生平

张衡出身于南阳大族，祖父张堪是蜀郡太守。他少年时曾到雒阳太学读书，通晓五经，好学不倦，不分日夜。张衡为人谦虚，意志坚定，淡泊名利。曾受举荐「孝廉」，被大将军外戚邓骘徵召，但张衡都不接受。100年，22岁的张衡出任南阳郡太守鲍德的主簿，8年后辞官读书。鲍德升职为大司农后，热心推荐张衡；111年，张衡被汉安帝所召，出任尚书台郎中，3年后迁任尚书侍郎；115年，37岁的张衡开始出任太史令，121年调职公车司马令，126年复任太史令。任职太史令期间，他制作了浑天仪与地动仪。张衡掌领太史令先后达14年之久，这个职位相当于现在中国科学院国家天文台的台长。张衡长期掌管历史记载和历法，没有升官，被同僚所笑。他写下《答难》来表明心志，不慕官位。他又曾上疏痛陈事弊，提出必须禁止大臣奢侈和僭越的主张。133年雒阳大地震，张衡藉此上谏，批评宦官越权，主张大权归还天子。同年张衡迁任侍中。因受当权宦官排斥，136年外调河间相。在河间政绩良好，138年他升迁尚书，次年过世，享年61岁他的传世著作有文集11卷，《灵宪》、《浑天仪》、《玄图》各一卷及数学著作《算罔论》。

家族

祖父张堪曾任蜀郡太守。

西晋大臣张辅是其后代。

贡献

天文学

张衡主张浑天说，认为天是球状的，像个鸡蛋，天相当于蛋壳，大地像蛋黄，天把大地包在当中，大地是平面的，周围是水，大地浮在水上。他改进西汉耿寿昌的设计，制造了浑天仪，并著有《浑天仪》一卷加以解说。浑天仪一具安装在室内，一具安装在观测台「灵台」之上。浑天仪以铜铸造，是空心球体，直径约五尺，上画二十八宿、中外星官及黄道、赤道；天球半露在地平圈上，半隐在地平圈下，天轴则支架在子午圈上，天球可绕天轴自行转动，与实际天球运动相一致，可预报天体运动情况；其外安装了地平环、赤道环和子午环，内部设置四游环。有学者认为，张衡的浑天仪上面装置了可以眺望天体位置的望筒，兼具演示和观测效用；也有学者认为，此浑天仪没有望筒，只有演示作用，性质上是天球仪。浑天仪每日均匀地绕中轴旋转一周，以滴水为原动力，与漏刻相连，水不断定量而缓缓地流入刻漏的水斗中。水斗原是静止不动的，当注水达到某个份量时，其重量就胜过浑天仪和齿轮的阻力，凸耳使齿轮转动一齿，然后抵住下一齿而再次静止下来，通过齿轮传动而使浑天仪缓慢地旋转。张衡所造浑天仪是个原型、早期的时钟，在五胡乱华中毁坏；在西方，类似能自动旋转的浑象在16世纪出现。

张衡在东方最早正确说明月蚀，指出月蚀是由于地球的影子「暗虚」遮掩了月亮而引起的，并测得日、月的视直径约为\frac{365.25} {730}度，约等于0.5度，与现今测值相近。张衡绘制了星图，记录星官124个，星星有2500颗，其中320颗有名字，指出历法制定必须根据实测结果，曾在123年参与历法辩论，反对依据图谶而制定的「甲寅历」，根据月亮运行有迟疾的规律，以「九道法」为基础提出新历，但没有被朝廷采纳。他提出五星视运动的理论，认为就同一行星而言，其运行轨道与地面时而接近，时而远离，「近天则迟，远天则速」，解释五星运行的或快或慢；运动缓慢的外行星火星、木星、土星，张衡归类为阳，运动较快的内行星水星和金星，归类为阴。张衡没有认识到北极高度会随地点而变化，定出北极高度是36度，他也没有认识岁差，因冬至点难以观测，只从西汉末年所测的旧数值换算，定出冬至点以黄道度量为入斗宿20度，较当时实际情况偏东超过3度；他并根据观测，定出冬至黄道最远时去极115度，夏至黄道去极67度，因受仪器所限，数据稍欠精确。

