The armillary sphere made by Zhang Heng is a performance instrument used to demonstrate the movement of the celestial sphere. Its outer outline has the image of a ball, which is consistent with the armillary sky theory advocated by Zhang Heng, so it is named the armillary sphere. This armillary sphere is recorded in three places in "Jin Shu Tian Wen Zhi". One is in the "Celestial Bodies" section, which quotes the Jin Dynasty scientist Ge Hong: "Zhang Pingzi made a copper armillary sphere, turned it in a secret room with water leakage, and asked those who were waiting to close their doors and sing. In order to tell the observer of the sky at the spiritual platform, he said: Xuanji added that a certain star has just appeared, a certain star has been hit, and a certain star has disappeared now, all of which are consistent." There is another paragraph with more specific details in the "Yi Xiang" section. Description: "Zhang Heng also controls the muddy image. It has internal and external regulations, the north and south poles, and the yellow and equator. It lists the twenty-four qi, the twenty-eight constellations, the central and external star officials, the sun, the moon, and the five latitudes. It is transferred to the upper room of the palace by leaking water. The stars are in and out. , does not correspond to the sky. Because of its fierceness, it turns the auspicious wheel at the foot of the stairs, rising and falling with the moon. "It is also called the muddy image, which is a reflection of the irregular naming of the instrument in the early days. It does not mean that the armillary sphere is two different instruments. The third part is at the end of the "Yi Xiang" body, talking about the size of Zhang Heng's armillary sphere: "The ancient armillary sphere was divided into one degree by two, and the ordinary week was seven feet, three inches and a half. Zhang Heng's new system was divided into four parts, and the ordinary week was divided into one degree. Four feet, six inches and one minute." From these three records, we can see that the main body of Zhang Heng's armillary sphere is similar to the current celestial sphere. However, Zhang Heng's celestial sphere is painted with 444 officials and 2500 stars named by him. The twenty-four qi are drawn on the yellow and equator of the armillary sphere. There is a rotatable polar axis running through the south and north poles of the armillary sphere. There should be a horizontal ring in the center of the celestial sphere to represent the horizon. There should also be a pair of meridional double rings sandwiching the north and south axes and perpendicular to the horizontal ring. The center of the double rings is the meridian of the observation site. When the celestial sphere rotates, some of the stars on the sphere are exposed above the horizon ring, which is the star emergence; some stars are directly crossing the meridian, which is the star center; and the stars that submerge below the horizon ring are the stars. There are some stars on the celestial sphere that always rotate on the horizon ring without falling below it. The limit of this part of the sky is a small circle with the North Pole as the center and the local latitude as the radius, which was called the inner gauge at the time. Similarly, there is a small circle with the South Pole as the center and the local latitude as the radius, which is called the outer circle. The heavens within the outer limits will never rise above the horizon. There are also sun, moon and five stars on Zhang Heng's celestial sphere. In addition to the diurnal rotation of these seven celestial bodies, which rise in the east and set in the west together with the celestial sphere, they also have complex movements on the background of the starry sky. To simulate these complex movements is far beyond the capabilities of ancient mechanical technology. Therefore, they should be regarded as just an appendage attached to the celestial sphere and ready to be moved by hand. The purpose of the movement is to make the positions of the sun, moon, and five stars on the background of the starry sky match their true positions.
