生平

張衡出身於南陽大族，祖父張堪是蜀郡太守。他少年時曾到雒陽太學讀書，通曉五經，好學不倦，不分日夜。張衡為人謙虛，意志堅定，淡泊名利。曾受舉薦「孝廉」，被大將軍外戚鄧騭徵召，但張衡都不接受。100年，22歲的張衡出任南陽郡太守鮑德的主簿，8年後辭官讀書。鮑德升職為大司農後，熱心推薦張衡；111年，張衡被漢安帝所召，出任尚書台郎中，3年後遷任尚書侍郎；115年，37歲的張衡開始出任太史令，121年調職公車司馬令，126年復任太史令。任職太史令期間，他製作了渾天儀與地動儀。張衡掌領太史令先後達14年之久，這個職位相當於現在中國科學院國家天文台的台長。張衡長期掌管歷史記載和曆法，沒有升官，被同僚所笑。他寫下《答難》來表明心志，不慕官位。他又曾上疏痛陳事弊，提出必須禁止大臣奢侈和僭越的主張。133年雒陽大地震，張衡藉此上諫，批評宦官越權，主張大權歸還天子。同年張衡遷任侍中。因受當權宦官排斥，136年外調河間相。在河間政績良好，138年他升遷尚書，次年過世，享年61歲他的傳世著作有文集11卷，《靈憲》、《渾天儀》、《玄圖》各一卷及數學著作《算罔論》。

貢獻

天文學

張衡主張渾天說，認為天是球狀的，像個雞蛋，天相當於蛋殼，大地像蛋黃，天把大地包在當中，大地是平面的，周圍是水，大地浮在水上。他改進西漢耿壽昌的設計，製造了渾天儀，並著有《渾天儀》一卷加以解說。渾天儀一具安裝在室內，一具安裝在觀測台「靈台」之上。渾天儀以銅鑄造，是空心球體，直徑約五尺，上畫二十八宿、中外星官及黃道、赤道；天球半露在地平圈上，半隱在地平圈下，天軸則支架在子午圈上，天球可繞天軸自行轉動，與實際天球運動相一致，可預報天體運動情況；其外安裝了地平環、赤道環和子午環，內部設置四遊環。有學者認為，張衡的渾天儀上面裝置了可以眺望天體位置的望筒，兼具演示和觀測效用；也有學者認為，此渾天儀沒有望筒，只有演示作用，性質上是天球儀。渾天儀每日均勻地繞中軸旋轉一周，以滴水為原動力，與漏刻相連，水不斷定量而緩緩地流入刻漏的水斗中。水斗原是靜止不動的，當注水達到某個份量時，其重量就勝過渾天儀和齒輪的阻力，凸耳使齒輪轉動一齒，然後抵住下一齒而再次靜止下來，通過齒輪傳動而使渾天儀緩慢地旋轉。張衡所造渾天儀是個原型、早期的時鐘，在五胡亂華中毀壞；在西方，類似能自動旋轉的渾象在16世紀出現。

張衡在東方最早正確說明月蝕，指出月蝕是由於地球的影子「闇虛」遮掩了月亮而引起的，並測得日、月的視直徑約為\frac{365.25} {730}度，約等於0.5度，與現今測值相近。張衡繪製了星圖，記錄星官124個，星星有2500顆，其中320顆有名字，指出曆法制定必須根據實測結果，曾在123年參與曆法辯論，反對依據圖讖而制定的「甲寅曆」，根據月亮運行有遲疾的規律，以「九道法」為基礎提出新曆，但沒有被朝廷採納。他提出五星視運動的理論，認為就同一行星而言，其運行軌道與地面時而接近，時而遠離，「近天則遲，遠天則速」，解釋五星運行的或快或慢；運動緩慢的外行星火星、木星、土星，張衡歸類為陽，運動較快的內行星水星和金星，歸類為陰。張衡沒有認識到北極高度會隨地點而變化，定出北極高度是36度，他也沒有認識歲差，因冬至點難以觀測，只從西漢末年所測的舊數值換算，定出冬至點以黃道度量為入斗宿20度，較當時實際情況偏東超過3度；他並根據觀測，定出冬至黃道最遠時去極115度，夏至黃道去極67度，因受儀器所限，數據稍欠精確。

宇宙論

張衡雖然反對圖讖，但他的宇宙論卻受當時流行的讖緯影響。他撰有天文學著作《靈憲》，敘述宇宙生成論，觀點接近西漢《淮南子·天文訓》。他提出宇宙形成的三個階段，首先是「溟滓」，是氣的原始狀態，什麼都沒有，是「無」的階段，道的根本；第二是「龐鴻」，是元氣開始發動、連結在一起、混沌不分的狀態；第三是「太元」，元氣分化，有剛柔清濁之分，天地各自形成，陰陽四時變化而生萬物。天圓地平，天是一個中空的球體，地是半球體，上平下圓，處於天體下半部。八極約長二億三萬二千三百里，南北少一千里，東西多一千里，天地距離和地的厚度，都等於八極的一半。他指出宇宙是無窮無極的，肯定時間與空間的無限性，提出以「氣」為基本的自然觀，人是元氣的聚合，如水之凝結為冰，人死是元氣消散，如冰塊融化為水，復歸於元氣，與自然成為一體。

