Since the year 25 AD, we have been using the "San Tong Li" calendar for over a hundred years. However, this calendar gradually became out of sync with reality. The new moon (the first day of the lunar month) always appeared earlier than calculated in the calendar, sometimes even appearing at the end of the month (last day), and the sighting of the new moon also did not align with the calendar. Upon closer examination of the calendar, it was discovered that the days were getting shorter while the months were getting longer; this was concerning!
By the year 32 AD, a eunuch named Zhu Fu and a senior official named Xu Shu repeatedly petitioned the emperor, saying that the calculation of the new moon in the calendar was incorrect and needed to be changed. At that time, the error was not too significant, and the emperor believed the country had only recently been stabilized, leaving him little time to address the issue. It was not until the year 52 AD that the official calendar predicted a lunar eclipse on the sixteenth day of the seventh month, but what actually occurred?
An official named Yang Cen noticed that in recent lunar eclipses, the actual occurrence was earlier than calculated in the official calendar. After calculating, he discovered an error in the lunar calculations and wrote to the emperor, saying, "The lunar eclipse should occur on the fifteenth day; the official calendar is wrong!" The emperor then ordered Yang Cen to observe carefully and compare with the official calendar. From July to November, he observed the moon's phases (lunar calendar seventh, eighth, twenty-second, and twenty-third days) five times, and each time the official calendar consistently miscalculated, while Yang Cen's observations were accurate!
The emperor was thrilled and, on an indeterminate date, he ordered Yang Cen to be in charge of calculating the moon phases and lunar eclipse times. At the same time, officials Zhang Sheng, Jing Fang, and Bao Ye were asked to use the "Four Divisions Method" to calculate alongside Yang Cen and see who was more accurate. Over a year later, Zhang Sheng and his colleagues made six more errors than Yang Cen. On an unknown date in November of the year 52 AD, the emperor ordered Zhang Sheng and Jing Fang to replace Yang Cen in calculating the moon phases and lunar eclipse times, and their calculations were subsequently adopted. However, at that time, Zhang Sheng and his team had yet to fully grasp the fundamental principles of the calendar, nor could they adequately correct its divisions.
Legend has it that nine years had passed when a Grand Astrologer named Dong Meng reported that the calendar we were using was incorrect. This matter was entrusted to several high-ranking officials in the court, along with calendar experts, for discussion. By the fourth month of the tenth year, no one could provide clear evidence to explain the situation.
In the second year of Yuanhe, the "Tai Chu Calendar" was increasingly misaligned with celestial phenomena. The positions of the sun, moon, and stars were misaligned, and everyone knew that on the winter solstice, the sun should be at twenty-one degrees in the Dipper constellation, but according to the calendar, it hadn't even reached five degrees in the Cowherd constellation yet; the calendar claimed the sun was in the middle of the Cowherd constellation. The months and dates calculated by this calendar were also off by a day from the actual situation, and the positions of the constellations were off by five degrees. Emperor Zhang of the Han Dynasty knew that this calendar was incorrect, so he asked the historians, who also recognized the inaccuracies but felt powerless to change it. Therefore, Emperor Zhang summoned several experts in calendar calculation, such as Li Fan, to study the matter together. On the day of Jia Yin in the second month, the emperor issued a decree saying, "I have heard that wise ancient kings always aligned with the will of heaven and did not defy its way. The 'He Tu' says, 'The ninth red will prosper, the tenth generation will be bright, and the eleventh will flourish,' and also says, 'In the ninth generation, the emperor practices virtue, enfeoffment and engraving of policies.' My virtues are not enough, but I bear this great responsibility and remain vigilant day and night, not daring to become complacent. As a mere mortal, can I continue this prosperity, honor my ancestors, and save the people? The 'Shang Shu Xuan Ji Qian' says, 'Describe the world of Yao, release the culture of Tang,' and the 'Di Ming Yan' says, 'Follow the virtue of Yao, set the period and establish the image.' Furthermore, the calendar has varied throughout the ages, with varying degrees of superiority and inferiority. Moreover, our current calendar is rough and backward, completely inadequate! Although I want to continue using it, I truly cannot! Every time I see these books, I feel very uneasy. Recently, state affairs have been troubling, with yin and yang out of balance, disasters constantly occurring, epidemics spreading, affecting cattle and sheep, and agricultural yields failing. These signs of fortune and misfortune, the reactions of the five elements, are all manifesting in me. It seems that I am indeed lacking; how can I make up for it? The 'Shang Shu' says, 'Only by first pretending to be a king can one do his job properly,' and it also says, 'In the second month of the year, go on a hunting tour to the east, reach Mount Tai, burn incense, and observe the time, month, and day.' Imitating Emperor Yao to worship Mount Tai, standardize weights and measures, and refer to the Xuan Ji Jade Balance to correct the calendar may be of some help. The 'Spring and Autumn Bao Qian Tu' says, 'Three hundred years of the Dou calendar will be changed.' Now the historians are using the calculation method of Deng Ping's "Tai Chu Calendar," and every three hundred years, there will be an extra part; over time, the error will become larger and larger, leading to the calendar becoming more and more inaccurate. The position of the Xuan Ji star is incorrect; celestial phenomena do not match the calendar. On the winter solstice, the sun is clearly at twenty-one degrees in the Dipper constellation, but the calendar says it is in the middle of the Cowherd constellation. The day of Li Chun is one day early; that is the Li Chun day of the "Four Division Calendar." Using such a calendar to judge cases and determine punishments has already violated the laws of nature; using it to predict good and bad omens has also deviated from the right path. Now, I have resolved to adopt the 'Four Division Calendar,' following the example of Emperor Yao and obeying the decree of Confucius. I hope that all gentlemen and the people can unite in adhering to it. If this brings peace and prosperity to the realm, it will fulfill our ancestors' wishes." So, the "Four Division Calendar" began to be used.
However, Li Fan and the others felt that in November, the larger dates should precede the smaller ones, to ensure the new moon and full moon dates align, and to have fixed dates for each month. This would allow the algorithm of seven leap months over nineteen years to be established; otherwise, errors would occur in the lunar calendar. Not long after the new calendar was implemented, Emperor Zhang of Han began to reconsider this issue. He consulted various classics and sent the Left Central Lang Jia Kui to inquire with ten experts including Wei Cheng, Li Chong, Liang Wei, Yan Xu, Xu Zhen, Su Tong, and Li Fan. They believed that the smaller dates should precede the larger ones, as the "Spring and Autumn Annals" only recorded the new moon and not the full moon, suggesting that the new moon must exhibit both light and dark phases. If there was no new moon, it would have to be that month. If the larger dates came before the smaller ones, it would mean two new moons in one month, followed by a month with no new moon, which was clearly impossible. Li Fan and the others maintained that the larger dates should come first, but lacking concrete evidence, solely to ensure the full moon occurred on the 16th day, in accordance with the lunar cycle, and that the full moon coincided with the waning phase of the moon. Also, the full moon and new moon could not fall on the same day. Emperor Zhang, upon learning of Li Fan and the others' thoughts, ordered that they should not be constrained by the previously established calendar and decreed that the months beginning with Tianyuan should have the smaller dates precede the larger ones. This way, the calculations in the subsequent calendars proved accurate. During the Yongyuan era, the court instructed the historiographers to use the "Nine-Path Method" for calculating the new and full moons, and discovered no discrepancies. Jia Kui compiled all the opinions into a written document, and future calendar reforms referenced his insights, which is why these were meticulously recorded.
