Monogamous marriages were also normal, although nobles and high officials were wealthy enough to afford and support concubines as additional lovers. Under certain conditions dictated by custom, not law, both men and women were able to divorce their spouses and remarry. However, a woman who had been widowed continued to belong to her husband's family after his death. In order to remarry, the widow would have to be returned to her family in exchange for a ransom fee. Her children would not be allowed to go with her.
Apart from the passing of noble titles or ranks, inheritance practices did not involve primogeniture; each son received an equal share of the family property. Unlike the practice in later dynasties, the father usually sent his adult married sons away with their portions of the family fortune. Daughters received a portion of the family fortune through their marriage dowries, though this was usually much less than the shares of sons. A different distribution of the remainder could be specified in a will, but it is unclear how common this was.
Women were expected to obey the will of their father, then their husband, and then their adult son in old age. However, it is known from contemporary sources that there were many deviations to this rule, especially in regard to mothers over their sons, and empresses who ordered around and openly humiliated their fathers and brothers. Women were exempt from the annual corvée labor duties, but often engaged in a range of income-earning occupations aside from their domestic chores of cooking and cleaning.
The most common occupation for women was weaving clothes for the family, sale at market or for large textile enterprises that employed hundreds of women. Other women helped on their brothers' farms or became singers, dancers, sorceresses, respected medical physicians, and successful merchants who could afford their own silk clothes. Some women formed spinning collectives, aggregating the resources of several different families.
Education, literature, and philosophy.
The early Western Han court simultaneously accepted the philosophical teachings of Legalism, Huang-Lao Daoism, and Confucianism in making state decisions and shaping government policy. However, the Han court under Emperor Wu gave Confucianism exclusive patronage. He abolished all academic chairs or erudites ("bóshì" 博士) not dealing with the Confucian Five Classics in 136 BCE and encouraged nominees for office to receive a Confucian-based education at the Imperial University that he established in 124 BCE. 
Unlike the original ideology espoused by Confucius, or Kongzi (551–479 BCE), Han Confucianism in Emperor Wu's reign was the creation of Dong Zhongshu (179–104 BCE). Dong was a scholar and minor official who aggregated the ethical Confucian ideas of ritual, filial piety, and harmonious relationships with five phases and yin-yang cosmologies. Much to the interest of the ruler, Dong's synthesis justified the imperial system of government within the natural order of the universe. 
The Imperial University grew in importance as the student body grew to over 30,000 by the 2nd century CE. A Confucian-based education was also made available at commandery-level schools and private schools opened in small towns, where teachers earned respectable incomes from tuition payments.
Some important texts were created and studied by scholars. Philosophical works written by Yang Xiong (53 BCE – 18 CE), Huan Tan (43 BCE – 28 CE), Wang Chong (27–100 CE), and Wang Fu (78–163 CE) questioned whether human nature was innately good or evil and posed challenges to Dong's universal order. The "Records of the Grand Historian" by Sima Tan (d. 110 BCE) and his son Sima Qian (145–86 BCE) established the standard model for all of imperial China's Standard Histories, such as the "Book of Han" written by Ban Biao (3–54 CE), his son Ban Gu (32–92 CE), and his daughter Ban Zhao (45–116 CE). There were dictionaries such as the "Shuowen Jiezi" by Xu Shen ( – CE) and the "Fangyan" by Yang Xiong.
Biographies on important figures were written by various gentrymen. Han dynasty poetry was dominated by the "fu" genre, which achieved its greatest prominence during the reign of Emperor Wu.
Law and order.
Han scholars such as Jia Yi (201–169 BCE) portrayed the previous Qin dynasty as a brutal regime. However, archaeological evidence from Zhangjiashan and Shuihudi reveal that many of the statutes in the Han law code compiled by Chancellor Xiao He (d. 193 BCE) were derived from Qin law.
Various cases for rape, physical abuse and murder were prosecuted in court. Women, although usually having fewer rights by custom, were allowed to level civil and criminal charges against men. While suspects were jailed, convicted criminals were never imprisoned. Instead, punishments were commonly monetary fines, periods of forced hard labor for convicts, and the penalty of death by beheading. Early Han punishments of torturous mutilation were borrowed from Qin law. A series of reforms abolished mutilation punishments with progressively less-severe beatings by the bastinado.