Multi-level engraved bezel
The engraved bezel is the most important timing instrument in ancient my country. The three engraved leaks from the Western Han Dynasty that have been handed down so far are all so-called "water-draining sinking arrow-type single leaks". This kind of engraved cup only has a cylindrical water container. A small tube protrudes from the bottom of the device and drips water outward. The water level in the container continues to decrease. The carved arrows held by the arrow boat (i.e. float) floating on the water gradually descended. The engraved arrow passes through the hole in the container lid and extends outward. The time can be read from the edge of the hole. The timing accuracy of this kind of leak engraving mainly depends on whether the leakage drips out at a uniform speed. The dripping speed changes in proportion to the water pressure at the nozzle. That is, as the water drips away, the water level in the container becomes lower and lower, and the water drips out slower and slower. In order to improve the uniformity and accuracy of the engraving operation, the ancients thought of two steps. The first step is to change the water-draining sinking arrow type to the water-storage floating arrow type, that is, collect the water dripping from the engraved leak into another cylindrical container, and put the arrow boat and the engraved arrow in this water storage container Inside, the accumulated water gradually increased, and the arrow boat gradually rose upwards holding the carved arrows, from which the time reading was obtained. The second step is to add a dripper on top of the dripper. The water dripping from the upper dripper replenishes the water lost from the lower dripper. In this way, the drop of the water surface of the lower dripper can be greatly delayed, thereby improving the stability of the water outlet speed of the lower dripper. This kind of leakage is called secondary leakage. If we follow this idea and analogy, we can add one level above the two-level engraving, and then the stability of the engraving operation can be improved. This becomes level three, and so on. Probably after the Sui and Tang Dynasties, China developed four-level and above-level engraving. However, when did the critical step from single leakage to secondary leakage occur? There is no obvious information provided in Zhang Heng's previous documents and archaeological objects.
However, in an article titled "Zhang Heng's Leakage Transformed into an Armillary Sphere System", it is described that the engraved leaks used by Zhang Heng were a set of secondary engraved leaks. This article is probably the work of Zhang Heng or his contemporaries. The original text has been lost, and now only a few fragments remain in Volume 25 of "Ji Xue Ji" in the early Tang Dynasty. The text is as follows: "Use copper as a vessel, then stack it up and place it in different places. In fact, use clear water, and make holes in each bottom. Use a jade dragon to spit water into two pots, with night on the right and day on the left." "(The lid is also) made of gold and bronze. The immortal is placed on the left pot; the golden disciple is placed on the right pot." "Hold the arrow with your left hand and carve it with your right hand to tell the difference between morning and evening." The so-called superimposition refers to two engraved patterns placed one on top of the other. The so-called differential placement means that the upper and lower containers are placed so that they are not overlapping but staggered. The so-called stacking and differential placement means that there are three layers of containers stacked in a staggered manner. As for the kettle below, which is divided into left and right kettles, this is because the ancient time system was different at night and during the day, so Zhang Heng simply used two kettles. At the same time, this also facilitates the continuous operation of the engraving system.
Zhang Heng’s Armillary Sphere
Zhang Heng once wrote an article after creating the Armillary Sphere. The full text of this article has been lost. It was only in the Liang Dynasty that Liu Zhao quoted a large section of it when he annotated "Lü Li Zhi" in the Book of the Later Han Dynasty and passed it down to the world. Liu Zhao's note titled this passage "Zhang Heng's Armillary Sphere". Calling it the "armillary sphere" may be a simplification made by Liu Zhao. In ancient times, the naming of instruments was not strict. Although later generations standardized the term "armillary sphere" to specifically refer to observation instruments, before the Sui and Tang Dynasties, "armillary sphere" could also be used for performance instruments. Whether this article quoted by Liu Zhao and the aforementioned "Zhang Heng's Leakage of Water to the Armillary Sphere System" are originally the same article is impossible to test. However, since the title text of the two is very different, it is reasonable to say that they are two articles. No matter what the matter is, if it is quoted by Liu Zhao, recent people