Kui said, "Look at what is written in the 'Tai Chu Calendar'. On the day of the winter solstice, the sun is at the starting point of Aquila, which is the star in the middle of Aquila. However, in ancient times, from the time of the Yellow Emperor to the Xia, Shang, Zhou, and Lu dynasties, the winter solstice sun was always at the position of the Big Dipper (which is what we now call the Big Dipper). In the 'Tai Chu Calendar', it is said that the Big Dipper is at twenty-six degrees and thirty-eight minutes on the ecliptic, while Aquila is only eight degrees. If you look at the records of the historians, the actual positions of the winter and summer solstices differ by less than five degrees from what is calculated in the 'Tai Chu Calendar'. The actual position of the winter solstice sun is at twenty-one and a quarter degrees in the Big Dipper. In Shi Shen's 'Star Manual', it is written: "The ecliptic intersects the starting point of Aquila, exactly opposite the Big Dipper at twenty degrees, twenty-five degrees from the North Pole." Calculated on the equator, that would be twenty-one degrees in the Big Dipper. The 'Four Divisions Calendar' and the observations of the historians show that the celestial degrees are all very similar. The 'Shangshu Kao Lingyao' also says: "The Big Dipper is at twenty-two degrees, without any remainder, and the winter solstice sun rises in the place of Aquila." The position we currently observe is five degrees away from the central star in Aquila, probably at twenty-one and a quarter degrees in the Big Dipper, which is similar to what is said in the 'Kao Lingyao', so this statement is more reliable. In the second year of Yuanhe, in August, the emperor ordered, "Shi Shen's point of view cannot be discarded!" He then had two groups observe separately to see who could calculate more accurately. The Grand Astrologer Xuan and his team observed from the second year of Yuanhe to the first year of Yongyuan, a total of five years, and calculated the degrees the sun moved each day. The result was that on the day of the winter solstice, the sun's position was at twenty-one and a quarter degrees in the Big Dipper, which aligns with the position of the Big Dipper in ancient calendars and the position where the sun rises as mentioned in the 'Kao Lingyao', and the distances between the celestial bodies were also the same as recorded by Shi Shen. Those who said that the winter solstice sun was at the starting point of Aquila were subsequently proven incorrect."
Kui said that using the "Taichu Calendar" to calculate the 23 solar eclipses that occurred from the first year of Emperor Yuan of the Han Dynasty to the first year of Taichu, 17 of them corresponded to the new moon, 4 corresponded to the full moon, and 2 corresponded to the day after the new moon; while using the new calendar system, 7 corresponded to the new moon, 14 corresponded to the full moon, and 2 corresponded to the day after the new moon. Furthermore, using the "Taichu Calendar" to calculate the 24 solar eclipses that occurred from the first year of Taichu to the second year of Gengshi, 10 corresponded to the full moon; using the new calendar system, 16 corresponded to the new moon, 7 corresponded to the day after the new moon, and 1 corresponded to the full moon. Finally, using the "Taichu Calendar" to calculate the 23 solar eclipses that occurred from the first year of Jianwu to the first year of Yongyuan, 5 corresponded to the new moon, and 18 corresponded to the full moon; using the new calendar system, 17 corresponded to the new moon, 3 corresponded to the full moon, and 3 corresponded to the day after the new moon.
In addition, when using the new calendar system to retroactively calculate the 24 solar eclipses and new moons recorded in the "Spring and Autumn Annals," 23 of them were found to be inaccurate. This indicates that the movements of celestial bodies are irregular, with inevitable gains and losses, and the degree of gains and losses is also different, and cannot be measured by a single standard. The creators of the calendar usually use a 76-year cycle, gradually eliminating gains and losses, and ensuring the accuracy of each day. The hexagram in the Book of Changes that talks about the alternation of gold and fire says, "A wise ruler uses this knowledge to manage the calendar and understand the seasons." It also says, "Tang and Wu initiated changes, following the will of heaven, in accordance with the hearts of the people." This means that sages must establish a calendar based on the laws of the sun, moon, and stars, because over millennia, the patterns of celestial movements will inevitably change, so it is necessary to first calculate a certain cycle, and then adjust the calendar based on the positions of the sun, moon, and stars. Therefore, calculating cycles and adjusting the calendar to match the movements of the sun, moon, and stars is a technology that transcends the era. The "Taichu Calendar" cannot be used continuously to this day, and the new calendar system cannot be traced back to the time of Emperor Yuan of the Han Dynasty. A calendar system typically remains effective for about three hundred years, so the prophecy states, "After three hundred years, the calendar must be revised." After the establishment of the Han Dynasty, the "Taichu Calendar" was used without modification until 120 years later in the first year of Taichu when modifications were made. Therefore, before this time, there were instances when the new moon appeared a day earlier, and during the reigns of Cheng Di and Ai Di, there were instances when the new moon was delayed by a day, so most cases of new moons occurred after the full moon, which serves as clear evidence.