Acting as a judge in lawsuits was one of many duties of the county magistrate and Administrators of commanderies. Complex, high-profile or unresolved cases were often deferred to the Minister of Justice in the capital or even the emperor. In each Han county was several districts, each overseen by a chief of police. Order in the cities was maintained by government officers in the marketplaces and constables in the neighborhoods.
Food.
The most common staple crops consumed during Han were wheat, barley, foxtail millet, proso millet, rice, and beans. Commonly eaten fruits and vegetables included chestnuts, pears, plums, peaches, melons, apricots, strawberries, red bayberries, jujubes, calabash, bamboo shoots, mustard plant, and taro. Domesticated animals that were also eaten included chickens, Mandarin ducks, geese, cows, sheep, pigs, camels, and dogs (various types were bred specifically for food, while most were used as pets). Turtles and fish were taken from streams and lakes. Commonly hunted game, such as owl, pheasant, magpie, sika deer, and Chinese bamboo partridge were consumed. Seasonings included sugar, honey, salt, and soy sauce. Beer and wine were regularly consumed.
Clothing.
The types of clothing worn and the materials used during the Han period depended upon social class. Wealthy folk could afford silk robes, skirts, socks, and mittens, coats made of badger or fox fur, duck plumes, and slippers with inlaid leather, pearls, and silk lining. Peasants commonly wore clothes made of hemp, wool, and ferret skins.
Religion, cosmology, and metaphysics.
Families throughout Han China made ritual sacrifices of animals and food to deities, spirits, and ancestors at temples and shrines. They believed that these items could be utilized by those in the spiritual realm. It was thought that each person had a two-part soul: the spirit-soul ("hun" 魂) which journeyed to the afterlife paradise of immortals ("xian"), and the body-soul ("po" 魄) which remained in its grave or tomb on earth and was only reunited with the spirit-soul through a ritual ceremony.
In addition to his many other roles, the emperor acted as the highest priest in the land who made sacrifices to Heaven, the main deities known as the Five Powers, and the spirits ("shen" 神) of mountains and rivers. It was believed that the three realms of Heaven, Earth, and Mankind were linked by natural cycles of yin and yang and the five phases. If the emperor did not behave according to proper ritual, ethics, and morals, he could disrupt the fine balance of these cosmological cycles and cause calamities such as earthquakes, floods, droughts, epidemics, and swarms of locusts.
It was believed that immortality could be achieved if one reached the lands of the Queen Mother of the West or Mount Penglai. Han-era Daoists assembled into small groups of hermits who attempted to achieve immortality through breathing exercises, sexual techniques and use of medical elixirs. 
By the 2nd century CE, Daoists formed large hierarchical religious societies such as the Way of the Five Pecks of Rice. Its followers believed that the sage-philosopher Laozi () was a holy prophet who would offer salvation and good health if his devout followers would confess their sins, ban the worship of unclean gods who accepted meat sacrifices and chant sections of the "Daodejing".
Buddhism first entered Imperial China through the Silk Road during the Eastern Han, and was first mentioned in 65 CE. Liu Ying (d. 71 CE), a half-brother to Emperor Ming of Han ( CE), was one of its earliest Chinese adherents, although Chinese Buddhism at this point was heavily associated with Huang-Lao Daoism. China's first known Buddhist temple, the White Horse Temple, was constructed outside the wall of the capital, Luoyang, during Emperor Ming's reign. Important Buddhist canons were translated into Chinese during the 2nd century CE, including the "Sutra of Forty-two Chapters", "Perfection of Wisdom", "Shurangama Sutra", and "Pratyutpanna Sutra".
Government and politics.
Central government.
In Han government, the emperor was the supreme judge and lawgiver, the commander-in-chief of the armed forces and sole designator of official nominees appointed to the top posts in central and local administrations; those who earned a 600-bushel salary-rank or higher. Theoretically, there were no limits to his power. 
However, state organs with competing interests and institutions such as the court conference ("tingyi" 廷議)—where ministers were convened to reach majority consensus on an issue—pressured the emperor to accept the advice of his ministers on policy decisions. If the emperor rejected a court conference decision, he risked alienating his high ministers. Nevertheless, emperors sometimes did reject the majority opinion reached at court conferences.
