Chapter 5 The fourth section of the calendar - "Shoushi Calendar"
"In March, Sanxing is about to set on the western horizon. At this time, mulberry leaves are sprouting, willows are sprouting, mole crickets are singing, and the ice has melted...women are going to start raising silkworms." This is "Xia Xiaozheng" a paragraph.Due to the ancient language, we translate it into vernacular.In the history of astronomy, this method of arranging the seasons and months of the year by observing astronomical phenomena and phenology is called "observation timing". "Savages have no calendar, but birds know the four seasons."Under the condition of incomplete calendar knowledge, the activity of "observing the time and giving time" has lasted for a long period of time. "Xia Xiaozheng" is said to be the calendar of the Xia Dynasty. Although it is now believed that the book was written in the Spring and Autumn Period and the Warring States Period, the book undoubtedly preserves the time-telling data accumulated by people long ago.In addition to "Xia Xiaozheng", "Book of Rites·Yueling", "Huainanzi·Tianwenxun" and "Yi Zhou Shu·Shi Ze Jie" and other early works of Yueling have the content of observing the time.
Around the mid-to-late Spring and Autumn period, our country produced a calendar with 3651/4 days as the length of the return year and seven leap weeks in 19 years as the leap week, which we call the quarter calendar.The two basic data of the quadrant calendar were very advanced in the world at that time, about a hundred years earlier than the same discovery by the ancient Greek Meton (Meton). Its appearance marks that the Chinese calendar has entered a relatively mature period.
In ancient China, the calendar was related to all aspects of the national economy and the people's livelihood. Therefore, promulgating the calendar is an extremely important matter.During the Warring States period, various countries competed for hegemony, and many vassal states promulgated their own calendars, mainly including the Yellow Emperor, Zhuanxu, Xia, Yin, Zhou, and Lu.The six calendars are all four-point calendars, but the prescribed calendar start year (epoch) and the month (the beginning of the year) of each year are different.The Qin State used the Zhuanxu calendar, so when Qin wiped out the six kingdoms and unified the country, the Zhuanxu calendar became the national calendar issued by Qin Shihuang, and it continued to be used until the early Han Dynasty.By the time of Emperor Wu of the Han Dynasty, the Zhuanxu calendar had been gradually neglected, which affected agricultural production, so Emperor Wu of the Han organized a group of astronomical talents to promulgate a new calendar, the "Taichu Calendar".The reform of the calendar by Emperor Wu of the Han Dynasty established the tradition of changing the calendar during the change of dynasty in China, and the appearance of "Taichu Calendar" marked the formation of the ancient Chinese calendar system. "Taichu Calendar" for the first time puts forward the principle of taking the month without Zhongqi (rain, vernal equinox, grain rain and other twelve solar terms) as the leap month.This method has been used in the lunar calendar (or summer calendar) until now. The "Taichu Calendar" also clearly put forward for the first time the concept of an eclipse cycle in which there are 23 eclipse seasons in 135 synodic months, and established a set of methods for calculating the positions of the five stars based on the dynamic understanding of the five stars in a conjunction cycle.It can be seen that the "Taichu Calendar" is not a simple calendar, but a comprehensive reference book that integrates Qishuo, leap method, five stars, eclipse, etc., similar to the current astronomical calendar.It became the model basis for the compilation of various calendars later.
Since the ancient Chinese calendar has rich content, the reform of the calendar is also multi-faceted, including the introduction and application of new theories, the measurement of precise data, and the improvement of calculation methods.The reform of the calendar led to the development of the entire ancient astronomy, so some people think that the history of ancient astronomy in my country is, in a certain sense, a history of calendar reform.In ancient China, there were more than 100 calendars that appeared successively.
