正初刻。 《大明曆》，食甚在子正初刻。
The Shoushi Calendar is a close match for both the beginning of eclipse and total lunar eclipse; the Daming Calendar is an exact match for the beginning of eclipse and a close match for total lunar eclipse. Liang, second year of Zhongdatong (gengxu): lunar eclipse on the gengyin full moon of the fifth month, at the zi double-hour. Shoushi Calendar: greatest eclipse at the first ke of the exact zi hour. Daming Calendar: greatest eclipse at the first ke of the exact zi hour.
96
右皆密合。 大同九年癸亥，三月乙巳望食，三更三唱虧初。 《授時曆》，虧初三更一點。 《大明曆》，虧初三更三點。
Both are exact matches. Ninth year of Datong (guihai): lunar eclipse on the yisi full moon of the third month, with the beginning of eclipse at the third chime of the third watch. Shoushi Calendar: beginning of eclipse at the first point of the third watch. Daming Calendar: beginning of eclipse at the third point of the third watch.
97
右《授時》次親，《大明》密合。 隋開皇十二年壬子，七月己未望食，一更三唱虧初。 《授時曆》，虧初在一更四點。 《大明曆》，虧初在一更五點。
The Shoushi Calendar is a second-close match; the Daming Calendar is an exact match. Sui, twelfth year of Kaihuang (renzi): lunar eclipse on the jiwei full moon of the seventh month, with the beginning of eclipse at the third chime of the first watch. Shoushi Calendar: beginning of eclipse at the fourth point of the first watch. Daming Calendar: beginning of eclipse at the fifth point of the first watch.
98
右《授時》親，《大明》次親。
The Shoushi Calendar is a close match; the Daming Calendar is a second-close match.
99
十五年乙卯，十一月庚午望食，一更四點虧初，二更三點食甚，三更一點復滿。
Fifteenth year of Kaihuang (yimao): lunar eclipse on the gengwu full moon of the eleventh month, with the beginning of eclipse at the fourth point of the first watch, greatest eclipse at the third point of the second watch, and repletion at the first point of the third watch.
100
《授時曆》，虧初在一更三點，食甚在二更二點，復滿在二更五點。
Shoushi Calendar: beginning of eclipse at the third point of the first watch, greatest eclipse at the second point of the second watch, and repletion at the fifth point of the second watch.
101
《大明曆》，虧初在一更五點，食甚在二更三點，復滿在二更五點。
Daming Calendar: beginning of eclipse at the fifth point of the first watch, greatest eclipse at the third point of the second watch, and repletion at the fifth point of the second watch.
102
右《授時》虧初、食甚、復滿皆親； 《大明》虧初、復滿皆親，食甚密合。 十六年丙辰，十一月甲子望食，四更三籌復滿。 《授時曆》，復滿在四更四點。
The Shoushi Calendar is a close match for the beginning of eclipse, greatest eclipse, and repletion; the Daming Calendar is a close match for the beginning of eclipse and repletion, and an exact match for greatest eclipse. Sixteenth year of Kaihuang (bingchen): lunar eclipse on the jiazi full moon of the eleventh month, with repletion at the third chime of the fourth watch. Shoushi Calendar: repletion at the fourth point of the fourth watch.
103
《大明曆》，復滿在四更五點。 右《授時》親，《大明》次親。 後漢天福十二年丁未，十二月乙未望食，四更四點虧初。 《授時曆》，虧初四更五點。
Daming Calendar: repletion at the fifth point of the fourth watch. The Shoushi Calendar is a close match; the Daming Calendar is a second-close match. Later Han, twelfth year of Tianfu (dingwei): lunar eclipse on the yiwei full moon of the twelfth month, with the beginning of eclipse at the fourth point of the fourth watch. Shoushi Calendar: beginning of eclipse at the fifth point of the fourth watch.
104
《大明曆》，虧初四更一點。 右《授時》親，《大明》次親。 宋皇祐四年壬辰，十一月丙辰望食，寅四刻虧初。 《授時曆》，虧初在寅二刻。
Daming Calendar: beginning of eclipse at the first point of the fourth watch. The Shoushi Calendar is a close match; the Daming Calendar is a second-close match. Song, fourth year of Huangyou (renchen): lunar eclipse on the bingchen full moon of the eleventh month, with the beginning of eclipse at the fourth ke of the yin hour. Shoushi Calendar: beginning of eclipse at the second ke of the yin hour.
105
《大明曆》，虧初在寅一刻。 右《授時》次親，《大明》疏。 嘉祐八年癸卯，十月癸未望食，卯七刻甚。 《授時曆》，食甚在辰初刻。
Daming Calendar: beginning of eclipse at the first ke of the yin hour. The Shoushi Calendar is a second-close match; the Daming Calendar is loose. Eighth year of Jiayou (guimao): lunar eclipse on the guiwei full moon of the tenth month, with greatest eclipse at the seventh ke of the mao hour. Shoushi Calendar: greatest eclipse at the first ke of the chen hour.
106
《大明曆》，食甚在辰初刻。 右皆親。
Daming Calendar: greatest eclipse at the first ke of the chen hour. Both are close matches.
107
熙寧二年己酉，閏十一月丁未望食，亥六刻虧初，子五刻食甚，醜四刻復滿。 《授時曆》，虧初在亥六刻，食甚在子五刻，復滿在醜三刻。 《大明曆》，虧初在子初刻，食甚在子六刻，復滿在醜四刻。
Second year of Xining (jiyou): lunar eclipse on the dingwei full moon of the intercalary eleventh month, with the beginning of eclipse at the sixth ke of the hai hour, greatest eclipse at the fifth ke of the zi hour, and repletion at the fourth ke of the chou hour. Shoushi Calendar: beginning of eclipse at the sixth ke of the hai hour, greatest eclipse at the fifth ke of the zi hour, and repletion at the third ke of the chou hour. Daming Calendar: beginning of eclipse at the first ke from the start of the zi hour, greatest eclipse at the sixth ke of the zi hour, and repletion at the fourth ke of the chou hour.