Below the emperor were his cabinet members known as the Three Councillors of State ("San gong" 三公). These were the Chancellor or Minister over the Masses ("Chengxiang" 丞相 or "Da situ" 大司徒), the Imperial Counselor or Excellency of Works ("Yushi dafu" 御史大夫 or "Da sikong" 大司空), and Grand Commandant or Grand Marshal ("Taiwei" 太尉 or "Da sima" 大司馬).
The Chancellor, whose title was changed to 'Minister over the Masses' in 8 BC, was chiefly responsible for drafting the government budget. The Chancellor's other duties included managing provincial registers for land and population, leading court conferences, acting as judge in lawsuits and recommending nominees for high office. He could appoint officials below the salary-rank of 600 bushels.
The Imperial Counselor's chief duty was to conduct disciplinary procedures for officials. He shared similar duties with the Chancellor, such as receiving annual provincial reports. However, when his title was changed to Minister of Works in 8 BC, his chief duty became oversight of public works projects.
The Grand Commandant, whose title was changed to Grand Marshal in 119 BC before reverting to Grand Commandant in 51 AD, was the irregularly posted commander of the military and then regent during the Western Han period. In the Eastern Han era he was chiefly a civil official who shared many of the same censorial powers as the other two Councillors of State.
Ranked below the Three Councillors of State were the Nine Ministers ("Jiu qing" 九卿), who each headed a specialized ministry. The Minister of Ceremonies ("Taichang" 太常) was the chief official in charge of religious rites, rituals, prayers and the maintenance of ancestral temples and altars. The Minister of the Household ("Guang lu xun" 光祿勳) was in charge of the emperor's security within the palace grounds, external imperial parks and wherever the emperor made an outing by chariot.
The Minister of the Guards ("Weiwei" 衛尉) was responsible for securing and patrolling the walls, towers, and gates of the imperial palaces. The Minister Coachman ("Taipu" 太僕) was responsible for the maintenance of imperial stables, horses, carriages and coach-houses for the emperor and his palace attendants, as well as the supply of horses for the armed forces. The Minister of Justice ("Tingwei" 廷尉) was the chief official in charge of upholding, administering, and interpreting the law. The Minister Herald ("Da honglu" 大鴻臚) was the chief official in charge of receiving honored guests at the imperial court, such as nobles and foreign ambassadors.
The Minister of the Imperial Clan ("Zongzheng" 宗正) oversaw the imperial court's interactions with the empire's nobility and extended imperial family, such as granting fiefs and titles. The Minister of Finance ("Da sinong" 大司農) was the treasurer for the official bureaucracy and the armed forces who handled tax revenues and set standards for units of measurement. The Minister Steward ("Shaofu" 少府) served the emperor exclusively, providing him with entertainment and amusements, proper food and clothing, medicine and physical care, valuables and equipment.
Local government.
The Han empire, excluding kingdoms and marquessates, was divided, in descending order of size, into political units of provinces, commanderies, and counties. A county was divided into several districts ("xiang" 鄉), the latter composed of a group of hamlets ("li" 里), each containing about a hundred families.
The heads of provinces, whose official title was changed from Inspector to Governor and vice versa several times during Han, were responsible for inspecting several commandery-level and kingdom-level administrations. On the basis of their reports, the officials in these local administrations would be promoted, demoted, dismissed or prosecuted by the imperial court.
A governor could take various actions without permission from the imperial court. The lower-ranked inspector had executive powers only during times of crisis, such as raising militias across the commanderies under his jurisdiction to suppress a rebellion.
A commandery consisted of a group of counties, and was headed by an Administrator. He was the top civil and military leader of the commandery and handled defense, lawsuits, seasonal instructions to farmers and recommendations of nominees for office sent annually to the capital in a quota system first established by Emperor Wu. The head of a large county of about 10,000 households was called a Prefect, while the heads of smaller counties were called Chiefs, and both could be referred to as Magistrates. A Magistrate maintained law and order in his county, registered the populace for taxation, mobilized commoners for annual corvée duties, repaired schools and supervised public works.
Kingdoms and marquessates.