宇宙论

张衡虽然反对图谶，但他的宇宙论却受当时流行的谶纬影响。他撰有天文学著作《灵宪》，叙述宇宙生成论，观点接近西汉《淮南子·天文训》。他提出宇宙形成的三个阶段，首先是「溟滓」，是气的原始状态，什么都没有，是「无」的阶段，道的根本；第二是「庞鸿」，是元气开始发动、连结在一起、混沌不分的状态；第三是「太元」，元气分化，有刚柔清浊之分，天地各自形成，阴阳四时变化而生万物。天圆地平，天是一个中空的球体，地是半球体，上平下圆，处于天体下半部。八极约长二亿三万二千三百里，南北少一千里，东西多一千里，天地距离和地的厚度，都等于八极的一半。他指出宇宙是无穷无极的，肯定时间与空间的无限性，提出以「气」为基本的自然观，人是元气的聚合，如水之凝结为冰，人死是元气消散，如冰块融化为水，复归于元气，与自然成为一体。

数学

130年前后，张衡完成推算圆周率。根据三国时刘徽《九章算术注》，张衡认为立方体及其内接球体积之比，是8:5，由此推论圆周率是10的平方根：。南北朝祖暅《浑天论》则提到张衡提出的另一个数字：；有学者认为今本文献有衍文，张衡的数字其实是较准确的，此说未被广泛接受。张衡的圆周率数字其实颇为粗疏，受刘徽严词批评，西汉末年刘歆指出圆周率为3.1547，已比张衡更准确；但张衡的计算并非倚靠实测，而是从理论出发，从立圆术公式推求圆周率，仍有开创性的贡献。张衡也曾研究球体体积，但没有重大改进。

地理学

132年，张衡发明和制造了世上第一部验震器「候风地动仪」，形状像圆形的酒瓮，断面直径八尺，其内中央置有一根很重的柱子，称「都柱」，可以向八个方向倾侧或倾摆；酒瓮外部的八个方向各有一个龙头，龙头下各有一只蟾蜍，张口对著龙头，八条龙各口含铜丸一颗，当都柱向某一方倾侧时，该方向的龙口张开，铜丸落下，掉入蟾蜍口中。地震发生时，只有震源方向上的龙头张口，据此可知地震的方向。范晔《后汉书》记载，地动仪放在雒阳，134年12月13日，陇西发生地震，当时雒阳并无震动，但一个龙口掉出铜丸，其后才传来陇西地震的消息，证实其探测地震方向的功效。而候风地动仪所谓的「候风」，是指测定风的变化，地震相信是因为阴阳两气相搏而形成，气的变化会产生风；哪个地方有地震，哪个方向就有气的变化，就有风来可以测到。候风地动仪流传到隋代，北朝信都芳、隋代临孝恭都研究过，到唐代失传。

地动仪利用物体的惯性来测震，其构造学者有两种看法，其一认为，都柱是个挂起的悬摆，又重又粗，都柱下有一小铜球，组成触发机制，在地震波水平运动中，都柱移位，小铜球脱落，撞击机关，又或都柱带动八条向八个方位伸出去的臂，连接扛杆，当悬摆向某一方向摆动时，龙口就会张开。另一种观点是，都柱是一种倒立的震摆，附有重锤，安装在底座上，周围有八组机械装置，一旦地震，重锤倾侧，都柱失去平衡，触道机械装置，使相应的龙口张开。现代中、日学者都尝试复原地动仪，日本学者曾以直立震摆式的地动仪模型做实验，证明地震初震很强的话，铜丸会因初到的纵波而落下，确定地震的方向；但其他地震学者却指出，直立震摆的倾倒方向有随机性，对震动反应迟钝，没有验震作用，直立震摆底部所用的弹簧，也不可能是汉代技术水平的产物，而悬摆式的地动仪模型，在2000年代则通过中国地震学者用振动台模拟地震状态的试验，得到中国学术界的认可。张衡地动仪比直至19世纪前期西方的水银地震仪更先进，但亦有个别学者质疑《后汉书》中有关地动仪的记载，指出从现代地震学的观点看，若单独一个仪器，仅在一个地点进行测量，难以测定震源。

116年，张衡绘制和呈献地图「地形图」，流传到唐代；李约瑟推测张衡曾运用计里画方的网格绘图，但此说受其他学者质疑。

其他发明

浑天仪和候风地动仪以外，张衡发明了指南车、「自飞木雕」和机械日历，并改良了漏刻的构造。指南车是双轮马车，内置齿轮装置，即使行驶时多次转向，车上人像亦永远指向正南；张衡所造指南车在汉末战乱中被毁。自飞木雕是一只木鸟，有羽翼，腹内有机械，能飞起，张衡〈应间〉曾提到这只能飞的木雕：「木雕犹能独飞」。李约瑟推测自飞木雕以弹簧为动力，推动直升陀螺的螺旋桨。张衡在漏刻使用虹吸管（称为「玉虬」），代替壶底的漏咀，并在贮水壶和受水壶之间加入一个补偿壶，使计时更准确；受水壶盖上铸有个小塑像，左手持著可以上下浮动的垂直指示杆（「漏箭」），右手则指向指示杆上的刻度。机械日历「瑞轮蓂荚」像浑天仪一样，都是水力推动的，能显示月相和朔望月的天数。有学者认为张衡也制造了风向仪，古书上「候风地动仪」其实是指风向仪和地动仪两种仪器，这种风向仪是鸟状的，能随风转动。