Kui said, "I used to calculate the waxing and waning of the sun and moon using the ecliptic along with Fu An and found that it was very close to the actual situation. However, the historians used the equator to calculate, which is different from the actual route of the sun and moon. Now, the calendar's waxing and waning times are over a day off from the actual situation! They always report that this is because the speed of the sun and moon has changed, and even say that the sun is moving backwards! However, if we use the ecliptic for calculations, we can obtain the correct speed of movement without needing any adjustments. So I request to compare the data recorded by the historian on the positions and speeds of the sun, moon, and stars with officials specializing in the study of astrology." The emperor approved. Kui continued, "I carefully examined the previous records and found that the winter solstice is 115 degrees from the North Pole, the summer solstice is 67 degrees from the North Pole, and the spring and autumn equinoxes are 91 degrees from the North Pole. The 'Hong Fan' says, 'The movement of the sun and moon determines the changes in winter and summer'; the 'Five Discourses' also says, 'The sun and moon move along the ecliptic, reaching the southernmost point at the Cowherd star and the northernmost point at the Eastern Well star, with the sun moving one degree per day and the moon moving thirteen degrees and nineteen minutes.' Now the historians use the equator to calculate, which is different from the actual route of the sun and moon. For example, near the Big Dipper, the Cowherd star, the Eastern Well star, and the Chariot star, the equatorial measurement is fifteen degrees, while the ecliptic measurement is only thirteen and a half degrees; near the Eastern Wall, Kui, Lou, Zhen, Jiao, and Kang star clusters, the equatorial measurement is seven degrees, while the ecliptic measurement is eight degrees; sometimes the distance between the sun and moon can actually decrease when the moon travels further, and the historians say that this is because the sun is moving backwards. I found that when the ecliptic passes through the Cowherd star, it deviates 24 degrees south of the equator, and when it passes through the Eastern Well star and the Chariot star, it deviates 24 degrees north of the equator. The equator is the celestial sphere's equator, and it is 91 degrees away from the North Pole, which is not the orbit of the sun and moon at all. Using it to measure the movements of the sun and moon will inevitably lead to errors. I checked the forty-nine observations of the moon's movement near the Cowherd star and the Eastern Well star recorded by the historian since September of the Yuanhe era, and none of them recorded eleven degrees. I also checked the thirty-seven observations of the moon's movement near the Lou and Jiao star clusters, and none of them were fifteen or sixteen degrees, which contradicts the historian's claims! I also asked twelve officials in charge of astronomical observations, including Yao Chong and Jing Bi, and they all said, 'The star chart follows a certain pattern, and the sun and moon do move along the ecliptic, but the government lacks the proper instruments, so they don't know how to calculate.' In the second year of Ganlu, the Deputy Minister of Agriculture Geng Shouchang reported that he used astronomical instruments to measure the movement of the sun and moon, verified the laws of celestial movement, and found that when the sun and moon moved near the Cowherd star and the Eastern Well star, the sun moved one degree per day, and the moon moved fifteen degrees per day; when they moved near the Lou and Jiao star clusters, the sun moved one degree per day, and the moon moved thirteen degrees per day, which is a phenomenon attributed to the equator, well known to the ancients. If the ecliptic is used for calculations, it will conform to the laws of celestial movement, the sun will not appear to move backward, the time of the sun and moon's waxing and waning will not be off by a day, it is more accurate than calculating with the equator, therefore, the ecliptic should be used for calculations." Many officials agreed with Kui's assessment. This was the proposal Kui presented in the fourth year of Yongyuan.
On the Jia Chen day of the fifteenth year of Yongyuan, the emperor issued a decree to create a set of bronze astronomical instruments inscribed with the degrees of various constellations: Jiao 13 degrees, Kang 10 degrees, Di 16 degrees, Fang 5 degrees, Xin 5 degrees, Wei 18 degrees, Ji 10 degrees, Dou 24 and a quarter degrees, Niu Xing 7 degrees, Xu Nu Xing 11 degrees, Xu 10 degrees, Wei 16 degrees, Ying Shi 18 degrees, Dong Bi 10 degrees, Kui 17 degrees, Lou 12 degrees, Wei 15 degrees, Ang 12 degrees, Bi 16 degrees, Zi 3 degrees, Shen 8 degrees, Dong Jing 30 degrees, Yu Gui 4 degrees, Liu 14 degrees, Xing 7 degrees, Zhang 17 degrees, Yi 19 degrees, Zhen 18 degrees, totaling 365 and a quarter degrees. The sun at the winter solstice is located at 19 and a quarter degrees in Dou. Although historians used this instrument to accurately calculate the movements of the sun and moon, as well as their waxing and waning, they did not utilize it for routine observations and records. Since this set of equatorial instruments was not particularly convenient for measuring the ecliptic and tracking celestial bodies, it saw little use afterward.
Kui said: "Nowadays, the calculations of the historians for the timing of the new moon, crescent moon, full moon, and lunar eclipse are largely inaccurate because they do not understand the moon's varying speeds. During the Yongping period, the court issued an edict for the former chief historian Zhang Long to use the 'Four Divisions Method' to calculate the timing of the crescent moon, full moon, and lunar eclipse. Zhang Long claimed that he could use the nine, six, seven, and eight hexagrams of the I Ching to calculate the moon's movement. However, upon checking Zhang Long's calculations, many of them were incorrect. When I asked him to recalculate his previous results, they were also incorrect. Sometimes, the calculated results were far off from the actual celestial phenomena, differing by more than ten degrees. Together with Fan, we cross-checked the records of the historians and found that the moon's movement indeed varies in speed, not limited to the stars associated with the Cowherd, Eastern Well, Lou, and Jiuxing constellations, nor is it due to any special phenomena like 'tiao' or 'ce ni', but rather due to variations in the moon's orbital path. Approximately, in a month, the moon's faster-moving segments will shift by three degrees, and it will return to its starting position after nine cycles, totaling nine cycles. After one hundred and seventy-one years, the new moon, winter solstice, and the eleventh month's new moon will coincide again. The statements in the Spring and Autumn Annals and the Three Dynasties Calendar regarding the nine cycles are consistent with this result, which enables us to accurately calculate the timings of the new moon, crescent moon, full moon, and lunar eclipse. I calculated the lunar eclipses since the Jianwu period using the official astronomical units, a total of thirty-eight times, with very small errors and good results, suggesting an assessment should be conducted."
There used to be a calculation method called the "Nine Paths Technique" used by the historians, which eventually fell out of use. During the Xiping period, the former calendar officer Liang Guozong reorganized the "Nine Paths Technique" and submitted it to the court. The court ordered the Imperial Academy to review the old calculation methods for comparison. The Crown Prince's Aide Feng Xun was responsible for the review, and he also compiled a set of the "Nine Paths Technique," adding and modifying the original method. When compared to Liang Guozong's version, Feng Xun's version was more accurate. The Chief Historian Yang used Feng Xun's algorithm to calculate the crescent moon and full moon, but the calculated timings still did not align with the actual celestial events, with errors sometimes reaching more than ten degrees.
In the year 78 AD, the Astronomer Royal Huo Rong, in charge of astronomical observations, reported: "The water clock we are currently using is off by a quarter of an hour compared to the actual astronomical time. Sometimes it even deviates by two and a half quarters of an hour, which is less accurate than the Xia calendar." Upon hearing this, the emperor ordered the Ministry of Rites to collaborate with Huo Rong and the historians to verify the time using astronomical instruments.
