Zhang Heng

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Zhang Heng (Chinese: 張衡; pinyin: Zhāng Héng; Wade-Giles: Chang Heng) (AD 78–139) was an astronomer, mathematician, inventor, geographer, cartographer, artist, poet, statesman, and literary scholar from Nanyang, Henan during the Eastern Han Dynasty (AD 25–220) of China. He was educated in the capital cities of Luoyang and Chang'an, began his career in a minor civil service in Nanyang, and eventually became Chief Astronomer, Prefect of the Majors for Official Carriages, and then Palace Attendant at the imperial court. With unyielding stances on certain historical and calendrical issues, Zhang was seen as a somewhat controversial figure and hence was barred from becoming an official court historian. His political contention with palace eunuchs over influencing the policies of Emperor Shun (r. 125–144) led to his retirement from the central court to serve as an administrator of Hejian in Hebei. He retired and returned home to Nanyang for a short period of time, but was recalled to serve at the capital once more in 138, where he died a year later.

Zhang had extensive knowledge of mechanics and gears, applying this to several of his known inventions. He invented the world's first water-powered armillary sphere to represent astronomical observation,^[1] improved the inflow water clock with an additional tank,^[2] and invented the world's first seismometer device, which discerned the cardinal direction of earthquakes from incredibly far distances.^[1][3][4] He improved previous Chinese calculations of the formula for pi. In addition to recognizing some 14,000 stars in his extensive star catalogue, Zhang also posited theories about the moon and its relationship to the sun, specifically the moon's sphericity, its illumination by reflecting sunlight on one side and remaining dark on the other, and the nature of solar and lunar eclipses. His fu poetry, shi poetry, and rhapsodies were also renowned and commented on by later Chinese writers. For his scholarship and ingenuity, he was given many posthumous honors in his own day and throughout the centuries.

[edit] Life

[edit] Early life

A 2nd century lacquered basket with paintings of famous figures from Chinese history; Zhang Heng became well-versed at an early age in the Chinese classics and the philosophy of China's previous sages

Born in Xi'e of Nanyang Commandery (located north of modern Nanyang City, Henan province), Zhang Heng came from a distinguished yet not incredibly affluent family.^[5][6][7] His grandfather Zhang Kan had been a governor of a commandery and one of the leaders supporting the restoration of the Han Dynasty by Emperor Guangwu (r. 25–57), following the death of the usurper Wang Mang and his short-lived Xin Dynasty (AD 9–23).^{[5][8][9][10]} At age ten, Zhang's father died, leaving him in the care of his mother and grandmother.^[9] An accomplished writer in his youth, Zhang left home in 95 to pursue his studies at universities in the capital cities of Chang'an and Luoyang.^[5] While travelling to Luoyang, Zhang passed by a hot spring at Mount Li, and dedicated one of his earliest fu poems to it, the Wenquan (溫泉).^[11] Studying for some years at Luoyang's Imperial University (Taixue), he became well-versed in the classics and befriended notable persons such as Cui Yuan (78–143), Ma Rong (79–166), and Wang Fu (78–163).^[5][7] With his talents known, many promotions were offered to Zhang that would have greatly advanced his career, such as positions as one of the Three Excellencies, yet he acted modestly and turned these invitations down.^[5][11] At age twenty-three he returned home with the title Officer of Merit in Nanyang, staffed as a master of documents under the administration of Governor Bao De (in office from 103–111).^[5][8][7] Since he was charged with composing inscriptions and dirges for Bao De, he gained experience in writing official documents.^[8] He spent much of his time writing rhapsodies on the capital cities, and when Bao De was recalled to the capital in 111 to serve as a minister of finance, Zhang continued his literary works at home in Xi'e.^[5][8][11] Zhang Heng began his studies in astronomy at the age of thirty, and began publishing his works in astronomy and mathematics.^[8]

[edit] Official career

In 112, Zhang was summoned to the court of Emperor An of Han (r. 106–125), who had heard of Zhang's expertise in mathematics.^[8] When he was nominated to serve at the capital, Zhang was escorted by carriage to Luoyang where he became a court gentleman working for the Imperial Secretariat.^[5][8] He was promoted as the Chief Astronomer for the Han court under Emperor An (serving his first term from 115–120, his second term under the next emperor from 126–132),^[8] as well as Prefect of the Majors for Official Carriages under the Ministry of Guards, which controlled the reception of memorials to the throne and nominees for official appointment.^[5][12]

When the official Dan Song proposed the Chinese calendar should be reformed in 123 to adopt certain apocryphal teachings, Zhang opposed the idea. He believed that errors could arise and that such teachings were of questionable stature considering they were not written by confirmed historical sages.^[5] Since many other debaters agreed with Zhang, the calendar was not altered, yet Zhang's proposal that apocryphal writings should be banned were rejected.^[5] The officials Liu Zhen and Liu Taotu, who were members on a second committee to compile the dynastic history Dongguan Hanji (東觀漢記), sought permission from the court to gain the input of Zhang Heng on this history work.^[5] However, Zhang was barred from contributing anything to the committee due to his controversial views on apocrypha and his view that Emperor Gengshi (r. 23–25) should not be relegated to a minor position in comparison to his successor Emperor Guangwu in restoring the Han Dynasty.^[13][14] Any fleeting opportunity that Zhang might have had in serving as a court historian was closed to him with the death of Liu Zhen and Liu Taotu.^[13]

A Western Han terra cotta cavalier figurine wearing official robes and hat; as Court Astronomer, Zhang Heng earned a specific salary and rank of 600 bushels of grain (which was mostly commuted to payments in coinage currency or bolts of silk), and so he would have worn a specified type of robe, rode in a specificied type of carriage, and held a unique emblem that distinguished his status level in the official hierarchy.^[15][16]

