linguistic:paraphrasing
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.