In the Eastern Han Dynasty, the movement of the moon and the issue of eclipses were a focus of debate in the calendar reform activities.When Emperor Jia Kui used his own zodiac armillary sphere to observe, he discovered that the movement of the moon was uneven.Subsequently, there appeared "Nine Dao Techniques", "Lunar Eclipse Technique", "Lunar Eclipse Notes" and other works devoted to the discussion of lunar movement and lunar eclipse.At the end of the Eastern Han Dynasty, Liu Hong introduced the slow movement of the moon into the calendar for the first time in the "Qianxiang Calendar", and set a relatively accurate number of days in the anomalous month and the actual degree of the moon every day in an anomalous month. Solar and lunar eclipses can be calculated more accurately. "Qianxiang Calendar" also set the value of the food limit for the first time, which is an important invention in the forecast of food.In addition, "Qianxiang Calendar" also made breakthroughs in the research of the node month, the length of the return year, and the distance between Huang and Baidao, thus opening up a new era in the development of ancient Chinese calendars.
The period of the Three Kingdoms, Jin and Southern and Northern Dynasties was a period of great social turmoil. The local regimes of various ethnic groups and regions changed rapidly, so many new calendars appeared.The progress of the calendar at this time is mainly manifested in three aspects: First, Yang Wei, the state of Wei during the Three Kingdoms period, proposed the calculation method of the eclipse and the starting position of the solar eclipse in the "Jingchu Calendar", which promoted the development of the theory of eclipse.Secondly, Zu Chongzhi in the Liu Song Dynasty introduced the discovery of Yuxi in the Eastern Jin Dynasty into the calendar calculation for the first time in the "Da Ming Calendar", which improved the accuracy of the calculation of the winter solstice point.The third is that Zhang Zixin, a folk astronomer in the Northern Qi Dynasty, used self-made instruments to observe on an island, and found that the sun and five stars, like the moon, have uneven apparent motion speeds in the sky.It tells people that the number of days in one solar term may not be equal to that of another solar term, and the calculation of solar and lunar eclipses must not only consider the unevenness of the moon's movement, but also the unevenness of the sun's movement.This discovery heralds another major change in the history of history.
The calendar in the Sui and Tang dynasties produced a new leap on the basis of the accumulation of achievements of the previous dynasties.First of all, Liu Zhuo of the Sui Dynasty adopted the method of determining Shuo in the "Huangji Calendar" instead of Pingshuo, and created a second-time equidistant interpolation method to estimate the positions of the five stars and the beginning and end of solar and lunar eclipses (the initial loss and the compound circle) ) time and eclipse points, etc., and the method is also used to calculate the degree of daily travel and the time of delivery.In Li Chunfeng's "Linde Calendar" in the early Tang Dynasty, the Dingshuo method was affirmed, and it has since replaced the Pingshuo method.The most famous calendar in the Tang Dynasty was "Da Yan Li" by Yixing.In order to compile the new calendar, he and his party conducted a large number of actual observations. The most well-known one is the first meridian measurement in the world conducted by scientific methods under his presidency.Yixing's "Da Yan Li" made a more realistic description of the law of the sun's movement than Zhang Zixin, Liu Zhuo and others.He thinks that the movement of the sun is the fastest during the winter solstice, and the slowest during the summer solstice; his solar movement table (日躔 [chan] table) is compiled according to the fixed energy.Due to the inhomogeneity of the sun's motion, the time required between two fixed qi is different.In order to solve this problem mathematically, Yixing created the quadratic interpolation method with unequal spacing. "Da Yan Li" has also made great progress in the calculation of solar and lunar eclipses and five-star motions. For example, considering the impact on eclipses, a set of empirical formulas for calculating the impact of parallax has been established. "Da Yan Li" is divided into seven chapters, and the content and structure are very systematic, which shows that the calendar system in ancient my country has been fully mature.The subsequent calendar revisions generally followed the structure of the "Da Yan Li".After the mid-Tang Dynasty, Cao Shizhen [wei pseudo] first used a quadratic function to describe the unevenness of the sun's annual movement in "Fu Tian Li"; after that, Biangang also introduced the quadratic function into the yellow equator in "Chongxuan Calendar" For the conversion of coordinates and the calculation of the moon's yellow latitude and eclipse difference, the cubic function is used in the calculation of the shadow length, and the quartic function is used in the calculation of the sun's declination and day-night omission.These works made the high-order function method become another important method for the calculation of the ancient Chinese calendar, and created a new tradition of formulating various astronomical tables and their algorithms.