數學

130年前後，張衡完成推算圓周率。根據三國時劉徽《九章算術注》，張衡認為立方體及其內接球體積之比，是8:5，由此推論圓周率是10的平方根：。南北朝祖暅《渾天論》則提到張衡提出的另一個數字：；有學者認為今本文獻有衍文，張衡的數字其實是較準確的，此說未被廣泛接受。張衡的圓周率數字其實頗為粗疏，受劉徽嚴詞批評，西漢末年劉歆指出圓周率為3.1547，已比張衡更準確；但張衡的計算並非倚靠實測，而是從理論出發，從立圓術公式推求圓周率，仍有開創性的貢獻。張衡也曾研究球體體積，但沒有重大改進。

地理學

132年，張衡發明和製造了世上第一部驗震器「候風地動儀」，形狀像圓形的酒甕，斷面直徑八尺，其內中央置有一根很重的柱子，稱「都柱」，可以向八個方向傾側或傾擺；酒甕外部的八個方向各有一個龍頭，龍頭下各有一隻蟾蜍，張口對著龍頭，八條龍各口含銅丸一顆，當都柱向某一方傾側時，該方向的龍口張開，銅丸落下，掉入蟾蜍口中。地震發生時，只有震源方向上的龍頭張口，據此可知地震的方向。范曄《後漢書》記載，地動儀放在洛陽，134年12月13日，隴西發生地震，當時洛陽並無震動，但一個龍口掉出銅丸，其後才傳來隴西地震的消息，證實其探測地震方向的功效。而候風地動儀所謂的「候風」，是指測定風的變化，地震相信是因為陰陽兩氣相搏而形成，氣的變化會產生風；哪個地方有地震，哪個方向就有氣的變化，就有風來可以測到。候風地動儀流傳到隋代，北朝信都芳、隋代臨孝恭都研究過，到唐代失傳。

地動儀利用物體的慣性來測震，其構造學者有兩種看法，其一認為，都柱是個掛起的懸擺，又重又粗，都柱下有一小銅球，組成觸發機制，在地震波水平運動中，都柱移位，小銅球脫落，撞擊機關，又或都柱帶動八條向八個方位伸出去的臂，連接扛桿，當懸擺向某一方向擺動時，龍口就會張開。另一種觀點是，都柱是一種倒立的震擺，附有重錘，安裝在底座上，周圍有八組機械裝置，一旦地震，重錘傾側，都柱失去平衡，觸道機械裝置，使相應的龍口張開。現代中、日學者都嘗試復原地動儀，日本學者曾以直立震擺式的地動儀模型做實驗，証明地震初震很強的話，銅丸會因初到的縱波而落下，確定地震的方向；但其他地震學者卻指出，直立震擺的傾倒方向有隨機性，對震動反應遲鈍，沒有驗震作用，直立震擺底部所用的彈簧，也不可能是漢代技術水平的產物，而懸擺式的地動儀模型，在2000年代則通過中國地震學者用振動台模擬地震狀態的試驗，得到中國學術界的認可。張衡地動儀比直至19世紀前期西方的水銀地震儀更先進，但亦有個別學者質疑《後漢書》中有關地動儀的記載，指出從現代地震學的觀點看，若單獨一個儀器，僅在一個地點進行測量，難以測定震源。

116年，張衡繪製和呈獻地圖「地形圖」，流傳到唐代；李約瑟推測張衡曾運用計里畫方的網格繪圖，但此說受其他學者質疑。

其他發明

渾天儀和候風地動儀以外，張衡發明了指南車、「自飛木雕」和機械日曆，並改良了漏刻的構造。指南車是雙輪馬車，內置齒輪裝置，即使行駛時多次轉向，車上人像亦永遠指向正南；張衡所造指南車在漢末戰亂中被毀。自飛木雕是一隻木鳥，有羽翼，腹內有機械，能飛起，張衡〈應間〉曾提到這隻能飛的木雕：「木雕猶能獨飛」。李約瑟推測自飛木雕以彈簧為動力，推動直升陀螺的螺旋槳。張衡在漏刻使用虹吸管（稱為「玉虯」），代替壺底的漏咀，並在貯水壺和受水壺之間加入一個補償壺，使計時更準確；受水壺蓋上鑄有個小塑像，左手持著可以上下浮動的垂直指示桿（「漏箭」），右手則指向指示桿上的刻度。機械日曆「瑞輪蓂莢」像渾天儀一樣，都是水力推動的，能顯示月相和朔望月的天數。有學者認為張衡也製造了風向儀，古書上「候風地動儀」其實是指風向儀和地動儀兩種儀器，這種風向儀是鳥狀的，能隨風轉動。

