Since the first year of the Yuan era, we have been using the "San Tong Li" calendar for over a hundred years. However, this calendar gradually became inaccurate as the new moon (the first day of the lunar month) consistently appeared earlier than predicted, sometimes even appearing on the last day of the lunar month (the 30th or 29th day), and the actual appearance of the new moon did not align with the calendar. Upon closer examination, it was found that the solar calculations in this calendar were consistently lagging, while the lunar calculations were always ahead.
In the eighth year of Jianwu, a court official named Zhu Fu and a physician named Xu Shu repeatedly petitioned the emperor, stating that the calculations of the new moon in the calendar were incorrect and needed to be revised. At that time, the error was deemed insignificant, and the emperor felt that there was no time to address this matter as the empire had just been pacified. It was not until the fifth year of Yongping that the government calendar predicted a lunar eclipse on the sixteenth day of the seventh month, but a court official named Yang Cen noticed that the actual timing of the lunar eclipse had been consistently earlier than the calendar's prediction. He suspected there was an error in the calculations of the sun's movement and thus petitioned the emperor, stating, "The lunar eclipse is supposed to occur on the fifteenth day; the government calendar is wrong!" The emperor then ordered Yang Cen to observe carefully and compare with the government calendar. From July to November, Yang Cen observed the phases of the moon (on the eighth and twenty-third days of the lunar month) five times in total, and each time, the government calendar was incorrect while Yang Cen's calculations were accurate.
Later, the emperor appointed Yang Cen to calculate the timing of lunar eclipses and the moon's phases, and appointed Zhang Sheng, Jing Fang, and Bao Ye, a few court officials, to use the "Four-Part Method" to calculate together with Yang Cen and compare who was more accurate. Over the course of a year, Zhang Sheng and the others were inaccurate more often than Yang Cen. On the bingzi day of the eleventh month of the twelfth year of Yongping, the emperor ordered Zhang Sheng and Jing Fang to take over from Yang Cen and be responsible for calculating the timing of lunar eclipses and the moon's phases, along with time corrections. The "Four-Part Method" was then officially adopted. However, at that time, Zhang Sheng and the others had not yet fully grasped the fundamental principles of the calendar, nor were they able to completely correct the calculations, so they initially used it only to calculate the timing of the moon's phases.
Legend has it that nine years have passed, and an official named Dong Meng submitted a memorial saying that the calendar we’re using is wrong. This matter was handed over to the Three Dukes and the Ministry of Rites for discussion by those who understand the calendar. By the fourth month of the tenth year, no one could provide clear evidence to prove whether it was right or wrong. In the second year of Yuanhe, it was discovered that the "Tai Chu Calendar" deviated more and more from the actual situation, with the positions of the sun, moon, and stars all out of whack. Everyone knows that on the day of the winter solstice, the sun should be near the 21st degree of the Dipper constellation, but it has not even reached the position of five degrees of the Cowherd star! Moreover, according to the "Tai Chu Calendar," the length of a day is a quarter shorter than it should be, the new moon and full moon days are off by a day, and the positions of the stars are off by five degrees. Emperor Zhang of Han knew that this calendar was wrong, so he asked the court historians. Although the historians knew it was wrong, they could not change it. Therefore, Emperor Zhang summoned experts in the calendar, such as Li Fan and Liu Biao (this should be Liu Biao, there is an error in the original text), to study the problem together. On the first day of the second month, Emperor Zhang issued an edict, saying, "I have heard that the wise kings of ancient times followed the timing of heaven and did not go against the will of heaven. The 'He Tu' says: 'The red nine will prosper, ten generations will be bright, and eleven will flourish,' and also says 'In the ninth generation, the emperor practices virtue, and seals and carves policies.' I’m not virtuous enough, but I’m shouldering such a huge responsibility, and I am diligent every day, not daring to slack off. As a small person, the fate of the country rests on my shoulders. How can I continue the ancestral foundation and save the common people? The 'Shang Shu Xuan Ji Qian' says: 'Describe the world of Yao, release the literature of Tang,' and the 'Imperial Order Verification' says: 'Follow the examination of Yao's virtue, establish the period and the image.' Furthermore, each calendar has its strengths and weaknesses, not to mention that the calendar we currently use is so rough that it is fundamentally inadequate! Even if I want to continue using it, I cannot! Every time I see these books, I feel particularly uncomfortable. In recent years, the country's affairs have not been going well, yin and yang are out of balance, disasters are continuous, epidemics are spreading, even the cattle are dying, and the farmers cannot cultivate. These disasters are weighing heavily on me; it seems that I am indeed lacking. How should I make up for it? The 'Shang Shu' says: 'Only the king can truly carry out his duties first,' and also says: 'In the second month of the year, go on an eastern inspection tour, arrive at Mount Tai, chop wood, look at the rivers and mountains. Then present offerings to the Eastern Mother, and observe the time, month, and day.' I plan to follow Emperor Yao’s footsteps and make sacrifices at Mount Tai, unify weights and measures, refer to the Xuan Ji Jade Balance, to correct the calendar, hoping for improvement. The 'Spring and Autumn Bao Qian Tu' says: 'After three hundred years, the calendar needs to be revised.' Now the court historians use the algorithm of the "Tai Chu Calendar" by Deng Ping. Every three hundred years, there will be an additional minute, and over time, the error will become larger, resulting in the winter solstice sun position not matching what the calendar says, and the beginning of spring being a day early. Relying on this calendar for making judgments goes against natural laws; using such a calendar for calculating solar terms has long been too far off. Now, I’ve made up my mind to switch to the "Si Fen Calendar" to follow Emperor Yao, adhere to the Confucian idea of "serving heaven," hoping that all the people of the world can work together with one heart and one mind, so that the country can be peaceful and prosperous, to honor our ancestors and make them proud." Therefore, the "Si Fen Calendar" began to be used.
However, Li Fan and Liu Biao (should be Liu Biao here, original text is incorrect) believed that in November, the larger month should precede the smaller month, in order to coordinate the new moon with the full moon, to maintain a consistent number of days in each month, and to create a system of seven leap months every nineteen years, thus preventing any discrepancies in the new moon. But shortly after this method was put into practice, Emperor Zhang began to reconsider the issue. After reviewing various classical texts, he sent Jia Kui, the Left Central Cavalry Commander, to seek the opinions of ten experts including Wei Cheng, Li Chong, Liang Wei, Yan Xu, Xu Zhen, Su Tong, Liu Biao (should be Liu Biao here, original text is incorrect), and Li Fan. They believed that the month should begin with the smaller days and end with the larger days, since the new moon must have both a visible and an invisible side, and it must fall within that month. If the full moon comes before the new moon, there would be two new moons in one month and none in the next, which would not reflect the actual lunar cycle. Li Fan and others believed that starting with the larger month and ending with the smaller month would keep the full moon on the 16th day, and the full moon should not occur during the waning phase. Furthermore, the full moon and the new moon cannot fall on the same day. After understanding the viewpoints of Li Fan and Liu Biao (should be Liu Biao here, original text is incorrect), Emperor Zhang ordered that they should not be constrained by the existing calendar, and decided that starting from the first year of Tianyuan, the month should begin with the smaller days and end with the larger days. This led to greater accuracy in subsequent calendars. During the Yongyuan era, the court historians employed the "Nine Methods" to determine the new and full moons, and found no errors. Jia Kui compiled the opinions of these experts into a document, which later calendar reformers would reference, hence the detailed record here.
