Calendar Dates in Southern Ming and Zheng Dynasty

First draft: April, 2022

In April 1644, the peasant rebel leader Li Zicheng (李自成) conquered Beijing (北京), the capital of the Ming dynasty. The Chongzhen (崇禎) Emperor committed suicide the next day. Li was later defeated and the Qing army took over Beijing. The Ming loyalists and imperial members of the Ming dynasty fled to southern China and established a series of dynasty rump states to oppose the Qing dynasty. Historians refer to those rump states as the Southern Ming dynasty (1645-1661). In the imperial China, the annual production and distribution of imperial calendars was considered as an exclusive privilege and special duty of the ruling house. Being the successor of the Ming dynasty, the Southern Ming dynasty naturally produced the Datong calendars, which were calendars calculated according to the Datong astronomical system used in the Ming dynasty. However, the Southern Ming dynasty didn't have a stable government and had to deal with internal conflicts among various forces, which resulted in several versions of Datong calendars being produced in the Southern Ming dynasty. Hongguang (弘光), Longwu (隆武) and Yongli (永曆) were considered as three legitimate emperors in the Southern Ming dynasty and their governments all produced Datong calendars. However, the Prince of Lu (魯王) proclaimed himself as Regent (監國) and established a separate government from the Yongli emperor in 1646-1653. The Lu government produced the Lu Datong calendars. Also, the military commander Zheng Chenggong (鄭成功) led anti-Qing naval forces on China's southeastern coast. Zheng was loyal to the Southern Ming dynasty and was awarded the titles Koxinga (國姓爺 or "Lord of the Imperial Surname") and Prince of Yanping (廷平王). However, since copies of the emperor's Datong calendars were unable to be sent to Zheng's region in time because of war, Zheng ordered his officials to expediently produce unofficial Datong calendars for civilian use. The Yongli emperor was in exile in 1659. He was captured and sent to the Qing army in 1662, and the Southern Ming dynasty ended. At about the same time, Zheng was defeated by the Qing army. He marched his remaining forces to the Dutch occupied Taiwan. Zheng defeated the Dutch and established the Zheng dynasty (1662-1683), also known as the House of Koxinga and Kingdom of Tungning (東寧王國). Zheng and his successors were still loyal to the Southern Ming dynasty even though it no longer existed. On the cover pages of the Datong calendars produced by the Zheng dynasty, there was a statement that said the Datong calendars were produced and promulgate expediently because the emperor's calendars had not arrived. Since the official Datong calendars of the Southern Ming dynasty were no longer produced at that time, Zheng's unofficial Datong calendars became the de facto official Datong calendars of the state. The Zheng dynasty ended in 1683 when the ruler Zheng Keshuang (鄭克塽) surrendered to the Qing dynasty.

There were at least 5 to 6 versions of Datong calendars produced in the Southern Ming and Zheng dynasty in the 39-year period from 1645 to 1683. The Datong calendars in the Ming dynasty were calculated by the officials in the Imperial Astronomical Bureau (欽天監). These officials were hereditary. After the fall of the Ming empire, most of them probably stayed in Beijing and became the officials in the Qing dynasty. Hence the calendar makers of the Southern Ming dynasty most likely had no experience in making the official Ming calendars. At that time, the most important thing was to resist the Qing army, not making calendars. I suspect that the calendar markers didn't spend much time to find out how exactly the Ming calendars were computed. They probably did the calculations based on their understanding of the Datong system, so their computed times of lunar conjunctions and solar terms might deviate slightly from those calculated using the algorithms by the Ming calendar markers. In fact, there is evidence to show that different versions of the Southern Ming calendars sometimes deviated from each other. However, the deviations were largely small as their calculations were based on the same Datong system.

A complete record of calendar dates of the Southern Ming and Zheng dynasty can be found in Cán Míng Dà Tǒng Lì (殘明大統曆 or Datong Calendar of the Waning Ming Dynasty) compiled by the scholar Fu Yili (傅以禮) in the 19th century. Fu's work is included in the last volume of the book series Èr Shí Wǔ Shǐ Bǔ Biān (二十五史補編 or Supplement to The Twenty-Five Official Dynastic Histories). Several calendar dates in the Southern Ming dynasty were also recorded in various sources on the history of the Southern Ming dynasty. However, there are many mistakes and discrepancies among these sources. Apart from the fact that there were several versions of Datong calendars produced in this period, some sources mix up the calendar dates between the Southern Ming and Qing calendars. The Qing calendars were computed by the Shixian astronomical system (時憲曆), which was very different from the Datong system the Southern Ming calendars were based on.