Kingdoms—roughly the size of commanderies—were ruled exclusively by the emperor's male relatives as semi-autonomous fiefdoms. Before 157 BC some kingdoms were ruled by non-relatives, granted to them in return for their services to Emperor Gaozu. The administration of each kingdom was very similar to that of the central government. Although the emperor appointed the Chancellor of each kingdom, kings appointed all the remaining civil officials in their fiefs.
However, in 145 BC, after several insurrections by the kings, Emperor Jing removed the kings' rights to appoint officials whose salaries were higher than 400 bushels. The Imperial Counselors and Nine Ministers (excluding the Minister Coachman) of every kingdom were abolished, although the Chancellor was still appointed by the central government.
With these reforms, kings were reduced to being nominal heads of their fiefs, gaining a personal income from only a portion of the taxes collected in their kingdom. Similarly, the officials in the administrative staff of a full marquess's fief were appointed by the central government. A marquess's Chancellor was ranked as the equivalent of a county Prefect. Like a king, the marquess collected a portion of the tax revenues in his fief as personal income.
Up until the reign of Emperor Jing of Han, the Emperors of the Han had great difficulty bringing the vassal kings under control, as kings often switched their allegiance to the Xiongnu Chanyu whenever threatened by Imperial attempts to centralize power. Within the seven years of Han Gaozu's reign, three vassal kings and one marquess either defected to or allied with the Xiongnu. Even imperial princes in control of fiefdoms would sometimes invite the Xiongnu to invade in response to threats by the Emperor to remove their power. The Han emperors moved to secure a treaty with the Chanyu to demarcate authority between them, recognizing each other as the "two masters" (兩主), the sole representatives of their respective peoples, cemented with a marriage alliance ("heqin"), before eliminating the rebellious vassal kings in 154 BC. This prompted some vassal kings of the Xiongnu to switch their allegiance to the Han emperor from 147 BC. Han court officials were initially hostile to the idea of disrupting the status quo and expanding into the Xiongnu steppe territory. The surrendered Xiongnu were integrated into a parallel military and political structure under the Han Emperor, and opened the avenue for the Han dynasty to challenge the Xiongnu cavalry on the steppe. This also introduced the Han to the interstate networks in the Tarim Basin (Xinjiang), allowing for the expansion of the Han dynasty from a limited regional state to a universalist and cosmopolitan empire through further marriage alliances with another steppe power, the Wusun.
Military.
At the beginning of the Han dynasty, every male commoner aged twenty-three was liable for conscription into the military. The minimum age for the military draft was reduced to twenty after Emperor Zhao's ( BC) reign. Conscripted soldiers underwent one year of training and one year of service as non-professional soldiers. The year of training was served in one of three branches of the armed forces: infantry, cavalry or navy. The year of active service was served either on the frontier, in a king's court or under the Minister of the Guards in the capital. A small professional (paid) standing army was stationed near the capital.
During the Eastern Han, conscription could be avoided if one paid a commutable tax. The Eastern Han court favored the recruitment of a volunteer army. The volunteer army comprised the Southern Army ("Nanjun" 南軍), while the standing army stationed in and near the capital was the Northern Army ("Beijun" 北軍). Led by Colonels ("Xiaowei" 校尉), the Northern Army consisted of five regiments, each composed of several thousand soldiers. When central authority collapsed after 189 AD, wealthy landowners, members of the aristocracy/nobility, and regional military-governors relied upon their retainers to act as their own personal troops. The latter were known as 部曲, a special social class in Chinese history.
During times of war, the volunteer army was increased, and a much larger militia was raised across the country to supplement the Northern Army. In these circumstances, a General ("Jiangjun" 將軍) led a division, which was divided into regiments led by Colonels and sometimes Majors ("Sima" 司馬). Regiments were divided into companies and led by Captains. Platoons were the smallest units of soldiers.
Economy.
Currency.
The Han dynasty inherited the "ban liang" coin type from the Qin. In the beginning of the Han, Emperor Gaozu closed the government mint in favor of private minting of coins. This decision was reversed in 186 BC by his widow Grand Empress Dowager Lü Zhi (d. 180 BC), who abolished private minting. In 182 BC, Lü Zhi issued a bronze coin that was much lighter in weight than previous coins. This caused widespread inflation that was not reduced until 175 BC when Emperor Wen allowed private minters to manufacture coins that were precisely 2.6 g (0.09 oz) in weight.