思想

政治上，張衡堅持批判現實，對宮廷政治的污濁奸詐深感憂憤，反對王侯貴族的奢侈生活。他受道家思想影響，傾向老、莊，主張無為，有人生無常、遁隱厭世的思想，企圖超越世俗生活，其宇宙論也體現道家觀念，晩期作品〈思玄賦〉道家傾向更強。他繼承了西漢儒家董仲舒的災異、天人感應之說，認為星象變異和地震等災異，是上天對世人和朝廷的譴告，促使他製造更精密的儀器去認識宇宙和偵測地震，以察知天意；但他反對讖緯預言，曾上〈請禁絕圖讖疏〉，指出圖讖弄虛作假，為迎合當權者而偽造。他推崇西漢揚雄的《太玄》，認為「玄」是宇宙的根本原理，《太玄》一書深奧而難以理解。他相信天上有許多神、星神、四方神、天皇等等，不但天上有神，山林原野都有神靈，天體的組織，則與地上朝廷政府的組織相對應，月亮上有蟾蜍，由嫦娥所變，星星會影響人的命運。張衡熟悉「風角」之術，認為可透過觀風而知禍福，相信占卜，宇宙間有某種神秘力量，絕非所有事物都可用理性解釋。

文學

張衡是辭賦名家，將漢賦推向高峰，由歌功頌德的辭賦發展為抒情小賦，現存大致完整的作品有〈溫泉賦〉、〈南都賦〉、〈二京賦〉、〈思玄賦〉、〈歸田賦〉、〈髑髏賦〉、〈天象賦〉、〈應間〉、〈七辯〉九篇。〈溫泉賦〉描寫長安附近驪山著名的溫泉，屬早期作品；〈二京賦〉長達7700字，是模倣班固〈兩都賦〉的大賦，辭藻典雅瑰麗，誇張鋪陳，堪稱不朽佳作。〈西京賦〉假借憑虛公子之口，描寫長安地理形勢、漢高祖的定都、西都的豪華、宮殿的宏偉、城廓的寬大、市場的繁榮、商賈的欺詐、遊俠的作風、園林中的遊獵，〈東京賦〉則假借安處先生之口追溯歷史，從周、秦、兩漢各代帝王，贊頌漢高祖、漢文帝、漢武帝等，描寫雒陽形勝和漢室儀軌；二賦也描述宗教活動和民間風俗，如持守色戒的西域僧人、雜技歌舞等「百戲」表演、驅邪的大儺儀式，有其史料價值，可補正史的不足；〈西京賦〉即為南北朝《三輔黃圖》和北宋宋敏求《長安志》多次引用，以說明長安面貌。〈二京賦〉引用不少五經句子，文句為何晏〈景福殿賦〉、左思〈蜀都賦〉等後世辭賦襲用，並有東吳薛綜等人的注釋。〈南都賦〉則盛讚當時被朝廷忽略的南陽城，但形式較呆板笨拙，語言則較艱深晦澀。

張衡〈思玄賦〉是抒情表志的作品，發表自己的理想，模倣楚辭〈遠遊〉和班固的〈幽通賦〉，重覆屈原在〈遠遊〉中的尋求，先去東、南、北三方，登上蓬萊，在瀛州採芝，又去拜會西王母，上了仙宮「瓊宮」，盡享聲色之娛，然後回到故鄉。張衡深受楚辭影響，常引用楚地傳統的神話，〈思玄賦〉引用最多的就是楚辭。〈歸田賦〉開拓辭賦中田園歸隱的主題，表達其退隱之心，反對宦官當權，政治腐敗而自己無力拯救，有不願同流合污之意，文中讚美民間的田園生活，山水景色使人心曠神怡，是漢賦中罕見的短篇，啟導陶淵明〈歸去來辭〉等後世抒發歸隱之情的作品，所寫自然風景歡樂和諧，也啟導王羲之〈蘭亭集序〉等後世文章，文中道家思想鮮明，則可說是後世玄言詩的先驅。〈髑髏賦〉以對話體擴充鋪陳《莊子·至樂》篇中的寓言，賦中的髑髏就是莊子。有後人批評，張衡的辭賦缺乏獨創性，主要模倣前人著作，如〈二京賦〉模倣班固〈兩都賦〉，〈南都賦〉模倣揚雄〈蜀都賦〉，〈應間〉模倣東方朔〈答客難〉，〈七辯〉則模倣枚乘〈七發〉。

詩歌方面，張衡初次撰寫七言古詩〈四愁詩〉，脫離了楚歌的句式，接近純粹的七言詩，並為後世詩人模倣，如晉代傅玄撰有〈擬張衡四愁詩〉。張衡〈同聲歌〉則是新娘向新郎的傾訴，描寫新婚的優美，詩中提到房中術著作《素女經》的內容。

經學、史學、美術

張衡通曉經學，曾撰寫《周官訓詁》，但稍欠特色，失傳於世。他對漢朝歷史亦相當了解，有志於史學，擔任侍中時，曾請求到東觀專心撰寫東漢史書，但不獲批准；又曾上書指摘司馬遷《史記》和班固《漢書》兩書的錯失，提出漢朝史書應有的體例。張衡亦是個畫家，列為東漢六大畫家之一，唐代《歷代名畫記》曾記載他曾用腳趾畫怪獸這一傳說。