It seems that printed copies of the Datong calendars from the Southern Ming dynasty are not preserved. However, several printed copies of the Datong calendars promulgated by the Zheng dynasty are preserved in English libraries. They were Datong calendars for the years 1671, 1676 and 1677. These calendars were obtained and brought to England by East India Company merchants. The calendars were among the presents given to the merchants by the Zheng dynasty government when the merchants tried to establish trade relation between the company and Taiwan. Four copies preserved in the English libraries have been digitized and are available online: Datong Calendars for the 25th Year of the Yongli Reign (1671) preserved in the Bodleian Library and Christ Church, Oxford, the 30th Year of the Yongli Reign (1676) in St John's College Library , and the 31st Year of the Yongli Reign (1677) in Bodleian Library. I reproduced photos of several pages containing useful information for validating calendar dates in the Southern Ming and Zheng dynasty in accord with their photo licenses. I also reproduced the Chinese texts in the photos with English translation on these three pages: calendars for 1671, 1676 and 1677. Apart from the calendar dates provided there, these three calendars also contain records of leap months in the decades preceding the calendar years, which are useful in studying the Datong calendars promulgated in the period.

The calendar data for the Southern Ming and Zheng dynasty on this website are based on the information in Fu's Datong Calendar of the Waning Ming Dynasty, with two dates corrected according to the information in the printed copies of the Datong calendars mentioned above. In the following, I compare the differences between the calendar dates computed by the Datong system and those in Datong Calendar of the Waning Ming Dynasty, in the printed copies of Datong calendars and in various other sources.

Datong system adopted the same astronomical system as the Shoushi system (授時曆) developed in 1280 with only minor modifications. The conjunction and solar-term calculations in the Shoushi system are explained in and . The calculation of the times of solar terms is explained in an article by Yong Li, in which he also verified that his calculated solar-term times match exactly the times listed in the Datong calendar for the 6th year of the Jiajing reign (1527) promulgated by the Ming dynasty.

In fact, the solar terms before the Qing dynasty were computed by taking into account only the mean motion of the Sun. They were linear function of time and very easy to calculate. It's very easy to verify that the solar-term times listed in the (de facto) official Datong calendars for 1671, 1676 and 1677 also match exactly with the calculation by the Datong system. By examining the dates of 937 solar terms from 1645 to 1683 in Datong Calendar of the Waning Ming Dynasty, I only find two discrepancies. According to Datong Calendar of the Waning Ming Dynasty, the date of J8 in 1663 was on the 4th day in the 8th Chinese month and the date of Z11 (winter solstice) in 1676 was on the 16th day in the 11th Chinese month. But J8 in 1663 was on the 5th day in the 8th Chinese month and Z11 in 1676 was on the 17th day in the 11th Chinese month according to the calculation of the Datong system. Fortunately, the official date of Z11 in 1676 can be found in the printed copy of the Datong calendar for 1676 and it was on the 17th day in the 11th month, which is consistent with the calculation of the Datong system. As the computation of the Datong solar terms is very simple, it was unlikely for the calendar markers to make mistakes in the calculation and we can assume that almost all solar terms in the Datong calendars of the Southern Ming and Zheng dynasty match the calculation of the Datong system.

The calculation of lunar conjunctions in the Datong system is more complicated because it also takes into account the nonuniform motions of the Sun and Moon. Two methods are discussed in Li's article : D1 algorithm and D2 algorithm and Li thinks that the D1 algorithm was used by the calendar markers in the Ming dynasty. I confirmed in my article "Lunar Conjunction Calculation in the Ming Dynasty and Corrections to the Ming Calendar Data" that the conjunction times calculated by Li's D1 algorithm match the 56 times listed in Datong calendars for 1531, 1532, 1604, 1616, 1629 and 1639. This means that the D1 algorithm was the method the imperial astronomers used to calculate the conjunctions for the Datong calendars before the fall of Ming dynasty in 1644. By examining the 483 conjunction dates from 1645 to 1683 in Datong Calendar of the Waning Ming Dynasty and the printed copies of the Datong calendars, I find 7 discrepancies, which are listed in the table below. All the discrepancies occurred in 1671 and later. From these discrepancies we can deduce that the conjunction times calculated by the calendar markers in the Zheng dynasty could deviate from Li's D1 algorithm by up to two hours.