思想

政治上，张衡坚持批判现实，对宫廷政治的污浊奸诈深感忧愤，反对王侯贵族的奢侈生活。他受道家思想影响，倾向老、庄，主张无为，有人生无常、遁隐厌世的思想，企图超越世俗生活，其宇宙论也体现道家观念，晩期作品〈思玄赋〉道家倾向更强。他继承了西汉儒家董仲舒的灾异、天人感应之说，认为星象变异和地震等灾异，是上天对世人和朝廷的谴告，促使他制造更精密的仪器去认识宇宙和侦测地震，以察知天意；但他反对谶纬预言，曾上〈请禁绝图谶疏〉，指出图谶弄虚作假，为迎合当权者而伪造。他推崇西汉扬雄的《太玄》，认为「玄」是宇宙的根本原理，《太玄》一书深奥而难以理解。他相信天上有许多神、星神、四方神、天皇等等，不但天上有神，山林原野都有神灵，天体的组织，则与地上朝廷政府的组织相对应，月亮上有蟾蜍，由嫦娥所变，星星会影响人的命运。张衡熟悉「风角」之术，认为可透过观风而知祸福，相信占卜，宇宙间有某种神秘力量，绝非所有事物都可用理性解释。

文学

张衡是辞赋名家，将汉赋推向高峰，由歌功颂德的辞赋发展为抒情小赋，现存大致完整的作品有〈温泉赋〉、〈南都赋〉、〈二京赋〉、〈思玄赋〉、〈归田赋〉、〈髑髅赋〉、〈天象赋〉、〈应间〉、〈七辩〉九篇。〈温泉赋〉描写长安附近骊山著名的温泉，属早期作品；〈二京赋〉长达7700字，是模仿班固〈两都赋〉的大赋，辞藻典雅瑰丽，夸张铺陈，堪称不朽佳作。〈西京赋〉假借凭虚公子之口，描写长安地理形势、汉高祖的定都、西都的豪华、宫殿的宏伟、城廓的宽大、市场的繁荣、商贾的欺诈、游侠的作风、园林中的游猎，〈东京赋〉则假借安处先生之口追溯历史，从周、秦、两汉各代帝王，赞颂汉高祖、汉文帝、汉武帝等，描写雒阳形胜和汉室仪轨；二赋也描述宗教活动和民间风俗，如持守色戒的西域僧人、杂技歌舞等「百戏」表演、驱邪的大傩仪式，有其史料价值，可补正史的不足；〈西京赋〉即为南北朝《三辅黄图》和北宋宋敏求《长安志》多次引用，以说明长安面貌。〈二京赋〉引用不少五经句子，文句为何晏〈景福殿赋〉、左思〈蜀都赋〉等后世辞赋袭用，并有东吴薛综等人的注释。〈南都赋〉则盛赞当时被朝廷忽略的南阳城，但形式较呆板笨拙，语言则较艰深晦涩。

张衡〈思玄赋〉是抒情表志的作品，发表自己的理想，模仿楚辞〈远游〉和班固的〈幽通赋〉，重覆屈原在〈远游〉中的寻求，先去东、南、北三方，登上蓬莱，在瀛州采芝，又去拜会西王母，上了仙宫「琼宫」，尽享声色之娱，然后回到故乡。张衡深受楚辞影响，常引用楚地传统的神话，〈思玄赋〉引用最多的就是楚辞。〈归田赋〉开拓辞赋中田园归隐的主题，表达其退隐之心，反对宦官当权，政治腐败而自己无力拯救，有不愿同流合污之意，文中赞美民间的田园生活，山水景色使人心旷神怡，是汉赋中罕见的短篇，启导陶渊明〈归去来辞〉等后世抒发归隐之情的作品，所写自然风景欢乐和谐，也启导王羲之〈兰亭集序〉等后世文章，文中道家思想鲜明，则可说是后世玄言诗的先驱。〈髑髅赋〉以对话体扩充铺陈《庄子．至乐》篇中的寓言，赋中的髑髅就是庄子。有后人批评，张衡的辞赋缺乏独创性，主要模仿前人著作，如〈二京赋〉模仿班固〈两都赋〉，〈南都赋〉模仿扬雄〈蜀都赋〉，〈应间〉模仿东方朔〈答客难〉，〈七辩〉则模仿枚乘〈七发〉。