地位與紀念

張衡名列「漢賦四大家」之一，受尊崇為中國歷史上的大科學家。在東漢，崔瑗稱讚他能知天文地理，製作巧奪天工，「數術窮天地，製作侔造化，與神合契」，南陽人為他修建廟宇；三國時傅玄則惋惜他不在其位，工藝才華未能盡情發揮；他的地動儀和天文學成就都沒有傳人，天文學著作殘缺不全，科學貢獻漸被後人遺忘。有學者猜測，地動儀的原理在古代可能已輾轉傳到波斯和日本。19世紀末，西方地震學家開始留意到張衡地動儀的開創性成就，有學者認為，米爾恩所造的首座現代地震儀，就是受地動儀啟發的。1920年代，中國史家也注意到張衡的科學成就，1924年，張蔭麟首先稱讚張衡為中國「第一位大科學家」，李約瑟特別推崇張衡，大部份現代中國學者亦稱張衡為偉大的科學家。學者認為張衡可與西方幾乎同時代的托勒密相媲美，但在數學、幾何學、科學方法和研究成果，張衡都不如托勒密。

南陽張衡墓地久已荒廢，偶有士人加以修葺，當地人亦不知墓主是誰；1956年，南陽縣政府重建張衡墓園，建立張衡博物館，附有倣漢建築與石雕，1988年定為國家級重點文物保護單位，館內展示張衡發明的地動儀、渾天儀、指南車等模型。為了紀念張衡，1970年，國際天文學界用張衡名字為月球背面一座環形山命名；1971年，以他來命名小行星1802；中國天文學會設立「張衡特殊貢獻獎」，2002年首次頒發；2003年，小行星9092以張衡故鄉南陽命名；一種銅鋅合金的天然礦物亦以張衡命名，即張衡礦。此外，廣東深圳、上海浦東新區等地，均有以張衡命名的街道「張衡路」。

相關條目

• 渾天說、渾象、渾儀

• 地震儀、候風地動儀

• 指南車、瑞輪蓂莢

• 張衡一號

• 令和

註釋

Life

Early life

Born in the town of Xi'e in Nanyang Commandery (north of the modern Nanyang City in Henan province), Zhang Heng came from a distinguished but not affluent family. His grandfather Zhang Kan (張堪) had been governor of a commandery and one of the leaders who supported the restoration of the Han by Emperor Guangwu (r. 25–57), following the death of the usurping Wang Mang of the Xin (AD 9–23). When he was ten, Zhang's father died, leaving him in the care of his mother and grandmother.

An accomplished writer in his youth, Zhang left home in the year 95 to pursue his studies in the capitals of Chang'an and Luoyang. While traveling to Luoyang, Zhang passed by a hot spring near Mount Li and dedicated one of his earliest fu poems to it. This work, entitled "Fu on the Hot Springs" (Wēnquán fù 溫泉賦), describes the throngs of people attending the hot springs, which later became famous as the "Huaqing Hot Springs", a favorite retreat of imperial concubine Yang Guifei during the Tang dynasty. After studying for some years at Luoyang's Taixue, he was well-versed in the classics and friends with several notable persons, including the mathematician and calligrapher Cui Yuan (78–143), the official and philosophical commentator Ma Rong (79–166), and the philosopher Wang Fu (78–163). Government authorities offered Zhang appointments to several offices, including a position as one of the Imperial Secretaries, yet he acted modestly and declined.

At age 23, Zhang returned home with the title "Officer of Merit in Nanyang", serving as the master of documents under the administration of Governor Bao De (in office from 103 to 111). As he was charged with composing inscriptions and dirges for the governor, he gained experience in writing official documents. As Officer of Merit in the commandery, he was also responsible for local appointments to office and recommendations to the capital of nominees for higher office. He spent much of his time composing rhapsodies on the capital cities. When Bao De was recalled to the capital in 111 to serve as a minister of finance, Zhang continued his literary work at home in Xi'e. Zhang Heng began his studies in astronomy at the age of 30 and began publishing his works on astronomy and mathematics.

Official career

In 112, Zhang was summoned to the court of Emperor An (r. 106–125), who had heard of his expertise in mathematics. When he was nominated to serve at the capital, Zhang was escorted by carriage—a symbol of his official status—to Luoyang, where he became a court gentleman working for the Imperial Secretariat. He was promoted to Chief Astronomer for the court, serving his first term from 115 to 120 under Emperor An and his second under the succeeding emperor from 126 to 132. As Chief Astronomer, Zhang was a subordinate of the Minister of Ceremonies, one of Nine Ministers ranked just below the Three Excellencies. In addition to recording heavenly observations and portents, preparing the calendar, and reporting which days were auspicious and which ill-omened, Zhang was also in charge of an advanced literacy test for all candidates to the Imperial Secretariat and the Censorate, both of whose members were required to know at least 9,000 characters and all major writing styles. Under Emperor An, Zhang also served as Prefect of the Majors for Official Carriages under the Ministry of Guards, in charge of receiving memorials to the throne (formal essays on policy and administration) as well as nominees for official appointments.