^* Datong Calendar of the Waning Ming Dynasty records the New Year day in 1671 on Feb 9, but the official Datong Calendar for 1671 indicates that the New Year day was on Feb 10.
^† Datong Calendar of the Waning Ming Dynasty records a leap month after the 6th month in 1675. The associated conjunction was on July 23, which is one day later than the conjunction day calculated by the Datong system (July 22). This results in a discrepancy in the leap month: the leap month occurred after the 5th Chinese month according to the calculation of Datong system, but it was after the 6th Chinese month in Datong Calendar of the Waning Ming Dynasty. The official Datong calendars for 1676 and 1677 record that the leap month in 1675 was after the 6th month, which validates the information in Datong Calendar of the Waning Ming Dynasty.

Below I briefly analyze the discrepancies in the calendar dates in the Southern Ming Dynasty among various sources.

As mentioned above, the Prince of Lu established a separate government from the Yongli emperor and produced the Lu Datong calendars in 1646-1653. In an article by Dianquan Huang, several conjunction dates in Lu's Datong calendars were deduced from various sources. Two discrepancies in the conjunction dates are found between Lu's Datong calendars and the information in Datong Calendar of the Waning Ming Dynasty. In Lu's Datong calendars, the New Year Day in 1649 was on Feb 12 and the New Year day in 1652 was on Feb 9. The two New Year days in Datong Calendar of the Waning Ming Dynasty were on Feb 11 and Feb 10, respectively. According to the calculation of the Datong system (Li's D1 algorithm), the lunar conjunction associated with the New Year day of 1649 occurred on Feb 11 at 22:31 and the conjunction associated with the New Year day of 1652 occurred on Feb 10 at 0:22. These data show that the conjunction times calculated in Lu's Datong calendar could deviate from Li's D1 algorithm by 1.5 hours.

Datong Calendar of the Waning Ming Dynasty and Yán Píng Wáng Hù Guān Yáng Yīng Cóng Zhēng Shí Lù (延平王戶官楊英從征實錄 or Account of the quartermaster Yang Ying's campaign with Prince Yanping) both record a leap month after the 11th Chinese month in 1650, which is consistent with the calculation of the Datong system. However, the official Datong calendars for 1671, 1676 and 1677 record a leap month after the 12th month. Dianquan Huang in pointed out that the leap month 11 was supported by a few other sources. He believed that leap month 11 was correct on the basis of majority rule. He thought the leap month 12 recorded in the official Datong calendar for 1671 was probably a misprint. He didn't have access to the Datong calendars for 1676 and 1677 and didn't know leap month 12 was also recorded in these two official calendars, which essentially rules out the misprint hypothesis. The following table shows the conjunctions and major solar terms (relevant to the leap month) calculated by the Datong system.

We see from the table that the Chinese month associated with the Jan 21 conjunction contained the major solar term Z12 and so it was month 12. The month associated with the Dec 23 conjunction didn't contain any major solar term and so was an intercalary month. As mentioned above, the solar term calculation in the Datong system is very simple and calendar markers were unlikely to make mistakes. We can assume that the major solar terms computed by the calendar markers in the Southern Ming dynasty match the dates computed by the Datong system. Times of lunar conjunctions, on the other hand, could deviate from the calculation of the Datong system (Li's D1 algorithm). The Jan 21 conjunction time was about two hours from the midnight of the following day. If the calendar marker used a different algorithm and calculated the conjunction to be on Jan 22, the Chinese month associated with the Dec 23 conjunction would contain Z11 and became month 12, and the month associated with the Jan 22 conjunction would contain no major solar term and became leap month 12. We see in the previous section that the conjunction times computed by the Datong calendars in the Zheng dynasty could deviate from those computed by the Datong system by up to two hours, and the leap month 12 information is from the Datong calendars produced by the Zheng dynasty. It's therefore reasonable to assume that the leap month 12 was the intercalary month in the unofficial Datong calendar for 1650 produced expediently by the Zheng government. Since Zheng's calendars produced before the fall of the Southern Ming dynasty were not official, leap month 11 should be used.