In 144 BC Emperor Jing abolished private minting in favor of central-government and commandery-level minting; he also introduced a new coin. Emperor Wu introduced another in 120 BC, but a year later he abandoned the "ban liangs" entirely in favor of the "wuzhu" (五銖) coin, weighing 3.2 g (0.11 oz). The "wuzhu" became China's standard coin until the Tang dynasty (618–907 AD). Its use was interrupted briefly by several new currencies introduced during Wang Mang's regime until it was reinstated in 40 AD by Emperor Guangwu.
Since commandery-issued coins were often of inferior quality and lighter weight, the central government closed commandery mints and monopolized the issue of coinage in 113 BC. This Central government issuance of coinage was overseen by the Superintendent of Waterways and Parks, this duty being transferred to the Minister of Finance during Eastern Han.
Taxation and property.
Aside from the landowner's land tax paid in a portion of their crop yield, the poll tax and property taxes were paid in coin cash. The annual poll tax rate for adult men and women was 120 coins and 20 coins for minors. Merchants were required to pay a higher rate of 240 coins. The poll tax stimulated a money economy that necessitated the minting of over 28,000,000,000 coins from 118 BC to 5 AD, an average of 220,000,000 coins a year.
The widespread circulation of coin cash allowed successful merchants to invest money in land, empowering the very social class the government attempted to suppress through heavy commercial and property taxes. Emperor Wu even enacted laws which banned registered merchants from owning land, yet powerful merchants were able to avoid registration and own large tracts of land.
The small landowner-cultivators formed the majority of the Han tax base; this revenue was threatened during the latter half of Eastern Han when many peasants fell into debt and were forced to work as farming tenants for wealthy landlords. The Han government enacted reforms in order to keep small landowner-cultivators out of debt and on their own farms. These reforms included reducing taxes, temporary remissions of taxes, granting loans and providing landless peasants temporary lodging and work in agricultural colonies until they could recover from their debts.
In 168 BC, the land tax rate was reduced from one-fifteenth of a farming household's crop yield to one-thirtieth, and later to a one-hundredth of a crop yield for the last decades of the dynasty. The consequent loss of government revenue was compensated for by increasing property taxes.
The labor tax took the form of conscripted labor for one month per year, which was imposed upon male commoners aged fifteen to fifty-six. This could be avoided in Eastern Han with a commutable tax, since hired labor became more popular.
Private manufacture and government monopolies.
In the early Western Han, a wealthy salt or iron industrialist, whether a semi-autonomous king or wealthy merchant, could boast funds that rivaled the imperial treasury and amass a peasant workforce of over a thousand. This kept many peasants away from their farms and denied the government a significant portion of its land tax revenue. To eliminate the influence of such private entrepreneurs, Emperor Wu nationalized the salt and iron industries in 117 BC and allowed many of the former industrialists to become officials administering the state monopolies. By Eastern Han times, the central government monopolies were repealed in favor of production by commandery and county administrations, as well as private businessmen.
Liquor was another profitable private industry nationalized by the central government in 98 BC. However, this was repealed in 81 BC and a property tax rate of two coins for every 0.2 L (0.05 gallons) was levied for those who traded it privately. By 110 BC Emperor Wu also interfered with the profitable trade in grain when he eliminated speculation by selling government-stored grain at a lower price than demanded by merchants. Apart from Emperor Ming's creation of a short-lived Office for Price Adjustment and Stabilization, which was abolished in 68 AD, central-government price control regulations were largely absent during the Eastern Han.
Science and technology.
The Han dynasty was a unique period in the development of premodern Chinese science and technology, comparable to the level of scientific and technological growth during the Song dynasty (960–1279).
Writing materials.
In the 1st millennium BC, typical ancient Chinese writing materials were bronzewares, animal bones, and bamboo slips or wooden boards. By the beginning of the Han dynasty, the chief writing materials were clay tablets, silk cloth, hemp paper, and rolled scrolls made from bamboo strips sewn together with hempen string; these were passed through drilled holes and secured with clay stamps.
The oldest known Chinese piece of hempen paper dates to the 2nd century BC. The standard papermaking process was invented by Cai Lun (AD 50–121) in 105. The oldest known surviving piece of paper with writing on it was found in the ruins of a Han watchtower that had been abandoned in AD 110, in Inner Mongolia.