Despite this obstruction in his official career, Zhang was reappointed as Court Astronomer in 126 after Emperor Shun of Han (r. 125–144) ascended to the throne.^[15][17] His intensive astronomical work was rewarded only with the rank and salary of 600 bushels, or shi, of grain (mostly commuted to coin cash or bolts of silk).^[15][18] To place this number in context, in a hierarchy of twenty official ranks, the lowest-paid official earned the rank and salary of 100 bushels and the highest-paid official earned 10,000 bushels during the Han.^[19] The 600 bushel rank was also the lowest ranking official the emperor could directly appoint to a central government position; any official of lower status was overseen by central or provincial officials of high rank.^[20]

Zhang's official status at court saw considerable improvement. In 132, Zhang introduced an intricate seismometer device to the court which he claimed detected the exact cardinal directions of distant earthquakes.^[21] When his device was tripped indicating an earthquake occurred in the northwest, there was no perceivable tremor that could be felt in the capital, so his political enemies relished in his device's failure.^[21] However, a messenger arrived in the capital soon after to report that indeed an earthquake had occurred roughly 400 km (248 mi) to 500 km (310 mi) northwest of Luoyang in Gansu province.^{[21][22][23][24]} A year after he presented his seismometer device to the court, officials and candidates were asked to provide comments about a series of recent earthquakes which could be interpreted as signs of displeasure from Heaven.^[15] Zhang's memorial criticized the new recruitment system of Zuo Xiong which fixed the age of eligible candidates for the title 'Filial and Incorrupt' at age forty. The new system also transferred the power of the candidates' assessment to the Three Excellencies rather than the Generals of the Household, who by tradition oversaw the affairs of court gentlemen.^[15] Zhang's memorial was rejected, yet his status was significantly elevated soon after to Palace Attendant, a position he used to influence the decisions of Emperor Shun.^[15][12]

As Palace Attendant to Emperor Shun, Zhang Heng gained the ire of the eunuchs at court. This was due to his attempts to convince the Emperor that the eunuchs represented a traditional menace for the imperial court, pointing to specific examples of court intrigues of the past involving eunuchs.^[15] Zhang used this argument to convince Emperor Shun that he should assume greater authority while limiting the influence of the eunuchs.^[15] The eunuchs made efforts to slander Zhang, which the latter retorted against through a rhapsody called "Contemplating the Cosmos".^[15][25] Rafe de Crespigny states that in this rhapsody Zhang used imagery similar to Qu Yuan's (340–278 BC) poem "Li Sao" and focused on whether or not good men should flee the corrupted world or remain virtuous within it.^[15][25]

[edit] Retirement and death

Zhang did retire from his office under Emperor Shun in 136, although this was not the end of his career.^[15][8] He was appointed as Chancellor of Hejian (in modern Hebei) and served in his office there for two years.^[15][8] He used his energies there to monitor and control the actions of the local King Liu Zheng and rather lawless powerful elite families who were awarded special privileges by the king.^[15][8] After making a series of arrests of lawbreakers, Zhang gained a reputation among the people of Hejian as a strict administrator.^[8][26] Zhang's writings of this time reflect his bitter attitude in being unable to effectively serve the Emperor.^[15][8] In 138, Zhang retired from office and returned home to Nanyang.^[8][26] There he composed a rhapsody rejoicing over his retirement where he could pay attention to reading books and playing his lute.^[15][26] Only months after returning home, Zhang received an appointment to serve under the Imperial Secretariat, and so traveled back to the capital where he died in 139 while in office.^[27] By the time of his death, Zhang had composed thirty-two written works on literature, philosophy, science, and mysticism.^[28] He was buried in his hometown in Xi'e, Nanyang Commandery, while his friend Cui Yuan composed the inscription for his tomb.^[28][8]

[edit] Literature and poetry

An Eastern Han earthenware figurine of the Queen Mother of the West, who Zhang fantasized about in his "Rhapsody on Contemplating the Mystery" (思玄賦), yet the pleasures of the flesh and immortality that she could offer were not tempting enough to sway his heart which was set elsewhere, as described in this rhapsody.^[29]

While working for the central court, Zhang Heng had access to a variety of written materials since he was allowed to peruse the Archives of the Eastern Pavilion.^[30] Zhang read many of the great works of history in his day, as he even offered a bit of criticism by claiming he had found ten instances where the Records of the Grand Historian by Sima Qian (145–90 BC) and the Book of Han by Ban Gu (AD 32–92) differed from other ancient texts that were available to him.^[31][5] This account of Zhang's was preserved and recorded in the 5th century text of the Book of Later Han by Fan Ye (398–445).^[31] In many references found in Zhang's rhapsodies and other literary works he displayed a deep knowledge of classic texts, Chinese philosophy, and histories.^[5] He also compiled a commentary on the Taixuan (太玄, "Great Mystery") by the Daoist author Yang Xiong (53 BC–AD 18).^[15][8][7]

Xiao Tong (501–531), a crown prince of the Liang Dynasty (502–557), immortalized several of Zhang's works in his anthology of literature, Wen xuan. His rhapsodies (fu 賦) include "Western Metropolis Rhapsody" (西京賦), "Eastern Metropolis Rhapsody" (東京賦), "Southern Capital Rhapsody" (南都賦), "Rhapsody on Contemplating the Mystery" (思玄賦), and "Rhapsody on Returning to the Fields" (歸田賦).^[32] The latter fu is an especially interesting piece, as its fusion of Daoist ideas with Confucianism was a precursor to later Chinese metaphysical nature poetry, according to Liu Wu-chi.^[33] A set of four short lyric poems (shi 詩) entitled "Lyric Poems on Four Sorrows" (四愁詩), is also included with Zhang's preface. This set constitutes some of the earliest heptasyllabic shi Chinese poetry written.^[26][34] While he was still in Luoyang, Zhang became inspired to write his "Western Metropolis Rhapsody" and "Eastern Metropolis Rhapsody", which were based on the "Rhapsody on the Two Capitals" by the historian Ban Gu.^[5] Zhang's work was similar to Ban's, although the latter fully praised the contemporaneous Eastern Han regime while Zhang provided warning that it could suffer the same fate as the Western Han if it too declined into a state of decadence and moral depravity.^[5] These two works satirized and criticized what he saw as the excessive luxury of the upper classes.^[11] Zhang's "Southern Capital Rhapsody" was a work which served to commemorate his home city of Nanyang, home of the restorer of the Han Dynasty, Emperor Guangwu.^[5]