Datong Calendar of the Waning Ming Dynasty records a leap month after the 7th Chinese month in 1653, which is consistent with the calculation of the Datong system. However, Account of the quartermaster Yang Ying's campaign with Prince Yanping records the leap month to be after the 8th month. The chronicle Xíng Zài Yáng Qiū (行在陽秋) and the official Datong calendar for 1671 both record the leap month to be after the 6th month. Interestingly, the official Datong calendars for 1676 and 1677 change the leap month in this year to be after the 8th month. Dianquan Huang in thought that leap month 6 was the leap month in the official Datong calendar for 1653 produced by the Yongli government, and leap month 8 was probably the intercalary month appearing in the unofficial Datong calendar for 1653 expediently produced by Zheng's officials. He speculated that the leap month 6 recorded in the Datong calendar for 1671 was corrected based on Yongli's official Datong calendars obtained later. He didn't have access to the Datong calendars for 1676 and 1677 and didn't know that the leap month in 1653 was changed to be after the 8th month, making his speculation unlikely to hold. A more likely explanation for the leap month 6 recorded in the Datong calendar for 1671 was that it was a misprint. The following table shows the conjunctions and major solar terms (relevant to the leap month) calculated by the Datong system.

We see from the table that the Sep 21 conjunction is less than one hour from the midnight of the following day. If the calendar marker used a different method to compute conjunctions, it was possible that the computed conjunction might fall on Sep 22 instead. If that was the case, the Chinese month associated with the Aug 23 conjunction would contain Z8 and became month 8, and the month associated with the Sep 22 conjunction would contain no major solar term and became leap month 8. So from the point of view of calendar calculation, both leap month 7 and leap month 8 were possible. Leap month 6 was very unlikely since in order for the month associated with the July 24 conjunction to miss the major solar term Z7, the Aug 23 conjunction would have to be moved two days earlier to Aug 21. This major adjustment could not be achieved by assuming that the calendar marker used a slightly different method to compute conjunctions. It would instead require the calendar marker to make a serious mistake in the computation of the conjunction. In fact, the intercalary month in the Qing calendar in this year was after the 6th month. That's why Shuwu Wang suspected in the article that the leap month 6 recorded in Xíng Zài Yáng Qiū was caused by mixing up the calendar dates between the Southern Ming and Qing calendars.

Since leap month 8 is recorded in both the official Datong calendars for 1676 and 1677, I think it was likely to be the intercalary month in the unofficial Datong calendar for 1653 produced expediently by Zheng's officials. It's not clear to me, however, whether the leap month 7 in Datong Calendar of the Waning Ming Dynasty was the intercalary month in the official Datong calendar produced by the Yongli government. Huang doubted that Fu had access to all the official Datong calendars in this period and so he might need to fill in the missing calendar dates by his own calculation when compiling Datong Calendar of the Waning Ming Dynasty. Huang speculated that the leap month 7 in 1653 was Fu's calculation.

Datong Calendar of the Waning Ming Dynasty, the official Datong calendars for 1671, 1676 and 1677 all record a leap month after the 3rd Chinese month in 1648, which is consistent with the calculation of the Datong system. However, Shuwu Wang in argued based on various sources that the correct intercalary month was after the 6th month. The following table shows the conjunctions and major solar terms (relevant to the leap month) calculated by the Datong system.

According to Wang's table in , the Jul 20 conjunction should occur on Jul 21 instead, all the other conjunction dates remained unchanged but leap month 3 should be changed to month 4, month 4 to month 5, month 5 to month 6, and month 6 to leap month 6. I think the proposed changes are problematic. The Jul 20 conjunction calculated by the Datong system was more than 6 hours from the midnight of the following day. It would require the calendar marker to make a serious calculation mistake to move the conjunction to Jul 21. It also requires moving the dates of three major solar terms: Z4 has to move to a day earlier in order to change leap month 3 to month 4; Z5 has to move to a day earlier in order to change month 4 to month 5; Z6 has to move to 2 days earlier to Jul 20 in order to change month 6 to leap month 6 (with the proposed conjunction date on Jul 21). As mentioned above, solar-term computation in the Datong system is very simple. The proposed changes in the three major solar terms again require the calendar marker to make further serious calculation mistakes. That's why I think Wang's proposed calendar dates for 1648 are very unlikely.