In the Song Dynasty, calendar calculations developed again.The various calculations in Zhou Cong's "Morrow Calendar" all use higher-order functional formulas, and use quintic functions.This calendar is the most formulaic calendar in ancient China.Later, Yao Shunfu took another step forward in the "Jiyuan Calendar", and many empirical calculation formulas were simpler and more precise than the previous calendars.Among the calendars of the Song Dynasty, Yang Zhongfu's "Tongtian Calendar" is the most creative.The length of the tropical year in this calendar is 365.2425 days, which is exactly the same as the Gregorian calendar adopted by Europe after 1582 AD, but it is nearly 400 years earlier.Not only that, Yang Zhongfu also pointed out that the length of the return year is not fixed, and its value is larger than the present, which is an important discovery in the history of astronomy.
The peak of the development of the ancient Chinese calendar was the "Shoushi Calendar" compiled by Guo Shoujing and others in the Yuan Dynasty. "Shoushi Li" absorbed the advantages of previous calendars, and developed and innovated, becoming an epoch-making product in the history of ancient Chinese calendars.
"Shoushi Li" is the best calendar in ancient China, compiled by Wang Xun, Guo Shoujing and others in Yuan Dynasty.The first draft of the calendar was completed in the seventeenth year of Yuan Shizu to Yuan Dynasty (AD 1280), and it was issued to the world in the second year.The final draft of the calendar will not be until the 23rd year of the Yuan Dynasty (1286 A.D.).
As early as when Yuan Shizu Kublai Khan first came to the throne, his adviser Liu Bingzhong suggested reforming the calendar. After Kublai Khan captured Jiangnan in 1276, he ordered the reform of the calendar, set up the Taishi Bureau, appointed Zhang Wenqian and Zhang Yi as the main leaders, Wang Xun as the actual person in charge, and Guo Shoujing as his deputy.Wang Xun (1235-1281 A.D.) styled Jingfu, was born in Tang County, Hebei Province.Guo Shoujing (AD 1231-1316), styled Ruosi, was born in Xingtai, Hebei.Both Wang and Guo were proficient in astronomy and mathematics when they were young, and they were both students of Liu Bingzhong when he lived in seclusion in Zijin Mountain, southwest of Xingtai.In the revised calendar, Wang Xun was in charge of calculations, and Guo Shoujing was in charge of manufacturing instruments and observations.Later, Xu Heng and Yang Gongyi, famous scholars in the south, were successively hired to work on expounding the calendar.At that time, there were dozens of astronomical workers from the north and the south who participated in the reform of the calendar.After four years of hard work, the first draft of the new calendar was completed, and Emperor Shizu of the Yuan Dynasty named it "Shou Shi Li", which was taken from the old saying "respect for the time of the people". The new calendar was promulgated in 1281.In the same year, Wang Xun died of illness, and Zhang Wenqian, Zhang Yi, and Xu Heng also died around this time, and Yang Gongyi resigned.In the next few years, Guo Shoujing independently completed all the work of sorting out and finalizing the new calendar.Later generations often think that Guo Shoujing is the author of "Shoushi Li", but in fact the completion of "Shoushi Li" is the crystallization of the collective wisdom of a group of outstanding talents at that time.