A Han terracotta figurine of a serving lady; in his poetry, Zhang Heng expressed his affinity for gracious and commendable women. In addition to being a painter, Zhang also crafted figurine sculptures like this.^[12]

In Zhang Heng's poem Four Sorrows, he laments that he is unable to woo a beautiful woman due to the impediment of mountains, snows, and rivers.^[15][8] Rafe de Crespigny, Tong Xiao, and David R. Knechtges claim that Zhang wrote this as an innuendo hinting at his inability to keep in contact with the Emperor as unworthy rivals and petty men hindered him from doing so.^[15][8] This poem is also one of the first in China to have seven words per line.^[26] His Four Sorrows reads as thus:

In another poem of his called "Stabilizing the Passions"—preserved in a Tang Dynasty (618–907) encyclopedia but referred to earlier by Tao Qian (365–427) in praise of Zhang's lyrical minimalism—Zhang displays his admiration for an attractive and exemplary woman.^[36] This simpler type of fu poem influenced later works by the prominent official and scholar Cai Yong (132–192).^[26] Zhang wrote:

Western Han tomb painting of two men engrossed in conversation; Zhang's 'shelun' or 'hypothetical discourse' involved a written dialogue between imaginary or real personas to demonstrate how one could lead an exemplary life

A Western Han gilt-bronze oil-lamp shaped as a maidservant; Zhang Heng indirectly criticized Eastern Han emperors by denouncing the decadence and unruly behavior of Western Han emperors with prostitutes and singing girls outside the palace

Zhang's long lyrical poems also revealed a great amount of information on urban layout and basic geography, with his rhapsody "Sir Based-On-Nothing" providing details on terrain, palaces, hunting parks, markets, and prominent buildings of Chang'an, the Western Han capital.^[32][11] In exemplifying his attention to detail, his rhapsody on Nanyang described gardens filled with spring garlic, summer bamboo shoots, autumn leeks, winter rape-turnips, perilla, evodia, and purple ginger.^[37] Zhang Heng's writing confirms the size of the imperial hunting park in the suburbs of Chang'an, as his estimate for the circumference of the park's encircling wall agrees with the historian Ban Gu's estimate of roughly 400 li (one li in Han times was equal to 415.8 m, or 1,364 ft, making the circumference of the park wall 166,320 m, or 545,600 ft).^[38] Along with Sima Xiangru (179–117 BC), Zhang listed a variety of different animals and hunted game inhabiting the park, which were divided in the northern and southern portions of the park according to where the animals had originally came from: northern or southern China.^[39] Somewhat similar to the description of Sima Xiangru, Zhang described the Western Han emperors and their entourage enjoying boat outings and sights of water plays, fishing, and archers shooting birds and other animals with stringed arrows from the tops of tall towers along Chang'an's Kunming Lake.^[40] The focus of Zhang's writing on specific places and their terrain, society, people, and their customs could also be seen as early attempts of ethnographic categorization.^[41] In his poem "Xijing fu", Zhang also shows that he was aware of a new foreign religion of Buddhism introduced via the Silk Road and the legend of the birth of Buddha with the vision of the white elephant bringing about conception.^[42] In his "Western Metropolis Rhapsody", Zhang described court entertainments such as juedi, a form of theatrical wrestling accompanied by music where participants butted heads with bull horn masks.^[43]

With his Response [to Criticism] of my Idleness (Yingxian), Zhang was an early writer and proponent of the Chinese literary genre 'shelun', or 'hypothetical discourse'. Authors of this literary genre created a written dialogue between themselves and an imaginary person (or a real person of their entourage or association); the latter poses questions to the author on how to lead a successful life.^[44] He also used it as a means to criticize himself for failing to obtain high office but coming to the self-conclusion that the true gentleman displays virtue instead of greed for power.^[15] In this work, Dominik Declercq asserts that the person urging Zhang to advance his career in a time of government corruption most likely represented the eunuchs at court or the Empress Liang Na's (116–150) powerful relatives in the Liang clan.^[17] Declercq states that these two groups would have been "anxious to know whether this famous scholar could be lured over to their side," but Zhang flatly rejected such an alignment by declaring in this politically-charged piece of literature that his gentlemanly quest for virtue trumped any desire of his for power.^[45]

Zhang wrote about the various love affairs of emperors, not satisfied with the imperial harem, going out into the city incognito to seek out prostitutes and sing-song girls. This was seen as a general criticism of present Eastern Han emperors and their imperial favorites, guised in the criticism of earlier Western Han emperors.^[46] Besides criticizing the Western Han emperors for lavish decadence, Zhang also pointed out that their behavior and ceremonies did not properly conform with the Chinese cyclical beliefs in yin and yang.^[47] In a poem criticizing the previous Western Han Dynasty, Zhang wrote:

[edit] Achievements in science and technology

[edit] Astronomy and mathematics

Printed star map of Su Song (1020–1101) showing the south polar projection

For centuries the Chinese approximated pi as 3, while Liu Xin (d. AD 23) made the first known Chinese attempt at a more accurate calculation of 3.154, but there is no record detailing the method he used to obtain this figure.^[48][49] In his work around 130,^[50] Zhang Heng's comparison of the celestial circle to the diameter of the earth, Zhang proportioned the former as 736 and the latter as 232, thus calculating pi as 3.1724.^[51] In Zhang's day, the ratio 4:3 was given for the area of a square to the area of its inscribed circle, and that the volume of a cube and volume of the inscribed sphere should also be 4²:3².^[51] In formula, with D as diameter and V as volume, D³:V = 16:9 or V=D³; Zhang realized that the value for diameter in this formula was inaccurate, noting the discrepancy as the value taken for the ratio.^[51][49] Zhang then attempted to remedy this by amending the formula with an additional D³, hence V=D³ + D³ = D³.^[51] With the ratio of the volume of the cube to the inscribed sphere at 8:5, the implied ratio of the area of the square to the circle is √8:√5.^[51][52] From this formula, Zhang calculated pi as the square root of 10 (or approximately 3.162).^{[53][15][51][12][52]} The calculation for pi was made more accurate in the 3rd century with Liu Hui's π algorithm, while Liu Hui (fl. 3rd century) had several variations (3.142704, 3.1428, and 3.14159).^[54]

In his publication of 120 AD called The Spiritual Constitution of the Universe (靈憲, Ling Xian),^[15] Zhang Heng theorized that the universe was like an egg "as round as a crossbow pellet" with the stars on the shell and the Earth as the central yolk.^[4][55] This universe theory is congruent with the geocentric model as opposed to the heliocentric model. Although the ancient Warring States (403–221 BC) Chinese astronomers Shi Shen and Gan De had compiled the world's first star catalogue in the 4th century BC, Zhang nonetheless catalogued 14,000 stars (2,500 of these he placed in a 'brightly shining' category) and recognized 124 constellations.^[15][55] In comparison, this star catalogue featured many more stars than the 850 documented by the Greek astronomer Hipparchus (c. 190–c.120 BC) in his catalogue, and more than Ptolemy (AD 83–161), who catalogued over 1,000.^[56] Zhang supported the 'radiating influence' theory regarding solar eclipse and lunar eclipse phenomena, a theory which was opposed by Wang Chong (AD 27–97).^[57] In the Ling Xian, Zhang wrote:

Zhang Heng believed that one side of the moon was fully-lit with the reflected rays of light from the sun while the other side remained dark

The sun is like fire and the moon like water. The fire gives out light and the water reflects it. Thus the moon's brightness is produced from the radiance of the sun, and the moon's darkness is due to (the light of) the sun being obstructed. The side which faces the sun is fully lit, and the side which is away from it is dark. The planets (as well as the moon) have the nature of water and reflect light. The light pouring forth from the sun does not always reach the moon owing to the obstruction of the earth itself—this is called 'an-xu', a lunar eclipse. When (a similar effect) happens with a planet (we call it) an occultation; when the moon passes across (the sun's path) then there is a solar eclipse.^[58]

Zhang Heng viewed these astronomical phenomena in supernatural terms as well. The signs of comets, eclipses, and movements of heavenly bodies could all be interpreted by him as heavenly guides on how to conduct affairs of state.^[15] Contemporary writers also wrote about eclipses and sphericity of heavenly bodies. Writing more than a century before Zhang Heng, Jing Fang (78–37 BC) wrote about the spherical shape of the sun and moon while discussing eclipses:

The moon and the planets are Yin; they have shape but no light. This they receive only when the sun illuminates them. The former masters regarded the sun as round like a crossbow bullet, and they thought the moon had the nature of a mirror. Some of them recognized the moon as a ball too. Those parts of the moon which the sun illuminates took bright, those parts which it does not, remain dark.^[59]

The theory posited by Zhang and Jing were supported by later pre-modern scientists such as Shen Kuo (1031–1095), who expanded on the reasoning of why the sun and moon were spherical.^[60]

[edit] Extra tank for inflow clepsydra

Diagram of Ctesibius' 3rd century BC clepsydra, similar to Zhang's statuettes guiding the indicator rod and pointing out graduations

The outflow clepsydra was an timekeeping device used in China as long ago as the Shang Dynasty (c. 1600–c.1050), and certainly by the Zhou Dynasty (1122–256 BC).^[61] The inflow clepsydra with an indicator rod on a float had been known in China since the beginning of the Han Dynasty in 202 BC and had replaced the outflow type.^[61] The Han Chinese noted the problem with the falling pressure head in the reservoir, which slowed the timekeeping of the device as the inflow vessel was filled.^[61] Indicated in his writing in 117, Zhang Heng was the first to address this problem by adding an extra compensating tank between the reservoir and the inflow vessel.^[2][15] Zhang also mounted two statuettes of a Chinese immortal and a heavenly guard on the top of the inflow clepsydra, the two of which would guide the indicator rod with their left hand and point out the graduations with their right.^[62] Joseph Needham states that this was perhaps the ancestor of all clock jacks that would later sound the hours in later hydraulic clocks, but he notes that these figures did not actually move like clock jacks or sound the hours.^[62] Many additional compensation tanks would be added to later clepsydras in the tradition of Zhang Heng, while in 610 the Sui Dynasty (581–618) engineers Geng Xun and Yuwen Kai would craft an unequal-armed steelyard balance able to make seasonal adjustments in the pressure head of the compensating tank so that it could control the rate of water flow for different lengths of day and night during the year.^[63] Zhang mentioned a 'jade dragon's neck' which in later times meant a siphon.^[64] He wrote of the floats and indicator-rods of the inflow clepsydra as follows:

Bronze vessels are made and placed one above the other at different levels; they are filled with pure water. Each has at the bottom a small opening in the form of a 'jade dragon's neck'. The water dripping (from above) enters two inflow receivers (alternately), the left one being for the night and the right one for the day. On the covers of each (inflow receiver) there are small cast statuettes in gilt bronze; the left (night) one is an immortal and the right (day) one is a policeman. These figures guide the indicator-rod (lit. arrow) with their left hands, and indicate the graduations on it with their right hands, thus giving the time.^[64]

[edit] Water-powered armillary sphere

The original diagram of Su Song's (1020–1101) clock tower, featuring an armillary sphere powered by a waterwheel, escapement mechanism, and chain drive

Zhang Heng is the first known person in history to apply hydraulic motive power (ie. by employing a clepsydra) to rotate the astronomical instrument of the armillary sphere.^[65][66][67] The Greek astronomer Eratosthenes (276–194 BC) invented the first armillary sphere in 255 BC, while the Chinese armillary sphere was developed in earnest by 52 BC, due to the adding of a permanently fixed equatorial ring by the astronomer Geng Shouchang.^[68] In 84 AD the astronomers Fu An and Jia Kui added the ecliptic ring, and finally Zhang Heng added the horizon and meridian rings to the armillary sphere by 125.^[68][15] Zhang described this invention in his written work of 125, Apparatus for Rotating an Armillary Sphere by Clepsydra Water. Besides being one of the most impressive inventions of his day, it would influence later Chinese horologists in making waterclocks and lead to the discovery of the escapement mechanism by the 8th century.^[69] The historian Joseph Needham (1900–1995) states:

What were the factors leading to the first escapement clock in China? The chief tradition leading to Yi Xing (725 AD) was of course the succession of 'pre-clocks' which had started with Zhang Heng about 125. Reason has been given for believing that these applied power to the slow turning movement of computational armillary spheres and celestial globes by means of a water-wheel using clepsydra drip, which intermittently exerted the force of a lug to act on the teeth of a wheel on a polar-axis shaft. Zhang Heng in his turn had composed this arrangement by uniting the armillary rings of his predecessors into the equatorial armillary sphere, and combining it with the principles of the water-mills and hydraulic trip-hammers which had become so widespread in Chinese culture in the previous century.^[69]

The Chinese tradition of hydraulic engineering was not initiated by Zhang in any sense, as it spanned back as far as the mid Zhou Dynasty (c. 6th century BC), with engineers such as Sunshu Ao and Ximen Bao.^[70] Zhang's contemporary Du Shi (d. AD 38) was the first to apply the motive power of waterwheels to a mechanical device that operated bellows of the blast furnace to smelt cast iron.^[71] As noted above, Zhang provided a valuable description of his water-powered armillary sphere in the treatise of 125, stating:

The equatorial ring goes around the belly of the armillary sphere 91 and 5/19 (degrees) away from the pole. The circle of the ecliptic also goes round the belly of the instrument at an angle of 24 (degrees) with the equator. Thus at the summer solstice the ecliptic is 67 (degrees) and a fraction away from the pole, while at the winter solstice it is 115 (degrees) and a fraction away. Hence (the points) where the ecliptic and the equator intersect should give the north polar distances of the spring and autumn equinoxes. But now (it has been recorded that) the spring equinox is 90 and 1/4 (degrees) away from the pole, and the autumn equinox is 92 and 1/4 (degrees) away. The former figure is adopted only because it agrees with the (results obtained by the) method of measuring solstitial sun shadows as embodied in the Xia (dynasty) calendar.^[72]

The water-powered armillary sphere of Zhang Heng would have profound effects upon Chinese astronomy and mechanical engineering in later generations. With Zhang Heng's complex use of gears and ingenious model, he would greatly influence later astronomers and engineers such as Yi Xing (683–727), Zhang Sixun (fl. 10th century), Su Song (1020–1101), Guo Shoujing (1231–1316), and many others. Zhang Heng's water-powered armillary sphere was continued in the eras of the Three Kingdoms (220–280) and Jin Dynasty (265–420), yet the design for it was temporarily out of use from the years 317 until 418, due to external invasions by northern Xiongnu nomads.^[73] The old instruments of Zhang Heng were recovered in 418 when Emperor Wu of Liu Song (r. 420–422) captured the ancient capital of Chang'an, and although still intact, the marks of graduation and the representations of the stars, moon, sun, and planets were quite worn down by time and rust.^[73] In the year 436, the emperor ordered Qian Luozhi, the Secretary of the Bureau of Astronomy and Calendar, to recreate Zhang's device, which was a success.^[73] Qian's water-powered celestial globe was still in use by the time of the Liang Dynasty (502–557), while successive models of water-powered instruments in the tradition of Zhang Heng were designed.^[73]

[edit] Zhang's seismometer

A replica of Zhang Heng's seismometer, the Houfeng didong yi, featured in the Chabot Space & Science Center in Oakland, California

From the earliest times, the Chinese were concerned with the destructive force of earthquakes. It was recorded in Sima Qian's Records of the Grand Historian of 91 BC that in 780 BC an earthquake had been devastative enough to divert the course of three different rivers.^[74] The ancient Chinese did not understand the cause of earthquakes as being the shift of tectonic plates in the earth's crust. Chinese of the ancient Zhou Dynasty explained the natural phenomenon of earthquakes in terms of disturbances with cosmic yin and yang, along with the heavens' displeasure with acts committed (or the common peoples' grievances ignored) by the current ruling dynasty.^[74] These theories were ultimately derived from the ancient text of the Yijing (Book of Changes), in its fifty-first hexagram.^[75] There were other early theories about earthquakes by those in ancient Greece. Anaxagoras (c. 500–428 BC) believed that they were caused by excess water near the surface crust of the earth bursting into the earth's hollows; Democritus (c. 460–370 BC) believed that the saturation of the earth with water caused them; Anaximenes (c. 585–c. 525 BC) believed they were the result of massive pieces of the earth falling into the cavernous hollows due to drying; and Aristotle (384–322 BC) believed they were caused by instability of vapor (pneuma) caused by the drying of the moist earth by the sun's rays.^[75]