When the government official Dan Song proposed the Chinese calendar should be reformed in 123 to adopt certain apocryphal teachings, Zhang opposed the idea. He considered the teachings to be of questionable stature and believed they could introduce errors. Others shared Zhang's opinion and the calendar was not altered, yet Zhang's proposal that apocryphal writings should be banned was rejected. The officials Liu Zhen and Liu Taotu, members of a committee to compile the dynastic history (東觀漢記), sought permission from the court to consult Zhang Heng. However, Zhang was barred from assisting the committee due to his controversial views on apocrypha and his objection to the relegation of the Gengshi Emperor's (r. 23–25) role in the restoration of the Han dynasty as lesser than Emperor Guangwu's. Liu Zhen and Liu Taotu were Zhang's only historian allies at court, and after their deaths Zhang had no further opportunities for promotion to the prestigious post of court historian.

Despite this setback in his official career, Zhang was reappointed as Chief Astronomer in 126 after Emperor Shun of Han (r. 125–144) ascended to the throne. 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). 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. The 600-bushel rank was the lowest 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.

In 132, Zhang introduced an intricate seismoscope to the court, which he claimed could detect the precise cardinal direction of a distant earthquake. On one occasion his device indicated that an earthquake had occurred in the northwest. As there was no perceivable tremor felt in the capital his political enemies were briefly able to relish the failure of his device, until a messenger arrived shortly afterwards to report that an earthquake had occurred about 400 km (248 mi) to 500 km (310 mi) northwest of Luoyang in Gansu province.

A year after Zhang presented his seismoscope 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. The ancient Chinese viewed natural calamities as cosmological punishments for misdeeds that were perpetrated by the Chinese ruler or his subordinates on earth. In Zhang's memorial discussing the reasons behind these natural disasters, he 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. Although Zhang's memorial was rejected, his status was significantly elevated soon after to Palace Attendant, a position he used to influence the decisions of Emperor Shun. With this prestigious new position, Zhang earned a salary of 2,000 bushels and had the right to escort the emperor.

As Palace Attendant to Emperor Shun, Zhang Heng attempted to convince him that the court eunuchs represented a threat to the imperial court. Zhang pointed to specific examples of past court intrigues involving eunuchs, and convinced Shun that he should assume greater authority and limit their influence. The eunuchs attempted to slander Zhang, who responded with a fu rhapsody called "Fu on Pondering the Mystery", which vents his frustration. Rafe de Crespigny states that Zhang's rhapsody 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.

Eastern Han tomb brick depicting the courtyard of a wealthy family's home. Zhang enjoyed a short period of retirement at his home in Xi'e, Nanyang, before being called back to the capital, where he died in 139.

Literature and poetry

While working for the central court, Zhang Heng had access to a variety of written materials located in the Archives of the Eastern Pavilion. Zhang read many of the great works of history in his day and claimed 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. His account was preserved and recorded in the 5th-century text of the Book of Later Han by Fan Ye (398–445). His rhapsodies and other literary works displayed a deep knowledge of classic texts, Chinese philosophy, and histories. He also compiled a commentary on the Taixuan (太玄, "Great Mystery") by the Daoist author Yang Xiong (53 BC–AD 18).

Xiao Tong (501–531), a crown prince of the Liang dynasty (502–557), immortalized several of Zhang's works in his literary anthology Selections of Refined Literature. Zhang's fu rhapsodies include "Western Metropolis Rhapsody" (Xī jīng fù 西京賦), "Eastern Metropolis Rhapsody" (Dōng jīng fù 東京賦), "Southern Capital Rhapsody" (Nán dū fù 南都賦), "Rhapsody on Contemplating the Mystery" (Sī xuán fù 思玄賦), and Return to the Field. The latter fuses Daoist ideas with Confucianism and was a precursor to later Chinese metaphysical nature poetry, according to Liu Wu-chi. A set of four short lyric poems entitled Lyric Poems on Four Sorrows (Sì chóu shī 四愁詩), is also included with Zhang's preface. This set constitutes some of the earliest heptasyllabic shi Chinese poetry written. While 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. Zhang's work was similar to Ban's, although the latter fully praised the contemporaneous Eastern Han regime while Zhang provided a warning that it could suffer the same fate as the Western Han if it too declined into a state of decadence and moral depravity. These two works satirized and criticized what he saw as the excessive luxury of the upper classes. Zhang's "Southern Capital Rhapsody" commemorated his home city of Nanyang, home of the restorer of the Han dynasty, Guangwu.

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. Scholars Rafe de Crespigny and David R. Knechtges claim that Zhang wrote this as an innuendo hinting at his inability to keep in contact with the emperor, hindered by unworthy rivals and petty men. This poem is one of the first in China to have seven words per line. His "Four Sorrows" reads:

In another poem of his called "Stabilizing the Passions" (Dìng qíng fù 定情賦)—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. This simpler type of fu poem influenced later works by the prominent official and scholar Cai Yong (132–192). Zhang wrote:

Eastern Han tomb models of watchtowers; the one on the left has crossbowmen in the top balcony. Zhang wrote that Western Han emperors were entertained by displays of archery from the balconies of towers along Chang'an's Kunming Lake.