Kui said, "Look, it's written in the 'Tai Chu Calendar' that on the day of the winter solstice, the sun is in the starting position of the Cowherd constellation, near the star of the Cowherd. 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 in the position of the Big Dipper (which is what we now call the Big Dipper). According to the 'Tai Chu Calendar,' the Big Dipper is at 26 degrees and 385 minutes on the ecliptic, while the Cowherd constellation is only 8 degrees. If you look at the records of historians, the actual observational results of the winter and summer solstices are always less than 5 degrees different from the results calculated in the 'Tai Chu Calendar,' with the actual position of the winter solstice sun being at 21.25 degrees in the Big Dipper. In Shi Shen's 'Star Manual,' it is written, 'The ecliptic passes through the starting position of the Cowherd constellation, which is exactly 20 degrees in the Big Dipper, 25 degrees from the North Celestial Pole.' According to equatorial coordinates, that would be 21 degrees in the Big Dipper. The 'Four-Part Calendar' and the observational results of historians are consistent with respect to astronomical measurements. The 'Shang Shu Kao Ling Yao' also states, 'At 22 degrees in the Big Dipper, without any additional minutes, the winter solstice occurs where the Cowherd constellation rises.' Furthermore, those who compiled the calendar found that the position of the winter solstice sun is 5 degrees from the center of the Cowherd constellation, approximately at 21.25 degrees in the Big Dipper, which aligns with the results in the 'Kao Ling Yao,' so this result was used to determine the date of the winter solstice. In the second year of Yuanhe, in August, the emperor decreed, 'Shi Shen's views cannot be abandoned!' and 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 until the first year of Yongyuan, a total of five years, calculating the degrees the sun moved each day, ultimately determining that the winter solstice sun is at 21.25 degrees in the Big Dipper, matching the ancient calendar's position of the Big Dipper and the records in the 'Kao Ling Yao,' as well as the distances between celestial bodies matched Shi Shen's records. Those who believed that the winter solstice sun was in the starting position of the Cowherd constellation had their claims dismissed from that point forward."
Kui said that, using the "Tai Chu Li" to calculate the 23 solar eclipses from the first year of Emperor Yuan of the Tai Chu era to the end of that same year, 17 times were aligned with the new moon, 4 times were aligned with the full moon, and 2 times were aligned with the day after the new moon; when calculated with the new calendar, there were 7 times aligned with the new moon, 14 times aligned with the full moon, and 2 times aligned with the day after the new moon. Furthermore, using the "Tai Chu Li" to calculate the 24 solar eclipses from the first year of the Tai Chu to the end of the second year of Geng Shi, 10 times were aligned with the full moon; when calculated with the new calendar, there were 16 times aligned with the new moon, 7 times aligned with the day after the new moon, and 1 time aligned with the full moon. Finally, using the "Tai Chu Li" to calculate the 23 solar eclipses from the first year of Jian Wu to the end of the first year of Yong Yuan, 5 times were aligned with the new moon, and 18 times were aligned with the full moon; when calculated with the new calendar, there were 17 times aligned with the new moon, 3 times aligned with the full moon, and 3 times aligned with the day after the new moon. Additionally, when calculating the solar eclipses and new moons recorded in the "Spring and Autumn Annals" in reverse, a total of 24 times, the results showed that 23 times were inaccurate. The movement of the celestial bodies is uneven; there will inevitably be discrepancies, and the size of the discrepancies also varies, so it cannot be generalized. Historians usually use a 76-year cycle, which can gradually reduce or increase the discrepancies, nearly accounting for a whole day. Thus, the hexagram in the Book of Changes that talks about the transformation of metal into fire says: "A wise ruler manages the calendar and understands the times." It also says: "Tang and Wu initiated a revolution, following the heavens and responding to the people." This means that a sage must formulate a calendar based on the laws of the movement of the sun, moon, and stars, and the calculated numbers cannot be precise to the level of tens of millions of years. Adjustments must be made during this period, first calculating the degrees based on distance, and then aligning it with the actual positions of the sun, moon, and stars. Therefore, thus, calculating the degrees to align with the movements of the sun, moon, and stars is a timeless skill. The "Tai Chu Li" is no longer used today, and the new calendar cannot calculate back to the time of the Han Yuan Emperor. A calendar can only be used for about three hundred years. Therefore, the prophecy states "Three hundred years of fighting over the calendar will change the constitution." After the establishment of the Han Dynasty, the "Tai Chu Li" was used for a long time without modification, until it was changed 120 years after the first year of Tai Chu. Therefore, before that, sometimes the new moon would be observed a day earlier, and during the reigns of Cheng and Ai emperors, two days were taken as the new moon, so the new moon day often fell on the full moon, which clearly illustrates this point.
Kui said, "I used to calculate the waxing and waning of the sun and moon with the ecliptic together with Fu An, and the results were very accurate. However, the historian calculated using the equator, which does not align with the actual movements of the sun and moon. The calculated timings for the waxing and waning can now differ by more than a day from reality! They reported that they wanted to change the calendar, and even said that the sun's movement had slowed down and was even moving backwards. But if we calculate using the ecliptic, we can obtain the correct speed of movement, and there is no need to change it." "I would like to request that the Court Astronomer bring the records and star charts of the movements of the sun, moon, and stars for verification with the astronomy specialists." The emperor approved. Kui then carefully examined the historical records and said, "It has been said that at the winter solstice, the sun is positioned 115 degrees from the North Pole, at the summer solstice, it is 67 degrees from the North Pole, and at the spring and autumn equinoxes, it is 91 degrees from the North Pole. The 'Hong Fan' says 'the movement of the sun and moon determines the changes of winter and summer'; the 'Five Chronicles' also state 'the sun and moon move along the ecliptic, reaching the most southern point at Niu Lang star and the most northern point at Dong Jing star, the sun moves one degree each day, while the moon moves 13 degrees, 19 minutes, and 7 seconds each day.' The historian now uses the equator to calculate, which is different from the actual path of the sun and moon. For example, near Dou Su, Niu Lang star, Dong Jing star, and Yu Gui star, the equator measures 15 degrees, whereas the ecliptic only measures 13.5 degrees; near Dong Bi, Kui Su, Lou Su, Zhen Su, Jiao Su, and Kang Su, the equator measures 7 degrees, while the ecliptic measures 8 degrees. Sometimes, even as the moon travels further, the distance between the sun and moon decreases, and they claim the sun is moving backwards!"