108
右《授時》虧初、食甚密合，復滿親； 《大明》虧初次親，食甚親，復滿密合。 四年辛亥，十一月丙申望食，卯二刻虧初，卯六刻甚。 《授時曆》，虧初在卯初刻，食甚在卯五刻。
The Shoushi Calendar is an exact match for the beginning of eclipse and greatest eclipse, and a close match for repletion; the Daming Calendar is a second-close match for the beginning of eclipse, a close match for greatest eclipse, and an exact match for repletion. Fourth year of Xining (xinhai): lunar eclipse on the bingshen full moon of the eleventh month, with the beginning of eclipse at the second ke of the mao hour and greatest eclipse at the sixth ke of the mao hour. Shoushi Calendar: beginning of eclipse at the first ke from the start of the mao hour, and greatest eclipse at the fifth ke of the mao hour.
109
《大明曆》，虧初在卯四刻，食甚在卯七刻。 右虧初皆次親，食甚皆親。
Daming Calendar: beginning of eclipse at the fourth ke of the mao hour, and greatest eclipse at the seventh ke of the mao hour. Both calendars are second-close matches for the beginning of eclipse, and close matches for greatest eclipse.
110
六年癸丑，三月戊午望食，亥一刻虧初，亥六刻甚，子四刻復滿。 《授時曆》，虧初在戌七刻，食甚在亥五刻，復滿在子三刻。 《大明曆》，虧初在亥二刻，食甚在亥七刻，復滿在子四刻。
Sixth year of Xining (guichou): lunar eclipse on the wuwu full moon of the third month, with the beginning of eclipse at the first ke of the hai hour, greatest eclipse at the sixth ke of the hai hour, and repletion at the fourth ke of the zi hour. Shoushi Calendar: beginning of eclipse at the seventh ke of the xu hour, greatest eclipse at the fifth ke of the hai hour, and repletion at the third ke of the zi hour. Daming Calendar: beginning of eclipse at the second ke of the hai hour, greatest eclipse at the seventh ke of the hai hour, and repletion at the fourth ke of the zi hour.
111
右《授時》虧初次親，食甚、復滿皆親； 《大明》虧初、食甚皆親，復滿密合。 七年甲寅，九月己酉望食，四更五點虧初，五更三點食既。 《授時曆》，虧初在四更五點，食既在五更三點。
The Shoushi Calendar is a second-close match for the beginning of eclipse, and a close match for greatest eclipse and repletion; the Daming Calendar is a close match for the beginning of eclipse and greatest eclipse, and an exact match for repletion. Seventh year of Xining (jiayin): lunar eclipse on the jiyou full moon of the ninth month, with the beginning of eclipse at the fifth point of the fourth watch and total lunar eclipse at the third point of the fifth watch. Shoushi Calendar: beginning of eclipse at the fifth point of the fourth watch, and total lunar eclipse at the third point of the fifth watch.
112
《大明曆》，虧初在四更三點，食既在五更二點。 右《授時》虧初、食既皆密合； 《大明》虧初次親，食既親。 崇寧四年乙酉，十二月戊寅望食，酉三刻甚，戌初刻復滿。
Daming Calendar: beginning of eclipse at the third point of the fourth watch, and total lunar eclipse at the second point of the fifth watch. The Shoushi Calendar is an exact match for the beginning of eclipse and total lunar eclipse; the Daming Calendar is a second-close match for the beginning of eclipse and a close match for total lunar eclipse. Fourth year of Chongning (yiyou): lunar eclipse on the wuyin full moon of the twelfth month, with greatest eclipse at the third ke of the you hour and repletion at the first ke from the start of the xu hour.
113
《授時曆》，食甚在酉一刻，復滿在酉七刻。 《大明曆》，食甚在酉三刻，復滿在戌二刻。 右《授時》食甚、復滿皆次親； 《大明》食甚密合，復滿次親。
Shoushi Calendar: greatest eclipse at the first ke of the you hour, and repletion at the seventh ke of the you hour. Daming Calendar: greatest eclipse at the third ke of the you hour, and repletion at the second ke of the xu hour. The Shoushi Calendar is a second-close match for greatest eclipse and repletion; the Daming Calendar is an exact match for greatest eclipse and a second-close match for repletion.
114
本朝至元七年庚午，三月乙卯望食，醜三刻虧初，寅初刻食甚，寅六刻復滿。 《授時曆》，虧初在醜二刻，食甚在寅初刻，復滿在寅六刻。 《大明曆》，虧初在醜四刻，食甚在寅一刻，復滿在寅七刻。
Our dynasty, seventh year of Zhiyuan (gengwu): lunar eclipse on the yimao full moon of the third month, with the beginning of eclipse at the third ke of the chou hour, greatest eclipse at the first ke from the start of the yin hour, and repletion at the sixth ke of the yin hour. Shoushi Calendar: beginning of eclipse at the second ke of the chou hour, greatest eclipse at the first ke from the start of the yin hour, and repletion at the sixth ke of the yin hour. Daming Calendar: beginning of eclipse at the fourth ke of the chou hour, greatest eclipse at the first ke of the yin hour, and repletion at the seventh ke of the yin hour.
115
右《授時》虧初親，食甚、復滿密合； 《大明》虧初、食甚、復滿皆親。
The Shoushi Calendar is a close match for the beginning of eclipse, and an exact match for greatest eclipse and repletion; the Daming Calendar is a close match for the beginning of eclipse, greatest eclipse, and repletion.