Zhang's long lyrical poems also revealed a great amount of information on urban layout and basic geography. His rhapsody "Sir Based-On-Nothing" provides details on terrain, palaces, hunting parks, markets, and prominent buildings of Chang'an, the Western Han capital. 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. Along with Sima Xiangru (179–117 BC), Zhang listed a variety of animals and hunting game inhabiting the park, which were divided in the northern and southern portions of the park according to where the animals had originally come from: northern or southern China. Somewhat similar to the description of Sima Xiangru, Zhang described the Western Han emperors and their entourage enjoying boat outings, water plays, fishing, and displays of archery targeting birds and other animals with stringed arrows from the tops of tall towers along Chang'an's Kunming Lake. 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. In his poem "Xijing fu", Zhang shows that he was aware of the new foreign religion of Buddhism, introduced via the Silk Road, as well as the legend of the birth of Buddha with the vision of the white elephant bringing about conception. In his "Western Metropolis Rhapsody" (西京賦), Zhang described court entertainments such as juedi (角牴), a form of theatrical wrestling accompanied by music in which participants butted heads with bull horn masks.

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

With his "Responding to Criticism" (Ying jian 應間), a work modeled on Yang Xiong's "Justification Against Ridicule", Zhang was an early writer and proponent of the Chinese literary genre shelun, or hypothetical discourse. Authors of this 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. He also used it as a means to criticize himself for failing to obtain high office, but coming to the conclusion that the true gentleman displays virtue instead of greed for power. 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 or Empress Liang's (116–150) powerful relatives in the Liang clan. 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.

Zhang wrote about the various love affairs of emperors dissatisfied 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 the Eastern Han emperors and their imperial favorites, guised in the criticism of earlier Western Han emperors. 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. In a poem criticizing the previous Western Han dynasty, Zhang wrote:

Achievements in science and technology

Mathematics

For centuries the Chinese approximated pi as 3; Liu Xin (d. CE 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. In his work around 130, Zhang Heng compared the celestial circle to the diameter of the earth, proportioning the former as 736 and the latter as 232, thus calculating pi as 3.1724. In Zhang's day, the ratio 4:3 was given for the area of a square to the area of its inscribed circle and the volume of a cube and volume of the inscribed sphere should also be 42:32. In formula, with D as diameter and V as volume, D3:V = 16:9 or V=\tfrac{9}{16}D3; Zhang realized that the value for diameter in this formula was inaccurate, noting the discrepancy as the value taken for the ratio. Zhang then attempted to remedy this by amending the formula with an additional \tfrac{1}{16}D3, hence V=\tfrac{9}{16}D3 + \tfrac{1}{16}D3 = \tfrac{5}{8}D3. 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. From this formula, Zhang calculated pi as the square root of 10 (or approximately 3.162). In the 3rd century, Liu Hui made the calculation more accurate with his π algorithm, which allowed him to obtain the value 3.14159. Later, Zu Chongzhi (429–500) approximated pi as \tfrac{355}{113} or 3.141592, the most accurate calculation for pi the ancient Chinese would achieve.

Astronomy

In his publication of AD 120 called The Spiritual Constitution of the Universe (靈憲, Ling Xian, lit. "Sublime Model"), 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. 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 China's first star catalogue in the 4th century BC, Zhang nonetheless catalogued 2,500 stars which he placed in a "brightly shining" category (the Chinese estimated the total to be 14,000), and he recognized 124 constellations. In comparison, this star catalogue featured many more stars than the 850 documented by the Greek astronomer Hipparchus in his catalogue, and more than Ptolemy (AD 83–161), who catalogued over 1,000. Zhang supported the "radiating influence" theory to explain solar and lunar eclipses, a theory which was opposed by Wang Chong (AD 27–97). In the Ling Xian, Zhang wrote:

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. Contemporary writers also wrote about eclipses and the sphericity of heavenly bodies. The music theorist and mathematician 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 look bright, those parts which it does not, remain dark.

The theory posited by Zhang and Jing was 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. The theory of the celestial sphere surrounding a flat, square Earth was later criticized by the Jin-dynasty scholar-official Yu Xi (fl. 307–345). He suggested that the Earth could be round like the heavens, a spherical Earth theory fully accepted by mathematician Li Ye (1192–1279) but not by mainstream Chinese science until European influence in the 17th century.

Extra tank for inflow clepsydra

The outflow clepsydra was a timekeeping device used in China as long ago as the Shang dynasty (c. 1600–c. 1050 BC), and certainly by the Zhou dynasty (1122–256 BC). 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. 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. Zhang Heng was the first to address this problem, indicated in his writings from 117, by adding an extra compensating tank between the reservoir and the inflow vessel. 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. Joseph Needham states that this was perhaps the ancestor of all clock jacks that would later sound the hours found in mechanical clocks by the 8th century, but he notes that these figures did not actually move like clock jack figurines or sound the hours. Many additional compensation tanks were added to later clepsydras in the tradition of Zhang Heng. In 610 the Sui dynasty (581–618) engineers Geng Xun and Yuwen Kai crafted 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. Zhang mentioned a "jade dragon's neck", which in later times meant a siphon. He wrote of the floats and indicator-rods of the inflow clepsydra as follows:

Water-powered armillary sphere

Zhang Heng is the first person known to have applied hydraulic motive power (i.e. by employing a waterwheel and clepsydra) to rotate an armillary sphere, an astronomical instrument representing the celestial sphere. The Greek astronomer Eratosthenes (276–194 BC) invented the first armillary sphere in 255 BC. The Chinese armillary sphere was fully developed by 52 BC, with the astronomer Geng Shouchang's (耿壽昌) addition of a permanently fixed equatorial ring. In AD 84 the astronomers Fu An and Jia Kui added the ecliptic ring, and finally Zhang Heng added the horizon and meridian rings. This invention is described and attributed to Zhang in quotations by Hsu Chen and Li Shan, referencing his book Lou Shui Chuan Hun Thien I Chieh (Apparatus for Rotating an Armillary Sphere by Clepsydra Water). It was likely not an actual book by Zhang, but a chapter from his Hun I or Hun I Thu Chu, written in 117 AD. His water-powered armillary influenced the design of later Chinese water clocks and led to the discovery of the escapement mechanism by the 8th century. 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 (AD 725 ) 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.

Zhang did not initiate the Chinese tradition of hydraulic engineering, which began during the mid Zhou dynasty (c. 6th century BC), through the work of engineers such as Sunshu Ao and Ximen Bao. Zhang's contemporary, Du Shi, (d. AD 38) was the first to apply the motive power of waterwheels to operate the bellows of a blast furnace to make pig iron, and the cupola furnace to make cast iron. 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.

Zhang Heng's water-powered armillary sphere had profound effects on Chinese astronomy and mechanical engineering in later generations. His model and its complex use of gears greatly influenced the water-powered instruments of later astronomers such as Yi Xing (683–727), Zhang Sixun (fl. 10th century), Su Song (1020–1101), Guo Shoujing (1231–1316), and many others. Water-powered armillary spheres in the tradition of Zhang Heng's were used in the eras of the Three Kingdoms (220–280) and Jin dynasty (266–420), yet the design for it was temporarily out of use between 317 and 418, due to invasions of northern Xiongnu nomads. Zhang Heng's old instruments were recovered in 418, when Emperor Wu of Liu Song (r. 420–422) captured the ancient capital of Chang'an. Although still intact, the graduation marks and the representations of the stars, Moon, Sun, and planets were quite worn down by time and rust. In 436, the emperor ordered Qian Luozhi, the Secretary of the Bureau of Astronomy and Calendar, to recreate Zhang's device, which he managed to do successfully. Qian's water-powered celestial globe was still in use at the time of the Liang dynasty (502–557), and successive models of water-powered armillary spheres were designed in subsequent dynasties.

Zhangs seismoscope

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 powerful enough to divert the courses of three rivers. It was not known at the time that earthquakes were caused by the shifting of tectonic plates in the Earth's crust; instead, the people of the ancient Zhou dynasty explained them as 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. These theories were ultimately derived from the ancient text of the Yijing, in its fifty-first hexagram. There were other early theories about earthquakes, developed by those such as the ancient Greeks. 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.

During the Han dynasty, many learned scholars—including Zhang Heng—believed in the "oracles of the winds". These oracles of the occult observed the direction, force, and timing of the winds, to speculate about the operation of the cosmos and to predict events on Earth. These ideas influenced Zhang Heng's views on the cause of earthquakes.

In 132, Zhang Heng presented to the Han court what many historians consider to be his most impressive invention, the first seismoscope. A seismoscope records the motions of Earth's shaking, but unlike a seismometer, it does not retain a time record of those motions. It was named "earthquake weathervane" ( 候風地動儀), and it was able to roughly determine the direction (out of eight directions) where the earthquake came from. According to the Book of Later Han (compiled by Fan Ye in the 5th century), his bronze urn-shaped device, with a swinging pendulum inside, was able to detect the direction of an earthquake hundreds of miles/kilometers away. This was essential for the Han government in sending quick aid and relief to regions devastated by this type of natural disaster. The Book of Later Han records that, on one occasion, Zhang's device was triggered, though no observer had felt any seismic disturbance; several days later a messenger arrived from the west and reported that an earthquake had occurred in Longxi (modern Gansu Province), the same direction that Zhang's device had indicated, and thus the court was forced to admit the efficacy of the device.

To indicate the direction of a distant earthquake, Zhang's device dropped a bronze ball from one of eight tubed projections shaped as dragon heads; the ball fell into the mouth of a corresponding metal object shaped as a toad, each representing a direction like the points on a compass rose. His device had eight mobile arms (for all eight directions) connected with cranks having catch mechanisms at the periphery. When tripped, a crank and right angle lever would raise a dragon head and release a ball which had been supported by the lower jaw of the dragon head. His device also included a vertical pin passing through a slot in the crank, a catch device, a pivot on a projection, a sling suspending the pendulum, an attachment for the sling, and a horizontal bar supporting the pendulum. Wang Zhenduo argued that the technology of 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.