have proved that it should be the original work of Zhang Heng. When we examine this passage quoted by Liu Zhao, there are approximately three contents. The first part talks about the mutual relationship between the celestial pole, the equator and the ecliptic in the armillary sphere theory and the armillary sphere, as well as the degrees away from each other. The second part talks about how to find the so-called equatorial difference and the changing rules of this difference. This is the longest part of this fragment. The third part talks about the distance between the 28 constellations of the ecliptic and the positions of the ecliptic at the winter and summer solstice points. Two important pieces of information can be obtained from a careful study of this fragment. First, the article introduces the method of directly comparing on the celestial sphere to obtain the degree of the ecliptic: use a piece of bamboo strips to thread through the two poles of the celestial sphere. The length of the strip is equal to the semicircle of the celestial sphere. Starting from the winter solstice, move the bamboo strips one degree along the equator, read the ecliptic degree intercepted by the center line of the bamboo strips, and subtract this number from the corresponding equatorial degree to obtain the ecliptic degree at that equatorial degree (or ecliptic degree). Equatorial difference. From this comparison method, we can understand that ancient China did not have the concept of the yellow meridian circle like ancient Greece. The ecliptic degrees in ancient China were actually obtained by intercepting arc segments on the ecliptic based on the right ascension circle. This degree of yellow longitude obtained from the basic point of the red pole is now known as the "pseudo yellow longitude", "the extreme yellow longitude" (actually it is called the "red pole yellow longitude") and so on. For a celestial body like the sun that moves on the ecliptic, its false ecliptic longitude and true ecliptic longitude are equal. For celestial bodies outside the ecliptic, there is a difference between the two (except, of course, for the points exactly on the two solstice circles - the great circles of the winter and summer solstice points and the red and ecliptic poles). The further away, the greater the difference. Secondly, the article gives the changing rules of the so-called yellow-equator difference. Divide the equator into 24 equal parts. Use the above method to find the equivalent ecliptic degree for each segment. The difference between this degree and the corresponding equatorial degree is the so-called equatorial difference. This is the first ecliptic-equator difference law obtained in ancient China. The equatorial difference later played an important role in the calculation of the Chinese calendar. As the pioneer, Zhang Heng's contribution was also indelible. In addition to the text quoted by Liu Zhao, Ge Hong quoted in the "Astronomical Records" of the "Shu" of the Jin and Sui Dynasties quoted a text titled "Notes on the Armillary Sphere"; in the "Kaiyuan" of the Tang Dynasty The first volume of "Zhao Jing" contains a paragraph titled "Annotations on Zhang Heng's Armillary Sphere" and a paragraph titled "Annotations on Zhang Heng's Armillary Sphere". Comparing these three paragraphs with the article "The Armillary Sphere" quoted by Liu Zhao, we can see that the text in the "Commentary on the Armillary Sphere" quoted by Ge Hong is not found in the "Commentary on the Armillary Sphere" cited by Liu Zhao, but in the "Commentary on the Armillary Sphere by Zhang Heng". The remaining parts of "Zhang Heng's Notes on the Armillary Sphere" and "Zhang Heng's Notes on the Armillary Sphere" are divisions of the text quoted by Liu Zhao, but with some additions and deletions. In addition, there are three short paragraphs titled "Armillary Sphere" in Volume 26 of "Kaiyuan Divination", "Star Filling Divination"; there is a title in the small note under "Tian Shi Yuan Divination" in Volume 65. This is a sentence from "Zhang Heng's Armillary Sphere". These four paragraphs are not quoted by Liu Zhao.
To sum up the above situation, two conclusions can be drawn: First, Liu Zhao quoted only an excerpt from Zhang Heng's "Armillary Sphere". The content of Zhang Heng's original text is richer. But to what extent it is rich has yet to be determined. Moreover, in the bibliographic works since "Sui Shu·Jing Ji Zhi", the article "Armillary Sphere" (or "Armillary Sphere") has always been marked only as "one volume". Therefore, it is not expected that there will be a surprising amount of discrepancy. Secondly, Zhang Heng's article "Armillary Sphere" has indeed been annotated by someone, and the illustrations have also been supplemented. The annotations and illustrations were probably not written by one person, and probably not by Zhang Heng himself, otherwise there would not have been a separate article on "The Armillary Sphere". Among these passages related to the Armillary Sphere, what contemporary researchers are most concerned about