116
九年壬申，七月辛未望食，丑初刻虧初，醜六刻食甚，寅三刻復滿。 《授時曆》，虧初在子七刻，食甚在醜四刻，復滿在寅一刻。 《大明曆》，虧初在醜二刻，食甚在醜六刻，復滿在寅二刻。
Ninth year of Zhiyuan (renshen): lunar eclipse on the xinwei full moon of the seventh month, with the beginning of eclipse at the first ke from the start of the chou hour, greatest eclipse at the sixth ke of the chou hour, and repletion at the third ke of the yin hour. Shoushi Calendar: beginning of eclipse at the seventh ke of the zi hour, greatest eclipse at the fourth ke of the chou hour, and repletion at the first ke of the yin hour. Daming Calendar: beginning of eclipse at the second ke of the chou hour, greatest eclipse at the sixth ke of the chou hour, and repletion at the second ke of the yin hour.
117
右《授時》虧初親，食甚、復滿皆次親； 《大明》虧初次親，食甚密合，復滿親。
The Shoushi Calendar is a close match for the beginning of eclipse, and a second-close match for greatest eclipse and repletion; the Daming Calendar is a second-close match for the beginning of eclipse, an exact match for greatest eclipse, and a close match for repletion.
118
十四年丁丑，四月癸酉望食，子六刻虧初，醜三刻食既，醜五刻甚，醜七刻生光，寅四刻復滿。
Fourteenth year of Zhiyuan (dingchou): lunar eclipse on the guiyou full moon of the fourth month, with the beginning of eclipse at the sixth ke of the zi hour, total lunar eclipse at the third ke of the chou hour, greatest eclipse at the fifth ke of the chou hour, emergence of light at the seventh ke of the chou hour, and repletion at the fourth ke of the yin hour.
119
《授時曆》，虧初在子六刻，食既在醜四刻，食甚在醜五刻，生光醜六刻，復滿寅四刻。
Shoushi Calendar: beginning of eclipse at the sixth ke of the zi hour, total lunar eclipse at the fourth ke of the chou hour, greatest eclipse at the fifth ke of the chou hour, emergence of light at the sixth ke of the chou hour, and repletion at the fourth ke of the yin hour.
120
《大明曆》，虧初在丑初刻，食既醜七刻，食甚在醜七刻，生光在醜八刻，復滿寅六刻。
Daming Calendar: beginning of eclipse at the first ke from the start of the chou hour, total lunar eclipse at the seventh ke of the chou hour, greatest eclipse at the seventh ke of the chou hour, emergence of light at the eighth ke of the chou hour, and repletion at the sixth ke of the yin hour.
121
右《授時》虧初、食甚、復滿皆密合，食既、生光皆親； 《大明》虧初、食甚、復滿皆次親，食既疏遠，生光親。
The Shoushi Calendar is an exact match for the beginning of eclipse, greatest eclipse, and repletion, and a close match for total lunar eclipse and emergence of light; the Daming Calendar is a second-close match for the beginning of eclipse, greatest eclipse, and repletion, far off for total lunar eclipse, and a close match for emergence of light.
122
十六年己卯，二月癸酉望食，子五刻虧初，醜二刻甚，醜七刻復滿。 《授時曆》，虧初在子五刻，食甚在醜二刻，復滿在醜七刻。 《大明曆》，虧初在子七刻，食甚在醜三刻，復滿在醜七刻。
Sixteenth year of Zhiyuan (jimao): lunar eclipse on the guiyou full moon of the second month, with the beginning of eclipse at the fifth ke of the zi hour, greatest eclipse at the second ke of the chou hour, and repletion at the seventh ke of the chou hour. Shoushi Calendar: beginning of eclipse at the fifth ke of the zi hour, greatest eclipse at the second ke of the chou hour, and repletion at the seventh ke of the chou hour. Daming Calendar: beginning of eclipse at the seventh ke of the zi hour, greatest eclipse at the third ke of the chou hour, and repletion at the seventh ke of the chou hour.
123
右《授時》虧初、食甚、復滿皆密合； 《大明》虧初次親，食甚親，復滿密合。 八月己丑望食，醜五刻虧初，寅初刻甚，寅四刻復滿。 《授時曆》，虧初在醜三刻，食甚在寅初刻，復滿在寅四刻。
The Shoushi Calendar is an exact match for the beginning of eclipse, greatest eclipse, and repletion; the Daming Calendar is a second-close match for the beginning of eclipse, a close match for greatest eclipse, and an exact match for repletion. Lunar eclipse on the jichou full moon of the eighth month, with the beginning of eclipse at the fifth ke of the chou hour, greatest eclipse at the first ke from the start of the yin hour, and repletion at the fourth ke of the yin hour. Shoushi Calendar: beginning of eclipse at the third ke of the chou hour, greatest eclipse at the first ke from the start of the yin hour, and repletion at the fourth ke of the yin hour.
124
《大明曆》，虧初在醜七刻，食甚在寅二刻，復滿在寅四刻。
Daming Calendar: beginning of eclipse at the seventh ke of the chou hour, greatest eclipse at the second ke of the yin hour, and repletion at the fourth ke of the yin hour.
125
右《授時》虧初次親，食甚、復滿皆密合； 《大明》虧初、食甚皆次親，復滿密合。 十七年庚辰，八月甲申望食，在晝，戌一刻復滿。 《授時曆》，復滿在戌一刻。
The Shoushi Calendar is a second-close match for the beginning of eclipse, and an exact match for greatest eclipse and repletion; the Daming Calendar is a second-close match for the beginning of eclipse and greatest eclipse, and an exact match for repletion. Seventeenth year of Zhiyuan (gengchen): lunar eclipse on the jiashen full moon of the eighth month, during daylight, with repletion at the first ke of the xu hour. Shoushi Calendar: repletion at the first ke of the xu hour.