诗歌方面，张衡初次撰写七言古诗〈四愁诗〉，脱离了楚歌的句式，接近纯粹的七言诗，并为后世诗人模仿，如晋代傅玄撰有〈拟张衡四愁诗〉。张衡〈同声歌〉则是新娘向新郎的倾诉，描写新婚的优美，诗中提到房中术著作《素女经》的内容。

经学、史学、美术

张衡通晓经学，曾撰写《周官训诂》，但稍欠特色，失传于世。他对汉朝历史亦相当了解，有志于史学，担任侍中时，曾请求到东观专心撰写东汉史书，但不获批准；又曾上书指摘司马迁《史记》和班固《汉书》两书的错失，提出汉朝史书应有的体例。张衡亦是个画家，列为东汉六大画家之一，唐代《历代名画记》曾记载他曾用脚趾画怪兽这一传说。

地位与纪念

张衡名列「汉赋四大家」之一，受尊崇为中国历史上的大科学家。在东汉，崔瑗称赞他能知天文地理，制作巧夺天工，「数术穷天地，制作侔造化，与神合契」，南阳人为他修建庙宇；三国时傅玄则惋惜他不在其位，工艺才华未能尽情发挥；他的地动仪和天文学成就都没有传人，天文学著作残缺不全，科学贡献渐被后人遗忘。有学者猜测，地动仪的原理在古代可能已辗转传到波斯和日本。19世纪末，西方地震学家开始留意到张衡地动仪的开创性成就，有学者认为，米尔恩所造的首座现代地震仪，就是受地动仪启发的。1920年代，中国史家也注意到张衡的科学成就，1924年，张荫麟首先称赞张衡为中国「第一位大科学家」，李约瑟特别推崇张衡，大部份现代中国学者亦称张衡为伟大的科学家。学者认为张衡可与西方几乎同时代的托勒密相媲美，但在数学、几何学、科学方法和研究成果，张衡都不如托勒密。

南阳张衡墓地久已荒废，偶有士人加以修葺，当地人亦不知墓主是谁；1956年，南阳县政府重建张衡墓园，建立张衡博物馆，附有仿汉建筑与石雕，1988年定为国家级重点文物保护单位，馆内展示张衡发明的地动仪、浑天仪、指南车等模型。为了纪念张衡，1970年，国际天文学界用张衡名字为月球背面一座环形山命名；1971年，以他来命名小行星1802；中国天文学会设立「张衡特殊贡献奖」，2002年首次颁发；2003年，小行星9092以张衡故乡南阳命名；一种铜锌合金的天然矿物亦以张衡命名，即张衡矿。

深圳市龙岗区阪田街道华为基地有一条以张衡命名的街道——张衡路。

相关条目

• 浑天说、浑象、浑仪

• 地震仪、候风地动仪

• 指南车、瑞轮蓂荚

• 张衡一号

• 令和

注释

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 very affluent family. His grandfather Zhang Kan 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 温泉赋), 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 103–111). 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 115–120 under Emperor An and his second under the succeeding emperor from 126–132. 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 (东观汉记), 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 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 (Wen xuan 文选). Zhang's fu rhapsodies include "Western Metropolis Rhapsody" (Xī jīng fù 西京赋), "Eastern Metropolis Rhapsody" (Dōng jīng fù 东京赋), "Southern Capital Rhapsody" (Nán dū fù 南都赋), "Rhapsody on Contemplating the Mystery" (Sī xuán fù 思玄赋), and "Rhapsody on Returning to the Fields" (Guī tián fù 归田赋). 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 (shi 诗) entitled "Lyric Poems on Four Sorrows" (Sì chóu shī 四愁诗), 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. 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, 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 定情赋) — 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. 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). 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 came 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" (西京赋), Zhang described court entertainments such as juedi (角抵), 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 应间), 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. AD 23) made the first known Chinese attempt at a more accurate calculation of 3.1457, 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). Zhang also calculated pi as \tfrac{730}{232} = 3.1466 in his book Ling Xian (灵宪). 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 (灵宪, 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 (c. 190–c.120 BC) 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 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 (Book of Changes), 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" (hòufēng dìdòngyí 候风地动仪), 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 (王振铎) 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 Ti Hsing Thu.

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 (记里鼓车, "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).