The Astronomer Royal Shu, Cheng, Fan, and others replied together: "According to the record in Chapter 6 of the 'Regulations of the Calendar' in the 'Ling Jia', during the third year of Emperor Xuan of Han, on the day of Yibing in the twelfth month (December of 47 BC) and during the tenth year of Jianwu, on the day of Renwu in the second month (February of 34 AD), the emperor issued decrees specifying the method of using the water clock. The water clock's scale is adjusted according to the daily sunlight duration, with the sun moving one degree and four minutes of arc north or south each day, causing the water clock to increase or decrease by one quarter accordingly. Each solar term lasts for a total of fifteen days, with the sun's distance from the North Pole or South Pole varying each day. The water clock we’re currently using loses a quarter every nine days and does not change with the movement of the sun. The Xia calendar's water clock, on the other hand, is adjusted based on the length of sunlight each day, making it more accurate than the current water clock, and it can be fully implemented."
In November of that year, on the day of Jia Yin (November of the year 78 AD), the emperor issued another edict, saying: "Tell the Minister of Works and Minister of Public Works: the purpose of the water clock is to measure time and determine the length of day and night. The changes in the length of day and night depend on the sun's distance from the North Pole. The sun follows a circular orbit and cannot be calculated using a fixed ratio. It should be determined based on the results of astronomical instrument observations. The water clock we are currently using calculates the length of day and night based on a fixed ratio, with a difference of one quarter of a day from the actual situation. This deviation is too significant, and we should adopt a more accurate method. The Chief Historian Huo Rong also reported that the current water clock does not align with astronomical time. Historians from the Ministry of Ceremonies, after verifying with astronomical instruments, found that the official water clock can be off from astronomical time by as much as three quarters of an hour. Using sundials for timekeeping results in much smaller errors and is very effective. Now, we have created a sundial water clock with 48 arrows, officially equipped for use in various government offices. After calculation, it will be distributed." Due to the volume of information, the emperor specifically recorded the positions of the twenty-four solar terms, the distance of the ecliptic from the North Pole, sundial timekeeping, water clock timekeeping, length of day and night, and the moment of the meridian star.
It is said that the establishment of the "Tai Chu Calendar" began during the Yuanfeng period and was finalized in the same period. It took thirty years to clarify the inaccuracies. Later, the "Four-Part Calendar" was implemented starting from the Jianwu period and continued to be used until the Yuanhe and Yongyuan periods. It took over seventy years to refine various ceremonies and regulations, and astronomical observations finally had standards. As you can see, celestial phenomena are quite mysterious, making the establishment of a calendar a challenging task!
Since the revival of the Eastern Han Dynasty, prophecies and divinations have been spreading everywhere. In books like "Kaolingyao" and "Minglixu," the year of Jia Yin is regarded as the starting year. However, the calculated starting time falls 114 years after the Geng Shen year in the "Sifenli," resulting in a discrepancy of two days in the calculation of the new moon (the first day of the lunar calendar). How did those scholars studying calendars in the community manage to calculate the correct date? It's truly unbelievable! Furthermore, after the "Taichuli," people found that there were problems with the day calculations. Those who revised the calendar said, "After 144 years, the year star (Jupiter) will shift by one position. After 171 years, we need to discard the remainder of 63 new moon days, and in between, add 1197, in order to use it in the long term." However, from the first year of Taichu to the eleventh year of Yongping, exactly 171 years, the remainder that should have been discarded was not discarded, so the calendar became increasingly inaccurate. Both of these calendars each insisted on its own methods and sought to promote its own calendar. Whenever disputes arose, the court officials would hold meetings to discuss, as a group of Confucian scholars debated and shared their views. These discussions greatly contributed to everyone's understanding, so I detailed recorded these situations. In the second year of Emperor An of the Han Dynasty, an official named Dan proposed continuing the use of the "Jiayin Yuan" calendar, while Liang Feng from Henan said that the "Taichu Calendar" should be continued. The officials responsible for these matters, Zhang Heng and Zhou Xing, were both knowledgeable about calendars. They debated with Dan and Feng, and it became clear that some of Dan's and Feng's responses were incorrect, and some of their statements were flawed. Zhang Heng and Zhou Xing carefully reviewed historical calendar records, comparing ancient and modern practices, and concluded that the "Nine Dao Method" was the most accurate. Therefore, the emperor commanded the court officials to engage in detailed discussions.
General Kai and his colleagues reported to Palace Attendants Shi Ting and his associates the outcomes of their discussions: "The calculation of celestial movements in the 'Tai Chu Calendar' has errors; the daily speed of movement varies, the dates of the crescent moon (on the 8th and 23rd of each lunar month) are also incorrect, the moon appears in the west at month’s end, and the timing of solar eclipses does not align with celestial events. The 'Four-Quarter Calendar' was adopted during the Yuanhe period. Although the 'Four-Quarter Calendar' is more accurate than the 'Tai Chu Calendar', it is still inaccurate and cannot be used. The 'Jia Yin Yuan' calendar aligns with celestial phenomena and also fulfills the prophecy of the oracles, so it can be implemented." Doctor Huang Guang and Da Xing Ling Ren Qian also believe that the 'Nine-Dao Method' should be used. Henan Yin Zhi, Taizi Sheren Li Hong, and more than forty others believe: "If the 'Jia Yin Yuan' calendar is adopted, the one hundred fourteen years concerning the creation of heaven and earth and the acquiring of the unicorn in the 'Yuan Ming Bao' must be eliminated, and adjustments must be made to the leap months and dates. In this way, there will be numerous discrepancies in the timings of the new moon, full moon, crescent moon, and the twenty-four solar terms. If the 'Nine-Dao Method' is employed to determine the new moon, the lengths of the months will be irregular and inconsistent. The creation of the 'Four-Quarter Calendar' was initially intended to fulfill the prophecy in the oracles regarding 'the alteration of the celestial calendar after three hundred years', which is the most precise and should not be altered lightly." General Kai and eighty-four others argue that the 'Tai Chu Calendar' should remain in use.