"I consulted the data and found that when the ecliptic passes through the star Qian Niu (牵牛), it is offset by twenty-four degrees south of the equator; when it passes through the stars Jǐng (东井) and Yú Guǐ (舆鬼), it is offset by twenty-four degrees north of the equator. The equator is the celestial equator, ninety-one degrees north of the equator, and it is not the orbit of the sun and moon. Using the equator to measure the movements of the sun and moon can lead to errors! I reviewed the observation records from the Imperial Astronomer starting in September of the second year of Yuanhe (元和); there were forty-nine observations of the moon nearby the stars Qian Niu and Jǐng, none of which showed an eleven-degree deviation; there were thirty-seven observations of the moon nearby Lóu Xiù (娄宿) and Jiǎo Xiù (角宿), none of which showed a fifteen or sixteen-degree deviation, which contradicts previous reports."
"I asked Yáo Chóng, Jǐng Bì, and twelve other astronomers; they all said: 'The star chart has a consistent pattern, and the sun and moon do indeed follow the ecliptic, but the government lacks the appropriate instruments, so they don't know how to calculate.'"
"In the second year of Gān Lù (甘露), the Deputy Minister of Agriculture Gěng Shòu Chāng reported that he used astronomical instruments to measure the movements of the sun and moon and observed changes in celestial phenomena. He found that when the sun and moon reach near the stars Qian Niu and Jǐng, the sun moves one degree each day, and the moon moves fifteen degrees each day; when they reach near Lóu Xiù and Jiǎo Xiù, the sun moves one degree each day, and the moon moves thirteen degrees each day. These results were obtained using equatorial measurements, which the ancients have always known. However, if we use the ecliptic to calculate, it will align with celestial phenomena; the sun will not appear to retrograde, and the timing of the waxing and waning of the sun and moon will not differ by a day. It is more accurate than calculations based on the equator, and the ecliptic should be adopted for calculation."
"Many officials concurred with my assessment." This argument was presented by Kuí in the fourth year of Yǒng Yuán (永元).
Until the seventh day of the seventh month in the fifteenth year of Yongyuan, the emperor ordered the manufacture of the Huangdao copper instrument, which indicated the degrees between various constellations: Jiao constellation: thirteen degrees, Kang constellation: ten degrees, Di constellation: sixteen degrees, Fang constellation: five degrees, Xin constellation: five degrees, Wei constellation: eighteen degrees, Ji constellation: ten degrees, Dou constellation: twenty-four and a quarter degrees, Qian Niu: seven degrees, Xu Nu: eleven degrees, Xu constellation: ten degrees, Wei constellation: sixteen degrees, Ying constellation: eighteen degrees, East Wall: ten degrees, Kui constellation: seventeen degrees, Lou constellation: twelve degrees, Wei constellation: fifteen degrees, Ang constellation: twelve degrees, Bi constellation: sixteen degrees, Zi constellation: three degrees, Shen constellation: eight degrees, East Well: thirty degrees, Carriage Ghost: four degrees, Liu constellation: fourteen degrees, Star constellation: seven degrees, Zhang constellation: seventeen degrees, Yi constellation: nineteen degrees, Zhen constellation: eighteen degrees, totaling three hundred sixty-five degrees and a quarter. The winter solstice sun is located at nineteen and a quarter degrees in the Dou constellation. Although historians used this instrument to calculate the movements and gains and losses of the sun and moon, the accuracy was fairly precise, but it did not alter the original method of recording. Since measuring the degrees and trajectories on the ecliptic with the Huangdao copper instrument was challenging, it was seldom used in practice.
Kui said: "Nowadays, the calculations of the historians for the dates of the new moon, the first quarter, the full moon, and lunar eclipses are mostly inaccurate because they do not understand the varying speeds of the moon's orbit. During the Yongping period, the court decreed that the former Court Astrologer Zhang Long should use the 'Four Divisions Method' to calculate the timing of the first quarter, the full moon, and lunar eclipses. Zhang Long claimed that he could use the nine, six, seven, and eight hexagrams of the I Ching to calculate the moon's movements. However, it now appears that Zhang Long's calculations were mostly incorrect. I asked Zhang Long to re-calculate his previous results, but they did not match up. Sometimes, the discrepancies between his calculations and the actual positions of celestial bodies exceeded ten degrees. Fanti and I carefully examined the records of the historians and found that the moon's movements do indeed vary in speed, and this does not necessarily only occur near the constellations of the Cowherd, Eastern Well, Lou, and Jiao, nor is it due to phenomena like 'tao' or 'ce ni.' This variation is caused by the differences in the moon's orbital distances. Approximately, the moon reaches its fastest point three times each month, and after nine cycles, it returns to the starting point, totaling 171 years. The new moon aligns with the eleventh month, coinciding with the end of the nine cycles in the 'Spring and Autumn Annals' and 'Three Statistics Calendar,' allowing for the calculation of the dates of the new moon, the first quarter, the full moon, and lunar eclipses. According to the official astronomical measurement units, by using this method to trace back the records of lunar eclipses since the Jianwu period, there were a total of 38 occurrences with minimal errors and effective results, so this method should be promoted for study."
The historians previously had a method called the 'Nine Methods' for calculations, but it was later abandoned. During the Xiping period, the former Calendar Supervisor Liang Guozong compiled and submitted the 'Nine Methods,' and the court decreed that the Court Astrologer should refer to the old method to see if the two were consistent. Feng Xun, the Crown Prince's Attendant, was tasked with the review, and he also created a new set of 'Nine Methods,' making additions and modifications to the original method. Feng Xun compared his version with Liang Guozong's, and the comparison showed that Feng Xun's version was somewhat more accurate. The Court Astrologer then used Feng Xun's method to calculate the first quarter and the full moon. However, there were still discrepancies between the calculated dates and the actual circumstances, with errors exceeding ten degrees in some cases.