Metallurgy and agriculture.
Evidence suggests that blast furnaces, that convert raw iron ore into pig iron, which can be remelted in a cupola furnace to produce cast iron by means of a cold blast and hot blast, were operational in China by the late Spring and Autumn period (722–481 BC). The bloomery was nonexistent in ancient China; however, the Han-era Chinese produced wrought iron by injecting excess oxygen into a furnace and causing decarburization. Cast iron and pig iron could be converted into wrought iron and steel using a fining process.
The Han dynasty Chinese used bronze and iron to make a range of weapons, culinary tools, carpenters' tools and domestic wares. A significant product of these improved iron-smelting techniques was the manufacture of new agricultural tools. The three-legged iron seed drill, invented by the 2nd century BC, enabled farmers to carefully plant crops in rows instead of casting seeds out by hand. The heavy moldboard iron plow, also invented during the Han dynasty, required only one man to control it, two oxen to pull it. It had three plowshares, a seed box for the drills, a tool which turned down the soil and could sow roughly 45,730 m2 (11.3 acres) of land in a single day.
To protect crops from wind and drought, the grain intendant Zhao Guo (趙過) created the alternating fields system ("daitianfa" 代田法) during Emperor Wu's reign. This system switched the positions of furrows and ridges between growing seasons. Once experiments with this system yielded successful results, the government officially sponsored it and encouraged peasants to use it. Han farmers also used the pit field system ( 凹田) for growing crops, which involved heavily fertilized pits that did not require plows or oxen and could be placed on sloping terrain. In southern and small parts of central Han-era China, paddy fields were chiefly used to grow rice, while farmers along the Huai River used transplantation methods of rice production.
Structural and geotechnical engineering.
Timber was the chief building material during the Han dynasty; it was used to build palace halls, multi-story residential towers and halls and single-story houses. Because wood decays rapidly, the only remaining evidence of Han wooden architecture is a collection of scattered ceramic roof tiles. The oldest surviving wooden halls in China date to the Tang dynasty (AD 618–907). Architectural historian Robert L. Thorp points out the scarcity of Han-era archaeological remains, and claims that often unreliable Han-era literary and artistic sources are used by historians for clues about lost Han architecture.
Though Han wooden structures decayed, some Han-dynasty ruins made of brick, stone, and rammed earth remain intact. This includes stone pillar-gates, brick tomb chambers, rammed-earth city walls, rammed-earth and brick beacon towers, rammed-earth sections of the Great Wall, rammed-earth platforms where elevated halls once stood, and two rammed-earth castles in Gansu. The ruins of rammed-earth walls that once surrounded the capitals Chang'an and Luoyang still stand, along with their drainage systems of brick arches, ditches, and ceramic water pipes. Monumental stone pillar-gates, twenty-nine of which survive from the Han period, formed entrances of walled enclosures at shrine and tomb sites. These pillars feature artistic imitations of wooden and ceramic building components such as roof tiles, eaves, and balustrades.
The courtyard house is the most common type of home portrayed in Han artwork. Ceramic architectural models of buildings, like houses and towers, were found in Han tombs, perhaps to provide lodging for the dead in the afterlife. These provide valuable clues about lost wooden architecture. The artistic designs found on ceramic roof tiles of tower models are in some cases exact matches to Han roof tiles found at archaeological sites.
Over ten Han-era underground tombs have been found, many of them featuring archways, vaulted chambers, and domed roofs. Underground vaults and domes did not require buttress supports since they were held in place by earthen pits. The use of brick vaults and domes in aboveground Han structures is unknown.
From Han literary sources, it is known that wooden-trestle beam bridges, arch bridges, simple suspension bridges, and floating pontoon bridges existed in Han China. However, there are only two known references to arch bridges in Han literature, and only a single Han relief sculpture in Sichuan depicts an arch bridge.
Underground mine shafts, some reaching depths over , were created for the extraction of metal ores. Borehole drilling and derricks were used to lift brine to iron pans where it was distilled into salt. The distillation furnaces were heated by natural gas funneled to the surface through bamboo pipelines. These boreholes perhaps reached a depth of 600 m (2000 ft).
Mechanical and hydraulic engineering.