126
《大明曆》，復滿在戌四刻。 右《授時》密合，《大明》疏。
Daming Calendar: repletion at the fourth ke of the xu hour. The Shoushi Calendar is an exact match; the Daming Calendar is loose.
127
已上四十五事，密合者，《授時》十有八，《大明》十有一； 親者，《授時》十有八，《大明》十有七； 次親者，《授時》九，《大明》十有四； 疏者，《授時》無，《大明》二； 疏遠者，《授時》無，《大明》一。
Of the forty-five cases above, of exact matches the Shoushi Calendar has eighteen and the Daming Calendar eleven; of close matches the Shoushi Calendar has eighteen and the Daming Calendar seventeen; of second-close matches the Shoushi Calendar has nine and the Daming Calendar fourteen; of loose matches the Shoushi Calendar has none and the Daming Calendar two; of distant matches the Shoushi Calendar has none and the Daming Calendar one.
128
日平行一度，月平行十三度十九分度之七，一晝夜之間，月先日十二度有奇，曆二十九日五十三刻，復追及日，與之同度，是謂經朔。 經朔雲者，謂合朔大量不出此也。 日有盈縮，月有遲疾，以盈縮遲疾之數損益之，始為定朔。
The sun's mean motion is one degree per day and the moon's mean motion thirteen degrees and seven-nineteenths of a degree; in one day and night the moon outruns the sun by somewhat more than twelve degrees; after twenty-nine days and fifty-three ke it again overtakes the sun and shares the same position—this is called mean new moon. "Mean new moon" means that the bulk of conjunctions fall within this reckoning. The sun has variation in speed and the moon has fast and slow motion; by adding and subtracting the correction numbers for solar variation and lunar anomaly, one obtains true new moon.
129
初曆法用平朔，止知一大一小，為法之不可易，初聞三大二小之說，皆不以為然。 自有曆以來，下訖麟德，而定朔始行，四大三小，理數自然，唐人弗克若天，而止用平朔。 迨本朝至元，而常議方革。 至如進朔之意，止欲避晦日月見，殊不思合朔在酉戌亥，距前日之卯十八九辰矣，若進一日，則晦不見月，此論誠然。 茍合朔在辰申之間，法不當進，距前日之卯已逾十四五度，則月見於晦，庸得免乎？ 且月之隱見，本天道之自然，朔之進退，出人為之牽強，孰若廢人用天，不復虛進，為得其實哉。 至理所在，奚恤乎人言，可為知者道也。
Early calendars used mean new moon, recognizing only the alternation of one large and one small month as an unalterable rule; when people first heard of three large and two small months in a sequence, none found it credible. From the first calendars down to the Linde era, true new moon was finally adopted, with four large and three small months arising naturally from the reckoning; the Tang could not follow Heaven's pattern and reverted to mean new moon alone. Only in our dynasty's Zhiyuan era was this longstanding practice finally reformed. The purpose of advancing the new moon was merely to keep the moon from being visible on the last day of the month; they never considered that when conjunction falls in you, xu, or hai, it is already eighteen or nineteen double-hours past the mao of the previous day—advancing a day would indeed prevent the moon from appearing on the last day. This argument is sound. If conjunction falls between chen and shen, the rule should not advance it; when it is already more than fourteen or fifteen degrees past the mao of the previous day, the moon will appear on the last day—how can that be avoided? Moreover, the moon's visibility and invisibility follow Heaven's natural course, whereas advancing or delaying the new moon is a human contrivance—how much better to set aside human manipulation, follow Heaven, and make no empty advance, thereby obtaining the true reckoning? Where ultimate principle lies, why worry about popular opinion? This may be told to those who understand.
130
不用積年日法
Not Using Accumulated Years and Day Fraction
131
曆法之作，所以步日月之躔離，候氣朔之盈虛，不揆其端，無以測知天道，而與之吻合； 然日月之行遲速不同，氣朔之運參差不一，昔人立法，必推求往古生數之始，謂之演紀上元。 當斯之際，日月五星同度，如合璧連珠然。 惟其世代綿遠，馴積其數至逾億萬，後人厭其布算繁多，互相推考，斷截其數而增損日法，以為得改憲之術，此歷代積年日法所以不能相同者也。 然行之未遠，浸復差失，蓋天道自然，豈人為附會所能茍合哉？ 夫七政運行於天，進退自有常度，茍原始要終，候驗周匝，則象數昭著，有不容隱者，又何必舍目前簡易之法，而求億萬年宏闊之術哉？
Calendars are made to track the courses and positions of the sun and moon and to observe the surplus and deficit of qi and new moon; without gauging the starting point, there is no way to measure the Way of Heaven and align with it; Yet the sun and moon move at different speeds, and the cycles of qi and new moon vary unevenly; in making calendars, the ancients always traced back to the beginning of numerical generation in antiquity, calling this the ephemeris epoch or upper origin. At that moment, sun, moon, and the five planets shared the same position, like jade combined on a disc or pearls strung together. Because the ages stretch so far back and the numbers accumulate gradually to more than hundreds of millions, later people grew weary of the numerous computations; they consulted one another, truncated the numbers and adjusted the day fraction, thinking they had found the art of reforming the calendar—this is why accumulated years and day fractions could not be the same across dynasties. Yet when put into practice it did not go far before errors gradually reappeared; the Way of Heaven follows its own course—how could artificial forced alignment ever achieve a true fit? The seven luminaries move through the heavens, each advancing and retreating by fixed regular measure; if one traces matters from origin to completion and observes and verifies through a full cycle, the numerical correspondences stand forth plainly and cannot be hidden—why then abandon the simple methods at hand and pursue grand techniques spanning hundreds of millions of years?