In the year 78 AD, the palace official responsible for astronomy and the calendar, Huo Rong, submitted a memorial to the emperor, saying: "The water clock we are currently using is off by a quarter of an hour compared to the celestial time, sometimes even up to two and a half quarters, which does not align with celestial time. The timing of the Xia calendar is indeed more precise." The emperor then ordered the Ministry of Ceremonial to have the historians and Huo Rong calibrate the time with astronomical instruments to see which one is more accurate. Chief Astronomers Shu, Cheng, Fan, and others countered: "The method we currently use for timing with the water clock is based on the regulations of the sixth chapter of 'Ling Jia' and 'Chang Fu Lou Pin,' which was issued on the day of Yiyu in the twelfth month of the third year of Emperor Xuan of Han, and officially implemented on the day of Renwu in the tenth year of Jianwu. The water clock timing is calculated based on the length of sunlight each day, with the sun moving two degrees and four minutes north or south every day, resulting in an increase or decrease of a quarter of an hour on the water clock. Each solar term lasts fifteen days, and the sun's distance from the North or South Pole varies each day. The palace's water clock is only off by a quarter of an hour over nine days, since it does not adjust according to the sun's movement. The water clock timing of the Xia calendar changes based on the length of sunlight each day, making it more accurate than the palace's water clock and fully implementable."
In the eleventh month of the same year, on the Jia Yin day, the emperor issued a decree saying: "Inform the Minister of Works and the Minister of State: The function of the water clock is to measure time and determine the length of day and night. The variations in the length of day and night are due to the sun's distance from the North or South Pole. The sun travels in a circular path and cannot be calculated by a fixed ratio. It should be measured with astronomical instruments and then calculated based on the length of the shadow. Currently, the water clock in the palace calculates the length of day and night using a fixed ratio, which is off by a quarter of an hour compared to the actual time. The Imperial Historian Huo Rong also reported that the palace's water clock does not align with the celestial time. The officials of the Ministry of Rites measured with astronomical instruments and found that the discrepancy between the palace's water clock and celestial time can reach up to three quarters of an hour. Measuring time using the length of the shadow results in significantly less error and is more accurate upon verification. Now we will use the length of the shadow to make new water clocks, a total of forty-eight water clocks. After they are made, they will be sent for distribution to various government offices. Once the officials have received them, they will be distributed uniformly." Due to the extensive content, only excerpts detailing the sun's positions during the twenty-four solar terms, the distance of the ecliptic from the North Pole, the length of the shadow, the timing of the water clock, the length of day and night, and the time of the central star are included here. It is said that our ancient "Tai Chu Calendar" was developed from the Yuan Feng period and finalized during the Yuan Feng period, which took thirty years to clarify its accuracy. Later, the "Si Fen Calendar" was adopted, implemented from the Jian Wu period to the Yong Yuan period, taking over seventy years to refine various ceremonies and regulations, and to standardize astronomical observations. As you can see, astronomy is incredibly mysterious and complex; grasping it is quite challenging!
Since the rise of the Han Dynasty, prophecies and divinations have been widespread, as noted in books such as "Kao Ling Yao" and "Ming Li Xu," all mentioning the Jia Yin period. This Jia Yin period is calculated based on the Geng Shen year in the "Four Divisions Calendar," 114 years later, with the calculated date of the new moon (first day) being off by two days. How did those rural scholars studying astronomy arrive at such accurate results? It's truly unbelievable! Furthermore, after the "Tai Chu Calendar," people found that the calculations of days were becoming increasingly rapid. Astronomy scholars claimed, "In 144 years, the Grand Duke will exceed one Chen (one of the twelve Chen), and in 171 years, we need to subtract 63 excess new moons, and in between, we need to add 1197, in order to continue using it." However, from the first year of Tai Chu to the eleventh year of Yong Ping, exactly 171 years, the excess new moons that should have been deducted were not, so the calendar became increasingly inaccurate. These two calendars each adhere to their own methods and try their best to implement them, resulting in frequent disputes. Every time someone raises an objection, the court officials have to hold meetings to discuss, with a group of Confucian scholars brainstorming and sharing their views. These debates greatly contributed to everyone's understanding, so I have detailed these situations. In the second year of Emperor Yan Guang, a mid-ranking official named Dan suggested using the Jia Yin calendar, while He Nan Liang Feng argued for the continued use of the "Tai Chu Calendar." The Shang Shu Lang Zhang Heng and Zhou Xing were both experts in calendars, and they debated with Dan and Feng; some were unable to respond, while others made errors in their statements. Zhang Heng and Zhou Xing consulted the ritual texts, researched ancient and modern calendars, and believed that the "Nine Methods" were the most accurate. The emperor subsequently ordered the officials to engage in a detailed discussion.
General Kai and others reported the results of the discussion to the attendants Shi Ting and his colleagues: "The calculations of the 'Tai Chu Calendar' for celestial phenomena are inaccurate, the degrees of daily movement are incorrect, the predictions for the lunar phases (specifically on the eighth and twenty-third of each month) are also inaccurate, the moon appears in the west on the last day of the lunar month, and the timing of solar eclipses does not align with the celestial calculations. During the Yuanhe period, the 'Four-Part Calendar' was subsequently adopted; although it is more accurate than the 'Tai Chu Calendar', it is not entirely accurate, so neither of these calendars is suitable. The Jia Yin Yuan Calendar aligns with the celestial phenomena and also fits the prophecies of the diagrams, so it can be implemented." Dr. Huang Guang and the Chief Envoy Ren Qian also believe that the 'Nine-Path Method' should be used. The Henan Intendant Zhi, the Prince's Attendant Li Hong, and forty others believe: "If the Jia Yin Yuan Calendar is adopted, the 114 years mentioned in the 'Yuan Ming Bao' concerning the creation of heaven and earth and the appearance of auspicious signs must be removed, and adjustments to the leap months and dates must be made, leading to numerous inconsistencies in the celestial positions of the new moon, last day, lunar phases, and the twenty-four solar terms. If the 'Nine-Path Method' is used to calculate the new moon, there will be significant differences in the size of each month, which would be unreasonable. The change of calendar during the Yuanhe period was in response to the reference in the 'Bao Gan Diagram' stating 'three hundred years of calendar reform.' The 'Four-Part Calendar' was initially developed based on the diagrams and is most aligned with actual circumstances, so it should not be altered lightly." General Kai and 84 others believe that the 'Tai Chu Calendar' should continue to be used.