During the Han Dynasty, many learned scholars—including Zhang Heng—gave credence to the 'oracles of the winds' at court.^[76] These oracles of the occult made observations of direction, force, and timing of the winds to speculate ideas about the operation of the cosmos and predictions of events on earth.^[77] This influenced the ideas of Zhang Heng about earthquakes; going against the grain of the early theories proposed by his fellow Chinese and contemporary Greeks, Zhang Heng believed earthquakes were caused by wind and air, writing:

The chief cause of earthquake is air, an element naturally swift and shifting from place to place. As long as it is not stirred, but lurks in a vacant space, it reposes innocently, giving no trouble to objects around it. But any cause coming upon it from without rouses it, or compresses it, and drives it into a narrow space ... and when opportunity of escape is cut off, then 'With deep murmur of the Mountain it roars around the barriers', which after long battering it dislodges and tosses on high, growing more fierce the stronger the obstacle with which it has contended.^[78]

In 132, Zhang Heng presented to the Han court what many historians consider his most impressive invention. Zhang Heng invented the first seismometer, called Houfeng didong yi (候风地动仪, lit. instrument for measuring the seasonal winds and the movements of the Earth), for determining the exact direction of tremors and earthquakes.^[66][15] According to the Book of Later Han (compiled by Fan Ye in the 5th century), his copper-made urn-shaped device, with swinging inverted pendulum inside, was able to detect the direction of an earthquake from hundreds of miles/kilometers away.^[79][80] This was essential for the Han government in sending quick aid and relief to regions devastated by this natural disaster.^[81][3][82]

[edit] Book of Later Han description

In the Book of Later Han there is a detailed description of Zhang's device in his biography. The device was also deemed important enough for mention in the 'Annals' chapter of the Book of Later Han that detailed the reign era of Emperor Shun.^[83] In Zhang's biography, the Book of Later Han states:

In the first year of the Yangjia reign period (132) Zhang Heng also invented an 'earthquake weathercock' (i.e. a seismograph). It consisted of a vessel of fine cast bronze, resembling a wine-jar, and having a diameter of eight chi (Note—8 chi is roughly 1.8 m or 6 ft). It had a domed cover, and the outer surface was ornamented with antique seal-characters and designs of mountains, tortoises, birds, and animals. Inside there was a central column capable of lateral displacement along tracks in the eight directions, and so arranged (that it would operate) a closing and opening mechanism.

Outside the vessel there were eight dragon heads, each one holding a bronze ball in its mouth, while round the base there sat eight (corresponding) toads, with their mouths open, ready to receive any ball which the dragons might drop. The toothed machinery and ingenious constructions were all hidden inside the vessel, and the cover fitted down closely all round without any crevice. When an earthquake occurred the dragon mechanism of the vessel was caused to vibrate so that a ball was vomited out of a dragon-mouth and caught by the toad underneath. At the same instant a sharp sound was made which called the attention of the observers.

Now although the mechanism of one dragon was released, the seven (other) heads did not move, and by following the (azimuthal) direction (of the dragon which had been set in motion), one knew (the direction) from which the earthquake (shock) had come (lit. where the earthquake was). When this was verified by the facts there was (found) an almost miraculous agreement (i.e. between the observations made with the apparatus and the news of what had actually happened). Nothing like this had ever been heard of before since the earliest records of the Shu (Jing).

On one occasion one of the dragons let fall a ball from its mouth though no perceptible shock could be felt. All the scholars at the capital were astonished at this strange effect occurring without any evidence (of an earthquake to cause it). But several days later a messenger arrived bringing news of an earthquake in Longxi (Gansu). Upon this everyone admitted the mysterious power of the instrument. Thenceforward it became the duty of the officials of the Bureau of Astronomy and Calendar to record the directions from which earthquakes came.^[84]

Furthermore, Zhang Heng's seismograph device incorporated the following in order to function properly: eight mobile arms radiating in as many directions and each connected with cranks which are provided with catch mechanisms at the periphery; any one of the cranks which raises a dragon head and so releases a ball is thus at the same time caught and held, thus immobilising the instrument; a right-angle lever for raising the dragon's head; a vertical pin passing through a slot in the crank; an arm of the pendulum; the pendulum; a catch device; a pivot on a projection; a sling suspending the pendulum; attachment of the sling; a horizontal bar supporting the pendulum; the lower jaw of the dragon supporting the ball.^[85] Wang Zhenduo (王振铎) argued that technology by the Eastern Han era was sophisticated enough to produce such a device, as evidenced by contemporary levers and cranks used in other devices such as crossbow triggers.^[86]

[edit] Recreations and modern developments

Sample of an original seismometer of Emil Wiechert's design of 1898, featured in the GeoForschungsZentrum at Potsdam, Germany

Later Chinese of subsequent periods were able to reinvent Zhang's seismometer. This included the 6th century mathematician and surveyor Xindu Fang of the Northern Qi Dynasty (550–577) and the astronomer and mathematician Lin Xiaogong of the Sui Dynasty (581–618).^[87] Like Zhang, Xindu Fang and Lin Xiaogong were given imperial patronage for their services in craftsmanship of devices for the court.^[88] By the time of the Yuan Dynasty (1271–1368), it was acknowledged that all devices previously made were preserved, except for that of the seismometer.^[89] This was discussed by the scholar Zhou Mi around 1290, who remarked that the books of Xindu Fang and Lin Xiaogong detailing their devices were no longer to be found.^[89] Horwitz, Kreitner, and Needham speculate if Tang Dynasty (618–907) era seismographs found their way to contemporary Japan; according to Needham, "instruments of apparently traditional type there in which a pendulum carries pins projecting in many directions and able to pierce a surrounding paper cylinder, have been described".^[90]