"Shoushi Li" now only narrowly refers to the second volume and seven chapters of "Shoushi Lijing" preserved in "Yuan Shi·History".The seven chapters are: 1. Bu Qi Shuo, which introduces the method of calculating the time of solar terms, Shuo, Xian, and Wang; , Find the daily speed and position of the sun on the ecliptic.Introduce the mutual derivation of the sun's yellow and equatorial longitude; 4. Step away from the moon, find the movement of the moon and the intersection point of the lunar path and the equator, etc.; 6. Step rendezvous, the calculation method of the solar and lunar eclipse; 7. Step five stars, calculate the movement and position of the five planets. The chapter structure and content of "Shi Shi Li Jing" basically followed the calendar tradition since "Da Yan Li".However, in a broad sense, "Shoushi Calendar" should also include the calendar theory and astronomical observation results related to the Shishi Calendar, which are the results obtained by Guo Shoujing's arrangement of the new chronology: "Tuibu" seven volumes, "Licheng" two volumes , "Draft of Calendar Discussion" in three volumes, "Zhuanshen Selection" in one volume, and "Upper, Middle and Lower Three Calendar Notes" in 12 volumes. In 1286, Guo Shoujing was promoted to Taishiling, and wrote two volumes of "Time Notes", one volume of "Modification of Origin and Flow", two volumes of "Yixiang Fashi", 10 volumes of "Er Zhi Sun Ying Ying Kao", and 50 volumes of "Five Stars and Fine Lines". , "Ancient and Modern Cross-eating Test", one volume, "New Survey of Twenty-Eight Constellations, Miscellaneous Sitting Stars Going to the Pole", one volume, "New Test of Unknown Stars", one volume of "Yue Li Kao", and so on.It is a pity that most of these books have not been handed down.North Korea and other countries preserve "Licheng".In recent years, people have discovered "Sanyuan Lie She Ru Xing Ji Ji Ji" from the Ming Dynasty manuscript "Tian Wen Hui Chao" in the Beijing Library, and they think it is an improvement of Guo Shoujing's "New Measurement of Twenty-eight Mansions Miscellaneous Sitting Stars Entering Xing Xing Xing Ji Ji". transcript.In addition, "Yuan History·Historical Records" preserves "Shoushi Liyi" written by Li Qian under the order of Yuan Shizu, which should be written based on "Liyi Draft" and other relevant materials.The information about the instruments created by Guo Shoujing in "Yuan History · Tianwen Zhi" may also be rewritten according to the book "Yixiang Fashi".All of these can be regarded as an integral part of the "Shoushi Calendar".
"Shoushi Calendar" is an excellent calendar created on the basis of summarizing previous calendar experience and careful observation and calculation.It has made brilliant achievements in the accuracy of astronomical observation data and the mathematical method of calendar calculation, which are generally referred to as "seven things of examination and correction" and "five things of creation".
Guo Shoujing attached great importance to the role of astronomical observation in the calendar reform.He believes: "The essence of the calendar lies in the test, and the instrument of the test is not prior to the instrument." He really grasped the key to the calendar.In order to obtain accurate astronomical data, Guo Shoujing and others conducted astronomical observations on an unprecedented scale.They set up observatories in 27 places including Beijing, Taiyuan, Chengdu, and Leizhou, twice as many as in the Tang Dynasty.Guo Shoujing also transformed and innovated many astronomical instruments, such as Guibiao, Jianyi, Yangyi, Qibaodenglou, Xingdun timing instrument, etc. There are more than a dozen kinds.These works have made the astronomical data in the "Shoushi Calendar" far more precise than previous generations.For example, the Sui Shi (return year) in "Shou Shi Li" is 365.2425 days, which is calculated by Guo Shoujing and others after nearly four years of precise measurement, combined with reliable data in the previous calendar.It is the same as the actual year of Yang Zhongfu's "Tongtian Calendar" in the Southern Song Dynasty, and it is the same as the return year value of the Gregorian calendar commonly used in the world today.For another example, the Shuo Ce (that is, the synodic month) in "Shoushi Li" is 29.530593 days, and the precision value of the modern synodic month is 29.530589 days, the difference between the two is 0.000004 days, and the accuracy is indeed very high.In addition, the anomalous month in the calendar is 27.554608 days, and the node month is 27.212224 days, and the accuracy is also very high.