Zhong Shang, the Minister of Rites, reported: "Those who advocate the continued use of the 'Tai Chu Calendar' have no substantial evidence, merely claiming that during Emperor Shizong's reign, the country prospered due to territorial expansion; therefore, the 'Tai Chu Calendar' is favorable. Some say that after Emperor Xiaozhang switched to the 'Four-Part Calendar', many disasters occurred, and no signs of improvement followed. I believe that wise rulers will create different calendars to adapt to contemporary circumstances. After Emperor Gaozu of Han established the Han Dynasty, he continued to use the Qin Dynasty's method of counting years, where October marked the start of the year and leap months were added at the end. Ignoring the calendars of previous dynasties contradicts our ancestral system. During the reign of Emperor Taizong of Han, the calendar was revised, society stabilized, auspicious signs emerged, and the legal system was refined. During the reigns of Emperors Ai and Ping, the 'Tai Chu Calendar' was used, but numerous disasters ensued. Those who advocate the use of the 'Tai Chu Calendar' fail to critically compare the merits of the calendars, blindly believing in some unreliable statements, attributing all the benefits to the 'Tai Chu Calendar' and all the drawbacks to the 'Four-Part Calendar'. The 'Tai Chu Calendar' was established by many wise men, and the merits and flaws have long been established. During the Yuanping period, the dates of the solstices and equinoxes were re-evaluated; is it wise to change them once more? Although the 'Four-Part Calendar' has errors, it is not fit for use. The appearance of the phoenix bird during the Yuanhe period is unrelated to the calendar. We should praise the merits of ancient calendars while subtly acknowledging the shortcomings of more recent calendars. Those one-sided statements should not be trusted. I have once again thoroughly reviewed the views of Zhang Heng and Zhou Xing. They believe that the calculations of the Five Epochs are closer to the actual speed of the stars, but they still fail to verify ancient calendars. In the past, Xiang Xiang wanted to use the calendar to verify the records of the 'Spring and Autumn Annals', arbitrarily changing the years, reducing the years of the Xia Dynasty and increasing the years of the Zhou Dynasty, which significantly diverged from historical accounts. Compared to the two calendars, there is a difference of 6,156 years, with the 'Tai Chu Calendar' being one day longer. The winter solstice sun is directly above the Dipper, but it is said to be near the Cowherd star, which is implausible and cannot be utilized any longer. Historians have seen these errors, not only Zhang Heng and Zhou Xing. It was previously believed that the 'Nine Dao Method' was more accurate, but now some claim it is inaccurate. The 'Jiayin Yuan' calendar also has many errors and cannot be used. Confucius, to maintain the monarch's authority, accepted the misleading title of Marquis; not to mention the laws of celestial motion, which cannot be speculated upon arbitrarily, and mistakes should not be considered correct!" The Emperor accepted his advice and stopped the proposal to alter the calendar.
During the second year of Emperor Han Shun, a minister named Bian Shao submitted a memorial to the emperor, stating, "If the world loses its order, it will decline; if it adheres to order, the country will prosper." Previously, Emperor Xiaowu was particularly wise. On the winter solstice of the eleventh month in the seventh year of the Yuanfeng era, he ordered the Grand Historian Sima Qian and officials in charge of calendars such as Deng Ping to revise the calendar—the "Taichu Calendar," changing the era name and the start date of the month, adopting the calendar standards of the Xia Dynasty, using "eighty-one divided by forty-three" from the "Qianzhuo Du" as the calculation standard for days, and establishing a special observation platform to observe celestial phenomena and evaluate the accuracy of the calendar, resulting in the "Taichu Calendar" being the most accurate.
Later, Liu Xin further studied and referenced the theories of the "Spring and Autumn Annals" and the "Book of Changes," using the "Hetu Luanchi" and "Luoshu Qianyaodu" to improve the "Nine Dao" calendar. He calculated that every 171 years required an adjustment of 63 parts and a major adjustment every 144 years to match the celestial phenomena and rarely make mistakes. From the start of the Taichu Calendar to the eleventh year of Yongping, a total of 171 years, there should have been 63 parts to adjust, but the officials responsible for the calendar were unsure how to address these extra parts. Because the calculated lunar orbit did not match the actual observations, those unreliable calendar theories were eliminated. By the second year of Yuanhe, the small cycle of the calendar ended, and the extra parts increased, leading to discrepancies between the moon's phases and the calculated results.
Emperor Xiaozhang saw on the "Baoqian Diagram" that "after three hundred years, the calendar should be changed," so he adopted the "Sifen Calendar." He changed the year of the reappearance of Jupiter, which was a Jiazi year, to a Guihai year, forcibly making the celestial phenomena match the calculated results, and designated the Gengshen year as the epoch, but there was no clear literary support, stating that the Gengshen year was the year of the unicorn's appearance, which did not match what was said in the "Ganjing Fu." Historians of successive generations followed suit, leading to many questions, with few able to conduct thorough research and trace the origins. In fact, as long as one carefully observes the changes in the moon's phases, one can know the accuracy of the calendar.
Then, the emperor sent this memorial to the Three Dukes and the officials, asking them to discuss it together. The Grand Astrologer Yu Gong and those in charge of the calendar, such as Zong, proposed their opinions:
The foundation of establishing a calendar is to first determine the starting point of the calendar, which is the Yuanzheng. With the Yuanzheng, the daily degrees of movement can be established, the weekly movements can be calculated, and the solar terms can be determined. Once these three things are established, the calendar can be formulated. The starting point of the "Calendar of Four Divisions" is from the third year after Emperor Xiaowen, the year of Gengchen. Going back forty-five years, we arrive at the year of Yiwei, which is the first year of the Han Dynasty. Going back another two hundred and seventy-five years, we reach the year of Gengshen, which is the year Confucius received the unicorn. Going back another two hundred and seventy-six thousand years, continuing upwards, you will encounter the year of Gengshen again. Calculating year by year from the bottom up will yield accurate results. This is documented in the "Yuanming Wen Tu Chen" section of the "Calendar of Four Divisions."
The first year of Taichu is the Dingchou year. Going back to its starting point, it should be the Gengxu year, but in reality, it is the Bingzi year, indicating a miscalculation of 144 years; a total of 993 years have been miscalculated, and there are an extra 82 weeks to reach the Bingzi year. Analyzing the calculation of the years, at the winter solstice of Jiazi on the first day of the eleventh month of Tianyuan, both the sun and the moon have been slightly miscalculated. The sun moves one degree per day, accumulating three hundred and sixty-five degrees plus a quarter to complete a week, which is referred to as a year. One year corresponds to a star sequence. If the sun does not skip a week in its cycle, the year will not miscalculate the star sequence. Analyzing the cycle of one hundred and seventy-one years, which is two cycles plus one chapter, the remainder is sixty-three, which is the principles of natural numbers.
Numbers are accumulated starting from small units. Small units accumulate to become larger units, and larger units accumulate to become measurements. After the determination of the two energies of yin and yang, the sun and moon operate independently. Initially, this movement produces fractions, which accumulate to become degrees. The sun moves one degree in a day, completing a full cycle in a year. Therefore, those who establish calendars have different algorithms for degrees, some using 940 degrees, while others use 81 degrees. The algorithms vary in precision, leading to two different results, but ultimately leading to the same conclusion. The daily solar movement is the number of degrees the sun moves in a day. The movement of the sun follows a clear pattern and rhythm, and the scope of the solar day is vast and limitless. Even the slightest increase or decrease in values can lead to significant deviations, indicating that numerical calculations must be precise. Attempting to correct errors in regular and leap years by reducing the fractional values in the solar calculations may affect the fundamental principles of the calendar. Calculating the degrees of the sun and moon's movements using different methods results in different outcomes, and the four-part cycle cannot yield a remainder of one for the new moon. Although the "Nine Paths" can adjust calculations, it may not be sufficient to compensate for its shortcomings. Furthermore, the calendar calculation rules rely on lunar phases and solar and lunar eclipses, making them crucial. Currently, using a method that reduces the calendar by sixty-three minutes, this method has been validated against twenty solar eclipses and twenty-eight lunar eclipses recorded since the beginning of the Yuan dynasty. Compared to the "Four-Part Calendar," the margin of error is larger, and when compared, the "Four-Part Calendar" proves to be more accurate and practical.