132
今《授時曆》以至元辛巳為元，所用之數，一本諸天，秒而分，分而刻，刻而日，皆以百為率，比之他曆積年日法，推演附會，出於人為者，為得自然。
The Shoushi Calendar now takes the xinsi year of Zhiyuan as its epoch; the numbers it employs all derive from heaven—seconds to minutes, minutes to ke, and ke to days, all reckoned by hundreds—and compared with the accumulated years and day fractions of other calendars, which are worked out by forced alignment and human artifice, it attains what is natural.
133
或曰：「昔人謂建曆之本，必先立元，元正然後定日法，法定然後度周天以定分至，然則曆之有積年日法尚矣。 自黃帝以來，諸曆轉相祖述，殆七八十家，未聞舍此而能成者。 今一切削去，無乃昧於本原，而考求未得其方歟？」 是殆不然。 晉杜預有云：「治曆者，當順天以求合，非為合以驗天。」 前代演積之法，不過為合驗天耳。 今以舊曆頗疏，乃命厘正，法之不密，在所必更，奚暇踵故習哉。 遂取漢以來諸曆積年日法及行用年數，具列於後，仍附演積數法，以釋或者之疑。
Some say: 'The ancients held that in establishing a calendar one must first set the epoch; once the epoch is fixed one then determines the day fraction; once the fraction is fixed one then measures the circuit of heaven to fix the equinoxes and solstices—thus calendars have always relied on accumulated years and day fractions. From the time of the Yellow Emperor, calendars have been handed down in succession, totaling some seventy or eighty schools, and none are known to have succeeded by abandoning this practice. Now that all of this has been entirely cut away, might one not be ignorant of the fundamental source and fail to find the right method of inquiry?' This is probably not so. Du Yu of Jin said: 'In regulating calendars, one should follow heaven to seek alignment, not seek alignment in order to verify heaven.' The ephemeris computation methods of former ages were nothing more than aligning the calendar to verify heaven. Because the old calendar was rather loose, an order was issued to rectify it; where the method is insufficiently precise, change is inevitable—why linger over old habits? Accordingly, the accumulated years, day fractions, and years in use of every calendar since the Han are fully listed below, with the method of ephemeris computation appended, to resolve the doubts of those who question.
134
《三統曆》 〈（西漢太初元年丁丑鄧平造，行一百八十八年，至東漢元和乙酉，後天七十八刻。）〉 積年，十一四萬四千五百一十一。 日法，八十一。
Santong Calendar (Made by Deng Ping in the first year of Taichu of the Western Han (dingchou); in use for 188 years, until the yiyou year of Yuanhe of the Eastern Han; 78 ke behind heaven.) Accumulated years: 144,511. Day fraction: 81.
135
《四分曆》， 〈（東漢元和二年乙酉編造，行一百二十一年，至建安丙戌，後天七刻。）〉 積年，一萬五百六十一。 日法，四。
Quarter-Day Calendar, (Made by Bian Xi in the second year of Yuanhe of the Eastern Han (yiyou); in use for 121 years, until the bingxu year of Jian'an; 7 ke behind heaven.) Accumulated years: 10,561. Day fraction: 4.
136
《乾象曆》 〈（建安十一年丙戌劉洪造，行三十一年，魏景初丁巳，後天七刻。）〉 積年，八千四百五十二。 日法，一千四百五十七。
Qianxiang Calendar (Made by Liu Hong in the eleventh year of Jian'an (bingxu); in use for 31 years, until the dingsi year of Jingchu of Wei; 7 ke behind heaven.) Accumulated years: 8,452. Day fraction: 1,457.
137
《元嘉曆》 〈（宋元嘉二十年癸未何承天造，行二十年，至大明七年癸卯，先天五十刻。）〉 積年，六千五百四十一。 日法，七百五十二。
Yuanjia Calendar (Made by He Chengtian in the twentieth year of Yuanjia of Song (guiwei); in use for 20 years, until the seventh year of Daming (guimao); 50 ke ahead of heaven.) Accumulated years: 6,541. Day fraction: 752.
138
《大明曆》 〈（宋大明七年癸卯宋祖沖之造，行五十八年，至魏正光辛丑，後天二十九刻。）〉 積年，五萬二千七百五十七。 日法，三千九百三十九。
Daming Calendar (Made by Zu Chongzhi of Song in the seventh year of Daming (guimao); in use for 58 years, until the xinchou year of Zhengguang of Wei; 29 ke behind heaven.) Accumulated years: 52,757. Day fraction: 3,939.
139
《正光曆》 〈（後魏正光二年辛丑李業興造，行一十九年，至興和庚申，先天十三刻。）〉 積年，一十六萬八千五百九。 日法，七萬四千九百五十二。
Zhengguang Calendar (Made by Li Yexing in the second year of Zhengguang of Later Wei (xinchou); in use for 19 years, until the gengshen year of Xinghe; 13 ke ahead of heaven.) Accumulated years: 168,509. Day fraction: 74,952.
140
《興和曆》 〈（興和二年庚申李業興造，行一十年，至齊天保庚午，先天九十九刻。）〉 積年，二十萬四千七百三十七。 日法，二十萬八千五百三十。
Xinghe Calendar (Made by Li Yexing in the second year of Xinghe (gengshen); in use for 10 years, until the gengwu year of Tianbao of Qi; 99 ke ahead of heaven.) Accumulated years: 204,737. Day fraction: 208,530.