The Prefect of the Masters of Writing, Zhong Shang, reported: "Those who advocate for the continued use of the 'Tai Chu Li' calendar do not have any actual evidence; they only say that because during the reign of Emperor Shizong the territory expanded and the country endured, the 'Tai Chu Li' calendar is good. Some say that after Emperor Xiaozhang switched to the 'Si Fen Li' calendar, there were many disasters and no benefits. I believe that when a wise king rises, the calendar will also change accordingly, which is in line with historical laws. After Emperor Gaozu took the throne, he continued to use the Qin Dynasty's method of dating years, with October as the beginning of the year and leap months added at the end of the year. We should not neglect the calendar of our ancestors and violate their system. After the revision of the calendar during the reign of Emperor Taizong, society was stable, auspicious signs appeared, punishments were fair, and the country was peaceful. During the reigns of Emperor Ai and Emperor Ping, the 'Tai Chu Li' calendar was used, but disasters continued. Those who advocate for the 'Tai Chu Li' calendar did not seriously compare the advantages and disadvantages of the calendars, but blindly believed in some unreliable claims, attributing all benefits to the 'Tai Chu Li' calendar and all faults to the 'Si Fen Li' calendar. The 'Tai Chu Li' calendar was established by many wise men, and its merits and demerits have been determined. During the Yongping period, the method of calculating solar terms was changed without careful examination. Although the 'Si Fen Li' calendar has errors, it should not be used. The appearance of the phoenix during the Yuanhe period is unrelated to the calendar. Ancient calendars can explain their auspiciousness; modern changes to calendars often hide their benefits. These claims are unfounded. I have carefully reviewed the opinions of Zhang Heng and Zhou Xing again. They believe that the calculations of the Five Epochs are closer to reality, but they still have not examined ancient calendars. Previously, Xiang Zixin wanted to use the calendar to verify the 'Spring and Autumn Annals,' arbitrarily changing the years, reducing the years of the Xia Dynasty and increasing those of the Zhou Dynasty, which is significantly different from historical records. When comparing the two calendars, there is a difference of 6156 years, with the 'Tai Chu Li' calendar being one day longer. The winter solstice sun is directly above the Dipper, while the 'Tai Chu Li' calendar says it is near the Cowherd star. These errors are too significant to continue using. These observations are not solely the opinions of Zhang Heng and Zhou Xing; they are shared by historians as a whole. Previously, it was believed that the 'Nine Methods' were more accurate, but now it is said to have errors, and the Jia Yin Yuan calendar also has many errors, so these calendars cannot be used. Confucius once used the name of a fictitious horse to respect the principles of the monarch; let alone the celestial calendar, which cannot be speculated out of thin air, replacing correctness with errors!" The emperor took his advice and abandoned the plan to revise the calendar.
During the second year of Emperor Hanshun's reign, a vice minister named Bian Shao submitted a memorial to the emperor, stating that the world's decline was due to violating the laws of nature, and a country's prosperity stemmed from adhering to the laws of nature. Violating these laws leads to decay, while adhering to them brings prosperity. Emperor Xiaowu was exceptionally astute, and in the eleventh month of the seventh year of the Yuanfeng era, on the day of the winter solstice, he ordered Chief Astrologer Sima Qian and the calendar official Deng Ping to revise the "Taichu Calendar," modifying the era and the new moon day, adopting the Xia Dynasty calendar, applying the method of "subtracting forty-three from eighty-one" in the "Qianzao Degree" to calculate days, and establishing a dedicated observatory to study celestial phenomena, monitoring six unusual celestial phenomena, and evaluating the accuracy of the calendar computations. The "Taichu Calendar" was the most accurate. Later, Liu Xin undertook extensive research on calendars. Drawing from the records of the "Spring and Autumn Annals" and the principles of the "Book of Changes," he used the "Hetu Emperor's View of Xi" and the "Luoshu Qianyao Degree" to improve the "Nine Dao Calendar," calculating a cycle of 171 years with a remainder of 63 minutes, with a major adjustment every 144 years, which corresponded to celestial changes with few errors. From the Taichu Calendar to the eleventh year of Yongping, a total of 171 years, with a remainder of 63 minutes, those responsible for the calendar were unsure how to manage these surplus minutes. The calculations of the twelve lunar phases were also inaccurate, with some individuals researching the discarded calendars, mixing their interpretations. By the second year of Yuanhe, the values at the end of the minor cycle gradually surpassed, the surplus increased slowly, and the timing of the moon's new and full phases became unreliable. Emperor Xiaozhang adopted the "Four-Fen Calendar" based on the saying in the "Baoqian Diagram" that "the calendar should be changed every three hundred years." He designated the year of Jupiter's return as the year of Genghai, confirming the results through celestial observations, which aligned with the current circumstances. He also set the year of Gengshen as the era, but there was no definitive written record; it was claimed that this was due to the acquisition of a Qilin that year, but this contradicted the "Ganjing Fu," which referred to a different year. Historians in later generations built upon each other's work, leading to many questions, with few capable of conducting in-depth research to trace the origins. Ultimately, observing lunar phases suffices to ascertain accuracy.
After this imperial edict was issued, the Three Excellencies and the officials began to discuss among themselves. Chief Historian Yu Gong and those responsible for the calendar also shared their thoughts.
The foundation of a calendar begins with determining its starting point, which is the Yuan Zheng. Only with the Yuan Zheng can the degree of daily operation be determined, and only with the degree of daily operation can the annual cycle be calculated, thus determining the solar terms. Once these three are determined, the calendar can be established. The starting point of the "Four-Fold Calendar" is calculated from the third year after the Xiaowen Emperor, starting from the year of Gengchen. Calculating back forty-five years, it is the year of Yiwei, which is the first year of the Han Dynasty. Calculating back another two hundred and seventy-five million years, it is the year of Gengshen, which is the year Confucius received the auspicious unicorn (Lin). Calculating back another two hundred and seventy-six million years, continuing upward, will again arrive at the year of Gengshen. Year after year, calculating from the bottom up, the calculations will be accurate. This is recorded in the "Four-Fold Calendar" Yuanming Wenti Prediction. The first year of Taichu is the year of Dingchou, and tracing back to its starting point, it should be the year of Gengxu, but the text states it is the year of Bingzi, leading to the designation of the year as Bingzi, because there was an extra Chen in one hundred and forty-four years, a total of nine hundred and ninety-three times, causing an extra eighty-two weeks in a year. Analyzing the discrepancies in the years, on the day of the winter solstice in November of Jiazi year, both the sun and the moon showed deviations. The sun travels one degree each day, three hundred and sixty-five and a quarter degrees is a week, called a year. A year corresponds to a Chen; if the sun does not skip a week in its movement, then there will be no phenomenon of exceeding a Chen in a year. One hundred and seventy-one years equals two Bu plus one Zhang, with sixty-three remaining; this follows the principles of natural numbers. Numbers accumulate from the smallest unit, accumulating from millimeters to become a foot. Once the two energies