Emperor Xiaozhang carefully corrected the calendar, created astronomical instruments and timekeeping devices that aligned with celestial phenomena, and there would be no further use of other calendars. "Wen Yao Gou" says: "Gao Xinshi was ordained by heaven, and Zhong Li established the calendar. Tang Yao ascended to the throne, Xihe established the celestial sphere. The Xia Dynasty established virtue and governance, and the Kunwu clan calculated the stars. The Zhou Dynasty changed the calendar, with Chang Hong responsible for astronomy and the calendar." "Yun Dou Shu" states: "The official astrologers have specialized calendar books, as clearly documented in historical records." "Hong Fan Wu Ji Lun" mentions: "There are various calendars from the time of the Yellow Emperor among the people, but they are not as accurate as the calendars recorded by the official historians." From ancient times to the present, wise emperors have consulted Xihe and the official astrologers, used precise astronomical instruments to correct the calendar, resolved everyone's doubts, preserved the calendar in the Central Secretariat, and adopted the calculation method of the "Four Divisions Calendar." Emperor Guangwu issued decrees many times, began to formulate the calendar, Emperor Xiaoming corrected the calendar, and Emperor Xiaozhang promulgated the calendar. After three generations of emperors and decades of verification, it was finally promulgated and implemented. Its starting point can be traced back to the beginning of the creation of heaven and earth, and its algorithm has restored the algorithm of the "Four Divisions Calendar." This should be executed in accordance with the decree from the Jia Yin year. Ready for submission. In the year 175 AD, during the fourth year of Emperor Ling of Han, Feng Guang, the Wuguan Lang, and Chen Huang, the subordinate official of the county magistrate of Peixian, reported that the current calendar was incorrect, resulting in numerous rebellions and bandits in Yizhou, causing continuous chaos. The calendar should begin with the Jia Yin year, rather than the Geng Shen year. There is no mention of the Geng Shen year as the starting year in those astronomical books. The calendar currently in use is based on the starting year of the Zhou Dynasty inherited from the Qin Dynasty. Lang Guo Xiang and Liu Gu, who are in charge of astronomical calendars, deliberately fabricated lies and requested the use of the Geng Shen year as the starting year of the calendar, which is nothing short of deceiving the emperor and warrants severe punishment! On the second day of the second month, the emperor ordered the three grand ministers, nine ministers, and Confucian scholars to carefully discuss and find the correct calendar. He ordered all the ministers to convene in the Central Secretariat for discussion. The Yi Lang Cai Yong spoke:
Speaking of calendars, it is a meticulous job; from ancient times to the present, it has been revised repeatedly, often lacking precision. The Han Dynasty inherited the Qin Dynasty's calendar, using the Zhuanxu calendar, beginning with the Yi Mao year. One hundred and two years later, Emperor Wu of Han began to use the Taichu calendar, starting from the Ding Chou year, for a complete duration of one hundred eighty-nine years. Later, Emperor Xiaozhang adopted the Four-Fen calendar, starting from the Geng Shen year. Now, the Imperial Secretary and the Grand Astrologer both believe that the Geng Shen year is inaccurate, and the Jia Yin year is correct. Checking the history of calendars, the Yellow Emperor, Zhuanxu, Xia, Shang, Zhou, and Lu—these six dynasties—each have their own era. The era of the Shang calendar that the Imperial Secretary and the Grand Astrologer refer to is actually one of them. Even though the other eras are not documented in the prophecies, they were all effective calendars at the time, each with its own reasoning.
After Emperor Wu of Han used the Taichu calendar starting from the Ding Chou year, these six calendar systems became a mess, with everyone claiming that the others were incorrect. There was a Grand Astrologer named Zhang Shou-Wang who raised concerns about the Jia Yin year, saying that the Han Dynasty's calendar was wrong. As a result, he was impeached over this issue and subsequently lost his position. However, the Taichu calendar functioned effectively, without any significant issues. So, even if it is not the era mentioned in the prophecies, as long as it was useful at the time, it is fine. Later, the Four-Fen calendar was used, which was more accurate than the Taichu calendar, demonstrating that new calendars can also be reliable.
In the first year of Yanguang, a central official named Dansong also felt that the Geng Shen year in the Four-Pillar Calendar was incorrect, and said that the Jia Yin year mentioned in the "Order of Destiny" should be used instead. This issue caused quite a stir in the court, leading to discussions among everyone, but in the end, no changes were made. In fact, the movements of the sun, moon, and stars are unpredictable; they don’t have to match. Those who calculate calendars do so based on the circumstances at the time, which explains the differences between ancient and modern calendars. It's normal that current calendars can't calculate back to ancient times, and ancient calendars can't project forward to now. The "Yuanming Bao" and "Qian Zao Du" both state that from the creation of the world to when the qilin appeared, a total of 2,760,000 years passed; while the "Order of Destiny" calculates from the appearance of the qilin to the Han Dynasty, totaling sixty-nine years plus twenty-three years, making a total of ninety-two years. The first year of the Han Dynasty was a Yi Wei year, and when calculated back to the year of the qilin, it was a Geng Shen year. Calculating further back, all the way to the creation of the world, the original year was a Geng Shen year. Although it is not written in the prophecies, the numbers are there. However, Guanglu Xun and the Grand Historian said that from the creation of the world to the appearance of the qilin, it was a total of 2,759,886 years, and from the appearance of the qilin to the Han Dynasty, it was one hundred and sixty-one years, which was off by one hundred and fourteen years from the earlier calculation. They claimed to be accurate in their calculations, but this discrepancy meant that they did not match with the "Qian Zao Du" and "Yuanming Bao", the timing of the qilin also didn’t match, and it didn’t line up with historical records.
Now it is the first day of the first month in the year of Guǐhài, but Guāng and Huǎng say it is the first day of the first month in the year of Yǐchǒu. There are no clear records to help distinguish the first days of Guǐhài and Yǐchǒu, and they can only be verified by observing the waxing and waning of the moon and the new moon. However, the Guāng and Huǎng calendar is based on the "Kǎo Líng Yào," which differs from the ancient texts of historians Gān and Shí and cannot be verified at all; current astronomical instruments also do not align with the "Kǎo Líng Yào." If Guāng and Huǎng can make new instruments for observing celestial phenomena according to their own methods to accurately measure the degrees of celestial motion, this will not only verify the records in the book but also align with the actual astronomical phenomena. Then they can replace the Gān and Shí calendar, rendering other calendars obsolete, which is the calendar that should be used. We didn't ask Guāng and Huǎng how they calculated it specifically; they just said it was a prophecy, and we do not believe them at all.