141
《天和曆》 〈（後周天和元年丙戌甄鸞造，行一十三年，至大象己亥，先天四十刻。）〉 積年，八十七萬六千五百七。 日法，二萬三千四百六十。
Tianhe Calendar (Made by Zhen Luan in the first year of Tianhe of Later Zhou (bingxu); in use for 13 years, until the jihai year of Daxiang; 40 ke ahead of heaven.) Accumulated years: 876,507. Day fraction: 23,460.
142
《大象曆》 〈（大象元年己亥馬顯造，行五年，至隋開皇甲辰，後天十刻。）〉 積年，四萬二千二百五十五。 日法，一萬二千九百九十二。
Daxiang Calendar (Made by Ma Xian in the first year of Daxiang (jihai); in use for 5 years, until the jiachen year of Kaihuang of Sui; 10 ke behind heaven.) Accumulated years: 42,255. Day fraction: 12,992.
143
《開皇曆》 〈（隋開皇四年甲辰張賓造，行二十四年，至大業戊辰，後天七刻。）〉 積年，四百一十二萬九千六百九十七。 日法，一十萬二千九百六十。
Kaihuang Calendar (Made by Zhang Bin in the fourth year of Kaihuang of Sui (jiachen); in use for 24 years, until the wuchen year of Daye; 7 ke behind heaven.) Accumulated years: 4,129,697. Day fraction: 102,960.
144
《大業曆》 〈（大業四年戊辰張胄玄造，行一十一年，至唐武德己卯，後天七刻。）〉 積年，一百四十二萬八千三百一十七。 日法，一千一百四十四。
Daye Calendar (Made by Zhang Zhouxuan in the fourth year of Daye (wuchen); in use for 11 years, until the jimao year of Wude of Tang; 7 ke behind heaven.) Accumulated years: 1,428,317. Day fraction: 1,144.
145
《戊寅曆》 〈（唐武德二年己卯道士傅仁均造，行四十六年，至麟德乙丑，後天四十七刻。）〉 積年，一十六萬五千三。 日法，一萬三千六。
Wuyin Calendar (Made by the Daoist Fu Renjun in the second year of Wude of Tang (jimao); in use for 46 years, until the yichou year of Linde; 47 ke behind heaven.) Accumulated years: 165,003. Day fraction: 13,006.
146
《麟德曆》 〈（麟德二年乙丑李淳風造，行六十三年，至開元戊辰，後天一十二刻。）〉 積年，二十七萬四百九十七。 日法，一千三百四十。
Linde Calendar (Made by Li Chunfeng in the second year of Linde (yichou); in use for 63 years, until the wuchen year of Kaiyuan; 12 ke behind heaven.) Accumulated years: 270,497. Day fraction: 1,340.
147
《大衍曆》 〈（開元十六年戊辰僧一行造，行三十四年，至寶應壬寅，先天一十三刻。）〉 積年，九千六百九十六萬二千二百九十七。 日法，三千四十。
Dayan Calendar (Made by the monk Yixing in the sixteenth year of Kaiyuan (wuchen); in use for 34 years, until the renyin year of Baoying; 13 ke ahead of heaven.) Accumulated years: 96,962,297. Day fraction: 3,040.
148
《五紀曆》 〈（寶應元年壬寅郭獻之造，行二十三年，至貞元乙丑，後天二十四刻。）〉 積年，二十七萬四百九十七。 日法，一千三百四十。
Wuji Calendar (Made by Guo Xianzhi in the first year of Baoying (renyin); in use for 23 years, until the yichou year of Zhenyuan; 24 ke behind heaven.) Accumulated years: 270,497. Day fraction: 1,340.
149
《貞元曆》 〈（貞元元年乙丑徐承嗣造，行三十七年，至長慶壬寅，先天十五刻。）〉 積年，四十萬三千三百九十七。 日法，一千九十五。
Zhenyuan Calendar (Made by Xu Chengsi in the first year of Zhenyuan (yichou); in use for 37 years, until the renyin year of Changqing; 15 ke ahead of heaven.) Accumulated years: 403,397. Day fraction: 1,095.
150
《宣明曆》 〈（長慶二年壬寅徐昂造，行七十一年，至景福癸丑，先天四刻。）〉 積年，七百七萬五百九十七。 日法，八千四百。
Xuanming Calendar (Made by Xu Ang in the second year of Changqing (renyin); in use for 71 years, until the guichou year of Jingfu; 4 ke ahead of heaven.) Accumulated years: 7,070,597. Day fraction: 8,400.
151
《崇玄曆》 〈（景福二年癸丑邊岡造，行十四年，後六十三年，至周顯德丙辰，先天四刻。）〉 積年，五千三百九十四萬七千六百九十七。 日法，一萬三千五百。
Chongxuan Calendar (Made by Bian Gang in the second year of Jingfu (guichou); in use for 14 years, and for 63 years thereafter, until the bingchen year of Xiande of Zhou; 4 ke ahead of heaven.) Accumulated years: 53,947,697. Day fraction: 13,500.
152
《欽天曆》 〈（五代周顯德三年丙辰王樸造，行五年，至宋建隆庚申，先天二刻。）〉 積年，七千二百六十九萬八千七百七十七。 日法，七千二百。
Qintian Calendar (Made by Wang Pu in the third year of Xiande of Zhou of the Five Dynasties (bingchen); in use for 5 years, until the gengshen year of Jianlong of Song; 2 ke ahead of heaven.) Accumulated years: 72,698,777. Day fraction: 7,200.
153
《乾元曆》 〈（太平興國六年辛巳吳昭素造，行二十年，至咸平辛丑，合。）〉 積年，三千五十四萬四千二百七十七。 日法，二千九百四十。
Qianyuan Calendar (Made by Wu Zhaosu in the sixth year of Taiping Xingguo (xinsi); in use for 20 years, until the xinchou year of Xianping; in agreement.) Accumulated years: 30,544,277. Day fraction: 2,940.