Later Chinese of subsequent periods were able to reinvent Zhang's seismoscope. They 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). Like Zhang, Xindu Fang and Lin Xiaogong were given imperial patronage for their services in craftsmanship of devices for the court. By the time of the Yuan dynasty (1271–1368), it was acknowledged that all devices previously made were preserved, except for that of the seismoscope. This was discussed by the scholar Zhou Mi around 1290, who remarked that the books of Xindu Fang and Lin Xiaogong detailing their seismological devices were no longer to be found. 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."

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. Wang Zhenduo presented two different models of the seismoscope based on the ancient descriptions of Zhang's device. In his 1936 reconstruction, 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. According to Needham, while working in the Seismological Observatory of Tokyo University in 1939, Akitsune Imamura and Hagiwara made a reconstruction of Zhang's device. While it was John 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. 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. On June 13, 2005, modern Chinese seismologists announced that they had successfully created a replica of the instrument.

Anthony J. Barbieri-Low, a professor of early Chinese history at the University of California, Santa Barbara, names Zhang Heng as one of several high-ranking Eastern-Han officials who engaged in crafts that were traditionally reserved for artisans (gong 工), such as mechanical engineering. Barbieri-Low speculates that Zhang only designed his seismoscope, but did not actually craft the device himself. He asserts that this would most likely have been the job of artisans commissioned by Zhang. He writes: "Zhang Heng was an official of moderately high rank and could not be seen sweating in the foundries with the gong artisans and the government slaves. Most likely, he worked collaboratively with the professional casters and mold makers in the imperial workshops."

Cartography

The Wei (220–265) and Jin dynasty (266–420) 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. However, map-making in China had existed since at least the 4th century BC with the Qin state maps found in Gansu in 1986. 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. 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. Rafe de Crespigny asserts that it was Zhang who established the rectangular grid system in Chinese cartography. Needham points out that the title of his book Flying Bird Calendar may have been a mistake, and that the book is more accurately entitled Bird's Eye Map. 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). It is documented that a physical geography map was first presented by Zhang Heng in 116 AD, called a Dixingtu (地形圖).

Odometer and south-pointing chariot

Zhang Heng is often credited with inventing the first odometer, an achievement also attributed to Archimedes (c. 287–212 BC) and Heron of Alexandria (fl. AD 10–70). Similar devices were used by the Roman and Han-Chinese empires at about the same period. By the 3rd century, the Chinese had termed the device the jili guche (記里鼓車, "li-recording drum carriage" (the modern measurement of li = 500 m/1640 ft).

Ancient Chinese texts describe the mechanical carriage's functions; after one li was traversed, a mechanically driven wooden figure struck a drum, and after ten li had been covered, another wooden figure struck a gong or a bell with its mechanically operated arm. However, there is evidence to suggest that the invention of the odometer was a gradual process in Han dynasty China that centered on the "huang men"—court people (i.e. eunuchs, palace officials, attendants and familiars, actors, acrobats, etc.) who followed the musical procession of the royal "drum-chariot". There is speculation that at some time during the 1st century BC the beating of drums and gongs was mechanically driven by the rotation of the road wheels. 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.

The south-pointing chariot was another mechanical device credited to Zhang Heng. It was a non-magnetic compass vehicle in the form of a two-wheeled chariot. Differential gears driven by the chariot's wheels allowed a wooden figurine (in the shape of a Chinese state minister) to constantly point to the south, hence its name. The Song Shu (c. AD 500 ) records that Zhang Heng re-invented it from a model used in the Zhou dynasty era, but the violent collapse of the Han dynasty unfortunately did not allow it to be preserved. Whether Zhang Heng invented it or not, Ma Jun (200–265) succeeded in creating the chariot in the following century.

Legacy

Science and technology

Zhang Heng's mechanical inventions influenced later Chinese inventors such as Yi Xing, Zhang Sixun, Su Song, and Guo Shoujing. Su Song directly named Zhang's water-powered armillary sphere as the inspiration for his 11th-century clock tower. 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. The seismologist John Milne, who created the modern seismograph in 1876 alongside Thomas Gray and James A. Ewing at the Imperial College of Engineering in Tokyo, commented in 1886 on Zhang Heng's contributions to seismology. The historian Joseph Needham emphasized his contributions to 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." More than one scholar has described Zhang as a polymath. However, some scholars also point out that Zhang's writing lacks concrete scientific theories. Comparing Zhang with 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.

Poetic literature

Zhang's poetry was widely read during his life 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". 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. 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".

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, 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?"

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. Cui stated, "Heng's 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." The minor official Xiahou Zhan (243–291) of the Wei dynasty made an inscription for his own commemorative stele to be placed at Zhang Heng's tomb. It read: "Ever since gentlemen have composed literary texts, none has been as skillful as the Master Heng in choosing his words well ... if only the dead could rise, oh I could then turn to him for a teacher!"

Several things have been named after Zhang in modern times, including the lunar crater Chang Heng, the asteroid 1802 Zhang Heng, and the mineral zhanghengite. In 2018, China launched a research satellite called China Seismo-Electromagnetic Satellite (CSES) which is also named Zhangheng-1 (ZH-1).