In the Western world, de la Hautefeuille established the method of spilling liquid mercury from an overfilled dish in 1703, in order to determine the direction of earthquakes.^[91] The Benedictine monk Andrea Bina built a device in 1751 that recorded the relative displacement of the ground and a pendulum bob during an earthquake.^[92] The Italian inventor Filippo Cecchi (1822–1887) built a low-sensitivity seismograph in 1875.^[92] While working in Japan during the 1880s, British scientists developed a seismograph as a research instrument.^[92] While entering the faculty of the Imperial College of Engineering in Tokyo in 1876, John Milne teamed up with Thomas Gray and J. Alfred Ewing to perform experiments with pendulum instruments that could record ground movements.^[93] In the 1886 edition detailing his work, Milne acknowledged the contribution of Zhang Heng to the field of early seismology.^[78] The seismograph Milne developed in 1894 was greatly improved in 1898 by Emil Weichert who incorporated a large viscous damping pendulum weighing over a ton.^[94] Hong-sen Yan states that "Weichert's seismograph recorded a wide spectrum of seismic signals, accurately reproducing ground motions".^[93]

Hong-sen Yan states that modern replicas of Zhang's device have failed to reach the level of accuracy and sensitivity described in Chinese historical records.^[92] Wang Zhenduo presented two different models of the seismometer based on the ancient descriptions of Zhang's device.^[95] In his reconstruction of Zhang's device in 1936, the central pillar (du zhu) of the device was a suspended pendulum acting as a movement sensor, while the central pillar of his second model in 1963 was an inverted pendulum.^[95] While working in the Seismological Observatory of Tokyo University in 1939, Akitsune Imamura and Hagiwara made a reconstruction of Zhang's device based on the work of British historian of science Robert Temple.^[96][86] While it was Milne and Wang Zhenduo who argued early on that Zhang's 'central pillar' was a suspended pendulum, Imamura was the first to propose an inverted model.^[97] He argued that transverse shock would have rendered Wang's immobilization mechanism ineffective, as it would not have prevented further motion that could knock other balls out of their position.^[86] On June 13, 2005, modern Chinese seismologists announced that they had successfully created a replica of the instrument.^[98]

[edit] Cartography

The Yu Ji Tu, or Map of the Tracks of Yu Gong, carved into stone in 1137, located in the Stele Forest of Xi'an. This 3 ft (0.91 m) squared map features a graduated scale of 100 li for each rectangular grid. Although Pei Xiu is credited with the first description of graduated scale and grid references for maps, there is evidence that Zhang Heng was the innovator of these

Odometer cart from a stone rubbing of an Eastern Han Dynasty tomb, c. 125

The Wei (220–265) and Jin Dynasty (265–420) cartographer and official Pei Xiu (224–271) was the first in China to describe in full the geometric grid reference for maps that allowed for precise measurements using a graduated scale, as well as topographical elevation.^[99][100] However, map-making in China had existed since at least the 4th century BC with the Qin state maps found in Gansu in 1986.^[101] Pinpointed accuracy of the winding courses of rivers and familiarity with scaled distance had been known since the Qin and Han Dynasty, respectively, as evidenced by their existing maps, while the use of a rectangular grid had been known in China since the Han as well.^[102][103] Historian Howard Nelson states that, although the accounts of Zhang Heng's work in cartography are somewhat vague and sketchy, there is ample written evidence that Pei Xiu derived the use of the rectangular grid reference from the maps of Zhang Heng.^[104] Historian Florian C. Reiter notes that Zhang's narrative "Guitian fu" contains a phrase about applauding the maps and documents of Confucius of the Zhou Dynasty, which Reiter suggests places maps (tu) on a same level of importance with documents (shu).^[105] Rafe de Crespigny asserts that it was Zhang who established the rectangular grid system in Chinese cartography.^[15]

[edit] Odometer and South Pointing Chariot

Zhang Heng is often accredited with the invention of the first odometer (also pronounced hodometer) device in China,^[55][12] an achievement alongside earlier contemporaries Archimedes (c. 287–212 BC) and Heron of Alexandria (fl. AD 10–70) from the Hellenized West. An odometer is a device which mechanically or electronically measures the distance traveled by an operated vehicle (found standard in modern automobiles), and was a mechanical device used by the Roman and Han-Chinese empires in roughly the same time frame. By the 3rd century, the Chinese had termed the device as the 'ji li gu che', or 'li-recording drum carriage' (Note: the modern measurement of li = 500 m/1640 ft).^[106] Ancient Chinese texts tell of the mechanical carriage's functions, and as one li is traversed, a mechanical-driven wooden figure strikes a drum, and when ten li is traversed, another wooden figure would strike a gong or a bell with its mechanical-operated arm.^[106] However, there is evidence to suggest that the invention of the odometer was a gradual process in Han Dynasty China that centered around the huang men court people (ie. eunuchs, palace officials, attendants and familiars, actors, acrobats, etc.) that would follow the musical procession of the royal 'drum-chariot'.^[107] There is speculation that some time in the 1st century BC the beating of drums and gongs were mechanically driven by working automatically off the rotation of the road wheels.^[107] This might have actually been the design of Luoxia Hong (c. 110 BC), yet by at least 125 the mechanical odometer carriage was already known as it was depicted in a mural of the Xiao Tang Shan Tomb.^[107]