154
《儀天曆》 〈（咸平四年辛丑史序造，行二十三年，至天聖甲子，合。）〉 積年，七十一萬六千七百七十七。 日法，一萬一百。
Yitian Calendar (Made by Shi Xu in the fourth year of Xianping (xinchou); in use for 23 years, until the jiazi year of Tiansheng; in agreement.) Accumulated years: 716,777. Day fraction: 10,100.
155
《崇天曆》 〈（天聖二年甲子宋行古造，行四十年，至治平甲辰，後天五十四刻。）〉 積年，九千七百五十五萬六千五百九十七。 日法，一萬五百九十。
Chongtian Calendar (Made by Song Xingu in the second year of Tiansheng (jiazi); in use for 40 years, until the jiachen year of Zhiping; 54 ke behind heaven.) Accumulated years: 97,556,597. Day fraction: 10,590.
156
《明天曆》 〈（治平元年甲辰周琮造，行一十年，至熙寧甲寅，合。）〉 積年，七十一萬一千九百七十七。 日法，三萬九千。
Mingtian Calendar (Made by Zhou Cong in the first year of Zhiping (jiachen); in use for 10 years, until the jiayin year of Xining; in agreement.) Accumulated years: 711,977. Day fraction: 39,000.
157
《奉元曆》 〈（熙寧七年甲寅衛樸造，行十八年，至元祐壬申，後天七刻。）〉 積年，八千三百一十八萬五千二百七十七。 日法，二萬三千七百。
Fengyuan Calendar (Made by Wei Pu in the seventh year of Xining (jiayin); in use for 18 years, until the renshen year of Yuanyou; 7 ke behind heaven.) Accumulated years: 83,185,277. Day fraction: 23,700.
158
《觀天曆》 〈（元祐七年壬申皇居卿造，行一十一年，至崇寧癸未，先天六刻。）〉 積年，五百九十四萬四千九百九十七。 日法，一萬二千三十。
Guantian Calendar (Made by Huang Juqing in the seventh year of Yuanyou (renshen); in use for 11 years, until the guiwei year of Chongning; 6 ke ahead of heaven.) Accumulated years: 5,944,997. Day fraction: 12,030.
159
《占天曆》 〈（崇寧二年癸未姚舜輔造，行三年，至丙戌，後天四刻。）〉 積年，二千五百五十萬一千九百三十七。 日法，二萬八千八十。
Zhantian Calendar (Made by Yao Shunfu in the second year of Chongning (guiwei); in use for 3 years, until the bingxu year of Chongning; 4 ke behind heaven.) Accumulated years: 25,501,937. Day fraction: 28,080.
160
《紀元曆》 〈（崇寧五年丙戌姚舜輔造，行二十一年，至金天會丁未，合。）〉 積年，二千八百六十一萬三千四百六十七。 日法，七千二百九十。
Jiyuan Calendar (Made by Yao Shunfu in the fifth year of Chongning (bingxu); in use for 21 years, until the dingwei year of Tianhui of Jin; in agreement.) Accumulated years: 28,613,467. Day fraction: 7,290.
161
《大明曆》 〈（金天會五年丁未楊級造，行五十三年，至大定庚子，合。）〉 積年，三億八千三百七十六萬八千六百五十七。 日法，五千二百三十。
Daming Calendar (Made by Yang Ji in the fifth year of Tianhui of Jin (dingwei); in use for 53 years, until the gengzi year of Dading; in agreement.) Accumulated years: 383,768,657. Day fraction: 5,230.
162
《重修大明曆》 〈（大定二十年庚子趙知微重修，行一百一年，至元朝至元辛巳，後天一十九刻。）〉 積年，八千八百六十三萬九千七百五十七。 日法，五千二百三十。
Revised Daming Calendar (Revised by Zhao Zhiwei in the twentieth year of Dading (gengzi); in use for 101 years, until the xinsi year of Zhiyuan of the Yuan dynasty; 19 ke behind heaven.) Accumulated years: 88,639,757. Day fraction: 5,230.
163
《統元曆》 〈（後宋紹興五年乙卯陳得一造，行三十二年，至乾道丁亥，合。）〉 積年，九千四百二十五萬一千七百三十七。 日法，六千九百三十。
Tongyuan Calendar (Made by Chen Deyi in the fifth year of Shaoxing of Later Song (yimao); in use for 32 years, until the dinghai year of Qiandao; in agreement.) Accumulated years: 94,251,737. Day fraction: 6,930.
164
《乾道曆》 〈（乾道三年丁亥劉孝榮造，行九年，至淳熙丙申，後天一刻。）〉 積年，九千一百六十四萬五千九百三十七。 日法，三萬。
Qiandao Calendar (Made by Liu Xiaorong in the third year of Qiandao (dinghai); in use for 9 years, until the bingshen year of Chunxi; 1 ke behind heaven.) Accumulated years: 91,645,937. Day fraction: 30,000.
165
《淳熙曆》 〈（淳熙三年丙申劉孝榮造，行一十五年，至紹熙辛亥，合。）〉 積年，五千二百四十二萬二千七十七。 日法，五千六百四十。
Chunxi Calendar (Made by Liu Xiaorong in the third year of Chunxi (bingshen); in use for 15 years, until the xinhai year of Shaoxi; in agreement.) Accumulated years: 52,422,077. Day fraction: 5,640.