In the second month of the second year of Yuánhé, on the day Jiǎyín, the emperor issued a decree saying, "I have heard that ancient sage kings followed the principles of heaven, did not violate its will, and adhered to its timing. Historians use the method of Dèng Píng from the Tàichū calendar to calculate that the sun is at twenty-one degrees in the Dǒu constellation on the day of the winter solstice, but the calendar says it is near the star of Niúxīng, and the beginning of spring is one day early, equivalent to advancing the beginning of spring of the Sìfēn calendar by one quarter. Using this calendar for judgments and convictions contradicts actual celestial phenomena; it is absurd to use this method in the pursuit of peace and prosperity! Now we will use the "Sìfēn calendar," which is in accordance with the will of Emperor Yáo and the teachings of Confucius, and embodies the way of the sages, following the way of heaven." This is the decree of the first year of Gēngshēn to start using the "Sìfēn calendar." The decree extensively cites the prophecies of the "Hé Tú" and "Luò Shū" to prove the correctness of the calendar, which was not simply devised by the historians. However, Guāng and Huǎng say that this is a deliberate lie fabricated by Xiāng and Gù, which contradicts the classics and is utterly absurd!
Emperor Yao ordered Xihe to observe the sun, moon, and stars and create a calendar. Emperor Shun continued to use and improve it. After the revolutions of Tang of Shang and King Wu of Zhou, they also established calendars that suited the situation at the time. This was the right thing to do. Yet, they still faced floods and droughts, warning people to stay alert against "barbarians and treacherous foes." Guang and Huang argued that the imbalance of yin and yang, along with corrupt officials and thieves, stemmed from the first year's issue, which is fundamentally unreasonable. It's been ninety-two years since the adoption of the Gengshen year in the second year of Yuanhe. Guang and Huang claimed that the Qin Dynasty used a different first year from the Zhou Dynasty, but they failed to realize that the Han Dynasty changed the first year three times after the Qin Dynasty, and the Gengshen year was not continuously used. They’re narrow-minded, believing only what they've learned and spinning lies to deceive others, which is truly a shame! As for changing the lunar New Year and the first day of the month, the method King Shou used in the past has been shown to be ineffective, and no one adopts this view. The Yuanhe year edict is comprehensive and clear, not something ministers can change at will. The three ministers, Duan, Wei, and Xun, were accused by Guang and Huang of disrespecting the court and were impeached using the "Zhenggui Xinfu" law. In the end, the emperor ordered to drop the matter and not investigate further.
The lunar eclipse times calculated by the Tai Chu calendar were often inaccurate. The Si Fen calendar adopted the methods of the Tai Chu calendar, starting from the year of He Ping Gui Si, and lasted for five years. In the first year of the Yongyuan era, a lunar eclipse appeared in the seventh month, but according to the Si Fen calendar, it should have been in the eighth month. In the second year, on the twelfth day of the first lunar month, a person named Meng Gongcheng Zong Gan wrote a letter saying: "The moon will be eclipsed on the night of the sixteenth of this month, but the calendar indicates it's the second month." On the sixteenth day, it indeed happened as Zong Gan had predicted. The Grand Historian thought Zong Gan's calculations were useful, so he promoted him to an assistant position. On the Jia Chen day, the emperor ordered the compilation of a calendar using Zong Gan's method. This calendar remained in use for fifty-six years. In the first year of Ben Chu, a lunar eclipse occurred in December, but the calendar indicated it was in the first month of the following year, marking the beginning of errors. By the third year of Xi Ping, in the span of twenty-nine years, there were sixteen instances of miscalculated lunar eclipses. Liu Hong, the Chief Historian of Changshan Commandery, authored a book titled "The Seven Luminaries." On the Jia Chen day, the emperor instructed the officials Liu Gu and Feng Xun from the Tai Shi Department to study Liu Hong's "The Seven Luminaries" and create a new calendar known as "The Eight Elements Art." Liu Gu also developed a "Lunar Eclipse Technique" for further research and comparison. Liu Gu's calculations were similar to "The Seven Luminaries." Everyone was puzzled by the lunar eclipse calculations; for example, in the year of Ji Wei, a lunar eclipse should have occurred in April, but Feng Xun's calculations said it was March, while the official calendar stated it was May. The imperial officials examined these calendars and ultimately selected the most accurate one for use. On the day of Ding Si, the emperor approved the new calendar. In the fourth year, Zong Cheng, Zong Gan's grandson, wrote a letter saying: "My grandfather's calculations also need to be modified. A lunar eclipse should occur in December this year, but the official calendar states it's in January of the following year." On that day, it indeed happened as he had predicted. The emperor appointed Zong Cheng as an assistant. On the day of Bing Shen, the emperor ordered the adoption of Zong Cheng's calculations.
In the second year of Guanghe, the Jiwei year, both March and May experienced endless rain. Based on their calculations, Zhang Xun and his colleagues in the Department of Harmony under the Ministry of Rites believed March was closer and April was further. They ultimately decided to use April's data. They requested to abolish Xiu's algorithm and adopt Zhang Xun's algorithm. Three years later, Xiu's elder brother Xiu Zheng submitted several memorials stating, "Last year, there was no solar eclipse in March, so we should use the data from April. The historians discarded Xiu's correct algorithm in favor of Xun's incorrect one." Xiu Zheng submitted the memorials to the Minister of Rites, but the Minister of Rites never acknowledged the argument that March was closer to April. Calculating solar eclipses should rely on actual observations, not proximity. Therefore, the emperor issued an edict to the Ministry of Ceremonies saying, "You must carefully examine the records, evaluate the pros and cons of different algorithms and verify their validity." The Ministry of Ceremonies then sent officials including Han Shuo, Cai Jiao, Liu Hong, and Chen Diao to re-examine the records and discuss the contentious issues. Zhang Xun and Xiu each presented their algorithms. Zhang Xun's algorithm was based on 961 solar eclipses out of 5,640 months, followed by division and addition and subtraction operations to calculate the number of solar eclipses since the Jianwu period, totaling 327 times, with 15 discrepancies. According to official records, the recorded number of solar eclipses was 98, which aligned with both algorithms' results, but the discrepancy amounted to 2,100. Xiu's algorithm counted 23 solar eclipses over 135 months, with multiplication and division operations, subtracting 41 before Jiankang and 35 after Jiankang, as there were no solar eclipses in those periods. Zhang Xun's algorithm updated the old method, while Xiu's algorithm also made modifications to the original; when comparing the strengths and weaknesses of both, there was no significant difference. Both sides cited scriptures and astronomical texts to prove their algorithms, but these texts held no practical value, serving only to pursue celestial accuracy.