of Yin and Yang are determined, the sun and moon begin to move. The initial movement produces Fen, and Fen accumulates to become a degree. The sun moves one degree every day, completing a week in a year. Therefore, those who establish calendars each have their own algorithms; some use nine hundred and forty, some use eighty-one. There are coarse and fine algorithms, resulting in two types of calendars, but the ultimate goal is the same. The solar degree is the number of degrees the sun moves each day. The regularity of the sun's movement is clear, with a fixed rhythm, and the concepts encompassed by the solar degree are vast and limitless. If there is a slight increase or decrease, there will be a big difference, indicating that numerical calculations cannot have any errors. Now, trying to make up for the mistakes of leap years and common years by reducing the degrees in the solar degree, it is feared that this will disrupt the fundamental principles of the calendar. Using steps to calculate the degrees of the sun and moon's movement, the final result is different, and even after four chapters, it is impossible to obtain the remainder of one. Although the "Nine Methods" can adjust forward and backward, it may not be enough to make up for its shortcomings. Furthermore, the methodology for calculating calendars is validated through the phases of the sun and moon, which is very important. Now, using the method of reducing sixty-three minutes to establish a calendar, it is found that there have been twenty solar eclipses and twenty-eight lunar eclipses recorded since the first year of Zhang and Yuan, compared to the "Four-Fold Calendar," the discrepancies are larger; using the method of fixed division, the "Four-Fold Calendar" actually has a smaller error and is more convenient. Emperor Xiaozhang meticulously calibrated the calendar's measurements, made instruments and sundials, which matched the celestial phenomena, and there is no need to adopt other calendars. The "Wenyao Gou" says: "The Gaoxin clan was appointed to establish the calendar. Tang Yao ascended the throne, and Xihuo established the celestial sphere. The Xia Dynasty established the system of rites and music, and the Kunwu clan worshipped the heavenly gods. The Zhou Dynasty changed the calendar, and Chang Hong was responsible for managing the calendar." The "Yundou Shu" says: "Official diviners have specialized calendars, which are recorded in historical books." The "Hongfan Wujilun" says: "There are various calendars from the time of the Yellow Emperor among the people, but they are not as accurate as recorded by the official historians." From ancient times to the present, the wise emperors have consistently sought the counsel of Xihuo and official astrologers, carefully corrected with instruments, resolved various doubts, and preserved the calendar within the Ministry of Rites, following the original method of the "Four-Fold Calendar." Emperor Guangwu issued several edicts to begin the establishment of the calendar, Emperor Xiaoming verified the calendar, and Emperor Xiaozhang promulgated the calendar. After three generations of wise rulers, after decades of time, and through verification, it was finally promulgated and implemented. Its starting point can be traced back to the creation of heaven and earth, and its algorithm follows the "Four-Fold Calendar." It should be treated similarly to the edict issued in the Jia Yin year.
Approved for submission.
The emperor approved.
In the fourth year of Xiping, during the reign of Emperor Ling of Han, there were two officials: Feng Guang, a Langzhong of the Five Officials, and Chen Huang, the official in charge of the Xiangfu in Pei County. They submitted a memorial saying: "The current calendar is incorrect, leading to turmoil in Yizhou, where rebellions and banditry are rampant. The calendar should start with Jiayin, not Gengshen. The astronomical books do not consider Gengshen as the starting year of the calendar. Gengshen was used by the Qin Dynasty, following the Zhou Dynasty, which is fundamentally incorrect. The Langzhong Guo Xiang and Liu Gu below the Grand Historian deliberately fabricated false information, requesting an investigation into the true situation of the Gengshen calendar and severe punishment for those who deceive the court." On the day of Yimao in the second month, the emperor issued an edict to the Three Dukes, Nine Ministers, and esteemed scholars in the Confucian community, instructing them to thoroughly discuss and determine the correct calendar. They were to have a meeting at the Situ Mansion to discuss together.
Yilang Cai Yong participated in the meeting and expressed his opinion:
"This discussion about ancient calendars is quite complex and overwhelming! Let's take it one step at a time."
First, "The calendar's calculations are intricate, its origins are ancient, its gains and losses vary, and there is no constant method." This means that the calendar is very complex and has changed throughout the ages, with no fixed method.
Then, "Han inherited the calendar from Qin, using Zhuang Xu, with the starting year being Yimao." After the establishment of the Han Dynasty, they inherited the Zhuang Xu calendar from the Qin Dynasty, with the starting year being Yimao.
"In the 102nd year of Emperor Xiaowu's reign, he changed the calendar to Taichu, with the starting year being Dingchou, which was used for 189 years." In the 102nd year of Emperor Xiaowu's reign, he reformed the calendar, starting to use the Taichu calendar with the starting year being Dingchou, which was used for 189 years.
"Emperor Xiaozhang changed to the Sifeng calendar, with the starting year being Gengshen." Emperor Xiaozhang of Han changed to the Sifeng calendar, with the starting year being Gengshen.
"Currently, both Guanglu Xun and the Grand Historian believe that Gengshen is the incorrect starting year, and Jiayin is the correct one."
"The calendar history, Huangdi, Zhuanxu, Xia, Shang, Zhou, Lu, six dynasties in total, each with its own origin. Based on the records of calendar history, Huangdi, Zhuanxu, Xia, Shang, Zhou, and Lu each had their own starting year for calendars. Guanglu Xun and Taishi Ling based their calculations on the calendar origin of the Shang Dynasty.
Although the origins of other dynasties are not clearly recorded in the prophecies, each dynasty's methods were effective in their time.
Emperor Wu began using the 'Taichu Calendar' after Dingchou, causing confusion and disputes among the six dynasties.
Taishi Ling Zhang Shouwang used the Jiayin year to challenge the Han calendar, but due to his careless mistakes, he faced repeated accusations. However, the predictions of the 'Taichu Calendar' were accurate and did not miss anything.
Although not recorded in the prophecies, it was effective before. Since the use of the 'Sifen Calendar', the calculations have been more accurate, making the new starting year valid as well.
In the first year of Yanguang, the middle envoy Dansong also argued that the Gengshen year in the 'Sifen Calendar' was incorrect, suggesting the use of the Jiayin year in the 'Mingli Xu'. However, after discussion among the officials, it was not implemented.
The movements of the three luminaries, whether fast or slow, do not need to be uniform. Experts calculate and strive to align with the current situation. Thus, methods have evolved from ancient to modern times."
"The current calendar cannot completely coincide with the ancient calendar, just as the ancient calendar cannot completely coincide with the current calendar."
"The 'Yuan Ming Bao' and 'Qian Zao Du' both believe that it took a total of two million seven hundred sixty thousand years from the creation of heaven and earth to the appearance of the Qilin during the fourteenth year of Duke Ai of Lu; and 'Ming Li Xu' calculates that from the appearance of the Qilin to the Han Dynasty, it was a total of two hundred seventy-five years."
"In the first year of the Han Dynasty, it was the year of Yi Wei, when the appearance of the Qilin was the year of Geng Shen. Continuing this calculation, tracing back to the beginning of creation, the year also corresponds to Geng Shen. Although there is no written record in the prophecy, the numbers exist."