166
《會元曆》 〈（紹熙二年辛亥劉孝榮造，行八年，至慶元己未，後天一十刻。）〉 積年，二千五百四十九萬四千八百五十七。 日法，三萬八千七百。
Huiyuan Calendar (Made by Liu Xiaorong in the second year of Shaoxi (xinhai); in use for 8 years, until the jiwei year of Qingyuan; 10 ke behind heaven.) Accumulated years: 25,494,857. Day fraction: 38,700.
167
《統天曆》 〈（慶元五年己未楊忠輔造，行八年，至開禧丁卯，先天六刻。）〉 積年，三千九百一十七。 日法，一萬二千。
Tongtian Calendar (Made by Yang Zhongfu in the fifth year of Qingyuan (jiwei); in use for 8 years, until the dingmao year of Kaixi; 6 ke ahead of heaven.) Accumulated years: 3,917. Day fraction: 12,000.
168
《開禧曆》 〈（開禧三年丁卯鮑浣之造，行四十四年，至淳祐辛亥，後天七刻。）〉 積年，七百八十四萬八千二百五十七。 日法，一萬六千九百。
Kaixi Calendar (Made by Bao Huanzhi in the third year of Kaixi (dingmao); in use for 44 years, until the xinhai year of Chunyou; 7 ke behind heaven.) Accumulated years: 7,848,257. Day fraction: 16,900.
169
《淳祐曆》 〈（淳祐十年庚戌李德卿造，行一年，至壬子，合。）〉 積年，一億二千二十六萬七千六百七十七。 日法，三千五百三十。
Chunyou Calendar (Made by Li Deqing in the tenth year of Chunyou (gengxu); in use for 1 year, until the renzi year of Chunyou; in agreement.) Accumulated years: 120,267,677. Day fraction: 3,530.
170
《會天曆》 〈（寶祐元年癸丑譚玉造，行十八年，至咸淳辛未，後天一刻。）〉 積年，一千一百三十五萬六千一百五十七。 日法，九千七百四十。
Huitian Calendar (Made by Tan Yu in the first year of Baoyou (guichou); in use for 18 years, until the xinwei year of Xianchun; 1 ke behind heaven.) Accumulated years: 11,356,157. Day fraction: 9,740.
171
《成天曆》 〈（咸淳七年辛未陳鼎造，行四年，至至元辛巳，後天一刻。）〉 積年，七千一百七十五萬八千一百五十七。 日法，七千四百二十。
Chengtian Calendar (Made by Chen Ding in the seventh year of Xianchun (xinwei); in use for 4 years, until the xinsi year of Zhiyuan; 1 ke behind heaven.) Accumulated years: 71,758,157. Day fraction: 7,420.
172
此下不曾行用，見於典籍經進者二曆。
Below are two calendars that were never put into use but are recorded in the classics as having been submitted to the throne.
173
《皇極曆》 〈（大業間劉焯造，阻難不行，至唐武德二年己卯，先天四十三刻。）〉 積年，一百萬九千五百一十七。 日法，一千二百四十二。
Huangji Calendar (Made by Liu Zhuo during the Daye period; obstructed and never implemented; by the second year of Wude of Tang (jimao), 43 ke ahead of heaven.) Accumulated years: 1,095,517. Day fraction: 1,242.
174
《乙未曆》 〈（大定二十年庚子耶律履造，不曾行用，至辛巳，後天一十九刻。）〉 積年，四千四十五萬三千一百二十六。 日法，二萬六百九十。
Yiwei Calendar (Made by Yelü Lü in the twentieth year of Dading (gengzi); never put into use; by xinsi, 19 ke behind heaven.) Accumulated years: 40,453,126. Day fraction: 20,690.
175
《授時曆》 〈（元至元十八年辛巳為元。）〉 積年、日法不用。 實測到至元十八年辛巳歲。 氣應，五十五日六百分。
Shoushi Calendar (Yuan dynasty: the xinsi year, eighteenth year of Zhiyuan, taken as the epoch.) Accumulated years and day fractions are not used. Actual observation extended to the xinsi year, the eighteenth year of Zhiyuan. Qi correspondence: 55 days and 600 parts.
176
閏應，二十日一千八百五十分。 經朔，三十四日八千七百五十分。
Intercalation correspondence: 20 days and 1,850 parts. Mean new moon: 34 days and 8,750 parts.
177
日法，二千一百九十，演紀上元己亥，距至元辛巳九千八百二十五萬一千四百二十二算。 氣應，五十五日六百二分。 閏應，二十日一千八百五十三分。
Day fraction: 2,190; ephemeris-era superior epoch jihai, 98,251,414,422 counts from the xinsi year of Zhiyuan. Qi correspondence: 55 days and 602 parts. Intercalation correspondence: 20 days and 1,853 parts.
178
經朔，三十四日八千七百四十九分。
Mean new moon: 34 days and 8,749 parts.
179
日法，八千二百七十，演紀上元甲子，距辛巳五百六十七萬五百五十七算，日命甲子。 氣應，五十五日五百三十三分。 閏應，二十日一千八百八分。
Day fraction: 8,270; ephemeris-era superior epoch jiazi, 5,670,505,057 counts from xinsi; day designation jiazi. Qi correspondence: 55 days and 533 parts. Intercalation correspondence: 20 days and 1,808 parts.
180
經朔，三十四日八千七百二十五分。
Mean new moon: 34 days and 8,725 parts.
181
日法，六千五百七十，寅紀上元甲子，距辛巳三千九百七十五萬二千五百三十七算。 氣應，五十五日六百三十一分。 閏應，二十日一千九百一十九分。
Day fraction: 6,570; yin-era superior epoch jiazi, 39,752,505,037 counts from xinsi. Qi correspondence: 55 days and 631 parts. Intercalation correspondence: 20 days and 1,919 parts.
182
經朔，三十四日八千七百一十二分。
Mean new moon: 34 days and 8,712 parts.