Since the Han Dynasty, the intersection angle between the ecliptic and the ecliptic plane (that is, the angle between the ecliptic plane and the equator plane) has been considered to be 24 degrees. After more than 1,000 years, no one has corrected it.In fact, the angle between yellow and red is decreasing year by year.In "Shou Shi Li", based on precise astronomical measurement, Guo Shoujing calculated the intersection angle of yellow and red as 23°90′30″ (ancient degree), which is converted into today’s 360-degree system as 23°33′33″9, and the exact value It is 23°31'58", and the error is only 1.6'. In addition, the average error of the measurement of the twenty-eight mansions in "Shoushi Calendar" is only 4'.5, which also reached the most advanced level in the world at that time.
The "Shoushi Calendar" also completely abolished the long-used Shangyuan Jinian.The old calendarists calculated the year of the Shangyuan to seek a so-called "auspicious" starting point for timing. It is necessary to "unite the sun and the moon", "five stars and pearls", that is, the sun, the moon and the five stars are seen on one side.All these conditions are met, and as the starting point of timing, it is Shangyuan.The accumulative year is the number of years accumulated from the calendar year to the Shangyuan year.This shows how heavy the work is. "Shoushi Calendar" abandoned this traditional algorithm, but based on actual observation data, so that the winter solstice of Xinsi Sui in the eighteenth year of the Yuan Dynasty (AD 1281) was the epoch, which made the calculation method more simple and reasonable.This method is consistent with that used in modern times.This is a major reform of the ancient Chinese calendar.
In addition to verifying astronomical data based on actual measurements, "Shoushi Calendar" also applied the most advanced mathematical knowledge at that time to astronomical calculations.After assiduous research, Guo Shoujing and others created five new calculation methods in astronomy in the "Shoushi Calendar", that is, calculating the movement of the sun and the moon by using the method of travel, calculating the speed of the sun on the ecliptic every day, and calculating the daily orbit of the moon. The speed of the earth, etc.; use the sagittal cutting circle method to push the sun yellow, equatorial latitude and longitude, and calculate the intersection point of the lunar path and the equator. The recruiting technique in "Shoushi Li" is equivalent to the interpolation method of three or higher orders, and its astronomical basis is to consider the non-uniform motion of the sun, moon and five stars.This problem was solved by Liu Zhuo in the Sui Dynasty and a group in the Tang Dynasty by using equal-spaced quadratic interpolation method and unequal-spaced quadratic interpolation method respectively, but they were not thorough. "Shoushi Calendar" adopts the principle of three-time difference interpolation method, which has become a major pioneering work in the calendar.The sagittal cut circle method is similar to two spherical trigonometry formulas. It is a unique spherical trigonometry in my country and a great innovation in the application of mathematical methods in astronomy.
In "Shoushili", the method of expressing data with complex fractions is also abolished.The ancient Chinese calendar generally used fractions to represent the odd zero part after the integer of astronomical data, and the calculation was very cumbersome.Although the "Shenlong Calendar" mentioned by Nangong in the Tang Dynasty and the "Futian Calendar" written by Cao Shiluo had already introduced the concept of decimal numbers, they were not taken seriously by ordinary astronomers.It was not until 500 years later that people such as Wang Xun and Guo Shoujing adopted it in the "Shoushi Calendar". "Shoushi Calendar" uses a day as 100 quarters, a quarter as 100 minutes, and a minute as 100 seconds. Units below seconds are also in hundreds, so the data of a day can be accurate to the sixth decimal place, with high precision and scores The notation is much simpler and clearer.
"Shoushili" is the oldest and most precise calendar in ancient my country. It was used for more than 360 years from 1281 to the end of Ming Dynasty. It was renamed "Datongli" in Ming Dynasty. "Shouji Calendar" has also been spread overseas. During the Yuan Dynasty, the Korean and Koryo Dynasty copied "Shouji Calendar" intact. The "Zhenxiang Calendar" adopted by Japan in 1684 also used the principles and methods of "Shouji Calendar".
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