is whether the "Notes on the Armillary Sphere" quoted by Ge Hong is Zhang Heng's original work. Because this passage has always been regarded by modern researchers as the representative work of ancient Chinese Huntian theory, and its status is even regarded as higher than that of "Lingxian". In the past, people certainly regarded it as Zhang Heng's work. But by the end of the 1970s, some people completely rejected this. It is believed that all the Armillary Sphere, Notes on the Armillary Sphere, Notes on the Armillary Sphere, Notes on the Armillary Sphere, etc., with or without the name of Zhang Heng, are the works of later generations. Later, someone else made a comprehensive refutation of it and defended the traditional view. This controversy lasted for 12 years. Now it seems that the argument that completely denies Zhang Heng’s "Armillary Sphere" has been handed down to ancient times has basically failed. That is to say, it is at least certain that the "Armillary Sphere" cited by Liu Zhao is Zhang Heng’s original work. But the denier still made his historical contribution by inspiring people to pay attention to the complications in the circulation of ancient documents. For example, in the past, people did not realize that the article "The Armillary Sphere" also included planets and stars. At the same time, there are still reasons to doubt whether the passage in the Armillary Sphere Notes quoted by Ge Hong is Zhang Heng's original note. Because first, this paragraph is called "Notes", and in ancient documents, there is an essential difference between adding the word "Notes" or not. Those without the word "note" refer to the original text, and those with the word "note" refer to the original text. Since there is an "Armillary Sphere" without the word "note", the "Notes on the Armillary Sphere" with the word "note" is not only the original text of the "Armillary Sphere", but also annotations. Secondly, in terms of its correctness, the ideas of "Comments on the Armillary Sphere" do not go beyond "Lingxian". If we regard the earth in "Lingxian" as floating on the water, living alone in the center of the sky, and being much smaller than the sky, then this is consistent with what the "Annotations to the Armillary Sphere" said: "The earth is like a yellow chicken, living alone in the center of the sky." There is no contradiction in these programmatic words. On the contrary, the "Notes on the Armillary Sphere" holds that "the North Pole...is thirty-six degrees above the ground." This passage cannot be the conclusion of Zhang Heng who paid attention to actual observations. Nanyang, the birthplace of Zhang Heng, and Luoyang, the place where he has been the Taishi Ling for a long time, do not have the phenomenon of thirty-six degrees above the North Pole. Based on his experience of traveling to many places across the country, it seems that Zhang Heng should not have the concept of a fixed value for the Arctic. This is probably the reason why he did not mention the value of the Arctic land in his article "Lingxian". In view of this, it is better to regard the authorship of "Notes on the Armillary Sphere" as doubtful and look forward to future research and discovery.
Zhang Hengrui Wheel
The pod is an unprecedented mechanical device. The so-called pod is a mythical plant. It is said that it grew up under the steps of Emperor Yao's residence. With the appearance of the new moon, one pod grows per day, and by the full moon, 15 pods grow. After the full moon, one pod is dropped a day. In this way, by counting the number of pods, you can know which day of the synodic month it is today and the moon phase on that day. This myth tortuously reflects the progress of the astronomical calendar during the reign of Emperor Yao. Zhang Heng's mechanical device was inspired by this myth. It is said that "it waxes and wanes with the moon, rises and falls according to the calendar", and its function is equivalent to the date display in today's clocks. Unfortunately, there are no historical records about the specific power and transmission devices in Zhang Heng's armillary sphere. Only fragments of Zhang Heng's article on the armillary sphere remain. There is also no mention of power and transmission issues in this clip. In recent decades, people have used modern mechanical technology knowledge to conduct some discussions on this device. Initially, people thought it consisted of a water wheel driving a set of gear systems. However, there are records that clearly state that the Armillary Sphere was "returned by leaking water", and there are records that clearly stated that the leaking water flowed into a water-holding pot to measure time. Therefore, this leakage water cannot be used to push the original water wheel. Therefore, the solution of motive water wheel and gear transmission system has been questioned in recent years. Recently someone came up with a completely different design. They used a rope to wrap the float in the clepsydra around the polar axis of the celestial sphere and connect it to a counterweight.