The South Pointing Chariot is another mechanical contraption accredited to Zhang Heng.^[12] It is a non-magnetic compass-vehicle shaped in the form of a wheeled chariot, and functioning off of differential gears. The mechanical device of the differential provides equal amount of torque to wheels rotating at different speeds. This device allowed a fixed wooden figurine (in the shape of a Chinese state minister) to constantly point in the southern direction, hence the name of the device. The Song Shu (c. 500 AD) records that Zhang Heng re-invented it from its earliest model found in the Zhou Dynasty period, but the violent collapse of the Han Dynasty unfortunately did not allow it to be preserved. Whether the ancient passage of this book on Zhang Heng is valid or not, Ma Jun (200–265) of the following century was successful in creating it.^[108]

[edit] Legacy

[edit] Science and technology

A Florentine marble carving of Ptolemy (86–161), who created an earth-centered universe theory that the scholars Jin Guantao, Fan Hongye, and Liu Qingfeng compare with Zhang Heng's theory published in 125^[109]

Zhang Heng's mechanical inventions influenced the likes of later Chinese inventors, such as Yi Xing, Zhang Sixun, Su Song, and Guo Shoujing. Su Song directly named the water-powered armillary sphere of Zhang Heng as the inspiration for his clock tower.^[110] The cosmic model of nine points of Heaven corresponding with nine regions of earth conceived in the work of the scholar-official Chen Hongmou (1696–1771) followed in the tradition of Zhang's book Spiritual Constitution of the Universe.^[111] The historian Joseph Needham emphasized the contributions Zhang Heng made to the course of pre-modern Chinese technology, stating that Zhang was noted even in his day for being able to "make three wheels rotate as if they were one".^[112] More than one scholar has described Zhang as a polymath.^{[34][7][82][24]} However, some scholars also point out that Zhang's writing lacks concrete scientific theories.^[109] In relation to the theory of his contemporary Ptolemy (83–161) of Roman Egypt, Jin Guantao, Fan Hongye, and Liu Qingfeng state:

Based on the theories of his predecessors, Zhang Heng systematically developed the celestial sphere theory. An armillary constructed on the basis of his hypotheses bears a remarkable similarity to Ptolemy's earth-centered theory. However, Zhang Heng did not definitely propose a theoretical model like Ptolemy's earth-centered one. It is astonishing that the celestial model Zhang Heng constructed was almost a physical model of Ptolemy's earth-centered theory. Only a single step separates the celestial globe from the earth-centered theory, but Chinese astronomers never took that step.

Here we can see how important the exemplary function of the primitive scientific structure is. In order to use the Euclidean system of geometry as a model for the development of astronomical theory, Ptolemy first had to select hypotheses which could serve as axioms. He naturally regarded circular motion as fundamental and then used the circular motion of deferents and epicycles in his earth-centered theory. Although Zhang Heng understood that the sun, moon and planets move in circles, he lacked a model for a logically structured theory and so could not establish a corresponding astronomical theory. Chinese astronomy was most interested in extracting the algebraic features of planetary motion (that is, the length of the cyclic periods) to establish astronomical theories. Thus astronomy was reduced to arithmetic operations, extracting common multiples and divisors from the observed cyclic motions of the heavenly bodies.^[109]

[edit] Poetic literature

Zhang's poetry was widely read during and after his death. In addition to the compilation of Xiao Tong mentioned above, the Eastern Wu official Xue Zong (d. 237) wrote commentary on Zhang's poems "Dongjing fu" and "Xijing fu".^[113] The influential poet Tao Qian wrote that he admired the poetry of Zhang Heng for its "curbing extravagant diction and aiming at simplicity," in regards to perceived tranquility and rectitude correlating with the simple but effective language of the poet.^[114] Tao wrote that both Zhang Heng and Cai Yong "avoided inflated language, aiming chiefly at simplicity," and adding that their "compositions begin by giving free expression to their fancies but end on a note of quiet, serving admirably to restrain undisciplined and passionate nature".^[115]

[edit] Posthumous honors

Zhang was given great honors in life and in death. The philosopher and poet Fu Xuan (217–278) of the Wei and Jin dynasties once lamented in an essay over the fact that Zhang Heng was never placed in the Ministry of Works. Writing highly of Zhang and the 3rd century mechanical engineer Ma Jun (fl. 3rd century), Fu Xuan wrote:

... neither of them was ever an official of the Ministry of Works, and their ingenuity did not benefit the world. When (authorities) employ personnel with no regard to special talent, and having heard of genius neglect even to test it—is this not hateful and disastrous?^[116]

In honor of Zhang's achievements in science and technology, his friend Cui Ziyu (Cui Yuan) wrote a memorial inscription on his burial stele, which has been preserved in the Guwen yuan.^[8] Cui stated of Zhang Heng:

His mathematical computations exhausted (the riddles of) the heavens and the earth. His inventions were comparable even to those of the Author of Change. The excellence of his talent and the splendour of his art were one with those of the gods.^[117]

Xiahou Zhan (243–291), who came from an illustrious family intermarried with the ruling Cao family of the Wei Dynasty and then the ruling Sima family of the Jin Dynasty, nonetheless led a rather unsuccessful career as a minor official.^[118] In addition to Cui Yuan's memorial inscription, Xiahou Zhan made an inscription for his own commemorative stele to be placed at Zhang Heng's tomb, which read:

Ever since gentlemen have composed literary texts, none has been as skillful as the Master [Zhang Heng] in choosing his words well ... if only the dead could rise, oh I could then turn to him for a teacher!^[119]

Zhang Heng has also been given posthumous honors of several things named after him, including the Zhang Heng lunar crater,^[120] the asteroid 1802 Zhang Heng,^[121] and the mineral Zhanghengite.

[edit] Notes

[edit] References

[edit] External links

Wikimedia Commons has media related to:

Zhang Heng

• Zhang Heng at Chinaculture.org
• Zhang Heng at the University of Maine, USA
• Zhang Heng at the University of St Andrews, Scotland
• The Early History of Seismology (to 1900)