"But Guang Lu Xun and the Grand Historian believed that the time from the creation of heaven and earth to the appearance of the Qilin was two million seven hundred fifty-nine thousand eight hundred eighty-six years, and from the Qilin to the Han Dynasty was one hundred sixty-one years, a difference of one hundred fourteen years. If this claim is accepted, it would contradict the records of 'Qian Zao Du', 'Yuan Ming Bao', and 'Ming Li Xu'."
It is now the first day of the first month in the year of Guihai, but Guang and Huang believe it is the first day of the first month in the year of Yichou. It can only be verified by observing the waxing and waning of the moon. However, the calendar that Guang and Huang use is based on the "Kao Lingyao," which records the positions of the twenty-eight constellations and the winter solstice differently from the records of the historians Gan and Shi in the past, which makes verification impossible; observations made with the current celestial globe also do not align with the "Kao Lingyao." If Guang and Huang can make new observation instruments according to their own methods to accurately measure celestial phenomena, it would be more accurate than the written records and better reflect the laws of the movements of the sun, moon, and stars, replacing Gan and Shi's calendar and rendering other calendars obsolete; then their calendar should indeed be adopted. However, when we inquire, they only speak of divination and cannot provide a clear explanation.
In the second month of the second year of Yuanhe, the emperor issued a decree stating, "I have learned that the wise rulers of antiquity followed the will of heaven, did not violate the principles of heaven, and also followed the timing of heaven. The historians are currently using Deng Ping's calculations of the Taichu calendar. On the day of the winter solstice, the sun is at twenty-one degrees in the Dipper constellation, but the calendar places it near the Altair star, advancing the day of the spring equinox by one day, which corresponds to the spring equinox in the Sifen calendar. Using this calendar to judge and convict is already inconsistent with the actual situation. It is unrealistic to attain a peaceful and prosperous era using this calendar. Now we are switching to the Sifen calendar to adhere to the systems of Yao and Shun and align with Confucius' concept of 'serving heaven.'" This is the Gengshen decree, which marks the beginning of the Sifen calendar's adoption. The decree extensively references divinatory texts like the "He Tu" and "Lo Shu" to prove the correctness of the calendar, which was not conceived by the historians themselves.
But Guang and Huang regarded this as a falsehood deliberately fabricated by Xiang Gu, which violated the classics and was simply absurd. Emperor Yao had ordered Xihe to observe the sun, moon, and stars to establish a calendar, which was continued and refined by Emperor Shun. After the revolutions of King Tang of Shang and King Wu of Zhou, new calendars were established as well, all of which were considered relatively accurate. However, disasters such as floods and droughts still occurred. Ancient emperors also warned people to beware of "barbarian invasions and banditry." Guang and Huang, on the other hand, believed that the imbalance of yin and yang, corrupt officials in power, and rampant banditry were all faults of the Yuanhe period, which is utterly nonsensical. It has been ninety-two years since the adoption of the Gengshen era in the second year of Yuanhe. Guang and Huang claimed that the Qin Dynasty also used the Gengshen era instead of the Zhou Dynasty, but they did not know that the Han Dynasty had changed the era three times since the Qin Dynasty, showing that the Gengshen era was not static. They stubbornly adhered to their own teachings, spinning lies to deceive others. As for changing the era, the method suggested by Lord Shou had already been shown to be ineffective, and his suggestions were not accepted by anyone. The Yuanhe period's imperial edict clearly stated that it was not something that ministers could change at will. The Grand Chancellor Dan, Minister of Works Wei, and Minister of Finance Xun, these three high-ranking officials, wanted to punish Guang and Huang severely for their disrespectful actions according to the law. However, the Emperor commanded, "Forget it; let’s not pursue this matter further."
"The Taichu Calendar" calculated lunar eclipses many times inaccurately. "The Four-Part Calendar" was an improvement based on the method of "The Taichu Calendar," starting from the year of He Ping in the Gui Si cycle, and took five years to develop. In the first year of Yong Yuan, a lunar eclipse occurred in the seventh month, but "The Four-Part Calendar" recorded it as occurring in the eighth month. On the twelfth day of the first month of the second year of Yong Yuan, a noble named Meng Gong Cheng Zong wrote a letter stating, "The moon will be eaten on the sixteenth day of this month, but the calendar says it's in the second month!" On that day, it indeed happened just as Zong had predicted. The Chief Historian thought Zong was quite impressive and promoted him to an official position. On the day of Jia Chen, the emperor ordered the official adoption of Zong's method for calculation. This method was employed for fifty-six years until the first year of Ben Chu, when a lunar eclipse occurred in the twelfth month, but the calendar recorded it as occurring in the first month of the following year, starting to show discrepancies. In the third year of Xi Ping, including the previous twenty-nine years, there had been sixteen instances of lunar eclipses miscalculated by the calendar.
In Changshan, there was a Chief Historian named Liu Hong, who authored a book titled "The Seven Planets Technique." On the day of Jia Chen, the emperor instructed officials Liu Gu and Feng Xun to investigate its reliability. Consequently, they created "The Eight Elements Technique" and "The Lunar Eclipse Technique," collaborating and cross-referencing their findings. Liu Gu's algorithm was similar to "The Seven Planets Technique." Regarding the calculation of lunar eclipses, opinions were divided. For example, in the year of Ji Wei, some claimed a lunar eclipse occurred in April, others in March, while the official calendar stated it was in May. The officials collaborated and ultimately settled on a reliable algorithm for official use. On the day of Ding Si, the emperor approved it.
In the fourth year of Xi Ping, Zong Cheng, the grandson of Zong Gan, also submitted a letter stating, "My grandfather's method needs to be updated. A lunar eclipse will occur in December this year, but the official calendar indicated it would occur in January of the following year." As a result, on that day, it happened exactly as Zong Cheng had predicted. The emperor was thrilled and promptly promoted Zong Cheng to an official position. On the day of Bing Shen, the emperor decreed the official adoption of Zong Cheng's method.
In the second year of Guanghe, which was the year of Jiwei. Both March and May had continuous rainy weather. Chief Historian Xiu and his subordinates, including Zhang Xun, calculated that March was nearer, while April was further. They ultimately decided to adopt April. They requested to abolish Xiu's algorithm and adopt Zhang Xun's algorithm.
Three years later, Xiu’s brother submitted a memorial stating, "It did not rain in March last year, so we should use the data from April." The Chief Historian dismissed Xiu’s accurate algorithm and adopted Zhang Xun’s flawed one. The brother submitted the memorial to the Chief Historian, but the Chief Historian never accepted the notion that March was nearer to April. He said that whether it rained should depend on actual conditions, without considering proximity. The Emperor then issued an edict to the Ministry of Ceremonies, saying, "You must carefully review the records, compare the merits of various algorithms, and verify their authenticity."