When the clepsydra receives water, the amount of water in the kettle increases, the float rises, and the counterweight at the other end of the rope descends. At this time, the rope affects the polar axis of the celestial sphere, causing rotation. This kind of structure is more reasonable than the structure of water wheel driving gear train. Because (i) the gear structure in Zhang Heng's era was still quite rough and could not meet the accuracy requirements of Zhang Heng's armillary sphere. (ii) This gear system must contain a considerable number of gears, and the more gears there are, the greater the power required to drive the gears to rotate. The small and slow flow of water in the clepsydra makes it more difficult to drive the system. (iii) More importantly, the flowing water from the clepsydra mentioned above cannot both push the instrument and display the time. The rope transmission controlled by the float can avoid the above three major difficulties. Small simulation experiments have been carried out on this idea. Using a cylindrical float with a diameter of 6.5 cm and a height of 3.5 cm and a counterweight weighing 27 grams, the rotating shaft with a mass of 1040 grams can be driven to rotate relatively uniformly through the rope. Its uneven jumps only occur a few times in a day and night, and the jump range is mostly below 2°. This error is allowable under ancient conditions. Therefore, it seems that the float-counterweight-rope system is more reasonable than the motive water wheel-gear system. However, Zhang Heng's instrument was a large copper object with a diameter of more than 1 meter. The current small-scale experiments are not enough to guarantee success with Zhang Heng's instrument. Further simulation experiments with very similar conditions are needed to draw more credible conclusions. Regardless of the actual situation of Zhang Heng's power and transmission system, in short, he used a mechanical system to achieve a mechanical movement that is synchronized with the rotation of the celestial sphere in nature. This approach itself is unprecedented in China. From this, we have a tradition of making water-moving instruments, which strive to use mechanical movements to accurately reflect the diurnal rotation of the celestial sphere. Until the invention and adoption of atomic clocks in the second half of the 20th century, all mechanical clocks were based on the rotation of the earth, that is, the daily rotation of the celestial sphere. Therefore, China’s water transportation ritual tradition was the beginning of mechanical clocks and watches in later generations. It is true that in the Hellenistic era from the 4th century BC to the 1st century BC, a float anaphoric clock also appeared in the West. Its structure is similar to the armillary sphere of float-balance-weight-rope system that people recently imagined. However, what it brought was not a celestial globe, but a flat star map. However, in the subsequent Roman era and the dark Middle Ages, the tradition of floating bells was completely interrupted and disappeared. Therefore, China's water transportation ritual tradition is of extremely important significance to the development of mechanical clocks and watches in later generations. The achievements of Zhang Heng, the founder of this tradition, are naturally indelible. Judging from the descriptions of people at the time, Zhang Heng's armillary sphere could perfectly match the rotation of the natural celestial sphere, "all of them are in perfect harmony", which shows that the stability of the rotation speed of the armillary sphere is quite high. The armillary sphere is based on the operation of the inscription. From this we can know that Zhang Heng’s engraving skills are also very good.
Calendar Discussion
Zhang Heng once participated in a major calendar discussion in the Eastern Han Dynasty, which happened in the second year of Emperor Yanguang of Han'an (AD 123). According to "Hanshu Lvli Zhi", Zhang Heng was serving as Shangshulang at that time. The cause of this great discussion was that some people, based on superstitious concepts such as prophecies and disasters, criticized the more scientific "Sifen Calendar" of the Eastern Han Dynasty that was in use at that time, and proposed that the "Jiayin Yuan Calendar" which was suitable for prophecies should be used instead. Some people started from the view that Emperor Wu of the Han Dynasty "repelled the barbarians and expanded the territory and enjoyed the country for a long time" and believed that we should go back and adopt the "Taichu Calendar". Zhang Heng and another minister, Zhou Xing, criticized and challenged the above two opinions, leaving the proposers of these two wrong opinions either speechless or wrong in their answers, thus contributing to preventing the retrogression of the calendar. During the discussion, Zhang Heng and Zhou Xing also studied many years of astronomical observation records, compared them with the theoretical calculations of various calendars, and proposed an appraisal. They believed that the "Nine Ways of Law" was the most precise and recommended its adoption. Indeed, the numerical values ??of the length of the tropical year and the length of the synodic moon in the "Nine Paths Method" are more precise than those in the "Taichu Calendar" and the Eastern Han Dynasty's "Four Points Calendar". Moreover, the "Nine Ways of Law" recognized that the moon's movement speed was uneven, while other calendars at that time were only calculated based on the uniform speed of the moon. Therefore, the conjunction and lunar calendar calculated by the "Nine Ways of Law" are more consistent with astronomical reality than other calendars at that time. However, if calculated according to the "Nine Ways of Law", it is possible that there will be three consecutive 30-day big months, or two consecutive 29-day small moons, etc.