Han-era mechanical engineering comes largely from the choice observational writings of sometimes-disinterested Confucian scholars who generally considered scientific and engineering endeavors to be far beneath them. Professional artisan-engineers ("jiang" 匠) did not leave behind detailed records of their work. Han scholars, who often had little or no expertise in mechanical engineering, sometimes provided insufficient information on the various technologies they described. Nevertheless, some Han literary sources provide crucial information. 
For example, in 15 BC the philosopher and writer Yang Xiong described the invention of the belt drive for a quilling machine, which was of great importance to early textile manufacturing. The inventions of mechanical engineer and craftsman Ding Huan are mentioned in the "Miscellaneous Notes on the Western Capital". Around AD 180, Ding created a manually operated rotary fan used for air conditioning within palace buildings. Ding also used gimbals as pivotal supports for one of his incense burners and invented the world's first known zoetrope lamp.
Modern archaeology has led to the discovery of Han artwork portraying inventions which were otherwise absent in Han literary sources. As observed in Han miniature tomb models, but not in literary sources, the crank handle was used to operate the fans of winnowing machines that separated grain from chaff. The odometer cart, invented during Han, measured journey lengths, using mechanical figures banging drums and gongs to indicate each distance traveled. This invention is depicted in Han artwork by the 2nd century, yet detailed written descriptions were not offered until the 3rd century. 
Modern archaeologists have also unearthed specimens of devices used during the Han dynasty, for example a pair of sliding metal calipers used by craftsmen for making minute measurements. These calipers contain inscriptions of the exact day and year they were manufactured. These tools are not mentioned in any Han literary sources.
The waterwheel appeared in Chinese records during the Han. As mentioned by Huan Tan about AD 20, they were used to turn gears that lifted iron trip hammers, and were used in pounding, threshing and polishing grain. However, there is no sufficient evidence for the watermill in China until about the 5th century. The Nanyang Commandery Administrator and mechanical engineer Du Shi (d. 38 AD) created a waterwheel-powered reciprocator that worked the bellows for the smelting of iron. Waterwheels were also used to power chain pumps that lifted water to raised irrigation ditches. The chain pump was first mentioned in China by the philosopher Wang Chong in his 1st-century "Balanced Discourse".
The armillary sphere, a three-dimensional representation of the movements in the celestial sphere, was invented in Han China by the 1st century BC. Using a water clock, waterwheel and a series of gears, the Court Astronomer Zhang Heng (AD 78–139) was able to mechanically rotate his metal-ringed armillary sphere. To address the problem of slowed timekeeping in the pressure head of the inflow water clock, Zhang was the first in China to install an additional tank between the reservoir and inflow vessel. 
Zhang also invented a device he termed an "earthquake weathervane" ( 候風地動儀), which the British biochemist, sinologist, and historian Joseph Needham described as "the ancestor of all seismographs". This device was able to detect the exact cardinal or ordinal direction of earthquakes from hundreds of kilometers away. It employed an inverted pendulum that, when disturbed by ground tremors, would trigger a set of gears that dropped a metal ball from one of eight dragon mouths (representing all eight directions) into a metal toad's mouth. 
The account of this device in the "Book of the Later Han" describes how, on one occasion, one of the metal balls was triggered without any of the observers feeling a disturbance. Several days later, a messenger arrived bearing news that an earthquake had struck in Longxi Commandery (in modern Gansu Province), the direction the device had indicated, which forced the officials at court to admit the efficacy of Zhang's device.
Mathematics.
Three Han mathematical treatises still exist. These are the "Book on Numbers and Computation", the "Arithmetical Classic of the Gnomon and the Circular Paths of Heaven" and the "Nine Chapters on the Mathematical Art". Han-era mathematical achievements include solving problems with right-angle triangles, square roots, cube roots, and matrix methods, finding more accurate approximations for pi, providing mathematical proof of the Pythagorean theorem, use of the decimal fraction, Gaussian elimination to solve linear equations, and continued fractions to find the roots of equations.
One of the Han's greatest mathematical advancements was the world's first use of negative numbers. Negative numbers first appeared in the "Nine Chapters on the Mathematical Art" as black counting rods, where positive numbers were represented by red counting rods. Negative numbers were also used by the Greek mathematician Diophantus around AD 275, and in the 7th-century Bakhshali manuscript of Gandhara, South Asia, but were not widely accepted in Europe until the 16th century.