The Ministry of Ceremonies summoned Han Shuo, Cai Jiao, Liu Hong, and Chen Diao to reexamine the records and discuss the disputed issues. Zhang Xun and Xiu both explained their algorithms. Zhang Xun's algorithm was based on 9,561 rainy days recorded over 5,640 months, calculating a total of 327 rainy days since the Jianwu era, with 15 errors in calculation. According to official records, there were 98 instances of rain, which aligned closely with both algorithms, but Zhang Xun's algorithm had discrepancies totaling 2,100 instances. Xiu's algorithm was based on 135 months, with 23 rainy days per month, subtracting 41 and 35 rainy days before and after the Jiankang period, respectively, as there was no rain during these times. Zhang Xun's algorithm changed the old algorithm, while Xiu's algorithm made adjustments in the middle. In terms of advantages and disadvantages, there was little difference between them. Both sides cited scriptures and astronomical texts to prove their points, but these texts held no practical significance and merely served to align with celestial phenomena.
The rules governing the movements of the sun and moon state that the sun follows the ecliptic, while the moon travels along nine distinct orbits. Using an equatorial instrument for measurement, the sun is 115 degrees away from the North Pole at the winter solstice. When the sun enters the 28 mansions, the equator is at 21 degrees in the Dipper mansion, while the ecliptic is at 19 degrees. The two orbits intersect each other, and the trajectories of the sun and moon exhibit varying degrees of curvature, leading to changes in their apparent motion. Therefore, when the moon moves to the Well mansion and the Ox mansion, it exceeds 14 degrees; when it moves to the Horn mansion and the Dipper mansion, it exceeds 12 degrees. These observations deviate from the conventional rules of motion. Thus, if the algorithm lacks accuracy or applicability, it should be disregarded. The intricacies of the heavens are profound, making precise measurements challenging; there are various algorithms, and the records of calendars differ. Without verification, one cannot ascertain its correctness, and without deviations, it is impossible to know where the errors lie. Errors should be corrected as they arise, and only adopted once verified; this is known as "adhering to the mean." The current algorithm accounts for 135 months and 23 rainy seasons, recorded in books, and scholars have relied on it for many years. Officials adhere to this rule, calculating the movements of the sun and moon, and have maintained accuracy over a long period, earning the trust of the astronomical community, though they have continued to use it without innovation. Zhang Xun has long worked in the waiting department, known for his meticulous thinking and analytical skills, capable of mastering instruments and measurements, formulating algorithms, calculating the past, and verifying the present, aligning with actual conditions.
However, in the establishment of the calendar and the compilation of official history, one should respect the heavens and follow old precedents, just like the decrees from the years Jia Chen and Bing Shen, which should be based on actual circumstances. Now we should adopt Xiu's calculation method and abandon Zhang Xun's calculation method. Historians should supervise, and if it proves effective later, then we can implement his method to verify the calculations and adapt to changes. The Ministry of Ceremonies submitted a report based on the views of Han Shuo and others, which the emperor agreed to. Zhang Xun, Zheng, and Xiu each submitted petitions, with Zhang Xun saying that Xiu's calculation method should not be adopted, and Zheng saying that Zhang Xun's calculation method should not be used again. Because Liu Hong's opinion carried more weight, this matter was sent to the Yong'an Platform for review, and the results fell short of the opinions of Zhang Xun and Xiu. As a result, they were accused of misleading the emperor. The emperor issued a decree, fining Zhang Xun and Xiu for two months each as punishment, and fining Zheng for two months as well. Finally, the opinion of Liu Hong and others was adopted, and Xiu's calculation method was implemented.
In the second year of Guanghe, Wang Han, the magistrate of Wannian County, submitted a report on lunar eclipses. From the first year of the Heping era to this year, he was already ninety-three and had witnessed a total of one hundred ninety-six lunar eclipses. The calendar he used was established in the first year of Heping, with the Ji Si year as the epoch. This matter was handed over to the Grand Historiographer for review, and the Grand Historiographer reported back, "There are two discrepancies between Wang Han's report and actual observations of lunar eclipses, and twenty-nine instances where the same phenomenon is described differently." The court then summoned Liu Hong, a junior official at Gu Cheng Gate. The emperor ordered, "Previously, the Lang Zhong Feng Guang, the Minister of Works Chen Huang, and the Yilang Cai Yong had all debated calendar issues, and Cai Yong had also participated in revising the calendar. Now you, Liu Hong, are to work with Wang Han, calculate the epoch and intercalary months of the calendar, and thoroughly review the lunar eclipse records. If Wang Han's Ji Si epoch is accurate and backed by reliable evidence, you will accept his findings. If not, you will refute him directly."
Liu Hong reported: "If we calculate according to Wang Han's Jisi era, the year of Zhan Meng referred to in 'Kao Lingyao' should be the Yimao year as the era. This contradicts the Jia Yin era used by Feng Guang and Chen Huang. There are many omissions in using this to calculate celestial phenomena and verify the laws of the sun, moon, and stars. Confucius recorded an event in the 'Spring and Autumn Annals' with two different interpretations, indicating that the establishment and abolition of calendars should be adjusted according to changes in celestial phenomena. The Jia Yin calendar was in use during Confucius' time; the Jisi calendar was established in the era of Zhuan Xu and continued in the Qin and early Han dynasties without changes. During the Yuanfeng period, it was noted that this calendar had significant inaccuracies, so the 'Tai Chu calendar' was adopted, with the calendar being revised over 300 times. Although the Jia Yin and Jisi eras are recorded in literature, the specific years are relatively unclear, leading to differing opinions among scholars and inconsistent results in calculations. In the Jia Yin era, the first day of the first month is the winter solstice; the starting point of the seven luminaries is the initial degree of the Ox constellation. In the Yimao era, the first day of the first month is the beginning of spring; the celestial coordinates in the sky are five degrees. Comparing these two eras, the discrepancy in leap months is 152 and 1/3, the new moon day difference is 304 days, and the solar term difference is 29 days. Since it is difficult to verify which is more accurate, Wang Han's explanations are unclear, only saying that this is ancestral information. If Wang Han's annotations are used to guide calendar practice, there will be 29 inconsistencies with actual observations and two discrepancies with observed lunar eclipses. I believe Wang Han blindly believed in the Jisi era without understanding the reasoning behind the sages' establishment and abolition of calendars, and the historians have the secret method of calculating calendars based on celestial phenomena. The Jia Yin and Jisi eras were both used in the past but were later abandoned due to poor results. The Heping calendar also had its flaws and has already been discarded by historians, but Wang Han continues to debate past matters, which likely isn't his true intention. Even if his arguments are based on something, they do not match reality. His calculation method is common knowledge understood by numerologists and not worth adopting." Finally, the court sent Wang Han back to his hometown.