The rules governing the movements of the sun and moon state that the sun moves along the ecliptic, and the moon follows nine distinct orbits. Using an equatorial instrument for measurement, the sun is positioned at 115 degrees from the North Pole at the winter solstice. When the sun enters the 28 mansions, the equator is positioned at 21 degrees in the Dou mansion, and the ecliptic is at 19 degrees in the Dou mansion. The two orbits intersect each other, and the trajectories of the sun and moon differ between curved and straight paths, leading to variations in their apparent motion. So when the moon reaches the Jing mansion and Niu mansion, it exceeds 14 degrees; when it moves to the Jiao mansion and Lou mansion, it exceeds 12 degrees. These speeds are not constant. Therefore, if the algorithm is inaccurate, it needs to be modified, and if it is not applicable, it needs to be abandoned. The workings of the heavens are intricate; the measurements are challenging to ascertain, there are multiple algorithms, and the records of calendars are not the same. Without verification, it is impossible to discern right from wrong, and without deviation, it is impossible to know mistakes. Once an error is identified, it is corrected, and after verification, it is adopted, a principle known as "adhering to the mean." The currently revised algorithm shows no apparent errors, and Zhang Xun's algorithm is not particularly accurate because altering an error-free algorithm without verification aims to discover the correct algorithm later. The revised algorithm documents 23 solar eclipses over 135 months in written records, which scholars have been using for a long time. The government has utilized this algorithm to calculate the movements of the sun and moon for an extended period without significant errors, so everyone believes in this astronomical algorithm and continues to use it without modification. Zhang Xun worked in the astronomical department for many years, with meticulous thought and strong analytical skills, proficient in using instruments, formulating algorithms, calculating the past, checking the present, and this aligns with the actual number of observed solar eclipses.
However, in formulating the calendar and calculating the solar terms, care must be taken, just as one would revere the heavens. It is necessary to follow the old regulations, as seen in the edicts from the years of Jia Chen and Bing Shen, based on the actual number of solar eclipses observed. We should now adopt Xiu's calculations and discard Zhang Xun's. The historians should oversee the implementation, and if verification results come in later, then new calculations should be put into practice. The Ministry of Rites reported to the court based on the views of Han Shuo and others, and the emperor agreed. Zhang Xun, Xiu Zheng, and Xiu Du submitted their memorials again, with Zhang Xun stating that Xiu's calculations should not be used, while Xiu Zheng stated that Zhang Xun's calculations should not be used again. Due to Liu Hong's influence on the matter, it was referred to the Yong'an Pavilion for a reexamination, and the findings didn't align with what Zhang Xun and Xiu claimed. As a result, they were impeached for misleading the emperor. The emperor decreed that Zhang Xun and Xiu each be fined two months' salary as punishment. Xiu Zheng was also demoted to Left Colonel for a duration of two months. Finally, the opinions of Liu Hong and others were adopted, and Xiu's calculations were implemented.
In 78 AD, County Magistrate Wang Han submitted a commentary on lunar eclipses. From 7 AD to this year, there were a total of 196 lunar eclipses over 93 years; the official calendar "He Ping Li" from 7 AD (the first year of He Ping) did not align with the lunar eclipse records, and Wang Han took the Ji Si year as the starting year of the calendar. This issue was referred to the Chief Astrologer for resolution, who reported, "Wang Han's commentary on lunar eclipses has two discrepancies compared to actual observations, and there are twenty-nine instances where the same phenomenon is described differently." The court then called upon Liu Hong, a deputy official from Gu Cheng County.
The emperor ordered: "Former Lang Zhong Feng Guang, Sima Yuan Chen Huang, and Yi Lang Cai Yong have all debated the calendar, and Cai Yong has also participated in repairing and continuing to write the historical records of the calendar. Now, you Liu Hong will work with Wang Han to determine the starting year and leap months of the calendar, carefully cross-checking the lunar eclipse records. If Wang Han's claim that the Ji Si year is the starting year is accurate and well-supported, you will accept Wang Han's viewpoint; if not, you will directly challenge him."
Liu Hong reported: "If we take the Ji Si year as the starting year as Wang Han suggested, then the year of Zhanmeng mentioned in the 'Kao Ling Yao' would be the Yi Mao year as the starting year. This contradicts the starting year of Jia Yin suggested by Feng Guang and Chen Huang. Using this method to calculate celestial phenomena and establish calendars, as well as to correct the movements of the sun, moon, and stars, seems too rough now. Confucius referred to the same matter in the 'Spring and Autumn Annals' but provided two different interpretations, which shows that the evolution of calendars needs to be adjusted with the changes in celestial phenomena. The Jia Yin calendar was effective during Confucius' time; the Ji Si calendar was established during the reign of Zhuan Xu, continued in the Qin Dynasty, and also in the early years of the Han Dynasty, so it was not changed. During the Yuan Feng period, it was found to be inaccurate, and the 'Tai Chu Li' was used instead, with many changes to the calendar over the three hundred years. Although the Jia Yin and Ji Si calendars are recorded in literature, the specific years are relatively vague, so scholars have different opinions, leading to incorrect results when correcting the calendar. The starting year of the Jia Yin calendar is Tian Zheng Yuan, with the first day of the first month being the winter solstice; the initial position of the seven celestial bodies is in the constellation of Ox. The starting year of the Yi Mao calendar is Ren Zheng Yuan, with the first day of the first month being the beginning of spring; the sun, moon, and stars converge five degrees above the Tai Miao. Comparing these two starting years, the difference in leap months is three out of one hundred fifty-two parts, the difference in new moon days is three hundred and four days, and the difference in solar terms is twenty-nine days. Due to the difficulty in verifying which is more accurate, Wang Han also cannot explain clearly, just saying that it is recorded by his ancestors. If Wang Han's annotations are used to establish the calendar, there are twenty-nine discrepancies with reality, and two recorded lunar eclipses do not align. I believe Wang Han only noticed the Ji Si year as the starting point and assumed it was correct, not knowing the reasons for the rise and fall of the saints in establishing calendars, and historians also possess specialized methods for establishing calendars based on celestial phenomena. The Jia Yin and Ji Si calendars have been used before but were later abandoned due to lack of accuracy. Historians have already abandoned the crude calculation method of the He Ping calendar, yet Wang Han uses it to argue, which is probably not his intention. Even if his arguments have some basis, they do not reflect reality and the results lack sufficient accuracy. His remarks about the Bu number are common knowledge among numerologists and have no reference value." So, the court let Wang Han return to his hometown.