The Han applied mathematics to various diverse disciplines. In musical tuning, Jing Fang (78–37 BC) realized that 53 perfect fifths was approximate to 31 octaves while creating a musical scale of 60 tones, calculating the difference at 177147⁄176776 (the same value of 53 equal temperament discovered by the German mathematician Nicholas Mercator [1620–1687], i.e. 353/284).
Astronomy.
Mathematics were essential in drafting the astronomical calendar, a lunisolar calendar that used the Sun and Moon as time-markers throughout the year. During the spring and autumn periods of the 5th century BC, the Chinese established the Sifen calendar (古四分历), which measured the tropical year at 3651⁄4 days. This was replaced in 104 BC with the Taichu calendar (太初曆) that measured the tropical year at 365385⁄1539 days and the lunar month at 2943⁄81 days. However, Emperor Zhang later reinstated the Sifen calendar.
Han Chinese astronomers made star catalogues and detailed records of comets that appeared in the night sky, including recording the 12 BC appearance of the comet now known as Halley's Comet.
Han dynasty astronomers adopted a geocentric model of the universe, theorizing that it was shaped like a sphere surrounding the earth in the center. They assumed that the Sun, Moon, and planets were spherical and not disc-shaped. They also thought that the illumination of the Moon and planets was caused by sunlight, that lunar eclipses occurred when the Earth obstructed sunlight falling onto the Moon, and that a solar eclipse occurred when the Moon obstructed sunlight from reaching the Earth. Although others disagreed with his model, Wang Chong accurately described the water cycle of the evaporation of water into clouds.
Cartography, ships, and vehicles.
Evidence found in Chinese literature, and archaeological evidence, show that cartography existed in China before the Han. Some of the earliest Han maps discovered were ink-penned silk maps found amongst the Mawangdui Silk Texts in a 2nd-century-BC tomb. The general Ma Yuan created the world's first known raised-relief map from rice in the 1st century. This date could be revised if the tomb of Emperor Qin Shi Huang is excavated and the account in the "Records of the Grand Historian" concerning a model map of the empire is proven to be true.
Although the use of the graduated scale and grid reference for maps was not thoroughly described until the published work of Pei Xiu (AD 224–271), there is evidence that in the early 2nd century, cartographer Zhang Heng was the first to use scales and grids for maps.
Han dynasty Chinese sailed in a variety of ships different from those of previous eras, such as the tower ship. The "junk" design was developed and realized during the Han era. Junk ships featured a square-ended bow and stern, a flat-bottomed hull or carvel-shaped hull with no keel or sternpost, and solid transverse bulkheads in the place of structural ribs found in Western vessels. Moreover, Han ships were the first in the world to be steered using a rudder at the stern, in contrast to the simpler steering oar used for riverine transport, allowing them to sail on the high seas.
Although ox-carts and chariots were previously used in China, the wheelbarrow was first used in Han China in the 1st century BC. Han artwork of horse-drawn chariots shows that the Warring-States-Era heavy wooden yoke placed around a horse's chest was replaced by the softer "breast strap". Later, during the Northern Wei (386–534), the fully developed horse collar was invented.
Medicine.
Han-era medical physicians believed that the human body was subject to the same forces of nature that governed the greater universe, namely the cosmological cycles of yin and yang and the five phases. Each organ of the body was associated with a particular phase. Illness was viewed as a sign that "qi" or "vital energy" channels leading to a certain organ had been disrupted. Thus, Han-era physicians prescribed medicine that was believed to counteract this imbalance. 
For example, since the wood phase was believed to promote the fire phase, medicinal ingredients associated with the wood phase could be used to heal an organ associated with the fire phase. Besides dieting, Han physicians also prescribed moxibustion, acupuncture, and calisthenics as methods of maintaining one's health. When surgery was performed by the Chinese physician Hua Tuo (d. AD 208), he used anesthesia to numb his patients' pain and prescribed a rubbing ointment that allegedly sped the process of healing surgical wounds. Whereas the physician Zhang Zhongjing ( – ) is known to have written the "Shanghan lun" ("Dissertation on Typhoid Fever"), it is thought that both he and Hua Tuo collaborated in compiling the "Shennong Ben Cao Jing" medical text.