According to the calendar arrangement that people have been accustomed to for thousands of years, the big and small months have always been connected. At most, two big months have been connected once every 17 months, and there have never been three big months connected, let alone two small months. connected phenomena. Therefore, the phenomenon of connecting three big months or two small months brought about by the "Nine Ways of Law" is difficult for people with conservative habits to accept. In this way, Zhang Heng and Zhou Xing's suggestion to adopt the "Nine Ways of Law" was the most reasonable and progressive one at the time, but it failed to pass in this great discussion. This is a loss in Chinese history. The adoption of uneven monthly movements into the calendar was delayed for more than half a century. It was not until Liu Hong's "Qianxiang Calendar" that it was officially adopted for the first time.
Zhang Heng’s seismograph
Another scientific field in which Zhang Heng made outstanding contributions is seismology. His representative work is the invention of the Houfeng Seismometer, which has shocked the past and present. However, it must be stated that the seismograph seen in China today is not the one invented by Zhang Heng, but restored by later generations. The seismograph invented by Zhang Heng had long been destroyed by war. The seismograph was invented in the first year of Yangjia (132 AD). This was his last major task in his tenure as Taishi Ling. There is a more detailed record of this incident in "Book of the Later Han·Zhang Heng Biography". Since the 19th century, some people have been trying to use modern scientific and technological knowledge to restore Zhang Heng's great invention based on the records in the "Book of the Later Han". In the 1950s, Mr. Wang Zhenduo "restored" the Zhang Heng seismograph (see picture on the right), which was considered scientific and was even widely included in primary school textbooks. However, the seismometer restored by Wang Zhenduo has been shown in public many times. It either cannot move or stamping its feet will be regarded as an earthquake. However, people mistakenly believe that Wang Zhenduo's restoration was Zhang Heng's original invention. Therefore, domestic and foreign scholars have long Start denying it over and over again. Many of them spoke fiercely, which had a great negative impact on the reputation of Zhang Heng and even the entire ancient Chinese science and technology. Now it has been proven that it was not Zhang Heng's seismometer that was wrong, but Mr. Wang Zhenduo's restoration that was wrong in principle. However, Wang Zhenduo's restoration of the appearance of the seismometer is still very successful, and this should be affirmed.
As for the structure of the seismometer, there are currently two popular versions: Wang Zhenduo's model, that is, the "Du Zhu" is a cylinder shaped like an inverted wine bottle, and the mechanism that controls the dragon's mouth is around the "Du Zhu". This model has recently been largely dismissed. Another model proposed by Feng Rui of the Seismological Bureau, that is, the "Du Zhu" is a hanging pendulum (seen in Yuan Hong's "Hou Han Ji"). There is a small ball below the pendulum, and the ball is located at the intersection of the "meter" shaped slides (i.e. " ("Guan" mentioned in "The Book of the Later Han·Zhang Heng Zhuan"), during an earthquake, the "Du Zhu" moves the ball, and the ball fires the mechanism that controls the dragon's mouth, causing the dragon's mouth to open. In addition, Feng Rui's model also changed the toad from facing the bottle to facing away from the bottle and acting as the feet of the instrument (see left picture). The model has been simulated and tested, and the results are consistent with historical records. Zhang Heng's instrument has good performance and once predicted an earthquake in Luoyang. According to records at the time: "It is tested by things, and the agreement is like a god." It can even detect earthquakes that happened thousands of miles away but no one in Luoyang felt it. earthquake. This instrument not only won the admiration of people at the time, but also was admired by today's scientists. There are frequent earthquakes in the world, but it was only after the 19th century that instruments could be used to observe earthquakes abroad. Houfeng seismograph is the ancestor of seismographs in the world. Although its function is still limited to measuring the approximate location of the epicenter, it surpasses the development of world science and technology by about 1,800 years!